andrewp123

I don’t know how any experiment like this could be taken seriously. Your action could change 15 minutes apart if you feel like having sugar, if the guy felt intimidating or not, if the last thing he said seemed friendly or if his facial expression was off at the very end, etc.

There must be a better way of judging the validity of a social experiment using first principles. There’s a huge psychological side that people completely ignore.

Algorithms are graphs, data structures are graphs, networks are graphs, relationships are graphs.

Let’s use text to describe everything!

I’m not sure how interesting this is - of course rotation causes the paths to differ and become measurable.

I’ve been wondering about sending photons away from earth and having their paths bend due to gravity (and later have them interfere). That would be interesting because GR would be involved.

I was thinking of creating something like this but centered around posting one’s intuitions on research, instead of the papers themselves (which are hard to read, even the list of titles are hard to parse). But researchers are afraid to say anything stupid and would prefer saying nothing at all.

It’s a hard problem but could be a good platform for research discussions considering none exists today. Best of luck.

I just wanted to comment on how good the homepage is - it's immediately clear what you do. Most people working with "combinators" would feel a need to use lots of scary lingo, but OP actually shows the simple idea behind the tool (this is the opposite take of most academics, who instead show every last detail and never tell you what's going on). I really appreciate it - we need more of this.

The word dynamic was popular in naming around that time - dynamic programming is another example (1950s).

Somehow just by internalizing the old meaning of the world “dynamic”, I feel I have a better idea of what the world felt like back then.

A powerful method in math is to assume the thing you're looking for is continuous, in which case you can write it F(n) = a0 + a1 n + a2 n^2 + ... .

You can solve Fibonacci by writing it as

a0 + a1 n + a2 n^2 + ...

= a0 + a1 (n-1) + a2 (n-1)^2 + ...

+ a0 + a1 (n-2) + a2 (n-2)^2 + ...

Expand terms, then match the n, n^2, n^3 etc terms and solve for a0, a1, a2, etc. This works in solving differential equations too - it's called "Method of Frobenius" (easier in diffeq because you don't have to do annoying binomial coefficient math).

I can't imagine you believe P=NP.

Always a bad idea to destroy musical instruments.

Yep, they're essentially giant brute force machines. You can find the period of a function by passing all the inputs through it at once and destructively interfering the result.

Why is there a speedup in quantum, though? Why can't you just brute force classically? The answer is that whether quantum or classical, you can always build a hard-coded circuit that essentially swaps the time and space complexity - just make it so that for every operation you were doing in time, instead, every operation happens at its own place in space.

Quantum is special because it also takes the "log" of the space complexity b/c n qubits represent 2^n bits. So quantum lets you swap space with time and then take the log of time, lol. Superposition, interference, etc aren't really even needed in the explanation.

Correct - superposition doesn't fork the world - measurement does. And correct, you can't communicate with the other universe after the split has happened [1]. I'm glad you mentioned that quantum computers can't solve NP-complete problems - my next blog post was going to be about why. Here's an overview of what I plan on saying:

A typical quantum algorithm like Shor's works by sending every possible input through a gate, and so you get every possible output out in a superposition. If you were to just measure that, you'd get a random result - so instead, you need to somehow interfere the output to get the actual result. You do this by taking advantage of the fact that the superposition is a periodic function and the amplitude repeats. This is literally the core assumption of the algorithm.(a common way of doing this using the QFT).

Every quantum algorithm requires some kind of structure in the output like this. Deustch's algo, dumb ones like Simon's algo, etc. NP-Complete problems have no structure to them, so even if you build a gate that creates the superposition you want, it's not possible to destructively interfere it to get an answer (I don't know how to prove that there's no structure to NP-Complete outputs - it just feels trivial, since they're only solvable in exponential time, so there must be an exponential amount of "structure" there).

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[1] The only way to communicate with the other universe would be to try to use quantum mechanics with something like an entangled pair. But no information can be communicated through an entangled pair if all you just have 1 of the 2 particles! Measurement collapses a state nonlocally, and if you could somehow measure one particle and change the probability distribution of the other, you'd be communicating faster than light. The measurement genuinely changes the state and the amplitudes, but not in a way that the other person can detect. It's really interesting and leads to stuff like teleportation.

If you roll a regular coin without any quantum effects, every version of you will either see only heads, or only tails. You need quantum in order to make the choice nondeterministic.