Mu. :-)

Assuming that each holds *only* two coins, which was implied but is not the only possible interpretation of the text, the odds are one in four.

Giving the top coin first and the bottom second, the solution sets are:

Smith - GG, GS
Jones - GG, GS, SG

Odds that Jones has more are 1/2 * 1/3 = 1/6

(We need Smith to have one gold coin -- GS -- hence the 1/2. We need Jones to have two gold coins -- GG -- hence the 1/3)

It depends how many coins there are in Lemuria in total.

The easy case is if there are four. Then Smith and Jones each have one gold and one silver, and the probability that Jones has more than Smith is zero.

The other easy case is if there are a sufficiently large number that it's effectively infinite (in the context of this problem). Then Smith has either one gold (50% chance) or two gold (50% chance), while Jones has a 2/3 chance of one gold (four options: SS, SG, GS, GG, but SS is ruled out by the conditions) and 1/3 of two gold. The distributions for Smith and Jones aren't related (by our assumption that there are a large number of coins), and so the probability that Jones has more than Smith is 1/3 * 1/2 = 1/6.

If there are (say) 100 Lemurian coins in total, then it gets complicated.

I can't do logic when it's over 100F out.

Without looking at the existing answers:

Ms Smith has two coins, and the one on top is gold. This means there are two possibilities: that the one on the bottom is also gold or that the one on the bottom is not gold. We can call these S1 (in which Ms Smith has 2 gold coins) and S2 (in which Ms Smith has 1 gold coin).

Mr Jones has two coins, and at least one is gold. This means, I think, that there are three possibilities: that only the top one is gold, that only the bottom one is gold, or that both are gold. J1 (1 gold), J2 (1 gold), J3 (2 gold).

(I worry that there's going to be some sneaky probability thing that means that "the one on top is gold and so is the one on the bottom" and the "the one on the bottom is gold and so it the one on top" count as two separate possibilities, but for the moment I choose to ignore it.)

The combined possibilities are S1/J1, S1/J2, S1/J3, S2/J1, S2/J2, S3/J3. Of these six possibilities, S2/J3 is the only one in which Mr Jones has more gold coins than Ms Smith.

Therefore, my answer is: 1 in 6

And if my final answer is wrong, I expect to still get points for showing my working.

Also, we really need to assess the probability that one or both of Smith and Jones are lying or mistaken.

I have no idea, but S&P just downgraded Lumeria's credit.

Actually, thinking about it, the conditions set in the problem are impossible. "Assuming gold and silver coins are evenly and randomly distributed in Lemuria, and otherwise unidentified coins in the hands of Smith and Jones are no more likely to be silver than gold" can't happen unless the number of coins is actually infinite. Assuming there are 2n coins in total (it has to be an even number), then the probability that an unidentified coin is gold is (n-2)/(2n-2) while the probability that an unidentified coin is silver is n/(2n-2) -- because we know of two gold coins, but no silver coins. Either the distribution of coins is not even and random, or an unidentified coin is slightly more likely to be silver than gold.

Wouldn't it be slightly more than 1/6, though?

Gold is nearly twice as dense as silver, so if you have coins being randomly jiggled about (in a pocket, or a loosely cupped hand, say), the gold-on-the-bottom configuration should be lower-energy and thus more likely.

So if the top coin is gold, the likelihood that the other coin is also gold is better than the 50% that chance would suggest.

All of this assumes that each of them is holding exactly two coins — because even if each is holding exactly two Lemurian coins, there is no indication of whether there are foreign coins (probably made of some base metal) in either hand.

Stephen makes a good point. We have no information at all about how many non-Lemurian gold coins each person is holding, so we have no way to assess the probabilities at all (except to note that the total mix of all coins in Lemuria, whether foreign or not, is exactly 50:50 and random, which doesn't help enough).

Ms Smith has two coins. We don't know if she has more than two coins. If she were holding five coins, it would be true (if misleading) for her to say she is holding two coins. She would be. She would be holding them with another three coins, which she didn't mention, but her omission wouldn't make her utterance false. From her statement, we have only a lower limit on the number of coins she holds, not an upper limit.

Mr Jones likewise.

Making the simplifying assumption that each of Ms Smith and Mr Jones holds exactly two coins, and the further assumption that the coin supply is essentially limitless, the problem becomes one of probability theory. However, these are assumptions, and are not the only possible interpretations of the text. In light of the multitude of possible interpretations, the problem is essentially unsolvable as stated. Selected simpler problems implied by the stated problem are solvable, but the relative chances of occurrence of these simpler problems cannot be calculated from the available information.

This seems the best place to announce to the Flourosphere that I am now a resident of Jersey City, New Jersey.

This is like the Monty Hall problem, or the boy born on Tuesday: one of those problems where being given partial information screws up our intuition of statistics, because we don't think the information should change the odds, and it does. What's Tuesday got to do with it, and why do I care that Monty's shown me an empty box? Because it changes the population under consideration.

Speaking of population, a less contrived example is life expectancy, and how if the average life of a newborn is sixty five, that doesn't mean the average years left to a sixty-year-old is five.

100%, because Jones mugged Smith, grabbing her coins (that's consistent with the sequence in the puzzle) ;-)

I've seen the place. Neither one has any coins, and they're just trying to brag. Soon, the hollowness of their lives will overwhelm them, and they will each stand in front of a train. One train goes from east to west at 30 kph. The other makes four stops, each time either picking up a goose or letting off a monkey.

I make it one chance in three, assuming each person is telling the truth, and that neither would say "I have two coins in my hand" when s/he has three or more (and ignoring Mike's point about infinities because I'm not sure how to take those into account with combinatorics).

If we list each person's top coin first, the possible coins are GG, GS, SG, and SS.

Jones has equal chances of GG, GS, or SG (and cannot have SS); Smith has equal chances of either GG or GS (and cannot have SG or SS).

So, there are six possible pairings of Smith's coins and Jones's:

Smith   Jones
GG     GG
*GG   GS
*GG   SG
GS     GG
GS     GS
GS     SG

Two of those six combinations (starred), or 1/3, fit the condition "Smith has more gold coins than Jones does." Note that for the problem as stated, it doesn't matter how likely it is for Jones to have more gold coins versus how likely it is for them to each have the same number.

Hyperlocal news: Local woman came home from the Greenmarket with yellow peaches, yellow plums, and some late strawberries and blueberries. So far we have eaten about a half pint of strawberries (in oatmeal) and one peach each.

Cheating by representing this situation as a computer program:

coins =
    choice [True, False] >=> \msSmithBottomCoin ->
    choice [True, False] >=> \mrJonesTopCoin ->
    choice [True, False] >=> \mrJonesBottomCoin ->
    returnP (if msSmithBottomCoin then 2 else 1) >=> \msSmithGoldCount ->
    returnP ((if mrJonesTopCoin then 1 else 0) +
             (if mrJonesBottomCoin then 1 else 0)) >=> \mrJonesGoldCount ->
    assert (mrJonesGoldCount > 0) >>=>
    returnP (if mrJonesGoldCount > msSmithGoldCount then
             "More Jones" else "not More Jones")

Using the haskell probability library linked to from the page linked to by my name, I then get:

coins:
"More Jones" ==> 1 % 6
"not More Jones" ==> 5 % 6

I really need to recover or rebuild my ruby probability library; it yielded much clearer (albeit slower) programs.

Assuming honest communication on the parts of Smith and Jones, aren't the odds even? Telling us that the coin on top is gold is functionally equivalent to telling us that at least one is gold, yes? Because in the case of Jones we know that either the top or bottom coin (and maybe both) is gold, so if the coin on top is not gold, just flip the arrangement, and now we have the exact same conditions and information as what we have for Smith.

We know they are in Lemuria, and that in Lemuria gold and silver coins are evenly distributed, so it doesn't matter whether the coins in the hands of Smith and Jones are Lemurian, the undesignated coins each have even odds of being gold or silver.

Or am I missing something obvious?

The order of the coins is irrelevant. So, to reword:
Smith has two coins, one of which is gold.
Jones has two coins, one of which is gold.
Any undefined coins have a 1/2 chance of being gold, and a 1/2 of being silver.

Assuming Smith and Jones aren't being devious wordsmiths and only have two coins each, the only way Jones can have more gold than Smith is if his second coin is gold (1/2 chance) and Smith's second coin is silver (1/2 chance).

Answer: 1/4

It's certainly actually possible to reach the correct answer without ignoring the ordering, but it's more complicated since not all outcomes are equally likely. In particular, Jones' GG, SG and GS are 1/2, 1/4 and 1/4 respectively.

@Mike D, #20:

"In particular, Jones' GG, SG and GS are 1/2, 1/4 and 1/4 respectively."

Why?

If these were pre-rolled d20s, not coins, and Jones said "Al least one of my dice is showing '20'", would you assign the same probability to '20'&'20' as to '20'&'1-19' and '1-19'&'20'?

No. p('20'&'20') would be the same as p('20'&'1'), p('20'&'2'), etc.

Each individual outcome gets the same possibility, and these correspond to GG, SS, GS, SG.

Mike Dixon @20 -- This is a minor variant on the Monty Hall Problem. The probability of each of the three states (GG, GS, SG) is equal (1/3 each) for Jones's coins, with the information we have. For Smith, we know that the first coin is gold, p = 100%. That is subtly different than knowing you have at least one gold coin, believe it or not.

Dawno @910: the program PDF says it'll be from 7-8 in room KK2 "Beading Make & Take"

That's odd. Page 71 of my pdf says 8-9.

@rosyatrandom, 21:
We know that one coin is gold. It's 1/2 that the known-gold coin is the first coin, and 1/2 that it's the second. So G* and *G are equally likely. But whichever coin is gold, the other coin's chances are unaffected, so it's 1/2 that the other coin is gold.

So there are four equally likely outcomes for Jones:
#1: First gold, other gold (1/4): GG
#2: First gold, other silver (1/4): GS
#3: Second gold, other gold (1/4): GG
#4: Second gold, other silver (1/4): SG

#1 and #3 are both GG, so GG actually has a 2/4 = 1/2 chance of happening.

The d20 case is similar. We know that one die is a 20. It's 1/2 that the known-20 is the first die, and 1/2 that it's the second. So 20&* and *&20 are equally likely. Whichever die is 20, the other one is unaffected, so each outcome for the other die (including 20) has a 1/20 chance.

This gives us 40 equally-likely outcomes:
#1: First 20, other 20: (1/2 * 1/20 = 1/40): 20&20
#2-20: First 20, other 1-19: (1/2 * 1/20 = 1/40): 20&x
#21: Second 20, other 20: (1/2 * 1/20 = 1/40): 20&20
#22-40: Second 20, other 1-19: (1/2 * 1/20 = 1/40): x&20

#1 and #21 are both 20&20, so P(20&20) is 2/40, and each P(20&x) and P(x&20) is 1/40.

The order of the coins in the hand, or in the bush, doesn't matter. We have two coins in each hand, we know that one of them is gold. Disregarding stacking order, there are 4 possible sets of contents: hand1=GG or GS hand2=GG or GS

Therefore, the odds that one hand or the other contains 2 gold coins is 1 in 2, or 50%

If we don't specify that h2 contains at least one gold coin, then the odds change:
h1=GG or GS h2=GG or SS or GS

Oops, misread the final condition == h1 has MORE gold coins than h2. Oops

1/4 or 25% in that case

Anaea @ #19: "Telling us that the coin on top is gold is functionally equivalent to telling us that at least one is gold, yes?"

You'd think so, yes? But you'd be wrong. It doesn't matter how you distinguish the coins, but telling you that one particular coin is gold is a very different thing from "at least one coin is gold". This is one of those "screws up our intuition of statistics" statements mentioned in #14.

Consider this: Of all families with two children of different ages, one fourth of them have both children boys, one fourth have two girls, one fourth have an older sister and younger brother, and one fourth have an older brother and younger sister.

Therefore, of the parents of two children of unequal ages who can accurately say "at least one of my children is a girl", one third will have two girls. Of those that can accurately say "my eldest child is a girl", one-half will have two girls.

Therefore, the statements "at least one of my children is a girl" and "my eldest child is a girl" are fundamentally different in that the second statement gives more information(*) even though our intuition says that it shouldn't matter.

(*) ~0.585 bits worth extra information, if you're counting.

And after a few people answering correctly, we now have a stream of people being led off the rails.

If you got 1/4 or 1/2, you've likely made the mistake that the two statements by our coin holders are equivalent. They aren't; I think my parents example may help to clarify why.

Vicki@17: You have correctly answered the wrong question. We are asked what is the probability that Jones has more than Smith. That corresponds to the fourth entry in your table, and only the fourth, so the chance is then one out of six, just as others have said.

We need information about under which conditions Jones and Smith would say what they happened to say here. Are we to understand, implicitly, that the only thing that could possibly have prevented Jones from saying his piece was it would be false (i.e. only if she has two silver coins would say something else than "at least one is gold")? Or could it be that under appropriate conditions Smith would choose randomly between saying "the one on top is gold" and saying "the bottom one is silver"?

The answer to such assumptions inform which kind of probabilistic conclusions we can draw from the observations.

Daniel Martin - I follow you, and that's the coolest thing I've learned all week. Thanks for the explanation.

@Mike D, #24

You've counted GG twice; your 4 equally likely outcomes are in fact 3 equally likely outcomes.

Terry Karney @13: Yes, but what is the distribution of gold and silver coins in Jersey City, and how does it compare to Lemuria?

Their hands are empty. "Smith" and "Jones" are actually spies, and they're exchanging passwords.

If we know that one coin of two is gold, there are two possible states: GG or GS. It matters not at all, the order in which they are stated.

If we are to make a statistical distinction based on stacking order, then we have *four* possible states in each hand GG, GG, GS, SG.

To put it another way: If my oldest of two children is a girl, there is a 50-50 chance my other child is a girl. If *one* of my two children is a girl, there is a 50-50 chance the other is a girl.

Stacking order makes no difference unless the outcome is dependent on stacking order. Had the question been, "What is the likelihood that h1 will have coins in the same order as h2?", stacking order would be important.

siriosa@ 23 said: That's odd. Page 71 of my pdf says 8-9.

You're absolutely correct, my error. It's from 8 - 9. Sorry!

Kip W @16
You Remember Lemuria?
That is a Mystery!

It seems to me that one gets 1/6 if and only if one presumes that Ms Smith preserved the order in which she received her coins.

For example, it is possible that Ms Smith received two coins drawn at random from the pool of all Lemurian coins and put them in her pocket (which had no coins until then). Upon meeting Mr. Jones, she drew the two coins from her pocket in random order, and found that a gold coin was on top. If this is the case, then (I believe) the probability of Jones having more gold coins than Smith is 1/4.

FWIW, that is how I read the problem. Your milage may vary.

Best,
Jim Bales

Walter Hawn @ 35: Flip two coins several hundred times. Each time, ask yourself whether at least one came up heads, and if so, keep track of whether one coin or both was heads. You will find that both were heads one-third of the time, not one-half. TH and HT are separate outcomes, and no amount of saying the order doesn't matter will make them not be so. Or, to put it another way, if you want to say the order doesn't matter, you have to bear in mind that the probability of one coin being heads and one coin being tails is twice that of both coins being heads.

Similarly, of the four equal-probability outcomes for each pocket, Smith's statement eliminates SG and SS. Jones' statement eliminates only SS. Therefore, the chance of Jones' pocket holding GG is one-third, not one-half.

If *one* of my two children is a girl, there is a 50-50 chance the other is a girl.

Not so. Of two-child families with at least one girl, two-thirds have a boy and a girl, and one-third have both girls (ignoring the slight difference in probability between boy and girl births). So if all I know is that you have at least one girl, then from my state of knowledge the probability that both your children are girls is one-third; that is, if a large population of parents with two children answers the question "do you have a daughter?" accurately, I know that about one-third of them will have two girls.

Probability estimates are really statements about one's knowledge. In this case the information we get from Jones is different enough from that we get from Smith that we have to assign a different probability to each.

iamnothing @37: It's been a while. I haven't seen the place since I was a little shaver.

Jim Bales @ 38: If you add information other than what Smith and Jones are telling us, you can come up with any probability you want. For example, if you know what all the coins are, the probability will be either one or zero.

But if we randomly assign two coins to Smith and Jones many times, and consider those cases where both Smith and Jones can honestly make the stated claims, Jones will have more gold coins than Smith about one-sixth of the time.

39
The order may or may not matter (it wasn't specified, so I'm going with 'doesn't matter'). Combinations aren't the same as permutations - order matters for permutations, but not for combinations.

Tim Walters @ 41

When Smith says "the top one is gold", we do not know if that a statement about:
a) the order in which Smith received the coins from the population of all Lemurian coins, or
b) the order in which Smith retrieved the coins from the population of the two in her possesion.

Smith does not say, yet we must choose one of the two meanings. Whichever we choose, we add information.

Best,
Jim Bales

Yes, but which is it? Smith and Jones or Smith and Jones?

P J Evans#42: yes, but each combination represents a different number of permutations, so in the "standard case" where each permutations has equal probability, the combinations do not necessarily have equal probability.

Bigger example: Flipping three coins has four combinations (T³, T²H, TH², H³), but eight combinations (TTT, TTH, THT, THH, HTT, HTH, HHT, HHH) that gather unevenly into the combinations. T²H simply does not have the same probability as T³, it has three times the probability.

It always amazes me how this and related issues can make people cling so stubbornly to a wrong answer that's not just wrong, but easily provable as wrong. But then, honest casinos live off such mistakes....

Myself @ 38

I convinced myself that I was wrong in believing the odds are 1/4 if Smith's "The top one is gold" is a statement about the order in which she retrieved the coins from the population of the two in her posession.

In this case, Smith drew two coins from the population of all Lemurian coins, and we know that at least one of the two is gold. Then the odds of the other being gold are 1/3, and the odds of it being silver are 2/3.

Similarly, the odds of Jones having two gold coins are 1/3.

So, the odds of Jones having two gold coins and Smith only one are 1/3 x 2/3 = 2/9 (a bit less than 1/4).

(If, on the other hand, we decide that Smith's statement "the top one is gold" is a statement about the order in which she drew two coins from the population of all Lemurian coins, then the odds are 1/6, as others have noted.)

Best,
Jim Bales

Bah. Eight permutations. Serves me right for playing with superscripts.

Tim Walters... I've been seeing a few suggestions come up thru your meetup. I voted for dinner on Wednesday.

#38: No.

That is, you have not given a scenario which results in 1/4 probability. The second scenario you give results in 1/6, still.

It seems that probability problems like this are excellent tools for triggering SIWOTI syndrome among Making Light regulars.

Jim Bales @ 43: No, we don't have to (and can't) choose. That's the whole point. We are assured that the process by which the coins were chosen and ordered is random and unbiased, so that's what we base our estimate on. As far as I can tell, you're wrong in thinking that it makes a difference, but if if it does, it's because (at least) one of your alternatives is not random, and therefore contradicts the problem statement.

If Smith were to say "if I get a gold coin, I'll put it on top," that would make the difference you say. But that's not random.

In the land of Lemuria, all coins that are not gold are silver.

In the land of Argentina, all coins that are not gold are lemurs.

Kip W@40: If I lived in a place where they made the coins out of real gold, I might take up coin clipping too.

I hate this problem. Not for itself, but it always comes up in Statistics 101, and most professors get it wrong. Instead of saying "at least one of the two glybnorfs is kryzniak," they say "one of the glybnorfs is," or "the first glybnorf is," or some other language that leads to the 1/2 probability instead of the 1/3, but expect "1/3" for an answer. Which leads to the same ObXKCD as the last open thread, but doing that gets you an F, or sometimes an "Incomplete" because of rotting in prison.

Last I heard, Lemuria had been under salt water for several millennia, making it unlikely that silver coins would still be anything other than corroded lumps of silver salts. So the odds of all coins being gold is pretty high. On the other hand, their razor blades, having been stored in pyramidal cabinets, have remained sharp to this day.

A geologist was playing around with some volcanic rock. Her friend, a chemist, asked "Do you think you could make a galvanic cell out of that?" So they extracted some compounds and played around with it a bit.

Then, the cops showed up and handcuffed them.

Why?

They were naked.

#46: The error here is significantly more subtle than in #38.

The error is this: in your post, you say:

In this case, Smith drew two coins from the population of all Lemurian coins, and we know that at least one of the two is gold. Then the odds of the other being gold are 1/3, and the odds of it being silver are 2/3.

That's not quite true - we actually know more than that. What we know is that Smith drew two coins from the population of all Lemurian coins, and that when she drew them out, the top coin was gold. This is something that is much more likely to happen if she had two gold coins than if she had just one.

In fact, it's exactly twice as likely to happen if she has two gold coins than if she has one. The end result is that in fact she is equally likely to have two gold coins as one of each.

This leads back to 1/2 * 1/3 == 1/6 chance once again that Mr. Jones has more gold than Ms. Smith.

I've been musing on the question of whether saying "The foo coin is gold", where I don't know whether foo is a differentiator. If, for example, I said "The older one is gold", that might make a difference; but if I said "The yellow one is gold", it doesn't. If I said "The lighter one is gold", and I don't know whether that's referring to weight or color (if the silver were tarnished, it would definitely be darker in color, for example), or even whether it is a well-defined linear metric, would that make a difference? There's a certain problem with ambiguity here, and I'm not sure how to express it.

Tom Whitmore #57: The question is whether the distinction adds information about the problem set, which in this case means "does it tell us whether the coin is gold or silver?" Given that we don't know the sizes of the coins, weight doesn't add information, and as as you note, "lighter" is ambiguous.

This reminds me of when I managed to turn my D&D habit into a class paper, for math class. Lots of graphs of various die rolls.

One amusing discovery from then: rolling two of any one die type gives you a triangular probability distribution (for example 2d6 gives weights 1,2,3,4,5,6,5,4,3,2,1 for the numbers 2-12), but if you roll two different dice, you get a truncated triangle (for example 1d6+1d4 gives a range of 2-10, with probabilities 1,2,3,4,4,4,3,2,1). Also, 3d6 looks like a bell curve, but when you draw over it a real bell curve (with the same mean and deviation), you find it isn't quite as close as it looks.

While the Lemurians (and Smith and Jones are really unusual names for Lemurians, I'd thought they had names more on the lines of Blavatsky) were playing logic games with gold and silver coins, Mu, Atlantis, and Islandia formed an alliance and conquered the dratted place.

#57: The question is whether being foo is something that is equally likely to apply to gold and silver coins.

Or rather, what percentage of people with one gold and one silver coin would be able to honestly say "the foo coin is gold"; if that's 50%, then we're fine. (so really, all that matters is the property in the hands of people with one coin of each metal)

Going back to my parents example, suppose we are dealing with parents of post-pubescent children only, so that the puberty-inspired growth spurts have hit. Then the statement "my tallest child is a boy" is a weaker statement (in the sense of conveying less information) than the statement "my eldest child is a boy".

#40 ::: Kip W ::: (view all by) ::: August 06, 2011, 06:20 PM:

iamnothing @37 [You Remember Lemuria?
That is a Mystery!]

It's been a while. I haven't seen the place since I was a little shaver.

Lemuria was in Burma?

We make the nation out of heart and mind
but give allegiance only when we're paid
which means this kingdom's truly of the blind.

For all that we have been to truth inclined
its consequences make us all afraid;
we make the nation out of heart and mind

yet cannot doubt that we've still been consigned
to the old trap. We're in the same old trade,
which means this kingdom's truly of the blind,

and thus we know already what we'll find
once we unravel all the plots we'd laid.
We make the nation out of heart and mind

expecting history will be more kind,
granting some measure of good ease and aid
which means this kingdom's truly of the blind

since no such hope has ever been designed,
instead we'll have to do with what we've made.
We make the nation out of heart and mind,
which means this kingdom's truly of the blind.

Fish!

I was convinced both by 1/4 and by 1/6 when I read the respective explanations, which I find rather odd.

But after thinking about it, the difference between the two explanations is the question of whether you assume that the gold coin, no matter whether it's the top coin or not, is known. Or to put it a different way, in the 1/6 explanation, "the top coin" is assumed to specify a specific coin (and the probability of the other coin being gold is one half), but "the gold coin that I'm informing you about" is assumed to not specify a specific coin (because it could be either the top or the bottom coin...but the only reason you're even thinking about top or bottom is because the statement before had a top coin...)

I think that in fact, "the gold coin that I'm informing you about" is a specifier of a specific coin, it doesn't matter if it's top or bottom, it's still a specific coin. Therefore the probability of the other coin being gold is 1/2, just like the probably of the bottom coin being gold was 1/2.

So the answer is 1/2 * 1/2 = 1/4.

Kip W @16 wins the internet.

I understand that the probability that Ms Smith has two golden coins is 1/2.

I understand that the probability that Mr. Jones has two golden coins is 1/3.

But if Ms Smith shakes the two coins in her hands, the probability drops from 1/2 to 1/3, right?

IJWTS that Kip Williams is as brilliant as he was when we were tadpoles together, which is pretty brilliant, pretty much.

The second coin is a cat. Now, the next question--

Komavary #67: Not after we've already learned her odds! While Mr. Jones's permutations GS, SG, GG all have equal odds, Ms. Smith now has GS and SG sharing half the probability, while GG has the other half all to itself. (I suspect this is related to the transition in the true Monty Hall problem.)

Logic problems. Pfft. What *I* want to know is what people called the Monty Hall problem before Monty Hall got famous.

Unless, of course, Smith is as OCD as I am (which is slightly but not very) and always carries her coins in the same order.

In my case, if I tell you I have a 20, or the middle bill of my 2 bills is a 20, I've given exactly the same information.

David Harmon @58 -- one of the problems from a human engineering viewpoint is that the person giving the information almost undoubtedly thinks it makes a difference about the data set, because s/he has chosen to add that information. It's the same sort of ambiguity explored in the opening of the last OT here. Whether the person is looking at the same data set we're trying to analyze is a difficult question to answer (particularly since most people don't disambiguate their data sets well, which could lead me off on a long diatribe based on some work I once did with the Language of Data Project).

