microcode, compilers, and supercomputer architecture

From: Eric Smith <eric_at_brouhaha.com>
Date: Mon Apr 5 13:56:19 1999

[I'd suggested that we take this discussion off the list. I'm continuing
to reply here in this case only because I don't want people to get the
incorrect idea that Godel's Incompleteness Theorem can be used to magically
explain away any philosophical problem regarding computers.]

> Is this use of the word "assembly" not yours? I, sir, am quoting you, not
> me!

OK, that one was mine. It wasn't in the context you originally quoted, or
even from the same message you quoted
(<19990405060635.29296.qmail_at_brouhaha.com>). I had used it three
hours earlier in the discussion (<19990405030452.28640.qmail_at_brouhaha.com>).
So perhaps you see why I didn't understand what you were complaining about.
It is customary to include a brief quote of the actual context you are
referring to.

> That says nothing about the general case
> that humans have superior intellectual capacity vis-a-vis the computer.

In the general case, I've never claimed that they do. I've only claimed that
in a sufficiently limited problem domain with a time limit (i.e., the solution
value vs. time curve is a flat with a sharp drop to zero), a computer may
reach a better solution than a human would. I also claim that this is true
for other common solution value vs. time curves; if the solution is worth $x
today but only $x/2 tomorrow, the computer may produce a more valuable
solution than would a human.

> What you have failed to address is that the human intellect is not limited
> by the capacity to algorithmatise a solution.
[and later:]
> Humans have the capacity to make judgements by means outside of those
> mathematical and logical, hence the reference to Penrose.

Sure. A human may proceed in a manner that is not based upon logical
deduction or any (obvious) deterministic algorithm.

It is yet to be proven that this human ability (as manifested in complex
problem-solving) is not equivalent to a non-deterministic algorithm,
or even to a sufficiently complex deterministic system. Penrose claims
that quantum uncertaintly is necessary to intelligence. While he provides
insufficient proof of this claim (really just anecdotal evidence), as an
argument against machine intelligence it is a red herring, since it is
not especially difficult to build a system that uses quantum uncertainty
to influence nondeterministic algorithms.

> in particular, the notions of Godel: that within any axiomatic system, th
> answers to some positable questions are indeterminable.

You know, since you mentioned the book GEB, I thought you might have been
trying to bring Godel's Incompleteness Theorem into the discussion. But
since you didn't specifically state that, I wanted to give you the benefit
of the doubt.

The Incompleteness Theorum if very useful for certain lines of reasoning.
And it might be relevant to the strong AI problem. But it has no relevance
to the compiler problem we've been discussing.

In the compilers "axiomatic system", it is not possible to even construct
the kind of questions to which GIT refers.

The compiler is not burdened with proving that it is correct, or that its
own output is correct. At most we are asking it to select the more efficient
of several proposed solutions. This in some sense does involve a "proof",
but the required proof is no of the validity of the axioms (i.e., the
compiler algorithm), nor is it a proof that the "system" is self-consistent.

> For all the nit-picky details of the works of these masters, the points they
> make are far grander. The real value of their works is not kept solely
> within the realm from which their conclusions emerge, but within which
> such conclusions find additional value.

If you know where to apply them. You can't just willy-nilly claim that
GIT applies to any random problem.

If you are going to maintain that GIT precludes compilers generating code
as efficient as the best human-generated code, you'd best be prepared to
present a logical argument as to why GIT applies. It's not a magic wand,
and I'm not going to concede your point at the mere mention of it.
Received on Mon Apr 05 1999 - 13:56:19 BST