Some Light Bedtime Reading... NOT

These are generally above my pay grade, but a couple of interesting-looking, heavy pieces from the latest online issue of "Inference":

Math, infinity, theology, Ω, and "The Perfect Language" covered by the always-interesting Gregory Chaitin:
http://inference-review.com/article/the-perfect-language
...and in the same issue, this longish-read on the work of Grothendieck:
http://inference-review.com/article/tohoku

Give 'em a read and please send me a 3-sentence synopsis of each when you get a chance... ;-)

Chaitin on the Seduction of Mathematics

I didn't have any Sunday reflection picked out for today, but then Joselle Kehoe posted something that makes for a good one:

http://mathrising.com/?p=1160

It's about Gregory Chaitin reflecting on Ramanujan, Cantor, Euler, and mathematics as a seductress!

a couple of provocative lines:

From Chaitin:

"I believe mathematics is based only on emotion and inspiration and it’s totally irrational and we don’t know where it comes from especially in cases where it’s an obsession."

 and from Joselle:

"...maybe the right way to think about the universe is that the universe is a computation  – computing its future state from its current state.  One can think of everything as a computation – understanding, the physical universe, DNA, as well as current technology."

"Proving Darwin"… Readin' Chaitin

I've already briefly referred to Gregory Chaitin's new compact volume, "Proving Darwin: Making Biology Mathematical," in a couple of posts, but time for a longer blurb…

Chaitin is known for his emphasis on uncertainty and 'unknowability' in mathematics, a topic I find of great interest (even though what most of us love about math is its precision!). His previous popular book, "Meta Math," was a volume that some might say starts where Gödel left off.

His new book (barely 100 pages), is a compendium of university course lectures -- as such, it is a bit choppy, terse, repetitive at points, and informal, but still, I think, a wonderful read from this stimulating, creative thinker. According to Chaitin the book was, interestingly, provoked in part by David Berlinski's "The Devil's Delusion."

In the volume, Chaitin proposes a new field of study he calls "metabiology," or the study of "the random evolution of artificial software (computer programs) instead of natural software (DNA)." He regards DNA as a computer program and his "mad dream" is to develop a "fundamental mathematical theory for biology." His "purpose" is "to lay bare the deep inner mathematical structure of biology, to show life's hidden mathematical core"… or, as he also puts it, "If Darwin's theory is as fundamental as biologists think, then there ought to be a general, abstract mathematical theory of evolution that captures the essence of Darwin's theory and develops it mathematically."

Chaitin presents what he terms a "toy model of evolution" and tries to demonstrate among other things that mathematically, the evolutionary diversity we witness today, can be explained in terms of mathematical algorithms of random mutation over the given immense time scale. I don't know how many will feel he succeeds in his goals, but it is fascinating to see him try [mind you, I don't myself grasp the technical aspects of Chaitin's presentation here. Also, it seems unfortunate that he calls the model of mutation he ends up favoring, "intelligent design," even though it doesn't necessarily imply the more widespread use of that term entailing a deity at work.]
And Chaitin himself knows he may not yet be convincing: at the conclusion of the book he remarks, "Even if almost everything in this book is wrong, I still hope that "Proving Darwin" will stimulate work on mathematical theories of evolution and biological creativity. The time is ripe for creating such a theory." "Creativity" (both mathematical and biological) is what Chaitin is all about, and the 'algorithmic information' that underlies it, and in this case predicts the rate of evolution. (Possibly worth noting that this book might be more apt for computer science and bioinformatics folks than for either straight mathematicians or biologists.)