Daniel Martin @ 56:

Please note that the piece of #46 you quote begins "In this case ..."

The case being considered is set forth in the prior paragraph of #46, namely Smith's "The top one is gold" is a statement about the order in which she retrieved the coins from the population of the two in her posession.
[Emphasis added]

In that case (the case expressly set forth in #46), we know nothing of the order in which she drew the coins from the population of all the coins in Lemuria.

Best,
Jim Bales

45
8 permutations of three items, but 4 combinations.
As I said, order matters in permutations - but that's not part of the problem as given.
(I had math classes that covered permutations and combinations, thank you. It was algorithm design, IIRC.)

60
ROFLMAO!

Daniel Martin @56 writes:
"What we know is that Smith drew two coins from the population of all Lemurian coins, and that when she drew them out, the top coin was gold." [Emphasis in the original]

The italicized portion is not to be found in the problem statement, which states:
Ms. Smith says, “I have two Lemurian coins in my hand. The one on top is gold.”

We are told that a gold coin is on top when Smith and Jones meet. Nothing is said of the ordering of the coins before that instant in time.

If one presumes that Ms Smith preserved the ordering of the coins from the momment she drew them until the momment she met Jones, then the probability of her having two gold coins is 1/2. If one presumes that Ms Smith did not preseve the ordering then the probability of her having two gold coins is 1/3.

Either way, one makes a presumption. The answer depends on one's presumption, and is either 1/6 (she preserves the order) or 2/9 (she does not preserve the order).

Best,
Jim Bales

A.J. Luxton @ 54: for Basalt and Battery?

I'm increasingly convinced that the answer is 50%, because seriously, the number of coins in the kingdom is presumably large enough to not be affected by the removal of a single other coin from the pool. The odds on the specific coin are 50% the first time they draw it, the odds on a specific coin are still 50% the 72nd time they draw it, and the "coin on top" is a statistically insignificant distraction. The entire conversation looks like an extended gambler's fallacy to me.

Open threadery:

I read the story about Florida journalism students having to put out a paper using pre-computerisation tech with interest. I'd worked in newsrooms** in the 1970s and early 1980s (we still had copyboys who would come running when veteran reporters yelled "copy!", we had a spike on which unused copy went to die, we used manual typewriters on which we typed with two fingers at the amazing speed of 20 wpm, I kid you not) and found the shock exhibited by those young people most amusing. We kept some slugs of cold type around to remind us of the old days since the printers used plastic moulds to make the pages. They made decent paperweights.

*At the second, where I worked for three years, my desk was at the back of the morgue, since I was the research officer -- my title was research officer/staff writer -- and I combined the duties of a librarian, translator, feature and occasional editorial writer, and general dogsbody. Plus I was the shop steward for that branch of the administrative workers' union.

P J Evans #75: Combinations are derivative; they represent the summation of available permutations. Ms. Smith's "drawing" of one coin rules out two of four possible permutations for her hand, while Mr. Jones' statement only rules out one for his.

Jim Bales #77: We don't need to know anything prior to the moment, because "dice have no memory". On the other hand, if Ms. Smith then shuffles her coins (as per Komavary #67), and then "draws" again -- say, announcing that the new top coin is again gold -- then our memory of the prior draw lets us refine the probability that she has two gold coins (to 3/4, I believe). (Of course, if her new top coin is silver, then we know she has one of each, with probability 1.)

Smith and Jones could both be liars holding two gold *clad* coins with centers of lead, each hoping to deceive the other into advocating a return to the gold standard.

Why this isn't like the Monty Hall problem:

In the Monty Hall problem, someone added information. You started off with a known probability of a certain outcome, and then the host (who knows more than you do) changed the probability by opening a door, and the tricky part is that it's easy to think you should calculate probability according to the current situation as if it had sprung up without history, but actually you have to look at the original situation plus the action of the knowledgeable host. But the key thing is that the point at which you actually know the probabilities in the Monty Hall problem is what I'm going to call the original situation.

It seems to me that the 1/6 answer is trying to go back to the original situation (when the coins were picked up, they were picked up in some order, and the possibilities are four, but we have to eliminate one based on our current knowledge). However, unlike the Monty Hall problem, there's no new information added in at any time, and all we actually know about is the current situation. We don't know anything about the "original situation" except what we can reason about it based on the current situation. So we have to calculated using the probabilities we know, which are the probabilities of the current situation.

Did Ms. Smith look before she spoke? If not, then she knew for certain without seeing it that the top coin was gold — therefore, they were both gold! If she didn't look.

ps: I'm not still a tadpole? Oh, crap.

My father, when he was a kid, worked as a copy-boy for the New York Times. He says he filled up the paste pots in the morning, and he carried news stories to the people who arranged letters on the conveyor belt for the lighted-sign headlines.

Ms. Smith did not say anything about Mr. Doe. Everyone knew that Mr. Doe was at the war, like so many of the men. No one but Ms. Smith knew what he had left behind, what she kept for him, and now Ms. Smith had no way to tell anyone else. Ms. Smith did not let her worries wisp upward from her heart, keeping them away from the corners of her eyes. It would be improper if Mr. Jones would see the worry in the corners of her eyes.

Mr. Jones remembered Ms. Smith from before, long before, when the world was less careful. He remembered a handful of nights then, when his hand had been in hers. He shifted painfully on his bad leg and shook the memory away, pleased that all it left behind for him was kindness. With a small smile he pressed his coins into her hand and touched his hat.

The odds that Mr. Jones has more gold coins than Ms. Smith are nil.

David Harmon @81 writes:
We don't need to know anything prior to the moment, because "dice have no memory".

The differnece matters becuause there are two different populations in question:
1) The population of all coins in Lemuria, and
2) The population of the two coins in Smith's posession when she meets Jones.

When Smith says that "The one on top is gold", is that from when she drew from population 1 or population 2? The difference matters, and she does not tell us.

Best,
Jim Bales

Goob @ 86: Lovely. :)

TexAnne @ 71... Or the Teddy Bear Cholla before Teddy Roosevelt?

.. and that'll teach me to reread the question before popping off several hours later. Nice, self, very nice.

I'm another one of those who was initially sure of knowing the answer to be 1/6, but then got more and more confused by the back-and-forth.

So I wrote a computer program.

Smith1 = 2
Smith2 = rand(2)+1
Jones1 = rand(2)+1
Jones2 = rand(2)+1
while Jones1+Jones2 == 2 do
Jones1 = rand(2)+1
Jones2 = rand(2)+1
end

if (Jones1 + Jones2) > (Smith1+Smith2)

puts "Yes!"

else

puts "No!"

end

To explain: a gold coin is represented by 2, a silver coin by 1. The program gives Smith and Jones each two coins, coin1 and coin2. For Smith, coin1 is automatically a gold coin. The other coins are drawn at random -- but then I toss out any outcome where both of Jones's coins are silver.

The program prints out "Yes!" if Jones has a higher total than Smith (which can only happen if Jones has more gold coins).

I ran it 60 times, and got 11 "Yes" answers. I'm not knowledgeable enough in the ways of computer programs to get it to run a few hundred or thousand times and automatically tabulate the result, but it's close enough to make me feel I was right in thinking it should be 1/6.

i. She dreams of bridges,
soaring high above tempestuous bays,
dipping down in vertiginous arcs
to enter cities dense with winding pathways
and little whitewashed houses
stacked in impossible configurations.

ii. This is the measure of her innocence:
She sees the good shining clearly
through the hearts of those around her.
She sees the clear distinction
of evil; she knows well what can
and has
happened to the deserving and undeserving alike.
She does not make judgement.

This, then, is the measure of her naïveté:
She does not see the careless,
or, more precisely,
the Care-not.

iii. She dreams of water,
rivers flowing muddy and powerful;
waterfalls drowning viewpoints
in curtains of mist;
turgid lakes and stagnant swamps.

iv. Disillusionment is rarely large.
In literary fashion, one is hurt by something immense
and full of portent;
We do not write stories about the mundane.
But in truth, the armor of innocence
is fragile, shattered by the smallest things.

When one cares so much, it is impossible to comprehend
that some—
even the good and the kind—
are merely sleeping,
unconscious of the pain they leave behind.

v. She dreams of obstacles,
of pathways on the far side,
dark water under featureless skies,
boardwalks sinking into the mire,
of the coming flood and warnings left unsaid.

vi. He held her that night as she cried,
unable to articulate why.

vii. She dreams of rising waters,
and of dreamers who cannot swim.

NB: This poem has nothing to do with anything happening in my life right now. It's something I've been kicking around in my head for years.

Emily H. @ #91

I think you've just encoded your assumptions about the problem into a computer program.

Note that "otherwise unidentified coins in the hands of Smith and Jones are no more likely to be silver than gold" but it doesn't say anything about how the gold coins were acquired. We don't know that was random.

I disagree, but I have to bow out for the night. I genuinely don't understand -- if the unidentified coins are equally likely to be silver or gold, then does it matter how the coins were acquired?

94
I'm not sure that how they were acquired matters, either. Unless they were your Lemurian coins, of course.

(That's a nice example of Monte Carlo method.)

If your model acquires all the coins randomly and then throws out those cases that don't fit the information we have, you get a different result than if you take the gold coin as established and then acquire the other coin randomly.

The answer, of course, is language.

Aryllian@97: Yes, that's the whole point. In Smith's case you can take the gold coin as established and acquire the second one randomly, but in Jones's you can't.

David Goldfarb @ #99

I think that saying that is making an assumption about something that isn't stated in the problem. So far as I can see, we know five things:

1) Ms. Smith has a gold piece.
2) Mr. Jones has a gold piece.
3) Ms. Smith has a coin of unknown composition.
4) Mr. Jones has a coin of unknown composition.
5) Ms. Smith has (for whatever reason, and in whatever way) placed her gold piece on top of the coin of unknown composition.

I don't see how knowing #5 (or not knowing something similar to #5 about Mr. Jones) makes any difference to the probability of the coin of unknown composition being gold.

For better or worse, the last dream of the night (or morning) is the one that stands the best chance of being remembered later. Indeed, it often happens that, just as the car's air conditioning inexplicably seems to have a teaspoon of cold air waiting to come out before a lot of warm when you first turn it on on a hot day, touching down on my pillow will bring just enough of the last dream into my head again that I start to recognize it and it breaks up like mercury in a puzzle and runs off in several directions.

One of those stayed with me. I had my digital camera down on a table and was observing it closely. It had, in some way, acquired some form of awareness. I put a mirror down in front of it and it jumped back at first, then it got very interested and came closer to investigate.

I wanted to record this interesting encounter, but unfortunately, it was the only camera I had.

Kip W @ 101:

I am a camera.

The gnomes in the high tower are inspecting my most recent post, having taken a joke in four links for something potentially spamalicious.

I'll let you all know for sure what that second coin is if you help me get my cat out of this box.

Aryllian @ 100: "I don't see how knowing #5 (or not knowing something similar to #5 about Mr. Jones) makes any difference to the probability of the coin of unknown composition being gold."

But it's not the order that matters, it's the determinacy. For Ms. Smith, one coin is determined and the other is unknown; for Jones both coins remain unknown and the only valid statement is about the whole population.*

Knowing only that there are two coins, and that coins may be either silver or gold, there are four possibilities:

Gg Gs
Sg Ss

If we can determine that one--it doesn't matter if it's the first or the second--is gold, then we need no longer make statistical guesses about that coin. We can eliminate two of the above outcomes:

Gg Gs
Sg Ss

If all we know is that at least one coin is gold, but not which one, then both coins remain indeterminate. We can only eliminate a single outcome:

Gg Gs
Sg Ss

Thus, the chance of there being two gold coins is only 1/3. Gs and Sg are not interchangeable--not in the unmodified table, where they make the chance of getting one of each twice as likely as two golds, and not after we've eliminated an outcome.

* The difference between knowing that there were two people in the room and one of them committed the murder, and knowing that there were two people in the room and that the tall one committed the murder.

Heresiarch @104 -- so you're saying there is an essential difference between being told (with absolute certainty) that one of two coins someone is holding is gold, and being shown that one of two coins that someone is holding is gold. Because the coin you're shown automatically becomes, in some sense, the first coin.

That's where this whole thing becomes completely counter-intuitive to me. I know what the answer is, and how to determine it -- but I really don't get how that magic works.

David Harmon #70

So let's do the same thing with Mr. Jones.

Now he looks at his hand, puts the certainly gold coin on the top, and declares that the top coin is gold.

There is no change in the probabilites (still there is 1/3 chance that he's got two gold coins).

So far, so good.

But how do we know that Ms Smith didn't do the same thing?

Jim Bales @#77: I see I should have been more clear.

What I mean to say is that we know that Ms. Smith drew two coins from the Lemurian coin population, and when she drew the coins out of her purse upon meeting Mr. Jones, there was a gold coin on top. I meant to imply something about the ordering at that point only, and I see that I could have phrased it better.

Aryllian@#97:
I think that the best way to think about it is to take nothing as established, then throw away the universes that don't fit our information. We could take Smith's (but not Jones's!) one gold coin as established and we get the same answer if we do, but for clarity's sake, let's not.

I have now reconstructed my ruby-based probability system that uses that technique, and applied it to the scenario Jim Bales was using to get his 2/9 answer. To run this, you first need to pull down ambenv.rb and probworlds.rb. Then, we can code up the whole thing as this:

require 'probworlds'

puts "coins"
probability_pretty(' ') { |u|
# Ms. Smith has two coins from the population on the island
msSmithCoinsPocket = [u.choose(:g, :s), u.choose(:g, :s)]
# When she meets Mr. Jones, she puts them into her hand at random
# I phrase this as "randomly choose an ordering, then pick out
# the pocket coins using that ordering to make the hand coins"
msSmithCoinsHand = u.choose([0,1],[1,0]).map {|i| msSmithCoinsPocket[i]}
# Mr. Jones has two coins from the population on the island
mrJonesCoins = [u.choose(:g, :s), u.choose(:g, :s)]
# The top coin in Ms. Smith's hand is gold; otherwise throw out the universe
u.assert(msSmithCoinsHand[0] == :g)
# Mr. Jones has a gold coin; otherwise throw out the universe
# you can read this as "there exists a coin among mrJonesCoins that is gold"
u.assert(mrJonesCoins.find {|x| x == :g})
# Now tally each person's gold coins.
# I do that by saying "make a list of all coins such that the coins are gold,
# and tell me how long that list is"
mrJonesGoldCount = mrJonesCoins.find_all {|x| x == :g}.size
msSmithGoldCount = msSmithCoinsHand.find_all {|x| x == :g}.size
# Finally, collect this as the statistic we care about - whether Jones has
# more gold than Smith
mrJonesGoldCount > msSmithGoldCount
}

I think that the only bits of slightly odd ruby syntax in there are {|var| expression}, which you can think of as an abbreviated way to pass a one-argument function and :symbolName which for these purposes you can think of as a fancy way to make a string. Anyway, when you run this, you get that the last line yields "true" 1/6 of the time, as expected.

Tom Whitmore @#105 -

The magic comes from the fact that if Mr. Jones looks at the top coin and sees a gold, he says, "At least one is gold."

_And then he stops._

Whereas if he looks at the top coin and sees a silver, _he keeps going._

He then looks at the bottom coin, and if he sees a gold coin, he says the exact same thing he would have said if he hadn't seen a silver first---"At least one is gold."

At least, that's the process that our culture's standard puzzle-solving logic assumes that he's using, and it means that he's effectively reporting, "Either I have a silver coin and a gold coin, or a gold coin and a coin I haven't looked at."

And let me rephrase that a bit. He's saying: "Either I have a gold coin and a silver coin, or a gold coin and a coin that has a 50% chance of being silver."

Rephrasing again: "I have a gold coin, and a coin that is definitely silver if it's on top and has 50% chance of being silver if it's on the bottom."

Rephrasing again: "I have a gold coin. Plus, I have a silver coin on top, or a silver coin on the bottom, or a gold coin on the bottom."

If that's not what he's saying, then our cultural puzzle-solving logic doesn't work, and we fall back to having no idea about the circumstances and being probably unable to solve the problem.

"At least one of these two coins is gold" is not, probabilistically speaking, equivalent to "the first of these two coins is gold." This may look like a strange exercise in hair-splitting, but it is incredibly important to think this way when one does genetic counselling. Looking at the standard rules of Mendelian inheritance, one would expect the chances of inheriting a condition to be 1/2 for an autosomal dominant condition and 1/4 for an autosomal recessive, but when you do a full genotype analysis of a family tree, you often end up with probabilities of 1/3 or 2/3.

And a nitpick: the ODDS are 1:5, the PROBABILITY is 1/6.

I really think people should examine my parents example from #27. The issue is that the population of people who can honestly say "at least one of my children is a girl" is larger than the population that can honestly say "my eldest child is a girl".

Likewise, if we have a bunch of people walking around each with two coins one on top of the other chosen at random with their ordering chosen at random, one fourth will have two gold coins, one fourth two silver coins, one fourth a gold and silver (gold on top), and one fourth will have a silver and gold (silver on top).

Therefore, of the people who can make the statement "at least one of my coins is gold" truthfully, one-third of them will have two gold coins.

Of the people who can truthfully say "My top coin is gold", one-half of them have two gold coins.

That is all. We make no assumptions about how the people making these statements came by their knowledge of the coins they carry.

We do assume that there's no bias for or against carrying coins of differing metals, and that if one has coins of different metals there's no bias for carrying a particular one of them on top. But once you get through the assumptions necessary to say that the four populations I mentioned four paragraphs ago are all the same size, the rest is just a matter of restricting ourselves to those cases where the statements made are true.

heresiarch @104 * The difference between knowing that there were two people in the room and one of them committed the murder, and knowing that there were two people in the room and that the tall one committed the murder.

To be more in line with the puzzle "...and one or both of them committed the murder..." and "...the tall one committed the murder and we don't know if the short one was involved, but it's pretty suspicious that they're hanging round with a tall guy murderer."

Also, being six and a half feet tall, I'd just like to note that I'm not always the murderer.

Daniel Martin #109

"if we have a bunch of people walking around each with two coins one on top of the other"

Why do you think that this is the Lemurian custom?

"with their ordering chosen at random"

Why do you think the order of the coins is random?

Right, can't stand it any more. Let's try to do this properly.

We shall assume that statements about "coins" are actually statements about Lemurian coins, and that Smith and Jones are both telling the truth, since without those two assumptions the answer cannot be determined. We shall also assume that of the two contradictory statements "Gold and silver coins are evenly and randomly distributed in Lemuria" and "Otherwise unidentified coins in the hands of Smith and Jones are no more likely to be silver than gold", the former is true, because the difference in likelihood that invalidates the second statement is probably small enough to be ignored by someone who isn't being very careful.

So, assuming there are n gold coins and n silver coins in Lemuria in total, we can make a little table:

Smith	Jones	Probability
GG	GG	((n-1) * (n-2) * (n-3)) / ((2n-1) * (2n-2) * (2n-3))
GG	GS/SG	((n-1) * (n-2) * (n)) / ((2n-1) * (2n-2) * (2n-3))
GG	SS	((n-1) * (n-1) * (n)) / ((2n-1) * (2n-2) * (2n-3))
GS	GG	((n) * (n-1) * (n-2)) / ((2n-1) * (2n-2) * (2n-3))
GS	GS/SG	((n) * (n-1) * (n-1)) / ((2n-1) * (2n-2) * (2n-3))
GS	SS	((n) * (n-1) * (n-2)) / ((2n-1) * (2n-2) * (2n-3))

(if you multiply it all out and remember to count the "GS/SG" cases twice, then add it all up, it does add up to 1.)

Now, we must exclude the cases where Jones has SS, which are not allowed by the conditions. So the total probability of all the allowed cases, which will then form the basis for our conditional probability, is: (6n^3 - 14n^2 + 16n - 6) / (8n^3 - 24n^2 + 22n - 6)

Jones has more gold then Smith in the GS GG scenario only, and the conditional probability of that is: (n^3 -3n^2 + 2n) / (6n^3 - 14n^2 + 16n - 6). And that is the real answer (based on my initial assumptions, which are the minimal assumptions needed for there to be an answer at all).

As a check, we note that it should be 0 when n=2, and it should approach 1/6 for large values of n. And indeed this is what we find. For fairly small values of n, the probability is significantly different from 1/6 -- for example, if Lemuria has 10 gold coins and 10 silver coins, the probability is 0.151 instead of 0.167.

Mike Scott @ 112:

I absolutely agree with your analysis as describing the case where we know that:
1) the first coin Smith drew is gold and
2) one of Jone's coins is gold.

However, I don't see how we know 1) from the problem statement. (Ms. Smith says, “I have two Lemurian coins in my hand. The one on top is gold.”)

It is reasonable to presume 1), but it is equally reasonable (IMHO) to read this text and presume that the ordering in Smith's hand is uncorrelated to the order in which the coins were drawn from the population of all Lemurian coins.

(I believe this is the point that is being made by Aryllian @ 100.)

Best,
Jim Bales

Chris Lawson @ 108:
Thank you for the picked nit -- I am one of the guilty parties!

Best,
Jim Bales

I really don't think there is an even probability that a Lemurian coin is either gold or silver. Wouldn't silver be more common?

Thongor says: enough of this; let's go kill some lizard men.

You know the logic problems about the two guards at two doors, and one always lies while the other tells the truth.

I get the feeling that somebody here would point out that we're only assuming the guy who explained the problem is telling the truth.

I think I shall go lie down in a darkened room.

Nancy, #117: That's assuming that the Lemuria in the problem is the same Lemuria from our mythology. If Lemuria is actually a colony world named after our mythical country, the relative distribution of various metals may be significantly different from that of Earth -- cf. Darkover, where copper is the rarest (and therefore most valuable) metal. :-)

Jim Bales #87, Mike Scott #112 :::: For starters, the problem has made it clear that before either speaks, their coins are assumed to be drawn randomly from "Lemurian coins". That "patter" signifies only that before they tell us anything, we are to assume that any coin has a 50/50 chance of being gold or silver.

The total number of coins in Lemuria is not on the table here! By problem conventions, a nation's currency is assumed to be "very large", such that the handfuls at issue do not noticeably affect the supply.

Heresiarch @104, Jim Bales #113: Expanding on Jenna Moran #107:

an essential difference between being told (with absolute certainty) that one of two coins someone is holding is gold, and being shown that one of two coins that someone is holding is gold.

No, that's a conflation. What you've been told is that a particular one of Smith's coins is gold, whereas at least one of Jone's coins is.

Because the coin you're shown automatically becomes, in some sense, the first coin.

Yes. As soon as you distinguish the coins, they're no longer "in a bag", they are ordered. If you only knew one of three coins, the calculations get more complex, but Smith still no longer has three coins in the bag, you'd have two in the bag and one "drawn". Jones, in contrast, has (still) given us partial information about the contents of his bag, so that we can now differentiate it from "Lemurian coins" in general.

Komavary #106: Yes, but perhaps not for the reasons you think -- By peeking and then potentially swapping two coins, Mr. Jones has simultaneously added, then destroyed information, leaving us with no more knowledge about his hand than before. In fact, that peek-and-swap was implicit in his ability to tell us that "at least one" of his coins is gold.

Consider a table listing all 16 possibilities for the four coins: Several of the rows are ruled out immediately by the two original statements: mark the ones Jones rules out with X, and the ones Smith ruled out with Y.

Jo Sm ??
------
Gg Gg
Gg Gs
Gg Sg Y
Gg SS Y

Gs Gg
Gs Gs
Gs Sg Y
Gs SS Y

Sg Gg
Sg Gs
Sg Sg Y
Sg SS Y

Ss Gg X
Ss Gs X
Ss Sg XY
Ss SS XY

Some rows are ruled out by Smith, some by Jones, some by both. Jones's peek-and-swap makes his Gs and Sg rows indistinguishable, but doesn't rule out any more rows. However his telling us that he has "at least one gold" does rule out 4 rows, but two of those are also ruled out by Ms. Smith's statement. There are six rows remaining, of which exactly one gives Jones more coins than Smith.

The best answer to this question can be determined by planting a Magnet-Shroom and upgrading it to the Gold Magnet, which will suck all Smith and Jones' coins away from them, both gold and silver, and then you can count them at your leisure.

Erik Nelson @85: did he also polish up the handles of the big brass door?

heresiarch @ (oops, did the numbers just change? they were different the first time I looked)

* The difference between knowing that there were two people in the room and one of them committed the murder, and knowing that there were two people in the room and that the tall one committed the murder.

I can see why someone would want to know which person is a murderer. It's a social thing, thinking that you might have to walk into a room and interact with a murderer. But logically, if you want to reason about the person who is not a murderer and you don't have to walk into the room and identify them by some visible trait, then identifying the two people as "murderer" and "not murderer" would identify them sufficiently for reasoning. I think the same is true for coins.

Also, you're assuming that each of the three options according to your arbitrary separation of the population into top vs. bottom had an equal chance of occurring, but I think that what we actually know (one coin is gold) affects the prior probabilities. Which is to say, I think that the probability of having drawn Gg given that we know one of the coins that was drawn is gold is different than the probability of drawing Gg if you get to retry when you don't get any gold pieces.

Jenna Moran

If that's not what he's saying, then our cultural puzzle-solving logic doesn't work, and we fall back to having no idea about the circumstances and being probably unable to solve the problem.

Are you a programmer? Because your cultural puzzle-solving logic looks a lot like how an if-then-else logic construct works. However, I don't think that there's any reason to assume that any of this looking and not looking was going on. Which is to say, your cultural puzzle-solving logic does not match my puzzle-solving logic, which I'd guess is also cultural? It's what I learned in school. I happen to think that your logic is adding a great deal to the problem that wasn't stated in the problem, while mine isn't, but I suppose YMMV. There are a lot of people who want to add exactly what you want to add to the problem.

