Mike Dougherty wrote:
On 10/5/07, Richard Loosemore <[EMAIL PROTECTED]> wrote:
My stock example: planetary motion. Newton (actually Tycho Brahe,
Kepler, et al) observed some global behavior in this system: the orbits
are elliptical and motion follows Kepler's other laws. This corresponds
to someone seeing Game of Life for the first time, without knowing how
it works, and observing that the motion is not purely random, but seems
to have some regular patterns in it.
Having noticed the global regularities, the next step, for Newton, was
to try to find a compact explanation for them. He was looking for the
underlying rules, the low-level mechanisms. He eventually realised (a
long story of course!) that an inverse square law of gravitation would
predict all of the behavior of these planets. This corresponds to a
hypothetical case in which a person seeing those Game of Life patterns
would somehow deduce that the rules that must be giving rise to the
patterns are the particular rules that appear in GoL. And, to be
convincing, they would have to prove that the rules gave rise to the
behavior.
with GoL you started with the rules and try to predict the behavior.
with planetary motion you observe the behavior and try to discover the rules.
I'm going to stop you here and deal with this alone.
Strictly speaking this is only half the story, because with planetary
motion you try to discover the rules and then you have to show that the
the hypothesised rules do indeed predict the behavior. (Several other
people besides Newton, if you remember, also suspected the inverse
square law, but Newton trumped them by inventing calculus and proving
that the inverse square law predicted elliptical orbits, etc).
"Explanation" in general is a two part process: hypothesise the
mechanism, then demonstrate that the mechanism really does give rise to
the behavior.
In my use of GoL in the paper I did emphasize the prediction part at
first, but I then went on (immediately) to talk about the problem of
finding hypotheses to test. Crucially, I ask if it is reasonable to
suppose that Conway could have written down the patterns he *wanted* to
see emerge, then found the rules that would generate his desired patterns.
It is *that* question that is at the heart of the matter. That is what
the paper was all about, and that issue is the only one I want to
defend. It is so important that we do not lose sight of that context,
because if we do ignore that (as many people have done), we just go
around in circles.
So, yes, i did say that it is extremely hard (read: impossible) to
"predict" or "explain" the patterns in GoL, given the rules ... but what
is happening right now, in the general discussion going on in this
thread, is that some people are trying to broaden the sense of "predict"
or "explain" so that it could be said that the patterns in GoL really
can be xplained or predicted. (In particular, Josh is obstinately trying
to insist that just doing lots of simulations and searching for the
patterns is the same thing as explaining or predicting them).
The problem is that this kind of distorted, special-case interpretation
of "explanation" is not only atypical of scientific explanations in
general, but also completely useless in the context of the question I
raised in the paper: If Conway had had the goal of inventing GoL rules
that would generate a specific set of patterns, what good would it have
done if the only way to predict the patterns from the rules was the kind
of "prediction" or "explanation" that Josh insists on (simulate and
test)? If there had been any way at all to find a compact explanation
of that relationship, the existence of that compact relationship would
have offered the hope that Conway could have worked backward from his
patterns to the rules that would generate them.
Similarly, if there did not exist any compact explanation for the shape
of planetary orbits, Newton would never have been able to guess the
rules that gave rise to the orbits. Just imagine that the orbits were
the result of a massive combination of exhange-interactions between five
million species of subatomic particles, and that orbits were not
elliptical, but some other bizarre shape: if the only way to find out
the shape was to simulate the five million different types of subatomic
interactions, how would Newton ever have come up with a hypothesis to
test? The existence of compact low-level to high-level relationship was
what made it possible for him to do that.
The two directions involved in the process of explanation (hypthesising,
which is going from high level to low level, and testing, which is going
from low level to high level) are interrelated.
My emphasis on the "testing" phase of this process, in the specific case
of GoL, was part of a larger plan to consider its impact on the whole
explanation process.
And that, in turn, was part of a larger goal about thinking about the
process of engineering (building) systems, rather than just explaining
them. Ultimately, of course, my goal was to talk about the engineering
of a certain class of systems (AI systems).
Let's just stick to this one issue for a bit and see if we can get this
sorted out to your satisfaction.
Richard Loosemore.
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