That struck me as rather odd as well.

Dr. Netz is lucky the puzzle wasn't an intricately carved and gilded box.

It will, of course, be some time before this connection leads to the famous Epiphany of Teresa of Brooklyn, wherein she woke (or will wake) in the middle of the night with a complete formulation of what will be (or has come to be) known as [censored by order of the Department of Temporal Security].

Do you ever find yourself thinking that wherever you go, people are surreptitiously watching you? And taking notes? And they're all grad students? And they're all time travellers? And you wonder: What am I going to do? Did I do it already? ... I always try to act like I haven't noticed them.

http://mathworld.wolfram.com/Stomachion.html
"...In November 2003, Bill Cutler found there to be 536 possible distinct arrangements of the pieces into a square, illustrated above, where solutions that are equivalent by rotation and reflection are considered identical ..."

My Math Advisor when I earned my 1st two B.S. degrees at Caltech was Herbert J. Ryser. He was considered by some "the King of Combinatorics."
[see footnote]

The official bio does NOT mention the effect his work had on Cryptography. That would put us into Neal Stephenson "Cryptonomicon" territory.

But consider this. If Archimedes was doing Combinatorics, and we know there were metal analog computers for Astronomy in the greater Greek worlds (Antikythera Mechanism), then -- could it be that Archimedes was actually like Babbage, invented the digital computer, it was built two millennia ago, and the ancient world was secretly computerized? I think the Dark Ages were caused by link rot. Or the Church cracking down on Gothic Blogs...

Footnote: [According to his bio on Ohio State's web domain: He was born on July 28, 1923 in Milwaukee, Wisconsin to Fred G. and Edna (Huels) Ryser. He attended the University of Wisconsin, receiving a BA. in 1945, an MA. in 1947, and a Ph.D. in 1948. His doctoral thesis "Rational Vector Spaces" was written under the direction of C. J. Everett and Cyrus C. MacDuffee. He then spent the year 1948-1949 at the Institute for Advanced Study in Princeton.]

[In 1949 he was appointed assistant professor at Ohio State. He was promoted to associate professor in 1952 and to professor in 1955. His presence at Ohio State together with Marshall Hall established a tradition of excellence in combinatorics in the department. While at Ohio State, Ryser directed four Ph.D. students.]

[In 1962 Ryser accepted an appointment at Syracuse University, then in 1967 he moved to California Institute of Technology, where he spent the rest of his life.]

[Ryser is widely regarded as one of the major figures in combinatorics in the 20th century. Already in his final year of graduate studies at Wisconsin, he collaborated with R. H. Bruck to prove the famous Bruck-Ryser theorem, which states that there are no projective planes of order n congruent to 1 or 2 mod 4, if n has an odd power prime factor congruent to 3. To date this is the only general nonexistence theorem for finite projective planes. In 1950 he and S. Chowla extended the nonexistence theorem to symmetric block designs. Later he found a short and elegant proof of this theorem using the Witt cancellation law.]

[Ryser contributed to many different parts of combinatorics, especially to the theory of combinatorial designs, finite set systems, and the permanent and other combinatorial functions. His seminal book "Combinatorial Mathematics" in the MAA Carus Monograph series is a classic which has enticed many young mathematics students into this area. He was a master expositor and a great teacher, winning several teaching awards at Caltech. He directed 12 Ph.D. students.]

[Ryser served as editor of the Journal of Combinatorial Theory, Linear and Multilinear Algebra, and the Journal of Algebra for many years. He also participated in the Visiting Lecturers' Program of the MAA for over 10 years.
He died on July 12, 1985 in Pasadena.]

http://www.magicdragon.com/UltimateSF/thisthat.html#time

[warning: part of huge 400+ Kilobyte page, loads slowly.

Some important early time travel subcategories, and their first published
examples include:

Present to Future: "Anno 7603", by Norwegian playwright Johan Hermann Wessel (1781)

Present to Past: "Missing One's Coach", anonymous, Dublin Literary Magazine,
1838, sends narrator back a millennium

Future to Present: "An Uncommon Sort of Spectre", Edward Page Mitchell, 1879
(or should I count the Ghost of Christmas Future in Charles Dickens'
"A Christmas Carol" (1843)?

Past to Present: "The Hour Glass", Robert Barr, [The Strand magazine,
December 1898]

Time Machine: 7 years before H. G. Well's "The Time Machine", there was
"The Clock That Went Backwards", by Edward Page Mitchell,
[The New York Sun, 18 September 1881]

Bottom line, however, so far a Physics, Math, and Philosphy agrees (excluding SF authors):

It MAY BE possible to "participate in the past" by travlling back in a time machine.