Daniel Martin

Your previous example about children is actually pretty interesting, but I don't think it proves what you think it proves. Here's why: Let's say you have a situation in which someone has one female child and another on the way. They haven't checked the gender of the unborn child. They can truthfully state that "My eldest child is a girl" and "after my unborn child is born, at least one of my children will be a girl". The probability of the unborn child being a girl is, however, still 50% (more or less, I read somewhere that actually slightly more boys than girls are born, but we shall ignore that for the purposes of this problem).

Since we know about the girls, or the gold pieces, we're not looking at the entire population. We are looking at the population of people who have gold pieces or girls, and trying to figure out the probability of their other coin or child being gold or girl. Having one gold piece or one girl doesn't change the probability of having another gold piece or girl.

I think that the best way to think about it is to take nothing as established, then throw away the universes that don't fit our information. We could take Smith's (but not Jones's!) one gold coin as established and we get the same answer if we do, but for clarity's sake, let's not.

I think that doing this will give the wrong answer. Throwing away universes is basically applying the probability of those universes equally to all the other universes as if we didn't know anything about their probabilities, but we know more than that.

We could take Smith's (but not Jones's!) one gold coin as established

Okay, one last thing. We do in fact know that Jones has a gold coin. Saying that we can't take Jones's gold coin as establish is denying information that we have.

Aryllian @ #123 said:

Throwing away universes is basically applying the probability of those universes equally to all the other universes as if we didn't know anything about their probabilities, but we know more than that.

No, it's applying the probability of those universes to the remaining universes in proportion to the known probabilities of those remaining universes. And it gives the proper answer, as any number of experiments here have shown.

Komavary @ #113:

When we are asked "what is the probability of something happening", the question is a bit vague - since the coins in Jones's and Smith's pockets aren't in a state of quantum flux at their meeting, in one sense the answer is "either 0 or 1". However, that's not meant. What's meant is "if we were to take all situations of equal likelihood in which the statements of the two could be truthfully made, what proportion would have Jones with more gold than Smith?"

Therefore, I'm not assuming anything about whether it is general Lemurian custom to wander around with two coins.

As for the order of coins and which one is on top when carrying two coins of dissimilar metals, I believe I did make it rather explicit (in the last paragraph of #111) that that is in fact a hidden assumption being pulled in by the general tradition of puzzles phrased in this way - when something is not explicitly stated, it is assumed to occur with uniform probability across all possibilities. If Lemurians with coins of differing metals prefer to carry the gold on top with probability p, then the probability of Ms. Smith having two gold coins given her statement is 1/(1+2p); we get 1/2 for the chance of Smith having two gold coins because we assume that p == 1/2. If p is 1, then Ms. Smith's statement tells us the same thing Mr. Jones's does (and each has a 1/3 chance of carrying 2 gold coins); if p is 0, then Ms. Smith's statement is equivalent to "I have two gold coins".

Aryllian: I fear we are talking past each other.

Let's try to simplify the problem by taking only one part of it: suppose Jones meets Smith and Jones says "I have two coins, and at least one of them is gold". Imagine that this is a normal sort of interaction in Lemuria and that Jones has not phrased his statements in this ambiguous way for any particular reason. Again, assume even, wide distribution of the Lemurian currency.

What then is the probability that Jones has two gold coins?

Am I correct in reading your arguments that you believe there is a case to be made for the probability in these circumstances being 1/2 ?

David Harmon #121 and Daniel Martin #125:

My problem with the 1/6 probability was illustrated well by Mike Scott (114):

"We shall also assume that of the two contradictory statements "Gold and silver coins are evenly and randomly distributed in Lemuria" and "Otherwise unidentified coins in the hands of Smith and Jones are no more likely to be silver than gold", the former is true"

Actually, both of the statements are true.
One is about Lemurian coins in general, and the other is about the exact four (or two) coins they hold.

From the first sentence, we know that the coins are evenly and randomly distributed in Lemuria - but we didn't know anything about how did Smith and Jones choose the pairs from their evenly and randomly distributed coins.

If we didn't have the second statement, we might assume that the distribution was random (therefore the answer is 1/6) or we could say that we need more information.

But we have that extra information. We have three statements. One from Smith, one from Jones, and one from the narrator of the puzzle.

So we know that (1) Smith has one gold coin (position doesn't matter), and one unidentified, and (2) Jones has one gold coin (position doesn't matter), and one unidentified, and (3) also know that the chance an unidentified coin is gold in this situation is 50% (or more) (therefore the distribution of the coins was not random).

Daniel Martin

No, it's applying the probability of those universes to the remaining universes in proportion to the known probabilities of those remaining universes. And it gives the proper answer, as any number of experiments here have shown.

I agree. This will calculate the answer correctly according to the assumptions under which you set up the problem.

I still feel like this sets up the problem in a way that assumes the 1/6 answer. Why should you ignore the fact that both parties have one known gold coin? That is what I can't get my mind around. Why are you assuming that there is any significant ordering involved at all? Isn't "top" an irrelevant description that could have come about in any way at all? Why would it change anything if Mr. Jones told us whether it was the top or the bottom coin that was gold? If he knows at least one of them is gold, he must know which one it is (assuming of course that he's even arranged his coins in a stack and not side by side).

But I think the most important question I have is: why should we look at the entire population of people who have two coins randomly acquired instead of looking at the population of people known to have one gold coin?

And yes. I think that if we have one known gold coin, and one unknown coin, then the gold coin is gold with 100% probability and the other coin is gold with 50% probability, and therefore the probability of having two gold coins is 50%.

Rikibeth @122 -- but you must not forget the Coffee Bean in the daytime, o Best Beloved. To mix references.

Erik Nelson #85: Paste pots? Those were always on the subs' desks. At the Gleaner we had two operations going simultaneously and two sets of editors supervising the product. That could make for a hectic time at mid-morning and late afternoon, since there were two "bedtimes" a day.

Sometimes I had odd things to do, such as the occasion when I phoned the leader of the opposition's wife to remind her husband that we were missing his Christmas message. I being the only person on the floor with her direct line.

B. Durbin #92: Very nicely done.

Tom Whitmore @129: I've experimented. While you need the Coffee Bean in the daytime to capture buckets, football helmets, screen doors, and ladders, it's perfectly possible to plant a sleeping Magnet-Shroom and add the Golden Magnet, and watch it immediately start capturing coins, no Coffee Bean needed.

Aryllian @ 123: "Also, you're assuming that each of the three options according to your arbitrary separation of the population into top vs. bottom had an equal chance of occurring, but I think that what we actually know (one coin is gold) affects the prior probabilities."

Again, it's not about top and bottom, it's about there being two unique, separate probabilistic occurrences. If we know anything for certain about one of those occurrences, it falls out of the realm of statistics and into determined reality. (Smith.) If all we know for certain is about the population as a whole, then it all remains probabilistic. (Jones.) Order doesn't matter; uniqueness does. I suspect you know this, and it is just the small population in question that is confusing the issue. So let's try it with a larger population:

GGG SGG
GGS SGS
GSG SSG
GSS SSS

When you flip a coin, or draw a coin from an infinitely large supply, if you disregard order there are four possible outcomes: three gold, two gold and one silver, one gold and two silver, or three silver. But, crucially, the chance of those four outcomes is not the same--the middle two are each three times as likely as the fore- and lattermost. Out of the possible outcomes where I could say, "at least one of the three is gold," what are the chances that I have three gold coins?

"They can truthfully state that "My eldest child is a girl" and "after my unborn child is born, at least one of my children will be a girl". The probability of the unborn child being a girl is, however, still 50% "

Yes, but they're not the only ones who could truthfully state that after their child is born. The population that you are crucially excluding are those who had a boy first and a girl second. In other words, why are you assuming that Jones didn't have to check both coins before finding at least one gold?

A few thoughts about your "What's Going On" .

I've heard that a bullet being stopped by an object in a pocket (commonly a Bible or a deck of cards) wasn't all that rare at an earlier tech level (American civil war?), but I haven't heard of a modern case. Have I just been missing out on cool unlikely events, or is it a highly implausible story?

It's my impression that a *lot* of riots, especially the long-lasting ones, are set off by police abuse. Not all riots, certainly-- there are also riots that result from sports event and demonstrations. Does anyone know if I'm seeing an actual pattern?

The police wanted to do horseback charges at crowds? Is this standard practice?

I realize the link is to a piece which is as much an editorial as reporting, but I don't know how much to discount any of it, and the same would apply to more mainstream sources.

#39 Tim Walters, your analysis is correct for items of pure chance, but here we have eliminated one half of the chances by specifying that, in each case, one of the two coins is gold.

If one coin held by each is gold, and we know that, and there is an equal chance of the other coin being gold, then the odds that a particular person has two gold coins and the other has just one is 1 in 4.

(NB: we are not drawing from the full population of coins, we are comparing two separate populations of two coins each, only one of which has an unknown state, and that state is equally likely to be gold or silver.)

In either hand we have only TWO possible states to determine whether Jones has more, equal or fewer gold coins: Therefore the odds are 1 in four that Jones has more gold coins (not an equal number, that's evens) than Smith

In your coin flipping, you are perfectly correct *if we flip both coins*, but here we are flipping only ONE of the two coins. The other stays at heads. Under that circumstance (excluding variables beyond our control), half of the flips result in both coins being heads.

I'm going to briefly note something here, harking back to Open Thread 161, though I probably will not wish to discuss it further:

Running into those 'Clarissa' cartoons last week really rattled me badly, particularly with no advance warning of the direction they were going to take.

I felt mentally off-balance and fragile for the better part of the week, even though they did not directly push buttons from my personal history. As it happens, someone very dear to me suffered regular "bedtime stories", called just that, and it's been difficult to let go of thinking about that after reading those cartoons. She is not the only close friend who went through some serious abuse in childhood. Even apart from our annual Dysfunctional Family Day, statistics - if you trust them - suggest that some number of the regular readers here have direct experience of sexual abuse and might be a wee bit sensitive on the subject even if they don't want to say so.

To be clear, I don't want to open up standard Internet spoilers discussion #17; you've all seen it before, please take all points on both sides as read. I'm glad the link was shared and I wouldn't want to have missed those cartoons, because they're brilliantly, angrily, well done. I'm still thinking about sharing them with the friend I mentioned above. However, a little bit of warning to brace yourself for a very bumpy ride would be considerate and appreciated. Thanks for reading, and thanks in advance if you're ever able to accommodate that request.

heresiarch

Again, it's not about top and bottom, it's about there being two unique, separate probabilistic occurrences. If we know anything for certain about one of those occurrences, it falls out of the realm of statistics and into determined reality. (Smith.)

Hmm. But how does naming one of the two occurrences change the probability? That's all that top really is so far as I can see, it's naming the gold coin that we know about top. We still don't know anything about the other coin, and we know exactly the same thing about Jones's situation: one gold coin, one unknown coin, we just don't know that the gold coin is also named top. I don't see how that makes a difference.

Out of the possible outcomes where I could say, "at least one of the three is gold," what are the chances that I have three gold coins?

I understand the math. I don't understand why you're starting with all possible outcomes when you know you have one gold coin. The only unknowns, the only thing you have to calculate probability for, are the coins that have not been stated to be gold.

Yes, but they're not the only ones who could truthfully state that after their child is born. The population that you are crucially excluding are those who had a boy first and a girl second. In other words, why are you assuming that Jones didn't have to check both coins before finding at least one gold?

I'm actually assuming that Jones looked at both of them at once, or at least that Jones knows what coins Jones has, and is choosing to give a certain amount of information about them. But I don't know that it really matters what Jones knows or what Jones checked, if Jones doesn't tell anyone that.

I wrote something longer right here and deleted it because I managed to completely confuse myself, so if anyone wants to explain why naming one of the instances changes the probabilities (or why top is more than a name), I would be interested in that, because I think I've managed to convince myself that it might but it still makes absolutely no sense.

Why are we doing your homework?

So let me see if I'm getting it.

Let us start with the case of Ms Smith.

Smith draws two coins at random from the pool of Lemurian coinage, and puts them in her pocket. We know that there are three possible outcomes:

Smith has two gold coins (p=0.25)
---OR---
Smith has one coin of each metal (p=0.5)
---OR---
Smith has two silver coins (p=0.25).

Later, Smith reaches into her pocket and randomly stacks one of her coins on top of the other. If the coins are different, it is equally likely that the gold will be on top as the silver being on top.

So, without looking at the stacked coins, the possible outcomes are:

a) Gold on Gold (p=0.25)
---OR---
b) Gold on Silver (p=0.25)
---OR---
c) Silver on Gold (p=0.25)
---OR---
d) Silver on Silver (p=0.25)

Now Ms Smith looks at the stack, sees the top coin, and finds that "The top coin is gold".

This excludes c) and d), so either a) or b) is true, and each now has p=0.5 (i.e., they are still equally likely, and are the only two remaining possibilities).

[To say it another way, let us assume we have an ensemble of many, many Smiths -- perhaps we cloned her. They all do the same experiment, and we have the ones who find a gold coin on top to stay, and those who find a silver coin on top we tell to go and become stormtroopers for Gearge Lucas. Of the ones who stayed -- i.e., the ones who found a gold coin on top when they randomly stacked the coins -- half will have two gold coins and half will have a gold and a silver.]

Now for Mr. Jones. He, too, picks two coins at random from the stock of Lemurian coins, and agian we know that there are three possible outcomes:

Jones has two gold coins (p=0.25)
---OR---
Jones has one coin of each metal (p=0.5)
---OR---
Jones has two silver coins (p=0.25).

He doesn't stack them up randomly, he just peeks in his pocket and says "I have at least one gold coin". This excludes the last category, leaving us knowing that there are two possible outcomes:

Jones has two gold coins (p=0.333...)
---OR---
Jones has one coin of each metal (p=0.666...)

And so the probability of Jones having more gold coins than Smith is 1/6.

Thoughts? Comments?

Best,
Jim Bales

THE LIVING DEAD DON'T NEED TO SOLVE WORD PROBLEMS.

Walter Hawn @ 135: but here we have eliminated one half of the chances by specifying that, in each case, one of the two coins is gold.

Not so. Jones has only eliminated one of four permutations.

Smith has GS or GG, with equal probability. Jones has GS, SG, or GG, with equal probability. Therefore the answer is 1/6.

Jim Bales @ 86: When Smith says that "The one on top is gold", is that from when she drew from population 1 or population 2? The difference matters, and she does not tell us.

No, it doesn't matter. For that matter, it could have been changed to gold by the fairies at the last second, or she could have drawn it from a pile of only gold coins just to mess with us. All we need to know is that (1) her first coin is gold, (2) all unspecified coins have an equal chance of being gold or silver, and (3) Jones has at least one gold coin.

I invite anyone who disagrees with this to do a simple experiment: toss two coins a bunch of times and keep track of the results (Daniel Martin has done this for you above, but maybe you should do it yourself). Then, letting heads stand for gold:

--how often can you make Smith's statement? (half the time)
--how often can you make Jones' statement (3/4 of the time)
--what fraction of Smith-compliant flips have two heads (1/2)
--what fraction of Jones-compliant flips have two heads (1/3)

Here's a Dr. Math FAQ about the Monty Hall problem, which is essentially the same.

Me @ 141: It occurs to me that you could also toss three coins at a time, representing Smith's second coin and Jones' two coins. Throw out tosses where both Jones' coins are tails, and again you'll see that 1/6 of the time Smith's second coins is tails and Jones' coins are both heads. This shows that it doesn't matter why Smith's first coin is gold.

Nancy @134

The bullet element of the story suggests that it was pretty low-powered round. .22 rimfire rather than 9mm Parabellum, for instance. That's still enough to kill somebody, but it would combine with the standard Police clothing, at least resistant to bullets.

The bullet which didn't quite wound my grandfather struck a .303 round, hitting the actual bullet, and the family story is that it was a "spent bullet". Long range, slowed by the air, still nasty if it hit in the wrong place. Shift the point of impact an inch, and it might have been a bit different. I don't know where he was carrying his ammunition, but the Pattern '08 ammunition pouches were on the waist-belt, so the bullet would otherwise have his him in the guts.

So, yeah, these things happen, but when a Mauser bullet can penetrate 4 inches of wood at around 2000 yards, pocket bibles aren't likely to make much difference.

Oh, one of the BBC reports is here.

One day, on a Lemurian street, Ms. Smith meets Mr. Jones. Ms. Smith says, “I have two Lemurian coins in my hand. The one on top is gold.”

Mr. Jones replies, “I have two Lemurian coins in my hand. At least one is gold.”

Smith and Jones are pickpockets, comparing loot. But both are hedging their statements, because Thieves' Guild rules say partners have to pool their loot and split evenly. And neither wants to admit they both have two gold coins.

In other words, the real question here is: How many coins do you have in your pocket?

Jacque @44: Yes, but which is it? Smith and Jones or Smith and Jones?

You forgot about Smith and Jones.

Aryllian (128): If [Jones] knows at least one of them is gold, he must know which one it is

Not if he could have started the day with a lot of coins, both gold and silver, and he kept track of his spending well enough to know that he has at least one gold coin left, but he's lost track of whether the second is gold and silver.

Why are we assuming that Smith and Jones both drew two coins from a population, instead of having two left after buying stuff that day? (Because it's unsolvable otherwise? Pfft.)

I'm also unsure how Smith's coin could be meaningfully "on top" after rattling around in her pocket or wallet. Does she habitually carry two coins stacked flat on her hand? Why?

-----------
In other news, logic problems like this bother me because the situation as recounted makes no sense. I'm with whoever it was up-thread who said that Smith and Jones are spies and these are their recognition codes.

Bruce Arthurs (144): How many coins do you have in your pocket?

None. They're all in my wallet, which is in my purse. They only time I have coins in my pocket is when I take a roll of quarters to the laundromat.

Nancy Lebovitz #134: Well, there was Teddy Roosevelt -- the bullet wasn't completely stopped by his folded speech, but he went on to give the two-hour speech (and wave the bloodied pages for emphasis!).

IIRC, the other "classic" bullet-stopper is a folded silk handkerchief -- that apparently happened often enough that nowadays, multiple layers of silk are commonly used in bulletproof vests and body armour.

@134 - the blog linked to is that of a very strange man who appears to believe that a descent into open 'class war' is a good idea. He also seems to believe that the police are both so cunning as to orchestrate riots for PR purposes, AND so stupid as to carry out their 'extra-judicial killings' by dragging people out of taxis and capping them on the ground. This view is akin to that, quite widespread amongst the deludedly bien-pensant, which holds that the police shot Jean-Charles de Menezes on purpose - as if a Brazilian electrician was some kind of second prize in the quest for an Al Qaeda cell. Conspiracy always trumps cock-up, apparently.

Tragically, this kind of mentality is fed by the police's tendency to spout the most transparently absurd arse-covering flannel as soon as anything goes wrong - worryingly suggesting that their operations are conducted in an atmosphere of ongoing panic. Still, the truth does come out, and I'd rather have policing conducted by publicly-accountable bodies than by people who call themselves 'Lenin' and almost audibly lick their chops at the prospect of deadly violence.

Aryllian @ #128: Would you like to play a game?

Here's the game: we have a dealer who everyone agrees is totally fair and impartial, who enjoys shuffling and dealing cards. I hand the dealer a full deck of cards (52, no Jokers - you can inspect the cards ahead of time), and he shuffles the deck and deals me two cards that I can see but you can't.

If I get two black cards, I show them to you and throw them back in the deck for the dealer to shuffle and deal again. Otherwise, I show you a red card, and you make a decision whether to bet that I have two red cards. If so, you pay me $2 to reveal the other card I got, and if it's red I'll pay you $5. (So if I had two reds, you're up $3, but if I had one of each color you're down $2)

Now if your theory is correct about the probability of having two gold coins when one says "I have two coins and at least one is gold", then this would be a good game for you to play over and over and over.

Would you care to guess what a computer simulation shows about your long-term financial prospects when playing this game over and over again?

Jim Bales #139: Yes, exactly!

Aryllian #137: Essentially, these, or any such collection of objects, are considered "naturally distinct" -- that is, you could conceivably line them up in a row and number them. That means that the probabilities you get are based on all possible permutations. If, in a given case, you can't distinguish between the objects, that means you have incomplete information, but "the world" still knows which coin (or whatever) is which.

The mathematics of combinations was developed largely to deal with exactly that situation, and for a more complicated case (say, drawing four coins out of an bag of ten), there would be various formulas that make the calculations practical.

Intuitively: Mr. Jones is saying "oh yeah, I've got a gold coin in here", while Ms. Smith is saying "so do I, and here it is!" Her "hand" looks stronger because she's shown something up front -- and the question at hand isn't so much about what they actually have, as about the odds we can fairly give for each to have a second gold coin.

Aryllian #137, cont'd: You can imagine that Ms. Smith pulled out a coin and slapped it on the table ("look, gold!"), whereas Mr. Jones rummaged in his pocket, pulled out a gold coin, but then dropped it back into his pocket. The difference shows up the next time they reach into their respective pockets....

Well, this has been a weekend for discovering toxic posts on the internet. There's a well-written blog about screenwriting by an aspiring screenwriter that I read courtesy of Harry Connolly, who pointed it out on his site and his LJ awhile ago. She put up a post yesterday because of cretins that are dropping in for personal attacks followed by sockpuppetry asking a) Don't be a dick, b) choose an identity and stick to it or the sockpuppets will be deleted, and c) if you're a lurker don't be afraid to join in on the conversation.

The second comment to show up was a furious flounce in what I think of as Subsection 1a: poor imitations of Jack Nickelson in the courtroom scene of A Few Good Men followed by the old "won't comment, won't read, you're all snobs and sycophants" line. Everyone here has seen this one before, usually executed better. I got curious enough to look at some recent comments, and they brought me back to the time where I commented on the upcoming release of The Spirit and which I found myself wishing to the Universe that I'd never made because it triggered Mike's unending ugly justifications of Frank Miller's sexism and rape in film and refusal to admit that there were reasons that folks were objecting to the skies over his continued defense of both, so in my case her post seemed both reasoned and reasonable.

Then I ran into a mention of a guy that had made a short SF film on YouTube which went over so well that he's been chosen to direct a remake of The Evil Dead which Rami and Campbell are producing. He posted about the film after he uploaded it to YouTube in the forums section of "CG Society The Society of Digital Artists" and mentioned they'd done the live action shooting for $300.00: you can see the final result here.

Well. He was promptly attacked for being a liar because it would be impossible to get the shots he needed with that amount of actors for $300.00 (clearly said by someone who's never experienced the power of offering something to go into an extra's portfolio), being a pirate because the software costs more than $300.00, for stealing from another filmmaker's work (who was listed in the credits, and who had helped out with the project), for being a liar because the whole thing couldn't have cost $300.00, and probably mopery.

It reminded me of William Goldman's comments about most directors and their relationship with scriptwriters, "They can't write, and it makes them crazy" and made me miss Mr. Ford's comments on film here. (This is not meant as a slight on Mr. Macdonald's postings on film: the difference to me has always seemed to be the difference between someone who knows and loves both theory and practice, and someone who knows both but is mainly concerned about what keeps or doesn't keep the audience in their seats.)

Maybe the underlying cause for both examples I've given was excess bile, or too much bad weather, or reading comprehension damage from too much exposure to bad screenplays: I'll admit that after I waded through the one written by the Wachowski brothers for Plastic Man I felt the way I did after running a fever for two days running, and that was just one script. Anyway, I make note of it for anyone reading up on film and film-related posts this week.

Julie L @ 145

There's also Smith and Jones (alas)

I've figured out what (else) is bothering me about this logic puzzle. Assuming for the sake of argument that Lemuria has the practice of issuing its each of its citizens with two coins, each of which could equally be silver or gold, Smith didn't say that her "first" coin was gold (or her second, for that matter), she said her "top" coin. Which doesn't tell us anything at all about the order in which it was issued to her. For that matter, for all we know the official Issuer of Coins reaches into a huge bag, picks up two coins, and hands them over at the same time, in which case there *is* no order. "Top" is a red herring. And, no, it's *not* as if "Mr. Jones rummaged in his pocket, pulled out a gold coin, but then dropped it back into his pocket." The puzzle clearly states that the issue is whether or not his other coin is *also* gold.

Aryllian @124: We do in fact know that Jones has a gold coin.
We know that he says he does. The puzzle statement doesn't confirm it. I don't even know if that's his real name.

***

Slider picture puzzles can be challenging. Especially if the blocks are all different sizes, and the pictures are correspondingly distorted within them.

Not to mention that you don't know what the finished picture is supposed to look like. Hippos at the top? At the bottom?

Helpful clue: try and find the blocks where a segment isn't distorted. Knowledge of Photoshop is a plus. Mumbling to yourself is perhaps helpful, or maybe it merely provides solace. If you finish the last one, take a screen shot before clicking "high score" — though I suspect they don't have a high score for that one, even though it pretends it does. (ps: There's a 'mute' button in the upper right of the window — I had to look for it after a couple of minutes of the music.)

I'm going to add to the group of people who think that the Lemurian coins question is underdetermined.

Basic probability

posterior odds = (likelihood ratio) x (prior odds)

We know the prior odds -- the probability of each configuration of Lemurian coins. We don't know the likelihood ratio, because we don't know anything about how likely Smith and Jones are to make these particular statements for particular arrangements of coins. Knowing they aren't lying or even that they aren't intentionally misleading isn't enough.

Suppose Mr Jones says "at least one of my coins is gold" only when he has two gold coins, and otherwise says "at least one of my coins is silver". Or suppose he says "at least one of my coins is gold" only when exactly one is gold, and says "I'll buy you a drink" if both are gold. Or whatever. The same applies to Smith.

This distinguishes the problem from Monty Hall, where we have an exact description of Monty's behaviour: he opens one of the doors with no car, choosing at random if there are two.

Now, the problem does become soluble if you adopt a rule that reduces the problem to binary, eg, if you say that each person thinks up a statement that they could make about their coins without knowing whether it's true, and then checks to see if it is true, and then says whether it is true. In that case the answer is that Jones is more likely to have more money. But that's such an unnatural way to produce speech that it's hardly surprising it causes problems.

Lee@120: My recollection is that Darkover was metal-poor, and so copper took the cultural place of gold because they didn't have any silver or gold.

