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Neal Stephenson on Zeta Functions
Introspective writes "Over on Cryptome they have published an Email from Neal Stephenson explaining his use of Zeta functions in Cryptonomicon. It gives a nice insight into writing about advanced cryptography ( in fiction, that is ) and the kind of reactions he gets back from his readers."
...at this...
A good example of this was the account of Alan Turing and how he intuited the idea of a digital computer by contemplation of Goedel's Incompleteness Theorem: I knew Turing conceived of the idea of computers long before they were invented. I knew he was very much aware of Goedel (his Noncomputability Theorem rests entirely on Goedel's methods).
But I had never heard it said that he had figured out that computers were possible based on the implications of Goedel. We can see that today, but we have the benefit of hindsight. Was this just something Neal made up based on that hindsight? Or did Turing really see this back then?
There were clearly fictional parts of the book's Turing. We can safely assume the bicycle ride was invented. (Am I the only one who noticed the fact that he introduced the bike-chain explanation of why prime numbers are so key to crypto without ever doing anything with it?) The vicar's wife probably never peeked at her bowl full of balls (I think).
Where did the Goedel inspiration go on this truth-fiction spectrum? Neal's blurring of the line makes it hard to determine from the novel. That's good. It makes for a ripping good yarn. But it also makes me less than sympathetic to the author's complaints about readers. Yeah, those readers just assume more of the novel is real than is actually the case.
That's right. Mess with our minds and then complain that we're confused.
For those who are wondering, yes, Enos Root did die in Sweden in 1944 only to reappear 50 years later in a prison in the Philippines. And, for those who are wondering about my question, I have found evidence that Turing's inspiration was indeed based on Goedel.
Of course, there's always the possibility some reality hacker read the book, decided it was better than the actual story, and started spreading historical references to the Goedellian inspiration of Turing. The universe is, after all, controlled by those who have an understanding of the source code.
Reading is FUNdamental, according to the vicar's wife. I don't think she peeked. Really.
Eternal vigilance only works if you look in every direction.
If I figure out a really neat idea for a faster-than-light drive but there's just one minor problem with it, I write a hard sci-fi novel based on it, glossing over the problem.
If I figure out a really neat idea for a faster-than-light drive with no problem, I don't have time to write the novel. I'm out in the back yard building my spaceship.
Eternal vigilance only works if you look in every direction.
And if you would like to achieve ever lasting fame and noteriety you could try to prove the Riemann Hypothesis which conjectures that every x satisfying Zeta(x) = 0 has real part 1/2 .
I'd like to see a proof posted on slashdot.
:wq
...for warning us about the spoilers.
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silence is poetry.
Dr. Michael Anshel is a professor in the department of computer science at my school --
City College of New York. He offered a little background info into the discussion over zeta functions that Mr. Stephenson is referring to.
From: MikeAt1140@aol.com
Date: Sun, 11 Mar 2001 19:07:28 EST
You may find the following exchange prior to Neal
Stephenson' letter of interest. Feel free to forward. Best.-Mike Anshel
In a message dated 2/23/01 1:33:10 PM, schneier@counterpane.com writes:
>
A simple acknowledgment in future discussions of this work by the author and
his agents that there is a cryptography based on zeta functions,introduced in
the open literature by Michael Anshel and Dorian Goldfeld and whose patent
rights are assigned to Arithmetica Inc would do for a starter.
Michael Anshel
w o r l d w i d e w e b e r
Now I know why Cryptonomicon was such a thick book...
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s needs to be greater than 1 for the series to converge.
The series Sum 1/n from n=1 to n=inf does not converge although it diverges very slowly. This can more easily be seen by looking at the integral S 1/n dn which is like log n, which diverges. And more so, for s less than one, the integral really diverges.
Duke Mathematical Journal is a pretty good journal, so it must be a good paper.
Most writers on the subject haven't really captured the scale of the operation. This wasn't done by a few smart people. WWI cryptanalysis was like that, but WWII made it into an industrial operation. Friedman was the one who first used IBM gear for cryptanalysis (in 1934, and it was a really tough sell getting the money during that period). Once the operation really got going, tens of thousands of people, and thousands of machines of various types, were involved.
