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I think you're confusing "finite" and "small enough that I can imagine something that size". A billion operations per billionth of a second for a billion years

I think you're confusing "finite" and "small enough that I can imagine something that size". A billion operations per billionth of a second for a billion years is still finite, it's just big.

ars 16y ago
I am not confusing them. My argument is that each time you add a question to the table, you need to encode an answer that depends on all the other questions asked. Meaning the number of answers is exponential (actually factorial) to the number of questions in it. Such a table is essentially infinite. i.e. if you have 10 questions you have 3 million possible answers. But with a million questions you have 8 x 10^5565708 answers. I hope you realize how big this number is.
- 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?
- AndrewDucker 16y ago
  It's very big. That doesn't make it anywhere near infinite.

I think you're confusing "finite" and "small enough that I can imagine something that size". A billion operations per billionth of a second for a billion years is still finite, it's just big.

ars 16y ago

I am not confusing them. My argument is that each time you add a question to the table, you need to encode an answer that depends on all the other questions asked. Meaning the number of answers is exponential (actually factorial) to the number of questions in it. Such a table is essentially infinite. i.e. if you have 10 questions you have 3 million possible answers. But with a million questions you have 8 x 10^5565708 answers. I hope you realize how big this number is.

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?
AndrewDucker 16y ago
It's very big. That doesn't make it anywhere near infinite.