David Harmon @152, thomas @157

I think these two comments spell out the issue quite clearly. The proposed procedures at 152 (take out one coin and, on the one hand, put it on the table, while on the other hand put it back in the pocket) are very slightly implied in the question, but they are by no means necessary.

Because Smith and Jones say different things, the puzzle-trained mind leaps to suspecting that they have different knowledge, or have done different things. And perhaps they have, but we don't actually know that. They are, after all, different people. Perhaps Smith holds her coins tightly, so she knows which is on top, while Jones habitually bounces them in a loose fist, so he doesn't know their current position. They both looked at what they had in hand when they took the coins out, but aren't looking presently. In that scenario, the odds are equal but the statements (and the differences in the statements) make sense.

Since Atlas Shrugged Part Two is probably dead, we can decide if this violates the Geneva Conventions.

So Daniel Craig and Harrison Ford each have two actual gold coins. By Hollywood convention, who winds up with them at the end of the movie?

The female lead, of course.

HLN: Discovered that some people unknown to me have (yet again) gone and dumped things on the end of my (city, alleyway) driveway. Am considering tripwires and explosives, also putting up a 12' fence[0].

Reasonable suggestions appreciated, however.

[0] Time and money make both of these less likely than I'd really prefer, unfortunately.

Aryllian @ 137: "But how does naming one of the two occurrences change the probability?"

It makes it not a probability at all, but a certainty. Whereas if all we know is that, out of the statistical population a certain number of them have a certain value, we still cannot say with certainty what the value of any particular coin is, meaning that Gs and Sg are both still live probabilities. Let me put it another way: if I have twenty gold coins, and at least eight of them are gold, what is the most probable number of gold coins for me to have: 10 or 14?

To go up another order of magnitude, if I flip a coin one thousand times, and I tell you at least four hundred and ninety nine flips were heads, then what is the most probable number of heads flipped? Do you see how that is different from flipping the coin and getting heads four hundred and ninety nine times in a row, then flipping it another five hundred and one times?

Mary Aileen @ 155: ""Top" is a red herring."

You are quite correct that the order doesn't matter, but here "top" or "first" is standing in linguistically for "a specific occurrence," as opposed to "one of a number of occurrences."

Let me put it another way: if I have twenty gold coins, and at least eight of them are gold, what is the most probable number of gold coins for me to have: 10 or 14?

Um. 20?

I flipped a quarter and a penny and at least one of them came up heads. What are the odds both came up heads?

Then I flipped a quarter and a penny and the quarter came up heads. What are the odds both came up heads?

heresiarch #164: I think some folks here have been bitten by too many quines, while others seem to get claustrophobic in problem boxes. :-)

xeger @ #163, cheap portable webcam/video recorder?

#156 ::: Kip W

Thanks for the game, I think.

Getting the pieces undistorted adds to the satisfaction of finishing the puzzle. I think I'm grateful that rotating the pieces isn't necessary.

heresiarch (164): You are quite correct that the order doesn't matter, but here "top" or "first" is standing in linguistically for "a specific occurrence," as opposed to "one of a number of occurrences."

It is possible that you are correct in puzzle-universe; however, I am not a resident of puzzle-universe and find it almost impossible to visit there. In other words...Huh?? If the order doesn't matter, why does the order matter?

#168 ::: Linkmeister @ 168 ...
xeger @ #163, cheap portable webcam/video recorder?

I've thought about it, but the closest 'safe'[0] place I'd be able to put such a thing is about 70' away, with a fence and part of a tree canopy in the way :(

Hmm... OTOH, there's nothing wrong with a warning sign and something that looks appropriate... and it'd be easy enough to (say) rig up a red led with a battery... and that'd last for ages...

Hmmm....

[0] Unattended objects still have a habit of vanishing without warning around here... it's a shame that the end of my driveway has started having things appear.

Mary Aileen @ 170: If the order doesn't matter, why does the order matter?

It's specificity that matters: something to distinguish between the two cases of one-of-each. Spatial order is a natural way to do this, since two coins can't be in the same place at the same time, but Smith could say "the coin that was minted earlier is gold" with the same effect, assuming that one could always determine that. For any ordering there are two one-of-each possibilities (GS and SG), and she's eliminating one of them from consideration, while Jones is not.

We're used to thinking about probability as describing reality, but while it's possible that probability is baked into reality at the quantum level, usually probability statements describe our knowledge of reality. That's why we don't need to worry about whether Smith and Jones are telling the truth, or whether the description of Lemurian currency is accurate; we have no knowledge of that, so it can't affect our calculations. All we can do is say that, given what we're told, Smith's coins can be in two equally probable states while Jones' can be in three.

Tim Walters (172): I...almost understood that. I think.

I grok that the order matters in the case when the coins were acquired in a certain order. I can't quite see it mattering when they already have the coins and are just describing them. But. I almost understood that explanation.

Although I still think they're really spies exchanging coded messages. ;)

173
The coins are hollow, and the messages are on microfilm inside them. Gold coins are clearly for more urgent messages.

xeger @ #171 wireless webcam for $27 plus s+h. Looks pretty unobtrusive. Channel the inner "Mission Impossible" spy of your choice when concealing it. I'd suggest Barney; he was the engineer. ;)

::shakes head::

Nope, sorry, I lost it again. They each have two coins. In each case, one coin is definitely gold and the other could be either gold or silver. I just don't see how knowing that Smith's definitely-gold coin is currently on top tells us anything at all about the probability of either's indeterminate coin being gold or silver. (Note that I'm not asking for further explanations. I see what you're saying, but it's just not going to make sense to me.)

P J Evans (174): Oh, yes, obviously!

Mary Aileen #173: Another way to put it is that initially the hands are standing in for what these problems normally call a "bag" -- that is, an unordered collection, about which you have limited information. Once an item is individually identified (Smith's gold coin) it has been "drawn", and is no longer in the bag.

The original wording is confusing here, because it describes the identified coin as still being in her hand. (Which is why up at #152, I reworded it in terms of "pockets", which are intuitively bags.)

Hmmm. This sounds related to the "socks in a drawer" problem. You have a drawer full of socks, all identical except that some are red and some are green. You must remove socks from the drawer without looking. How many socks do you have to pull out to be sure that you have a matching pair, color unspecified? How many do you have to pull out to be sure that you have a pair of red socks?

This is insanity! The answer is so obviously 1/4.

Think of it this way...

Ms. Smith has only one unknown coin. Regardless of anything else, she has a 50% chance of having two golds (GG), and a 50% chance of holding one gold and one silver (GS).

Mr. Jones, who definitely has one gold coin, has one other coin, which is unknown. 50% GG, 50% GS.

Each can pocket one gold coin without changing the equation.

I think I've figured out the disconnect here. We're actually talking about two slightly different situations:

Tim and David (and others) are dealing with the case where a large number of people are wandering around, each with two coins. In this scenario, Jones is in the set of people with at least one gold coin in any position, and Smith is in the smaller set of people with a gold coin on top.

DanR and I (and others) are dealing with two people, each of whom has two coins. Jones has one definitely-gold coin and one that could be either gold or silver; so does Smith. (Maybe their other coins are covered with crud or something.) The fact that Smith's definitely-gold coin is currently on top has no effect on her other coin. The other, indeterminate coin has an independent (though fictional) existence that is not affected by position. One or both of Smith's coins could be under the livingroom sofa, but they'd still be the same coins.

...And now I really am dropping this.

Wait, are we assuming that Ms Smith draws two coins randomly out of her pocket and looks at one and then passively reports that the top one is gold? I had assumed that Ms Smith deliberately placed the (or a) gold coin on top.

I suppose there's also the possibility that Ms Smith knows the one on top is gold, without looking. This implies that both of her coins are gold. Or maybe that she can taste things with her fingertips.

DanR @ 179: Mr. Jones, who definitely has one gold coin, has one other coin, which is unknown. 50% GG, 50% GS 33-1/3% GG, 33-1/3% GS, 33-1/3% SG.

FTFY.

Tim Walters @182:

If Mr. Jones takes his aforementioned gold coin and puts it on top, how is his situation different than Mrs. Smith's?

Avram @ 181: Wait, are we assuming that Ms Smith draws two coins randomly out of her pocket and looks at one and then passively reports that the top one is gold? I had assumed that Ms Smith deliberately placed the (or a) gold coin on top.

It makes no difference at all. We are assured that her second coin is equally likely to be gold or silver, and that's all we need to know.

I think people may be failing to realize that the probabilities that Smith and Jones calculate may be different from ours (in Jones' case, certainly will be). This is no weirder than the fact that my estimate of the probability of my having an ace in the hole in stud poker will be different from my opponent's--mine will be one or zero, his will be in between. Jones knows the location of at least one gold coin that we don't know; if he's looked at both his coins, from his point of view the probability is either 1/2 or 0. Likewise, if Smith has looked at her hole coin, for her the probability is either 1/3 or 0. (If she hasn't, her answer is the same as ours.)*

But the question is about our knowledge, not theirs, so the probability is 1/6.

Mary Aileen @ 180: Tim and David (and others) are dealing with the case where a large number of people are wandering around, each with two coins.

This is what probability means. Given a repeated series of events with the same information, in what proportion of them will Jones have more gold coins than Smith? If our information is different, our calculation of the probability may be different, even though the reality is the same.

*I hope I did all these right. But if not, it's the principle of the thing, mmkay? I had a gig last night and I'm still trying to wake up...

DanR @ 183: Jones can put the gold coin on top, chuck it into a wishing well, or turn it into a newt. As long as he doesn't tell us about his numismatic activities, our probability estimate doesn't change, because we have no new info.

Puzzles and logic problems tend to fall into two categories for me:
1) This is a trivial question that requires no effort and thus is boring.
2) Someone is mocking me and trying to make me feel stupid.
I should avoid logic problems, I really should.
It helps to know that "probability" is not a real thing, in the sense of being something that can be collected in a sack of probability or distorted by an Improbability Field. That's why "probability" problems like the Monty Haul and the gold and silver coins things make no sense in relation to the way things happen in the real world.

Okay... assume that Lemurians can only fit three coins into a hand... what becomes of the probablilty calculations if one of these characters always tells the truth and the other always lies? Better yet, if one always tells the truth and the other only lies when carrying gold?

Even better... disregard this message.

I'm backing off the main problem because at this point, it's been explained quite thoroughly, several times by several people in different ways. I do need to object to this:

Dr. Psycho #186: That's why "probability" problems... make no sense in relation to the way things happen in the real world.

On the contrary... the particular problems may be somewhat contrived (and always somewhat simplified), but probability is all about how things happen in the real world -- a real world where "sure things" usually aren't, and you almost never have complete knowledge of the situation.

Probability and statistics are how we can deal sensibly with uncertainty, and folks who don't understand them, are just that much more vulnerable -- both to natural "flukes of chance", and to exploitation by the malicious.

Linkmeister @ 175 ...
xeger @ #171 wireless webcam for $27 plus s+h. Looks pretty unobtrusive. Channel the inner "Mission Impossible" spy of your choice when concealing it. I'd suggest Barney; he was the engineer. ;)

Hmm... I wonder how well that'd do hooked up to a solar panel... Hmmm.... :D

My thanks to David Harmon and Tim Walton for sticking with me in working out the conditional probabilities embedded in the problem posed in the original post!

I think that I now have a better understanding of conditional probability than when I first encountered -- learning of the Monty Hall problem some 25 years ago, while having dinner with other grad students at Crossroads Pub and Grill on Beacon Street.

(What allowed me to get it then was actually running 15 trials of the Monty Hall problem while waiting for our pizzas to reach the table. My friend [a computer scientist] who played Monty noted that he only had a choice as to which door to reveal one time out of three.)

Best,
Jim Bales

Dr. Psycho @ 186: That's why "probability" problems like the Monty Haul and the gold and silver coins things make no sense in relation to the way things happen in the real world.

But they do, very much so. See Chris Lawson @ 110, or how Bayes' Theorem comes up in counterintuitive medical test results.

I wish I were better at explaining it, because I think probability is something people should understand. I wish I understood it better myself. Until we achieve omniscience, probability is what we're stuck with.

Mary Aileen @ 180 writes:
Tim and David (and others) are dealing with the case where a large number of people are wandering around, each with two coins.

Let me reinforce Tim Water's reply @ 184:
This is what probability means.

When studying Statistical Mechanics as a grad student back in the Reagan administration, we spoke of ensembles -- that is, we imaginged running the same experiemt on multiple, identicle, indepedent systems in parallel. If one quarter of those systems would have the same outcome, then the probability of that outcome was 0.25.

If Mary Aileen should decide that she is not *quite* done with the topic after all, perhaps she (or anyone else doubting the 1/6th result) might look over my analysis of #139 and let me know what seems less than persuasive and what seems to be reasonable.

Best,
Jim Bales

Jim Bales @190 (& Tim Walters):

The difference between this and the Monty Hall problem lies with the knowledge of the revealer... that is, Monty Hall deliberately does not reveal the car, and thus gives the contestant a 2/3 chance of selecting it by switching doors.

In this problem, we are not told whether Jones has seen both coins or only one, and so we must work under the simple premise that one of Jones' coins is a known entity and the other an unknown. The same goes for Smith. We do not know if she purposely placed the gold coin on top, or if it just landed there. Since we cannot assume anything further from the framing of the question, Jones' matrix should be taken as identical to Smith's.

DanR @ 193: In this problem, we are not told whether Jones has seen both coins or only one, and so we must work under the simple premise that one of Jones' coins is a known entity and the other an unknown.

The passive voice is revealing your problem. The question isn't what is a known entity (to whom?)—it's what you know. You know that Jones doesn't have two silver coins, and that's all you know about his coins. That eliminates SS, but not GS or SG.

Again, I suggest running a few trials with coin tosses. You will quickly see that Jones will report that he has at least one head three times out of four on average, and that one of those three will be GG.

Tim Walters @194: You know that Jones doesn't have two silver coins, and that's all you know about his coins.

Again, how does this differ from what you know about Smith's coins?

...and suppose we make it even more like the Monty Hall problem: instead of telling you he has at least one gold coin, he looks at both his coins and plunks a gold one on the table. The probability of his having another one is still 1/3, not 1/2, because we already knew that he had a gold coin, and can produce one this way from any of those three states where he has at least one gold coin. Just as Monty's revealing the goat doesn't give you any info about the box you picked (because he can always reveal a goat), Jones' revealing the gold coin doesn't give you any info about his other coin (because he can always reveal a gold coin).

Jones' knowledge doesn't affect your estimate, because you only know what Jones tells you.

DanR @ 195: Again, how does this differ from what you know about Smith's coins?

You know that a specific coin of Smith's is gold, leaving only one unknown coin. You don't know that about Jones--he has two unknown (to you) coins. Knowing he has at least one gold coin doesn't determine the metal of either of his coins.

Smith has ruled out SG, but Jones has not.

What we know:

Mrs. Smith has 1 gold coin.
Mr. Jones has 1 gold coin.

Is there supposed to be an implied distinction between a coin being "on top" or somewhere else in the hand?

Tim Walters @197: Knowing he has at least one gold coin doesn't determine the metal of either of his coins.

Aha! Schroedinger's coin... Still, I assert this does not matter. We are not trying to determine the metal of "either of his coins," but both.

Can you see that one-third of the people who can make Jones' claim cannot make Smith's claim, but that everyone who can make Smith's claim can also make Jones' claim?

If not, I'm out of ideas for how to explain this.

Can you see that one-third of the people who can make Jones' claim cannot make Smith's claim, but that everyone who can make Smith's claim can also make Jones' claim?

If not, I'm out of ideas for how to explain this.

Lee@178: To be assured of a matching pair, I need to pull out three socks. With the information given, I have no way to be assured of getting a red pair, because I don't know that there are two red socks in the drawer. If I'm given that there are at least two red socks, then it depends on whether I know how many green socks there are -- if I do, I must pull out that many plus two; if I don't know how many green socks there are, then there's nothing for it but to pull out all the socks.

Tim Walters @200: Can you see that one-third of the people who can make Jones' claim cannot make Smith's claim, but that everyone who can make Smith's claim can also make Jones' claim?

See Avram @181.

So, from probability let's go to geometry. I got this from the latest MT VOID, so if anyone here subscribes to that (I'm pretty sure Kip W. does) you'll have seen this.

In _Harry Potter and the Deathly Hallows_, there's a geometric figure which represents the Hallows of the title. In the first movie we see this in two places, on some jewelry and in a signature. In both cases, it's a triangle enclosing a circle inscribed within it (the largest possible circle that the triangle can contain) with a single line over it, the perpendicular bisector from the triangle's apex.

(Those who aren't familiar with the sign and have trouble with the description can see it here.)

On the jewelry, the triangle is equilateral. In the signature, the triangle is an isosceles right triangle with the right angle as the apex.

For both cases, what is the length of the up-down line, in terms of r, the radius of the circle?

Dave Bell at # 119: You know the logic problems about the two guards at two doors, and one always lies while the other tells the truth.

Live action version.

The Order of the Stick had an amusing take on those problems as well.

DanR: See me at 184. We are assured that unknown coins have an equal chance of being gold or silver. If Smith is allowed to make her claim regardless of what order her coins were originally in (by reversing them if necessary), then her second coin has a two-thirds chance of being silver. So by the definition of the problem, that can't be what she's doing.

I think the problem would be clearer if something out of Smith's (ordinary) control like mint date were used, but it doesn't actually mattter.

Tim Walters @207:

You are referring to the wording, "otherwise unidentified coins in the hands of Smith and Jones are no more likely to be silver than gold."

I think this is where we diverge. I believe that by saying, "at least one of them is gold," Jones effectively identifies one of his coins. I do, however, see how this could be interpreted otherwise.

It's late and I am cooked... in the hour or so we've spent on this, the value of the Lemurian gold coins has gone up "at least" 1%.

Peace, D.

re the slider game mentioned in #156 - I *did* manage to finish it, but between NoScript, cookie blockers, and not counting as I did the sliders, I didn't realize I was at the end until I'd actually finished (and the picture went away). So it can be done.

Okay, not done.

I know that's what probability means.

But I'm stuck on real people wandering around with real coins. Real coins don't change just because we know what/where another coin is. It may change what we can know about it, but the coin stays the same.

We're talking about different things.

----------------
You know, this is stupid. Even before I was dumb enough to get involved in it, I could tell that this was going to cause a bigger fluorospherical flame war than anything else in the last three years.

Good night.

I've gotten to the Chinese Seed Peddler screen of Not To Scale, and Crain of California doesn't show up in google. I suspect it isn't an American company.

Melissa Mead @ 78: Exactly. (With a conspiracy charge on top, of course.) Sorry so late to answer back. I got caught up in stuff.

General thread stuff: Statistics and probability is one of those fields of study that has always struck me as vaguely Lovecraftian. Gaze into it for long enough, and you'll go cuckoo-for-cocoa-puffs, usually at some staggering moment of "The Universe actually... works that way? FFFFFFUUUUUUUUUUU--"

(I don't know if Lewis Carroll did much in the way of prob & stats work, but I wouldn't be surprised.)

See, the thing bothering me here is that I don't understand Smith's motivation for telling us that the gold coin is on top.

In the case of the Monty Hall problem, I know the rules by which Monty is operating, so I can work from that to figure out that there's a 1:3 chance that staying with my first door choice is right, and a 2:3 chance that I'm better off switching.

In this case, I don't know how Smith's description of her coins fits into the probabilistic distribution of those coins in the space of potential-Smith-hand-contents. How does Smith behave with a pocket full of silver? With more than two coins? With just one coin? That's why I don't take the statement that the gold coin is on top is meaningful.

Terry Karney @13: Welcome to Hudson County!

Lenore (in Hoboken)

I went to see Xopher this afternoon (Sunday). He is still feeling pretty woozy. However, he perked up enough while I was there to enjoy hearing all the e-mail messages.

He was doing much better than yesterday. We had quite a conversation despite his inability to speak at the moment while the tongue heals. He filled several pages of his notebook with his part. He’s definitely up to visits. In fact, he’s bored! He’s a little too woozy to read, but not woozy enough to sleep. The pain meds are quite effective, but they have their downside, for sure.

He told me that the surgery went three hours longer than expected because they carefully removed layers of the tumor until they had clean margins. That was good to hear; we’d worried about why it went so long. Makes sense.

They told him the feeding tube is scheduled to come out Wednesday, when they anticipate the tongue will have healed enough for normal eating, and they would also then close up the tracheostomy. He’s sure looking forward to that, and to coming home, but he’s healing well, and his spirits are good (if woozy).

Lenore

Avram: Would it work better for you if it was like this?

You're there on the street. Jones holds up a gold coin in her right hand and shows it to you. "I have two coins," she says. "One in my hand, one in my pocket. This one in my hand is gold." (And as you can see it, you can tell that she's correct.) Smith looks in his pocket. "I have two coins in my pocket," he says. "At least one of them is gold."

To my mind this is an equivalent formulation to what Jim gave.

OK, I think I've successfully explained it to myself: Smith and Jones each get get a random coin on Saturday, and another random coin on Sunday. On Monday they meet at the pub, but each only shows up if he or she got at least one gold coin, because the drinks are expensive. Smith reveals that the coin she got on Saturday is gold. What are the odds that Jones has more gold than Smith?

I think there are 16 possibilities as of Sunday night:

• Smith got gold on Sat, gold on Sun; and Jones got gold on Sat, gold on Sun
• Smith got gold on Sat, gold on Sun; and Jones got gold on Sat, silver on Sun
• Smith got gold on Sat, gold on Sun; and Jones got silver on Sat, gold on Sun
• Smith got gold on Sat, gold on Sun; and Jones got silver on Sat, silver on Sun
• Smith got gold on Sat, silver on Sun; and Jones got gold on Sat, gold on Sun
• Smith got gold on Sat, silver on Sun; and Jones got gold on Sat, silver on Sun
• Smith got gold on Sat, silver on Sun; and Jones got silver on Sat, gold on Sun
• Smith got gold on Sat, silver on Sun; and Jones got silver on Sat, silver on Sun
• Smith got silver on Sat, gold on Sun; and Jones got gold on Sat, gold on Sun
• Smith got silver on Sat, gold on Sun; and Jones got gold on Sat, silver on Sun
• Smith got silver on Sat, gold on Sun; and Jones got silver on Sat, gold on Sun
• Smith got silver on Sat, gold on Sun; and Jones got silver on Sat, silver on Sun
• Smith got silver on Sat, silver on Sun; and Jones got gold on Sat, gold on Sun
• Smith got silver on Sat, silver on Sun; and Jones got gold on Sat, silver on Sun
• Smith got silver on Sat, silver on Sun; and Jones got silver on Sat, gold on Sun
• Smith got silver on Sat, silver on Sun; and Jones got silver on Sat, silver on Sun

• Smith got gold on Sat, gold on Sun; and Jones got gold on Sat, gold on Sun
• Smith got gold on Sat, gold on Sun; and Jones got gold on Sat, silver on Sun
• Smith got gold on Sat, gold on Sun; and Jones got silver on Sat, gold on Sun
• Smith got gold on Sat, silver on Sun; and Jones got gold on Sat, gold on Sun
• Smith got gold on Sat, silver on Sun; and Jones got gold on Sat, silver on Sun
• Smith got gold on Sat, silver on Sun; and Jones got silver on Sat, gold on Sun
• Smith got silver on Sat, gold on Sun; and Jones got gold on Sat, gold on Sun
• Smith got silver on Sat, gold on Sun; and Jones got gold on Sat, silver on Sun
• Smith got silver on Sat, gold on Sun; and Jones got silver on Sat, gold on Sun

• Smith got gold on Sat, gold on Sun; and Jones got gold on Sat, gold on Sun
• Smith got gold on Sat, gold on Sun; and Jones got gold on Sat, silver on Sun
• Smith got gold on Sat, gold on Sun; and Jones got silver on Sat, gold on Sun
• Smith got gold on Sat, silver on Sun; and Jones got gold on Sat, gold on Sun
• Smith got gold on Sat, silver on Sun; and Jones got gold on Sat, silver on Sun
• Smith got gold on Sat, silver on Sun; and Jones got silver on Sat, gold on Sun

I agree that's an equivalent formulation of the problem, and a correct solution.

@216 Thanks for the Xopher update, Lenore! More good thoughts heading his way!

#44, #145, #154:

The original post specifies that Smith is a Ms., so it's not any of those. (Nor is it Smith and Jones, since in that case it's Jones who's the Ms.)

Dave Bell #115, Allen Beatty #205: When I clicked the link, I thought it was going to be the scene from Labyrinth. Would an actress and two Henson Labs creatures count as live action?

Lenore #216: Yay, good to hear he's doing well!

And with 217 and 218, I think I can articulate why this is so baffling/irritating to some people.

In the situation in 218, the answer is clearly 1/6. In the situation in 217, and the situation in the problem, it's not clear that the "coin on top"/"coin in hand" was selected at random, and unless it was, then the answer is NOT 1/6.

The equivalence of the 3 questions is a convention, and it adds information. If you work with probability math regularly, you are so used to the convention that you don't notice it.

*Note that probability is very closely related to what I do; I'm definitely in the "seen these problems before" camp.

I apologize for losing my temper last night.

I know, I know, the thread's moved on. But it took me long enough to explain this to myself* that I can't not post it here. The large number of people who've got this now can just skip ahead :D

It started making sense to me when I thought of the situation in terms of properties of the coins themselves.

We exist in a limited universe where Coins A, B, C and D are objects which have only have two properties, properties whose values consist of mutually exclusive pairs: top/ bottom and silver/ gold. Top implies not bottom, silver implies not gold, and vice versa.

The rules of the universe are such that:

The {top, bottom} properties of A and B connected as a pair with a rule. The {top, bottom} properties of C and D are connected as a pair with the same rule. The rule is that if one of the pair is top, the other is bottom (this rule is deduced from the assumed physics of our pocket** universe).

The {gold, silver} property is connected for AB with the rule “one is gold”. Let’s call this physical law “Jones”.

