From: Ben Goertzel (email@example.com)
Date: Mon Nov 27 2000 - 05:33:47 MST
> In some areas, mathematics may turn out to be applicable, when particular
> systems have underlying behaviors that turn out to give rise to
> mathematical dynamics. This would be especially expected of systems in
> which some quantity is conserved, or in which there is an analogue to
> potential energys surfaces, or where you can use statistical mathematics
> to describe systems containing a stochastic element, and so on.
You're listing the physicist's mathematical toolkit, but I suspect that the
math for complex systems like the mind/brain will be something different...
think: (abstract algebra + algorithmic information theory + functional
> > Yes, where differ is then in our intuition about the
> relationship between
> > mathematics and cognitive science. I think that a new kind of math is
> > needed to transform cognitive science into a real science. Perhaps AI's
> > will help us create this new kind of math.
> That is exactly and precisely the vision that I disagree with.-
Well I hope we both live long enough, in one form or another, to find out
was right ;>
> Cognitive science will not become a real science as the result of math.
> It will not advance as a result of advances in mathematics. As we
> understand the mind better, cognitive science will approach computer
> programming. And the best computer programmers are not computer
> scientists; they are hackers. Now, any hacker gets a bonus to their
> intuitive understanding by understanding complexity theory and computer
> science and potential energy surfaces and, in fact, everything under the
> Sun - but actual computer programming uses very little mathematics.
> Sometimes a hacker winds up in a mathematical situation, yes;
> cryptographers do, and sometimes the parallel processing people need to
> resort to "something more complicated than simple arithmetic" to
> understand the behavior of resource wait times and so on. But these are
> the exceptions, not the rule.
In building Webmind, it is the rule, not the exception. You may say this
is because I'm taking the wrong approach in building Webmind, but I don't
so.... engineering a mind is very different from engineering most other
one of the differences is that the dynamics is very complex, so that
concepts are much more useful than they are for thinking about most software
And I acutely feel the lack of an operational math of very complex systems
like Webmind --
I feel that we'll be developing one as we go along, to keep the conceptual
engineering progress properly aligned...
> In computer programming we build upwards, and mathematics is useful for
> digging downwards. The farther upwards we build, the farther we get from
> mathematics. Sometimes the low-level behavior of our own systems starts
> to contain an element we didn't plan on, and we then have to debug it
> using mathematics - thread resource conflicts, for example. But the
> *frontier*, the cutting edge, the place where we're building one step
> higher and inventing something new, will never involve somebody solving an
> equation to find out what to invent, because equations can't tell us
> that. The interesting, high-level parts of the mind will resemble the
> piece of code you're playing with and that you didn't need any mathematics
> to write, rather than the one time in a month that you needed an actual
> equation to describe memory pool allocation conflicts as a function of the
> percentage of utilization -
My experience is that the interesting ~emergent~ behaviors that come out of
of various mind modules, can only occur because of mathematical insight
applied to the
particular workings of these modules. We don't yet have a mathematics
that's really useful for
understanding the emergent behaviors -- but I believe that the data we
gather while experimenting
with various versions of Webmind will help us to get there.
I understand your intuition now and I can't say that it's an invalid or
senseless intuition, it's
plausible enough. I just think it's wrong... not only does it contradict my
intuition, it contradicts
my own recent experience on "the *frontier*, the cutting edge... inventing
something new" ...
If you can engineer a thinking machine without using math as a significant
component, more power to you!
You're smarter than us, or have a better intuition.
Don't get me wrong -- there's more intuition than math in the Webmind
design. But without mathematical
analysis applied to key parts -- not just system-level parts like memory
pool allocation -- it just
Here's one way to think about it: Evolution often arrives at optimal
solutions by long experimentation.
If we want to avoid simulating millions of generations of evolution, we need
to get at these optimal
solutions in the first few experiments.... Mathematics is a way of doing
this, in many contexts. It doesn't
tell you how to structure the mind (at least not yet). It helps you figure
out how to get the general
structure you've intuitively conceived to ~actually~ work.
I think you're kidding yourself that you can hack a thinking computer
program. But, I could be wrong.
I dare you to show me I'm wrong ;>
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