Re: [sl4] what's with all the math?

From: Luke (wlgriffiths@gmail.com)
Date: Wed Oct 14 2009 - 09:37:42 MDT


@Pavitra:
Many points, presented in no particular order. Bullet points are great for
that.

   - I've read some of GEB (Hoftstader) and some of The Emperor's New Mind
   (Penrose), so I'm familiar with the "formal" definition of "formal
   mathematical" - i.e. not just 2 + 2 but also !Q => !P, etc.
   - I may not have specified levels correctly on that task in version 0.
    When I said "When will we know we have succeeded?" I should have said "When
   will we know we have succeeded in creating a friendly AI?", and not "When
   will we know we have succeeded in creating design requirements?"
   - I kinda like Yudkowski's definition of intelligence as "that which hits
   a target in less than chance time." This allows things like heat-seeking
   missiles to be considered intelligent. Not mathematically rigorous, but
   pretty close.
   - I've debated with some MIT kids on the value of "understanding"
   intelligence, and whether this is a necessary step in the creation of
   intelligence. Being a zen buddhist, I'm incredibly skeptical that anything
   can be fully understood. Yet I'm still able to get things done here and
   there (though I'm always ignorant of the full effects of my actions). I
   just want to invent a cheap, mass-producible neural network implemented in
   hardware and sell it like the laptop-for-every-child machine, and have kids
   developing a good intuition for what can and cannot be achieved with neural
   networks, the same way they know what can and cannot be achieved with a
   plasma grenade (see Halo franchise).
   - I'm also a web developer, and I'm pretty confident that at least some
   aspect of our future strong AI will be written in code. However, I predict
   that the code will be simply managing tasks which are handled by black-box
   systems like neural networks. Something like "if(@picture.contains("a
   pizza")){ say "I see you're thinking about pizza - would you like me to
   order you some?"}, where "contains a pizza" will be handled by a neural
   network.
   - Mathematical definition of friendliness - good luck with that. Perhaps
   we could start with English definitions, then slowly start constraining our
   language more and more until we can get a formal mathematical definition.
    Does anyone know of a body of formal mathematical definitions of
   sociological interactions?
   - Being a civil engineer by training, web developer by trade, serial
   entrepreneur, musician, masseuse, and meditator-at-large, and psychedelic
   enthusiast, I see myself as bringing some project management expertise to
   the table. I'd be curious to know what everyone else's background and
   day-to-day line of work is. What do you all do? How can we forge ourselves
   into an effective team, and not just a bunch of idly-chattering
   idea-machines? Do we have any mathematicians in the group? Musicians?
    Artists? Billionaires? Hippies? Politicians? Child psychologists?

I think there's a big tradeoff between rigor and applicability. Linear
systems (cannon firing at from horizontal with velocity V - where will the
cannonball land?) lend themselves nicely to mathematical analysis - i.e. we
can answer the question without performing the experiment. Nonlinear
systems (6 * 10 ^ 23 concepts interconnecting and mutually
activating/inhibiting within a Jupiter Brain - will it try to kill us?) not
so much - i.e. we won't really know until we build the darn thing and turn
it on.

I'm really quite (1) optimistic about our ability to spawn intelligence
greater than our own, and (2) pessimistic that the resulting machines will
be so easily taken out with a simple EMP blast, let alone be guaranteed
friendly. But I'm willing to explore the space, because I think it's our
only hope.

But rest assured, I'm doing my best to live it up now because I don't have
much hope of living beyond 2040.

 - Luke

On Tue, Oct 13, 2009 at 3:03 AM, Pavitra <celestialcognition@gmail.com>wrote:

> 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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