The {gold, silver} and {top, bottom} properties are connected for CD with the rule “the top one is gold”. Let’s call that rule “Smith”.

Other than these rules, A, B, C, and D have an equal chance to be distributed top, bottom, gold and silver - the relationship of AB has no influence on the relationship of CD.

In this universe, under Jones, AB can be:

A is {top, gold} B is {bottom, gold}
A is {top, gold} B is {bottom, silver}
A is {bottom, gold} B is {top, gold}
A is {bottom, gold B is {top, silver}
A is {top, silver} B is {bottom, gold}
A is (top, silver} B {bottom, silver}
A is {bottom, silver} B is {top, gold)
A is {bottom, silver B is {top, silver}

In 2 of these 6 combinations, AB is gold/gold
     => the probability of Jones having GG is 1/3

CD under Smith can be:

C is {top, gold} D can be {bottom, gold}
C is {top, gold} D can be {bottom, silver}
C is {bottom, gold} D can be {top, gold}
C is {bottom, gold D can be {top, silver}
C is {top, silver} D is {bottom, gold}
C is (top, silver} D is {bottom, silver}
C is {bottom, silver} D is {top, gold)
C is {bottom, silver, B {top, silver}

In 2 of these 4 combinations, CD is gold/silver => the probability of Smith not having GG is ½

     =>The probability of Jones having GG when Jones does not is (independent probabilities multiply) 1/3 * 1/2 = 1/6
Or another way of putting it - the total possibility space is 6 * 4 = 24 combinations (for each of the six ABs there are four possible CDs) and of these there are 4 cases where AB is GG when CD is not:

A is {top, gold} B is {bottom, gold} ; C is {top, gold} D is {bottom, silver}
A is {top, gold} B is {bottom, gold} ; C is {bottom, silver} D is {top, gold}
A is {bottom, gold} B is {top, gold}; C is {top, gold} D is {bottom, silver}
A is {bottom, gold} B is {top, gold}, C is {bottom, silver} D is {top, gold)

* Yes, I really did have to write it out long hand before I could convince myself.

** Heh.

SamChevre (224): I think you've got it.

Also, I at least was (became) distracted by a possibly-unrelated point: probabilities are all very well, but they don't actually tell us about the reality of a particular case.

Two examples, to hopefully make this clearer:
1) Tim mentioned a card game in #184. He knows whether or not his hole card is an ace, so for him the probability is either one or zero. (Talking about probabilities when he already knows strikes me as deeply weird, but let's leave that aside.) His buddy doesn't know and has to figure the probabilities. But no matter how much information the buddy has or doesn't have, or how accurately he does the computations, none of that changes what Tim's hole card actually is *in this hand*.
2) A few years ago I had a very rare drug reaction. It took quite a while to diagnose, because my doctors were (quite understandably!) looking for the horses that made the hoofbeats, when I had been run over by a metaphorical zebra. (Probably escaped from the zoo. ;) They were right to consider the more-probable causes first, but that didn't change the fact that I really did have a 1-in-10,000 drug reaction.

Mary Aileen:

The thing that gets confusing in a lot of probability problems is that you can reason that X has no effect on Y, but due to the other information you've been given, knowledge about X gives you new information about Y. So you can have a situation where X can't possibly do anything to Y in the physical world, and yet when you find out X you also find out Y.

A simple example of this: suppose I have flipped two fair coins. Now, because they're fair coins, they have no effect on each other. The first coin coming up heads has nothing to do with whether the second coin comes up heads. So right now, if I tell you that the first coin came up heads, this doesn't help you at all guessing the second coin.

But suppose I also tell you that the coins came up the same--both heads or both tails. Now, with that information added, if I show you the first coin, you know the second coin, even though the two coins have no physical connection. Nothing about the coins is connected except the information I've given you about them.

The first time I needed to think in terms of things that were physically independent, but where learning one changed my information about the other, I remember finding it really confusing. Playing with probabilities in tricky ways is a lot of what I do for a living, so I've gotten used to it. But it still makes my head hurt a bit when I think about it in words instead of in math.

Open threadiness:

I wonder whether, ten or twenty years from now, we'll look back at the downgrade of US debt as a funny historical blip, or as a sign telling where we were headed.

Lenore @216--thank you--I am so glad to hear that Xopher is doing as well as he is, and hope to hear more good news soon.

Kip W @ 156

I was meant to be doing some work before sleep and somehow I got distracted...

(I did actually take a picture of the last one if anyone wants it.)

Andy @209: Yeah, I solved them all as well. I thought I'd said that, but apparently it's ambiguous, so I'm saying it now. (Because what other reward do I have for solving it, apart from saying so here? So said!)

Nancy @ 134, and David Bell and David Harmon @143 and 148--I think there are two big factors to keep in mind with regard to "stuff wot stops bullets", and they aren't the nature of the object stopping the bullet.

Type of powder is one--black powder has less oomph (non-technical, non-ordnance term) than more modern powders and so tends to impart less velocity to the projectiles it's used with.

Type of weapon is another--a rifled barrel as opposed to a non-rifled barrel. Rifling imparts spin to the projectile, which affects the manner in which it travels.

To take Nancy's American Civil War as a target date (there are plenty of stories about How a Bible* [or sometimes a deck of playing cards--less pious, but probably just as likely] Stopped a Bullet from that war), they were still using black powder, but most combatants had rifled muskets**. So projectiles had the advantage of rifling, but the disadvantage of black powder, and bullets were more likely to be stopped by a somewhat solid object (think, not a metal plate or thick piece of wood, but something with many layers, like a small book or deck of cards, or a wallet or cartridge box) at anything but close range. Before the general use of rifled muskets (about the time Minié developed his bullet and musket, which Wikipedia claims to be around the Crimean War), muskets were smooth-bore weapons and did not impart spin to their projectiles, and so these bullets were even more likely to be stopped.

In most cases, as I understand it, a bullet is easily stopped because it's losing force as it travels--becoming a "spent round" because it's spent its impetus. Bullets from non-rifled, black-powder-charged weapons lose their impetus earliest, those from rifled, black-powder-charged weapons next, and those from rifled weapons using modern powders last. So distance from shooter to target matters here, as does what's being fired and what it's hitting--and the type of weapon and propellant used have a direct effect on the first item--the distance at which a round has lost enough momentum*** to be easily stopped.

I suspect the Mythbusters have played with this one, but I can't recall which season.

*Probably a pocket New Testament, but I'm not arguing with popular culture here.

**The introduction of rifled muskets as general issue seriously screwed up infantry tactics, which is one of the things that made battles in the American Civil War so awful--mst senior officers had learned their tactics with smoothbores, and had no clue about how effective massed rifled musketry fire was going to be. See the career of Braxton Bragg for a specific example of this failure to comprehend.

***I am probably greatly abusing the sense of both "impetus" and "momentum" as technical terms in physics; I seem to be making them nearly interchangeable and I doubt they actually are. Please be kind; I was a Greek major.

My first reaction to this video (which does indeed show a mounted police charge, which knocks at an unmounted officer of his feet) was to note how much less effective the Metropolitan police are handling a real riot than they were at kettling and arresting students during a planned and peaceful protest. Clearly shooting fish is harder without the barrel.

Length of barrel of the weapon is another variable. A bullet from a revolver with a two-inch barrel will have less energy than the same round fired from a weapon with an eighteen-inch barrel.

You'll also find a bit of reporting bias. A bullet stopped by a Bible will be remembered. A bullet that goes in one side and out the other of a Bible, killing the trooper, won't be remarked.

Fidelio:

I thought rifling just made the bullet go in a more straight line. Does it keep the bullet from slowing down as much as it passes through the air? I guess if the bullet is oblong, keeping it from tumbling should make the bullet go faster (less cross section), but if it's a ball, it seems like spinning or not wouldnt have much effect. But I have no faith in my intuition here....

Open thread:

Child murderer wins damages over police torture threat

Warning: Might be triggery for the obvious reasons.

Since there have been many threads about torture as well as police violence before:
I am very happy that such a verdict is possible despite the fact that Germany's biggest tabloid was screaming and agitating against this. The usual suspects are more or less claiming now that convicted felons should have no human rights left and other b*llsh*t.
I begin to think that there is a significant part of the population who do not like the rule of law or is too stupid to understand what a great thing it is.

JMD @ 235: True on both counts. You can't get a good revival sermon out of a pocket testament that didn't stop a bullet.

albatross @236. Losing the tumbling increases both range and accuracy-I suppose that the tumbling effect wastes the energy that could otherwise contribute to speed/range. Wikipedia has an article on rifling and one on internal ballistics, which is all the things that happen inside the firearm, and the design choices that affect all of that. The internal ballistics piece also has links to the articles on external ballistics and terminal ballistics, for those that are interested enough to click.

The expert should feel free to argue; I admit I am at the limits of my understanding of the technical aspects at this point.

Jorg, #237: I begin to think that there is a significant part of the population who do not like the rule of law or is too stupid to understand what a great thing it is.

I think it's much simpler than that -- just the usual case of a double standard. What's wrong when They do it somehow becomes right when We do it. And always for the best of justifications; note that the situation described in the article was a real-life application of the "ticking time bomb" scenario.

Question for the assembled non-conservatives: Would you agree with the statement that "the radical left has never held as many levers of power in this country as they have under Obama"?

Jorg and Lee:

The value of the rule of law, morals, principles, etc., is always harder to see than the value of violating those things when they are getting in your way. Their value is subtle, stretched out over many years, and probabilistic.

And it seems like politicians and media types overwhelmingly push against those things. Every time there's another executive power grab, silent acceptance of some domestic spying scandal, decision to "walk on by" or "look forward, not backward" about official misbehavior by the powerful, acceptance of police abuses because "they're putting their lives on the line for us every day" or "no price is too high to keep our kids safe," we become a society that has fewer safeguards against becoming a police state, having a coup, or having the folks in power silence their political enemies, and the less safe every citizen is in their own home. (Note the way the war on drugs and excessive use of SWAT teams has led to deadly armed midnight raids by jackbooted thugs on the homes of suspected small-time drug dealers. Failing to push back on this has let it become all too common.)

C Wingate:

I sure don't see that from Obamas policies. It sounds like empty rhetoric, but it would be interesting to ask how we would know if it was true. For example, how would we measure the number of members of the radical left who have powerful positions? What actions would we expect to see in a world where the radical left held greater power than ever before? How would we define radical left to make the question meaningful?

Off the top of my head, I'd expect that in such a world, we'd see a large scale shift from military and intelligence resources to domestic spending, especially on social programs. I'd expect much more intervention in markets, both in terms of regulations and in terms of government takeovers of politically important industries. I expect we would see large rises in tax rates at he top income brackets, and large increases on capital gains and corporate taxes. I imagine we would see fewer illegal immigrants deported, and more favorable laws passed for making unions more powerful.

My impression is that we have seen very little of this, and that the leftward moves we have seen in policy have been relatively limited and primarily in Obamacare and re-regulation of the financial industry--both things that almost anyone in office would want to consider, given the impact of health care costs on the US economy and budget, and the huge financial meltdown that just happened.

Putting on my ballistics-geek hat. [1]

Bullet penetration is one of the endlessly-interesting questions. There are really only two big factors.

1) Bullet energy at impact
2) Bullet cross-section size

Engineering matters a lot. With a muzzle-loader, before the Minie ball, there's a very strong trade-off between how tightly the bullet fits the barrel and how fast you can re-load. And since black powder builds up carbon and crud in the barrel, the bullets generally were fairly loose-fitting so that even when firing repeatedly you could still load. With that loose fit, velocities were low--so lead ball worked fine. Old-style smooth-bore muskets were not unlike modern shotguns shooting old-style slugs. From physics, energy is mass * velocity^2--a slow-moving bullet needs to have substantial mass to have enough energy to be effective--so a big bullet is a necessity. The British Brown Bess was .75 caliber--about like a 12-guauge shotgun--so a bullet would have weighed 1 1/3 oz.

Rifling makes the bullet spin; with rifling, your bullet can (actually must) be longer than it is wide--so a rifle bullet has a smaller cross-section than a same-weight musket bullet. AND, since rifle bullets must fit tightly in the barrel, the achievable velocity is higher.

Once you have bullets that fit tightly in the barrel, you start trading mass for velocity--so the army goes from the .75 caliber Brown Bess, to the .58 caliber 1853 Enfield (34 grams at 900 fps), to the .45 caliber Springfield, to the .30 caliber rifles, to today's .22 caliber M16 (4 grams at 3000 fps).

Basically, slow-moving, large-diameter bullets don't penetrate as well, so they can be stopped by a pocket bible or a pack of cards. Think of the difference between having a thrown baseball hit you, and a bowling ball roll into you.

To accentuate the effect, lead is soft; as velocities go up, the bullet material that touches the barrel has to be harder, and so bullet expansion can be controlled. A lead bullet will squash out into a pancake-shaped object even a fairly low velocities. This cuts penetration even further. (Think of a lead bullet as a tomato, and a jacketed one as an apple.)

1) I do have a large collection of geeky hats, don't I?

C Wingate @ 240

I'm fairly conservative, but will take a shot at answering anyway.

I really don't think there's a unified left to talk about. Culturally, I'd say those who aren't classical liberals have more power in this administration than I've seen before (defining the classical liberal as concerned with reciprocal rights, and left as concerned with power/marginalization concerns). On economics and issues of force, the non-left technocrats seem clearly to be in the drivers seat, as they have been since the mid-1970's.

Well, this is special:

Your Meetup Group's content was brought to our attention as specifically promoting a one-time event, which is not in compliance with our Terms of Service.... As a result of our inquiry, we've closed your Meetup Group and refunded your Organizer Dues.

So my idea for planning the Renovation GoL must be considered a complete dud. I can probably reconstruct all the suggestions from e-mail, but before I do: how did people feel about Serge's suggestion? I thought it was the most appealing.

SamChevre @ 244... The idea of a Unified Left reminds me of Neil Gaiman's "Sandman" tale about when cats used to rule over mankind until one of them dreamed the opposite - a situation that'd easily be reversed if cats could agree with each other on anything. :-)

So, like, did I hallucinate the following? Seems to me, when I registered my PayPal account, they said they never communicate only in email, that if they had something to say to a user, they'd put the message through the internal message system, too.

Well, I got a notification that I have to validate my PayPal account by attaching it to a bank account, but I can't find the internal message. Also, I sent them a query about this, and haven't heard back. (Or haven't been able to find the answer in my account.) I can haz Fluorospheric Wisdom, plz?

Tim Walters #245: Wait, you'd paid for that, and they cut you off? As in "we don't need little people like you, we only want big customers who'll give us lots of repeat business"?

Oy gevalt, there's a service that's doomed by its own leadership!

Jacque #247: That would be a phishing message, wanting to harvest your password. Also, the reason they don't do announcements solely by E-mail.

As a check on this, I recommend looking at the Wikipedia page on Obama's cabinet and following a few of the links. Quickly browsing them, it seemed to me that there was one person who could plausibly be described as bring on the radical left, and two more that I couldn't tell enogh to judge. Overwhelmingly, his cabinet is full of moderates, including a number of people who were elected governor of red or redish states, many people who worked as prosecuting attorneys (not noted for their flaming liberal sentiments with respect to accused criminals), and a couple who'd been Republians at some point.

My guess is that this is a claim that sounds plausible enough to people who really don't like Obama that they'll believe it without checking. This is quite common in politics.

David Harmon @ 248: And to bring this back to probability, the chance of my forgetting to cancel the group in time to avoid being billed for a second month would have been noticeably greater than zero...

Seems like enforcing the provision would cost them more money, even ignoring goodwill issues, than letting it go. But whatever.

Jacque (247): Also, Paypal does want you to "validate" your account by giving them your bank account info, but as far as I can tell you don't actually have to. I've been successfully ignoring those notices (real ones) for years now.

I think the original problem needs to be broken down into two parts.

Problem 1, suitable for a freshman math class: Smith holds one of GG or GS, each with probability 1/2. Jones holds one of GG, GS, or SG, each with probability 1/3. What is the probability Smith has GS and Jones has GG?

Problem 2, which (given the above discussion) should be limited to a postgraduate course in educational psychology: Propose an alternate phrasing of problem 1 in the style of the original puzzle, but lacking any ambiguity.

Tim Walters #251: Let alone if you'd decided "hey, I'll be going to another few cons this year, maybe I should just keep the account active, and hey my company's talking about having a summer barbecue...."

And yeah, then there's that whole reputation thing. After all, if I'm looking for someplace to organize a meeting (say, a book discussion), I now know to find some other way/place to organize it. And if, say, my book discussion develops into a monthly book club... well, I already have a way to organize it, and no reason to drop that working system for these guys.

C. Wingate @ #240, if they have, I wish they'd start pulling them.

Tim Walters... Your worldcon meetup group is gone.

"It's not my fault!"
- Han Solo

Regarding the coin conundrum: I consider it essential to have much more information about the psychological state of persons who would offer such bizarrely phrased information about their financial status to an apparent stranger. Those who suspect espionage seem to be on a plausible track, although an evaluation with respect to Asperger's tendencies might also be useful given the anti-Gricean specificity. Do Smith and Jones have a prior history such that either boasting of or downplaying their cash-on-hand would make sense? What are the expected consequences of a financial inequity between them? Is the triggering of those consequences dependent on certain knowledge or only on each one's evaluation of the odds? And what is the narrator's percentage in all this? What is his/her prior history with Smith and Jones? And with Lemurian financial dynamics?

Normal human beings in normal social interactions do not make spontaneous statements of this kind. Therefore attempting to solve the riddle as if it depended purely on statistics with no element of human psychology or pathology is unlikely to produce a useful answer.

HLN: Juvenile sparrows have not yet come to terms with the concept of "glass." Local woman anticipates some iterative testing will be required to resolve the confusion.

@240: Without discussing Obama's particular appointments or laws:

There have been periods where the Democrats controlled both houses of Congress, there was a Democratic president, and we had a so-called "legislating from the bench" Supreme Court. I don't know how far left the Democrats were in the 90th Congress, but at that time we had:
64 D senators
247 D representatives
LBJ in the White House

And that was the Warren Court (although it looks like most of the famous civil rights cases were before 1967.)

They did a lot of fairly left-wing things, especially by the standards of today's right wing. Gun control and limits on wiretapping come to mind.

(all info skimmed from Wikipedia and not checked in detail.)

@243 - 'bullets' in rifles [such as the Kentucky long rifle, and the British Baker rifle] were actually 'balls' throughout the C18, and until the development of the 'minie [acute on the e] ball' around the mid-C19. So they don't have to be longer than they're wide.

That's with my history geek hat on... ;-)

Tim Walters @245:
Special indeed.

Okay, I've set up a yahoogroup: http://groups.yahoo.com/group/fluorosphere. As it's set up now, I think anyone can join. I'll try to piece together the suggestions from Meetup, and make it a poll.

I just realized: If García Márquez' Hundred Years of Soliitude were to be translated into English by somebody committed to using Kipling's "Just-So Stories" narrative voice (which would not be too far off the proper thing to do), the first clause of "El mundo era tan reciente, que muchas cosas carecían de nombre, y para mencionarlas había que señalarlas con el dedo." would become, "What with the world so new-and-all,..."

C Wingate @240:

I'm glad I wasn't drinking anything when I read that question.

Nobody within a bargepole's reach of a lever of power in the United States is part of any form of radical left. The fact that anyone is even asking it shows how far the Overton Window has moved.

albatross (228): This seems to be winding down, and we should probably let it go, but I do want to clear up one misconception.

Yes, you telling me more about your coin toss does affect my ability to predict the probabilities. I get that. I got that a while ago. But it is irrelevant to my point. My point is that my knowledge or lack thereof does not affect the results of your coin toss. It doesn't matter if I was standing there watching you toss them, or if you gave me partial information later, or if I was in Madagascar counting lemurs and never heard of you or your coins. In all those cases, your results were the same. My ability to predict the probabilities is different, but I'm not talking about the probabilities.

I've now said that at least three different ways, so I'm bowing out again unless someone addresses me by name.

And I've set up a poll:
http://groups.yahoo.com/group/fluorosphere/surveys?id=2691620

Join the group only if you're going to be at Renovation, please. We can keep the group going and use it for further organizational exercises.

albatross, #242: You're forgetting the BIG issue where "left-wing" gains have been particularly visible: gay marriage and the demise of DADT. For a lot of people, that swamps everything else.

Beyond that, it's a combination of "whatever we say must be true" and "this will mobilize our base".

C Wingate @ 240 - That's really a "coffee-all-over-the-keyboard" question. My answer would be "Absolutely", but not for the reason you think. Back before the Rove/Norquist/Neocon seizure of power in the Republican Party, which got George W. Bush elected, "radical left" meant people who were on the left, and radical. But now, at least on Fox News and the right-wing Angry Parrots who echo it, "radical left" means anybody to the left of Barry Goldwater, and even he was too much of a RINO to be acceptable to the New Bosses. And nobody else out there is using the phrase, except for a few young leftists who think they're "radical" because young people always do.

So yeah, if you think the radical left is people who would like there to be Social Security when they get old, or think that gay people should be allowed to exist (whether or not they should be allowed to marry), or think unions have at least sometimes been useful, then there are more radical leftists in holding the levers of power than ever before. But you can relax, because you've kept them too scared to actually pull any of those levers since about 2006 when they got a majority in Congress.

On the other hand, if you haven't bought into that worldview, and think that the "radical left" might or might not include the Progressives, then no, even the Progressives don't have any significant power in the Democratic Party, who've been telling them to shut up because they have to get Obama re-elected first, and having people wanting single-payer health-care or stopping the wars is just a distraction.

(I'm a Libertarian, so I get to claim to be neutral in the Democrat/Republican arguments (and whether that counts as "objective" or "clueless" will be left as an exercise for the reader.) It's been really annoying to see the right wingers calling Obama a "socialist", when I live near San Francisco and Berkeley and know actual socialists. Once Dennis Kucinich gets elected President and Medea Benjamin is secretary of either State or Defense, then we an have a discussion about whether there are any radical leftists holding the levers of power.)

xeger @171: Hmm... OTOH, there's nothing wrong with a warning sign and something that looks appropriate... and it'd be easy enough to (say) rig up a red led with a battery... and that'd last for ages...

If it doesn't add too much expense/time, make the led blink. Friend of mine couldn't afford a proper alarm system for his car, so he just rigged an led to a motion sensor, (spare electronic components were easy to hand) and put the light next to the locking button on his car door so it would blink irregularly.

Siriosa @ 261, 265: Thanks for rescuing the situation with a solution much better than the original one!

siriosa, #265: Joined and voted. Note: the poll is set up as multiple-choice checkboxes, presumably to duplicate Tim's original "vote for whatever you'd be able to attend and the most votes wins" scenario, so that's how I treated it.

I think the idea of having a Yahoo group for this and the coordination of future meetings is a good idea. Meetup never struck me as an ideal method, for exactly the reason that bit Tim -- it's designed for something entirely different than what we were trying to use it for. Evite or Socializr might have worked, but they're not as widely-used as Yahoo Groups. Also, I think both of those are host-driven (the host must send invitations to specific people), whereas this method is participant-driven.

I still think we should put "Fluorosphere" on the message board, as a backup method for communications at the con itself.

The Modesto Kid #262: I like that, but go on, would the second clause be the literal "many things lacked a name" or "many things didn't have a name"? Before going on to "and to mention them you had to point at them with your finger" or "to talk about them you had to point at them with the finger"?

Well, I know a couple of people who are out-and-out Marxists. I haven't actually asked them this, but it's hardly necessary; when they go on about the destruction of Capital I cannot imagine that they see Obama as an ally.

Lenore: Thanks again for the Xopher update!

Fragano -- I'm not yet sure exactly how to phrase that in Kipling's voice but I need to take a look at "Just-So Stories" -- it seems to me like there is a story about the invention of language, containing a very similar statement.

No, that is misremembered -- the story is about the invention of writing.

Lenore Jean Jones/jonesnori @215: Welcome to Hudson County! Lenore (in Hoboken)

Fascinating, Lenore. What is it in English?

Yar har.

C Wingate @272:

Out of curiosity:

* Why are you asking the question? What's the source of the quote?
* What do you think the answer is? Why?

C Wingate @ 272...

"One morning I shot an elephant in my pajamas. How he got into my pajamas I'll never know."
- Marx

Jörg Raddatz @237: I begin to think that there is a significant part of the population who do not like the rule of law or is too stupid to understand what a great thing it is.

Probably correlates closely with the part of the population that has (a) never lived without the rule of law, and/or (b) doesn't have the imagination to visualize what it would be like.

Tim Walters @ 245: Just for the heck of it, I looked at their terms of service and poked around their FAQ, and I couldn't find anything about one-time events.

David Harmon @249: That would be a phishing message, wanting to harvest your password. Also, the reason they don't do announcements solely by E-mail.

Thanks, I did recognize that possibility, and so deleted the message and went over and logged onto www.paypal.com independently—wherein I find a banner saying I need to validate my account (as I am reaching the threshhold for transfers from an unverified account).

What I'm saying is that I can't find the message center within Paypal.

Mary Aileen @252: Oh, cool! I may give that a try. (Since my account is funded by a credit card, and can't imagine what earthly difference it would make, aside from making my bank account more vulnerable to hacking. Which is why I have it pointed at a credit card in the first place.)

C. Wingate @240--in terms of things like economic policies and the surveillance state--Ha! it is to laugh. There are no radical leftists in the Obama administration. In fact, in those areas, the high water mark of leftism in national-level politics was Nixon/Ford. Despite his personal paranoias and addiction to the concept of the unitary executive, Nixon was as progressive as any of the Democratic presidents we've had since his terms in office, in Keynesian terms.

Of course, what with Teh Ghey and all, and Obama's unwillingness to go against the prevailing trend there, some might think the Dirty Godless Commies have taken over--unless they knew enough about 20th century Communist states to know how those treated LGBTQ people.