It is INCONSISTENT to think that you can "change the past." In what philosophers call the "block universe", looking at 4-dimesnional space-time as a whole, NOTHING CHANGES.

There is not one past, before a time traveller arrives, then a second, changed by said traveller (and then a 3rd after the time patrol changes back to status quo).

I've taught a class on Time Travel many times, and lectured on this at cons.

Or is that what THEY want you to think? Bwaahaaa ha ha haaaa...

MKK

I believe that opinions about the immutability of the past continue to be somewhat mutable.

In our own field, we've got Greg Egan's sleight of hand, where he attacks our notions of sequence and causality, attempting to shore up his pitch for multiple, branching universes with appeals to quantum mechanics. (Events that we're calling "the past" may not really have collapsed yet.)

Admittedly, Egan's rationale is kind of a shell game, but I've seen other statements from mathematicians, philosophers and physicists who now question the consistent "one-universe, only" model that Minkowski formulated.

((Of course, as we all know, the "one Universe only" conceit perpetrated by Marv Wolfman and his Linear Men collapsed on itself, several years ago, when Rip Hunter and Mark Waid restored the Multiverse.))

I remember an episode of Quantum Leap where he was sent back into Oswald. He didn't keep him from killing Kennedy, and he thought he'd failed, until they told him that "the first time" (I hear you screaming, JvP) he killed Jackie, too.

De Camp: attempting to alter the past creates such a huge stress in space-time that the would-be alterer gets snapped back to his point of origin, rather the worse for wear. ("A Gun for Dinosaur".)

Brunner: if it is possible to alter the past, some time traveler will do something to cancel the invention of time travel. ("The Fullness of Time" (last of three-part fixup Times Without Number).)

This reminds me of the reply to a question I asked many months ago here; looking at why so many would-be authors have (and act on) strange ideas about publishing, -"Is there anything as solitary and undemanding of resources as writing?"- was answered "Theoretical mathematics." I'm in no position to judge -- 30 years ago I gave up in the semester after first-year calculus -- but I'm not surprised that an individual thinker could have answered a mathematical poser long before the question categorized.

There have been a few novels about crypto lately, which overcomes the somewhat ethereal nature of "pure mathematics" stories by allowing you to have lots of people trying to kill each other over the big secret.

Suddenly it's obvious that Evariste Galois had gotten a crowbar into polyalphabetics, and the Tespies (Temporal Espionage folks) had to nail him for the chronoffence of Premature Inspiration. Rather like they got Kit Marlowe and Archimedes, but I'm working very close to the edge here.

*walks away muttering about prejudiced time travellers*

Patrick watches...Buffy???

:)

Or not. I'm suffering from final-exam brainmelt, so I think I'll just softly and silently go off and do some grading.

It's not science fiction, but you might look at Tom Stoppard's play, "Arcadia." Math professors write paens to it. The play is concerned with chaos theory, fractals, the Second Law of Thermodynamics, and dynamical systems.

I recently saw it performed here in Minneapolis, and it is a truly stunning work. It has the feeling of sf, in that it pursues two related story lines, the two being about 100 years apart. I haven't read it, it may not work as well in print. On stage, it very nearly lifted my hair right off.

You might also try Stoppard's "Hapgood," which is about quantum mechanics and the observer effect, if I remember correctly.

Add to Mr. Ford's great suggestion of MATHENAUTS the two miscellanies edited by Clifton Fadiman, FANTASIA MATHEMATICA and THE MATHEMATICAL MAGPIE. Stories, articles, poetry, fantasies, and just plain fun. They've even been reissued as trade paperbacks within the last few years. Also, of course, FLATLAND and all its followons. And Rudy Rucker (a mathematician himself, like Vernor Vinge) has written some stories that have great math interest.

One of the odder bits of math fiction is a few chapters in SORORITY HOUSE, a work by Frederik Pohl (possibly with Kornbluth, I'm not sure) under the Jordan Park pseudonym. Bear with my spotty memory: it's been at least 10 years since I read it, and my copy's in Seattle, and it's a bloody scarce book at this point. One of the sorority girls picks up a thin little book of every esoteric math with "elementary" in the title and tries to read it. She can't get past the first paragraph at first. But she knows it's elementary, and she knows she's not stupid enough not to understand an elementary book, so she keeps trying; and over several weeks actually gets hooked on serious math and starts seeing how it works. A very nice sequence in an almost unknown book; might be appropriate to see if someone would reprint that bit. The rest of the book, while fun, is nothing special.

