The recent discussion with Walter got me to thinking about a process we use
in Geophysics and while I was driving home from Thanksgiving, I mentally
calculated the number of possible acoustical impedance models one gets in
geophysics. So I wrote it up
Anti-creationists make a huge deal about the odds against finding a single
sequence of protein or DNA which they think is useful. The odds against
finding the workable solution are usually in the 10^-100 to 10^-300 range of
possibilities. Dembski claims that 10^-150 probability is some sort of
universal probability bound, in which anything with odds less than that
simply must be designed. He writes:
“In The Design Inference I justify a more stringent universal probability
bound of 10-150 based on the number of elementary particles in the
observable universe, the duration of the observable universe until its heat
death and the Planck time. A probability bound of 10-150 translates to 500
bits of information. Accordingly, specified information of complexity
greater than 500 bits cannot reasonably be attributed to chance. This
500-bit ceiling on the amount of specified complexity attributable to chance
constitutes a universal complexity bound for CSI.” William A. Dembski,
Intelligent Design, (Downers Grove: Intervarsity Press, 2001), p. 166
In my business we deal with probabilities which make those numbers
absolutely pale by comparison. The system I will describe has one chance in
10^126,000,000,000 of being right. That is 10 raised to the 126 billionth
power. This is much greater than this supposed probability bound. To help
you understand, I must explain a bit of geophysics.
In seismic exploration, we set off airguns or dynamite charges on the
surface of the ocean or land (respectively for each type of source—dynamite
is not used offshore) We then listen for the echoes of sound bouncing back
to the surface off of the various rock layers. This is important. We record
the sound wave field every 2 milliseconds and we record to 8 seconds or more
in time. This is equivalent to something like 40,000 feet deep and we end up
with a seismic trace which consists of a sequence of 4000 numbers which
represent the amplitude of the sound waves reflected off the rocks under the
earth. We record the data in such a manner that we end up with a seismic
trace every 25 meters in one direction and every 40 meters in another
direction and the size of some surveys is so large that they extend a
hundred kilometers or more in both directions. Most field seismic data is
around 10 km by 10 km for 100 sq. km of data. Thus we have 100,000 seismic
traces, each with 4000 different numbers. This would be a typical 3D seismic
program over an oil field.
The reflection of the sound (which is what causes the echo) is controlled by
the change in acoustic impedance from the upper layer to the lower rock
layer. Acoustic impedance (AI) is merely the multiplication of the rock’s
density by the velocity of sound in that rock.
AI = rho x vel
AI is what causes the seismic reflections.
Sound going:
Down Up
\ /
\ /
AI in rock 1 \ /
-----------------\/-----------------
AI in rock 2
We would really like to know the AI rather than what the seismic readily
offers which is energy of sound reflection. AI is tied to the rock
lithology and properties so it is more useful than merely knowing how much
sound energy is reflected back. We use this AI data to help us understand
the porosity of the rocks and to determine rock type.
To get to this information we do what is called an inversion. We guess at
the AI pattern and make a model acoustic impedence trace, then we apply the
reflection laws to it to produce a model seismic trace, compare that model
to the real seismic trace, and if it differs by a certain amount, we guess
again (randomly mutate the model), make a model seismic trace, compare it to
the real seismic trace etc. We continue this iterative process until the
model AI produces a model synthetic seismogram which matches closely the
observed data.
Now, what are the probabilities of us getting the right AI? All we know is
the seismic data which we have sampled every 2 milliseconds and have 4000
numbers for each seismic trace. We know that the density in rocks we are
interested in generally extend from 2 to 2.5 grams per cc and the velocity
of sound generally ranges from 5,000 to 12,000 feet per second. Thus, if we
let the density values go from 2 to 2.5 in steps of .01 and the velocity of
sound vary from 5,000 feet per second to 12,000 feet per second in
increments of 1 foot per second, we have 50 x 7000 = 350,000 different
possibilities for each sample of the seismic data. Remember we have 4000
samples. So the total possible AI solutions for a given seismic trace is
Total number of AI solutions = 4000^350,000 = 10^1,260,720.
This is 10 raised to the 1.2 millionth power!! The odds against finding the
correct answer is so much smaller than finding the ‘correct’ answer with
protein that one would bet on the protein long before betting on geophysics.
Protein probabilities are in the order of one chance in 10^300. But this is
merely the probability of getting ONE seismic trace AI correct. We have
100,000 other traces, so that the probability of getting the correct model
for the entire seismic survey is an astounding one chance in
10^126,000,000,000.
Or ten followed by 126 billion zeros.
If the anti-evolutionary probability arguments were correct, we
geophysicists would have no chance of finding anything useful in this
procedure. If one searched 10 quadrillion models per second for the age of
the universe we would only have searched 10^33 of the models to date. But,
I will tell you that we always find usable models via this technique. We do
reduce the number of samples we run the inversion over so in general we only
use 200 samples but that still gives us one chance in 10 followed by 80
billion zeros. We always get a useful AI output. Why?
Well it is because we don’t have to have absolutely the correct answer to
get a workable and useful answer. Billions upon trillions upon gazillions
of the AI inversions will give the very same answer (provide the very same
functionality). In other words, the answers are not unique. This is the
same reason that the probability arguments given by the anti-evolutionists
fail to impress. Those who are familiar with such systems know that one
doesn’t have to find the best solution to have a workable solution.
Hemoglobin is not the very best oxygen carrier anywhere among all possible
protein sequences; but it is a workable carrier. Cytochrome c as found in
humans is not the very best at that functionality; it is certainly a
workable solution. All through the biopolymers, this statement can be said.
And experiment shows that this is the case:
Andrew Ellington and Jack W. Szostak "used small organic dyes as the target.
They screened 10 13 random-sequence RNAs and found molecules that bound
tightly and specifically to each of the dyes.
"Recently they repeated this experiment using random-sequence DNAs and
arrived at an entirely different set of dye-binding molecules.
...
"That observation reveals an important truth about directed evolution (and
indeed, about evolution in general): the forms selected are not necessarily
the best answers to a problem in some ideal sense, only the best answers to
arise in the evolutionary history of a particular macromolecule."~Gerald F.
Joyce, "Directed Evolution," Scientific America, Dec. 1992, p. 94-95.
Low probabilities for finding the correct answer is only a meaningful
argument if one and only one solution works. We know this to be false in
geophysics and in biology. Cow, sheep, etc all have different proteins, but
we often have used their proteins to support our lives because their
different chemicals work fine and dandy in us and thus when we are sick we
live. But it means that there are more than one biological solution to the
functionality in question. The anti-evolutionary arguments simply won’t
stand up to scrutiny.
Received on Sun Nov 30 19:35:43 2003
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