George Romney, who lost in the Republican primaries to Nixon in 1968, was to the left of his son in a good many areas. I was quite young at the time, but I don't think there was that much excitement over his religious beliefs, either. He just wasn't enough of a hawk to make people like the Alsops (or JEdgar Hoover, for that matter) happy. The entire leftish wing of the Republic party is gone, now--the party has no place for someone like Nelson Rockefeller, and the dance rotuines that people like Christine Whitman must engage in to have any traction in the party are unreal (which is probably why, in the age of Michelle Bachman, Sharon Angle, Sarah Palin, and Christine O'Donnell we hear so little from her).

I can't think of anyone with a significant role in the Obama Administrative who would have counted as a radical leftist by late 1960s-early 1970s standards based on the opinions and policies they currently express, support, and design.

I have an open-thready request. I know the Fluorosphere is a geographically diverse group, and I am trying to get my little mitts on one or two issues each of a couple of periodicals from the UK. Since I'm in Tennessee, this has not been proving easy (neither of them have online issues).

The magazines in question are Woman's Weekly and The People's Friend, and I would be thrilled to Paypal someone (in advance, even) for the cover costs and the shipping.

The probably unnecessary background to this is that I got my very first rejection ever recently (to me this is very exciting), and so I'm working down my list of markets. I don't want to send a story to a market when I've never seen any sample of the fiction they print, but I don't want to give up on a possibility, either.

Any interested parti(cl)es (or waves?), please email me at alsafi (dot) khayyam (at) gmail.

Jacque @ 281, according to this post at the New York Times, fraud is the cover story but verifying with Paypal is actually about them making more money off you.

On the Lemurian coins, I found a lot of interesting comments, but not the two that leapt out at me.

First, the stipulation that unidentified coins are "no more likely to be silver than gold" suggests to me that we should consider the possibility that the unidentified coins may be less likely to be silver than gold. That leads to solutions parameterized by the probability of the unidentified coins being silver, which makes the restriction moot.

The second consideration is one I've discussed before, perhaps even in the dim past of Making Light if such a problem has come up here. Suppose in an alternate universe Mr. Jones comes to the meeting with two silver coins. I propose that it's most likely he'd say,

I have two Lemurian coins in my hand. At least one is silver.

Jacque (281): If there is a threshhold for transfers from an unverified account, you may not be able to ignore it. I don't usually use Paypal all that much, so I may just be comfortably under the threshhold.

And, on refreshing the page, I see that johnofjack's link in #284 has the answer. If you've hit their $10,000 threshhold, you have to give them your bank account information or you can't use your account. Bummer.

C. Wingate @ 240: "Question for the assembled non-conservatives: Would you agree with the statement that "the radical left has never held as many levers of power in this country as they have under Obama"?"

Keeping in mind that the "radical left" is a relational term, meaning that depending where you stand your judgment of what constitutes "radical" is going to be radically (natch) different, to my eyes the most extreme leftie fringe of the Obama administration is at least several orders of radicalness away from the raw uncut. The Obama administration's lefties would have to find someone they thought radical, who would in turn point to someone yet more radical, who would then point to someone else who even they thought was beyond the pale, and that person might be someone who I'd call radical.

Economically, Obama's team consists of the classically-influenced neo-Keynesians, the most gung-ho free-market economists who don't outright deny the capacity of government spending to affect positive economic change; in terms of state power the Obama administration has hewed the course set by Bush without interruption; culturally, his alleged leftie bias in repealing DADT is contraindicated by the fact that it was requested by the military itself; and the healthcare plan he passed was based on Republican outlines. No, there isn't a trace of the radical left in Obama's White House. It's sane billionaires, not lefties.

Jacque @281
I have a dummy bank account, with, I think, $136 in it. That's what my PayPal account points at. (The bank offered free checking, no minimum balance, about 20 years ago, and I took them up on it.)

I also have a PO Box and a generic voicemail number, for when a site insists on that kind of information. Paranoid? Nah. Merely prudent.

WRT leftists, rightists, and inbetweenists, I think one thing to remember is that we don't always gauge these things from where we sit right now. For some conservatives, they see where we are at this point and compare it to 60 or 70 years ago, and to them, we're scraping along the far left lane, leaving paint on the sidewalls. They think any further turn towards the left will cause some kind of horrendous crash.

It's not that the administration is so leftist, it's that they don't see any movement towards the center and that must be bad by definition.

(Dragging out the soapbox)

There's a natural tendency in people to focus on things...and on people. I don't think the presidency is nearly as influential as we like to believe. Certainly not now, with our tendency towards gridlock. But everybody focuses on that man in the Oval Office and if the weather is nasty, then By God, it must be Someone's fault! It's a bad idea to fall in love with politicians. Find someone who won't screw things up too much, vote for them, and save love -- and anger, for that matter -- for people you actually know.

On the Tottenham shooting:

The initial official account reported that a bullet had been found lodged in a Police Officer's radio.

Sunday night, there were reports that the initial forensic examination indicated that the bullet lodged in the radio was a Police bullet. That is, it appeared to be a hollow-point bullet of the correct calibre. That story is still being reported in the British press, without contradiction. It's a way from being certain, but it calls into question the initial Police account.

If the reports are correct, it won't be the first times that Police Officers with guns (and, by US standards, a lot of training) have shot somebody they didn't really need to. Though I can understand why a shot fired provokes a reaction.

Radicals?

"Have you got a mission, James?"
"Yes. I am to eliminate all free radicals."
"Ooh. Do be careful."
- from Never Say Never Again

Mary Aileen @286: If you've hit their $10,000 threshhold, you have to give them your bank account information or you can't use your account. Bummer.

Hrm. The threshhold they claim for me is $5K. Heh. In my history, they have me halfway between no transfers and the $5K limit.

siriosa @288: dummy bank account

Yeah, that's what I'm thinking about. This whole thing is very irritating, because things were bopping along so conveniently until now....

This probably explains the deafening silence in response to my question, i.e., can I set up my credit card to be my default.

Steve C @ 289: "For some conservatives, they see where we are at this point and compare it to 60 or 70 years ago, and to them, we're scraping along the far left lane, leaving paint on the sidewalls. They think any further turn towards the left will cause some kind of horrendous crash."

The historical element is a red herring, I think. They're not comparing the present to an actual historical moment, with all its complexities and complications--they're comparing it to an ideal that exists primarily in their own heads, which they find convenient to site in the past. The above statement is indistinguishable from "they see where we are and compare it to their ideal, and to them we're scraping the far left lane." What they're hitting the limit of isn't history but their ideological imagination.

This isn't a right/left thing, except insofar that lefties are less likely to site their political ideal in the past. (The baby boomers and the sixties being the big exception.) A few orders of radicalness away from one's own views in any direction, everyone starts to lump everything together as an undifferentiated mass of dangerous awfulness teetering on the brink of collapse.

Given that Obama is to the right of Nixon, I'd say that the radical left held more levers of power under Nixon than they do now.

Open threadiness: for sheer WTFery, I haven't seen anything to match this in a very long time. Mostly worksafe, but keep the brain bleach handy.

Open Thready: I just want to get this out there. (partial repost from Facebook)

We were nearly at a compromise on the debt ceiling four days before deadline when 22 Tea Party Republicans in the House screwed the debate. This will cost us, conservatively, half a percent on our interest, ie $73 billion a year.

These are their names. I wish never to forget them.

Justin Amash (Mich.), Michele Bachmann (Minn.), Paul Broun (Ga.), Jason Chaffetz (Utah), Chip Cravaack (Minn.), Scott DeJarlais (Tenn.), Jeff Duncan (S.C.), Trey Gowdy (S.C.), Tom Graves (Ga.), Tim Huelskamp (Kan.), Timothy Johnson (Ill.), Jim Jordan (Ohio), Steve King (Iowa), Tom Latham (Iowa), Connie Mack (Fla.), Tom McClintock (Calif.), Mick Mulvaney (S.C.), Ron Paul (Texas), Tim Scott (S.C.), Steve Southerland (Fla.), Joe Walsh (Ill.), and Joe Wilson (S.C.).

C Wingate @240, is it possible to hold fewer than zero levers of power?

@272, from a Marxist perspective, Obama is clearly a creature of Capital. Now, the funny bit is that he's enabling Capital's self-destruction, which is right in keeping with Marx's own projections of how the capitalist phase of history is supposed to end. Possibly one could regard him as a radical leftist by assuming that this is a form of the often-mentioned "11-dimensional chess" --- that Obama is a secret Marxist enabling Capital self-destructive urges because he knows it will usher in The Revolution. One could then extend this argument to claim that every US president for the past half-century or so has been a closet Marxist, that the entire engine of American capitalism has been a Marxist conspiracy to bring about a socialist revolution.

Open-threaded employment-seeking fun.

I saw an ad Friday for a programmer/analyst. Along with the requirements for MVS/DB2, it specified:

"Must work well with people."

I guess "must work well with others" isn't specific enough.

What the odds are depends on whether people come from the Village Where People Only Tell Lies.

The Village Where People Only Tell Lies has a problematic 911 system. Everybody keeps calling in and saying they're fine.

Avram @ 297: The Tea Party, then, is the most profoundly Marxist of them all.

Lee #295: Arggh ... they start the howlers with the very first sentence! I haven't even been to Burning Man, and their initial mention of it had me going "uh, what?"

The way they turn everything into deviant sex and Satanic orgies tells me all I need to know about what sort of "Christians" they are.... Possibly the most revealing sentence in the bit: ...the train’s smokestack is Satan’s love hammer of deviance and the billows are his forced streams of liquefied DNA. (Because you know, that DNA stuff must be from Satan, it's all scientific and stuff!)

Lee @ 295: That was so perfectly insane, I had to look it up. Sadly, or happily, or sappidly, it is a satirical site. Oh, but what satire.

Lee @295: Oh dear. It's hard to read that as anything other than parody. An article link at the bottom of the page provides even more, um, entertainment. It starts with the sentence: "I am extremely terrified of Chinese people, but I am not racist."

Um. Duh.

Lenore @216: Thanks for the update; really glad to hear that Xopher's op went (apparently) well and he's recovering okay.

HLN. Croydon is burning. That's just down the road from me, really. It's sad.

it isn't possible hold negative levers of power but it is possible to have a negative grip on one.

Erik Nelson @ 306: There must be fifty ways to love your lever.

heresiarch #302: Ouch, I've been bitten by Poe's Law!

Tim Walters (307): TMI ;)

Jacque @276 -- I expect you meant to ask, "What is it in Raven?"

Jacque, sounds like the light bulb went off between 303 and 304, so there's no point me adding to the glare. There are some specific clues there, but they're easy enough to overlook when the writers are adeptly dancing on my buttons (and perhaps yours as well).

Tim Walters #307

Yank on the tool, Jewel
Get a good grip, Pip
Exert steady force, Morse
And make the thing slide
Put oil in the slot, Mott
Look where it should go, Joe
And push it aside.

#307: One of those brass-handled levers that steampunks love so much?

* * *
Michelle Bachmann is blaming the S&P rating downgrade on the U.S. raising the debt ceiling.

Open thready: perhaps some of you resourceful Fluorosphereans will be able to help me with a question about Sendak's sources.

Lee @295: that made me laugh hard.

So, open-threadiness:

I've been warned that at least one of my hearing aids is likely to conk out RSN, and both are at the end of their expected lifetime. I am aware of the "racket" where audiologists mark up their aids insanely, and am hoping to try and get my new pair at a lower price.

Has anyone here had experience with buying hearing aids over the Web? I've seen at least one site that lets you enter an audiogram, but how is fitting handled for mail-order aids?

Modesto Kid @314: The story may've started as a political parable in "Punch", 1848.

I'm not familiar enough with the politics of the period to figure out who "Jack" is intended to be.

Julie L. #317: I note that they quote as a proverb, "Don't Care came to a bad end", suggesting that there may have been yet a prior related tale. The "chloroform" parties et al described in the next column are also amusing!

Thanks, Julie! That seems like a good candidate indeed. I will add it to my post...

Tim Walters @307:

That lever line yanked from quite possibly the best Muppet Show of all time (and the only one to use exclusively original songs from the guest artist.)

Yes, I do own the Muppet Show "Best of" Collection on DVD. Some of the discs are scratched from overuse. "At least" my Paul Simon episode isn't.

There's an alternate lead-in to the lion story in 1863, suggesting that the Punch article was a riff on an existing story.

Be careful with that "dummy bank acount". If you don't have activity in it for too many months in a row, the bank will likely start charging "dormancy fees" and the next time you bother to look, you might have a zero balance and the account's been cancelled.

Okay, there's definitely a pre-existing lion story, since there's a prior reference in 1845.

DanR @ 320: That lever line yanked from quite possibly the best Muppet Show of all time

It bubbled up from my subconscious without attribution, but it wouldn't surprise me if I saw that episode back in the day.

Ooookay. Dead end here; 19th-century search in Google Books on "don't care" "eaten by lions" turns up some tantalizing allusions, but I can't find the intervening lines anywhere.

There seems to be an alternate version that runs as follows:

"Don’t care didn’t care,
Don’t care was wild:
Don’t care stole plum and pear
Like any beggar’s child.

Don’t care was made to care,
Don’t care was hung:
Don’t care was put in a pot
And boiled till he was done."

But whither leonine gourmandise?

And some bad news from the Amazon:

'Uncontacted' tribe apparently attacked by drug dealers.

NBC says the tribe is now 'missing'.

1800 "Tommy and Harry" cite (with lovely engraving of Harry being et by a lion), but without "don't care" catchphrase.

Julie L #325: Well that ditty is an obvious source for the epigram, at least. I wouldn't be surprised if the lion story was Really Old, perhaps dating back to one or another mythology or folklore.

Wait, I typed too soon-- scrolling up a bit to p39 yields the following conversation, in which the virtuous Tommy chides his wicked brother Harry for bad behavior (spelling/formatting normalized to modern standards):

"[T]hey will be your ruin, Brother Harry, and you know it grieves poor Papa and Mama."

"I don't care for that," says naughty Harry.

"O fie! fie! Brother Harry" says Tommy, "how often have you been told that '"Don't care" has brought many a one to an evil end.'"

"I don't care for that neither," says the little Churl: and thus he went on (as you will soon hear) till "Don't care" was his ruin at last.

247
I didn't get an 'internal' e-mail when it happened to me, either. So I closed the PayPal account - I don't trust them (or anyone else I can't easily get hold of) with that kind of reach. (They also didn't say up front that you can only use them for a limited dollar amount before they want that kind of access.)

Daniel Fenning's The Universal Spelling-Book : or a New and Easy Guide to the English Language was originally published in London in 1756. [....] Pictured above is a detail from the wonderfully illustrated "Life truly painted, in the Natural history of Tommy and Harry," a moral tale that can be found in Fenning's 1760 Universal Spelling-Book.

In lesson 6 (p. 44) he repents of not caring, but it is too late, as he is cast away and prey for wild beasts. (Lions in particular are not mentioned, though.) And what beautiful type-setting!

263
One of the people who's apparently big in the teaparty universe was complaining about 'Washington getting slammed from the right by Communists'.
I have a hard time even figuring out how to parse that, in the non-grammatical sense.

Noah Webster did not think much of Fenning's composition.

286
I hint their limit at a couple of hundred dollars (maximum). (I couldn't find their 'message center' either, but I did find a page buried in there with e-mail information.)

Lenore @ #216. Thanks for the update on Xopher.

To add a bit more security against PayPal hacking, you can set up two-factor authentication (you enter username and password; you then enter a numerical code either generated with a dedicated bit of hardware, or texted to your phone, before you can actually log in).

There's info at this PayPal page.

Information on cost is fuzzy. It seems to be $29.95 to buy the dedicated piece of hardware to generate the codes, but the cost of using your phone isn't clear. When I signed up to use my phone, I thought it was free, but they charged me $5 (a little more digging after the fact got me a page stating that $5 fee, which I can't find now). The FAQ link on the page I linked above says there's no charge to use your phone, other than standard text messaging rates. Maybe they changed it. This other version of the FAQ implies that it costs $29.95 whether you use your phone or get the hardware.

I find PayPal's entire web interface utterly irrational and annoying, so I'm not surprised the information on this is contradictory and useless too. I like how the fee they charged me isn't even one of the available options. I still have to use the damn PayPal because there are situations in which it is the only feasible service. Grump.

But the two-factor authentication makes me feel at least slightly more secure in using it, and ultimately I would have paid $5 (but not $29.95). I just wish I'd known I was going to pay $5.

(Yes, I've been having a grumpy day today. How about you?)

Fidelio at # 233: As a long-ago physics major, I'm pretty sure you are using the term momentum correctly.

C. Wingate: It seems plausible that your question may be sincere, in these days when "liberal" means anyone with the politics of Eisenhower (who warned against the military/industrial complex) and Nixon (who founded the Environmental Protection Agency).

Fidelio at # 282: The entire leftish wing of the Republic party is gone, now.

Indeed. Mark Hatfield passed away yesterday.

Aaaaahhhh!

Sorry, had to get that out of my system. It's nice to have a civilised oasis in the web here at Making Light. I have just escaped from spending too much of my evening elsenet where too many people are whinging about the misfeatures in the new version of Yahoo Mail.

Allan Beatty @ 339...

"Only Nixon could go to China."
- Spock

Allan Beatty @ 339...

"Only Nixon could go to China."
- Spock

Bruce Arthurs @322
Be careful with that "dummy bank acount".

I take a look at the statement every month. If they start attacking it with fees, i'll write a check. So far (20 yrs on) so good.

It probably makes a difference that it's a local, small bank. I'm sure if it were eaten by a bigger bank, there'd be trouble.

Good news on Xopher!

Lenore Jean Jones/jonesnori @ 216: Thank you for the update on Xopher. It's good to hear that he's doing well.

In fact, he’s bored! He’s a little too woozy to read, but not woozy enough to sleep. The pain meds are quite effective, but they have their downside, for sure. What worked for me in that state was podcasts that I could fade in and out of -- not an audio book that I had to follow. Prairie Home Companion, This American Life, The Moth,...

Pardon my tardiness, but I must weigh in on the matter of the gold coins, especially since I spot no "correct answer" post yet from Jim M. and since I correctly analyzed the Monte Hall Problem within a minute of first hearing it. Maybe I'll get lucky again.

I say the probability is 0.5. By my reading, the statements by Ms. Smith and Mr. Jones are logically equivalent: I have one gold and one unspecified coin. The coins' relative manual order is irrelevant. The holders' knowledge of the unspecified coin's metal is also irrelevant, since it in no way affects the truth of their statements. Since they both have one randomly selected coin, equally likely to be either silver or gold, neither is more likely than the other to have more gold coins. Hence, 0.5. Yes, I'm assuming no diabolically subtle tricks of phrasing on Jim's part -- or gross obtuseness on mine.

Tortoises: Nope. That the two statements aren't equivalent is the whole point. (And I'm afraid that I can't resist pointing out that even by your own logic you have arrived at the wrong answer.) There have been numerous correct analyses post in the thread, so I'll just tell you to read it over -- and pay attention to the people who give an answer of 1/6.

HLN: Area man today has the first of what hopefully will be many sessions at Taping For The Blind.

I read the first chapter of Last Night at Twisted River, by John Irving. It was pretty interesting, and hopefully the book will be enjoyable. I haven't read anything else by Irving except The World According to Garp, which I didn't like -- but was pretty certainly too young for at the time (I was, I think, 12).

The controls were easy enough to handle, not all that different from what I do at home with Audacity. My workflow was a bit different; I edited as I went rather than reading through and editing after. It occurs to me belatedly that I could do it the other way. I should probably experiment with that. Editing as I went broke up my flow quite a bit.

I will say that I really really envy them their soundproof booths.

When I have the whole thing done it'll be broadcast. I wonder about copyright, but apparently their clients have specialized receivers, so it's not over the regular air. Because of that, and because it's charity, they assure me that their copyright situation is OK. Anyway, I guess that's their worry and not mine.

It's not just a "fail to recognise" by The Sun (Particle).

The photograph is a deliberate misrepresentation, using a wide angle lens, close to the subject, to distort the image and exaggerate the length of the saw-blade.

The blade on those things folds into a slot in the handle, so they're not so incredibly long.

Since the apparent sharpness of the photo is difficult to judge at the low pixel count of a photo on the web, but the scene lighting looks low-level, I can't be sure, but getting the depth-of-field has me thinking the camera had to be on a tripod for a long exposure. It's not something you get looking that way by chance. Somebody had to get down low with a camera, lined up with that fire in the background, with the pruning saw at the correct angle. This isn't likely to be down to luck. And it isn't likely to be a camera in a 'phone.

I don't think this is just ignorance. Whoever took the photograph is a liar.

[Technical Note: the distortion arises because we don't view the image from the correct distance. You could take a wide-angle picture, enlarge a tiny section from the middle, and get an image with the same apparent perspective as one taken with a long focal-length lens. When the object is a foot from the camera, a six-inch difference in distance has a huge effect. When you're a hundred yards away, "for your own safety", the rioter brandishing a weapon, ten yards beyond the Police, looks rather closer to them than he is.]

David @349

Talking books for the blind, using a specialised physical format, get certain copyright privileges in the UK. And there seem to be similar provisions in US copyright law. It's part of what's fueling some disputes over talking e-readers. "Blind", for the purposes of the law, includes a lot of people with some vision.

You'll remember previous experiences of the Flourospherians buying unusual garments from distant suppliers.

The BBC has a report on the last Palestinian factory making the Keffiyeh. With cheap imports from China, what is keeping the business afloat is a bunch of Arab supporters, based in Kuwait, who are using the internet to promote the authentic Palestinian product.

Pick the right colours for the fabric, and you could have something that appears on the fashion-show catwalks... Not something with a heavy dose of political symbolism, but still an aspect of the Arab Spring.

Dave Bell #350 - there's an entire blog devoted to the lies of the Sun and other tabloids. Those of us do historical fencing or re-enactment have known for years that they refuse to tell the difference between a sword, katana, machete, cleaver and kitchen knife.

There's going to be a lot more hysteria in the press over the current rioting and looting, with it being used as an excuse for racism and further crackdowns, and likely any real useful attempts to deal with deprived areas falling by the wayside.

Popping this in after #212, because the thread's getting longer faster than I can follow right now:

One of my pants pockets has 4d20 in it. The other has some pens. Which one has my wallet? Is there a flash drive in either one? And is there anything currently in my pockets?

--Dave, speaking of known unknowns...

PS: I'm purposely not saying anything about the coins.

@290, and anyone who's interested. At this stage, given what is happening, given who, what and where has been attacked and looted, I think we should all be able to agree that this has absolutely nothing to do with the original triggering incident. Some time soon we will be able to have a debate as to why hundreds of feral toerags feel able to loot, burn and pillage on our streets, and to what extent wider social conditions are somehow 'to blame'. However, anyone who tries to justify this behaviour, to pretend that in itself it has some kind of meaningful 'politics' or goal beyond immediate self-enrichment and thrill-seeking, needs to take a hard look at themselves, and at the real people who are being hurt out there.

And p.s., that may be a picture of a pruning saw, but do you want one waved in your face?

This is just to say
I have eaten
a coin
that was in
the puzzle

and which
you were probably
needing
for the solution

Forgive me
it was delicious
so rich
and so full of permutations

alex@355: Better the pruning saw than pretty much anything in my kitchen. It would be awkward to swing in a crowd, I think, although I suppose there is the potential for a nasty ripping cut if the person holding it managed to get it into contact with flesh and pull. But as a melee weapon I believe it would lack utility. If one has enough gardening tools that one has a proper pruning saw, one should certainly have something that's more appropriate to bring to an angry mob.

alex #355: Sorry dude, but the big difference is that the Egyptians had *support* from the local "police", who flatly refused Mubarak's orders to attack them.

The British protesters know that a peaceful protest will at best be ignored by both media and government (see the US anti-war protests). More likely, (as happened here) the police will simply attack them and face no consequences whatsoever for beating or killing peaceful protesters.

Also, given what I've heard from prior similar incidents (in the U.S. and Britain), I have no confidence that the "rioters and looters" were not set up by the police in the first place. In both countries, the police have a long history of using plainclothes agents to "supply" violence for protests by groups whose organizers had made it clear they had planned and organized a peaceful protest. Then of course, they use the incidents by their agents to justify unlimited violence against all protesters....

Steve C. @298

A colleague of mine has a sign on his office door that reads, "I work well with others. Others. Not you."

Sarah S. @ 359 -

Oh, I like that!

I'm thinking those looters and rioters in Britain need a good old ass whuppin'. Unbelievable that it's been going on for three days now. They have stamina, you have to give them that.

Hell, the LA riots only lasted a day - probably because by then everyone had stolen what they needed and were drunk on malt liquor

re 350: Not all pruning saws fold, and this looks like the sort that doesn't. Here's a pretty big example (16" blade).

Really, though, a saw is a lousy weapon. Trees stand still while you saw off their limbs; people don't. And those teeth get caught on things.

Also read that there were more cops, sorry bobbies, on teh streets of london for the royal wedding than there are for the riots.

screwed up priorities.

stock market crashing, riots in the streets, all we need now is some killer virus to unleash and it's The STand all over again

Julie L: searching for the slogan "Don't care came to a bad end" brings up some nice hits. Carroll used the lesson in Sylvie and Bruno Concluded, for one.

There was a report on BBC radio that the riot in Tottenham on Saturday was a result of police beating a sixteen-year-old girl who had the cheek to harangue them. There is a phone-video of the incident also on Youtube, but I can't tell much from it. Not much has been said about this since, the media prefering to concentrate on the line that everything since then has been opportunistic looting.

janetl @346: Don't forget the wonderful world of old radio shows from Archive.org! The Lux Radio Theater has good audio equivalents of a lot of swell movies (boiled down to about 48 minutes plus ads) with some remarkable casting — my favorite is Edward G. Robinson as Sam Spade in THE MALTESE FALCON. They have the first two Thin Man movies with, like, the first eight names from the original cast list. There's also a lot of Orson Welles. There are half-hour adaptations from Screen Guild, and the Gunsmoke programs are outstanding.