Cheers,
Tom

But a battered "Science Fiction Encyclopedia" [ed.Peter Nicholls, 1979] is before me, to say more about Mathematics in Science Fiction. I'm at the El Dorado County Library for a free 30
minutes of internet, in the middle of a skiing vacation at Lake Tahoe. This is one of the West's
primiere resort areas, and I've never stayed here
before.

Back to Math: H.G. Wells' The Platner Story" [1896, 4-D rotation makes 3-D object mirror-reversed]; Robert Heinlein, "And He Built a Crooked House--" [1940, Tesseract house folds into 4-d); Arthur C. Clarke, "Wall of Darkness" [1949, a toplogical weirdness]; L. Sprague de Camp & Fletcher Pratt, THE INCOMPLETE ENCHANTER [1942, mathematical logc equation is key to travel to alternate worlds]; James Blish "FYI" [1953, transfinite arithmetic]; David Duncan, "Occam's Razor" [1957, explains Calculus of Variations]; Robert Heinlein, "Misfit", [1939, math prodigy Libby]; Norman Kagan, various stories; William F. Orr, "Euclid Alone", [1975, in Orbit 16 anth., author a mathematician, too]; several books by Rudy Rucker.

Comments on loopholes in my claim dismissing "altering the past" are interesting. Truth is, we do not actually KNOW the topology of time. I stand by what I said, in the "default" consensus world of Physics. But it takes a 6-hour course to be even halfway convincing. The one definitive textbok on Time Travel in SF, other literature, math, physics, and toplogy has been republished, as a Ben Bova imprint [Original was American Physics Press]. Referenced on the anchor page in the long page I mnetioned in earlier posting. Author a SF writer turned Professor.

It is extravagently beautiful here, the snow-covered Sierra Nevadas, which we are in; the snow-laded firs and Ponderosa pines; the huge lake spread out below.

I am as happy as I've been in a long time.

Almost ashamed to admit that I'm addicted to the Web, and this blog, and my email.

Yesterday, at the ski lodge, I ran into Gwen Bell, wife of former DEC President Gordon Bell (now a Micro$oft VP). Her opening line to me, before we knew names, was "what was your first computer?"

Mine was an IBM 1130 in 1966. Gwen, FoundinG president of the Computer Mudeum, knew so many of the same pioneers that I do. She's kicking off a national competition for Best Computer Game built by a High School student. Winner gets full schlarship at Stanford. Cool idea!

Okay, back to the ski slopes, at 9,000 to over 10,000 feet abve sea level...

Bye for now...

Perhaps its time to write some then. . .
Thanks all!

Hey, wow, Teresa made a mistake. I know we don't expect that from her, but she is -- I hear by rumour at least -- human. And then she was too busy to notice and fix it for a couple days. SO WHAT? DEAL WITH IT. It's just italics. A little annoying, but nothing worth being a butthead over.

She doesn't seem upset about it, but I personally found particularly the two people I actually named to be unconscionably rude. You're a guest here, partaking of a free service that granted you may contribute to, but is nonetheless hosted by someone else on their own dime and their own free time, and you know what? You have no entitlements, only privileges.

Pointing out an error politely is one thing. But acting like Teresa, instead of making a small error, was ignorant of HTML or somehow committed a horrible faux pas by forgetting a close tag... that makes you a butthead in my book.

(I actually meant to post this the other day, but got busy myself, speaking of free time sometimes interfering with weblogs.)

"iceberg."

She is then whisked back to the film's present. I suppose she must have changed things just enough to delay the invention of the machine, because here comes the mad scientist again, and she's off to another era, and another, and another.

Somewhere along the way, as she dusts a groove into the marble, she's sent back to a limousine driving through Dealey Plaza, where she says:

"why don't you and Jackie trade places?"

The limo drives out of our view, shots ring out, and bystanders shout, "They've shot the First Lady!"

This was the crowd pleaser. The audience at the Naro loved it. It also gave me a fantasy that comes back at odd moments of a terminally unexcited housekeeper at the door of the Dakota, saying:

"why don't you and Yoko trade places?"

Another odd mathematical fantasy just read: KANDELMAN'S KRIM, by the mathematician J. L. Synge. Not a particularly good story, but the Introduction has several wonderful bits on the nature of books, some of which I've quoted elsewhere. The story itself has too much math and not enough plot. Ah well. If you're collecting mathematical fantasies, though, it's an essential work (like Mack Reynolds' CASE OF THE LITTLE GREEN MEN is essential for those collecting novels set at SF conventions).

http://math.cofc.edu/faculty/kasman/MATHFICT/default.html

which has lots of mathematical fiction references.

( Unless you're a Mac Zealot, then this doesn't even qualify as good Mac porn. )