“Just as, once upon a time, it was easier to imagine Thor throwing lightning bolts, than to imagine Maxwell’s Equations—even though Maxwell’s Equations can be described by a computer program vastly smaller than the program for an intelligent agent like Thor.”
Hmmm… perhaps we could define a “relative Kolmogorov complexity”, K[X], where the K[X] of Y is the size of the smallest .diff file that alters program X to make it output Y and then halt. K(Maxwell) < K(Thor), but it seems quite likely that KHuman > KHuman.
There is a relative notion of Kolmogorov complexity. Roughly K(X| Y) is the size of the smallest program that outputs X given Y as input. I agree that K(Thor | Human) << K(Thor), but I believe that this is still much larger than K(Maxwell|Human). This is because K(Maxwell|Human) ⇐ K(Maxwell), which is really small. On the other hand to specify Thor given a description of a human, you get huge savings on describing how a humanoid works, but still have the task of describing what lightning actually is (as well as the task of describing how Thor’s thoughts translate into lightning).
“Just as, once upon a time, it was easier to imagine Thor throwing lightning bolts, than to imagine Maxwell’s Equations—even though Maxwell’s Equations can be described by a computer program vastly smaller than the program for an intelligent agent like Thor.”
Hmmm… perhaps we could define a “relative Kolmogorov complexity”, K[X], where the K[X] of Y is the size of the smallest .diff file that alters program X to make it output Y and then halt. K(Maxwell) < K(Thor), but it seems quite likely that KHuman > KHuman.
To reply years after the original post...
There is a relative notion of Kolmogorov complexity. Roughly K(X| Y) is the size of the smallest program that outputs X given Y as input. I agree that K(Thor | Human) << K(Thor), but I believe that this is still much larger than K(Maxwell|Human). This is because K(Maxwell|Human) ⇐ K(Maxwell), which is really small. On the other hand to specify Thor given a description of a human, you get huge savings on describing how a humanoid works, but still have the task of describing what lightning actually is (as well as the task of describing how Thor’s thoughts translate into lightning).