Date: Thu Sep 08 2005 - 12:26:44 MDT
Eliezer S. Yudkowsky wrote:
>> [Richard Loosemore wrote:]
>> You make my point for me. The Ptolemaic astronomers would have used
>> exactly the same argument that you do: "Name some subtle ways in which
>> the heavenly bodies do not move according to the standard set of
>> epicycles, and I can describe how an infinite number of epicycles would
>> do it...." Yes, yes yes! But they were wrong, because the *real*
>> mechanism for planetary movement was not actually governed by epicycles,
>> it was governed by something completely different, and all the Ptolemaic
>> folks were barking up the wrong tree when though their system was in
>> principle capable of covering the data.
> First off, you didn't answer my challenge. Name three subtleties, heck,
> name one subtlety, and see what I make of it.
> Your Ptolemaic argument misses the point. Ellipses are not superior to
> epicycles because they are local, or cheaply computable, or any such
> computational advantage. Ellipses are superior to epicycles because
> they are simpler. If planets really moved in ellipses, but we had to
> try and approximate ellipses using epicycles because ellipses were just
> too darn expensive to compute directly, that would be an appropriate
> analogy to Bayesian probability versus cheaper approximations. If
> planets really moved in ellipses, but we had to approximate ellipses
> with epicycles because ellipses were intractable, then you'd damn well
> better understand that planets *really* move in ellipses. And use that
> knowledge to develop your fast epicycle algorithms and your programs
> that find good, simple epicyclic approximations when looking at elliptic
> data. It wouldn't be good to stare at the computer screen for months,
> go nuts, and start thinking that planets *really* moved in epicycles.
You have done exactly what I begged people not to do: completely failed to
understand the argument as a whole, and instead misconstrued (and worse,
misrepresented) individual arguments. So long as you refer to the CAS
argument as "proud ignorance," or keep demanding that I give you "one good,
solid, predictive equation applying to cognitive systems that stems from
CAS," or draw false analogies with Carnot Engines (which describe the
*non-Complex* aspects of thermodynamics), you only demonstrate that my core
point has still not been understood.
Here is why I introduced the Ptolemaic Epicycles analogy, spelled out in
the simplest possible language: the Ptolemaic crowd could have issued the
same pointless challenge that you are trying to issue, viz: "Name three
subtleties, heck, name one subtlety, and see what I make of it." You have
said yourself that you are going to meet the challenge, if need be, by
calling upon the resources of infinite computing power. The Ptolemaists
would have declared, in exactly the same way, that they were going to
respond to any challenge by using an infinite number of nested epicycles.
In fact, it is worth noting that the first people to challenge Ptolemy
actually had a very hard time of it. Here is a quote from John D. Fix,
Astronomy (2nd Ed. updated, page 58):
"[Copernicus still assumed circular motions, not ellipses, so...]
To account for variations in the speed with which the planets
and the Sun moved among the stars, he had to use epicycles.
Copernicus hoped that the advantages of his theory compared
with that of Ptolemy would be overwhelmingly obvious to other
astronomers. This was not the case, however. The heliocentric
theory was not immediately accepted by other astronomers.
Critics of the heliocentric solar system noted that the
astronomical evidence was completely neutral. There were no
observations that could be explained by Copernicus but not by
Ptolemy. Copernicus claimed that his theory was simpler and
more elegant than the geocentric one. Yet after Copernicus had
added epicycles that he needed to account precisely for motions
of the planets, his model had as many circles (or more) than
Copernicus claimed that his model possessed elegance and simplicity. I am
doing something similar, but you have to understand exactly what is the
nature of my attack, and not think it is something else.
I do NOT claim that there are some specific situations that the Bayesian
approach, implemented on an infinitely large computer, cannot handle. It
should have been obvious that that was not what I meant by "subtleties", so
you completely misrepresent me by demanding that I name one of them. If I
were to make such a dumb claim, or if I were to respond to your challenge,
it would be like Copernicus and one of his challengers getting into an
argument about the exact parameters of the orbit of Mercury.
