From: Brian Atkins (brian@posthuman.com)
Date: Tue Apr 24 2001 - 22:30:36 MDT
Check out the thread from last November about "limitations of finite minds":
http://www.sysopmind.com/archive-sl4/0011/
Ben Houston wrote:
>
> Hi Eliezer,
>
> May I ask what the reason we need infinite computing is? This is not
> meant to be a troll type of question but I actually am curious. Of
> course, I am assuming that finite computing (ie. classical and quantum)
> on earth or nearby is adequate for super human AI.
>
> Kind regards,
> -ben houston
> http://www.exocortex.org/~ben
>
>
> > -----Original Message-----
> > From: owner-sl4@sysopmind.com [mailto:owner-sl4@sysopmind.com] On
> Behalf
> > Of Eliezer S. Yudkowsky
> > Sent: Tuesday, April 24, 2001 8:14 PM
> > To: SL4
> > Subject: Infinite computing
> >
> > By request, I'm posting a summary of the known proposals for achieving
> > infinite computing power. Since it's easy to demonstrate that
> physical
> > law permits computing elements that operate millions of times faster
> than
> > neurons, and this quite suffices for superintelligent, far-transhuman
> AI,
> > I no longer have a need to speculate about Moore's Law literally going
> on
> > *forever*, with transhuman smartness finding loopholes in any and all
> > "physical limits". Which doesn't mean that I think infinite computing
> > power is implausible; just that I got sick of hearing catcalls about
> it.
> >
> > --
> >
> > The most famous way of achieving infinite computing power is, of
> course,
> > the Omega Point proposed by Tipler; as temperatures rise ever faster
> > during the Big Crunch, the asympotically increasing energy densities
> > permit the performance of an asymptotically increasing number of
> > computational operations, such that an infinite number of computations
> is
> > performed before the Universe ends. Unfortunately, this requires
> waiting
> > until the end of our Universe, which now appears to be open rather
> than
> > closed anyway.
> >
> > If you can perform infinite computation during a Big Crunch, you can
> > probably also perform infinite computations during a Big Bang. Thus,
> one
> > proposal for infinite computing power involves pinching off a section
> of
> > spacetime from our own Universe and creating a new Universe, with an
> > accompanying Big Bang. When this new Universe began to cool off,
> perhaps
> > after 1e-43 seconds (post-Planck-time), another Universe could be
> created
> > and so on ("Alpha Line" computing).
> >
> > Less ambitiously, the "Linde Scenario" would involve opening up a
> series
> > of basement Universes connected to our own via wormholes. "Each new
> > universe could be the parent of many new universes, so that the whole
> > population would grow exponentially, the gradual entropic degradation
> of
> > old universes playing only a negligible role in slowing down the
> > process." (Nick Bostrom.) This does not achieve actual infinite
> > computing speeds at any given point, but it does permit life and
> growth to
> > continue indefinitely, and the performance of an unboundedly large
> number
> > of computations as time goes on. Which is all we really care about,
> > right?
> >
> > Linde Scenario:
> > http://www.aleph.se/Trans/Global/Omega/linde.html
> >
> > Our Solar System contains a limited amount of mass, and Conservation
> of
> > Mass and Energy says that we can't just make more. However, the laws
> of
> > physics contain no statement asserting Conservation of Material. If
> > negative energy can be manufactured, then positive matter and negative
> > matter could be produced in paired amounts - in theory, in indefinite
> > quantities. Furthermore, because the total mass would be zero,
> > interlacing negative and positive matter would permit the construction
> of
> > arbitrarily large dense megastructures without those megastructures
> > collapsing into black holes. Thus, rather than life running into hard
> > limits when all the matter in our Solar System is consumed, growth
> could
> > continue indefinitely. Since negative energy would also permit FTL,
> time
> > travel, wormholes, and the violation of the second law of
> thermodynamics,
> > many people postulate that Cosmic Censorship prevents the manufacture
> of
> > negative energy. (Frankly, I think this is a rather warped way of
> > reasoning about the laws of physics; the only way to find out whether
> > negative energy can be manufactured is to try it. When did it start
> > becoming permissible to reason from a-priori philosophical constraints
> > instead of experiment? Oh, never mind.)
> >
> > As long as you're constructing arbitrarily large computers, why
> construct
> > them from mere molecules, which have a maximum theoretical switching
> speed
> > of 1e15 hertz before the energies used tear them apart? Neutronium,
> being
> > far denser, permits much faster computing speeds from a given amount
> of
> > mass, with a maximum switching speed of 1e21 hertz. An even denser
> > material is Higgsium, produced using the negative Higgsino at the
> center
> > of the nucleus, and orbiting protons serving the function now served
> by
> > electrons. Higgsium is 1e18 times denser than water; a thimbleful
> weighs
> > as much as a mountain. Monopolium uses a light monopole of one
> polarity
> > (North) bound to a heavy monopole of the opposite polarity (South);
> the
> > density is 1e25 times that of water, and a thimbleful weighs as much
> as
> > the Moon. (Hence the need to use interlaced positive and negative
> > monopolium structures, to prevent the collapse into a black hole of
> any
> > reasonably-sized structures.)
> >
> > Neutronium, Higgsium, and monopolium:
> >
> http://www.aeiveos.com/~bradbury/Authors/Computing/Moravec-H/HDPSF.html
> >
> > Of course, if you keep on manufacturing more and more zero-mass
> > "interlaced matter", you eventually run out of *space* in your Solar
> > System. I believe that I was the first one to propose solving this
> > problem using Van Den Broeck's "micro-warp" adaptation to Alcubierre's
> > warp drive - also known as the "tardis warp" or "warp bubble". Van
> Den
> > Broeck found a solution to the General Relativity equations which
> permits
> > a large space, say 100 meters in diameter, to be connected to the rest
> of
> > our Universe through a tiny bottleneck, much smaller than an atomic
> > diameter. Thus, you can pack a very large number of Van Den Broeck
> > bubbles into a volume the size of our Solar System. Furthermore, as
> far
> > as I know, there's no theoretical reason why you can't open up one Van
> Den
> > Broeck bubble inside another one, which would permit total living
> space to
> > keep growing exponentially forever. You'd probably want to use a
> wormhole
> > network to keep all the bubbles in communication.
> >
> > In short, this is a design for a galaxy-sized computer built of pure
> > monopolium that fits inside your pocket and weighs as much as a
> Kleenex.
> > As far as I know, I was the first to propose "fractal tardis
> computing" as
> > a means of achieving indefinite exponential growth.
> >
> > Alcubierre warp drive:
> > http://xxx.lanl.gov/abs/gr-qc/0009013
> > Van Den Broeck tardis pocket ("micro-warp"):
> > http://xxx.lanl.gov/abs/gr-qc/9905084
> > (Googling will uncover plenty of less technical explanations.)
> >
> > Finally, of course, there's the idea of using a closed timelike curve
> to
> > send the result of a computation back to before the computation
> started,
> > permitting an infinite number of iterations to be performed in what
> looks
> > to the outside Universe like a finite amount of time. Of course, this
> > only works if you can construct a closed timelike curve, which IIRC
> was
> > proved to require negative energy. Cool stuff, negative energy. (Ha
> ha
> > ha! Sorry.)
> >
> > I think someone also claimed infinite computing power using black
> holes,
> > but I haven't heard any specifics on that one.
> >
> > -- -- -- -- --
> > Eliezer S. Yudkowsky http://intelligence.org/
> > Research Fellow, Singularity Institute for Artificial Intelligence
-- Brian Atkins Director, Singularity Institute for Artificial Intelligence http://www.intelligence.org/
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