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Can someone explain the first bit of the last sentence? > if our world is a simulation, then whoever is simulating it seems to have a clear preference for the
by Myrmornis 10y ago
Can someone explain the first bit of the last sentence?
> if our world is a simulation, then whoever is simulating it seems to have a clear preference for the 2-norm over the 1-norm
Is it basically saying that space looks Euclidean at a range of scales and Pythagoras crops up everywhere or is it saying something else / more sophisticated? What would the Universe look like if its creator favored a 1-norm?
- gjm11 10y agoI think he's referring less to the geometry of space(-time) and more to the structure of quantum mechanics. Classical probabilities are positive real numbers that add up to 1. (The 1-norm of the vector of probabilities is 1.) Quantum ampltiudes are complex numbers whose squared absolute values add up to 1. (The 2-norm of the vector of amplitudes is 1.) A universe made by someone who preferred 1-norms would more likely be classical rather than quantum. For more on this from the author of the linked blogpost, see here: http://www.scottaaronson.com/democritus/lec9.html http://www.scottaaronson.com/democritus/lec9.html or the corresponding bit in his excellent book "Quantum computing since Democritus".
- Myrmornis 10y agoThanks! That was a really helpful reply. Started reading the Aaronson intro to QM you linked and it does seem like a very direct and understandable approach to the subject.