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.
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?