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The difference between infinite and "essentially infinite" is that one is infinite and one finite. That is a large number, but it's not infinitely large.

by almost 16y ago

ars 16y ago
You are speaking about math, I am speaking about complexity theory.
- jerf 16y ago
  The number of states the observable universe can have is quite possibly "finite" given some reasonable assumptions about QM and either a temporal end-point (big rip, crunch) or a spatial one ("after 50 billion light years I can no longer observe anything of interest"). With those assumptions, there's a finite limit on the space-time extent you can be observing, and within that volume a finite number of permutations of waves, even if we discard the need for them to have a plausible history just to bump the count up. As large as that number may be, following up on a discussion from yesterday, I would bet BB(10) is quite a bit larger. (Failing that BB(20) certainly is, because I suspect the TM to directly simulate the situation I just named could fit within 20 states. Mere permutation isn't actually that Turing-complex.) The human lookup table is a much smaller finite subset of that, for any definition of human you could name. Enormous, but also "enormously" smaller than the other things I've described.
- almost 16y ago
  As far as I'm aware complexity theory doesn't have it's own special definition of "infinite". Just to be clear, I'm totally in agreement with you that a lookup table based AI would not actually be possible in the real world, but I don't think any sane person would claim that.
  - ars 16y ago
    I didn't say infinite! I said "essentially infinite". I would have used the exact term from complexity theory, except I don't know what it is for n! - the highest they have is EXPSPACE which is 2^n (which is smaller - much smaller).
    - xenophanes 16y ago
      "Essentially infinite" is not a very good way to say "intractable" or "infeasible".
    - hugh3 16y ago
      I thought you said "pretty much infinite". Either way, neither "essentially infinite" nor "pretty much infinite" is a meaningful concept (I can just picture infinity, off at the nonexistent end of the number line, laughing at the puny numbers you describe as "essentially infinite"), so it'd be better to just rephrase it as "really really big", with as many "really"s as you feel is appropriate.
- vecter 16y ago
  What's the distinction?

The difference between infinite and "essentially infinite" is that one is infinite and one finite. That is a large number, but it's not infinitely large.

by almost 16y ago

The difference between infinite and "essentially infinite" is that one is infinite and one finite. That is a large number, but it's not infinitely large.

ars 16y ago

You are speaking about math, I am speaking about complexity theory.

jerf 16y ago
The number of states the observable universe can have is quite possibly "finite" given some reasonable assumptions about QM and either a temporal end-point (big rip, crunch) or a spatial one ("after 50 billion light years I can no longer observe anything of interest"). With those assumptions, there's a finite limit on the space-time extent you can be observing, and within that volume a finite number of permutations of waves, even if we discard the need for them to have a plausible history just to bump the count up. As large as that number may be, following up on a discussion from yesterday, I would bet BB(10) is quite a bit larger. (Failing that BB(20) certainly is, because I suspect the TM to directly simulate the situation I just named could fit within 20 states. Mere permutation isn't actually that Turing-complex.) The human lookup table is a much smaller finite subset of that, for any definition of human you could name. Enormous, but also "enormously" smaller than the other things I've described.
almost 16y ago
As far as I'm aware complexity theory doesn't have it's own special definition of "infinite". Just to be clear, I'm totally in agreement with you that a lookup table based AI would not actually be possible in the real world, but I don't think any sane person would claim that.
- ars 16y ago
  I didn't say infinite! I said "essentially infinite". I would have used the exact term from complexity theory, except I don't know what it is for n! - the highest they have is EXPSPACE which is 2^n (which is smaller - much smaller).
  - xenophanes 16y ago
    "Essentially infinite" is not a very good way to say "intractable" or "infeasible".
  - hugh3 16y ago
    I thought you said "pretty much infinite". Either way, neither "essentially infinite" nor "pretty much infinite" is a meaningful concept (I can just picture infinity, off at the nonexistent end of the number line, laughing at the puny numbers you describe as "essentially infinite"), so it'd be better to just rephrase it as "really really big", with as many "really"s as you feel is appropriate.
vecter 16y ago
What's the distinction?