Cryptanalysis on that scale had ever been done before. The Germans and Japanese had cryptanalytic operations, but at the "small group of smart people" level. Small groups would never have decrypted enough stuff to seriously affect the war. But the industrial-strength effort mounted by the Allies made a real difference.
It's instructive to look at the pictures. The stuff built by National Cash Register looks like the innards of a cash register. The stuff built by IBM looks like IBM tabulators. The stuff built by Bell Labs looks like a telephone central office. The Colossus machine, though, does have a vague resemblance to an early tube computer, although the big endless loops of paper tape clearly indicate its special purpose nature.
Colossus was actually based on some prewar British Telephone experiments with electronic switching. And nothing that came out of the crypto work worked anything like a general-purpose computer. All the crypto stuff was very special-purpose. This really isn't where computers came from. Babbage actually had a much more computer-like architectural concept.
The problem wasn't theoretical. It was that nobody had yet developed a useful high-speed data storage device that didn't involve moving parts. Using two tubes to store one bit was too expensive and bulky to be used for a general purpose computer. Delay line memory came after the war, and was an outgrowth of some radar gear that used delay lines. The stuff during the war stored its state in relays, tubes, paper tape, or punched cards. The hardware for a useful, programmable, general purpose computer just wasn't available yet.
There really is a National Puzzle Center run by the NSA. Typical question: Which of the following palettes represents a possible PNG palette?
Slightly OT, but the Zeta function, in addition to being of significance to primes is important to astronomy. That's because to derive the thermal emission from eg. a star as a function of Temperature you need to integrate the Planck Blackbody Function, which gives Zeta(4) = pi^4/90 The result is known as the Stephan-Boltzmann Law
that's why you read it in the new 'scientist' as opposed scietific american or nature...
A: None. The Universe spins the bulb, and the Zen master merely stays out of the way.
prove the RP, make a quick million... http://www.claymath.org/prizeproblems/index.htm
A: None. The Universe spins the bulb, and the Zen master merely stays out of the way.
The Xanth series after number 9 and the Adept series after the first three all sucked.
I liked it. I heartily recommend it to anyone who likes all his other books.
Ummm... Mute, Ox/Orn/Omnivore, Viscous Circle (series), and a bunch of others. Early Xanth, Incarnations, and Adept books.
I liked those ones much more than his later work which I stopped reading. I partly outgrew him, but he also got a lot more childish in later books.
IMHO the 80s were his strong period.
His books all seem to suffer from "Send In The Cavalry!" syndrome. One guy struggles against all odds for the whole book, and then suddenly his friends and the all-powerful mob/police/army/EPA/Allies come save the day.
They're called 'signatures'.
I just wonder how unique it is...?
I'll give you US$100 for it.
Not A Sig
Live with it, and pray your product isn't mentioned by name. Do you really expect "Sneakers" to provide cryto info, or "Dr Strangelove" to explain nuclear strategy? Any item more complex than a felt-tip pen should be made non-company specific by a rational author/screenwriter.
I have to laff at all this. Obviously some folks really need to get out more often. Sometimes the reality check bounces. Sometimes paranoia pays, and sometimes it becomes a self-fulfilling prophecy.
Never seen anything like that around here, of course.
"It is a greater offense to steal men's labor, than their clothes"
Don't buy it to read ... buy it because you collect neil stephenson.
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I wonder what kind of ass chewing Stephenson would have given Comstock if he whined about using his name as a bogus key.
"Black Holes Are Where God Divided By Zero"
Has anyone heard any rumours on Quicksilver, it's
been about 2 years since Cryptonomicon was released. Seems about time for the next one.
The difference between Canada and the USA is that in Canada healthcare is a right and gun ownership is a privilege.
It's not *that* bad! The plot's a bit loose, the writing might not be up to his usual standards, but it's really, really, funny. I'm almost tempted to read it again....
