On Wed, Jan 28, 1998 at 03:27:41PM -0800, Hal Finney wrote: > I think you're right that the amount of data would be very large. > You'd have to count the information content of each wave function collapse > since the creation of the universe.
I now think that I was probably wrong about this, but I still don't understand why. Suppose our administrator takes the universal wave function (which assuming the Everett Postulate never collapses during normal evolution), collapses it into a position eigenfunction according to the familiar probabilistic rules, and then examines the resulting position eigenfunction, treating it a sort of snapshot. Now if he just picks a random volume of space to look at, chances are he would see some unstructured interstellar gas. But with probability of about 2^-L, where L is the length of a complete uncompressed description of my brain (WDB), the volume of gas he sees would by coincidence turn out to have the same positional structure as WDB. If I'm to believe that I'm much more likely to be currently instantiated as a brain made of organic chemicals rather than of interstellar gas, it must be that the probability of finding the organic brain is much higher than 2^-L, which implies that it takes much less than L bits of information to find a description of WDB in the universal wave function. However I do not know how to derive this from the principles of quantum mechanics.