Comment by jerf | Hacker News Reader

Comment by jerf | Hacker News Reader

For a while I thought he was making a joke about how if you continue to abstract a given theory, you end up "encompassing" everything eventually, but not in a useful way. To put what I mean in programmer terms, if you take a Javascript framework, and just keep abstracting and abstracting and abstracting, to a pathological degree, you ultimately can end up with your "Javascript framework" consisting of:

    eval(x)

where the user supplies x. It is literally the most powerful Javascript framework ever!... and yet, obviously, also not useful. It trivially encompasses every possible Javascript program, at the price of not saying anything useful about any of them.

But then he threw me when he linked to what appears to be a real proof. I read through it, and found no signs it was tongue-in-cheek itself.

So I'll admit I'm at an impasse here; if he's got a real mathematical construct that is usefully better than what was presented, I don't get the tongue-in-cheek tone; if it really is tongue-in-cheek, I don't get what the real proofs are doing there, unless the proof is itself the best-disguised joke I've seen in the math world. (Generally I've got a pretty good eye for mathematician humor, even in fields I know little about.)

The way I read the joke is that amplituhedron seems to have done very well in giving overnight success to a breakthrough that has taken long painstaking work and has been a field long before it was media-branded, he is pointing out that the same work that spawned the amplituhedron has related work in quantum computing that is similarly important and groundbreaking, so it should have a cool name as well, and n-hedron seems to work.

The construct is a complexity class, meaning that it is a set of problems which can be[1] solved by quantum computers[2] in a reasonable[3] time. Those three aspects correspond to words which get initialized as the name of this complexity class -- BQP, bounded-error quantum polynomial-time.

Aaronson's proof involves an observation that PostBQP = PP, in other words, all of the problems you can solve with an especially powerful quantum computer can also be solved with an even more especially powerful classical computer, and vice versa. Since the quantum computer is easier to reason about, you get a hard result as a freebie.

BQP is not a tongue-in-cheek thing; it's also not a well-understood thing -- just "anything which quantum computers can do in this way quickly with bounded errors" -- but it's certainly better understood than this amplituhedron is. The real problem he's highlighting is that complexity classes like BQP have scary names.

For the sake of this discussion, you can imagine a similar problem with "programmable imperative syntax" and "monads". Really all that monads are, in a computing context, is a way of formalizing a programmable imperative syntax as a purely functional programming construct. The issue is that when you say "functional" and "monads" then people kind of just shut down, they don't want to hear about it. Does that make sense?

> eval(x)

Sort of like the number omega, which contains in each digits proofs to every theorem, but is not computable:

http://en.wikipedia.org/wiki/Chaitin's_constant

Also Greenspun's 10th rule of programming: http://c2.com/cgi/wiki?GreenspunsTenthRuleOfProgramming

This is the machine learning principle that the more a model explains the less accurate it is.

That's actually where I got the idea most clearly expressed to me in school; I just figured the Javascript thing was a bit more approachable, and conveyed what I was trying to say accurately enough.

That principle might be a good rule of thumb, but it's not universally true. Sometimes a new model comes along that both explains more and is more accurate. General Relativity is an example. Fundamental physics is funny that way.

Einstein always seems to be the exception that proves the rule.

> It is literally the most powerful Javascript framework ever

It doesn't meet the definition of a framework: http://en.wikipedia.org/wiki/Software_framework

> It trivially encompasses every possible Javascript program

Not every one.

slow golf clap

Wow... yes... you really straightened me out there. Way to go.

Blast. And I had such high hopes that my framework would become the Next Trendy Javascript Thing.

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