*From: Ethan Bradford
Location: Seattle
Date: 05/12/2007*

Your mention (at Google) of creating whole universes, and how you can't explicitly specify the digits of pi in a finite number of bits brought to mind this classic comic: http://xkcd.com/c10.html.

**From: Greg Bear**

Date: 05/14/2007

Thanks, Ethan! For those who weren't there, I had a great time at Google in nearby Kirkland discussing the theory of Universal Libraries, a key component in my soon-to-be-finished CITY AT THE END OF TIME. (A universal library is brilliantly described in Borges's "The Library of Babel." It contains all possible permutations of a string of symbols--in Borges's essay, a book of five hundred or so pages.) The Google team were sharp as tacks--no surprise--answering questions in seconds that it took me months to figure out on my own. So now I'm honing my take on this peculiar branch of linguistics/math/number theory based on their comments.

One thing I forgot to mention: when Carl Sagan, in CONTACT, posited that pi contained a metaphysical message, he was criticized for a mathematical impossibility: pi is an incompressible random number, therefore cannot contain anything that makes sense. Yet one of the questions I asked at Google was whether or not pi can contain a universal library. (The Google experts came down on both sides.) Does pi contain all possible variations of a string of numbers of length n? How long will it take before that string repeats? Does the repetition occur at random intervals? Some of these are not easy questions to answer, believe me.

*From: patrick
Location:
Date: 05/14/2007*

Ah, seems you and Bruce Sterling just missed each other in passing. And is there a video or transcript of your visit there?

Permutations....I know in music, at least in even-temperament, there {were} originally only four major transformations, each with 12 transpositions, making 48. Then, my theory instructor found 48 more by a sidereal rotation of the set.

The thing is, permutations are defined, not just by intervals, but, by some boundary. Which apparently hasn't been discovered yet in pi. Still, instead of grunt-crunching the string out, I would think there might be some elegant theoretical manner of finding more out about it.

**From: Greg Bear**

Date: 05/14/2007

There are a number of interesting methods of analyzing the complete permutations of a string of fixed length... revelation of which will have to be reserved for the novel! If I can fit it all in. Maybe in the Universal Library edition, along with all the alternate versions and drafts and outtakes...

*From: patrick
Location:
Date: 05/16/2007*

lookin forward to it!

*From: Fred
Location: Chicago
Date: 06/11/2007*

Pi is an incompressible random number?

You seem to know more than anyone else does about it. Do you expect the Fields Medal in Hyderabad?

It's not even proven that pi is normal, a prerequisite for randomness.

Pi is an uncompressed, apparently-random number. That it hasn't been done is not a sufficient indication that it cannot be done. It's impossible to prove the randomness of pi, or any number for that matter, by appealing to the characteristics of some subset of its digits. This is an identical problem to determining whether a coin is perfectly fair using a finite number of flips. Which is to say, an impossible problem.

That being said, any non-terminating random number contains an infinite quantity of universal libraries, in any arbitrary finite encoding scheme you can imagine. That's not self-evident? (Rhetorical question; it IS self-evident.)

**From: Greg Bear**

Date: 06/12/2007

All good points. How nice they are so obvious to you. And so--your practical exercise, not a proof, since I don't want to just hand you the Fields Prize: write pi out to a billion digits, then run it through any lossless compression filter, and tell me what you come up with. Then add one digit and try it again. Reiterate until you get tired. (This is easily doable, of course--I'm sure it's already been done, probably to a trillion or more.)

Compare with, say, a Dickens novel--or even Finnegans Wake.

Apparently, once you're past the first n digits (I don't know how many), pi and similar key numbers denature--that is, become indistinguishable from each other--which implies the first n digits are very important to the universe, while the rest are only important to mathematicians--who will never never be able to tell them apart, once the serial numbers are filed off, so to speak.

What value of n are we looking at here, and is it the same for any such number?

Any thoughts--any dissenters?

Pardon my ignorance if all the answers are immediately obvious.