471–480 of 839 posts
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It only has direction + magnitude right? (±h/4π)e_i for some unit vector e_i. So it can be written as a vector? No?
It's a vector. madhadron doens't know what he's talking about. (To be excruciatingly precise, it's a ray in Hilbert space. But that's close enough to a vector for the purposes of HN comments.)
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It's accurate. QC is just linear algebra with complex numbers, plus probability extended to the complex domain. Why that's useful is something I'm still struggling with as well.
I'd assume it's the speed advantage, but the only problem I can think of that would require that type of exponential speed is cracking hashing algorithms which just seems destructive and counterproductive, like building a digital nuclear bomb - and from my very limited understanding that's a long ways off from being achieved. I assume there's probably many more complex computational problems outside of my domain that…
Quantum Computers. Not like I'm five, but like I'm a software engineer who has a pretty decent understanding of how a classical turing machine works. I can't tell you how many times I've heard someone say "qubits are like bits except they don't have to be just 1 or 0" without providing any coherent explanation of how that's useful. I've also heard that they can try every possible solution to a problem. What I don't u…
Very simplified explanation: If you understand Turing Machines, you probably also understand other automata. So you probably understand nondeterministic automata [1]. A quantum computer is like a very restricted nondeterministic automaton, except that the "do several things a once" is implemented in physics. That means just like a NFA can be exponential faster than a DFA, a QC can be exponential faster than a normal…
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No, more things that are modifications without any genetic basis - like myopia. Doesn't seem to have any genetic/epigenetic basis. It's purely a physical use case, where the eye matures improperly if it's only exposed to near-field work.
ah, I see what you're saying. Luckily, I've looked into this specific topic! Myopia is definitely hereditary, especially the pathologic variants that can lead to retinal tears and the like. That being said, there is the process of refractive development that occurs early on in life. The eye develops at a frighteningly fast pace, and you achieve near-adult globe size after about 18 months. The genes that drive this re…
1. Carbon dating. Sure, I get that carbon decays over time and this changes the proportion of isotopes. But why does this give you any information? That carbon didn’t come into existence just to be in that bone, it was made in the sun billions of years before that, so why does the age of the carbon tell us anything about organic matter? The key fact, which I think is not emphasized enough, is that the ratio of isotop…
For recent times, you can also compare the dates of the C14 with other methods like counting tree rings, or the date of a total eclipse and check the calibration.
2) You are almost right. The tides are not produced by the gravity of the Moon, but from the differences in the gravity of the Moon in the water that is nearby and the average of the Earth.
You forgot to include the centrifugal force [when you are in the non-inertial frame frame that rotates like the Earth-Moon system https://xkcd.com/123/ ]. The centrifugal force is bigger in the water that is in the more far from the Moon and again the difference creates the other tide.
3) The sky is blue because the single molecules in the air disperse the blue/violet color more than the other colors. There are many ways to produce colors. In this case the light is dispersed by the whole molecule.
A different method to produce blue is using a CD to produce a rainbow and the using a slit block the other colors. Some birds and butterflies use a somewhat similar method. [Not very similar but closer to the CD method than to the air method.]
The blue in the die for cloth uses another method. You make a long chain of conjugate chemical bounds C-C=C-C=C-C=C-C, and pick length and atoms so the electrons absorb the colors you don't like and transform the energy into heat.
I'm probably forgetting a few more method, there are many of them, so it's interesting to understand which of them make the sky blue.
*) These are good questions. My explanations are not 100% complete (and probably not 100% accurate) but I hope you can fix the holes.
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ah, I see what you're saying. Luckily, I've looked into this specific topic! Myopia is definitely hereditary, especially the pathologic variants that can lead to retinal tears and the like. That being said, there is the process of refractive development that occurs early on in life. The eye develops at a frighteningly fast pace, and you achieve near-adult globe size after about 18 months. The genes that drive this re…
90% saturation in a few generations suggests that it is something other than purely hereditary mutations accumulating: https://www.nature.com/news/the-myopia-boom-1.17120
Frame dragging. How does space know a body is rotating if the body is "smooth"?
Quantum spin. Electrons aren't really spinning, right? But why do we call it spin? I know it has something to do with angular momentum. What are the possible values? Is it a magnitude or a vector? Is there a reason we call it "spin" instead of "taste" or some other arbitrary name? How do you change it? What happens to it when particles interact?
Why bicycles stay upright. For every authoritative-sounding, in-depth explanation, there is an equally plausible, yet conflicting and contradictory alternative.
One is gyroscopic forces. Ever picked up a spinning hard drive? Notice that it feels strangely hard to turn in some directions? Same idea.
The other is the feedback loop consisting of the bicycle and its rider.
If the bike is stationary, it's hard to keep it upright because you have no assistance from gyroscopic forces. At low speeds, you have some assistance but not enough. At higher speeds, the bike wants to maintain its current orientation, and it's easy to feed in the slight corrective forces needed to keep it that way. Hop off the bike and it will keep going until something causes it to veer off course.
You can throw a ton of math at it, as in the paper mentioned elsewhere in the thread, but at the end of the day, gyroscopic forces and negative feedback are all that's necessary. The Schwab paper appears to show that the gyroscopic forces aren't necessary, but no bicycle in the real world is ever going to work that way except in rare corner cases, e.g., if you're one of those riders who can stay upright at a standstill.