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May 20, 2004

Jonathan Vos Post
Posted by Teresa at 07:54 AM *

A distinctive body of comments that really deserve their own thread.

Comments on Jonathan Vos Post:
#1 ::: tnh/for JVP ::: (view all by) ::: May 30, 2004, 12:13 AM:

Jonathan Vos Post :: :: URL
Posted to Open thread 23
May 21, 2004 1:41:20 AM EDT


Tesseract: synonym for Hypercube. See:

Eric W. Weisstein. "Hypercube." From MathWorld--A Wolfram Web Resource.

Read, see pretty pictures, AND maneuver and rotate a simulated tesseract with the mouse. Watch the perspective shange it in fascinating way. Might give you an aesthetic/kinesthetic appreciation of hypercube/tesseract geometry!

Then click from there to:

Cross Polytope, Cube, Cube-Connected Cycle, Glome, Hamiltonian Graph, Hypercube Line Picking, Hypersphere, Orthotope, Parallelepiped, Polytope, Simplex, Tesseract and other pages at Eric W. Weisstein's MathWorld... IMHO the best Math Pages on the web.

"Polytope" is the multimdimensional generalization of polygon and polyhedron. It includes Tesseracts and other things.

If you google "Polytope Number" you'll find a page of mine that Google ranks #4 in the world, namely "Table of Polytope Numbers, Sorted, Through 1,000,000." This was inspired by Making Light's link to Erich Friedman's "What's Special About This Number?" Mine is longer, less colorful, and was darned hard work. I'm so happy to have met Erich through this blog!

Have survived 4th day at 5th International Conference on Complex Systems. Con Chair insist on having me ask Science Fiction personages from at least the New England area to come to ICCS 2006 here in greater Boston. Several Nobel laureates and the cloner of Dolly agree. Any suggestions?

I'm acting Session Chair for a series of panels on Science Fiction and Complexity; in Engineering, Biology, Physics, Social Systems, and so forth. probably some NSF and NIH money, maybe also Los Alamos money to help, but no guarantees. Con Chair agrees with my comment that Pakistan, Indonesia, India, China, Africa, Brazil underrepresdented this year per capita and in absilute attendees. Again, any ideas?
They didn't even know about Pocket programs and the floating Worldcon experts... Plenty of chances to expand Science Fiction's involvement with cutting edge interdisciplinary imaginative people from many countries and fields.


Jonathan Vos Post :: :: URL
Posted to Open thread 23
May 22, 2004 12:45:17 PM EDT



Visualization of 4-dimensional objects is possible for some people. It is extraordinarily rare to be "born with it," if possible at all. It can be learned with varying degrees of difficulty depending on the age that you start, how good you are at 3-D to begin with, and how good you are at geometry and math in general.

One well-documented case is Alicia Boole Stott, niece of THAT Boole, who invented Boolean Logic. He gave her a set of colored blocks with instructions on what colors could go next to what others. It was a toy designed to get her visualizing 4-dimensional shapes. She proved to be VERY good at doing so, into adulthood. She could also go 5-D and 6-D to some extent.

There was a burst of approximately 1,000 publications about the 4th dimension in the late 1800s. This forever influenced all nonfiction AND science fiction.

One Swiss gentleman who could visualkize 4-D was Ludwig Schläfli [umlaut over the a]

Born: 15 Jan 1814 in Grasswil, Bern, Switzerland
Died: 20 March 1895 in Bern, Switzerland


Schlaflipage by St.Andrew's University Math History

"Ludwig Schläfli first studied theology, then turned to science. He worked for ten years as a school teacher in Thun. During this period he studied advanced mathematics in his spare time..."

He discovered something profoundly important. Let me summarize:

* there are an infinite number of regular polygons, like an equilateral triangle, square, pentagon, hexagon... where all edges are the same length and all angles identical.

* there are exactly 5 regular polyhedra, with all faces the same and all angles the same: Tetrahedraon (triangular pyramid), Cube, Octahedron, Dodecahedron, Icosahedron. Everyone who plays Role Playing Games knows these now as dice shapes. They are called Platonic Solids.

* Schläfli, home, alone, over a decade, discovered that there are exactly SIX 4-D equivalents to Platonic Solids, namely the Pentatope (4-D Simplex), TESSERACT (a.k.a. hypercube, a.k.a. 4-D measure polytope), hyperoctahedron, hyperdeodecahedron, hypericosahedron, and one with no equivalent in any other dimension, the 24-cell.

* in all higher dimension, there are only 3: the equivalent of terahedron, cube, and octahedron.

His work was published, but ignored, in part, because so few could visualize. Alicia Boole Stott confirmed his work: she could "see" it was true.

When I was a child, I learned to visualize 4-D objects, in a hazy way. Later I became a mathematician, and now a part-time professor of math. Strangely, the visualization partially returned to me this year (age 53). So I have written 24 math papers for scholarly publication in the past 5 months, about half devoted to 4-D and higher dimension shapes.

My son is mad at me for never being able to find out the details of the colored blocks, and wishes he could visualize 4-D. There's a famous science fiction story about a toy that teaches children to visualize 4-D, and they use to to sort of Tesser away. Somebody else on this blog will tell you more, I bet.

One of the papers I co-presented 2 days ago in Quincy, Massachusetts, was on some multidimensional stuff by John Forbes Nash. You know, the subject of "A Beautiful Mind." His dissertation was sonlyt 28 pages long. It was about mult-D gemonetry, but changed Economics forever.

"The King of geometers" H.S.M. Coxeter just dies early this year. His book "Regular Polytopes" [a Dover paperback] helped me enormnously as a child. The photos and illustrations were beautiful. Now, much of those 2-D images of 3-D projections of 4-D objects are available on the web. I'd start at, if I were you. In theor search box, type "pentatope" or "hypercube" and manipulate 4-D objects with your mouse.

Some references from page on polytopes:

Bisztriczky, T.; McMullen, P., Schneider, R.; and Weiss, A. W. (Eds.). Polytopes: Abstract, Convex, and Computational. Dordrecht, Netherlands: Kluwer, 1994.

Coxeter, H. S. M. "Regular and Semi-Regular Polytopes I." Math. Z. 46, 380-407, 1940.

Coxeter, H. S. M. Introduction to Geometry, 2nd ed. New York: Wiley, 1969.

Eppstein, D. "Polyhedra and Polytopes."

Fukuda, K. "Polytope Movie Page."

MacHale, D. George Boole: His Life and Work. Dublin, Ireland: Boole, 1985.

Munkres, J. R. Analysis on Manifolds. Reading, MA: Addison-Wesley, 1991.

Sullivan, J. "Generating and Rendering Four-Dimensional Polytopes." Mathematica J. 1, 76-85, 1991.

Weisstein, E. W. "Books about Polyhedra."

Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, 1991.


Jonathan Vos Post :: :: URL
Posted to Open thread 23
May 22, 2004 1:17:58 PM EDT



BTW, a tesseract has 16 corners. I suspect that, if your friend could not see that, she was fooling herself, and you.

I would guess that there are roughly 100 people whose 4-D visualization is good enough that they can email each other and verbally explain things that the see, agree, and do new things from that dialog. I've read some of those emails. These folks are much better at it than I. But I can follow their dialog, aided by my lesser visualization, and have it make sense to me.

The definitive book on 4-D and multi-D polytopes has recently been issued in an expanded edition.

Convex Polytopes (Graduate Texts in Mathematics, 221) by Branko Grunbaum

$79.95 on Amazon. I've got a library copy. It is far too advanced for most people, even compared with other books I cited. But it summarizes the amazing work of the past 20 years or so, as built from 19th century (and earlier) insights.

Computers, you see, have changed the field forever. If you can visualize, and do the equations, and use computers, you can get what Schlafli got, a thousand times faster. But he did it first, alone, as an amateur. And there are others like him today, such as the Johnson of Johnson Solids (all edges the same length, don't care about angles or faces being the same).

It's taken me 37 years of computer work to finally realize the pupose of computing.

The Purpose of Computing is not Numbers or Pictures. The Purpose of Computing is Insight!"

and there are many roads to insight...


Jonathan Vos Post :: :: URL
Posted to Further excruciating embarrassment
May 22, 2004 2:27:03 PM EDT


This Chalabi-Iran fisco is an example of why Professor Philip Vos Fellman and I have been writing papers for 3 years (constituting most of a book) on what we've denoted Disinformation Theory. We reference classic Information Theory (invented by Claude Shannon (whom I knew personally yada yada) and many works of military strategy, including only recently declassified studies. We also believe that there is an optimal amount of disinformation for a corporation to put in their Annual Report.

But, to compare Bush et al. with the collapse of Periclean Athens:

Sailing the Wine Dark Sea: Why the Greeks Mattered

author Thomas Cahill
pages 304
publisher Doubleday
rating Excellent, 5 stars
reviewer Ursus Maximus
ISBN 0385495536
summary This book explores the Greek contribution to Western Civilization

"... the western way of total warfare has dominated the planet ever since; and it appears that Donald Rumsfeld and Dick Chaney are well versed in Mr. Hanson's theories, not to mention Greek hubris."

"The lessons for the USA in its war on terrorism alone are compelling, if not down right chilling. Central to the cultural echoes provided is a speech from Pericles, ruler of Athens at the beginning of the Peloponnesian War, a mighty struggle that lasted for 30 years, beginning with Athens at the height of its imperial, cultural and financial powers, and ending with Athens defeated and subjected to domination by Sparta and her allies, never again to regain the zenith of her glory and might."

"At an annual ceremony honoring and burying the bones of her young war dead after the first year of the 30 years war, Pericles orated about the Greek forefathers, and he sounds a lot like a contemporary American politician:

" '...generation after generation in unchanging and unbroken succession, they have, by their hard work and courage, handed down to us a free country...' "

"This comes from what is by far the longest of the many quotes Cahill intersperses in his book, and it sounds ever so much like George W. Bush..."


Jonathan Vos Post :: :: URL
Posted to Further excruciating embarrassment
May 22, 2004 2:38:35 PM EDT


Hortensia Patel comments (on the blog comments to the above):

"Certainly the parallels with today's "War on Terror" hysteria are striking:"

" 'They altered the accepted usage of words in relation to deeds as they thought fit. Reckless audacity was termed courageous loyalty to party; prudent hesitation, specious cowardice; moderation, a cover for spinelessness; and an ability to understand all sides, total inertia. Fanatical enthusiasm was rated a man's part; and cautious deliberation, a euphemism for desertion.' "
(From Thucydides' History of the Peloponnesian War [] III 82, written in the 5th century BC. Sound familiar?)


Jonathan Vos Post :: :: URL
Posted to Open thread 23
May 22, 2004 4:27:26 PM EDT


On an apparently unrelated subject, as I love to quote colorfully good writing, and writers on their craft:

"Leaves" in John Updike's new collection "The Early Stories: 1953-1975":

"The grape leaves where they are not in each other's shadows are golden. Flat leaves, they take the sun flatly, and turn the absolute light, sum of the spectrum and source of all life, into the crayon yellow with which children render it. Here and there, wilt transmutes this lent radiance into a glowing orange, and the green of the still-tender leaves -- for green persists long into autumn, if we look -- strains from the sunlight a fine-veined chartreuse."

Then a snippet of an interview:

"Writing is a way of taming the world," he says, "turning the inchoate, often embarrassing stream into a package."

The I's Have It
At 72, John Updike Still Hasn't Run Out Of Things to Write About . . . John Updike
By Linton Weeks
Washington Post Staff Writer
Wednesday, May 5, 2004; Page C01

He is one of the finest sometime-author of Science Fiction, and Science Fiction Poetry, you know...


Jonathan Vos Post :: :: URL
Posted to Open thread 23
May 23, 2004 12:47:32 PM EDT



(1) an interesting question. It leads to story ideas. "Just what is it that 4-Ds know that they've been hiding from us; and who -- or WHAT is behind it?"

(2) As soon as a few more of my papers get published, I'll find out if "the 4D community" (as you put it) welcome me with open arms.

