a pile of mud is incredibly complex—it would require an absurd amount of information to create an exactly equal pile of mud
Using this definition, everything containing the same number of atoms would be equally complex; you have to specify where each atom is. This does not feel correct. The authors modified the word complexity to something meaningless; and it most likely did not happen accidentally.
Using this definition, everything containing the same number of atoms would be equally complex; you have to specify where each atom is.
Not really. You can describe a diamond of pure carbon-12 at 0 K with much less information than that. (But IAWYC—there should be some measure of ‘complexity I care about’ by which music would rank higher than both silence (zero information-theoretical complexity) and white noise (maximum complexity).)
But IAWYC—there should be some measure of ‘complexity I care about’ by which music would rank higher than both silence (zero information-theoretical complexity) and white noise (maximum complexity).
How about the measures ‘sophistication’ or ‘logical depth’? Alternately, you could take a Schmidhuber tack and define interestingness as the derivative of compression rate.
Using this definition, everything containing the same number of atoms would be equally complex; you have to specify where each atom is. This does not feel correct. The authors modified the word complexity to something meaningless; and it most likely did not happen accidentally.
Fixing this problem is harder than complaining about it. A formal definition that captures intuitive notions of complexity seems to be lacking.
WRT VB’s original comment: surely this can’t be true. If two objects A and B contain the same number of atoms, and A’s atoms are in a loose irregular arrangement with many degrees of freedom, and B’s are in a tight regular arrangement with few degrees of freedom, specifying the position of one atom in B tells me much more about the positions of all the other atoms than specifying the position of one atom in A does. It seems to follow that specifying the positions of all the atoms in B, once I’ve specified the regularity, requires a much shorter string than for A.
But that said, I’ve always been puzzled by the tendency of discussions of the information-theoretical content of the physical world, especially when it comes to discussions of simulations of that world, to presume that we’re measuring all dimensions of variability.
Specifying a glob of mud in such a way as to reproduce that specific glob of mud, and not some other glob of mud, requires a lot of information. Specifying a glob of mud in such a way as to reproduce what we value about a glob of mud requires a lot less information (and, not incidentally, loses most of the individual character of that glob, which we don’t much value).
The discussion in this thread about the complexity of a glob of mud seems in part to be eliding over this distinction… what we value about a glob of mud is much simpler than the entirety of that glob of mud.
Using this definition, everything containing the same number of atoms would be equally complex; you have to specify where each atom is. This does not feel correct. The authors modified the word complexity to something meaningless; and it most likely did not happen accidentally.
Not really. You can describe a diamond of pure carbon-12 at 0 K with much less information than that. (But IAWYC—there should be some measure of ‘complexity I care about’ by which music would rank higher than both silence (zero information-theoretical complexity) and white noise (maximum complexity).)
How about the measures ‘sophistication’ or ‘logical depth’? Alternately, you could take a Schmidhuber tack and define interestingness as the derivative of compression rate.
My reply to cj applies to this as well.
Fixing this problem is harder than complaining about it. A formal definition that captures intuitive notions of complexity seems to be lacking.
WRT VB’s original comment: surely this can’t be true. If two objects A and B contain the same number of atoms, and A’s atoms are in a loose irregular arrangement with many degrees of freedom, and B’s are in a tight regular arrangement with few degrees of freedom, specifying the position of one atom in B tells me much more about the positions of all the other atoms than specifying the position of one atom in A does. It seems to follow that specifying the positions of all the atoms in B, once I’ve specified the regularity, requires a much shorter string than for A.
But that said, I’ve always been puzzled by the tendency of discussions of the information-theoretical content of the physical world, especially when it comes to discussions of simulations of that world, to presume that we’re measuring all dimensions of variability.
Specifying a glob of mud in such a way as to reproduce that specific glob of mud, and not some other glob of mud, requires a lot of information. Specifying a glob of mud in such a way as to reproduce what we value about a glob of mud requires a lot less information (and, not incidentally, loses most of the individual character of that glob, which we don’t much value).
The discussion in this thread about the complexity of a glob of mud seems in part to be eliding over this distinction… what we value about a glob of mud is much simpler than the entirety of that glob of mud.
Maybe Kolmogorov complexity will help?