Re: order, complexity, entropy and evolution

Glenn Morton (
Sat, 20 Dec 1997 21:21:28 -0600

At 03:40 PM 12/19/97 -0700, Don N Page wrote:

>However, the fact that the same DNA molecule occurs millions of time within an
>organism (Can someone tell me how many times for a human?) means that the
>collection of DNA molecules for an organism is also highly ordered.
I have seen a figure of 10^13 cells in the human body but don't have a
reference handy.

> In bed last night I began to have a half-baked idea that I wanted to
>try out for quantifying the combination of organization and order. The basic
>idea is that the information in an individual DNA molecule is much higher than
>the total information in all the DNA molecules of an organism divided by the
>number of such molecules (since the total information for a large number of
>identical molecules is just the information in one, plus the information of
>many there are), whereas for a random collection of similarly complex
>molecules, the information in each one would be roughly the total information
>divided by the number of molecules. (I'm ignoring the information of how all
>the molecules are arranged, which would presumably be most strongly influenced
>by environmental rather than genetic factors and which, as Glenn or someone
>else pointed out several weeks ago for the synaptic connections in the brain,
>would be far more information that than in any single DNA molecule.)

That was me that pointed that out and as I predicted during that exchange we
still have not seen a response to this issue from anyone in the ID camp to
the problem that the brain is too complex for the amount of information in
the DNA molecule.

> I'm not too clear how to quantify this measure for a large collection
>of non-identical molecules, such as those making up an organism when one also
>counts the large number of non-DNA molecules (or the DNA molecules that have
>mutated), but the following is my first stab at it:
> Take all the M molecules in an entity (e.g., in an organism, a species,
>or in the entire biosphere) and arrange them in decreasing order of
>Let 0 < m < M+1 be a label for each molecule, with m = 1 labeling the most
>complex and m = M labeling the simplest. If i_m is the information in each
>molecule separately (with _m being the TeX notation for subscript m), then
>order is such that i_m >= i_n (i_m greater than or equal to i_n) if m < n.
>Many molecules will be identical and so have identical i_m, but m is supposed
>to label each individual molecule and not just each type. (I.e., if there
>n of one type, there will be n m labels for those n molecules, and not just
>m label.)

I have a couple of questions on this approach which hit at the assumptions
so I won't go to the math until I am sure that the assumptions are ok. If
the molecules in an organism are derived ultimately by gene expression, then
the information in, say, a cytochrome c molecule is also included in the
DNA. This means that all you really need to deal with is the DNA of the
animal rather than each separate molecule. Including the molecules counts
the same information twice.
I don't think you can extend this to the entire biosphere IF you don't
subtract off the duplicate information which crosses species lines. We and
chimpanzees share 98% of our DNA. Thus we you can't count the information
in a chimp totally independently of that in a human. And you and I probably
share 99.9999% of our DNA information so the biosphere's info content must
account for that.
> Now let I_m be the total information needed to specify the first m
>molecules. I_1 = i_1 will be the information in the most complex molecule,
>I_M will be the total information in the collection of molecules making up
>entire entity

If I understand your approach correclty, I would point out that proteins are
derived from the DNA so you can't use all molecules (DNA + proteins)


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