(3) I've gotten some implicit recognition from 4-D authors such as
Cliff Pickover
Rudy Rucker

(4) At the 5th International Conference on Complex Systems, there were several discussions on 4-D geometry. As I've mention John Forbes "A Beautiful Mind" Nash used it to revolutionize Economics. One gentleman came over to my breakfast table and began sketching a chaotic system of differential equations defined over a pentatope (4-D Simplex) and I knew exactly what he was doing, and he knew I knew. But the other guy at the table was baffled. "Doesn't that part rotate around this point or that axis?" he said. Of course not, I said, "This is 4-D, so this 3-D part rotates around that 2-D plane." The newcomer agreed, and showed how, in what was, to me, obvious, but the other professor was baffled.

(5) I scribbled one of the three formulae about pentatopes that I discovered, and several people understood immediately.

(6) I'll be contacting a few of the top experts relatively soon, maybe before more papers are accepted. But the best-known leader, John Horton "Game of Life" Conway (whom I met in California in 1970 yada yada) admits that his office is utterly filled with papers that he hasn't yet had time to read.

(7) But anyone can do the arithmetic to tell certain things about 4-D shapes, without any visualization. For example, a generalization of
Descartes-Euler Polyhedral Formula

In 3-D, for any simply-connected (i.e. in one piece) polyhedron:

V + F - E = 2

where V is the number of vertices (corners), F is the number of faces, and E is the number of edges. Try that for the cube (V=8, F=6, E=12) or a triangular pyramid a.k.a. tetrahedron a.k.a. 3-D simplex (V=4, F=4, E=6), or other shape.

In 4-D we have (as discovered by the same Schlafli I wrote about before), there is an equivalent with one more term in the formnula, for the number of "facets" (i.e. 3-D parts).

Even without visualization, one can apply this formula from the verbal descriptions of many 4-D polytopes.

For instance: look a a cube as two squares (the top face and the bottom face) with each corner on top joined by a vertical edge to the corresponding vertex of the bottom square. We have 4 corners on the top square, plus 4 corners on the bottom square, so 4+4=8 corners of the cube. We have 4 edges on the top square, 4 edges on the bottom square, and 4 edges joining top and bottom, for 4+4+4=12 edges of a cube. Fine.

Now, for a tesseract, we can say it's made of two cubes (a top and bottom) with each of the corners of the top cube joined by an edge to the corresponding corner of the bottom cube. We have 8 vertices in each of the 2 cubes, for 16 vertices of the tesseract. We have 12 edges on each cube, plus one edge each for the 8 corners of the top cube joining the 8 vertices of the bottom cube, for 12+12+8=32 edges of the tesseract.

Does that make sense without visualization? It helps to look at pictures of tesseracts on the mathworld site I mentioned, plus its links.

So, the 4-D community can't fool all the 3-D people all of the time.

Okay, I'm ready to teach summer school Intermdiate algebra on Monday, day after tomorrow now. But they are likely to be surprised by some of what I teach;)


Jonathan Vos Post :: :: URL
Posted to Further excruciating embarrassment
May 25, 2004 10:57:33 AM EDT


Robert MacNamara was video-interviewed from the banquet at the 5th International Conference on Complex Systems, last week in Quincy, Massachusetts. I left the ballroom for the duration of that part of the event. A few others joined me in the silent protest. One told me: "He tried to kill us; I take that personally." Another commented: "He's trying to rewrite history to appear to be against the very policies of his that failed in Vietnam. Might as well be Rumsfield." A third complained that MacNamara's abuse of Systems Analysis discredited math/computer methodology in Social Systems for the Government for a very long time.

But we all rushed back to hear Keith Campbell speak and show videos on how he cloned Dolly. My question to Keith was that, from my teaching a Cloning class to over 100 students over the years, my students taught me that the Islamic world is actively in favor of Human Reproductive Cloning. It is the "cure" for the "disease" of sterility for married couples who desire a baby. Also, if Allah did not want us to have the technology, we wouldn't have it. Dr.Campbell agreed, but thought that my extrapolation that the first birth of a cloned human would be in an Islamic country. "That's Science Fiction," he said. But then spoke well of Science Fiction.


Jonathan Vos Post :: :: URL
Posted to Further excruciating embarrassment
May 25, 2004 11:08:30 AM EDT


Also, there was discussion over Samuel Adams beers and lobster rolls at the ICCS 2004 about Abu Gharib torture. One government-connected researcher told me:

"On the one hand, everyone held long term at Abu Gharib is, at a minimum, a murderer, as opposed to those rounded up and released soon. On the other hand, if we had a single very-high-level terrorist there, the best way to get him to talk would not be these amateur theatrics with hoods and dogs. It would be to transfer him for a week or two to the worst jail in Abu Dhabi. He would be beaten and raped repeatedly by his own Islamic malcontent colleages. On transfering him back to Baghdad, he would tell us anything to prevent permanent retransfer to Abu Dhabi."

I can't vouch for the accuracy of that claim, of course, but it was an interesting take -- from someone who favors torture! Even he thought that we screwed up at Abu Gharib. Makes me wonder...

There was also someone at ICCS2004 who'd worked for AID in Pkistan along the Afghan border. He was generally in favor of the Pakistan militray, but contemptuous of how the US is handling things in Pakistan, Afghanistan, and Iraq.

Germans (well-represented at the con) and British (ditto) all told me how well they love the USA, but condemn Bush/Cheney/Rumsfeld. "Don't they know," one asked me, "how many empires collapsed because they tried to over-extend?"


Jonathan Vos Post :: :: URL
Posted to Open thread 23
May 25, 2004 2:39:26 PM EDT


BEYOND VISUALIZATION.... Below, per our thread on visualizing the 4th dimension, is an excerpt from

When Even Mathematicians Don't Understand the Math

May 25, 2004
The New York Times

To most of us, smudgy white mathematical scrawls covering a blackboard epitomize incomprehensibility.

The odd symbols and scattered numerals look like a strange language, and yet to read them, neurologists tell us, we would have to use parts of our brains that have nothing to do with what we normally think of as reading and writing.


"It is a bit like trying to explain football to people who not only have no understanding of the word 'ball,' but are also rather hazy about the concept of the game, let alone the prestige attached to winning the Super Bowl," wrote Dr. Ian Stewart, professor of mathematics at the University of Warwick in England, in an email message.

Asked if there exist mathematical concepts that defy explanation to a popular audience, Dr. Stewart, author of "Flatterland: Like Flatland, Only More So" replied: "Oh, yes - possibly most of them. I have never even dared to try to explain noncommutative geometry or the cohomology of sheaves, even though both are at least as important as, say, chaos theory or fractals." ...

The Hodge conjecture deals not only with cohomology classes, a complicated group construct, but involves algebraic varieties, which Dr. Devlin describes as generalizations of geometric figures that really do not have any shape at all. "Those equations represent things that not only can we not visualize, we can't even imagine being able to visualize them," he said. "They are beyond visualization." This difficulty points to a math truism that ultimately framed his entire project.


In fact, it is difficult to explain what math is, let alone what it says. Math may be seen as the vigorous structure supporting the physical world or as a human idea in development. Some mathematicians say it is not in the same category as biology, astronomy or geology. While those fields have empirical systems of experimentation and discovery, some might say mathematicians rely on something more intuitive.

"It isn't science," said Dr. John L. Casti, the author of "Five Golden Rules: Great Theories of 20th-Century Mathematics and Why They Matter." "Mathematics is an intellectual activity - at a linguistic level, you might say - whose output is very useful in the natural sciences. I think the criteria that mathematicians use for what constitutes good versus bad mathematics is much more close to that of a poet or a sculptor or a musician than it is to a chemist."


"Our brains evolved so that we could survive out there in the jungle," he said. "Why in the world should a brain develop for the purpose of being at all good at grasping the true underlying nature of reality?"

Copyright 2004 The New York Times Company


Jonathan Vos Post :: :: URL
Posted to Bad advice on cover letters
May 25, 2004 2:53:34 PM EDT


Poetry scammer also run conventions, or conferences, or whatever starts with "con."

Once I was in Reno (I think it was) for a real conference, and noticed that the same hotel was hosting a big Poetry thing.

I picked up free registration materials. I stopped in on a plenary event in the main ballroom. I listened. It was not bad, for a solo presentation. But the audience members were paying thousands of dollars, assuming that the advice would make them professionals. Several attendees told me so. And they were happy, so far....

BTW, there are probably fewer than 10 people in the USA who actually support themselves in style from poetry royalties, not counting grant recipients, staff at magazines, greeting card writers, and writers-in-residence.

I spoke with the Con Chair. To paraphrase, I said "I'm an internationally known poet, co-author of award-nominated published poems with Ray Bradbury and Nobel Laureate Richard Feynman... yada yada ... can you slot me in for a presentation at the last minute? I wouldn't ask more than that my room be comped and maybe $1,000 honorarium."

His reply, carefully couched, translates as: "kid, I got a good scam going. I ain't gonna cut you in. But go run one of these yerself... there's an infinite number of victims out there..."


Jonathan Vos Post :: :: URL
Posted to Open thread 23
May 25, 2004 3:13:57 PM EDT


Math and your birth year:

the 4-digit numbers we may relate to best are the years of the 20th century, in which most of us were born. Check out also:

What's Special About This Number?

to which Teresa previously linked. So here's a tiny excerpt from
Table of Polytope Numbers, Sorted, Through 1,000,000
to give you something to drop into conversation the next time someone asks about your age...

1900: the 191-gonal Pyramidal Number 191Pyr(4)

1910: the 192-gonal Pyramidal Number 192Pyr(4)

1911: Hendecagonal Number, or 11-gonal number,
also the Heptagonal Pyramidal Number HepPyr(13),
also the 56-gonal Pyramidal Number 56Pyr(6)

1915: the 97-gonal Pyramidal Number 97Pyr(5)

1918: the Heptagonal Number Hep(28)

1920: the 193-gonal Pyramidal Number 193Pyr(4)

1923: the 31-D Hyperoctahedron 31-Cross(3)

1925: the Hexagonal Pyramidal Number HPyr(14)

1926: a Pentagonal Number P(36),
also the Heterogenous Jonathan Number P(S(6))

1930: the 194-gonal Pyramidal Number 194Pyr(4)

1932: the 36-gonal Pyramidal Number 36Pyr(7)

1935: the 98-gonal Pyramidal Number 98Pyr(5)

1936: a Square, S(44)

1940: the 195-gonal Pyramidal Number 195Pyr(4)

1946: the 57-gonal Pyramidal Number 57Pyr(6)

1950: the 196-gonal Pyramidal Number 196Pyr(4)

1951: Centered Hexagonal Number CH(26)

1953: the Triangular Number T(62)

1955: the 99-gonal Pyramidal Number 99Pyr(5)

1960: the 197-gonal Pyramidal Number 197Pyr(4)

1965: the 18-gonal Pyramidal Number 18Pyr(9)

1968: the 25-gonal Pyramidal Number 25Pyr(8)

1970: the 198-gonal Pyramidal Number 198Pyr(4)

1975: the 100-gonal Pyramidal Number 100Pyr(5)

1976: Octagonal Number O(26)

1980: the 199-gonal Pyramidal Number 199Pyr(4)

1981: the 58-gonal Pyramidal Number 58Pyr(6)

1985: a Centered Square Number CS(32)

1988: the 37-gonal Pyramidal Number 37Pyr(7)

1990: the Stella Octangula Number StOct(10),
also the 200-gonal Pyramidal Number 200Pyr(4)

1995: the 101-gonal Pyramidal Number 101Pyr(5)

1999: Centered Triangle CT(37)

2000: the 201-gonal Pyramidal Number 201Pyr(4)

2002: the 9-Simplex Number 9-Simplex(6),
also the 5-Simplex Number, 5-Simplex(10)

2010: the 202-gonal Pyramidal Number 202Pyr(4)

Any questions? Quiz in next class. Whoops, sorry. I just started teaching my accelerated 6-week Intermediate Algebra for the Visually Gifted class yesterday, at Woodbury University. Lots of slides of Da Vinci and M. C. Escher. Building polyhedra out of toothpicks. Math is hard. Let's go shopping.


