[asa] A question for Timaeus

From: Iain Strachan <igd.strachan@gmail.com>
Date: Tue Sep 30 2008 - 07:43:11 EDT


I've not had to find the time to follow this debate in great detail as
there is so much to wade through; indeed I wonder how all the
participants manage to get their normal jobs done with so much input
into the debate! However, with a lunch break to spare I'd like to
pose a question to Timaeus, which, I think gets to the heart of why I
can't accept any form of Intelligent Design as "science". (Note I was
once an advocate of ID, but have since changed my views).

I'll use what I do in my own field of work to illustrate the problem,
so forgive what might become a lengthy explanation.

I develop software algorithms that use mathematical models based on
empirical data. This involves collecting sets of observations, and
then deriving a mathematical model from the observations you have, so
that given a new set of observations, your model can make new
predictions. For example, you might make a model that predicts the
temperature in a certain part of a piece of working machinery from a
series of other measurements, e.g. of temperatures, pressures,
rotation speeds, etc that are elsewhere in the system. You might want
to do this as a way of measuring a temperature that is difficult to
measure except in lab conditions, or you might want to use the model
to determine if something has gone wrong with the system (when the
prediction of the model differs from the measured temperature; an
example of "condition monitoring").

One type of commonly used mathematical model is called a "neural
network", because of its resemblance in certain aspects to brain
architecture. However, to all intents and purposes it's just a set of
mathematical equations for doing curve fittin, and to each term in the
equation is attached a numerical coefficient, and the values of these
numerical coefficients are determined by using the initial collection
of data, so that the predictions are correct for that set of data.
This process is often termed "Training", because it involves
repeatedly presenting the data, and then adjusting the coefficients to
improve the prediction accuracy at each stage.

So you have in effect a black box with numbers and equations. You
then plug in numbers one side; the box performs calculations and
outputs a number that is its prediction.

The big question is how do you determine the coefficients, and even
more critically, how many coefficients do you use? (This is termed
"model order"). In the case of a neural network, the model order is
governed by how many "neurons" you put into it. The higher the model
order, the better you find the prediction is on the initial data set
(often termed "training data"). In fact there is a mathematically
proven theorem (due to Kolmogorov) that applies to a certain class of
neural network called a "feedforward network" that says that given
_any_ finite set of training data, there will exist a feedforward
neural network that can produce the outputs in the training data to
arbitrary accuracy, given a sufficiently high model order. Thats
_any_ set of training data. So I could use a random number generator
and produce random inputs and a random output, and a neural network
will exist that will reproduce it exactly.

Now let's take a silly example. Suppose I wanted to predict the next
digit of the number pi from, say the previous 25 digits of pi. So I
take my "training data" to be the first million digits of pi. My
black box takes in 25 successive digits anywhere from this stream, and
does its calculation and outputs the next one. Now Kolmogorov's
theorem states that it is possible in principle to construct such a
neural network. However, if you did construct one, you would almost
certainly find that the number of coefficients required (for a
sufficiently high model order) would require at least as much space to
write down on paper as the original million digits. Furthermore, if
you were to try out your black box on the 1000001st digit, it would
most likely get it wrong!

Now here's the key point I want to make. To say that a neural network
exists that predicts precisely what you want from the first million
digits, doesn't say anything useful scientifically as to whether there
is a pattern, or law governing the digits of pi. If, on the other
hand you found a neural network that had only 100 coefficients and
that predicted perfectly all the digits in my training set, then you'd
be justified in saying you'd discovered a law.

In other words, if we are to say that the neural network constructed
is the analogy of a scientific law, then we can say it's only any use
as a scientific law if a sensible constraint is placed on what it can
model. If it can model anything (ie a neural network of sufficient
size can model anything), then it's of no value scientifically.

This leads to my problem with ID. The problem is that we see systems
that are "irreducibly complex", and conclude it can't have evolved,
and then go on to postulate an "Intelligent Designer". Let's first
assume the position that this Designer might be a sufficiently
advanced alien life form. What we know is that life form must be
sufficiently smart to figure out how to determine the DNA sequences
that lead to the irreducibly complex organism. But as soon as I say
"sufficiently smart", I believe that this is falling into the same
trap as saying a sufficiently high model order in my neural network
(or related mathematical model) will "explain" the data. It simply
does not explain it, for the same reason. And when one postulates
that the Designer is God, then one gets into even deeper trouble,
because God by nature is Omnipotent.

I can't see any way round this problem. Not that I would rule out the
possibility that a Designer might have intervened at times and
installed a software patch on the system to make something crucial
happen. But equally you can't rule out the possiblility that our
understanding of evolutionary processes will improve and get refined,
and what previously seemed impossible now becomes pretty plausible.
(From what we know now of evolutionary processes, they are a lot more
subtle and rich than NS operating on the occasional "copying error" -
try reading "Darwin in the Genome - by Lynn Caporale" for a tour de
force of the kinds of mechanisms that are involved)..

So in a nutshell, a term I've used before comes to mind. A neural net
of unlimited size, an alien being of sufficient intelligence, or an
omnipotent God all fall into the category of what I call a Univesral
Explanatory Mechanism (UEM). To postulate a UEM as the "explanation"
to something we don't yet understand offers nothing useful, because by
definition it can explain anything; and therefore it can't be science.

I'd be very interested to know if you have a response to this.
Apologies for the length of the post.


Non timeo sed caveo
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Received on Tue Sep 30 07:43:49 2008

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