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by concordDance
979 days ago
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> Though we don't have the computing power for this currently I don't think you get how big BB748 is. To use a metaphor: If you took stuffed the entire observable universe full of computronium that can do more calculations in a fragment the size of a human cell than our entire civilization, then shrank that universe down to the size of a grain of sand and filled our entire universe with that, THEN did this once for every possible distinguishable person (ie. If you can say after a lifetime of detailed observation that person A isn't identical to person B then they're distinguishable) you still aren't even close to BB748. In fact, I'd be surprised if you're over BB10 and you're definitely under BB20. |
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After calculating this I found a quote in wikipedia[1]: "There is not enough computational capacity in the known part of the universe to have performed even S(6) operations directly." That cited this paper[2], which is probably better than my model at utilizing the total available physics of the universe for calculation purposes. Anyways, the mass of the known universe is on the order of 10^56 grams[3]. Converting this all to energy using E=mc^2 yields on the order of 10^70 Joules (10^88 electron volts). Setting or clearing a single bit of information requires at minimum 0.018 eV. That allows about 10^90 bits.
BB(6) may require on the order of 10^90^2 bit flips. So it is absolutely not computable using all the mass and energy in the universe. In fact, I don't think it's even storable using all the mass and energy in the universe.
I don't really understand Busy Beaver, so if I got any of this wrong please correct me for the record.
0: https://en.wikipedia.org/wiki/Landauer%27s_principle
1: https://en.wikipedia.org/wiki/Busy_beaver
2: https://arxiv.org/pdf/quant-ph/0110141.pdf
3: https://www.wolframalpha.com/input?i=mass+of+the+universe