From: brinkman@edseq4.llnl.gov
Newsgroups: talk.origins
Subject: Re: Why evolution is a BETTER theory (for Bob Bales)
Date: 9 Apr 92 19:08:15 GMT


   In article <4999@tekig7.PEN.TEK.COM> bobb@tekig1.PEN.TEK.COM (Bob Bales)
writes...

>Matt Brinkman writes:

>Matt outlines his basic position as follows:

>>>[*] It is often said that if evolution *predicts* something which creation
>>>merely *allows*, then evolution is a better theory.  Even leaving aside the
>>>failed predictions of evolution (which I discuss in this posting and
>>>elsewhere), the question is: better in what sense?  

>>Better in a scientific sense, and better in the sense of more likely to be
>>be THE correct theory, as I will demonstrate below.

>I've deleted some of Matt's introductory material.  I hope not too much!

   I have deleted all the rest of the introductory material.  I would also
like to add one of Bob's original comments (which he inadvertantly deleted)
back into the record...

>>> If you hope to be able to say "Evolution actually happened," your criteria
>>> must be based on liklihood of occurrance.

   I just wanted this in to show that you and I both agree the when deciding
between theories, probabilistic arguments are the best one can hope for.

>Statement of the Problem:

  [One seeks to decide between two theories x and y.  One is true (assumed
   a priori).  Set up probability distributions for the competing theories.]

>Notice the specification of "equal liklihood."  With the adoption of a
>probability distribution (which would not have to be equal likelihood),

   Bob, just a question here.  Why worry about the words "equal likelihood"
when I presented this as an example, and you correctly note that there is
no reason that equal likelihood is necessary?

>theory y has gone from being a theory which is consisten with thw measured
>result to a theory which predicts a different probablity for the result than
>does theory x.

   Wait a second, consistent with data and predicts different probabilities
for the result are two entirely distinct things.  Flipping a coin 100 times
and getting 100 consecutive heads is data consistent with a fair coin.  It
is also data consistent with a double-headed coin.  Now to decide between
these two theories we can go back to our agreed criteria that the more
likely theory is the correct one, but you cannot claim that the fair coin
theory is inconsistent with the data because it most assuredly is not.

>The reason that Matt can draw the above conclusion in this case is the uniform
>probability distribution.  Under these condxitions, the probability of any
>one result decreses in proportion to the number of results.  

   This is incorrect and seems to be based on a miscomprehension of what
I meant by uniform probability distributions (if I used this phrase).  Let me 
clarify...

1) For the coin flipping example, one has assumed that a fair coin will come
   50/50 heads and tails.  This is NOT what is implied by uniform probability
   distribution.  Similar arguments can be made under the assumption that
   some huckster has trained himself to flip heads 75% of the time.  The
   numbers change, but the qualitative argument remains the same.

2) When attempting to decide between two theories, one can start by assuming
   that the likelihood of both are the same.  This can occur when you have no
   data on either theory, and you want to give both the maximum benefit of the
   doubt.  Similar arguments can be made if you assume a priori that theory
   x is twice as likely as theory y.  The numbers change, but the qualitative
   argument remains the same.

In short, I am not even sure why the concept of uniform probability 
distribution is relevant (other than for making examples easier to grasp).

>								It is the
>probability that is important, not the number of results.  In this case, the
>distinction may seem to be splitting hairs, but it will become important later.

   Could you please explain what this means?  In the standard interpretation
of statistics, probability cannot be separated from the number of results.
Within a Bayesian framework, a priori knowledge can separate these two
concepts, but given multiple independent trials the results from the Bayesian
analysis must concur with the standard intepretation.  In short, given the
example, how do you propose to sample the probability distributions without
measuring a number of results?

>The important point about the argument is that it is *probabilistic.*  In other
>words, even though theory y would allow the measured results in each case, it
>is *statistically unlikely* that a *random choice* among the outcomes allowed
>by the theory would agree with the measured resuilts every time.

   Yes, this argument is *probabilistic*, and you were the one who set this 
forth as the criterion for deciding between theories.  Second, yes this example
deals with *random choice*, but this is in no way, shape, or form a requirement
for a Bayesian approach to questions of model choice.

>Here [i.e., the coin flipping example], the theories make *different* 
>predictions, so we can indeed judge them on how results agree with 
>predictions. The original situation I discussed involved a theory which 
>predicted results and another which is consistent with them.  But. . . .

   I suppose one could argue as your first statement has done, but I would
argue as your second statement has done.  The coin flipping example involves
a theory which predicted results (i.e., a double-headed coin WILL always
give heads) and another which is consistent with them (i.e., the fair coin
COULD always give heads).  You appear to be engaging in nothing beyond
sophistry at this point.

>It is theoretically possible, of course, for a fair coin to give a string of
>heads of any length.  But Matt's analysis is correct: after a time, the "fair
>coin" theory becomes silly.  

