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."

Comments

I just have to laugh...

[freeBill]

...at this...

But I can assure you that many readers of fiction underestimate just how much of a novel's content is simply made up. There is a common assumption among readers that much of what appears in a novel is thinly veiled and repackaged reality. You can imagine how provoking this is to a novelist who works so hard to invent it.

...especially since the brilliance of The Cryptonomicon is the degree to which it blended clearly historical facts with clearly fictional events. I found myself wondering time and again where the line was drawn between what was made up and what was not. Time and again Neal used a series of facts (say Fact A, Fact B, Fact C, Fact D, and Fact E) the first of which (Fact A) was based on history and the last of which (Fact E) clearly could not have happened. The fiction was blended so well with the fact that I couldn't tell where the transition between fact and fiction began (Fact B? Fact C? Fact D?).

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.

Re:I just have to laugh...

[schulzdogg]

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).

Incorrect! Turing's bicycle did have a broken chain! He did bury silver as a shore against accupation. Read his biography. It was amazing how realistic some of those things were...

Then there's the FTL drive problem

[freeBill]

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.

...

[ruin]

Now I know why Cryptonomicon was such a thick book...
--

The real history of WWII cryptanalysis

[Animats]

The book to read is "Battle of Wits, The Complete Story of Codebreaking in WWII". This has a broader overview of the entire operation, including pictures of codebreaking machines not previously published. The bombes are of course shown, but there are also film comparators that used 70MM film, as well as a building-sized machine built out of telephone switching equipment by Bell Labs. There's also considerable discussion of the use of standard and modified IBM punched card equipment.

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.

Hope for the Clueless?

[Alien54]

I liked this bit:

... I can assure you that many readers of fiction underestimate just how much of a novel's content is simply made up. There is a common assumption among readers that much of what appears in a novel is thinly veiled and repackaged reality. You can imagine how provoking this is to a novelist who works so hard to invent it. Furthermore, since my novel actually does contain an original cryptosystem, readers are even more inclined than usual to assume that all of the crypto mentioned in the book is real.

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.

The BIG U is in print

[YIAAL]

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.

Zeta functions...mmmm...

[Telal]

I'd function Catherine Zeta Jones anytime. :-)

Yes

[alewando]

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.

Re:Cryptonomicon

[Ryan J. Evans]

From Neal's webpage:

Since Finux was the principal operating system used by the characters in the book, I needed some creative leeway to have the fictitious operating system as used by the characters be different in minor ways from the real operating system called Linux. Otherwise I would receive many complaints from Linux users pointing out errors in my depiction of Linux. This is why Batman 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.

Re:So what is the zeta function ?

[ElJefe]

The zeta function is defined as an infinite sum:

zeta(s) = Sum from n=0 to infinity of 1/n^s

Here, s can be any real or complex number. For example, zeta(2) = Pi^2 / 6, and zeta(.5 + 14.134i) = 0.

The Reimann hypothesis is that all the zeroes of the function lie are of the form .5+b*i. where b is some real number. To date, this hasn't been proven and remains one of the great unsolved problems of math.

From what I've been told, the zeta function also shows up a lot in number theory and quantum mechanics, but I don't really know much about it...

-Chris
(I'm an applied mathematician, dammit.)