David Goldfarb @349: I got to do a radio show for the blind back in Virginia. I read "Love is a Fallacy" by Max Shulman and did a two-person reading of some archy and mehitabels. It went out live, I think. Not sure if it was taped.

David DeLaney @354: And is there anything currently in my pockets?
Doesss it have a ring, Precious?

NelC, let's hope some of her friends gave back as good as she got

Ledasmom @ 357: I like your pragmatic analysis!

David Harmon @358

One of the reasons the protests in Wisconsin have never turned violent is that whenever somebody shows up and starts inciting violence, or otherwise behaving poorly, everybody else stands back and accuses them of being a provocateur. It means even sincere would-be rioters can't get any traction.

There's also the fact that, once it looks like police resources are stretched too thin to respond, anyone inclined to do some looting has a reasonable chance of getting away with it. So even though your protest started for perfectly good reasons, and the violence started from some testosterone-poisoned idiot with either the protesters or the cops deciding to try busting some heads and see what happens, there's good reason to expect that looters will exploit the situation.

Gun owner of the year

alex @ 355: That's a false dichotomy--people are more complex than EITHER I am doing it for political reasons OR I am doing it for personal gratification. When the complaint is that we are not being heard, we are being denied prosperity, we are being screwed over even as others are being enriched, then looting the stores you can't afford is a political act. To become upset because their actions are counter-productive and negative sum is to ignore how their productive and positive sum options have been systematically cut off and marginalized.

ObSublime

It's a dirty secret of the new labour years that they never did manage to do much about the deprived areas left over from the 80's and 90's. Increased benefits kept the inhabitants fed, watered and with tv, but despite the hype not a lot happened.
Of course dealing with them would have meant dealing with the inequalities of a finance capitalist society, which might just have something to do with it...
That, and it does seem to be genuinely hard work turning an area round, involving so many things, from moving people in and out, careful policing, more jobs, better housing, schools etc.

The problem is, who is going to tell these people that breaking the law, taking things you don't own, and generally misbehaving yourself is not on?

Politicans? Law enforcement? Business leaders? The clergy? The media?

I suspect the cost to the nation of the riots will be several orders of magnitude smaller than what the rioters have seen pass unpunished, or punished with the merest slap on the wrist.

I don't condone lawbreaking and looting. But I don't think one can wink at it from the suits and then reasonably persuade the jeans to refrain.

#374 ::: abi

Hear her! Hear her! The scope of the crimes committed here by the institutional power elites are equal to those anywhere else.

Still, I'm not in favor of consumerist riots, unless it is for getting the food and water and other necessaries for yourself and family

.... Our friends P, K and M, came back last week from London where they were stayed as house sitters - dog-walkers, a friend's apartment. It's a neighborhood that's been hit hard by the rioting. Their friends sent them a video, complete with audio of what they're experiencing (video artists, like K, musician-composers like P & M), which P forwarded to us.

It's damned awful. Some of it is shot from inside their friends' home -- it really does give the sense of an invaded city being subjected to the victors' soldiers given their traditional three days of sack and riot.

Love, C.

Is it certain that gold and silver refer to chemical composition or colour, or something else of which coins can only be one or the other? Because it's totally different if coins can be gold AND silver[1] :)

[1] Eg. some coins are made of gold, some coins are silver coloured, some are both, some are neither. Which is very unlikley, but logically possible.

abi @374, Constance @375

ObBujold, from Shards of Honor

"The real unforgivable acts are committed by calm men in beautiful green silk rooms, who deal death wholesale, by the shipload, without lust, without anger, or desire, or any redeeming emotion to excuse them but cold fear of some pretended future.

But the crimes they hope to prevent in that future are imaginary. The ones they commit in the present - they are real."

Constance @375:

Still, I'm not in favor of consumerist riots, unless it is for getting the food and water and other necessaries for yourself and family

I'm not either, but I understand the impulse. It grows from the same rootstock as the one that left so many American households in foreclosure. We live in a society that uses possessions—consumption—as the marker of success, and tells us that success is everything. Is it any wonder that people will beg, borrow and steal to look like winners?

Big business would prefer that we only do one of the three. Please, sir, may I have a raise? Please may I have a job, if I work long and hard enough and stay away from the union organizer and parrot the corporate line even on my off hours? Oh please, sir?

But when the pleading doesn't work—because if we give to everyone who asks they'll come to expect it, you know, and demand it at a right—then not everyone sits in their poor but honest hovel and gnaws on their their meager but nutritious crumbs (assuming those crumbs haven't been taken away in the austerity drive). Because society is broad, and people vary. And some of them vary toward a kind of optimism that believes the experts when they say the market will rise forever, while others vary toward the idea that stealing is OK, or at least excusable, when everyone else is getting a piece of the action.

Our consumer economy looks like a plague to me right now, killing some of us slowly and some of us quickly, but getting us all in the end.

Hey, C Wingate, am I on the radical left yet?

Re: coins...

Okay, it's still bothering me, but I've finally worked it out to my own satisfaction. Yes, it's surely riddle & rhetoric, but here are (in my opinion) the most likely scenarios:

If Smith has purposely placed her gold coin on top, then her possible original permutaions: SG, GG, GS.

If Smith had always determined to reveal her top coin, and has not rearranged them, then her possible permutations: GG, GS.

If Jones has seen both of his coins, then his possible original permutations: GG, GS, SG.

If Jones has seen only one of his coins, then his possible permutations: GG, GS.

Therefore, the possible solutions:

IF Smith has arranged her coins, AND Jones has seen both of his coins, THEN Jones has a 2/9 chance of holding more gold than Smith.

IF Smith has not arranged her coins but had always meant to reveal her top coin, regardless of its metal, AND Jones has seen both of his coins, THEN Jones has a 1/6 probability of holding more gold.

IF Smith has arranged her coins so that a gold coin is on top, AND Jones has seen only one of his coins, THEN Jones has a 1/3 chance of holding more gold.

IF Smith has not arranged her coins, AND Jones has seen only one of his coins, THEN Jones has a 1/4 chance of holding more gold.

IF all of these possible scenarios are equally likely, then the probability of Jones having more gold coins than Smith is 35/144, or approximately 24%.

IF, on the other hand, we make no assumptions as to the motives of Smith and Jones, and we simply determine the probability based on the unknown coins in each hand, we fall back to an answer of 1/4.

abi @ 378:

am I on the radical left yet?

Not quite, but I can see you from there without a telescope.

Abi @ 378... Is that the left from where you're standing, or the left of someone facing you, in which case your left is their right, unless you're both looking in mirror, and hey, who's that guy with the goatee in the mirror?

abi:

I definitely see your point, and official lawlessness and impunity is a great force for evil in the world. But I am deeply skeptical that the looters in these riots are responding to lawlessness in high places. My guess is rather that most of them are responding to a short-term availability of TVs, shoes, clothing, etc., due to the police having been chased out of the neighborhood. This is common in every riot, whether triggered by police violence, unpopular court decisions, unpopular political decisions, sports victories or defeats, etc. Some folks see the short-term lawlessness as an opportunity to steal some stuff and maybe not get caught.

One of the hard lessons of any number of cnflicts and revolutions in history shows up here, as well--the fact that you or your ancestors were royally, unforgivably f--ked over by someone doesn't actually make you any more noble or decent. It's quite possible to transition quickly from the victims of repression to the oppressors, and it's quite possible to be both oppressed/screwed over by someone more powerful, and also to be surpassingly evil and nasty in your response. (A look at the Israel/Palestine conflict, or how the victims of German barbarity in WW1 approached acceptable terms for their surrender, or how post-colonial governments in any number of places treated their own people and ethnic or religious minorities offer a great many examples of all these things.).

At some level, we want evil to be punished by the universe. But most of the time, the universe doesn't oblige. Lawlessness in high places strikes me as probably having a pretty clear moral connection with looting stores during riots--in both cases, people are seeing their opportunity to get away with something evil and taking it. But i don't see where the causal link is.

Speculation:

Perhaps the existence of social networks and the ability to communicate peer to peer among arbitrarily large, fluid groups of people makes it much easier for all kinds of demonstrations, uprisings, riots, flash mobs, and other movements to happen. Perhaps this is simply a change in the world--the police can and will start monitoring these communications channels, but without extensive censorship, I think that won't change he fact that it has just become easier to organize protests and movements and such.

As evidence, I would point out the protests here in the US, including the Wisconson protests and also the Tea Party rallies (the origin of these was more bottom-up, later I think they were largely co-opted by the Fox News and talk radio crowd.). Then I'd point to the Arab Spring movements all over, to the protests in Spain and Greece, etc.

albatross @382:

Lawlessness in high places strikes me as probably having a pretty clear moral connection with looting stores during riots--in both cases, people are seeing their opportunity to get away with something evil and taking it. But i don't see where the causal link is.

It's not that the lawlessness is specifically in "high places" that's the issue, though my question of who, exactly, has standing and ability to lecture the looters is a serious one. There really is not a lot of establishment left untainted in the UK.

And that is my real point: to what society are these looters and rioters supposed to be loyal? Where are the institutions for them to believe in? It's the same shape of question as the other one I'm seeing asked around a lot: what future are they endangering? What prospects are they putting at risk?

As one commenter said on Crooked Timber, this is what it really looks like when there's no such thing as society. Heck of a job, Maggie.

Been a few years since a TV show featured Lucy Lawless.

Re #345; He's been eaten by a bank? ;)

Abi @ 384: Who has standing and ability to lecture the looters? Does vox pop count? I expect we'll hear interviews from people whose home or workplace is burned or looted and whose communities become wastelands from the lack of commercial services and economic opportunity. I'm not saying they were living in a capitalist paradise to begin with, but pillage doesn't improve the situation. I live in Washington, DC, and there are still areas depressed from the riots of 1968. A lot of neighborhoods have recovered greatly in the last couple of decades, but we are still paying the price.

I'm pretty torn by the whole demonstration/mass action dynamic. I really want to see justice done in the case of police, business, and political misconduct, and I'm unsure how that can be accomplished without taking it to the streets. On the other hand, there is a lot of room for riots to make things worse than they were before.

albatross @383

Perhaps the existence of social networks and the ability to communicate peer to peer among arbitrarily large, fluid groups of people makes it much easier for all kinds of demonstrations, uprisings, riots, flash mobs, and other movements to happen. Perhaps this is simply a change in the world--the police can and will start monitoring these communications channels, but without extensive censorship, I think that won't change he fact that it has just become easier to organize protests and movements and such.

I suspect it's best classed as another iteration of the broadsides and pamphlets that fueled the American revolution, and the photocopied fliers that used to publicize raves: similar in shape, a step further in degree.

ISTM that people are constraining the problem space rather than the solution space. Assuming that "evenly and randomly" means that a) the probability of a given coin being gold is 50% and b) it has no bearing on the probability of any other coin being gold ...

For Jones to have more gold coins than Smith, he must have two and she must have one, given the information we have. The probability of Jones having two gold coins is 1/4, and of Smith having one gold coin is 1/2 ... so the probability of Jones having more gold coins than Smith in this situation is 1/8.

Dan Hoey @387:
Who has standing and ability to lecture the looters? Does vox pop count? I expect we'll hear interviews from people whose home or workplace is burned or looted and whose communities become wastelands from the lack of commercial services and economic opportunity.

That's probably the only group that does have standing.

Look, don't get me wrong. I don't support the rioting and the looting, not in the least. But I think the way the media are portraying it, and the way the powers that be are talking about addressing it, is so seriously flawed as to be useless. Or, perhaps, the source of even more damage, so that next time is worse.

If the British government, and the British police, want to prevent a repeat of this, they're going to have to give the people in those communities some feeling that they're a valued part of society. That's going to involve money, even in these austere times, but it's also going to involve respect, attention, and genuine empowerment. It's going to involve actually giving a damn.

Unfortunately, I don't see much chance of that at the moment. So I suspect there will be a next time, and it will be worse.

albatross @ 382: "But I am deeply skeptical that the looters in these riots are responding to lawlessness in high places. My guess is rather that most of them are responding to a short-term availability of TVs, shoes, clothing, etc., due to the police having been chased out of the neighborhood."

It's not a lack of attention to legal form in high places they're responding to, it's a lack of reciprocity. The police aren't looking out for them; why should they look out for the police? The businesses aren't paying fair taxes or fair wages; why should they feel any obligation to their property? The government is cutting the social safety net, never enough in the first place--why should they listen to the government that isn't listening to them?

To come at abi's point from another angle, why should they abide by the rules of a system under which they can't win and which the winners ignore with impunity? While I dislike the alternate rule set they've enacted, I can't fault their distrust for the system.

(It's very easy to fault looters for stealing consumer goods when one is in the position of already having the consumer goods one wants.)

Anaea #369: That's a useful defensive strategy... but I'll note that in Wisconsin, too, the police were sympathetic to the protesters!

The basic strategy of "crush all protest" fails utterly when the folks the honchos expect to do the crushing, turn out not to be the obedient thugs that their employers expected.

Somewhat on a tangent, this is an interesting way to combat extremism:

'Trojan' T-shirts carry hidden message to extremists

heresiarch @ 391: Speaking as someone only 100 yards or so from some of last nights' rioting:

I can agree with you with the points about the police and the government, but as far as the businesses go - to a huge extent these are local businesses that are being trashed, and in many of them, the people running the businesses were barely getting by before this.

In many ways what's strange is the fact that they *haven't* gone for wealthier areas. London's a small place - the wealthy places aren't far away. I don't know if the thinking is that the police will protect those places harder - it wouldn't surprise me. Another alternative explanation I've heard/extrapolated is that they think *anyone* owning a business is "rich". I know many young people seem to have hopelessly inaccurate ideas of what business owners earn. Whereas I know many of the owners around me are actually pulling in under minimum wage.

As far as the way things are being portrayed - I think many Londoners would say things are being understated. I work in central London, my workmates are from all over London, and most of them had seen trouble over the last 24 hours; most of them know someone who has directly been affected.

As far as injuries go, my wife works in one of the London hospitals, and they are literally filled to capacity with trauma victims, with all non-essential operations being cancelled. One civilian has already died, and it seems likely others will follow (from news reports, I suspect the person injured a few hundred yards down the road from me isn't going to pull through).

I fear the outcome of all this is going to be a pretty unprecedented shift to the right in London - at least in terms of acceptable policing methods. Expect the police to be lobbying hard in a lot of areas in the aftermath.

FLDS leader Warren Jeffs has been sentenced to life in prison for raping two girls he had taken as "spiritual brides." The younger of the two victims was 12 years old. Jeffs recorded himself raping her in front of witnesses, and carried the tape around with him.

David Goldfarb @348: Thanks for your note. And I'm glad to see (e.g., Dave DuPlantis @389, DanR @379) that the controversy still rages. I should have known better than to ponder this at 2 AM. After looking at a few posts where the answer came to 1/6, I still didn't find the arguments entirely convincing. In any case, you're quite right to point out that I missed it even on my own terms, so let me start over. The correct probability is "of course" 0.25. But before explaining how I got there, let me ask you: What would your analysis be if Jones had instead said, "I have two Lemurian coins in my hand. The one on the left is gold"?

David Delaney at #354:
What have I got in my pocket?

Dave #394: In many ways what's strange is the fact that they *haven't* gone for wealthier areas. London's a small place - the wealthy places aren't far away. I don't know if the thinking is that the police will protect those places harder - it wouldn't surprise me.

The same pattern has shown up in American riots such as Watts (Los Angeles), Philadelphia and so on. At the time, I recall the same reasons being given -- in American terms, "if they'd tried going into the white areas, they'd be facing the National Guard with shoot-to-kill orders."

I'd also add that the shops near them are the shops they're familiar with, and which they've had personal experience with not being able to afford stuff they carry.

Infinitude of Tortoises #394: "The one on the left" is equivalent to "the one on top". Either way, it indicates a specific coin, rather than the less-informative "the total is more than...".

David Harmon @393: It only works if they wash the shirts, so there's a likely failure rate around 40% there.

Anaea, #369: It would be nice if those individuals were being recorded, identified, and their connections (or lack thereof) to Walker and his allies traced. Proof that even one such person was a paid provocateur would put him in a very bad position legally. Of course, it's always possible that some of them are amateur volunteer provocateurs as well.

Modesto Kid, wrt carelessness -> et by lions: I'm still trying to figure out who "Jack" was intended to be in the 1848 "Punch" satire.

Best guess so far is John Russell, who was Prime Minister at the time, but the Wikipedia overview doesn't say anything linking him to a failed attempt to raise the income tax, which seems to be the matter of contention in the cartoon.

Then again...

"[I]n 1848, Great Britain was in the throes of the distress caused by the railway crisis of 1847-1848. John Stuart Mill, in his great work published in that year, had lent the authority of his weight to the opponents of the tax. [....] With a large deficit staring him in the face, however, Lord John Russell had no thought of abandoning the income tax; on the contrary, in introducing the budget on November 18, he went so far as to recommend its renewal for five years, at the rate of five per cent, i.e. one shilling in the pound.

"This proposition aroused so great an uproar that on February 28 Sir Charles Wood, the Chancellor of the Exchequer, dropped the suggestion and asked only for a continuance of the tax at the old rate[*], and for another three years."

[*: Up on pp132-133 of the same book, it looks like that the 1842 Property and Income Tax Act had a 150 pound deduction and an income tax rate of 3.5% in England (slightly less in Scotland).]

Sadly, while this may be Punch's Jack, he doesn't seem to be the eponym of the Jack Russell Terrier.

Kip W.@399, re: David Harmon @393, does "not having enough sense to come in out of the rain" make up for not washing the shirts?

Me at #358: My comment about the failure of peaceful protests seems to be supported by one of Patrick's links (Penny Red):

"Two months ago we marched to Scotland Yard, more than 2,000 of us, all blacks, and it was peaceful and calm and you know what? Not a word in the press. Last night a bit of rioting and looting and look around you."

Eavesdropping from among the onlookers, I looked around. A dozen TV crews and newspaper reporters interviewing the young men everywhere ‘’’

Incidentally, I did not know about the protest he mentions....

OT: This robot is an electric sheep!

Some of the places looted, they're not local businessmen. I looked up Tottenham Hale Retail Park, and the only "local" businesses there are likely to be franchised fast-food.

I suspect reporter-bias, but the places reported as set on fire, not just in London, are national brands. I get an impression of a lot of other damage, but no details. Is it the big-name companies that are being targeted, and local businessmen being "collateral damage". Or do I need to watch Al-Jazeera rather than the BBC?

Anyway, it doesn't matter what the motive was if your place got damaged or destroyed.

And, missing Xopher here:
India's festival of Ganesha starts next month; shortage of priests leads to recruitment of teenagers.

Bill Stewart @403: That probably depends on a lot of factors — detergent action, mechanical action, temperature — any two of which would rule out the possibility of a pithy reply from me, so I can only shrug in bemusement.

350
If it's the same size as the folding pruning saws I've met, the blade might be a foot long. (I have a photo of my father sharpening one.)

Hey, Serge!

Tortoises@396: I agree with David Harmon@398. See also my reformulation @217.

The Modesto Kid @310: I expect you meant to ask, "What is it in Raven?"

No, that would be this. :)

Kip W @311: :) I do have a clue. I just don't want to wear it out. Ahem.

Caroline @337: Altogether, it sounds like there isn't a way to handle this that doesn't involve a lot of extra work. Which is stupid, because I thought the whole point of Paypal was that it was supposed to be convenient. ::sigh::

Hmm. To me, Jones's "At least one of them is gold" is no more or less informative in terms of solving the puzzle than Smith's "The one on top is gold." The end result of both their statements is that we know each has one gold coin and one unspecified coin. (Agreed?) As I see it, we can "subtract from both sides" the known gold coins and focus entirely on the one unspecified coin each holds. And I still fail to see how the "orientation" of the coins makes any difference here -- which is why I raised the perfectly legitimate possibility of Jones's gold coin being on the "left". It could just as well be aligned with Arcturus; Jones's possible "hands", in terms relevant to comparing her total gold coins with Smith's, would still be only GG or GS. (Remember, my "GS" represents coins listed in an arbitrary order and is equivalent to "SG". Jones's coins could be aligned with Aldebaran, or the Great Pyramid, or....) Hope I'm not boring you with all this, but there's clearly some facet I'm still not grokking in fullness!

Infinitude @413, Tim Walters, David Goldfarb, et al:

I think the basis of this ensnarement is explained fairly thoroughly here: Boy or Girl Paradox

abi @ 390:

the way the powers that be are talking about addressing it, is so seriously flawed as to be useless. Or, perhaps, the source of even more damage, so that next time is worse.

Dave @ 394:

One of the standard police responses to civil unrest is to contain it in the originating neighborhoods, on the theory that it will prevent damage to the neighborhoods of people who matter more, and will turn the rioters on "their own", which will serve them right. This, of course, completely ignores the fact that the rioters are only a small percentage of the people who live in that neighborhood, and that the rest don't deserve that violence either.

In my experience, news reports about riots and other forms of civil unrest are rarely accurate, and are often deliberately slanted and/or fabricated to justify any actions the police or their masters deem required to deal with the situation. The rioting is often used as an excuse not to discuss the socioeconomic situation that caused the deep alienation from society that allowed the riots to occur, because that situation is part and parcel of the political strategy of those in power.

As an example of fabrication of news, there were at least two cities in the US where riots occurred in 1968 that were never reported; the police cordoned off the affected neighborhoods and did not allow reporters anywhere near them. One of them was Philadelphia; I know about it because Eva got off the subway that night and saw the cordon before she was hustled back onto the subway.

DanR @ 414: None of the caveats and quibbles in that link apply here, since the problem unambiguously states that the unidentified coins have random values.

And you think that one of Jones' coins is identified, but since you can't identify which one, I don't agree. (Saying "the gold one" is tautological, like saying "the taller one" if I ask you which of Smith or Jones is taller.)

David Harmon @392 - Oh, absolutely - they may well have been the ones to teach the crowd to do that. There are a ton of reasons the protests in Madison never turned violent, but they all boil down to the local infrastructure being sympathetic to or actively supporting the protests. The same passion and anger without that support...it would have looked like London. Hell, without Ian's pizza, there were points where low blood sugar might have sparked a riot.

Lee @400 - some of that went on, though we had bigger priorities that usually took precedence. From what I saw, non-local anarchists were the biggest demographic of likely troublemakers. There was a consistent theme of people not being able to understand that nearly all of the authority figures were on our side, which changed what constituted appropriate tactics for dealing with authority. It's still my biggest source of frustration in dealing with people coming in from out of state.

And in other news, I'm finding it really easy to understand where the rioters in London are coming from. Really, frighteningly easy.

A columnist at The Grauniad tries to explain the riots here.

New US Poet Laureate is Philip Levine, succeeding W.S. Merwin. Both of them are 83. Here's a WaPo article. Levine's poetry tends to be about working people; Merwin's about nature. (I don't actually know anything about either one beyond the articles, except that Merwin's done some work on rainforest restoration in Maui that I think is the project my sister volunteered with.)

abi@390

I would tentatively suggest that the time to focus on the causes of the rioting is after the unrest itself has been contained and people's persons*, homes and businesses are safe.

Last night was quiet in London, although there was looting in some other cities. I suspect tonight will be quieter everywhere. Parliament has been recalled an will debate the situation on Thursday - I hold out hope that this will focus on more than simply police powers and how to handle a riot in progress.

In the mean time, there have been stories in the mainstream press** which try to take a nuanced view of the situation.

* Odd formulation, but I imagine you can see what I mean.

** Links are to the Guardian because it's the one I mostly read - for those unaware, it is a left leaning publication.

See this, from a man with impeccable 'liberal' credentials:

http://kenanmalik.wordpress.com/2011/08/09/five-quick-points-about-the-riots/

To regard these events in themselves as anything other than counter-productive, if one is actually interested in advancing social justice, rather than empty posturing, is impossible. If the aftermath of the events is constructive for that cause, it will be in the way the aftermath of a flood or a wildfire leads to better environmental management - but far more difficult to achieve, since the general run of opinion here is that the rioters deserve a good kicking. If anything does come of this, beyond a reversal of proposed cuts to policing budgets and an accelerating sense of general social malaise, it will surprise me, and I think the majority of observers.

TexAnne @ 410... Oooooh...

Dave Bell @ #406:

One of the stores set on fire in Croydon is a 100+ year old local furniture store. I guess mostly national brands than local stores, though, if nothing else because national brands stores seem to be more prevalent than local stores.

Here is a further article* I had in mind @420, but couldn't remember the provenance of earlier.

* The Independent, according to Wiki, is politically left leaning but pro-market.

Tortoises #413: The end result of both their statements is that we know each has one gold coin and one unspecified coin. (Agreed?)

NO. Smith has one specified coin. Jones has two unspecified coins and a constraint about their total. See my #152 for why you do not have the same information about the two sets of coins.

As I see it, we can "subtract from both sides" the known gold coins and focus entirely on the one unspecified coin each holds.

Hell, no. You do not have an equation here, you have two distinct sets. Bluntly, probabilities have very specific rules about how they combine and resolve. Subtracting Smith's known coin from Jones' pocket is not even in the same book.

Jim: Even after several people had worked through this problem correctly, in detail, and with clarifying analogies, this "Tortoises" person has tried to restart the "debate" from the beginning with "well, Jim didn't say what the right answer is!" You know, and I know, that authority is irrelevant to the solution of a mathematical problem -- but it can certainly help solve a social problem, and I suspect this is starting to become one of those.

A comment from someone on a website, taking the bigger view:
"Looting isn’t a political act? Nonsense, looting is a fundamental political act. The people doing the actual looting may not be acting through political motivation, but the act of looting is highly political.

Looting is THE MOST IMPORTANT political act, because looting is exactly what happens when people believe (rightly or wrongly )that the laws no longer apply to them.

Looting is an exact analogy to the Newspaper publisher who ignores the rules because the regulator is completely toothless and the lawmakers are in the back pocket. Looting is the hedge fund manager killing a currency, or the shareholder closing a factory. Looting is exactly the same as the MP who writes his own expense claim, because there is no-one there to check. Looting is the same as the millionaire footballer who thinks his bank account gives him the right to spit roast his way across Europe or the property developer who rips the heart of a city because he can.