Jonathan Vos Post :: :: URL
Posted to Open thread 23
May 25, 2004 3:36:05 PM EDT



I recall that deathbed reference. But who was the actor, again?

Based on years of argument with Marvin Minsky, Marvin finally published his mathematical theory of comedy. Don't remember where, though.

Others have speculated on bifurcations and Catastrophe Theory models of comedy. But good comedians do it without math. My 1st cousin, stand-up comic, Rich Vos, is a fine example. He earns 3 times as much now, since he was a finalist on "Last Comedian Standing." If he knew math, he'd probably make pi times as much.

The rigged winner, Dat Phan, did keep a detailed graphpaper database of his timing, shows, and audience reaction.


Jonathan Vos Post :: :: URL
Posted to Open thread 23
May 26, 2004 1:58:54 AM EDT


Paula Helm Murray:

Your friends might know (I don't remember) but there was once a professional American football player with a PhD in mathematics. And now there is an MIT graduate in Major League Baseball. Neither (so far as I know) Inuit.

John Forbes Nash tackled one unsolved math and physics problem after another, wrote a 28 page dissertation that changed Economics forever, and then went nuts. Or was it the other way around?

I thought I'd hit the wall when I was taking entirely graduate courses, while an undergraduate, and nearly helpless in Algebraic Number Theory. But I did go on to Category Theory in grad school, and there were certain concepts that the professor could not, in an entire semester, get me to comprehend. That's why I'm so surprised to suddenly be learning math now that scared me back then.

I'm still thinking about the story idea that the "4-D community" is hiding something from the rest of the world. But what? and Why?

I think it should end with a sentence such as:

"Who wants to keep it a secret?" he asked, his blue-gray eyes narrowing. "Not whom ... WHAT!"

At this Complex Systems conference, some were initially dubious about my credentials.

"You say that you're a part time adjunct professor of math at some funny little private college in Burbank that I never heard of, eh? SO, if you're a Mathematician, What is your Erdos Number?

"Five," I said. "I coauthored with Richard Feynman, and he coauthored with Murray Gell-Mann, and he..."

"Okay," he said, "You win. You're a mathematician."

Okay, class, everybody know what an Erdos Number is? Just google "erdos" to find out...


Jonathan Vos Post :: :: URL
Posted to Taking your own bad advice
May 26, 2004 2:19:49 AM EDT


I started as a Physics major at Caltech, switched to Astronomy, dropped out when my mother was dying, came back and restarted my Sophmore year, asking "which degree has the fewest required courses?"

That was Math, so I converged asymptotically towards a B.S. in Math. But someone noticed that so many of my electives were English Lit (and you all like to read, too!) that if I took a few more English courses, I could get a degree in that, too. So I got a double B.S. from Caltech in Math and English Lit. Then M.S. at UMass/Amherst in Computer and Information Science. BUT -- technically, I went to UMass because I was offered a joint fellowship in Computers and Linguistics. But when I got there, it turned out that Linguistics never knew that Computers had made me that offer. I'd taken Psycholinguistics at Caltech, and Computational Linguistics, and Chomskian Syntax, and stuff. So my M.S. was Cybernetics and A.I., and I was closing in on an MFA in Poetry, too, before my Ph.D. (ABD) bizarre situation shoved me out of the academic world until a random recent reentry at the professorial level, starting in Astronomy, of all things. Not counting the two MBA dissertations I wro
te for Fortune 100 executives, for cash under the table. Got them both MBAs with Honors from top schools.

But if there's a worldcon panel on linguistics, you've got to get Sheila Finch! She's so on top of Xenolinguistics! And Somtow Sucharitkul learned Lakota to make his Native American werewolves linguistically credible. And, oh wow! You MUST have Dr. Suzette Haden Elgin!


Jonathan Vos Post :: :: URL
Posted to Open thread 23
May 26, 2004 11:27:52 AM EDT


Andy Perrin,

Feynman and I worked on some Physics -- notably negative probability events in Quantum Mechanics. We also took an art class together (old-fashioned Lithography). But our only coauthorship was -- a poem!

"Footnote to Feynman", Jonathan V. Post and Richard Feynman,
[Engineering & Science, Caltech, Pasadena, CA, Vol.XLVI, No.5, p.28,
ISSN: 0013-7812, May 1983; reprinted in Songs from Unsung Worlds,
ed. Bonnie Bilyeu Gordon, intro by Alan Lightman (award winning author
of Einstein's Dreams), Birkhauser Boston/AAAS,
hardcover ISBN: 0-8176-3296-4, paperback ISBN: 3-7643-3296-4, 1985

It was also set to music by a student getting a Masters degree in composition.

By golly, I can't find the text on the Web either. I'll put it onb my web domain real soon. Thanks for the reminder!

The countless discussions we had on Nanotechnology (before the field was named, of course) are what led to my doctoral work.

I've made him the amateur detective/magician in my novel manuscript "Axiomatic Magic."


Jonathan Vos Post :: :: URL
Posted to Open thread 23
May 26, 2004 11:41:07 AM EDT


But speaking of coauthorship, allow me to hotlink and excerpt from:

Thumbing His Nose at Academe, a Scholar Tries to Auction His Services

CO-AUTHOR FOR SALE: In a society devoted to "reality shows" and rampant commodification, it had to happen some time. Late last month an independent scientist auctioned off his services as a co-author on eBay, with the promise of helping the highest bidder write a scientific paper for publication. The offer even had the added allure of a linkage with the legendary mathematician Paul Erdös.

But a few researchers saw the online auction as a net negative. Jose Burillo, an associate professor of mathematics at the Polytechnic University of Catalonia, in Spain, entered a fake, inflated bid of more than $1,000 in hopes of stopping the auction. "Nobody should pay anybody for writing or collaborating on a scientific project," he says. "This could open the door to many unethical problems."

The auction began as a bit of fun, admits William A. Tozier, a consultant in Ann Arbor, Mich., who specializes in machine learning and artificial-intelligence research. "I undertook it as a combination of a joke and conceptual art and a bit of an experiment in social networks," he says. The idea builds on the reputation of Erdös, a Hungarian mathematician who died in 1996. A prolific researcher, with more than 1,400 published papers, he spent the last several decades of his life moving from one colleague's house to another's, staying for extended periods at each place and collaborating on solving problems.


Jonathan Vos Post :: :: URL
Posted to Harry of Five Points
May 26, 2004 12:35:30 PM EDT


Hats off! Huzzah! Brilliant.

And I speak from experience, as the author of the (subsequently republished in a textbook on Shakespeare):

Jonathan Vos Post

a short, short story;
winner of Honorable Mention in the
1995 International Imitation Raymond Chandler Competition;
approx. 500 words

"Something was rotten in Denmark, rank and gross, as rotten as a dame
named Gertrude in bed with her husband's killer while the caterer recycled the
funeral baked meats for the wedding reception, at which the bride did not wear

"Hamlet was sharp for a prince, good with a knife, but not sharp enough to handle
his old man kicking the bucket with an earfull of murder."

"My name's Horatio, Hamlet's gumshoe buddy, trying to stay clean in a dirty castle.
A grizzled ghost pleaded the Fifth when I gave him the third degree, then split the scene
when the cock crew, like a guilty man before a marshall serving a summons."


I've been collection rejection letters for over a year for "Raymond Chandler's Lord of the Rings" -- which is uncomfortably novelette length, unless someone wants to pay me to expand it...

Mike Ford is consistently amazing.

Remember that Twlight Zone episode where a TV writer summons the ghost of Shakespeare to literally ghost-write sitcom episodes?

I heard from one of my Hollywood contact, btw, that there had been a special screening of "Troy" to studio executives. One rushed from the room and barked to his secretary: "get me the agent for this Homer guy. I want to buy an option on his next book."


Jonathan Vos Post :: :: URL
Posted to Open thread 23
May 26, 2004 11:24:26 PM EDT


Jill Smith:

I couldn't see the point of Trigonometry when they tried to get me to take it in 7th grade. Surveying? Boring. Height of a tree? Puh-leeze. So I taught myself Calculus froma college textbook the summer after 7th grade. Used it to figure out the trajectories of my model rocket flights. When it came time for Trigonometry, I learned as a Calculus thing. That is, in terms of the power series of the functions. Made things more clear, to me.

But Music! Yes! Profoundly mathematical, and profoundly human at the same time. As a Music Theory person, were you taught WHY there's a cycle of 5th and a chromatic scale? I mean, because there are 12 semitones in an octave, and the 5 of a cycle of 5ths does not divide 12, and so orbits through the whole octave, hitting each of the 12 notes. If there were, say, 31 (a prime) tones in an octave, there would be a cycle of 3rds, a cycle of 4ths, a cycle of 5ths, a cycle of 6ths, a cycle of 7ths, and so on. Or if 51 tones in an octave... And many different cultures do have alternate temperments.

And the mathematics of overtones, the psychophysics of what makes discords maximize at quarter-tones; so much math concealed in beauty.

How many possible 12-tone rows? A Group Theory question.

It is no coincidence that so many scientists love music, and Saint Albert Einstein played the violin...

But you make another good point. A rotten teacher can spoil any subject, and great teacher can inspire almost any student in almost any subject.

I was told that I had zero musical skill. I resented the imposed limits. I took an intense year of Classical Guitar from Barry Eisner, a student of Chrispher Parkening. Played some concerts at community colleges: baroque, Beatles, and original compositions. Played in some pick-up rock bands, rhythm guitar plus lyrics. Wrote a song that hit MTV. Publuished an underground music newspaper. And now have produced Opera. But, oddly enough, I really don't have musical talent as such. Everywhere I've gone. I've seen talented performers mired in poverty, and obvious no-talents raking in the big bucks from good managament and marketing. Music can break your heart, unless you do it because you love it, and have no choice.

And you don't need to know the math behind the music. But there it is... Pythagoras found it, and broke music loose from Musika -- left the dance and lyrics and masks in the dirt, and scended to heaven, as a divine subject. Opera put the pieces back together, and computers sealed the marriage.

I'm just rambling here. Riffing.

Can they turn your credits into frequent flyer miles?

Paula Helm Murray: I think that means that your Erdos Number is infinity. You are infinitely far the from the center. Erdos had an Erdos Number of zero. Any of the 575 or so people who coauthored with him have an Erdos Number of 1. Any of the 3,000 or so who coauthored with them have an Erdos Number of 2. I, with an Erdos Number of 5, am not even so far from the center. The diameter of the Erdos system is 28. There exist two mathematicians who take 28 links of coauthorship to connect them.

And I know the guy, Bruce Resnick, who has the lowest known total of Erdos Number + Kevin Bacon Number. He has an Erdos Number of 1 (coauthored with Erdos) and a Kevin Bacon number of 2 (appeared in "Goodwill Hunting" with someone who was in some other movie with Kevin Bacon). Unless Kevin Bacon writes a math paper...

Robert Silverberg wrote an essay once on the chains of coauthorship in Science Fiction...

They talk of "the small world theorem."

Whoops! Dinner time. Must go now. But Einstein was a rather good violinist, they say. Played with deep feeling. Might have been 2nd or 3rd fiddle in a minor orchestra. But the Music of the Spheres tempted him away from the concert hall...


Jonathan Vos Post :: :: URL
Posted to Open thread 23
May 26, 2004 11:56:43 PM EDT


*munch munch*, *sip, sip* see, for instance:

Mathematics and Music

Mathematics, Music and the Arts: Making Finite Math Relevant to the Arts Major

The Sound of Mathematics

The mathematics of electronic music

Oh, dessert time new. Bye!


Jonathan Vos Post :: :: URL
Posted to Open thread 23
May 27, 2004 9:32:15 AM EDT


Fun pages about Erdos Numbers:

Some Famous People with Finite Erdös Numbers

Thrill at how "Felipe Voloch found what seems to be the oldest mathematicican known to have a finite Erdös number, Richard Dedekind (1831-1916). His number is at most 7, via this path: H. Weber -- W. Jacobsthal -- R. Fuchs -- L.Hopf -- A. Einstein -- E. Straus -- P. Erdös."

