Your results don’t seem to show upper bounds on the amount of hardware overhang, or very strong lower bounds. What concrete progress has been made in chess playing algorithms since deep blue? As far as I can tell, it is a collection of reasonably small, chess specific tricks. Better opening libraries, low level performance tricks, tricks for fine tuning evaluation functions. Ways of representing chessboards in memory that shave 5 processor cycles off computing a knights move ect.
P=PSPACE is still an open conjecture. Chess is brute forcible in PSPACE. If P=PSPACE, and the overhead is a small constant, then it might be possible to program a vacuum tube machine to play perfect chess. Alternately, showing that stockfish is orders of magnitude better than deep blue, doesn’t actually show that there is a hardware overhead for chess. It shows that there was one when deep blue was created.
Also note that there never was a hardware overhang for integer binary addition. The problem is simple enough that the first answer that any reasonably smart person can come up with is nearly optimal. (It is fairly straightforward to do addition with only a few logic gates per input, and as the output depends bitwise on all inputs (changing any single bit changes the output) then you need at least one logic gate per input. ) It is plausible that playing chess is a problem simple enough that we have figured out how to do it nearly optimally, whereas on other problems there is a hardware overhang.
If we assume that the expert human brain is about equally efficient at AI design, general programming, airoplane engineering and a variety of other STEM tasks. (A plausible assumption, given that these tasks seem similarly far from the environment of evolutionary adaptedness, ) Then it should take a similar amount of compute to display top human performance in these, as in chess. On the other hand, doing arithmetic used to be a skilled job, and the compute needed for superhuman chess (with current algorithms) is way higher than that needed for arithmetic.
Your results don’t seem to show upper bounds on the amount of hardware overhang, or very strong lower bounds. What concrete progress has been made in chess playing algorithms since deep blue? As far as I can tell, it is a collection of reasonably small, chess specific tricks. Better opening libraries, low level performance tricks, tricks for fine tuning evaluation functions. Ways of representing chessboards in memory that shave 5 processor cycles off computing a knights move ect.
P=PSPACE is still an open conjecture. Chess is brute forcible in PSPACE. If P=PSPACE, and the overhead is a small constant, then it might be possible to program a vacuum tube machine to play perfect chess. Alternately, showing that stockfish is orders of magnitude better than deep blue, doesn’t actually show that there is a hardware overhead for chess. It shows that there was one when deep blue was created.
Also note that there never was a hardware overhang for integer binary addition. The problem is simple enough that the first answer that any reasonably smart person can come up with is nearly optimal. (It is fairly straightforward to do addition with only a few logic gates per input, and as the output depends bitwise on all inputs (changing any single bit changes the output) then you need at least one logic gate per input. ) It is plausible that playing chess is a problem simple enough that we have figured out how to do it nearly optimally, whereas on other problems there is a hardware overhang.
If we assume that the expert human brain is about equally efficient at AI design, general programming, airoplane engineering and a variety of other STEM tasks. (A plausible assumption, given that these tasks seem similarly far from the environment of evolutionary adaptedness, ) Then it should take a similar amount of compute to display top human performance in these, as in chess. On the other hand, doing arithmetic used to be a skilled job, and the compute needed for superhuman chess (with current algorithms) is way higher than that needed for arithmetic.