grondilu

Joined 15 years ago

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Comment · 2 years ago
It doesn't seem so at all from what I've tried.
Comment · 2 years ago
> so even theoretically this is hard to imagine.

Possibly a strech, but transistors are basically current amplifiers, so their optical equivalent should be... lasers. Indeed lasers are optical amplifiers. Whether or not they can be turned into logic gates as transistors can, I don't know.

Comment · 2 years ago
> Mechanical computers are computers that operate using mechanical components rather than electronic ones.

For anyone who's excited about mechanical computers, perhaps it is worth reminding that an electron is about a thousand times lighter than a nucleon. Therefore, it's probably fair to say that mechanical computers will always be more energy consuming than electronic ones, because they fundamentally need to move atoms around to operate.

Comment · 2 years ago
They took 20 bitcoins out of me, but I never bothered to fill the paperwork. Oh, well.
Comment · 2 years ago
I'm quite baffled by the fact that LLMs can generate a dataset used to train other LLMs. One would think that such a feedback loop would produce utter nonsense but apparently not. This seems to work.
Comment · 2 years ago
> But the first problem is, the number of legal transformations is actually infinite.

I am fairly certain the number of legal transformations in mathematics is not infinite. There is a finite number of axioms, and all proven statements are derived from axioms through a finite number of steps.

Comment · 2 years ago
Comment · 2 years ago
"I think in the future, instead of typing up our proofs, we would explain them to some GPT. And the GPT will try to formalize it in Lean as you go along. If everything checks out, the GPT will [essentially] say, “Here’s your paper in LaTeX; here’s your Lean proof. If you like, I can press this button and submit it to a journal for you.” It could be a wonderful assistant in the future."

That'd be nice, but eventually what will happen is that the human will submit a mathematical conjecture, the computer will internally translate into something like Lean, and try to find either a proof or a disproof. It will then translate it in natural language and tell it to the user.

Unless mathematics is fundamentally more complicated than chess or go, I don't see why that could not happen.

Comment · 2 years ago
Comment · 2 years ago

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