Laugh at how, among Nobel Laureates, Albert Einstein [1921, Physics] has an Erdos Number of 2, while Erwin Schrödinger [1933, Physics] has an Erdos Number of 8.

But wait... there's more!

Check out:
The Erdös Number Project Extended

to answer these burning questions:

* Who is The Youngest to Gain an Erdös Number?
* Which Movie Star has the lowest Erdös Number?
* Does Joan Baez have an Erdös Number of 3 ?
* Do any animals have an Erdös Number ? Is it possible ?
* Just what are the principles of Mathematical Genealogy ?
* Did my Partner Acquire an Erdös Number on marriage ? If Not, How can he/she acquire a finite one?
* Can a character in a novel gain an Erdös Number ?
* "Basic Rule for Assigning Erdös Numbers: Was enough Chutzbah involved in the claim for it to be taken seriously ???"


Jonathan Vos Post :: :: URL
Posted to Open thread 23
May 27, 2004 10:02:09 AM EDT


Source: Paul Hoffman, de man die van 9etallen hield, 1998

Paul Erdös (Hungarian mathematician, 1913-1996) had his own particular language:

* Supreme Fascist = God (Also abbreviated as SF)
(person who hides Erdös's socks, glasses, Hungarian passport and kept the
best equations to himself)
* straight from the book = beautiful, elegant proof
(from the book of the SF)
* boss = woman
* slave = man
* captured = married
* liberated = divorced
* recaptured = remarried
* epsilon = child (for the mathematical symbol)
= a little
* to preach = to give a math lecture
* to exist = to do math
* to die = to stop doing math
* trivial being = Someone who does not do math
* to leave = to die
* to arrive = to be born
* Joe = USSR (for Joseph Stalin)
* Sam = USA (for Uncle Sam)
* Sam and Joe show= International news
* Ned = Australia (for Ned Kelly, a famous Australian
bandit from the 19th century)
* János = Hungary (for János Kádár, ruler of Hungary 1956-1988)
* On the long wavelength = communist (for red)
* On the short wavelength = fascist (opposite of red)
* noise = music
* poison = alcohol
* my brain is open = I am ready to do mathematics
* what was that when it was alive? = what kind of meat is that?


Jonathan Vos Post :: :: URL
Posted to Open thread 23
May 27, 2004 10:21:41 AM EDT


Mathematics and Sex:

"Combinatorics without Algebra and Topology is like Sex without Love"
-- Anthony Joseph

[Omar Foda's corollary of Joseph's maxim: "Algebra without Combinatorics is like Love without Sex"]

"Mathematicians are like lovers...; Grant a mathematician the least principle, he will draw you a consequence that you must grant him as well, and from that consequence yet another...; and in spite of yourself, he will carry you to out-of-sight places that you would never believe existed. These two kinds of people, the mathematicians and lovers, always take more than what one has given them."
--- Fontenelle, quoted by Lucas, cover of Recreations Mathematiques IV (new printing: A. Blanchard, Paris, 1979)

"There is something inhuman and vaguely pornographic about statistics.... Pornography, on the other hand, with its loosely bound sequences of storyless sexual couplings (or triplings) often has the feel of a statistical survery."
-- John Allen Paulos (Once Upon A Number, Fall 1998)

above quotes excerpted from:
Doron Zeilberger's Plan


Jonathan Vos Post :: :: URL
Posted to Open thread 23
May 27, 2004 10:59:13 AM EDT


I'd lost my email to myself about this when Earthlink wiped out one of my family's accounts, so I've just, this morning, very painfully reconstructed my length-5 Erdos Number path [Post, Feynman, Gell-Mann, Glashow, Kleitman, Erdos], to clarify the procedure...

(5) Post to Feynman [Nobel Prize, Physics, 1965]:

"Footnote to Feynman", Jonathan V. Post and Richard Feynman,
[Engineering & Science, Caltech, Pasadena, CA, Vol.XLVI, No.5, p.28,
ISSN: 0013-7812, May 1983; reprinted in Songs from Unsung Worlds,
ed. Bonnie Bilyeu Gordon, intro by Alan Lightman (award winning author
of Einstein's Dreams), Birkhauser Boston/AAAS,
hardcover ISBN: 0-8176-3296-4, paperback ISBN: 3-7643-3296-4, 1985

(4) Feynman to Gell-Mann [Nobel Prize, Physics, 1969]:

R. P. Feynman, M. Gell-Mann & G. Zweig, Group U(6) \Omega U (6) generated by current
components, Phys. Rev. Lett. 13 (1964), 678-680

(3) Gell-Mann to Sheldon Lee Glashow [Nobel Prize, Physics, 1965]:

Sheldon L. Glashow & Murray Gell-Mann, Gauge theories of vector particles, Ann. Physics 15 (1961), 437-460

(2) Glashow to [his brother-in-law, the combinatorist] Daniel J. Kleitman:

S. L. Glashow & D. J. Kleitman, Baryon resonances in W 3 symmetry, Phys. Lett. 11 (1964), 84-86

[Because of the above, Glashow shares with Einstein the distinction of being, up until now, the only Nobel-winning physicists with Erdos number = 2]

Kleitman to God-Emperor Paul Erdos:

[7 papers by this pair, the earliest being in 1968]

I'll also comment that both Gell-Mann and Erdos were among the roughly 1,500 scientists who signed "World Scientists' Warning to Humanity", 18 November 1992


Jonathan Vos Post :: :: URL
Posted to Open thread 23
May 27, 2004 2:41:13 PM EDT


Andy Perrin:

I forget the name of the university, but their Math department had scheduled its annual lecture by a distinguished visitor. To their astonishment, the auditorium was packed, standing room only. Seems that the Events secretary had typed the lecture title:

"Prisms and Convex Sets"


"Prisons and Convict Sex"

Kip W:

Step 1: check official Erdos Project site. No listing for Jon Singer, or, indeed, anyone with last name Singer. Hence Jon Singer's Erdos Number cannot be 1.

Step 2: Next, search on their list
for "singer." This turns up such as "Weisinger, J. R.," "Bissinger, Barnard H.," "Schlesinger, Ernest C.," "Singer, Michael F.," but no more. Hence Jon Singer's Erdos Number cannot be 2 (as of February 2, 2002, anyway).

Step 3: Google "Jon Singer." This turns up:

Citizens of Summerspace,
Welcome to JoJo Bazilian's
Regrettably Destructive Testing Service.

Jon, a self-confessed polymath, mentions: "After two years (mid-1997 to mid-1999) on my most recent contract at Microsoft, working on the IIS 4.0 Resource Kit and then the IIS 5.0 Resource Guide, I was asked by The Joss Institute to become a full-time Research Technologist for three to six months on a trial basis."

"The work at Microsoft was challenging, stimulating, and good; I was in an excellent group, with thoughtful interesting people. Working with the IIS engineering and development teams was also good: the developers are a good crew."

"...But we came to the end of the cycle for what I was doing, and the Institute's offer was one I couldn't turn down: I had been trying for over two decades to figure out how I could find exactly such a job, and had gotten noplace, so when it landed in my lap I leapt upon it with all sixteen feet. Since late November, 1999, I have been in Laurel, MD. Here I get to do research of various small sorts, and learn many things. It is truly and abundantly joyous. Moreover, it is the only job I've ever had that I really truly fit...."

Step 4: ask him. Feel free. If he doesn't know, ask if he's still at The Joss Institute. If so, ask them to pay me (or someone) to keep searching, until Jon's Erdos Number is firmly established.

That's sort of the process...

BTW, Dr. George Hickney (Erdos Number = 3) emailed me to say:

"The Erdos Project answers [the question of what is the largest finite Erdos Number] when they talk about the diameter of the connected part of the graph. It's 28. The highest Erdos number is 15. There is a person in the graph such that the highest Np is 14; that person has an Erdos number of 2 or so, I think. The largest
disconnected collaboration graph had 39 nodes (a group of engineers mostly in China). This, of course, represents a snapshot on a given day for a given database."

"The Erdos question, as usually posed, does not address issues of identity of co-authors. That's a hard problem (what's N. Bourbaki's Erdos number? Or did Bourbaki never collaborate?)"

"These questions, surprisingly, don't affect the graph properties very much. One variation which gives the graph a higher diameter but doesn't change statistics is to only count collaborations
between exactly two authors. Another variation, which makes the disconnected piece much larger, is to require N collaborative works per edge. As you can see from the attached file [not attached here: VERY long], N=2 removes most of the Erdos collaborations."

Dr. Geoffrey Landis pointed out to me [Jonathan] that there was a physicist who listed his cat as a coauthor on a published Physics paper. So more than one animal has a finite Erdos Number. [one of the pages I linked to explains how a horse got an Erdos number].

Now I need to track down some of my Caltech classmates with Erdos Number = 1 (Andrew M. Odlyzko and Bruce A. Reznick to begin with) and see if they want to coauthor with me. My son strongly supports this effort. My son, you see, currently has an Erdos Number of 6, through me, as does my wife. For that matter, through me, Arthur C. Clarke and Ray Bradbury and oodles of others in the Science Fiction community have finite Erdos Numbers. I would be surprised if Clarke doesn't have a lower one than that...


Jonathan Vos Post :: :: URL
Posted to Open thread 23
May 28, 2004 12:30:30 PM EDT


Here's another math visualization example. I'll give you hotlinks, in a minute, to show you what this all looks like.

Imagine a square pyramid. Now imagine two of them, identical in size. Glue the two together, square-base to square-base.

What you should see in your mind's eye: an Octahedron, consisting of 8 equilateral triangles, with 4 meeting at each of 6 corners. The Octahedron is one of those Platonic Solids I mentioned a week or so ago. It's a Regular Polytope in 3 dimensions.

The Octahedron is the "dual" of the cube. Imagine the Octahedron surrounded by a cube. Each of the 6 vertices (corners) of the Octahedron just touches the center of one of the cube's 6 square faces.

Also, Imagine a cube inside the Octahedron. Each of the cube's 8 corners neatly touches the center of one of the Octahedron's 8 triangular faces.

Now imagine "stellating" the Octahedron by gluing 8 triangular pyramids (Tetrahedra) with a triangular base attached to each of the Octahedron's 8 triangular faces. That should give you a "Stella Octangula" -- a non-convex shape described (first?) by Johannes Kepler. Nonconvex meaning that the surface zig-zags in and out, like a planet with 8 equally spaced huge mountains sticking out into space.

Can you now visualize the Stella Octangula as some interpenetrating regular polyhedra? Can you imagine what it looks like to put a Stella Octangula inside a cube?

I found myself playing with a formula involving the Stella Octangula, just hours ago.

Last night I was just messing around on the computer after watching the Lakers smash the Timberwolves, and serving my son the turkey dinner that my wife cooked for him.

I found myself proving, to my nearly complete satisfaction:

A Stella Octangula Number StOct(n) is a perfect square for nonnegative integer n iff n = 0,1, or 169.

For a nice page on the geometrical object Stella
Octangula, where you can rotate it by mouse click and drag, see:

Stella Octangula [at MathWorld]

For the definition of Stella Octangula Number
StOct(n) = n(2n^2-1)


StellaOctangula.html">Stella Octangula Number [at MathWorld]

The nontrivial solution is:

StOct(169) = StOct(13^2) = 9653449 = 3107^2

I believe this is a new result.

Using the language Python, I see no other solutions on searching through n=100,000.

Then I went to bed, and started reading Mary Turzillo's cover story in the latest Analog. I think it's an award-winner!


Jonathan Vos Post :: :: URL
Posted to Taking your own bad advice
May 28, 2004 1:02:03 PM EDT


I gave my changes of majors, degrees (B.S., Math; B.S. English Literature; M.S. Computers; Ph.D., ABD Moledular Cybernetics), a few days ago here, but neglected to list my jobs, related and unrelated to degrees.

