Re: Cantor's Theory: Mathematical creationism
From: Curt Welch (curt_at_kcwc.com)
Date: 11/25/04
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Date: 25 Nov 2004 19:57:19 GMT
stephen@nomail.com wrote:
> I have noticed that many of the 'anti-Cantorians' seem to have
> some connection with AI. I have no idea if this is representative
> of the AI community or that these ideas are considered crankish
> in the AI community also. It does seem to be the case that AI
> attracts fuzzy thinkers, pun intended.
The AI community is full of cranks and "fuzzy" thinkers. It's because we
are trying to understand the nature of something that nobody has the
language to correctly explain yet. In order to solve AI, you have to find
a new way to talk about the problem because all the old ways we have
available to us have been proven to not be the full and complete answer.
The word "intelligence" is fuzzy as hell. Nobody knows how to formally
define it. If they did, then they could tell us how to build a human level
intelligent machine - and now one has even come close to that yet. So to
solve AI, we have to figure out how to remove all the "fuzz" from the
definition of intelligence.
So far, every attempt to do that has removed the intelligence from the
definition at the same time it removes the fuzz. There are hundreds of
different types of formal machine descriptions in the field of AI that
people hoped would lead to a description of intelligence - from logic based
systems, to symbol processing, to neural networks, to Bayesian networks to
emotion machines. But so far, nothing has proven to be intelligent.
Much of the accepted and funded work in AI and the various cognitive fields
are based on extending our knowledge in one of the many well defined areas
even if the area has been unable to produce intelligence. This is because
the well defined areas produce well define projects, and well defined
results.
But it's unlikely that any of those projects will solve AI on their own.
It's because we are still searching for the right approach. And to find a
new approach, you have to back up to the fuzzy, and then look for a path to
go forward to the non-fuzzy again. And you do that with creative, and
fuzzy, brain storming. You do it, like was said in another post, by
babbling. And it's damn hard to get anyone to fund, or to even respect,
babble. Yet, it's out of the babble which the solution to AI is going to
emerge.
But, back to the "crank" issue. There are a lot of us cranks in AI for two
reasons. First is the nature of the problem. When you use the tools of
logic and reason to try and understand logic and reason, it's impossible to
be objective - to separate the observer from the observed. This creates a
very dangerous trap. It creates an environment that allows you to put
forth just about any idea, and turn it into a self-supporting truth. Just
about any language you can create to explain what the mind is doing can be
made to support itself as "proof" of its validity. This fools many
beginners into believing that they language they use to explain
intelligence is the "obvious" correct answer, even if it's completely
different from what everyone else likes to talk about.
The second, and most important reason there are so many cranks is that
since no one has yet solved AI, no one has the logic to prove any of the
cranks wrong. So even if a new idea seems totally in the wrong direction
according to the instincts of the majority, we have no tools to prove the
direction is wrong. This allows the off-beat theories to live on, and
allows the creators of those theories to continue to believe in the
validity of the idea even when no one else does.
It also allows the people that believe AI is impossible to continue to
believe in that faith. None one has tools to prove anyone wrong in this
field. So it's a field full of conflicting beliefs.
The only ultimate proof of any AI theory is that if it is correct, it will
allow us to create human level intelligence. Many of the theories are
clearly counter productive to that goal. The theory that it is impossible
is the ultimate theory which is counter productive. But many of the other
theories of cognition are clearly not workable as a description of a
machine. So they, in their current forms, are no more productive than the
theory that it's impossible.
But there are many approaches that allow us to build machines, which when
built, don't seem intelligent. But there's the catch-all excuse to explain
that - the machine just isn't large enough, or fast enough, to produce a
level of intelligence which we are able to see as being intelligent. Or,
we just need to add more functionality - the catch all, "we just need a
little more" to create intelligence.
Every project that fails to create human level intelligence is just one
more data point to support all the other theories - including the theory
that it's impossible.
Repeating a point from above:
> I have noticed that many of the 'anti-Cantorians' seem to have
> some connection with AI.
I can explain my confusion with Cantor that I think relates to why people
like me will continue to bring up the question.