--Bruce Fields
I'll be honest, I found it a very tough book to read. The narrative was poor, and it wasn't easy to read without putting thought into it.
I'm sorry, if I want thought, I'll read philosophy or texts; when I read a novel, I'm after relaxation and entertainment.
Snow Crash and The Diamond Age both drew me in with fantastic narrative and were truly great books. Even The Big U was better than Cryptonomicom.
~Cederic
More like...
Veni,vidi, visa
I came, I saw, I shopped
Sadly, it has a typically poor Stephenson ending. He really needs to learn how to write a graceful ending that ties up some of the loose ends he's spent the whole book generating. I find it very frustrating to read about characters for hundreds of pages and develop some empathy for them and then have the book rudely chopped off just before finding out how their personal situations were resolved.
There's no point in questioning authority if you aren't going to listen to the answers.
>works in Gotham City, instead of New York--by putting him in Gotham City, the creators afforded themselves the creative license to put buildings in different places, etc. I always thought Metropolis was New York and Gotham is somewhere around where Chicago should be... that said, with DC comics continuity who knows?
erroneous: look me up in a dictionary
I always thought that Neal was using a clever pun in choosing FINux as the name of the OS. Fin, obviously due to Linus Torlvalds heritage.
-- Good judgement comes with experience. -- Experience comes with bad judgement.
There is a million dollar prize for proving the Riemann Hypothesis. See the Clay Institute Page.
One can show that \zeta(s) = 0 whenever s = -2k, for any k > 0. (\zeta(0)=-1/2.) This follows from the functional equation, which in pidgin-TeX is:
\zeta(s) = 2^{s} \pi^{s-1} \sin(\pi s/2) \Gamma(1-s) \zeta(1-s).
This says that once we know \zeta(s) for Re(s)>1 (and this is the region for which the Dirichlet series \sum_n 1/n^s converges), then we know \seta(s) for Re(s) 1, it follows that \zeta(-2k) must be zero to cancel the pole of the Gamma function.
bravo
That's weird. I thought a book was an instance of art and as such, one of its functions was to generate some sort of activity in the reader's brain.
This is not just aimed at the parent comment. I find the ubiquity of such anti-intellectual stance astonishing. Try any alt.books.* newsgroup and all people discuss is whether the story had a "good ending". Sigh.
"Only the small secrets need to be protected. The big ones are kept secret by public incredulity." - Marshall McLuhan
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Thanks for the info - I don't plan on selling, my actual goal is to get NS to sign both of them, and keep them.
Worldcom - Generation Duh!
Reason is the Path to God - Anon
This appears to have been a private communicate so I'm not totally sure it was appropriate for them to publish it on their web page, or slashdot to refer to it here. Interesting though...
Sig is taking a break!
Yeah, that confused me. And the fact that the Societas Eruditorium was poised to actually play a role in the plot, but didn't.
It's my understanding that Cryptonomicon is the first part of a series of books. Makes sense, when you consider the vast amount of material which was vaugely referenced but never used (who were the black and Indian guys with Rudy and Otto on the boat (he never even gives their names!)? What's up with that secret society? What was Root doing working for the NSA during the 50s? If he faked his death, why? If not, how is he still alive? Not to mention the data haven; plenty of interesting things could happen there).
If you haven't read Cryptonomicon yet, I heartily recommend you do so. It's three quarters of a good novel, and the last quarter has enough twists in it that you can overlook the cheese and the fanboy religious overtones.
You can read the prologue online and decide for yourself. Try before you buy, and see some of the zeta functions Stephenson is talking about.
If I figure out a really neat idea for a faster-than-light drive with no problem, I don't have time to write the novel. I'm out in the back yard building my spaceship.
If I'm not wrong, a FTL vehicle would go back in time, hence you would have lots of time to write. You could write it yesterday for example.
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Men with no respect for life must never be allowed to control the ultimate instruments of death.
GW Bu
Any mathematicans care to explain it ?
