At 01:47 PM 11/29/97 -0800, cliff@noevalley.com wrote:
>The 2d law does not apply to spelling in a hard and fast way. People
>could develop the same spelling for previously differently-spelled words
>through accident or through conscious processes. No specific claim can
>be made about any specific case based on the 2d law. And 'specific case'
>can apply to anything that is a subset of the universe.
I can make the claim that if I start out with the specific case of 10
million animals all with the same DNA, the 2nd Law, the law of increasing
entropy will drive the animals to the situation that they all have different
DNA sequences. This is a specific prediction that applies to all animals.
Let's look at this prediction (I am sure that I will get some corrections
from those better at physics than I but this should lead to the truth.) The
number of different permutations of a DNA molecule of length 3.5 billion is:
4^3,500,000,000= 10^2,107,209,969
Which number is too large to store on my computer. (as an aside, this number
is almost the number of different base 4 numerals in a 3.5 billion character
long number) Given a population of 10 million, what are the odds that all
ten million would have the identical string of DNA. The probability that
one animal will have this sequence of DNA is
1/1 x 10^2,107,209,969.
to find the probability that 10,000,000 animals would all have the same dna
sequence this number should be raised to the 10 millionth power. This is
because the number of possibilities do not decrease with every choice. An
simple example is the choosing of 5 1's out of a bucket with equal numbers
of 1's, 2's...9's If every time you choose you put the slip of paper back
into the bucket, the next choice has the same probability as the last. If
we do this with a bucket with a bucket of DNA 3.5 billion nucleotides long
each with a different sequence and we draw the same sequence 10 million
times, the odds of this are:
(1 x 10^-2,107,209,969)^10,000,000 = Omega S
Lets call this numer Omega S for Same DNA
What is the probability that all animals will have different DNA sequences?
This is a different selection process than the last. Everytime you draw a
slip, you DON'T put it back in the bucket. Thus, with each choice, the
number of possible choices decreases by 1. The odds that the 10,000,000
animals will have different DNA is (expressed in factorials):
1 x 10^-2,107,209,969!- 1 x 10^2,107,209,962! = Omega D
Lets call this number Omega D for Different DNA.
(the way to understand this is to note that (1/10)^2 is smaller than
1/(10*9) [which is .01 vs .11] and (1/10)^3 is smaller than
1/(10*9*8)[.001000 vs. .0013888])
This second number is much bigger than the first number. In fact, if I did
my math correctly, Omega D/Omega S=10^10,000,000. Omega D is 10 million
orders of magnitude bigger than Omega S. Thus it is much more probable that
each animal would have a unique DNA sequence, different from all his neighbors.
What is the relationship of this to the 2nd law? Using the relations in
statistical mechanics, this is the equivalent of thermodynamic
probability--Omega. (See Mark W. Zemansky, Heat and Thermodynamics, 1968, p.
255 ) and entropy is defined as
Entropy = k ln (Omega)
Since Omega D is 10 million orders of magnitude larger than Omega S, a
change from the initial state with 10 million animals with the same DNA
sequence to 10 million animals with different sequences represents a change
from a low entropy state to a high entropy state. Thus I would contend that
evolution is driven by the 2nd law.
>
>Sure, evolution uses a tendency to disorder as it generates mutations,
>just as hot air balloons use gravity as they defy gravity. Gravity is
>counteracted--one might say 'defeated'--in the localized event. And
>terrestrial evolution is a localized event. In the long run, gravity
>will win out over all the hot air balloons, but so what? Ultimate
>quasi-philosophical principles are worthless when it comes to puzzling
>out the historical specifics of evolutionary biology. To me, the 2d law
>is quasi-philosophical because it makes a claim about the final total
>nature of all the universe for all time, beyond what is observable,
>which
>the practical generalizations of physics do not. Its presumptiousness
>and
>lack of practical utility give it a metaphysical flavor.
The second law is more than a quasi philosophical statement about the
totality of the universe. You seem to be thinking that the 2nd law is
totally destructive. It isn't. It defines the direction of change in the
state of a system of particles or genomes. This does not require the
destruction of the system. The molecules in the atmosphere are governed by
the 2nd law. They achieve a state where the locations of the molcules are
NOT the same (i.e., they spread out throughout the room) This has nothing to
do with the destruction of atmospheric molecules or the destruction of the
atmosphere.
If you want to say that the death of the individual is due to the victory of
the 2nd law, it isn't in the sense that mutations don't cause the death. We
have an imperfect DNA copy mechanism in our somatic cells and it does not
copy the entire length of the DNA molecule. Our somatic cells apparently
lack the telomerase which allows the entire length of a DNA molecule to be
copied. At each division a small piece of DNA at the ends of the
chromosomes is not copied. Thus with each division the chromosomes become
shorter and shorter. We die because at around 50 cell divisions the
chromosomal DNA in our bodies has begun to grow so short that useful
functions are cut out. But this is not the result of the the second law.
Our germ cells, the sperm and egg, go through millions of cellular divisions
over the generations and they do not have the problem our somatic cells do.
The germ cells have a copy mechanism that doesn't cut off the ends of the
chromosomes and they seem to be able to divide forever with no ill effects
of the 2nd law.
The second law comes into this as the driving mechanism for DNA
differentiation. I just showed that the preferred direction of a group of
clones over time is toward diversity of DNA sequences. As long as sequences
are found which are viable, life goes on. The second law does not require
that all life eventually stop (apart from the heat death of the universe)
>
>> >Evolution to any degree is a matter of specific complex biological
>> >events that may or may not occur in a given physical system, be it
>> >open or closed, losing energy or gaining energy in an overall sense.
>
>> So a biological system is not a physical system? I would contend that it is.
>
>I don't see how you infer that from my statement that biological events
>occur within a physical system. Anything is a physical system; even
>codes
>of law, for example, can be viewed as extensions of human biology.
>
>Biology is subject to the laws of physics, but the 2d law doesn't have
>interesting implications for any specific problems in evolutionary
>biology.
Ah but it does. Have you ever used that screen saver with worms crawling
all over your screen? They move randomly but they start out at the same
spot on the screen. The fact that they end up at all locations is an effect
of the 2nd law. A DNA genome is nothing more than a billion dimensional
space and the 10 million animals are similar to putting 10 million worms at
the same spot in that multidimensional space. When you start 10 million
animals all at the same point in this billion dimensional space and allow
random mutations, the animal genomes over time will diverge from the
starting point. The path of the genomes over time is exactly like the worms
on your screen, only in higher dimensional euclidean spaces.
>So everything is going to blow up or run down or something in the end--
>what does that tell me about evolution?
That is NOT the meaning of the 2nd law!!!!! The 2nd law says that things go
from the improbable to the probable. It is more probable for the molecules
in my office to spread out throughout the volume than it is for them to be
concentrated in one corner. This is different than saying that the 2nd law
says things run down.
>
>> >BTW, when I respond to mail from this list, the addressee on my
>> >reply is the individual sender, not the list. I have to manually
>'Re: All' does work on my Netscape 3.0 but it sends a copy to the poster
>as well as to the list. Other lists I subscribe to have a reply to:
>header
>in the email (with the list name) such that a simple reply gets posted
>to the
>list with no cc to the original poster. This is preferable, I think,
>unless
>the writer fears his message may be censored by a moderator.
use Re: All. Most people do that sort of thing anyway.
glenn
Adam, Apes, and Anthropology: Finding the Soul of Fossil Man
and
Foundation, Fall and Flood
http://www.isource.net/~grmorton/dmd.htm