Vladimir Nesov wrote:
On Mon, Jun 2, 2008 at 8:37 PM, Richard Loosemore <[EMAIL PROTECTED]> wrote:
This misses the point I think.
It all has to do with the mistake of *imposing* simplicity on something by
making a black-box model of it.
For example, the Ptolemy model of planetary motion imposed a 'simple' model
of the solar system in which everything could be explained by a set of
nested epicycles. There would have been no need to use any other model
because in principle those epicycles could have been augmented to infinite
depth, to yield as good a fit to the data as you wanted.
That is a black-box model of the solar system because it stuffs all the real
complexity inside a black box and then models the black box with a
simplistic formalism. If all you care about is getting a precise model of
planetary movement across the sky, this would be (and was!) the simplest
model anyone could ask for.
But it was wrong. It was wrong because it obscured the real situation. The
real situation could not be understood without inventing a whole new type of
mathematics (calculus) and discovering a new law of nature (universal
gravitation). By any measure, that combination of calculus and gravitation
was a more "complicated" explanation.
Anyone at the time who knew that Isaac Newton was trying to do could have
dismissed his efforts and said "Idiot! Planetary motion is simple. Ptolemy
explained it in a simple way. I use simplicity-preferring prior, so
epicycles are good enough for me."
And if that same person insisted that there SHOULD be a simple model of
planetary motion (where "simple" meant 'as simple as epicycles") would have
been insisting that an explanation as complicated as calculus and
gravitation was in some sense bad or unparsimonious.
In the long run, of course, gravity plus calculus was perceived as being
'simple' and elegant in the extreme. But that is not the point, because
before it was discovered it could have been criticised as being far, far
more complicated than the epicycle explanation.
I could argue that your example is a strawman, but it's not a very
relevant issue. My point is that you have to have some prior, and
prior that prefers simplicity is as good as any (or better, by
exploiting implicit statistics-gathering during notation-building). If
you do have some additional information that says that this particular
distribution is not good enough, it should be updated. Probability
expresses incompleteness of knowledge. To believe that you need
something more complex, you need evidence.
The example was a strawman?
It was a precise analogue of the situation we are talking about, so
calling it a strawman, or calling it irrelevant, is just a way of
avoiding what I said.
I was refering to a specific attitude among some people who claim that
the function of a neuron can be completely modelled by treating it as a
black box and using a bayesian model to capture its I/O function.
There are two points at the heart of the debate.
First, even those people who claim that the neuron is really "simple"
(e.g. J Andrew Rogers) have not, in fact, modelled real neurons in
enough detail to be able to say that they understand them completely.
There are many different types of neurons, and the exact layout of the
connections to individual neurons has not been mapped except in simple
cases such as the sea-slug (Aplysia) and the squid. So the claim is at
best a "we could do it in principle" claim, not a "we have actually
modelled all known types of neurons in enough detail to exactly
reproduce their firing patterns" claim. One of the reasons this matters
is that, as I said before, there have been arguments that the exact
layout of synapses in the dendritic tree may be important in the
processing carried out by the neuron ... and most current models neglect
this completely, pretending that the tree is just an amorphous arrival
point for all signals. If the tree matters, then all of those older
models need to be trashed.
Second, even if we did have a complete catalog of neuron behaviors (with
exact information about tree layout, timing, etc etc), and even if
someone were to produce a complete bayesian model of all of the neurons
in that catalog, the result would only be an "epicycle-like" model of
the neuron. You will notice that in that recent article that was
mentioned on the parallel thread to this one ("Re: [agi] news bit: Is
this a unified theory of the brain? ......") the people who had
reservations about the bayesian claim of a unified theory made exactly
the point that I am making: they criticised that kind of model for
being non-falsifiable.
This non-falsifiability is exactly what I was referring to when I used
the epicycle example: you cannot criticise the epicycle model of
planetary motion because the model is infinitely flexible! It can
explain anything, because it is built in such a way that parameters can
be added to it to fit any data. Scientifically, this is a barren
exercise, as we have come to understand. So the example I chose was not
a strawman at all, but an exact summary of what other people (not just
me) are saying about this kind of 'modelling' of neuron function.
In your comments above you say things that make no sense, it seems to
me: what do you refer to when you say that "you have to have some
prior"? Is this a bayesian prior that you have in mind? I don't
understand how that can relate to the issue of *how* you go about
chosing between scientific models. The Newtonian model of planetary
motion is not 'simpler' than the epicycle model, if you take a very
crude measure of what 'simple' means in this context. And yet, in
another way there are many physicists who would say that in a deep way,
the Newtonian model *is* simpler, because it is less arbitrary, more
testable, and has fewer free parameters.
In this context, all of what you say above can be summarized as "If you
think that the epicycle model of neuron function is incomplete, you need
evidence." And my reply would be: I am not claiming that it is
incomplete, only that it is not falsifiable, and scientifically barren.
Richard Loosemore
-------------------------------------------
agi
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