From: Eliezer S. Yudkowsky (sentience@pobox.com)
Date: Wed Feb 20 2008 - 20:52:10 MST
William Pearson wrote:
>
> Now imagine you added a link to the outside, through which one bit
> could enter. Now depending upon that bit the system, the systems
> evolution could bifurcate, or it could ignore it and stay singular.
> Bifurcation leads to the potential for growing of the ability to
> predict the world, if parts of the world happen to correlate with the
> bit that was bifurcated on.
>
> More bits given to the system lead to more possible bifurcations.
> Exponentially increasing numbers of bifurcations are needed for
> exponential increases in predictive power.
You need a logarithmic number of bits in order to slice a prediction
to great fineness - i.e., predicting to within a factor of a billionth
requires 30 bits, not a billion bits. I know this is probably what
you meant, but nobody would hear you saying it unless they already
knew the answer.
The other thing to remember is that we do not live in a random
universe where it takes 1 bit of information to predict one more bit
of an important outcome, like trying to record a sequence of
coinflips. Gravity is the same all over, you don't have to learn it
again each time; and many important and manipulable aspects of the
universe are highly regular.
> A concrete example, let us say we are trying to get an AI to evolve to
> a state where it can consistently use my IP number to reach my
> computer. It follows its programming, let us say by incrementing a
> counter and using that in the IP field of TCP/IP packets. I give it
> no feedback nor any other bits of information about the world. It will
> never be able to bifurcate to a state where it always uses the correct
> IP address, it is just throwing out packets into the void. At some
> points it would even get the IP address right, but it wouldn't know
> that it had.
> Now say I give it a bit per second bandwidth input. If it has used the
> correct IP address in the previous second it gets a 1, otherwise a 0.
> Now it might guess the correct IP address first time (and only guess
> one IP address) and get a 1, and therefore get 4 bytes of information.
> But as we said the AI is deterministic and the IP address is fixed, so
> we might be forgiven in thinking that the game is rigged and the
> system already had that information. If we randomise the IP and set it
> off again, on average, no matter the computing power the system had,
> it would get only 7.45x10^-9 bits per second of the IP address. This
> isn't the most efficient coding of our input to it. We could simply
> give it the IP address, one bit per second. The system would still be
> limited to bifurcating once per second.
You are going down a correct path, mathematically speaking; but the
answer is going to end up being "In principle, it takes a ridiculously
small amount of information; the exact amount is theoretically
incomputable; and a superintelligence would require more, but we can't
guess how much more without actually running a superintelligence."
A cable modem connected to the Internet is certainly *vastly* more
bandwidth than is theoretically needed to grok and take over the
world, though. Or a 1200 baud modem, for that matter. Hell, give me
a millionfold subjective speedup and a few siderial days to think
about it and *I'll* take over the world with a 1200 baud modem (not
because I want it; just to demonstrate the point).
Remember that there are more reliable ways of making money than trying
to win the lottery - a wise agent can steer their pressure to the more
manipulable, more predictable, lower-entropy levers in the system.
When bifurcation is a limited resource, you can arrange to use less of
it - you don't *have* to let 50% of your selves emit alternate
versions of every bit you want to output.
-- Eliezer S. Yudkowsky http://intelligence.org/ Research Fellow, Singularity Institute for Artificial Intelligence
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