nyan_sandwich comments on A case study in fooling oneself - Less Wrong
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the ink blot analogy is not quite so good for counting worlds because it implies more ambiguity than there is.
In reality the most ambiguous amplitude-blot is the inside of a quantum computer. The difference between considering that as all one world or many not-quite-decohered worlds is at most a constant factor on the exponentially growing total number. Most different worlds are very much distinct. The amplitude blots are quite small (atom scale) and infinite-dimensional configuration space is huge. All it takes is one photon to have gone a different way and the blobs are lightyears apart.
Assuming all branches are intact and active (as implied by conservation of amplitude), the number of worlds is approximately
k*2^(r*t)wherekis your strictness of what counts as a world,ris how many decoherence events happen per time, andtis time. I chose a base of 2 because all decoherence complexes can be approximately reduced to single splits.rcan be adjusted if some other base is more natural.