Digital physics

Abstract
We discuss mathematical and physical arguments against continuity and in favor of discreteness, with particular emphasis on the ideas of Emile Borel (1871–1956).

Introduction
Experimental physicists know how difficult accurate measurements are. No physical quantity has ever been measured with more than 15 digits or so of accuracy. Mathematicians, however, freely fantasize with infinite-precision real numbers. Nevertheless within pure math the notion of a real number is extremely problematic.

We’ll compare and contrast two parallel historical episodes:
1. the diagonal and probabilistic proofs that reals are uncountable, and
2. the diagonal and probabilistic proofs that there are uncomputable reals.

Both case histories open chasms beneath the feet of mathematicians. In the first case these are the famous Jules Richard paradox (1905), Emile Borel’s know-it-all real (1927), and the fact that most reals are unnameable, which was the subject of Borel, 1952, his last book, published when Borel was 81 years old James, 2002. In the second case the frightening features are the unsolvability of the halting problem (Turing, 1936), the fact that most reals are uncomputable, and last but not least, the halting probability , which is irreducibly complex (algorithmically random), maximally unknowable, and dramatically illustrates the limits of reason Chaitin, 2005.

In addition to this mathematical soul-searching regarding real numbers, some physicists are beginning to suspect that the physical universe is actually discrete Smolin, 2000 and perhaps even a giant computer Fredkin, 2004, Wolfram, 2002. It will be interesting to see how far this so-called “digital philosophy,” “digital physics” viewpoint can be taken.

Internet download speeds could be improved dramatically by mimicking Darwin's evolution to "breed" the best networking strategies, say computer scientists.

Transferring popular data across the internet repeatedly can be inefficient and costly, so networking companies have developed ways of temporarily storing, or "caching", data at different locations to reduce costs and increase download speeds.

But figuring out where to store data and for how long is a complex problem. One solution might be to have caches "talk" to each other repeatedly, but this is inefficient as it takes up a lot of bandwidth.

To tackle the challenge, Pablo Funes of US company Icosystem and Jürgen Branke and Frederik Theil of the University of Karlsruhe in Germany used "genetic algorithms", which mimic Darwinian evolution, to develop strategies for internet servers to use when caching data. Using a simulation they were able to improve download speeds over existing caching schemes.

In finding an answer to “perhaps the greatest unsolved ecological riddle,” evolutionists propose that diversity is a testament to there being more than one way to make a living.

The riddle: Why are some habitats loaded with many more species than others?

The answer: Nature and evolution respect that there’s more than one way of doing things.

“What we’ve learned,” said Michigan State University scientist Charles Ofria, “is that if there isn’t just one way to succeed, you’ll see diversity.”

In an article published in the July 2 issue of Science, an interdisciplinary team of scientists at MSU, the California Institute of Technology and Keck Graduate Institute (KGI), with the help of powerful computers, has used a kind of artificial life, or ALife, to gain insight into questions of evolution.

Abstract:
Motivated by a recent article on open problems in artificial life, here I postulate three laws which form a mathematical framework to describe artificial life evolutionary dynamics. They are based on a continuous approximation of population dynamics. Four dynamical elements are required in this formulation: ascendant matrix, transverse matrix, fitness function, and the stochastic drive. The first law states that in the absence of stochastic drive the artificial life always seeks for a local fitness attractor and stay there. It gives the reference point to discuss the general evolutionary dynamics. The second law is explicitly expressed in a unique form of stochastic differential equation with all four dynamical elements. The third law defines the relationship between the focused level of description to its lower and higher ones, and also defines the dichotomy of deterministic and stochastic drives. These laws provide a coherence framework to discuss several current problems, such as emergency and stability. In particular, two quantities are emphasized: the fitness function as the standard for selection and the stochasticity as the source of creativity. Those three laws may appear almost self-evident from a statistical physics point of view. However, their equivalent to a most conventional approach for evolutionary dynamics is shown for the first time by the present author, to the best of his knowledge. The computational advantage of the present formulation in the study of artificial life evolution is also discussed.

Subj-class: Adaptation and Self-Organizing Systems
P. Ao
Departments of Mechanical Engineering and Physics, University of Washington, Seattle, WA 98195, USA

Elegance is more than just a frill in life; it is one of the driving criteria behind survival.
- Douglas Hofstadter

A long-standing challenge to evolutionary theory has been whether it can explain the origin of complex organismal features. We examined this issue using digital organisms—computer programs that self-replicate, mutate, compete and evolve. Populations of digital organisms often evolved the ability to perform complex logic functions requiring the coordinated execution of many genomic instructions. Complex functions evolved by building on simpler functions that had evolved earlier, provided that these were also selectively favoured. However, no particular intermediate stage was essential for evolving complex functions. The first genotypes able to perform complex functions differed from their non-performing parents by only one or two mutations, but differed from the ancestor by many mutations that were also crucial to the new functions. In some cases, mutations that were deleterious when they appeared served as stepping-stones in the evolution of complex features. These findings show how complex functions can originate by random mutation and natural selection.

Lenski, R. E., C. Ofria, R. T. Pennock, and C. Adami. 2003. The evolutionary origin of complex features. Nature 423:139-144.

Ninth International Conference on the Simulation and Synthesis of Living Systems (ALIFE9)

Boston, Massachusetts September 12-15th 2004

• What are the principles of evolution, learning and growth which can be understood well enough to simulate as an information process?
• Can robots be built faster and cheaper by mimicing biology than by the product design process used for automobiles and airplanes?
• What kinds of constraints should be placed on sciences, such as "Wet Alife" which work with self-replicating elements?
• What components of physics and chemistry support emergence and automatic discovery of physical and cognitive mechanisms of life forms?
• How can we unify theories from dynamical systems, game theory, evolution, computing, geophysics, and cognition?

"To how many places does nature carry out PI when she makes each successive bubble in the white-cresting surf of each successive wave before nature finds out that PI can never be resolved?... And at what moment in the making of each separate bubble in Universe does nature decide to terminate her eternally frustrated calculating and instead turn out a fake sphere? I answered myself that I don't think nature is using PI or any of the irrational fraction constants of physics."
-Buckminster Fuller(Synergetics II, p. 233).

There are living systems; there is no "living matter".
- Jacques Lucien Monod