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LessWrong is sci-fi. Check what's popular. Superintelligent AI, space travel, suspended animation, hyper-advanced nanotech...

It is true that people have written unrealistic books about these things. People also wrote unrealistic books about magicians flying through the air and scrying on each other with crystal balls. Yet we have planes and webcams.

Who is to say there even are concepts that the human mind simply can't grasp? I can't visualize in n-dimensional space, but I can certainly understand the concept

The human mind is finite, and there are infinitely many possible concepts. If you're interested in the limits of human intelligence and the possibilities of artificial intelligence, you might want to read The Hanson-Yudkowsky Debate .

Grey goo? Sounds plausible, but then again, there is zero evidence that physics can create anything like stable nanites. How fragile will the molecular bonds be?

Drexler wrote a PhD thesis which probably answers this. For discussion on LessWrong, see Is Molecular Nanotechnology "Scientific"? and How probable is Molecular Nanotech?.

Counterexample: P(3^^^...3)(n "^"s) = 1/2^n P(anything else) = 0 This is normalized because the sum of a geometric series with decreasing terms is finite. You might have been thinking of the fact that if a probability distribution on the integers is monotone decreasing (i.e. if P(n)>P(m) then n <m) then P(n) must decrease faster than 1/n. However, a complexity-based distribution will not be monotone because some big numbers are simple while most of them are complex.

Those are the probabilities that both halves of a pair of photons are transmitted, so you can't determine them without the information from both detectors. The distribution at each individual detector doesn't change, it's the correlation between them that changes.

A' doesn't become A'' by catching up to him, he becomes A'' when he uses his time machine to jump back 3 hours.

There would be three babies for 6 hours, but then the youngest two would use their time machines and disappear into the past.

A'' doesn't cease to exist. A' "ceases to exist" because his time machine sends him back into the past to become A''.

You don't need a time machine to go forward in time - you can just wait. A'' cant leave everything to A' because A' will disappear within three hours when he goes back to become A''. If A' knows A wasn't reminded the A' can't remind A. the other three Harrys use their time turners to go backwards and close the loop. You do need both forward and backward time travel to create a closed loop, but the forward time travel can just be waiting; it doesn't require a machine.

The nice part about modal agents is that there are simple tools for finding the fixed points without having to search through proofs; in fact, Mihaly and Marcello wrote up a computer program to deduce the outcome of the source-code-swap Prisoner's Dilemma between any two (reasonably simple) modal agents. These tools also made it much easier to prove general theorems about such agents.

Would it be possible to make this program publicly available? I'm curious about how certain modal agents play against each other, but struggling to caculate it manually.

If you can prove a contradiction, defect.

Should this be "If you can prove that you will cooperate, defect"? As it is, I don't see how this prevents cooperation with Cooperatebot, unless the agent uses an inconsistent system for proofs.

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