BB(6) might be too large even to store (let alone compute) using all the mass and energy of the universe. I think the computable limit if you converted all the mass in the observable universe to energy (E = mc^2) would be BB(5), assuming adherence to the Laundauer Limit[0].
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.
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