That's because I can't, easily. In my 25th college reunion, I won the award for most job titles held over a career. I had more than twice the number of the person who came in #2.

These include (for major coreporations, small companies, and government agencies such as Army, Navy, Air Force, FAA, and NASA), but are not even close to limited to:

Academic Honesty Board Member, Actor, Ad Writer, Algebra Teacher, Anthropology Instructor, Assembly Line Worker, Astronomy Professor, Aviation Engineer, Biophysicist, Board of Directors Secretary, Book Editor, Business Plan Writer, Calculus Teacher, CD-ROM producer, Chemistry Tutor, City Councilman, Coauthor, Comedian, Comic Book Author, Computer Science Professor, Consultant, Copyright Seminar Chairmn, Director, Documentation Manager, Economics Lecturer (Postdoc), English Composition Professor, Fencing Team Manager, Film Director (Industrial), Film Writer, Finite Math Teacher, Futurist, Independent Contractor, Interstellar Spacecraft Designer, Journalism Instructor, Keynote Address Speaker, Literary Agent, Magazine Publisher, Math Professor, Mission Planning Engineer (Voyager/Uranus), Moon Base Designer, Mars Base Designer, Multimedia Agent, Newspaper Publisher, Novelist, Oceanography Instructor, Opera Producer, Paralegal, Patent Law Consultant, Philosophy Instructor, Playwr
ight, Poet, Poet Guest of Honor at Doctor Who Con, Process Server, Private Eye, Programmer, Psychology instructor, Radio Broadcaster, Research Fellow, Resume Service Owner, Reverend, Short Story Author, Soccer Team Manager, Space Shuttle Engineer, Space Station Engineer, Systems Analyst, Teaching Assistant, Theologian, Treasurer (nonprofit organization), TV Talkshow Guest, TV Writer, Union Representative, Vice President of Software R&D, Video Assistant at Karate Dojo, Voiceover Actor, Web Systems Manager, Webmaster...

That's off the top of my head. People have been known to look at my resume with disgust and say: "you just can't keep a job, can you?"


Jonathan Vos Post :: :: URL
Posted to Open thread 23
May 28, 2004 10:58:29 PM EDT


Dr. Geoffrey Landis suggested, based on what was on Making Light about Erdos Number, that someone launch a project to build a database of Asimov Numbers.

Isaac Asimov has an Asimov Number of 0. Anyone who coauthored with him has an Asimov Number of 1. Anyone who coauthored with one of those has an Asimov Number of 2. And so forth.

I spent half a day, and verified 31 people with Asimov Number of 1, based on his 506 cited books. I have not yet looked at coauthored stories or Chemistry papers. For each link, I gave the earliest such coauthored or coedited book, title, and publisher.

Then I started on extending to Asimov Number of 2. Going alphabetically through G on last names of those with Asimov Number of 1, I quickly added 98 new names with Asimov Number of 2, from Adams through Zelazny. The biggest bunch came through anthologist Greenberg.

This database is far too large for Making Light already, as a 73 KB Word file and growing fast. I expect to put a draft on the web in the next few weeks.

There is a set of methodological questions. What kind of link should there be between an author who has a story in an anthology, and the editor(s)? Between an author who has a story in a magazine, and the editor(s)? With fanzines? With TV and film credits? With an author who blurbs another's book?

I think that this is a part of my role as Chairman of the Science Fiction track of ICCS 2006, 6th International Conference on Complex Systems. I wonder whom, besides perhaps Paul Allen's Science Fiction Experience, launching officially in June 2004 in Seattle, might fund and maintain such a database.

Just wondering.

Any ideas?

And by the way, what is Isaac Asimov's Erdos Number?


Jonathan Vos Post :: :: URL
Posted to Open thread 23
May 29, 2004, 09:45 PM:


LisaJulie Peoples: thank you for asking Jon Singer. I was on semitenterhooks.

J. R. R. Tolkien has an Asimov Number of 2...

I'm through a first pass up through last names beginning with letter "N." I count 31 people with Asimov Number of 1, and 192 people with Asimov Number of 2.

I estimate that roughly 300 people have Asimov Number of 2, and 3000 have Asimov Number of 3. That's 3 times the size of SFWA. By Asimov Number of 2 w

#4 ::: Avram ::: (view all by) ::: May 30, 2004, 12:48 AM:

You’re it!

#5 ::: Jonathan Vos Post ::: (view all by) ::: May 30, 2004, 01:37 AM:

Me? Joking about Asimov as the center of a vast conspiracy that embraces all authors? Can such things happen in the so-called real world? Can a cryptohistory really connect Tolkien and Zelazny, Hubbard and Somerset Maugham? Well...

I'm just waiting to see the rest of the 3 part series in The Villiage Voice:

Paranoid Nation
by Gary Indiana
No Such Thing as Paranoia
On the culture of conspiracism

May 25th, 2004 10:30 AM

with such gems as:

"The necessary proof of such a conspiracy, if we choose to call it that, often turns up 25 or 50 years after the fact, when the release of classified documents churns up no public outcry or indictments. Such was the recent case with the declassified revelation that the late Connecticut senator Prescott Bush, grandfather of the current president, along with his law partner W. Averill Harriman, a former governor of New York, managed a number of concerns on behalf of Nazi industrialist Fritz Thyssen. These included the Union Banking Corporation, seized under the Trading With the Enemy Act on October 20, 1942 (Office of Alien Property Custodian, Vesting Order No. 248), Seamless Steel Equipment Corporation (Vesting Order No. 259), and the Holland-American Trading Corporation (Vesting Order No. 261)."

"The Union Banking Corporation financed Hitler after his electoral losses in 1932; the other Bush-managed concerns have been characterized as 'a shipping line which imported German spies; an energy company that supplied the Luftwaffe with high-ethyl fuel; and a steel company that employed Jewish slave labour from the Auschwitz concentration camp.' Fuller details are documented in George Bush: The Unauthorized Biography, by Webster G. Tarpley and Anton Chaitkin; in Kevin Phillips's American Dynasty: Aristocracy, Fortune, and the Politics of Deceit in the House of Bush; as well as in the colorful, conspiracist history Fleshing Out Skull & Bones, by Anthony Sutton et al., and further confirmed by John Loftus, a former prosecutor in the Justice Department's Nazi War Crimes Unit. Since only the Nazi partners in the Bush-Harriman interests were permanently deprived of their frozen stock, Prescott Bush and his father-in-law, George Herbert Walker, waltzed off with $1.5 million when the Union Banking Corp. was liquidated in 1951. (This was, in effect, the foundation of the Bush family fortune: once a Snopes, always a Snopes.) Briefly picked up by the Associated Press and buried deep in the pages of American newspapers, this half-century-late disclosure led to no media follow-up and left no impression on the potential electorate for the 2004 U.S. presidential contest."

#6 ::: Jonathan Vos Post ::: (view all by) ::: May 30, 2004, 01:49 AM:


I had no intent to insult an old friend of yours. I don't think I did. I thought that I was honestly answering a question by one of the making Light clan:
Kip W ::: (view all by) :::
May 27, 2004, 11:58 AM:

What's Jon Singer's Erdös Number?

I do not deny that I have a big ego. I do not deny that I enjoy being connected with greater minds and greater writers. It is the glory of Literature that such is possible. And I am glad that you and Teresa have thrown the door wide open, and are so hospitable, even to those more annoying than myself.

You have raised issues of belief, and answered them brilliantly. I belive in infinitely more than my mere self.

I believe in Science.

I believe in Saint Albert Einstein, and jokester Richard Feynman.

I believe in Science Fiction.

I believe in Admiral Heinlein, Professor Asimov, and Sir Arthur C. Clarke.

Don't all of us herein share such belief, and the responsibility that comes with it?

#7 ::: Avram ::: (view all by) ::: May 30, 2004, 01:54 AM:

We believe in one Admiral, Robert Heinlein,
eternally begotten of Lazarus Long,...

#8 ::: Jonathan Vos Post ::: (view all by) ::: May 30, 2004, 02:42 AM:

Correct me if I'm wrong, but wasn'r Robert A. Heinlein's brother actually an Admiral? If so, would not RAH have risen to that rank as well, but for his medical situation? I'd like to imagine an alternate world where the two Admirals Heinlein fought for and won the U. S. Navy sending a man in space by, oh, let's say 1955 or so?

Was it not a fact that such an effort was killed in Roosevelt's or Truman's cabinet? Didn't we have a discussion touching on this some months back? And, crypothistorically, didn't L. Ron Hubbard claim to have commanded a Navy vessel, and fought The Enemy therefrom?

Lazarus Long is set before us an example of great wisdom coming from nobility of character, over great spans of time?

In the last vestiges of my youth, at 53, I seem less wise each year to my 15-year-old son, as he grows in stature -- literally filling my shoes now -- and confidence in his mental, physical, and moral strength?

My father is ill, in his 80s, where he once flashed with vigor, working with great writers of the 1940s, 1950s, 1960s and beyond. I did not consider it name dropping when he spoke of his lighting T. S. Eliot's cigarette, or strange business deals swirling around Hugo Gernsback as they met. I thought that, through Literature, one could touch immortality, and The Immortals.

My Mother learned Spanish, she said, just to read Cervantes in the original.

I have no gift for languages, but tonight, watching the Return of the King DVD, I remember the graffiti in Tengwar and Angerthas upon the subway billboards of New York in the 1960s. "Frodo Lives!" they said, in rune and cursive.

Did not Tolikien show us that we could recapture even History that never was, through languages never spoken? Are we not on tenterhooks to read his annotated translation of Beowulf?

Through our superiors, we learn our place in the world.

I exalt my teachers, and my teachers' teachers.

And I thank you again for giving me the place, now and again, to share my joy in the universes they imagined.

And the Dodgers beat the Diamondbacks -- what was it? 10 to 0 tonight. The Lakers lost, but Garnett and Sprewell rose in conflict to show their merit.

Argument is good, if we slip closer to the Truth. Conflict can stengthen. Competition is quintessentially American.

For all the horros from our so-called leadership in Washington, I am proud to live in the America of Asimov, Bradbury, and Heinlein.

So I believe...

#9 ::: Clark E Myers ::: (view all by) ::: May 30, 2004, 03:47 AM:

Nah (? spelling) Laurence Heinlein was IIRC correctly a Lieutenant General - would believe Major General or General but I'm pretty sure 3 star. Not to be confused with tribute Proxmire story and the rise of the high navy.

#10 ::: Teresa Nielsen Hayden ::: (view all by) ::: May 30, 2004, 10:50 AM:

Okay, Avram, start running.

I put up three nonce-comments immediately after creating this thread so I'd have a place to put JVP's collected remarks. If Movable Type has a way to insert a back-dated comment in the chronology of the thread, I've never found it, so the easiest way to make sure his compilation came first was to make the space, then go back and edit the comments. I made three because it's easy to delete extras, but impossible to create new ones, and who knows? Maybe I'd need one or two extra. That's the logical part. The reason I think of that as "tagging" is that I'm a veteran of the GEnie SFRT.

#11 ::: Bill Blum ::: (view all by) ::: May 30, 2004, 11:17 AM:

Movable Type's source code scares me-- I can't think of how you'd go about implementing a backdating system for comments.

#12 ::: Teresa Nielsen Hayden ::: (view all by) ::: May 30, 2004, 12:51 PM:

It's probably just as well you can't.

#13 ::: Jonathan Vos Post ::: (view all by) ::: May 30, 2004, 01:08 PM:

Clark E Myers:

Thank you! I did not know that about Laurence Heinlein probably being a Lieutenant General, nor do I know the story that you allude to about Proxmire. As to "high navy," I remember Robert A. Heinlein commenting that marijuana was more of a threat to the Navy than was alcohol, because a baggie could be hidden more easily than a bottle.