Stephenson's points about not linking his fiction too closely to real-world companies are interesting - I wonder if this has any bearing on an oddity in Cryptonomicon : Linux is disguised (barely) under the name Finux - however, if I recall correctly, Windows and Be are identified by name. I'd be interested to know the rationale behind this.
This is kinda offtopic, but Stephenson's first novel, "The Big U" is now back in print. I just bought a copy. For the many who've been looking for it in used bookstores, it's now available.
InstaPundit! Ahead of the Curve Since 30 Minutes Ago
A year or so back when _The Big U_ was pulling down absurd bucks on Ebay Neal made very clear he didn't consider it worth the fuss.
That warning made, I'll probably buy it myself because I'm such a fanboy.
Eternal vigilance only works if you look in every direction.
Although explicit permission was given in this case, John Young of Cryptome has a habit of publishing things that other people don't want published. He's gotten in semi-serious trouble for publishing classified documents before (and they're still on-line). Ironically enough, however, he took down the DeCSS code because 'enough other people were mirroring it' (paraphrase, can't find the link right now).
I'd function Catherine Zeta Jones anytime. :-)
Actually, this wasn't acknowledged by the international scientific comunity, but Mai (no last name), a papua mathematical savant who developed the equivalent of 2500 years of Western number theory from first principles using only the bones of defeated and eaten enemies, has developed an entire proof of the Riemann hypothesis, which has been photographed into microfilm by anthropologist Lucius Zingelberger, and is currently being stored in the local library at the village of Ikai, 200 miles into the deep woods of the island. As far as I know, it has no telephone number or Internet connection, so interested parties should visit Ikai Library in person; I believe the daily fee for borrowing microfilm from it is 8000 human bones (how one will acquire this amount is none of my business). Good luck on the trip, and don't forget to take your shots! (And your shotgun. White man's meat is very much appreciated in Papua New Guine. Just ask Prof. Zingelberger.)
-- Kaufmann
To the editors: your English is as bad as your Perl. Please go back to grade school.
I keep seeing references to this or that algorithm being used to generate a one-time pad. The whole point of a one-time pad is that it's generated randomly so that it cannot be uniquely decrypted to any particuar plaintext without knowing the pad used.
What Stephenson describes is a stream cipher using the zeta function to generate the bits, and using the date as the key. It's no more a one-time pad than would be, say, RC4.
That's right about Turing's bicycle. Please moderate the previous posting up.
I have two copies of the book, one in fully readable condition, and one "strange". I assume the "strange" one to be due to a publishing error, but I wonder how many got out of the publisher, and how many were kept (ie, not returned)?
Anyhow, my GF got the book for me a couple of xmases ago. She bought it off Amazon, and when I received it, I immediately began reading it. About a third of the way through, the book "repeated" - I thought I was losing my mind, but the text did repeat. I scanned farther forward, and it "repeated" again, never getting more than 50-75 pages "forward". I think there was a production problem, and multiple "leaves"(? Can't remember what the individual page bundles are called in publishing) got inserted. Funny thing was, the bundles weren't from near the end of the area I was at, but instead were from the mid-beginning, from a point I was well past.
Anyhow, it made the book unreadable, so I had my GF ask for another from Amazon - they complied, but never asked for the original back in return. I just wonder how unique it is...?
Worldcom - Generation Duh!
Reason is the Path to God - Anon
I'd explain it myself, but this page does a pretty good job, and I'd hate to duplicate efforts. It's an important function in number theory, particularly concerning prime numbers.
Having been in this business for quite a few years now I can assure you that the annoyance of people who are left out of novels is nothing compared to the fury of those who fancy that they have been inserted into novels without having given their permission.
:)
Bit of a passing reference to the reason he feels that the Big U is a bad book, perhaps?
Believe with me, my saplings.
Maybe that's what the 'number stations' are for...
Yeah, that confused me. And the fact that the Societas Eruditorium was poised to actually play a role in the plot, but didn't.
A number of Stephenson's books seem to have a problem where the reader is never quite sure if a character died or not, as his prose in these parts is perhaps deliberately vague.
Plus his endings always leave the reader danglingt, which is too bad, because the rest of the text is awesome.