   Yep and thanx (to the theoretically possible and my analysis is correct
statements, respectively).

>Why is this?  Because as time goes on, the "fair
>coin" theory becomes *less and less* consistent with results.  We discard the
>theory when we judge it to *be inconsistent* and we do so because it *is*
>inconsistent. This is a departure from the premise that we had a consistent
>theory.

   Wait a second.  You have just claimed that 1 head, or 100 consecutive heads,
or 1,000,000 consecutive heads, are possible outcomes for 1 or 100 or 
1,000,000 flips of a fair coin.  How can getting say 1,000,000 consecutive
heads be *inconsistent* with the theory that the coin is fair?  We do NOT
discard the theory because we view it to be inconsistent, we discard the theory
because we view the alternative theory, which has made a prediction consistent
with the data, to have a much greater likelihood of occurrance (i.e., your
criterion for deciding between theories).  In short, we can never prove that
the coin is fair because it is ALWAYS consistent with any data (i.e., it makes
no predictions), but one can easily prove that the coin is NOT fair because
one tail gives that theory a lie (i.e., it makes a prediction).

>But it is the predictions of theory #1 that allows us to make this judgement.
>Imagine, for the moment, that the "fair coin" theory said, that while it is
>possible to get a mixture of heads and tails using a fair coin, the probability
>of obtaining a given number of heads in a row is unknown.

   Oh, but the probability of getting N heads in a row is just p^N, where p is
the probability of getting 1 head in one flip, assuming, of course, independent
trial.  We will leave aside questions on how one a priori determines p, beyond
noting that the fewer the possible outcomes the larger is the value of p.

>Then, when we were given a string of, for example, 20 heads, we could say, "The
>probability of getting this result under theory #2 is 1, but the probability of
>getting this result under theory #1 is ???"  We could not say which theory
>would be more likely.  (We could say that theory #1 is no more likely than
>theory #2, but not that it is less likely).

   Unless you are going to claim that p = 1 in theory #1, in which case theory
#1 reduces to theory #2, you can say that theory #1 becomes exponentially less
likely than theory #2 as one looks at a larger sample of the data which is 
consistent with both theories.

>The ability to choose a theory derives from the ability to *compute* the
>probabilities involved.

   No, the ability to quantify the reasons for choosing a thoery derives from
the ability to compute the probabilities involved (one of the strongest
critiques of Bayesian inference is the subjective nature of a priori 
assignation of probability distributions).  One can always, however, note that
a theory which is consistent with all imaginable data (i.e., makes no specific 
predictions) is much^much less likely to be correct than a theory which makes 
specific predictions that turn out to all be consistent with the data, and that
this likelihood decreases exponentially with the number of correctly predicted
outcomes.

   In short, one does not penalize a theory for being consistent, one rewards
a theory that requires a much more stringent set of experimental observations
to be consistent.  If a theory is merely consistent (i.e., it doesn't make
any predictions) it doesn't participate in the rewards.

>In the case of creation, Matt has not even defined in a  clear way the
>probability that the obseved results are due, respectively, to evolution and
>to creation.  

   Okay, let me provide one qualitative example of what you ask for.  The
theory of evolution predicts that all species of vertebrates are related to
each other via a common ancestor.  If such is the case, than all species must 
share certain characteristics--for example, common means of storing genetic
information.  Thus, let us define a probability, p = 1, that all vertebrates 
have DNA within the theory of evolution.  Now for Creationism all species
of vertebrates are related by virtue of sharing a common Creator.  This,
however, does not firmly delimit that all species of vertebrates MUST have
DNA.  Therefore, we will assign a probability, q, that all vertebrates have
DNA within any theory of Creationism.  (Note that this is an extremely simple
case, used as an example.  A much more stringent argument could be made by
looking at similarities between sequences of junk DNA for various vertebrate
species, for example.)

   Now, as we test each vertebrate species the probability (using the 
handwaving methodology described earlier) of evolution being correct is
p^N (with N the consecutive number of vertebrate species tested that actually 
has DNA) and the probability of Creationism being correct is q^N.  

  Now it must be the case that q <= p (given that p = 1).  If a priori one 
assigns q == p, then you have a theory of Creationism which is identical to 
evolution in this regard and one which REQUIRES the Creator to use the method 
of identical DNA.  There seems to be very little reason why one should REQUIRE,
a priori, the Creator to use DNA as a common method for storing genetic 
information.  For the sake of argument, however, one could claim that this is 
a likely method for the Creator to use.  Let us therefore say that q = p - e 
(where e is some small quantity).  After finding that N consecutive species of 
vertebrates use DNA, Creationism now gets a probability (to first order in e)

   q^N =approx= p^N - N*p^(N-1)*e = 1 - N*e 

  As N grows large (i.e., as more and more consecutive vertebrate species are
found to use DNA), one is forced to do one of two things to maintain that
q^N is a viable alternative...

1) Retain higher orders in this expansion.