Teresa Nielsen Hayden: thank you very much for your judgment and work in this experiment. We shall now empirically determine if I am indeed boring to your readers or not. If I am above some threshhold of boring, then I will be in the position of a small panel discussion at a con, where there is no audience, or an audience outnumbered by the panelists. If there is a small but viable set of people who enjoy this conversation, then making it a separate "track" of the con is a good structural solution.

Patrick: By the way, I can indeed be boring, self-indulgently egocentric, and all else that you suggest. I hear those complaints often, but less often than that I hear positive feedback. What I am not is "mad" in the sense of "don't go away mad." I greatly respect you and your opinions. For instance, althgough I've been an elected city councilman twice, I believe that you know much more about politics than I do.

I take responsibility for what I do. If I bore or offend anyone, it is MY failure, not theirs. I am a teacher: if I bore my students, they don't learn, and I don't deserve to be paid. I am a writer: if someone doesn't "get" a poem or story or news article of mine, then I have failed to communicate.

Of the thousands of students I've taught, I get a mostly very positive response. I have writings and statistical analyses done by students and colleges. Some say that I am the best teacher that they have ever had. Some say that I tell jokes that aren't funny and stories that go on too long. The balance is on the high positive, but I do acknowledge and learn from the criticisms. Thus, again, I thank you.

To the extent that there's a lot of Math in this thread, I stand as a Math teacher and someone whom (as I've said perhaps too extensively) the Math Demon has possessed again for about half a year.

Erdos Numbers are not my baby. This is a rather deeply analyzed system, within the more general "Small World" phenomenon. Six Degrees of Kevin Bacon, y'know? It ties to several related fields:

(1) Scientific Collaboration theory;
(2) Social Networks and Organization Theory;
(3) Random Networks (a specialty of Erdos's work)
(4) Statistical Mechanics in Physics, Biology...
(5) Neural Networks;
(6) Computer Networks, particularly the Internet.
(7) Literary Theory.

Because I believe in Science, and believe in Science Fiction, I find it appropriate to use methods of contemporary Science to study the social network of Science Fiction. It goes without saying that those bored by Science Fiction might only care about what this study tells us about people in general; and that those bored by Science and Math would only care about my conclusions as they shed light on actual Science Fiction Literature and authors.

Rather than merely stand on a soapbox here, promulgating my beliefs, which is the noncollaborative part of Publishing within the Scientific Methods, I am happy to mix in an appropriate amount of conversation with your readers.

My mouth is open... but so are my ears!

#14 ::: Jonathan Vos Post ::: (view all by) ::: May 30, 2004, 01:18 PM:

Bill Blum:

You comment that "Movable Type's source code scares me-- I can't think of how you'd go about implementing a backdating system for comments."

Stephen Hawking has written about "imaginary time." Its a cute trick, but offensive to some scientists on a pragmatic and philosophical basis. It's just as well that we need not implement a system for comments that uses complex numbers in timestamps. Or matrices. Or quaternions. Or Cayley Alegbras. Or Clifford Algebras. Or other mind-boggling alternatives to traditional Newtonian/Euclidean time.

Newton did write that the "flow" of time is at a constant rate, and specifically, that for two possible time measures t and T:

dT/dt = 1.

He speculated that other solutions may exists, but that he had more important things to do. What do you think?

#15 ::: Jonathan Vos Post ::: (view all by) ::: May 30, 2004, 01:32 PM:

I was prodded to add a 2nd person with Asimov Number = 1:

ELLISON: Harlan Ellison 1977-78/1987

Serialized version in Asimov's Science Fiction magazine, and it appeared in the November, December and Holiday issues of 1987. In 1994, Warner Books also issued a hardcover edition of the script, with both color and black-and-white illustrations by Mark Zug. lists this as "I, Robot: The Illustrated Screenplay
by Isaac Asimov (Author), Harlan Ellison (Author)"
Paperback: 288 pages ; Dimensions (in inches): 1.00 x 9.00 x 6.25 Publisher: Warner Books; (December 1, 1994)
“It sounds like a Monty Python record: this is the novelization of the screenplay of the book I, Robot. Isaac Asimov, wrote the original, Harlan Ellison wrote the screenplay for Warner Brothers nearly twenty years ago, and when one dumbass producer helped prove that Hollywood doesn't understand SF more complex than Star Wars, the screenplay came out as a book. The practice of publishing movie scripts in book form isn't new, but then, I, Robot: The Movie never saw release.” (Comment originally published in Tangent, Fall 1995)

Okay, now I need to dig out screenwriters of films adapted from Asimov's fiction.

#16 ::: xeger ::: (view all by) ::: May 30, 2004, 01:41 PM:

Hrm. I have to admit that I'd like a way to hyperlink or otherwise refer easily between the entr[y|ies] being commented on by folks further down in the comments.

#17 ::: Patrick Nielsen Hayden ::: (view all by) ::: May 30, 2004, 02:30 PM:

JVP to me:

"I had no intent to insult an old friend of yours. I don't think I did."

Of course this is a red herring. Nobody thought JVP had "intent to insult" anybody.

#18 ::: Jonathan Vos Post ::: (view all by) ::: May 30, 2004, 02:51 PM:

Today's additions to:

"Asimov Numbers: Notes Towards a Small World Network of Science Fiction Authors"

Draft 1.3 of 30 May 2004, 38 pages, approx, 10,200 words
Jonathan Vos Post

Table of Contents:

Collaboration Link Definition
Asimov0: who wrote/edited a book with Isaac Asimov
Asimov 0-: coauthors/coeditors of shorter works
AsimovTV: List of all coauthors, TV Writers, and Screenwriters who Adapted Asimov works
Asimov 1: List of all coauthors, and/or co-editors of
People with Asimov Number = 1
Mathematical Analysis

By analogy with Erdos Numbers in Mathematics, and the Kevin Bacon Number in movies, a definition is given for Asimov Number in Science Fiction, Science Writing, and literature in general. 31 people with Asimov Number of 1 are identified by name, and by the citation of a work they coauthored or co-edited with the late Professor Isaac Asimov. 192 {replace with updated number} people of Asimov Number 2 are identified as coauthors or co-editors of works with those of Asimov Number 1. A further 27 are listed as Film/TV co-writers, for a tentative total of 59 with Asimov Number of 1, and 219 with Asimov Number of 2. We conjecture that the Asimov Graph contains almost all present-day publishing Science Fiction Authors, as well as everyone in the Erdos Network.

--- skip all text except AsimovTV: List of all coauthors, TV Writers, and Screenwriters who
Adapted Asimov works ---

AsimovTV: List of all coauthors, TV Writers, and Screenwriters who Adapted Asimov works

We first give a Filmography, fact-checked against the Internet Movie Database; and then an alphabetical listing of collaborator-writers. This section gives us 28 with Asimov Number = 1, only one of which (Robert Silverberg) is on the list for print collaboration as such. It also immediately adds 10 more with Asimov Number = 2, without following “Six Degrees of Kevin Bacon” links. Directors are not listed, unless credited as Writer-Director. Actors, Producers, Crew not listed.


 I, Robot (2004) (book and suggestion)
 Nightfall (2000) (Video) (story)
Also known as “Isaac Asimov's Nightfall” (2000) (V) (USA: complete title)
 Bicentennial Man (1999)(novel The Positronic Man) (short story The Bicentennial Man)
Also known as “Der 200 Jahre Mann” (2000) (Germany)
 Android Affair, The (1995) (TV) (story)
 Teach 109 (1990) (TV) (story)
 Feeling 109 (1988) (story)
 Nightfall (1988) (story)
 Robots (1988) (Video) (novels I, Robot et al)
 Probe! (1988) (TV Series) (creator)
 Gandahar (1988) (adaptation) (English version) ... aka Light Years (1988) (USA)
 Konets vechnosti (1987) (novel The End of Eternity)
 Ugly Little Boy, The (1979) (TV) (story) [no other writer credited]
 Naked Sun, The (1969) (TV) (novel) .. aka Out of the Unknown: The Naked Sun (1969) (TV) (UK: series title)
 Liar! (1969) (TV) (story) ... aka Out of the Unknown: Liar! (1969) (TV) (UK: series title)
 Prophet, The (1967) (TV) (story Reason) ... aka Out of the Unknown: The Prophet (1967) (TV) (UK: series title)
 Robot embustero, El (1966) (novel)
 Satisfaction Guaranteed (1966) (TV) (story) .. aka Out of the Unknown: Satisfaction Guaranteed (1966) (TV) (UK: series title)
 Sucker Bait (1965) (TV) (story) ... aka Out of the Unknown: Sucker Bait (1965) (TV) (UK: series title)
 Dead Past, The (1965) (TV) (story) ... aka Out of the Unknown: The Dead Past (1965) (TV) (UK: series title)
 Caves of Steel, The (1964) (TV) (novel)

#19 ::: Jonathan Vos Post ::: (view all by) ::: May 30, 2004, 02:54 PM:

Alphabetical listing of 28 TV/Film collaborator-writers:

ANDREVON: Jean-Pierre Andrevon 1988
“Gandahar” (1988) (novel: “Metal Men Against Gandahar”)

BOND: Julian Bond 1962
“Out of this World” (1962) (writer) (starring Boris Karloff)
[note writing credits for non-Asimov epsodes , which give Asimov Number = 2, include:
Dennis Butler (The Dark Star)
Philip K. Dick (Imposter)
Clive Exton (“Cold Equations”, “Target Generations”)
Tom Godwin (story credit “Cold Equations”)
Leon Griffiths (“The Yellow Pill”, “Divided We Fall”)
Katherine MacLean (story “Pictures Don’t Lie”)
Terry Nation (“Imposter”, “Botany Bay”, “Immigrant”)
Bruce Stewart (“Pictures Don’t Lie”, “The Tycoon”)
Richard Waring (“Vanishing Act”)
Robert Moore Williams (story “Medicine Show”)

CAMPTON: David Campton 1969
“Liar!” (1969) (Adaptation credit)

CLUZEL: Raphael Cluzel 1988
“Gandahar” (1988)

CORRINGTON: John William Corrington 2000
“Nightfall” (2000)

DE LARA: Antonio de Lara (1966)
“El Robot Embustero” (1966) (Writer-Director)

DRUXMAN: Michael B. Druxman 2000
“Nightfall” (2000) (credited as “cowriter”)

FERNANDEZ: Peter Fernandez 1988
“Gandahar” (1988) (English Dubbed Version, officially uncredited)

GIBBY: Gwyneth Gibby 2000
“Nightfall” (2000)

GOLDSMAN: Akiva Goldsman 2004
“I, Robot” (screenplay)

KAZAN: Nicholas Kazan 1999
“Bicentennial Man” (Screenplay)

KLETTER: Richard Kletter 1988
“The Android Affair” Story, Teleplay, also Teleplay of “Teach 109”
also “Feeling 109” (1988)

LALOUX: Rene Laloux 1988
“Gandahar” (1988) (Adaptation credit) (Director)

LEONARD: Hugh Leonard 1966
“Satisfaction Guaranteed” (1966) (Adaptation credit)

LINK: William Link 1988
“Probe” (1988) credited as “Creator”, same credit to Asimov

MAYERSBERG: Paul Mayersberg 1988
“Nightfall” (Screenplay and Director)

METALNIKOV: Budimir Metalnikov 1987
“Konets vechnosti” (1987) (from novel “The Enfdof Eternity”)

MULLER: Robert Muller 1967
“The Prophet” (1967) (Adaptation credit)
“The Naked Sun” (1969) (Adaptation credit)

NATION: Terry Nation 1964
“Caves of Steel” (1964) writer (teleplay?)