No, the attack I am making is that there are an array of subtle faults that
the Bayesian approach cannot get out of *unless* it makes recourse to e.g.
infinite computing power, or postulates that a Bayesian AGI would have a
certain freakish characteristic (outlined below). This argument is at the
So, one of those subtleties is that the Complex Systems folks are out there
saying, in effect:
******* Quote from a hypothetical CAS theorist *******
"Wait: have you tried to put together a complete Bayesian system that
understands and reasons about the world, *and* which can acquire its own
knowledge, ground its own concepts and interact with the world? The reason
we ask is that we have studied vast numbers of systems that are adaptive,
and we have noticed a trend: their global behavior tends to be very
different from their local mechanisms. (Indeed, the global seems to be
impossible to derive from the local.) The way this applies to your
specific case is that you want your AGI system to have certain global
features (like the ability to understand the world, learn new knowledge,
etc.) but you are trying to build it using local mechanisms that look very
much like something that you are hoping to get at the global level (the
system as a whole is supposed to have a global reasoning capacity that is
Bayesian in character). If you succeed in doing this - having Bayesian
global behavior *and* Bayesian local mechanisms - then the folks in the CAS
community will want to know about it, because you will have produced a
system that is utterly unique: it will have the same behavior at both
global and local level. In all our experience, we have never seen such a
thing: complex systems just don't do that!
"P.S. Please don't send us any more proofs or demonstrations or arguments
that your strict Bayesian core ideas have no Complexity in them; that they
are just like some conventional, complicated computer program of the sort
that exist today. It might well be true that your core Bayesian ideas are
that predictable, but that means nothing until you say exactly how a real
computing system (not some fantasy with infinite computing power!) would
implement a full AGI, one that also includes enough apparatus to establish
a mapping from internal representation to external referents as a result of
its learning system and its particular sensorimotor system. It is
precisely in this extended system that all the Complexity is likely to be,
because it is here that the system has its most reflexive, adaptive
components, and whenever we have watched people insert those kinds of
adaptive mechanisms in a system, it either becomes (a) chaotic, (b) dead,
or (c) complex.
"P.P.S. If you don't accept that an extended version of your Bayesian AGI,
in the sense just described, would actually need any Complex Adaptive
low-level mechanisms in the extended portion, then show us such a system
that actually works. Show us some really juicy, believable creation of
new, more and more abstract "concepts" by the system, in domains of
knowledge far removed from its original programming, where those concepts
arise from interaction with a non-trivial environment ... and do all of
this without inserting any code that would render it liable to get Complex.
Don't just claim that it will work, show it actually happening in a real
system. Don't just claim that it is obvious that you could do it: prove it."
******* end hypothetical quote *******
Here, then, is the Complex Systems equivalent of the "simple and elegant"
appeal that Copernicus made: Your fully implemented Bayesian AGI, if it
could be built, would be a Complex System (in the technical sense), but it
would also have a direct relationship between its global behavior and its
local mechanisms, and there is a massive body of evidence that such a
system would be an utter freak of a complex system. We don't believe in
freaks: Occam's Razor, plain and simple. If you believe, today, that you
can build such a freakish thing, you are going on blind faith.
This argument is at the paradigm level. It is not that there is some
specific system or equation, devised by someone working down at Santa Fe,
that can beat out your Bayesian formalism, it's that everything going on at
Santa Fe indicates that the paradigm on which the Bayesian approach rests
is flawed because of a "religious" belief that a Bayesian AGI would be
exempt from the observed characteristics of all other compex systems.
Am I trying to say that an AGI cannot be built at all? NO! I believe
there are other approaches that will let us do it, but I refuse to be drawn
into that discussion until such time as the above argument is actually
understood. There are some very interesting and deep discussions that we
could all be having about what to do next under such circumstances (I want
to have those discussions!), but I have to communicate the above argument
fully, and get it out of the way, before there is any hope of going on to
the next step.
If anyone does want to take it further, fine, but this is the last time I
try to explain this basic stuff. I am going to ignore any posts at that
level from now on.
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