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There are more real numbers than programs. Computers cannot represent the vast majority of real numbers. AFAICT, it's not even clear that the universe is cont

There are more real numbers than programs. Computers cannot represent the vast majority of real numbers. AFAICT, it's not even clear that the universe is continuous rather than discrete. I really don't believe that using approximations of real numbers is going to be the bottleneck for AGI.

YinLuck- 5y ago
I thought the whole point of quantum mechanics was to prove the universe was discrete and thus not continuous, no?
xamuel 5y ago
And yet computers have no problem symbolically representing non-rational numbers like sqrt(2), pi, etc. Neither is there any inherent reason why they cannot symbolically represent various levels of infinity, nor why those would be incomprehensible to AGIs (even if the universe is discrete). You're right that only countably many numbers can be represented, but nevertheless even countable subsets of extended number systems can exhibit structural properties that the reals do not exhibit.
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webmaven 5y ago
> AFAICT, it's not even clear that the universe is continuous rather than discrete. I'm not sure that makes any difference (in either direction). I mean, at the scale we care most about, the universe appears to be continuous, so an AGI has to be able to tackle continuous-appearing problems and use continuous-appearing representations. OTOH, the universe is likely to actually be discrete, so an AGI has to be able to tackle actually-discrete problems, and use representations that are actually-discrete on a fundamental level. There isn't much of a contradiction between these constraints, although the prospect of a continuous-appearing universe that is actually running on a discrete substrate seems to give a lot of people a brain cramp, and that same brain cramp gets elevated into 'proof' that current approaches cannot lead to AGI. Which is nonsense (there may be other limitations inherent in current approaches, but that can't be one of them). One might as well claim that computers are digital and brains are analog and conclude that digital image representations cannot possibly be used to communicate information to analog brains.

YinLuck- 5y ago

I thought the whole point of quantum mechanics was to prove the universe was discrete and thus not continuous, no?

xamuel 5y ago

And yet computers have no problem symbolically representing non-rational numbers like sqrt(2), pi, etc. Neither is there any inherent reason why they cannot symbolically represent various levels of infinity, nor why those would be incomprehensible to AGIs (even if the universe is discrete). You're right that only countably many numbers can be represented, but nevertheless even countable subsets of extended number systems can exhibit structural properties that the reals do not exhibit.

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webmaven 5y ago

> AFAICT, it's not even clear that the universe is continuous rather than discrete. I'm not sure that makes any difference (in either direction). I mean, at the scale we care most about, the universe appears to be continuous, so an AGI has to be able to tackle continuous-appearing problems and use continuous-appearing representations. OTOH, the universe is likely to actually be discrete, so an AGI has to be able to tackle actually-discrete problems, and use representations that are actually-discrete on a fundamental level. There isn't much of a contradiction between these constraints, although the prospect of a continuous-appearing universe that is actually running on a discrete substrate seems to give a lot of people a brain cramp, and that same brain cramp gets elevated into 'proof' that current approaches cannot lead to AGI. Which is nonsense (there may be other limitations inherent in current approaches, but that can't be one of them). One might as well claim that computers are digital and brains are analog and conclude that digital image representations cannot possibly be used to communicate information to analog brains.