OLATKA: Peter Olatka 1988
Robots (1988)

PAUL: Jeremy Paul 1965
“The Dead Past (1965) (Adaptation credit)

PILLER: Michael Piller 1988
“Probe” (1988) credited as “writer”

ROBERTS: Meade Roberts (1965)
“Sucker Bait” (1965) (Adaptation credit)

SHELDON: Lee Sheldon 1988
“Probe” (1988) credited as “writer”

SILVERBERG: Robert Silverberg 1999
“Bicentennial Man” (novel adaptation of Asimov Short Story)

VINTAR: Jeff Vintar 2004
“I, Robot” (screen story) and (screenplay)

WAGNER: Michael I. Wagner 1988
“Probe” (1988) credited as “writer”

YERMASH: Andrei Yermash 1987
“Konets vechnosti” (1987) (Writer-Director)

#20 ::: Jonathan Vos Post ::: (view all by) ::: May 30, 2004, 03:20 PM:


I apologize for throwing a red herring across the trail. I was trying to understand how I had offended you, other than my being admittedly verbose, boring, and egocentric. I honestly don't know if Jon Singer was in any way made uncomfortable by my reply to another's query, or that third party asking him. As a second-order phenomenon, I don't know exactly why you were offended, if your old friend was not. But I am willing to listen if you can tell me specifically why, as it is my fault that I did not understand you the first time.

You say: "Of course this is a red herring. Nobody thought JVP had 'intent to insult' anybody.

[in reply to my saying:
"I had no intent to insult an old friend of yours. I don't think I did."


You comment:
"...I have to admit that I'd like a way to hyperlink or otherwise refer easily between the entr[y|ies] being commented on by folks further down in the comments."

I agree, but don't want to further burden Teresa and Patrick, after their kindness is segmenting, partitioning, exiling, guest-blogging, or otherwise putting my postings somewhat out-of-context. But a good point. Hard to explain what sort of link is involved. Almost need to go back to Ted Nelson's full-blown Xanadu design where any hyperlink can itself be annotated.

#21 ::: Jonathan Vos Post ::: (view all by) ::: May 30, 2004, 03:40 PM:


You comment to Tom Whitmore"
"Tom, Bill's indexes don't have a good interface, though, like ISFDB, and, as far as I know, he doesn't intend to reach further back, while ISFDB does. ISFDB has also started putting web & email links on the author pages." Good point. I strive to go back ALL the way through history on my Ultimate Science Fiction Web Guide [listed as #4 yesterday by Google for "science fiction"] But that takes a semi-infinite amiunt of effort.

You also comment:
"Patrick, I just figured JVP was a friend of y'alls, since it went on so long."

I apologize if I offended you, from sheer length. I am not technically a friend of Patrick and Teresa, although I admire them tremendously. I believe that friendship usually has to be earned. As see it, there are two extremes in friendship-formation. One the one hand, you can draw "bright line" borders around your private life, and let nobody inside until the relationship has been exhaustively beta-tested. This tends to give you a small number of friends, but each is very stable and very welcome and very trusted. On the other extreme, you can let any acquaintance become, by your terms, a friend. This gives you a lot of friends, but many will turn out to not reciprocate, to be "fair weather friends", or to abandon and/or betray you easily.

Like many people, I try to walk the tightrope between these extremes. But I have been VERY wrong at times. Betrayal by friends of a decade or more have cost me somewhere between $100,000 and $2,000,000 and an intangible but huge amount of personal agony, and pain to my family.

One might ask: "am I paranoid enough?" in response to Intel founder Andy Grove's slogan "only the paranoiud survive."

Conversely, paranoids have (almost be definition) very few friends.

What is your theory of friendship?

The Erdos Number / Kevin Bacon Number / Asimov Number approach is another take on friendship.

As excerpted from:

Kevin Bacon, the Small-World, and Why It All Matters

"The small-world phenomenon formalizes the anecdotal notion that 'you are only ever six "degrees of separation" away from anybody else on the planet.' Almost everyone is familiar with the sensation of running into a complete stranger at a party or in some public arena and, after a short conversation, discovering that they know somebody unexpected in common. 'Well, it's a small-world!' they exclaim. The small-world phenomenon is a generalized version of this experience, the claim being that even when two people do not have a FRIEND in common, only a short chain of intermediaries separates them. Stanley Milgram made the first experimental assault on the problem (confined to the United States) by sending a series of traceable letters from originating points in Kansas and Nebraska to one of two destinations in Boston. The letters could be sent only to someone whom the current holder knew by first name and who was presumably more likely than the holder to know the person to whom the letter was ultimately addressed. By requiring each intermediary to report their receipt of the letter, Milgram kept track of the letters and the demographic characteristics of their handlers. His results indicated a median chain length of about six, thus supporting the notion of 'six degrees of separation," after which both a play and its movie adaptation have since been named.' "


"Since people meet most new FRIENDS through existing friends, the networks are locally ordered. (Here order means that if A knows B and B knows C, then A is more likely to know C than some other random element.) The outcome of local ordering in such a network is that one individual's friends are more likely than not to know one another: a characteristic that is called 'clustering.' Many real-world networks, including friendship networks, tend to be highly clustered, but they are not entirely so. If a person joins a club and meets new people or moves to a different city to take a job, new connections can form that are not ordered by the existing network."

#22 ::: Jonathan Vos Post ::: (view all by) ::: May 30, 2004, 03:52 PM:

I have a rather extensive annotated bibliography in my paper-in-progress. But, to take an shorter and objective 3rd party analysis,

Columbia University Sociology Dept.: Small World



``Kevin Bacon, the Small-World, and Why It All Matters.'' Santa Fe Institute Bulletin, 1999.

J. Kleinfeld. ``Could it be a big world after all? The `six degrees of separation' myth,'' Society, 2002.

S. Milgram. ``The small world problem.'' Psychology Today 2, pp. 60-67,, 1967.

S. Milgram. and J. Travers. ``An experimental study of the small world problem.'' Sociometry, 32(4), pp. 425-443, 1969.

D. J. Watts. ``Small Worlds: The Dynamics of Networks Between Order and Randomness.'' Princeton University Press, 1999.

D. J. Watts and S. H. Strogatz. ``Collective dynamics of `small-world' networks.'' Nature 393, 440-442 (1998).

Interesting to me that this straddles Myth and Science!

#23 ::: Bill Blum ::: (view all by) ::: May 30, 2004, 03:57 PM:

JVP wrote:
He speculated that other solutions may exists, but that he had more important things to do. What do you think?

Remember, proposing a solution is easy. The rest is often just a "small matter of programming." (Here's a reference)

Adding extra functionality (apparently in the form of plugins) to Movable Type would be an interesting exercise from a programming point of view, but from a practical standpoint, I really have no business mucking about with the stuff.

My technical interests are fairly narrow-- unless it's somehow related to antennas, electromagnetics, or signal processing, I really can't be bothered to give a topic the full attention it may (or may not) deserve.

Collaboration graphs and the like (the alarmingly popular outgrowth of the Erdos Number project) can offer some interesting insights into how people work together in an academic discipline (or across disciplines, as the case may be).

I can understand the perverse pride that comes with having a low Erdos number... but the idea of tracking Asimov numbers??? Count me out.

#24 ::: Jonathan Vos Post ::: (view all by) ::: May 30, 2004, 04:12 PM:

Bill Blum:

I appreciate your thoughtful comments.

Identifying a problem but not giving a solution: exclude this, and most of the Political world vanishes. Sometimes not a bad idea.

Movable Type: I've retired, after 37 years, as a Programmer. Let younger, more energetic, and smarter people do it. Open Source fits the bill.

antennas, electromagnetics, or signal processing: I mentioned an EE professor I know who claims to believe ONLY in electrons. I have known a guy for 20+ years who has a theory devolving from his observations athat almost all variety of UFOs are shaped like antennas (i.e. "flying saucer" = dish antenna; flying cone = horn antenna...).

Erdos Numbers: alarming... or not alarming enough?

Cross-discipline: central to my interest here. I've practically devoted my life to disproving C.P. Snow's "Two Cultures" theory.

Perverse Pride in Low Erdos Number: probably. Any egocentric (myself included) wants to be reassured that one is REALLY at or near the center of the universe. Of course: "the universe is a sphere whose center is everywhere."

Perverse Pride in Asimov Number: mine is not particularly low. Most people with Asimov Number = 2 probably don't know it, and might not care. Dr. Geoff Landis suggested Asimov as the natural place to start mapping. Might as easily been Harlan Ellison, Philip K. Dick, Theodore Sturgeon, Hugo Gernsback, John Campbell, or any number of others. To me, the numbers are just a way at formalizing structure, and, after that, dynamics.

#25 ::: Jonathan Vos Post ::: (view all by) ::: May 30, 2004, 04:28 PM:

Bill Blum and xeger:

Classic comment of Programming, per your comments:

In 1950, John von Neumann said that "science and technology will shift from a past emphasis on motion, force, and energy to communication, organization, programming, and control."

I just spotted this in the abstract of:
Santa Fe Institute: 2002 Ulam Lectures

Title: Propagation and Purpose: Parables from Complex Systems and Their Possible Meanings for Our Lives

Presented by: J. Doyne Farmer, McKinsey Professor, Santa Fe Institute
Dates: September 24, 25, & 26, 2002
Publication notes: TBA

"In 1950, John von Neumann said that 'science and technology will shift from a past emphasis on motion, force, and energy to communication, organization, programming, and control.' He was right. This has happened in almost every field of science and engineering, and has had a huge effect on the way we communicate, do business, and even entertain ourselves. But at a more fundamental level, we are slowly gaining a better (if still fragmentary) understanding of how the material properties of the world give rise to its informational properties. While the universe becomes in one sense more random, it also becomes in another sense more orderly. Patterns spontaneously emerge, grab energy, rearrange, compete, and perform complex tasks such as prediction of their environments, for the purpose of better propagating themselves through time. People and their societies are of course just one example. Professor Farmer will argue that viewing ourselves in the context of the broader organizational process of which we are a part can shed a little light on our beliefs and institutions, and our relation to the universe."

#26 ::: Jonathan Vos Post ::: (view all by) ::: May 30, 2004, 08:37 PM:

Semiquantitatively, John Clute has commented on the Small World phenomenon in Science Fiction:

to excerpt from

Excessive Candour: The Writing of Tomorrow
John Clute, review of Nebula Awards Showcase 2002

"But I need to intervene in my own person for a moment. What I need to say relates to the rather grandiose name given this column when it started in 1997. A long while earlier, I had used the term in a piece arguing that the SF world was so small, and its personnel so tightly interwoven, that the only way for a reviewer to do his job, which was to tell his form of truth about stories which purported to tell significant truths about the world, was to consciously attempt to ignore his own personal connections within the genre, to consciously try to be honest, even though it might be about friends; even though it might be hurtful."

"The downsides of this are obvious; an upside might be the believability of praise, even when it's about intimates. In the case of the 18 named contributors to Nebula Awards Showcase 2002, I have myself met or know pretty well 15; two I have never met, and now—it is now April 2002—I will never meet the great Damon Knight, teacher of us all, who has just died young at 80; and one is me."

#27 ::: Jonathan Vos Post ::: (view all by) ::: May 30, 2004, 09:02 PM:

How about social networks and the Intenet crashing? Can Asimov Numbers help us to avoid the end of civilization as we know it?

Networks: Growth, Form, Function, Crashes
By Cosma Shalizi Graduate Fellow,
Santa Fe Institute

"Networks are ubiquitous; they surround us; in our daily life we participate in dozens of them. Increasingly, the technologies and social institutions on which we depend for our daily life are explicitly engineered as networks. Our understanding of networks, however, has not kept up with our dependence on them...."

"Three themes ran through the conference ['Complex Interactive Networks'], : the connection between their growth and their form; the connection between their form and their function; and the all-but-inevitable catastrophic failures of their function."

"What, though, is a network? As used at the conference a network is essentially anything which can be represented by a graph: a set of points (also generically called nodes or vertices), connected by links (edges, ties) representing some binary relationship. In social networks, the nodes are people, and the ties between them are (variously) acquaintance, friendship, political alliance or professional collaboration. In metabolic networks [subject of JVP's PhD dissertation], the nodes are metabolites, chemicals, and two nodes are connected if there is a biochemical reaction in which they both participate. In the brain, as Olaf Sporns explained, there is both an anatomical network, where the nodes are various regions of the brain, and the links are actual nerve fibers running from one to another, and a functional network, where the same nodes now are joined to regions which share in the performance of various tasks. In the case of the Internet, the nodes are actual machines, and they are joined by a link when they are physically tied together. In the case of the World Wide Web, the nodes are Web sites, and they are joined when there is a hyper-link from one to the other...."

