3 ms·

Complexity and Intelligence by Eliezer Yudkowsky

9 points by MikeCapone 18y ago

ars 18y ago
Talk about a straw man argument! He builds up an entire argument, then shoots it down, and manages to generate pages of text, all based on a flawed premise. I don't agree that you can ignore the size of the working set when defining complexity. Quite frankly it's idiotic to do so. If you allow that, then why not just create every single possible permutation of every single possible thing? (Not randomly, start at 1 and start counting.) The complexity of that is 1 bit. So, basically everything, no matter what, has a complexity of 1 bit. What a pointless way of defining complexity. (Pointless for talking about the universe anyway, maybe it's useful in more specific math.)
- elijahbuck 18y ago
  Everything does not have a complexity of one bit. The object you describe with a complexity of 1 bit doesn't specify the object you want. In the permutation, there may be a string that specifies some universe, but then you have to specify where in the permutation that string is and how long it is, thus increasing the complexity required to describe that particular universe object.
DaniFong 18y ago
Wouldn't the 'Kolmogorov complexity of the universe' include initial conditions? How can we know that these aren't significant?
- jerf 18y ago
  The way he defined for most of that essay, it is more proper to speak of the "Kolmogorov complexity of the multiverse". The infinite possible starting conditions of your brand of physics merely adds the K-complexity of the TM necessary to describe the possible initial states, likely quite small. (Eliezer believes that many-worlds is the only possibility for the universe we live in, I believe.) The K-complexity of this specific universe is much higher, because it would necessarily require a description of the multiverse and some sort of identifier of how to pick out the universe of interest.
  - dhs 18y ago
    I don't understand this. If the multiverse is a system of a certain (appearantly low) complexity, it should not be allowed to have sub-systems like the "universe of interest" which have a higher complexity. Also, I don't see why the information which identifies a certain subsystem/universe should only be available from the point of view of that subsystem, increasing its complexity, but not the complexity of the system it's a part of.
    - jerf 18y ago
      It's the nature of K-complexity. If you don't understand, I'd suggest (in all humility and seriousness) pondering the nature of TMs and K-complexity further. Some time spent surfing through the Mandelbrot set can be enlightening, as a more concrete example. Remember, no matter what you see in Fractint (or your choice of fractal generator), the K-complexity of the Mandelbrot set is very, very low. (Not quite as small as the Mandelbrot-generation process alone because you also need to describe the coloring algorithm, but that's not that much either.) But, to uniquely identify the image you are looking at to someone else, you must transmit not just the Mandelbrot generation routines, but also the coordinates you are looking at, or a description of the routine you used to get there. This can easily be larger than the rather small Mandelbrot algorithm. (It's easy to lose track of how deep you are in the M-set, without realizing that your computer is chugging away on computations involving thousands of significant digits...) This is exponentially (super-exponentially?) more true to pick out a particular piece of a particular universe from a TM simulating all possible string theory universes. String theory may be simple (or may not be), by the time you're done identifying which of the 10^120 vacuum states you want to deal with (~400 bits right there), which initial conditions you want to deal with (no idea what that would take), and where in space and time you wish to point at (many thousands of bits minimum, no known upper limit), you can easily exceed the size of the part of the TM that describes the physics itself. It might be helpful to try to forget everything you know about "complexity"; the English meaning of the word misleads your mathematical intuition. K-complexity is really something completely different (as is part of Elizier's point), and, frankly, it's much less useful than it seems at first blush. It's part of the wild world of Turing Machines, which can not be tamed or understood by any finite being. (And it doesn't really help that you can't prove if you have the optimal TM for a given result.) It may also help to intuitively consider the difficulty of "pointing" at something, as in the essay. It is easy to gesticulate wildly at the Earth, from where you sit now. It is far, far harder to unambiguously specify which protozoan you are talking about right now. The part of the description that filters through the near-infinite possibilities to uniquely identify the topic of interest can be very, very large, and can easily exceed the size of the specification of "all possible topics of interest".
queensnake 18y ago
I hope that guy goes somewhere with all his talk, eventually.

