**From:** Eliezer S. Yudkowsky (*sentience@pobox.com*)

**Date:** Mon Nov 27 2000 - 00:44:54 MST

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Ben Goertzel wrote:

*>
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*> Eliezer Yudkowsky wrote:
*

*> >
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*> > Mathematics is an
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*> > extraordinarily powerful tool which will never be useful to cognitive
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*> > scientists. We'll just have to live with that.
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*>
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*> I'm finding it hard to resist using unpleasant language in response to this
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*> very silly statement.
*

Oh, go ahead - that statement was a bit too sweeping. No, that's not

enough. That statement was factually incorrect.

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. I do

think that such mathematics will tend to be far more crude than the math

used by physicists. And I think that the math will get less refined, not

more refined, as we start describing the mind rather than the brain.

But *this* vision:

*> Yes, where differ is then in our intuition about the relationship between
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*> mathematics and cognitive science. I think that a new kind of math is
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*> needed to transform cognitive science into a real science. Perhaps AI's
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*> will help us create this new kind of math.
*

That is exactly and precisely the vision that I disagree with.-

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. As we understand the mind even better, the

*kind* of similarity to computer programming will approach similarity to

hacking, rather than similarity to computer science. Results from

complexity theory or chaos theory will become *less* useful as time goes

on and the mathematically describable regularities are optimized out of

the system. And the ultimate core of intelligence, the ability to make

smart decisions, will never get reduced to an equation, because smartness

is at the top of the reductholistic heap, not at the bottom.

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 - while being infinitely more complex than both,

of course; the point I'm trying to make is that some causal systems just

don't have useful mathematical descriptions. And if you try to describe

one of those systems using mathematics, then that is not making it more

like "real science", but less.

-- -- -- -- --

Eliezer S. Yudkowsky http://intelligence.org/

Research Fellow, Singularity Institute for Artificial Intelligence

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