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I don't think the birthday paradox applies here. The birthday paradox requires a discrete set of pigeon holes, days of year, etc. If that set is infinite, then
by ryan_j_naughton 9y ago
I don't think the birthday paradox applies here. The birthday paradox requires a discrete set of pigeon holes, days of year, etc. If that set is infinite, then the countability [1] problem collapses.
While technically the world is discrete in space and time (planck length), for all intents and purposes it is infinite in practice.
[1] yes, there is countably infinite, but that doesn't work with the pigeon hole problem.
- setzer22 9y agoReality may or may not be discrete, but what is a discrete value is the output from a digital camera, so in case of photographs your argument does not hold. In other words, two photographs off by a planck length will generate the same set of pixels.
- maxerickson 9y agoIsn't the birthday paradox just the dissonance between typical intuition and mathematical reality? How does that not apply to this situation? The number of comparisons between photos is much much larger than the number of photos. It might not apply in a way that is interesting mathematically, but I don't think that is what the other poster was getting at.