Spider webs and a random walk in software space
Yesterday I happened upon a Huffington Post blog from Mario Livio. For anyone who has been following my blog, it will come as no surprise that this piece, about the surprising similarity between spider webs and computer generated cosmic webs, caught my attention. After showing us a few, Livio says:
For an astrophysicist, perhaps the most amazing aspect of these webs is how much they resemble computer simulations of the cosmic web — the filamentary structure of the Dark Matter in the universe.
And he tells us what the cosmic web is:
Dark matter provides the scaffolding on which the large-scale structure of the universe is constructed. Ordinary matter is gravitationally attracted to the densest parts of the cosmic web, and there galaxies and clusters of galaxies are formed, leaving large, relatively empty voids. To examine the filamentary intergalactic gas, astronomers use the light from distant quasars. Observing with the Hubble Space Telescope, they utilize the quasar light just like shining a flashlight through fog. Hubble observations have also helped to map the 3D distribution of dark matter through the effect of gravitational lensing — the deflection of light of distant objects by the gravitational field of Dark Matter along the line of sight.
Apparently some spider webs even resemble the graphics that describe how black holes warp their surrounding space. All of these images caught my attention because I am always looking for biology in mathematics or mathematics in biology. Livio, however, didn’t say much about it other than that artist Tomás Saraceno created a work called “14 Billion” in which he constructed a large spider-web-like sculpture composed of ropes and elastic chords. But he referred to a lively conversation at the World Science Festival involving Saraceno, Livio, arachnologist, P. Jäger, architect M. Wigley, and astrobiologist C. McKay. When I clicked the link to check this event out I found another discussion in which Livio participated, from a year earlier, and I hit the jackpot. It was called The Limits of Human Understanding, and included Rebecca Goldstein and Gregor Chaitin This one was organized around Gödel’s Incompleteness Theorem. I always enjoy listening to Rebecca Goldstein talk about Gödel. She does a nice job of both addressing the significance of his work and breathing life into the his history. Her voice can be heard in another recent blog of mine. But it was Gregor Chaitin who got my attention this time. As a way of introducing his own work, he said that he was using ideas inspired by biology and, in doing that, he found the positive implications of Gödel’s Theorem rather than the negative. Chaitin sees it this way: that the world of pure mathematics has infinite complexity while any one mathematical theory has finite complexity. This, he says, “makes incompleteness seem natural.”
Chaitin believes that Gödel and Turing (in his 1936 paper) opened the door to a provocative connection between mathematics and biology, between life and software. I’ve looked at how Turing was inspired by biology in two of my other posts. They can be found here and here.
But Chaitin is working to understand it with what he hopes will be a new branch of mathematics called Metabiology. I very much enjoyed hearing him describe the history of the ideas that inspired him in one of his talks: Life as Evolving Software in which he says:
After we invented software we could see that we were surrounded by software. DNA is a universal programming language and biology can be thought of as software archeology – looking at very old, very complicated software.
Chaitin is postulating that biological creativity = math creativity. And, in this light, Gödel’s Theorem helps to show that evolution is never-ending.
To begin, Chaitin invents a mathematical life form, one that satisfies the definition of ‘life’ as a system that has heredity and history, that can maintain itself, and that can evolve. He begins with the simplest case – a single software organism that has no body, no population, no environment and no competition – calling it a toy model of evolution. It’s a single software organism, a program, and it will mutate when it is given something challenging to do that requires creativity. The goal of this organism will be to name a very big positive integer (called the busy beaver problem in computer science). Chaitin insists, this is not a trivial problem. And I believe him.
The problem requires an unlimited amount of creativity and Gödel’s incompleteness theorem applies. No closed system will give you the best possible answer. There are always better and better ways.
There is no doubt that this will be a fascinating and productive effort. I will try to find out more. The title of this post (except for the spider) is his image.