9 points by MikeCapone 18y ago

ars 18y ago

Talk about a straw man argument! He builds up an entire argument, then shoots it down, and manages to generate pages of text, all based on a flawed premise. I don't agree that you can ignore the size of the working set when defining complexity. Quite frankly it's idiotic to do so. If you allow that, then why not just create every single possible permutation of every single possible thing? (Not randomly, start at 1 and start counting.) The complexity of that is 1 bit. So, basically everything, no matter what, has a complexity of 1 bit. What a pointless way of defining complexity. (Pointless for talking about the universe anyway, maybe it's useful in more specific math.)

elijahbuck 18y ago
Everything does not have a complexity of one bit. The object you describe with a complexity of 1 bit doesn't specify the object you want. In the permutation, there may be a string that specifies some universe, but then you have to specify where in the permutation that string is and how long it is, thus increasing the complexity required to describe that particular universe object.

DaniFong 18y ago

Wouldn't the 'Kolmogorov complexity of the universe' include initial conditions? How can we know that these aren't significant?

jerf 18y ago
The way he defined for most of that essay, it is more proper to speak of the "Kolmogorov complexity of the multiverse". The infinite possible starting conditions of your brand of physics merely adds the K-complexity of the TM necessary to describe the possible initial states, likely quite small. (Eliezer believes that many-worlds is the only possibility for the universe we live in, I believe.) The K-complexity of this specific universe is much higher, because it would necessarily require a description of the multiverse and some sort of identifier of how to pick out the universe of interest.
- dhs 18y ago
  I don't understand this. If the multiverse is a system of a certain (appearantly low) complexity, it should not be allowed to have sub-systems like the "universe of interest" which have a higher complexity. Also, I don't see why the information which identifies a certain subsystem/universe should only be available from the point of view of that subsystem, increasing its complexity, but not the complexity of the system it's a part of.
  - jerf 18y ago
    It's the nature of K-complexity. If you don't understand, I'd suggest (in all humility and seriousness) pondering the nature of TMs and K-complexity further. Some time spent surfing through the Mandelbrot set can be enlightening, as a more concrete example. Remember, no matter what you see in Fractint (or your choice of fractal generator), the K-complexity of the Mandelbrot set is very, very low. (Not quite as small as the Mandelbrot-generation process alone because you also need to describe the coloring algorithm, but that's not that much either.) But, to uniquely identify the image you are looking at to someone else, you must transmit not just the Mandelbrot generation routines, but also the coordinates you are looking at, or a description of the routine you used to get there. This can easily be larger than the rather small Mandelbrot algorithm. (It's easy to lose track of how deep you are in the M-set, without realizing that your computer is chugging away on computations involving thousands of significant digits...) This is exponentially (super-exponentially?) more true to pick out a particular piece of a particular universe from a TM simulating all possible string theory universes. String theory may be simple (or may not be), by the time you're done identifying which of the 10^120 vacuum states you want to deal with (~400 bits right there), which initial conditions you want to deal with (no idea what that would take), and where in space and time you wish to point at (many thousands of bits minimum, no known upper limit), you can easily exceed the size of the part of the TM that describes the physics itself. It might be helpful to try to forget everything you know about "complexity"; the English meaning of the word misleads your mathematical intuition. K-complexity is really something completely different (as is part of Elizier's point), and, frankly, it's much less useful than it seems at first blush. It's part of the wild world of Turing Machines, which can not be tamed or understood by any finite being. (And it doesn't really help that you can't prove if you have the optimal TM for a given result.) It may also help to intuitively consider the difficulty of "pointing" at something, as in the essay. It is easy to gesticulate wildly at the Earth, from where you sit now. It is far, far harder to unambiguously specify which protozoan you are talking about right now. The part of the description that filters through the near-infinite possibilities to uniquely identify the topic of interest can be very, very large, and can easily exceed the size of the specification of "all possible topics of interest".

queensnake 18y ago

I hope that guy goes somewhere with all his talk, eventually.