"... One implication of the Barabasi-Albert growth process that leads to "scale-free" networks has to do with the vulnerability of such networks to accidents and to deliberate attacks. If nodes are knocked out of the network in a uniform, random fashion --- no node is more likely to be removed than any other --- then scale-free networks are very robust. You have to knock out a very large fraction of all nodes before the giant component breaks up and the network fragments into separate parts. The reason is that most nodes don't connect to many other nodes, so getting rid of them doesn't do much to the over-all connectivity..."

"[John] Doyle goes further, and says that when systems, including networks, are designed to cope with insults below a threshold size as well as possible, the damage done by insults above that size is actually _increased_. He calls this 'highly optimized tolerance,' and it seems to offer a choice between constant petty failures, and sporadic but inevitable total breakdowns."

" As George Verghese of MIT explained, failure can actually be contagious in [electrical power] networks --- when one power-plant goes down, other stations, attempting to take up its load, are much more likely to fail themselves. Here the connectivity and clusteredness of the network lead to cascading failure, in a difficult-to-understand and difficult-to-stop way."

"... It may be possible to learn to avoid catastrophic network failures. It may also be possible to design other systems which will mitigate the effects of network failures when they do occur --- to have (reliable) insurance against them...."

#28 ::: Teresa Nielsen Hayden ::: (view all by) ::: May 30, 2004, 10:04 PM:


You have posted sixteen comments today.

Go to my main page and look at the log of recently-posted comments. Almost all of them are you. Most of those comments consist of stuff you happen to find interesting, regardless of its relevance to the rest of Making Light and the conversations other people are having.

I'm not running a hosting service here. It's neither difficult nor expensive to set up your own Live Journal or weblog, and at this point I think you ought to be doing it.

#29 ::: Jonathan Vos Post ::: (view all by) ::: May 30, 2004, 10:34 PM:

Teresa Nielsen Hayden:

Fair enough. Reasonable request. Unless/until a reasonable number of people comment on my postings of today, I'll take it as a troublesome (to you) vote of no confidence. Not that people are likely to see that I've replied to them, personally, if I haven't given them time to see.

So I'll stay off for a while.

I'll demur, for now, having my own blog, as I am behind schedule on filing my tax year 2002 returns, finishing an exam that I have to give on Wednesday, and getting in a job application for a tenure track position.

Perhaps Patrick is more right than I hoped, and I have allowed my obsessive-compulsive blogging on your site to interfere with your reader's agendae, and my own work.

History will judge if Asimov Number is a useful way to study the Science Fiction community; but it is not fair for me to impose on your hospitality.

Can I trust that you'll keep this archived, so that I can mine it for my paper, later?

Thanks again,


Jonathan Vos Post

#30 ::: Bruce Baugh ::: (view all by) ::: May 30, 2004, 11:17 PM:

Maintaining one's own LiveJournal would require precisely no more effort than posting here. Ditto with a Blogger-hosted weblog. Choose a layout and go to it; they handle everything but writing content. Just by way of information.

#31 ::: Jill Smith ::: (view all by) ::: May 30, 2004, 11:29 PM:


You obviously come from a place of great, genial goodwill. You delight in many subjects and write at great length.

Here comes the part where I may be overstepping my bounds as a guest, and for that I beg pardon of my hosts...

But you also seem a bit disingenous: "I'll demur, for now, having my own blog, as I am behind schedule on filing my tax year 2002 returns, finishing an exam that I have to give on Wednesday, and getting in a job application for a tenure track position." If you were interested in setting up your own blog it would take approximately ten minutes (less?) with blogger, livejournal, or any of the other major blog-hosting sites. I find it difficult to believe that a polymath such as yourself has not looked into such a thing.

If you truly have other things to do, please - go do them. Don't use Teresa's bandwidth as a procrastination device. It's like coming to a party and drinking lots of your hosts' wine, all the while saying, "I have better things to do."

You say earlier, "I agree, but don't want to further burden Teresa and Patrick, after their kindness is segmenting, partitioning, exiling, guest-blogging, or otherwise putting my postings somewhat out-of-context." The term "guest-blogging" seemed out of place. I don't think you are guest-blogging. Guest bloggers are explicitly asked or invited to take up their hosts' bandwidth on a subject. You seem to have many areas of expertise. Why you should need to use this platform to display them, when there are so many easy ways to create one of your own, seems absurd.

Jonathan, your open, eager, information-seeking-and-dispensing personality seems perfect to create your own corner of the web. It won't take but a few minutes. 'Tis far better to start your own party than to drink all your hosts' wine.

...and if I have overstepped my guestly duties, I humbly apologize.

#32 ::: Teresa Nielsen Hayden ::: (view all by) ::: May 30, 2004, 11:45 PM:

No. This is not subject to a vote, however counted.

Yes, you're being obsessive-compulsive. I nevertheless think you'd write a very interesting weblog or Live Journal, and I promise I'll link to it if you do.

#33 ::: xeger ::: (view all by) ::: May 31, 2004, 12:20 AM:

Here's the creation link to set up your own free livejournal, and here's the link for one of the many blog capable sites. If you'd rather roll your own, Moveable Type is quite nice, and comes in both a non-commercial and commercial version.

#34 ::: Jonathan Vos Post ::: (view all by) ::: May 31, 2004, 01:27 AM:

Teresa, Bruce Baugh, Jill Smith, and xeger,

Thank you for politely prompting me to have launched, seconds ago at:

I hope that you don't mind that my first page links to Making Light.

Feel free to link to me if you like; I've gulped too much of your party's wine, and want to serve my own to the thirsty.

#35 ::: Lenny Bailes ::: (view all by) ::: May 31, 2004, 01:29 AM:

Isaac Asimov numbers, such as the 1000 Year Plan, Nightfall 2, and Opus 100, may be signifiers of great import within certain Science Fictional communities -- even as the number of handshakes between ourselves and P.T. Barnum may measure our degree of separation from the U.S. Blues.

But, I submit to you, if Hel is the absinthe of Gort, the signifier history will use to proximate all of our separate degrees may well be our Medium Lobster number. It is a good number. It is not the loneliest number that we will ever do. Giblets and Fafnir (and maybe even Chris, whoever that may be), may possess lower Lobster numbers than ourselves. But all the world over, all those who read the wisdom of this ineffable being may partake equally of the superior knowledge from beyond time and space.

And this is good.

#36 ::: Bill Blum ::: (view all by) ::: May 31, 2004, 08:33 AM:


I never bothered to compute my Medium Lobster Number, but I know my Scallop Coefficient.

#37 ::: Epacris ::: (view all by) ::: May 31, 2004, 11:46 AM:

Have you worked out your KK/DD preference ratio?

Hereinsofar my DD integer perforce remains zero, but I've made a start on building up a modest KK one (see "K-Day")

#38 ::: Bill Blum ::: (view all by) ::: May 31, 2004, 05:00 PM:


I don't do Krispy Kreme-- I prefer Tim Hortons.

#39 ::: Epacris ::: (view all by) ::: June 01, 2004, 04:12 AM:

Is this the same Tim Horton - Architect, 30, of Surry Hills who was profiled for his reaction & the effect on his family of the recent Federal Budget in the Sydney Morning Herald? (see ) Didn't know he had a doughnut shop on the side :)

Does your preference still apply to the new pre-cooked, frozen, shipped & then "baked" versions? We do have Wendy's, their "parent", but one suspects this, like Dunkin', isn't present in Australia, though otherwise we have reasonably good relations with Canada. Except for that bit about the salmon. And pork products. Mmmm ... there's a little rivalry in the "cheap backlot for US movie productions" market too, but overall nothing really serious. What's the "Wegmans" version like?

Anyway, waited until the huge queues died down, then went & sampled varieties of KK's by sharing them around. With eyes closed it's hard to tell the difference except for the ones filled with different flavoured goop. The sugar or icing really overpowers the flavour, so we could only manage a mouthful of each. Happy now that we've tried them & haven't developed a craving.

#40 ::: Epacris ::: (view all by) ::: June 01, 2004, 04:12 AM:

Is this the same Tim Horton - Architect, 30, of Surry Hills who was profiled for his reaction & the effect on his family of the recent Federal Budget in the Sydney Morning Herald? (see ) Didn't know he had a doughnut shop on the side :)

Does your preference still apply to the new pre-cooked, frozen, shipped & then "baked" versions? We do have Wendy's, their "parent", but one suspects this, like Dunkin', isn't present in Australia, though otherwise we have reasonably good relations with Canada. Except for that bit about the salmon. And pork products. Mmmm ... there's a little rivalry in the "cheap backlot for US movie productions" market too, but overall nothing really serious. What's the "Wegmans" version like?

Anyway, waited until the huge queues died down, then went & sampled varieties of KK's by sharing them around. With eyes closed it's hard to tell the difference except for the ones filled with different flavoured goop. The sugar or icing really overpowers the flavour, so we could only manage a mouthful of each. Happy now that we've tried them & haven't developed a craving.

#41 ::: Brad DeLong ::: (view all by) ::: June 02, 2004, 02:03 AM:

What is my Medium Lobster number?

#42 ::: Clark E Myers ::: (view all by) ::: June 02, 2004, 02:04 AM:

There's no probably about Laurence being a Lieutenant General given that it literally takes an Act of Congress; he was or he wasn't. My memory is that he was, I'm quite certain that he had stars not certain that it was 3. Given that even in this obscure spot it has not yet been corrected it may be correct.

The Proxmire story is The Return of William Proxmire by Larry Niven in the tribute collection - Requiem : and Tributes to the Grand Master (TOR) - The story goes Proxmire resents Mr. Heinlein's influence as writer. That is Proxmire gave Golden Fleece Awards to projects inspired by Mr. Heinlein's writing. Proxmire gets a time machine and goes back to inject Mr. Heinlein with antibiotics at the critical moment. This action is intended to keep Mr. Heinlein healthy and in the Navy and too busy to write. On return to our day with a changed timeline Proxmire finds Mr. Heinlein to be Admiral Heinlein of the high that is space navy - having even more influence as healthy Navy than as an invalid writer.

#43 ::: Teresa Nielsen Hayden ::: (view all by) ::: June 05, 2004, 06:31 PM:

Medium Lobster and Giblet are godlike. It is true.

#44 ::: Anton Sherwood ::: (view all by) ::: September 07, 2004, 08:03 PM:

. . . the Johnson of Johnson Solids (all edges the same length, don't care about angles or faces being the same).

A Johnson solid (of which there are 92) is a convex nonuniform solid whose faces are regular. Norman Johnson, by the way, is currently active on a polytopes list hosted by Magnus Wenninger.

#45 ::: Jonathan Vos Post ::: (view all by) ::: September 08, 2004, 10:31 AM:

Anton Sherwood:

Right! And the pictures are pretty, as you can see at:

Eric W. Weisstein. "Johnson Solid." From MathWorld--A Wolfram Web Resource.

Sure, we all know what a Pentagonal pyramid looks like, and are not surprised at a Pentagonal cupola, or even a Pentagonal rotunda, but how about a Gyroelongated pentagonal pyramid, Metabiaugmented dodecahedron, or Pentagonal orthocupolarotunda?

The page I link to also has the paper patterns to blow up, cut out, fold up, and glue to make models...

As Eric W. Weisstein puts it:

"The Johnson solids are the convex polyhedra having regular faces and equal edge lengths (with the exception of the completely regular Platonic solids, the 'semiregular' Archimedean solids, and the two infinite families of prisms and antiprisms). There are 28 simple (i.e., cannot be dissected into two other regular-faced polyhedra by a plane) regular-faced polyhedra in addition to the prisms and antiprisms (Zalgaller 1969), and Johnson (1966) proposed and Zalgaller (1969) proved that there exist exactly 92 Johnson solids in all."

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