I'm an engineer. And as such, my focus has been on the physical universe
my entire life. Since I was only a few years old I was fascinated with how
the physical world of machines worked. I was using a screw driver to take
door knobs apart when I was 4 years old. I took every toy I owned apart
(even if it meant breaking it) because I just had to know how it worked.
How many of you have taken an etch-e-sketch apart to see how it worked for
example? How many of you have taken a 3 speed bicycle transmission apart
when you were in grade school to see how it worked?
I spent my entire childhood designing, and building machines. By the sixth
grade (1969), I was building radios. In the 7th grade, I built a binary
adding machine out of neon lights from a project in Popular Electronics
magazine. And I was learning woodworking from my dad at the same time.
But all this time, as I was fascinated by how the physical world and
machines worked, I had little to no interest in people, or the things they
used, like language. Though my analytical skills have been years ahead of
my peers, my language and social skills were years behind my peers. On my
SATs, I scored 780 in math, but only 450 on verbal.
Because of this bent, the only purpose of math in my mind was as a tool for
understanding the physical world. The only aspects of math that interested
me were the ones I could directly apply to the physical world. And for the
most part, everything I learned in 17 years of education about math was
stuff that did apply to the physical world.
So when I started to think more about this business of Cantor recently, it
seemed to me that the physical world was making it clear that this part of
math had to be invalid. But why was it invalid?
So I came here to find out. How was it possible for math to be in
conflict with the physical world it was meant to explain?
And the answer is that math isn't about the physical world. Just because
that's my only real interest doesn't mean that's the interest of everyone.
Real mathematicians are addicted to the properties of the language of math
as much as I'm addicted to the properties of the physical world. Math is
not a study of the properties of the physical world, it's a study of the
properties of language.
There are many people like me that are "materialists" at heart. We see,
explain, and try to understand, everything in terms of the physical world.
Philosophy, art, mathematics, emotions, are all properties of the mental
world, which for the most part, we have spent our life ignoring, or at
least, putting second in importance to the physical world which is the
"real" center of universe for those who learned to think like I do.
So to us, math is only there to explain the physical world, and when it
doesn't seem to explain it correctly, something seems broken. So we debate
this "obvious" contradiction with anyone who we can force to hear it.
But, now that I understand that math is a total abstraction from the
physical world, and higher math is just a study of the properties of the
language of math when not connected to any external "facts", I can
understand how this stuff of Cantor is valid. In language, this stuff is
valid, and real, and does exist, even if it's describing something we have
not yet found to be real, and valid, and existing, in the physical world.
Now, anyone that believes AI is possible has to be a person somewhat like
me that tends to see the mental world as something that grows out of the
physical world because that is what we are trying to do in AI. We are
trying to create the mental world out of physical stuff. People who
instead see the mental world as the center of our existence, and prefer to
look at the physical world as something that grows out of our mind, are the
ones who will be attracted to fields like math and philosophy instead of
engineering. They like to study the properties of the mental world and
ignore the physical world, or put it second in importance to the properties
of the mental world.
So it makes sense that people interested in AI, who have a physical world
focus, but yet are trying to define the mental world in physical terms, is
going to run into this Cantor problem and question it.
So, I believe that people that are attracted to, and who study, the
properties of the mental world, in fields like math and philosophy, are in
fact studying the properties of language. And in language, Cantor is real
and valid.
But people like me (an engineer), who's purpose in life, is to study and
understand the properties of the physical world, expect math to be our
slave. And when it doesn't follow the rules, something seems broken. But
once I grasped how and why math was not a slave to the physical world, it
all started to make a lot of sense. Math is only a slave to the powers of
the mind, and the powers of the mind, with it's ability to create and use
language, can do many things that aren't consistent with the limitations of
the physical world.
All it is really showing is that with the power of language, we can
describe, think about, and analyze things, that exist in the mental world
that don't happen to exist in the physical world. And that's not a
contradiction.
-- Curt Welch http://CurtWelch.Com/ curt@kcwc.com http://NewsReader.Com/
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