Re: ESSAY: Program length, Omega and Friendliness

From: Eliezer S. Yudkowsky (
Date: Thu Feb 23 2006 - 08:57:36 MST

Alejandro Dubrovsky wrote:
> On Thu, 2006-02-23 at 06:39 +0200, Mikko Särelä wrote:
>>Certainly, though we should probably not consider a gene to be one bit,
>>but more like a software component. Still we get an upper limit on the
>>complexity by considerint that the human genome has 3 billion DNA base
>>pairs. Since there are four different possible base pairs that means 2
>>bits of information giving us a maximum of 6 Gigabits ~ 700-800 Megabytes.
>>And that is very much overestimated by assuming that each base pair
>>actually codes useful information about brain structure. Overestimated for
>>the reason that no one should be able to claim that the complexity is
>>_higher_ than that. It is most certainly lower than that, probably on the
>>order of at least two decades (which would place it at 7-8MB) [reason
>>being at least 90% seems to be junk, not all genes code for brain
>>structure, and we know that a base pair does not code for 2 bits of
>>information (similarly claiming that a gene codes for only 1 bit of
>>information, if two different alleles exists is false idea).
>>Anything wrong with my analysis?
> Someone could claim that the optional methylation of the C base is
> another state, ie each base pair having 5 options. Then you can
> multiply by 3 to tell whether the stretch of DNA is in A-DNA, B-DNA or
> Z-DNA form (obvious overestimation there since the stretches cannot be
> one base long, and not all stretches can form Z-DNA). Then you can add 3
> to that multiplier to tell whether the DNA is hanging loose, it's
> wrapped around a histone, it's hanging between histones, or are more
> tightly packed (the tightness of the packing depends on the acethylation
> of the histones, but past some level of packing i'm assuming they are
> just not read at all, so there's probably no need to make the multiplier
> acethylation-level dependent) (again, gross overestimation since minimum
> size for each of these stretches is >> 1) (also, add, not multiply to
> the multiplier since these states afaik do not get a choice of whether
> they are in A-,B- or Z-). That'd be 5 x 6 = 30 choices per base. So
> that would be lg(30) x 3 billion about 15 billion bits, slightly under 2
> gigabytes as upper limit.

Heh. Unfortunately, this potential extra data storage buys you nothing
whatsoever in the way of information.

Natural selection pressure on mammals maxes out at O(1) bits (of Shannon
information) per generation. See, though the argument is older
than that - it appears for example in George Williams's "Adaptation and
Natural Selection".

Bases mutate at a rate of 1e-8 per base per generation.

Thus natural selection cannot maintain more than 1e8 bits of information
against the pressure of degenerative mutation.

Eliezer S. Yudkowsky                
Research Fellow, Singularity Institute for Artificial Intelligence

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