Chaitin's views are hard to capsulize. He calls himself "a Pythagorean" in the sense that he believes "the world is built out of mathematics, that the ultimate ontological basis of the universe is mathematical, which is the hardest, sharpest, most definite possible substance there is, static, eternal, perfect." Yet he is not a strict reductionist… as I've said, his overriding emphasis is on the "creative" nature of humans and of biology more generally. At one point he notes, "In biology nothing is static, everything is dynamic. Viruses, bacteria and parasites are constantly mutating, constantly probing, constantly running through all the combinatorial possibilities. Biology is ceaseless creativity, not stability, not at all." I'm not sure how professional biologists themselves will feel about Chaitin's ideas/assertions here. References to biologists aren't all that many in the volume (some to Haldane, Maynard Smith, Leigh Van Valen, and Ernst Haeckel), and I'm not sure many current biologists won't feel Chaitin has bypassed a lot in trying to make his case -- he accuses biologists of talking too much "about stability and fixed points" and not enough "about creativity" (they might take exception to that). It's just that the algorithms for biology are incredibly complex (far moreso than in physics) and thus difficult to readily discern. We'll be working on them for decades (centuries?) to come.
Chaitin notes that "every cell is run by software, 3- to 4-billion-year-old software" and "Our bodies are full of software, extremely ancient software. We have subroutines from sponges, subroutines from amphibia, subroutines from fish." It will require "postmodern math" (since Gödel and Turing, or what he calls "open, non-reductionist kind of math") to comprehend biology. This will be achieved via the computer: "The computer is not just a tremendously useful technology, it is a revolutionary new kind of mathematics with profound philosophical consequences. It reveals a new world."
Among those referenced frequently and favorably in the book are Leibniz, Gödel, Turing, Stephen Wolfram, and von Neumann (to whom the book is dedicated); even philosopher Paul Feyerabend gets a favorable nod.

Chaitin's book seems very much a work-in-progress, and it will be interesting to see what comes of his ideas over forthcoming years. If you're interested in both math and biology, or if you've read and enjoyed Chaitin's work in the past you'll want to peruse this small volume… or you can simply watch videos of his lectures on the subject via YouTube:

http://tinyurl.com/6mutwov

also, an older hour-long podcast interview with Chaitin from "Math Factor" here:

http://mathfactor.uark.edu/2010/05/gy-chaitin-on-the-ubiquity-of-undecidability/  



...Another book side-note: One other new volume recently arriving in my local bookstore catching my eye (though not strictly a math book), is John Casti's "X-Events: the Collapse of Everything." Casti is a mathematician and complexity theorist who is always interesting (though this volume looks a tad foreboding).

http://www.amazon.com/X-Events-Collapse-Everything-John-Casti/dp/0062088289

Couple a Books

I haven't read these yet, but already believe they're worth noting...:

Mathematician Gregory Chaitin is out with a new book (barely over 100 pgs., and looks good): "Proving Darwin: Making Biology Mathematical" -- a book that treats the DNA code as a universal programming language, while looking at the mathematical underpinnings of biology and evolution; definitely, adding it to my reading queue.

a blurb about it here:

http://physicsdatabase.com/2012/05/03/proving-darwin-making-biology-mathematical/
(includes a Chaitin lecture video)



Secondly, not exactly a math book… but from one of the best math explicators out there, and with a great title and story, worth mentioning here, the last book from Steven Strogatz: "The Calculus of Friendship."

It's the touching story of Strogatz' long-time relationship with one of his math teacher-mentors, and I can't help but think many a mathematician will relate to some aspects of that relationship. A couple of Web reviews of the book here:

http://www.americanscientist.org/bookshelf/pub/a-growing-affinity

http://www.bookslut.com/nonfiction/2009_09_015101.php

And a couple of clips of Strogatz talking about the volume here:

http://www.youtube.com/watch?v=9piYoYqIf3I

http://www.radiolab.org/2009/nov/30/calculove/ 

And Strogatz has a new book scheduled for release this coming fall:
 
"The Joy of x: A Guided Tour of Math From One to Infinity"

...gots to be good!

Contemplating Godel

Roger Penrose interviewed on Kurt Godel here:

http://simplycharly.com/godel/roger_penrose_godel_interview.html

...and Gregory Chaitin here:

http://simplycharly.com/godel/gregory_chaitin_interview.htm

...and lastly Raymond Smullyan here:

http://simplycharly.com/godel/raymond_smullyan_godel_interview.html