I think lean can verify it implements its own rules, but not that its own rules are sound (you can't prove a contradiction). If you are just prepared to trust that the rules are sound, then you would be able to trust…
I think people on here tend to somewhat fixate on the determinism issue. Even with a deterministic LLM - stabilising the floating point arithmetic, and choosing from the distribution by a fixed method, or just save the…
Did any mathematics done by G H Hardy turn out to be quite useful in the end? Ironically of course the answer is yes.
Yes indeed, it's about the time sound takes to travel 4mm
Bill 8 months at $8.33 and 4 months at $8.34?
No they don't - eg https://en.wikipedia.org/wiki/A_History_of_Britain_(TV_serie...
The dichotomy is more 'human understood' vs 'not human understood', I think
That was exactly my thought - taking out the problems that PhDs and early stage researchers work on kills the pipeline of developing mathematicians
It's an article written by a guest contributor - not an editorial written as the voice of the newspaper
Is the word "nonautological" nonautological ?
This is only the "problem solving" side of mathematics. Completely missing the theory builders who have completely reshaped the world of mathematics (and far beyond). AI is a long way from matching original thinkers of…
The normal term for the logic that has two truth values, the law of non-contradiction, and the law of the excluded middle is 'Classical Logic' which dates back centuries before George Boole. Non-classical logics which…
Rather COBOL is a living fossil? And today's Fortran is the FORTRAN family with horizontal gene transfer from the Algol lineage of programming languages.
Err? Peano Arithmetic is provably consistent in ZFC, but it is not in itself (if PA is consistent). Therefore if PA is consistent it is not equivalent to ZFC (regardless of whether ZFC is consistent or not)
"Embarrassingly" considered harmful?
To the contrary (as summarised by Gemini): Gödel showed that arithmetic cannot prove everything about itself. Turing showed that computers cannot predict everything about themselves. Rice showed that we cannot…
I don't think of 9 as really being a signal to the process at all, more of an instruction to the OS kernel to terminate the process
If that theory holds - have to ensure that the models have not been trained on any code that is licensed incompatibly with the GPL, in which case the models could not be distributed at all
So specified .. that it can actually prove it can't be completely specified by any single specification
Right so strictly speaking C++ could do anything here when passed a null pointer, because even though assert terminates the program, the C++ compiler cannot see that, and there is then undefined behaviour in that case
Shouldn't that be the "dam spelling" then?
Film score composers are quite famous for borrowing from 12 tone serialism - quite a bit of discussion on it available by Googling or using your favourite chatbot
Money is a social construct, not some kind of physical quantity subject to conservation laws, and can be and is introduced into the economic system all the time. The real question is really would introducing more money…
A trit is log(3)/(8log(2))=0.19812031259014 of a byte
The verifier doesn't need to be deterministic, just to output a proof artifact that can be independently validated for correctness.
I think lean can verify it implements its own rules, but not that its own rules are sound (you can't prove a contradiction). If you are just prepared to trust that the rules are sound, then you would be able to trust…
I think people on here tend to somewhat fixate on the determinism issue. Even with a deterministic LLM - stabilising the floating point arithmetic, and choosing from the distribution by a fixed method, or just save the…
Did any mathematics done by G H Hardy turn out to be quite useful in the end? Ironically of course the answer is yes.
Yes indeed, it's about the time sound takes to travel 4mm
Bill 8 months at $8.33 and 4 months at $8.34?
No they don't - eg https://en.wikipedia.org/wiki/A_History_of_Britain_(TV_serie...
The dichotomy is more 'human understood' vs 'not human understood', I think
That was exactly my thought - taking out the problems that PhDs and early stage researchers work on kills the pipeline of developing mathematicians
It's an article written by a guest contributor - not an editorial written as the voice of the newspaper
Is the word "nonautological" nonautological ?
This is only the "problem solving" side of mathematics. Completely missing the theory builders who have completely reshaped the world of mathematics (and far beyond). AI is a long way from matching original thinkers of…
The normal term for the logic that has two truth values, the law of non-contradiction, and the law of the excluded middle is 'Classical Logic' which dates back centuries before George Boole. Non-classical logics which…
Rather COBOL is a living fossil? And today's Fortran is the FORTRAN family with horizontal gene transfer from the Algol lineage of programming languages.
Err? Peano Arithmetic is provably consistent in ZFC, but it is not in itself (if PA is consistent). Therefore if PA is consistent it is not equivalent to ZFC (regardless of whether ZFC is consistent or not)
"Embarrassingly" considered harmful?
To the contrary (as summarised by Gemini): Gödel showed that arithmetic cannot prove everything about itself. Turing showed that computers cannot predict everything about themselves. Rice showed that we cannot…
I don't think of 9 as really being a signal to the process at all, more of an instruction to the OS kernel to terminate the process
If that theory holds - have to ensure that the models have not been trained on any code that is licensed incompatibly with the GPL, in which case the models could not be distributed at all
So specified .. that it can actually prove it can't be completely specified by any single specification
Right so strictly speaking C++ could do anything here when passed a null pointer, because even though assert terminates the program, the C++ compiler cannot see that, and there is then undefined behaviour in that case
Shouldn't that be the "dam spelling" then?
Film score composers are quite famous for borrowing from 12 tone serialism - quite a bit of discussion on it available by Googling or using your favourite chatbot
Money is a social construct, not some kind of physical quantity subject to conservation laws, and can be and is introduced into the economic system all the time. The real question is really would introducing more money…
A trit is log(3)/(8log(2))=0.19812031259014 of a byte
The verifier doesn't need to be deterministic, just to output a proof artifact that can be independently validated for correctness.