2) Constrain e to smaller and smaller values.

Although the first option will give a more accurate answer, it doesn't much 
help the fact that q^N -> 0).  If one chooses the second option, one has 
either a priori or a posteriori constrained the Creator to act in a manner
consistent with evolution.  If one wants to pretend to be doing science, one
must give reasons a priori (a posteriori means postdicting the data) why this 
constraint on the Creator exists.

   Now, one can play the argument by design game and claim that well, in this
example e = 0 (i.e., q == p), because a creator frequently uses similar methods
over and over and over again.  This argument I would answer in three ways:

1) The argument via design is fallacious, as I have already pointed out in
   another post to you.

2) This is at best a plausibility argument, not a scientific statement.
   Evolution requires p = 1, Creationism can, at best, merely be consistent
   with q = 1.  This is a huge qualitative distinction.

3) Once again, there are better examples one could use.  For example, sequences
   of junk DNA in different species can be correlated with the amount of time
   from their divergence from a common ancestor.  An argument that creators
   frequently use the same template over and over does not address these 
   issues.

>One undefined probability cannot be compared to another and cannot be called 
>vanishingly small.

   Agreed, but given any two probabilities, p and q, with q < p, multiple
measurements rapidly increases the probability that the theory based on p is
more likely to be correct (once again your criterion for deciding between 
theories).  Or, put another way, a theory based on q rapidly becomes 
vanishingly small, even if q itself is relatively large.

>Although he hasn't computed the probability of creation, judging from what he
>has said, and also extrapolating from common evolutionary arguments, he seems
>to me to be saying the following:

>1. Evolution would, with high probability, have produced something like we 
>    see.

   Just to expand on this contention.  Evolution requires that certain 
correlations exist between various features in the data, but it does not 
require that those features be expressed as they are.  For a simple example
of this, evolution does not require that all life be carbon-based, but it does
require that if any single life form is carbon-based that all other life forms
that have arisen in the same place must be carbon based.

>2. There would be many possibilities for creation besides what we see.

   Once again, we are back to the above statement.  Creationism does not 
require any correlations to exist between various features in the data.  One
can provide plausibility arguments why there may be such correlations, but
these correlations are not a requirement (i.e., a prediction) of Creationism 
as they are for evolution.

>3. If organisms had been created, out of all the possibilities in 2, for
>   the Creator to have chosen the ones we see would be unlikely.

   No.  If all organisms exhibit precisely the patterns of correlation required
by evolution then even if the chance of Creator choosing those modes is near
unity, the Creationist theory still has a vanishingly small probability to be
the correct theory when compared with evolution.  The only way Creationism
can compete in this regard is for one to constrain, a priori, the Creator to
act in a manner indistinguishable from the theory of evolution in all of these
regards.  Would you care to advance a plausibility argument as to why this
should be so?

>For a specific example, I'll use the conclusion that mankind and apes are
>related, based on DNA (and other) similarities, and discuss why each of these
>statements is not justified, based on what we see.

   [Bob's arguments, deleted.]

   Bob, looking at the arguments I have deleted, it is apparent that you are
dealing with a couple of strawmen.  First, the patterns of correlations are 
the predictions made by evolution (i.e., the experimental observations required 
by the theory).  You appear to have confused the patterns of correlations with 
how those correlations are expressed.  Second, these arguments do not have
anything to do with Creation being a random process.  Making the Creation a
strictly causal, logical process in no way effects the qualitative aspects of
this argument.  Reread my statements correcting what you thought I said, and 
you will see the difference.

>The stated reason that creation is to be rejected is that it would be expected
>to give results other than what we see.  

   Strawman alert.  The stated reason that creation is to be rejected is that
evolution predicts (i.e., requires) precisely the correlations between 
features that are seen, and creation makes no predictions (has no requirements)
whatsoever.  In such a case, the probability the creation is correct becomes
vanishingly small when compared with the prospects of evolution (once again,
Bob's criterion for choosing between competing theories).

>As I pointed out just above, there is
>no evidence that creation would be expected to give other results.  And the
>rational person can be expected to look at the evidence.  

   And as I pointed out in the previous post and above, evolution MUST give
the results that have been observed.  For evolution one does not need to 
invoke arguments based on plausibility to explain correlations between various
features observed in the data.  It is for this reason that evolution is the
much^much preferable theory scientifically and logically.

>Furthermore, Matt agrees that creationism is consistent with the evidence.

   You've got me there.  Any piece of evidence is consistent with creationism
because creationism is consistent with any imaginable piece of evidence.  Why
are sequences of junk DNA so similar?  The Creator made them that way.  Why
are sequences of junk DNA dissimilar as required by the theory of evolution?
The Creator made them that way.  You can't argue that this kind of all 
encompassing explanation is scientific because to provide any rationale for 
them you have to invoke theology and/or metaphysics.

>   Bob Bales

Matt Brinkman		brinkman@edseq1.llnl.gov