From: Pavitra (celestialcognition@gmail.com)
Date: Tue Oct 13 2009 - 01:03:45 MDT
Luke wrote:
> My question was this: You seemed to, for the most part, re-state a lot of
> the steps in terms of a problem of formal mathematics. Why? Do you
> consider English to be insufficient/imprecise? Do we get to count
> ruby<http://www.ruby-lang.org/en/>as a formal mathematical system?
>
> Is there a formal mathematical definition of intelligence? What's so great
> about formal mathematics?
I don't know whether a formal definition of intelligence exists or is
possible. (I left the checkbox on step C unchecked, you'll notice.)
As for the value of math:
This is a very difficult idea to explain, because it's very subtle. The
best hope I can offer you is that, once you get it, it feels utterly
simple and obvious in retrospect.
What follows is a very poor attempt to allude at the general direction
of the answer you're looking for. If you're already most of the way
there, it may make some sense to you.
Yes, I consider English to be insufficiently precise. (Note, though,
that certain proper subsets of English can be used to communicate
mathematically-rigorous ideas.)
Yes, I consider Ruby sufficiently formal. A Turing machine is specified
with mathematical rigor; a Turing machine (plus oracles for clock, HRNG,
etc.) can emulate a modern PC; therefore, any computer program is
mathematically rigorously defined.
The existence of a formal definition of a question is a necessary
prerequisite to being able to answer the question with certainty.
Consider the following text from version 0 of the document:
> Compile design requirements for "friendly AI". When will we know we
> have succeeded?
In order for this step to be properly completed, the design requirements
must be so clear and precise that there is no possible dispute over
their interpretation.
(There may of course be dispute over whether they correctly ask the
"friendly AI" question, but that problem is probably intractable even in
principle.)
This degree of total precision is, essentially, the definition of
mathematical rigor.
Mathematics is more than just the ability to manipulate numbers. It's
_logic_, the discipline of clear, precise, unambiguous thought. Logic
means seeing the world with sharp edges, and distinguishing with
absolute certainty between truth and falsehood.
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