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The Unitarihedron: The Jewel at the Heart of Quantum Computing
- dnautics 13y agoI don't usually like scott aaronson, (although I like his casting of QM as complex-valued probability space) - but this blog post was a gem.
- gonnakillme 13y agoCasting QM as a complex-valued probability space is how it's usually done.
- dnautics 13y agoI know that now but it was his specific casting that was entertaining and easy to understand. sorry, I'm a chemist - we just talked about and played around with wave functions (schrodinger formulation, not even heisenberg) without a word of referring to them as PDFs except in the psi*psi case (although as a math major in retrospect it's now plainly obvious to me that that's what they were).
- loup-vaillant 13y agoCalling "probability" something that's out there in the world. What a confusing thing to do… http://lesswrong.com/lw/oj/probability_is_in_the_mind/ http://lesswrong.com/lw/oj/probability_is_in_the_mind/
- gonnakillme 13y agoI'm not really sure what to make of this response. > The Bayesian says, "Uncertainty exists in the map, not in the territory. In the real world, the coin has either come up heads, or come up tails. Any talk of 'probability' must refer to the information that I have about the coin—my state of partial ignorance and partial knowledge—not just the coin itself. See, QM doesn't actually work like this. There is no hidden variable. This has been proven[1]. [1]: http://en.wikipedia.org/wiki/Bell%27s_theorem http://en.wikipedia.org/wiki/Bell%27s_theorem
- loup-vaillant 13y agoGenerally, when you know everything there is to know about an experiment, it makes you quite certain about the outcome you will observe. Yet this is not the case when you send a single photon through a half-sieved mirror. Even when you know everything there is to know about this experiment, you just don't know which sensor will go off, and if you repeat the experiment, you will find that previous results tells you nothing about the next one. Perfect independence. When total knowledge of the setup yields only partial knowledge about future observations, one is very tempted to look for "probabilities" in the setup itself. But it's a cop-out, a non-explanation. The fact that there is no hidden variable does not mean amplitudes (or their squared norm) are probabilities. So, what to make about our uncertainty about the perceived outcome of quantum experiments? Well, it's simple: the laws of physics as we know them are deterministic. When you send a photon through a half-sieved mirror, the actual result is always the same: the world splits in half. There will be one blob where the photon hit the first sensor, and one blob where the photon hit the second one. Subjectively, the result is the same: we still observe the Born statistics. But step further from the amplitudes as probabilities cop-out: the Born statistics are now more of an anthropic problem.
- tomrod 13y agoWhat is QM? Quantum Mechanics?
- gtr32x 13y agoCorrect.
- mfn 13y agoOut of curiosity, what don't you like about Scott Aaronson? I find him to be really good at making parts of TCS accessible to laypeople, his new book being a good example.
- gtr32x 13y agoCan someone help enlighten me a bit here. From a layman's standpoint after reading all the comments associated with the Amplituhedron article, it seems both from a semi-professional standpoint and layman standpoint it was an unique discovery. Now that a true professional has responded, is Scott here simply mocking at the marketting success of the Amplituhedron or is actually making a point about the existence of such mechanics prior to the discovery of Amplituhedron? Thanks.
- msie 13y agoSadly, the joke's lost on me. Is he making fun of the other "hedron" and this Unitarihedron is a joke too? Which is too bad. I was having high hopes for the future and I wasted time reading an inside joke.
- krapp 13y agoI was actually wondering whether the amplituhedron might possibly have some impact on quantum computing... but I'm not even smart enough with the math to know whether that's a stupid question. Now I don't even know if what I just read was satire.
- derefr 13y agoI think he's genuinely suggesting that if journalists are getting so excited about the amplituhedron, they should get even more excited about this, and probably can only do that if they have a fun word for it. No joke. (If it was a joke, the paper he linked to -- http://www.scottaaronson.com/papers/pp.pdf http://www.scottaaronson.com/papers/pp.pdf -- probably wouldn't be exactly what he described it as.)
- acadien 13y agoIt is 100% a joke. He seems to be pointing out that you can get the press to over hype a scientific/mathematical advance by giving it a neat name, e.g. dark matter, anti matter, god particle, quantum-anything, electro-anything, super-anything, hyper-anything.
- Dylan16807 13y agoBut wasn't the point of the other one that representing it as a multi-dimensional volume was novel? That had nothing to do with the name. What's the point of mocking the name?
- acadien 13y agoHe's not mocking the name or the finding, he's mocking the press coverage. This seems clear to me from the opening paragraph, maybe I'm missing something?
- jerf 13y agoFor 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.)
- polynomial 13y agoThis is the machine learning principle that the more a model explains the less accurate it is.
- jerf 13y agoThat'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.
- troymc 13y agoThat 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.
- polynomial 13y ago
- damianknz 13y agoThe article is definitely satirical and points out the futility of any -Hedron based device regardless of its theoretical truth. You can't calculate the volume of a fractal in fact some fractals can be proved to have zero volume!
- Groxx 13y agoThe Simon's Foundation version with discussion: https://news.ycombinator.com/item?id=6403285 https://news.ycombinator.com/item?id=6403285
- powertower 13y agoI don't quite get it. After looking at the linked to papers, I'm assuming this is not a joke, and he is not putting down (making fun) of the Amplituhedron, nor making up the Unitarihedron (just abstracting his work with a media-friendly name to itit). What he is joking about is simply that mathematicians should named their work as a (insert-something-here)-hedron, as that would cause the media to pick it up and report on it. Is this correct?
- killerpopiller 13y agoI don't know either, what a brick. I really hate expressions where you need context to understand it's intentions, or die stupid. He could have given context but prefered being condescending.
- bsullivan01 13y agoThough, in recent months, my research has focused even more on the diaperhedron Damn, we should compare notes, we're researching the same thing :-) I need to make a mental note that if the mathematician or physicist tries too hard to get on TV /news and sell something, he might not be as great as others.
- pintglass 13y agoI had a unitarihedron hanging from my rearview mirror in high school. It was pretty awesome.
- maxander 13y agoWhat I had taken away as the big impact of the original "amplituhedron" article was that the researchers had found a way to replace long calculations with a shorter, geometrical calculation. Which, unless there's some profound connection between quantum complexity classes and geometry that I'm not aware of, wouldn't be the case with the "unitarihedron." So perhaps Aaronson isn't giving the amplituhedron concept the quite credit it deserves? (Disclaimer- I haven't the background in complexity nor physics to have any idea, obviously. But geometrical calculations playing a key role in a theory that "did away with space" seemed like a wonderfully cool paradox.)
- teeja 13y agoBaj. Jumbug. Their hedrons are only special cases of my 42-dimensional Universahedron, which certifiably and undeniably contains everything, including all possible universes. The proof is too small to publish in this post.