Monday, October 01, 2007
Gödel and the mathematics of life
Albert Voie
(0) comments
Life expresses both function and sign systems. This parallels the logically necessary symbolic self-referring structure in self-reproducing systems. Due to the abstract character of function and sign systems, life is not a subsystem of natural laws. This suggests that our reason is limited in respect to solving the problem of the origin of life and that we are left accepting life as an axiom.
Topics: Meaning | life | logic | evolution
Labels: evolution, life, logic, meaning
Friday, July 20, 2007
Emergent Evolution and Design in Language
Terrence Deacon
(0) comments
[Mathematics has] for centuries prompted philosophical debates concerning the origins of abstract form. Consider the operations of addition, subtraction, multiplication, and division in elementary arithmetic. These are, in one sense, cultural creations. They are conventional operations using culturally created tokens that could be embodied in a seeming infinite variety of different patterns of tokens and manipulations. But it is not quite right to say that these operations were ‘invented’. Specific individuals over the history of mathematics did indeed invent the various notation systems we now use to represent mathematical relationships, but often these inventions came as a result of discoveries they made about the representation of quantitative relationships. Mathematical ‘facts’ have a curious kind of existence that has fascinated philosophers since the ancient Greeks. Being represented seems to be an essential constitutive feature of a mathematical entity, but this doesn‘t mean that anything goes. Mathematical representations are precisely limited in form. Generalizations about the representation and manipulation of quantity, once expressed in a precise symbolic formalization, limit and determine how other mathematical generalizations can be represented in the same formal system. For my purpose it is irrelevant whether these kinds mathematical entity are ‘latent in the world’ in some Platonic sense or whether they emerge anew with human efforts to formalize the way we represent quantitative relationships. What matters is that symbolic representations of numerical relationships are at the same time arbitrary conventions and yet subject to non-arbitrary combinatorial consequences. Because of this deep non-arbitrariness, we feel confident that mathematics done anywhere in the universe will have mostly the same form, even if the medium notation were to differ radically.
Topics: Design | Language | Evolution
Labels: Design, evolution, language
Friday, May 18, 2007
Study of protein folds offers insight into metabolic evolution
Gustavo Caetano-Anollés
(0) comments
Researchers at the University of Illinois have constructed the first global family tree of metabolic protein architecture....
Of 776 metabolic protein folds surveyed, 16 were found to be omnipresent, and nine of those occurred in the earliest branches of the newly constructed tree. "These nine ancient folds represent architectures of fundamental importance undisputedly encoded in a genetic core that can be traced back to the universal ancestor of the three superkingdoms of life," the authors wrote. The analysis also found that the most ancient metabolic protein folds are important to RNA metabolism, specifically the interconversion of the purine and pyrimidine nucleotides that compose the core of the RNA molecule. This discovery supports the hypothesis of an RNA world in which RNA molecules were among the earliest catalysts of life. This idea is based in part on the observation that RNA still retains many of its catalytic capabilities, including the ability to make proteins. Gradually, according to this theory, proteins began taking over some of the original functions of RNA. "The most ancient (protein) molecules were involved in the interconversion of nucleotides. But they were not synthesizing them," Caetano-Anollés said. "We see that all the enzymes that were involved in purine synthesis, for example, were very recent. Since these first proteins benefited the formation of building blocks for the primitive RNA world, it makes a lot of sense that we've found this origin encased in nucleotide metabolism."
Labels: evolution
Sunday, March 11, 2007
Coevolution and No Free Lunch Theorem
David H. Wolpert
(0) comments
One ramification of this is the “No Free Lunch” (NFL) theorems, which state that any two algorithms are equivalent when their performance is averaged across all possible problems. This highlights the need for exploiting problem-specific knowledge to achieve better than random performance.. . .
In contrast to the traditional optimization case where the NFL results hold, we show that in self-play there are free lunches: in coevolution some algorithms have better performance than other algorithms, averaged across all possible problems. However in the typical coevolutionary scenarios encountered in biology, where there is no champion, the NFL theorems still hold.
Topics: Evolution | AI | ArtificalLife
Labels: AI, ArtificalLife, evolution
Energy flow and the organization of life
Harold Morowitz
(0) comments
Life is universally understood to require a source of free energy and mechanisms with which to harness it. Remarkably, the converse may also be true: the continuous generation of sources of free energy by abiotic processes may have forced life into existence as a means to alleviate the buildup of free energy stresses.. . .
A deterministic emergence of life would reflect an essential continuity between physics, chemistry, and biology. It would show that a part of the order we recognize as living is thermodynamic order inherent in the geosphere, and that some aspects of Darwinian selection are expressions of the likely simpler statistical mechanics of physical and chemical self-organization.
Labels: evolution, life, meaning