That’s a non-sequitor. The human genome is not a synonym for “human life”, nor “human genome information” is a synonym for “human genome interaction”. You can encode the INFORMATION contained in the human genome using 4 natural numbers, but that doesn’t imply that you can model the interactions or evolution of that system using 4 natural numbers.

Agreed. I’m betting they can all be encoded in arithmetic, though.

I agree, but similarly there is more to human life than the human genome is able to tell you. I don’t mean to argue for the existence of an “uncodable essence”, as you put it, but instead for the same emergent complexity that you see in the natural numbers. Our sense of fairness is not expressed in the genome, nor is this conversation. True statements of human nature cannot all be derived from our genome.

The true statements of arithmetic cannot all be derived from any single set of axioms. (This is in contrast to the theory of the real numbers, where all true statements do follow from a single set of axioms.) Therefore there is more to the natural numbers than what your axioms about successors, etc. are able to tell you.

I think we’re using different definitions of “complex”, so I’ll try to offer mine. I think of the complexity of a set as a measure of how hard it would be to generate that set. Generating all the natural numbers is actually very easy, if time-consuming; once you know where to begin and how to add, you can just keep churning them out. By comparison, primes (still infinite, so not yet addressing your point directly) are harder to generate; you additionally need to understand the concept of divisibility, and in addition to the work required to generate natural numbers, you have to do fairly extensive checking that any given natural number is actually prime before including it in the set.

If that rather informal definition sounds reasonable to you, I would argue that the human genome is more complex than the natural numbers, and that the complexity lies in deciding whether any given natural number represents a valid human gene sequence.

If you prefer a different definition, I’d be interested to know what it is.

By contrast, the genetic code is completely describable within the language of the natural numbers and so cannot (in the sense I am using the word) be more complex. In fact, because it’s a finite structure, it is necessarily less complex.

I dispute the notion that supersets are necessarily more complex than subsets. For example, the set of prime numbers is more complex than the set of natural numbers, and the Mandelbrot set is infinitely more complex than the (unfortunately named, for the sake of my argument) complex plane. The decision of which elements of a set to keep and which elements to discard can itself be a source of immense complexity.

I too feel very sad about Dawkins destroying his reputation with The God Delusion. I don’t feel that he was one of the 20th century’s greatest scientists, as far as I know his main contribution to science was The Extended Phenotype – an important concept and a very readable text but not a world changing one.

In my opinion Dawkins main contribution was as a communicator of the understanding of science. His clear and concise explanation of the mechanism of natural selection in The Selfish Gene allowed myself and many others to understand very subtle processes without having to spend years studying biology. I only wish that other scientists in other fields had produced such elucidating books.

I recently heard someone writing him off because of TGD thereby suggesting that TSG was just as flaky. In TGD he sets up a paper tiger in order to shoot it down. In my experience each person who believes in “God” believes in something unique that they are completely incapable of defining in any satisfactory manner. For this reason there are probably as many concepts called “God” as there are believers. Most of these are discounted by Dawkins in a few sentences in the first couple of chapters as they are not disprovable. The only one he defines is the one that he thinks he can disprove.

Personally I don’t see any value in a word that cannot communicate any sense to another person. For this reason I no longer describe myself as an atheist but as an agnostic. If anyone cares to define the word I will quite happily say whether I believe in their concept. I think though that it must be up to the believers to define it. It strikes me as nonsense for someone to say “This is what the word means, this cannot exist therefore all believers are idiots.” The idiots must be allowed to show their idiocy in attempting to define the word themselves.

The main point is that our perception of the universe(s) is based on our position in it. we could never be created in a different universe without the properties which create life so therefore we could never view it. (i’m a little against this argument as bad science, for the same reason religion is “bad science” but none the less I find it more convincing than religious theories).

I wouldn’t mind your opinion Steve, or if anyone has ever heard of this universe theory before, if there is more discussion of it elsewhere on the net.