Looting is the population’s way of saying ‘there is no such thing as society’. What is that young guy doing with a plasma screen under his arm? He could never acquire that from working down Tescos, so he has waited for an opportunity and when the rules no longer apply to him and the prevailing culture has liberalised the property laws he has acted in his own self interest and to f.ck with everyone else. Isn’t that EXACTLY what we have been saying to everyone else? The only difference is that ‘we’ removed the rules willingly.

Looting is what happens when you replace rules with ‘voluntary codes of conduct’, ‘light touch, self regulation’ and Government getting out of the way."

http://liberalconspiracy.org/2011/08/09/only-poor-people-go-looting-and-other-silly-claims/

David Harmon @425, Tim Walters, Bruce Harmon, all the rest of the 1/6thers:

Your thoughts on my explanation @379?

Regarding the Boy vs. Girl Paradox, please read this excerpt:

Analysis of the ambiguity

If it is assumed that this information was obtained by looking at both children to see if there is at least one boy, the condition is both necessary and sufficient condition. Three of the four equally probable events for a two-child family in the sample space above meet the condition:

Older child Younger child
Girl Girl
Girl Boy
Boy Girl
Boy Boy

Thus, if it is assumed that both children were considered while looking for a boy, the answer to question 2 is 1/3. However, if the family was first selected and then a random, true statement was made about the gender of one child (whether or not both were considered), the correct way to calculate the conditional probability is not to count the cases that match. Instead, one must add the probabilities that the condition will be satisfied in each case[11]:

Older child Younger child P(this case) P("at least one boy" given this case) P(both this case, and "at least one boy")

Girl Girl 1/4 0 0
Girl Boy 1/4 1/2 1/8
Boy Girl 1/4 1/2 1/8
Boy Boy 1/4 1 1/4

The answer is found by adding the numbers in the last column wherever you woud have counted that case: (1/4)/(0+1/8+1/8+1/4)=1/2. Note that this is not necessarily the same as reporting the gender of a specific child, although doing so will produce the same result by a different calculation. For instance, if the younger child is picked, the calculation is (1/4)/(0+1/4+0+1/4)=1/2. In general, 1/2 is a better answer any time a Mr. Smith with a boy and a girl could have been identified as having at least one girl.

Point being, question is ambiguous. Statistically accurate answers must take into account possibility of different knowledge base by both Smith and Jones.

Hope that helps.

Tortoises:

One important way to think about the problem is "What is the possibility space (i.e. the set of all possible outcomes) here?" and "What possibilities are excluded by new information?"

In this case the total possibility space for both Jones and Smith is:

GG
GS
SG
SS

(Where GS means a gold coin on top of a silver coin, SS is two silver coins, etc. Also, it's worth stating here that each outcome has equal probability)

When Smith says "The top coin is gold" this excludes SS or SG as possibilities, leaving GG and GS, each with equal probability.

But Jones' statement that he has at least one gold coin does not exclude SG as a possibility, so the possibility space for Jones is GS, SG, GG (again, each with equal probability).

So Smith has a 1/2 chance of having two gold coins, but Jones only has a 1/3 chance. And the probability of Smith having one coin and Jones having two is (1-1/2)*(1/3)=1/6

Chris W @428:

I think what Tortoises is saying, *and what I'm saying* is that Smith declaring her top coin is gold means she placed her gold coin on top, and therefore does not exclude the possibility of her originally being dealt SG. Effectively, Tortoises' is a rhetorical argument, stating that Smith and Jones have equivalent probability matrices.

Really, I don't think anyone needs more nuts-and-bolts convincing about the 1/6th solution. It is a simple answer to a slightly different, non-ambiguous, statistical problem.

Another entry in the genre of "if male superheroes were drawn the way female superheroes so often are": What If Male Superheroes Posed Like Wonder Woman On The David Finch Justice League Cover?

Jacque @412: My understatement does you an injustice. I figured you had gotten it. Please excuse the phraseology.

Bruce Cohen @415: The rioting is often used as an excuse not to discuss the socioeconomic situation that caused the deep alienation from society that allowed the riots to occur…
This seems to me something like the situation where a teenager (or older) feels so strongly about something that their parents seem unable to take notice of that they pull out the strongest arrow in their quiver and use the f-word in relation to it, hoping that this will shock the folks into recognition of its magnitude... after which point the only only only thing the parents can think or talk about is how awful it is that their child used that word.

DanR:

Yes, you've identified two unstated assumptions in the problem (or at least the standard solution). To wit:

1) Mr. Jones achieved his knowledge that at least one of his coins in some way which did not privilege one coin over the other. (For example, by looking at both of them, rather than just the top one). Without this assumption, the problem is entirely uninteresting, since then Smith and Jones actually do have the same possibility spaces. Assuming that Mr. Jones has only looked at his top coin completely erases the distinction that the problem carefully draws between "My top coin is gold" and "At least one of my coins is gold."

2) Neither Smith nor Jones is manipulating their coins in any way towards any desired outcome.

So yes, if you use other assumptions you get other results. But the assumption that statements are based on complete information is a very common one in probability problems, and I see no reason not to turn an interesting problem into an uninteresting one by not using it here.

As for the assumption that Smith is manipulating her coins in order assure that a gold one is on top, it's interesting, but completely unsupported by the text of the problem. If we're going to start adding assumptions about the intentions of Jones and Smith, rather than simply assuming that they are ciphers who receive random coins and then make statements about them, then I could just as easily add a different assumption: "Smith is OCD and always places her silver coins on top, therefore the probability that the bottom coin is gold if the top coin is gold is 0"

And arbitrarily assigning equal probabilities to these different sets of assumptions is simply an exercise in calculation without any basis in fact or theory. (Why include these two sets of assumptions and not any number of other possible assumptions that could be added?)

DanR: Your analysis looks good, though you have missed some symmetrical cases, and also confused things a bit by reordering some of the permutation lists.

If [<someone>] had always determined to reveal [their] top coin, and has not rearranged them, is equivalent to if [<someone>] has seen only one of their coins. Either way, they are not tampering with the order provided by "the draw". Choosing a gold coin to present does not count as a draw.

Thus each of your cases are correct, but your second and third cases are symmetrically equivalent. Also, the second case is the conventional reading of the original problem.

Note that if they both pocket their coins¹, and then draw gold (as Smith originally did), we can (1) rule out that they have all silver, and (2) halve our suspicion that they are drawing from a mixed pair.

Choosing a gold coin only gives us (1), but (2) happens for each independent draw. That is, even if Jones never shows us both of his coins at once, every time he draws a gold coin (without ever drawing a silver), we become more confident that he does in fact have two gold.

¹Note that because they're drawing from a finite bag, drawing the second coin without replacing the first is not an independent draw -- that's where the folks who got onto "the size of Lemuria's currency supply" were coming from.
----

And Now I'm Really Finished With This! Gaah.

http://rosamicula.livejournal.com/540476.html

An essay about the young people (13% to 20% who leave school with no qualifications and no connection to society), and who are presumably most of the rioters.

Serge @381:
==and hey, who's that guy with the goatee in the mirror?

Dude, I'm NOT saying your name three times again!

--Dave, at least not until I've got the circle closed and charged

PS: For those who reflected the last pocketses question back at me, the correct answer is "No, there's not anything currently in my pockets, as I'm not wearing pants".

PPS: HLN - Local man now has in his possession a PHYSICAL COPY of Nobilis 3rd Edition, so it _exists_! Those of you who like Jenna's stuff, go thou to eos-sama and buy! (She's also blogging there now, in addition to the Hitherby Dragons posts.) ... or, er, after checking, don't, because they don't have any way to actually purchase it there yet. Bah.

Chris W. @432:

Valid points, all. However, I would argue that dealing with the assumptions is the more interesting part of this problem.

DanR @ 429: I think what Tortoises is saying, *and what I'm saying* is that Smith declaring her top coin is gold means she placed her gold coin on top, and therefore does not exclude the possibility of her originally being dealt SG.

If Smith places a gold coin on top whenever she has one, then the chance of her hole coin being silver is 2/3, not 1/2, which directly contradicts the problem statement. The same proviso also removes the ambiguity cited in the Wikipedia extract, not that I particularly agree with that anyway.

Worrying about Smith's and Jones' motivation or procedure is like grilling a joke-teller about exactly what mutation enabled a kangaroo to talk. The whole point of writing a problem in this style is to signify that your only concern is with the information you're given. Even without the proviso about the unspecified coins, yours would be a strained reading; with that proviso, it's simply wrong.

Stepping back in to Making Light after being away far too long (hectic segment of life), to post the following delightful link:

Unnecessaryquotes

So Smith and Jones look at their coins, then they put coins into two envelopes, and mark them "Smith" and "Jones".

"Now," Smith says to you, "pick an envelope, and you can keep the contents."

But do the names marked on each envelope correspond to the person who was holding the coins prior to putting them in the envelope? Does each envelope contain the same group of coins that one of the people was holding at the beginning of the story?

Tim Walters @437:

Arrgh! You got me on that one! Yes, the proviso does prove that Smith has not purposely arranged her coins, and therefore we must assume her matrix to contain only GS or GG.

That still leaves the question as to whether Jones has "identified" his gold coin by saying, "At least one is gold."

DanR @ 441: That still leaves the question as to whether Jones has "identified" his gold coin by saying, "At least one is gold."

How can he have identified it if you can't tell me which one it is?

I hadn't even been aware of the riots in English cities...

I suddenly was reminded of A Clockwork Orange....

Most rioting and looting is in relatively local areas--the people most victimized in high crime rate areas are the people who live in those areas, not people outside of them.

Most of a decade ago with the invasion of Iraq and and the obscenely misrun occuptation of the country, the invading militaries, particularly the US military, stood by and initially did nothing to deter vandalism, looting, thievery, robbery, arson, and even kidnapping, rape, and murder by such basic social obligations of governance as providing police patrols and surveillance and guarding and monitoring and protection etc. to public offices, city streets, facilities, museums, schools, etc.

There are "it's there, so take it" mentalities oin varying degrees, ranging from "nobody owns it and it's going unused so I'll take it" to "everyone else is looting, I want -my- share!" to "Looks like nobody's going to bother to notice or punish anyone who takes that, so I'll take it, since I can get away with it", to being caught up in mob psychology. Crooks will steal anything that they want that it looks like they can get away with stealing....

As to where thefts and lkooting and vandalism occur, there are ones of convenience--few people are going to on the spur of the moment drive two hours to commit looting and vandalism, that tends to take more time and attention and planning than most people tend to bother exerting..

#378 abi
Constance @375:

Still, I'm not in favor of consumerist riots, unless it is for getting the food and water and other necessaries for yourself and family

I'm not either, but I understand the impulse. It grows from the same rootstock as the one that left so many American households in foreclosure. We live in a society that uses possessions—consumption—as the marker of success, and tells us that success is everything. Is it any wonder that people will beg, borrow and steal to look like winners?

O yes, I get that very well. The politicans have to fly back from their post August vacations in places far, far, far away just to get put to speed on the crisis.

O yes, the damages to people who are not responsible for these things, including the toxic consumerist economy that they have made and shoved down everyone's throats, and then yanked away the means to even participate in it -- what do they expect is going to happen?

This is class war, but so many people of the out class are being damaged, maybe forever ....

Again, this actually happens to be a consequence, not a symptom, though it's also a symptom, perhaps, of a global economy gone berserk, a global economy whose only function is to consume, not create -- and especially not create anything productive and sustainable? While in the meantime punishing, turning into criminals, as we have done in the U.S., anyone who is poor and can't participate.

If / when it happens here, with everyone armed (except me) the streets will be knee deep in blood. The world of ultimate warlordism, whether they wear suits or not. Not good for small living things and animals.

Love, C.

@ #390

The blather by the so-called pundits and experts 30 + years down the road -- the titles of the articles and the features, the calls for study to find the real causes, the proposed remedies, blahblahblahblah -- ARE EXACTLY THE SAME NOW AS THEY WERE IN 1981. Or -- here, for instance, in 1965, 1971, you name it. Compare the captions and headlines and think pieces in the media in 1981 with those even in the UK Guardian today -- and they are the same.

Love, C.

Evidently, in the land of Lemuria, gold is not $1770 per ounce, as it is today in our world, since when gold is $1770 per oz anyone carrying gold coins is accompanied by armed guards.

Re the rioting: we've been here before, many times. I heard the British PM on NPR this morning blathering about "thugs," typical useless rhetoric. Please don't misunderstand, I don't excuse or applaud the looting and the violence. But guthrie at 426 makes an excellent point: this is a convenient specie of violence for the establishment to condemn.

And nothing will change. Yes, the stealing and smashing is political, but it is surely not revolutionary. (Lenin would be appalled at the triviality of the action.) It will not affect the power of the state in any way, except to increase it, and to temporarily harden positions, or slide them further to the right -- more police! Longer prison terms! Less help for people who truly need it, because the proles are clearly not sufficiently grateful for what they are given.

BTW, this morning I heard a report which said that due to the most recent budget shortfall in California, some cuts in state funding are about to go into effect; all targets predetermined in political agreements signed months ago. Among the sectors that will lose funding are community colleges, programs for the disabled, and health care for the very poor.

Marat, we're poor -- and the poor stay poor...

And the first three members of the Gang of 12 (the budget supercommittee) are announced: Democratic Senators John Kerry, Max Baucus, and Patty Murray. It will be interesting to see the others. Republicans are already attacking those choices.

http://rosamicula.livejournal.com/540476.html

An essay about a large number of young people in the UK who've never been brought into the culture and don't feel a part of it. The writer grew up close to that part of the culture and has taught many of the kids.

It's the most sensible-looking thing I've seen on the causes of the riots.

*****

It seems to me that people who set fires are much more alienated than people who steal stuff.

All right, have some vox pop from Manchester city centre yesterday and today. A summary of assorted overheard conversations in the street and on the bus, my colleagues, and the barrowman I get my daily fruit ration from.

-- the violence and looting were not spontaneous protests. It was organised looting by the local gangs, and there were rumours flying around the social networking sites as early as lunchtime that the planned time for kickoff was 4pm. (Which is why some of my colleagues left work early last night, and the rest of us kept a wary eye on the local news.)

-- the *organised* looting was planned to exploit the fact that half the Manchester police force was down in London last night.

-- a bunch of wastrels looking for a chance to thieve (the polite version of what the glorious proleteriat in the form of the cleaning staff were saying about being told to get out of town early because trouble was breaking out all over)

-- the police should have gone in and thrown the initial small groups hanging around waiting for the off straight into the vans, before they told their mates to come on down because the police wouldn't do anything (the polite version)

-- why the hell weren't the police breaking a few heads, or at least bringing out the water cannon? (the less polite version)

--they need to flood the centre with police tonight, and chuck them in the van and off to the nick as soon as someone even thinks about looking at them funny, preferably hitting them with a truncheon or two to make sure they stay down.

I have deleted most of the swearing.

Of course, there's a certain amount of bias here. I was lucky and managed to pick a route to the remote bus stop that was safe at the time (although it was trashed by looters a couple of hours later). Some of my colleagues legged it because they saw a crowd of looters coming towards their bus stop, some were chased by looters, and some of my colleagues live in flats above shops that were targeted by looters. We got in to an undamaged workplace this morning, but many of us have friends who weren't that lucky.

We are not impressed by people excusing the looting on the grounds that it's only what the fat cats do.

"What a shame that [group we approve of] have been driven to attack [group we disapprove of] by the actions of [group we disapprove of]. We don't, of course, condone the violence, but really, they brought it on themselves."

It doesn't sound any better coming from the fluorosphere than it does from wingnuts. And if you think I sound bitter, it's not entirely unconnected with wondering if a missile was about to come through the office window a couple of times this afternoon.

Niall @ 439

So Smith and Jones look at their coins, then they put coins into two envelopes, and mark them "Smith" and "Jones".

"Now," Smith says to you, "pick an envelope, and you can keep the contents."

And that is the moment at which I conclude Smith and Jones are con men and I am the pigeon. (If you don't want me to include human motivations and quirks in my analysis, don't have the logic problem involve human beings.)

#409 Julia

"domestic terrorists"

#446 Lizzy

[from me #119 http://nielsenhayden.com/makinglight/archives/009119.html back in 2007...

George Bush we're poor
We weren't always poor
George Bush each day
We hate your much more
We want our rights
That you took away
We want you [censored] TODAY.

Bush contributed to UK spending with his "I'm a Bigger Prick Than You Are" war against Saddam Hussein and consequent misadministration in Iraq, along with having the UK's Prime Minister at the time acting as something of a catamite....

#447 Tom
I remain incensed at the media repeating the lies calling Kerry and extreme liberal. He is NOT. For one thing, he BELIEVED the lies of the Pinocchio who occupied the White House in 2001-2008 and voted to hand over all sorts of authorizations to to the schnook... at the time he voted in favor of allowing the schnook to play dominance games with Saddam Hussein with the US taxpayers and the citizenry of Iraq and a whole lot of other people(Some by their taxes going to the Iraqi adventure, others by refugees fleeing to their countries....) and irreplaceable world heritage of manuscripts and museums holding, archaeological stratigraphy and knowledge that could be been gain by digs rather then destructive looters and the US military siting encampments on antiquity sites, all victims.... Kerry at the time said "he would be watching" but that part of his speech when he voted to let the schnook do what the schook and his neocon apocalytics greedy weasels wanted, got forgotten...

Kerry is NOT a liberal. He's not a blue dog Democrat, but he's no liberal. He's less liberal than Tricky Dick was.... and unlike the last Kennedy in Congress, he hasn;t got the political junk yard dog killer instinct for political infighting--Teddy was a political fighter of a degree most people don't appreciate, one of the last times there was any sort of opponent to speak of running against him, his fought hard, and his opponent was completely outfought. Id on;t remember any details of the debating, but the other guy came off as a nebbish.

Jacque, #412: PayPal is convenient, by comparison to having to write a check, dig out an envelope, find and copy the address, find and affix a stamp, get it to the post office. Even more so if the process involves buying a money order rather than writing a check. If you're on the vendor end, try Google Checkout as an easy, free alternative.

Kip, #431: That's a good analogy, to which I will add that if the parents are deliberately trying not to take notice of whatever the teen is upset about, then hijacking the argument into being about the use of the F-word is also an excellent diversionary tactic.

Lee, the little melodrama played out a while back in RASFF, when I finally got so tired of someone I said I didn't give a f***. For that, I got analyzed minutely by a battery of folks who contended that "f***" is a violent and shocking word.

Yes, not giving a f*** is a form of violence. This, from grownups.

Many people who know poorish areas of the big cities of the UK will know of elderly people whose lives are made a misery by lawless little juvenile shits. The usual low-level abuse that goes on for months and months, never quite reaching a point where it's big enough for the police to respond in more than a token manner. The elderly victims try to ignore the noise at all hours, and clean the urine from their doorsteps, and don't dare confront their tormentors. (Confront the tormentors' parents and you'll get another mouthful of abuse). It goes on for months and months, often till it kills the victims. Not in any way that can be pinned down as murder; usually it's a heart attack or stroke, exacerbated by the stress of being afraid in your own home all the time and being burgled every year or two, that does it.

These are in fact hate crimes, of a non-specific variety—the victims aren't necessarily gay or disabled or of a different ethnicity (though they might be); differences don't matter; the perpetrators and their mates are doing it for a laugh.

It is indeed a class war; the working classes are being oppressed horribly by the underclass and it's been going on for about 20 years now and the law-abiding poor are not at all averse to the idea of the non-law-abiding poor getting a truncheon or a rubber bullet in the face, now that the latter have picked a deliberate and public fight with the state (see Julia Jones's vox pops @449). And the elderly victims, in particular, aren't fond of hearing the this-is-an-explanation-not-a-justification line of social commentary that talks of social exclusion, the crimes of the rich, alienation. The elderly victims were children of the Crash, the Depression, the Means Test Man, the British Union of Fascists, the Board of Guardians, bread-and-dripping for tea, one family to a room with an outside toilet shared between 4 houses in the terrace. They were working in factories at 14 and they were at war at 18.

(A certain type of ironic interjector usually makes a hilarious crack about the Four Yorkshiremen sketch at this point. For the well-off to excuse the crimes of the poor on the grounds of their poverty is a liberal virtue; for the poor to condemn the crimes of the poor on the grounds that they were in the same boat or a worse boat once, and didn't commit crimes, is apparently letting the side down.)

This isn't a crack at anyone on ML; reading back on what I've written, it's more of an exasperated moan really. You may gather that I have had elderly relatives in the situation described above.

Julia Jones @449 We are not impressed by people excusing the looting on the grounds that it's only what the fat cats do....It doesn't sound any better coming from the fluorosphere than it does from wingnuts.

True. All of them should be arrested, tried and suitably punished.

My problem is that I'm hearing people saying "What can you expect from these guys? They're a deadweight on society. Rioters going to riot. Only way to deal with it is break some heads." Ignoring root causes of disaffection and alienation is just going to push the problem down the road a way. Waiting until it's over to discuss this will entrench the "they're all thugs, so let's break some heads" analysis.

So the rioters are to blame for the disorder. But we need to be responsible for trying to avoid it happening again.

Neil W @ 455:

But we need to be responsible for trying to avoid it happening again.

Exactly. Instead of pointing fingers and assessing blame, what needs to happen is something similar to an aircraft crash investigation, where the idea is to discover the causes of the crash and develop ways to prevent those causes from resulting in another crash in the future. Not that any such objectivity is likely in the current situation; I suspect any real investigation would uncover plenty of things that would piss off just about everybody from rich to poor, white to brown to black, and especially politicians and police¹.

1. It doesn't matter who started it or what the triggering incident was, handling civil disorder as a military problem is an extremely bad and ultimately self-defeating idea. And if the yabos committing the violence are not well-liked by their neighbors, treating the whole community as the enemy is giving up one of the best tools you've got to isolate and identify the miscreants.

Double standards...
I have the TV news on, for the first time in several days. The station gave air time to "President Obama is going to spend a week vacationing on (one of the Massachusetts islands, I can't remember if it's Martha's Vineyard or Nantucket...)in a manner connoting that this is very wrong of him, he should be skipping vacation and staying working on the job in DC--despite the fact that Congress had vacated DC for the summer except for the token less than handful necessary to technically keep Congress in session, preventing any recess appointments like the Schmuck made--despite the fact that are more than 200 appointments in limbo from secret holds by ratshit Republicans, the same ratshits who were screaming how all appointments and legislation should be held on "up down votes" on what -they- wanted ramrodded through with no discussion and no revisions or close examination--those more than 200 appointments in limbo (there might be fewer now, some people withdraw themselves as candidates sitting in limbo week after week, month after month... but the overall number is very very much higher than the appointments that the Schmuck wanted that he didn't get--and that INCLUDES people who got rejected... and some of the rejections, that sack of shit Bush appointed during recesses, ANYWAY....
>
I am not a big Obama fan. My opinion is that he is an APPEASER to evil people and the evil they perpetrate. But he's lightyears less abominable than anyone running for the Republican candidacy for President. They lot of them make Haman's sons look collectively worth one breath.... (the Purim service, the leader of the congregation is supposed to use a single breath to recite the names of the sons, because collectively that;s all they're worth... and every tine the name "Haman" gets uttered, little kids whirl noisemakers to drown out his name... )

Romney is a lying take-whatever-position-sucks-up-to-the-biggest-pressure-groups weasel and someone whose capital fund cut jobs in the USA and sent them to China and India etc. and invested in companies only if they offshored, and those are the -nicest- things I have to say about him... and the others aren't any more attractive than he is...

The sack of shit took the entire SUMMER of 2001 off, and continued taking most of the summer off the rest of his time fucking up the country with his misadministration. He acceded to allowing a briefing on Al Qaeda to be scheduled for I think it was September 12, 2001, after having refused to hear any briefin on the topic the first half of the year, and taking the entire summer off. Of course, Al Quaeda acted on September 11, 2001 hijacking four airliner and turning them into weapons of mass murder and horrific destruction.

But how much criticism and how much -cheerleading- to criticize the schmuck was there by the media for taking off the summer? Not much.... biased pieces of shit "media"....

Well, yes. Surplus population. Means no jobs no function no purpose.

It's all over the world.

What are we going to do?

Love, C.

I am leaving on a week's vacation on Friday.

This would be a convenient time for me, Mr. Jones, to receive all gold and silver coins, loose or in envelopes, due me.

Constance #458: Means no jobs no function no purpose.

More like "no profit to be made off them". The idea of investing in people is just as foreign to the fat cats as the idea of investing in anything else that won't turn a profit next quarter.

Happy things:

I now live in a house with a total of three women and two cats. The cats are very slowly getting to know each other-- Iggy, who is gray and friendly, wants to be friends with Patina, who is tortoiseshell and wary. They have been within a few feet of each other without any hissing or growling.

Also, the things that went wrong with my move-- mold in the climate-controlled storage unit, mostly-- are now fixed, mostly. And the broken pipe on the car is fixed, so I can drive the three of us and none of the cats to the State Fair. A housemate and I did four hours of errands and got things for the house. I am considering what exact shade of purple to paint my room, and which, if any, color of green will match it.

Besides, cats adjusting to each other: hilarious.

Tim Walters @442: How can he have identified it if you can't tell me which one it is?

If we assume Jones has seen both of his coins, as David Harmon says is the conventional interpretation of the problem, and if Jones has only one gold coin, then Jones is singling out this coin -- referring to his one gold coin specifically -- when he says "At least one of my coins is gold."

If, on the other hand, Jones is holding two gold coins, then his statement is equivocal, and does not "identify" one coin over another.

Thus, there is a 2/3 probability that Jones' statement identifies a specific gold coin, and that the solution to the problem of the Lemurian coins is 1/4.

Tim Walters...

Oops, I guess that last argument doesn't hold water either... If Jones is holding only one gold coin, then the probability of him having more than Smith is 0.

I guess I'll have to concede this and move on.

1/6.