But in a just world this will tend to be the people who are badly-off as a consequence of their own misbehavior.
The real world is not just though. Yes some people who are badly off are there as a consequence of their own actions: Eg. this is quite likely the case if they're in jail. But, like, the most common way to be badly off in a way that makes you a target for the assistance of effective altruists is to be born into a poor country without a good public health system. Non-effective altruists might try to help prisoners or do other things that oppose the justice people. But those choices seem more random: some of them will also just go and fund museums.
Of course, I agree with the overall point that it's very important to consider what incentives you will create when you try to help people.
You mean linearity equation?
If the ion is isolated, that means you take a tensor product of its state with the state of the environment. If are orthogonal, then and are still orthogonal.
Why does your "repeated measurement" method not also work to use entangled qubits to send signals faster than light? (Since measuring one qubit also collapses the state of the other.)
Or, maybe just tell me the density matrix for the ion that you expect the reciever to see if the sender sends a 0, and also the density matrix for if they send a 1?
No matter what basis they measure in, the receiver will observe results consistent with the ion being in whatever state it was already in before the senders even did anything. This is a result of the linearity of quantum mechanics. If the overall wavefunction is a sum of two nearly-orthogonal vectors, then the evolved wavefunction is the sum of each vector evolved separately, and the terms in this sum will also be nearly-orthogonal. In equations:
If wasn't there, then would still evolve to and see the exact same outcomes. To get communication, there would have to be significant amplitudes for the universe's state to spontaneously shift from being in one world to the other. (i.e. even if world 1 is initially the only world, it still has some amplitude to end up in world 2). This is not realistic for the physics of macroscopic objects. We don't see, either theoretically or experimentally, large amplitudes for a dead cat to turn into a live one, etc, even if the initial decision to kill the cat or not was made by measuring polarization of a single photon.
EDIT: Also, it is a well known fact in QM that "one does not simply measure whether a system is an eigenstate or a superposition". If you measure a spin of up for an electron, you do not know whether it was actually spinning up, or it was spinning left and you happened to measure the "up" component of the left spin.
But if you're just concerned about energy conservation, such a complicated fix is not needed anyways: There are many systems that have multiple quantum states with identical energy, momentum, angular momentum, etc, yet are still orthogonal (i.e. perfectly distinguishable by measurement).
So the real reason it doesn't work is linearity, not energy-conservation or anything like that.
No, I'm pretty sure publishing sightings of law enforcement is legal in the US. Some traffic radio stations report on where police are using radar guns for example, and this is fully legal. Indeed, considering that mapping ICE sightings could be of academic/intellectual interest (and that it is actually perfectly reasonable for law-abiding US citizens to want to limit their time spent in close proximity to ICE agents) this is far more centrally "helping people get away with doing illegal things" (speeding) than robertzk's project.
I didn't learn anything from this. It looks like there are things to learn here, but you seem to have deliberately chosen a writing style that does not permit it.
That is pretty annoying.
I think its spread through rationalist-land originated at this post by Alice Maz: https://alicemaz.substack.com/p/you-can-just-do-stuff
Though by following the trail of links from Haiku's comment one can find people saying similar things farther in the past.
Overall a nice insightful post, but recorded music is like upwards of a century old, so I don't think the timing works out. I was in a dancing club at one point and we used recorded music and I think that requiring us to use live music would have prevented the club from existing.
Yeah, there's definitely a few relevant things here:
- Representation theory is relevant (in particular representations of cyclic groups, which is basically the circle arithmetic you're talking about). Representation theory gives you matrices that use complex numbers, even for discrete finite groups. So number theory isn't the only place where complex numbers poke their nose into discrete business.
- There's apparently a whole theory of Dirichlet series and Dirichlet convolution which is analogous to Fourier series and Fourier convolution. Complex numbers are the nicest way to do Fourier series, so it makes sense that they're also the nicest way to do Dirichlet stuff.
- I guess just in general complex numbers are the best field and a lot of the math of number theory is turning things into vector spaces and linear operators and doing linear algebra on them. And if you're picking a field for your vector space, what better choice than ?
- A Dirichlet series is a function of a variable , and complex functions can have complex analysis done on them, and complex analysis is uniquely nice, so why not make a complex variable?
The post author seems to already know a lot of math, so I guess they're looking for a deeper kind of answer.
1Oh, cool, that's great.
I was referring to the older style of sailboat design, like this one, where the sails are all controlled by a bunch of ropes. Single rotating airfoil sounds a lot simpler. One advantage of an airfoil over a kite is that it would allow the ship to gain some propulsion, even when travelling at an angle upwind, right?
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Kettles and Hydro Dams
(linkpost)
I live in British Columbia, where we get a lot of our electricity from hydroelectric dams. While boiling some water in an electric kettle, the water in the kettle might get you thinking about the water that was dropped to generate the electricity to run the kettle. How much water do we have to run through the dam in order to boil a cup (250mL) of water?
To answer this, we need to know the heat capacity of water. (You might think we also need to know the latent heat of vaporization, but when we talk about "boiling" some water, the goal is not actually (usually) to turn all of that water into steam. We just want to heat the water to 100°C, while only a small fraction is boiled off.) The specific heat capacity of water is 4184 J/kg°C. Note the kg in the denomiator of the unit, which means that if we double the amount of water, it takes twice the energy to raise its temerature the same amount. So there exists some fixed ratio between the amount of water boiled and the amount of water lost from the reservoir in order to boil it.
The exact value of this ratio depends on the height of the dam and how full its reservoir is at the time. So, here's an even simpler thing we can calculate: Imagine I'm visiting a planet like Earth but with no atmosphere. I'm at the top of a cliff carrying a bucket of water. I dump the water over the edge of the cliff and it falls all the way down before striking the ground at the bottom of the cliff. How high up do I have to be before the water reaches 100°C from the sheer violence of its collision with the ground?
If we assume that the water can't lose any energy to external sources then:
A mass m falling a height h yields an energy of mh(9.8m/s2).
A mass m takes an energy of roughly m(75°C)(4184J/kg°C) to heat from 25°C to boiling.
Setting these equal and solving for h gives h=32000m, an altitude that would be well into the stratosphere on Earth.
Given that most dams aren't 32 kilometers high, it's clear that we'll have to use much more water to generate the energy than the amount we want to boil. Specifically, 320 times more water for a 100 meter dam with a full reservoir, and the ratio is even more extreme for shorter dams or less-full reservoirs. This is kind of a shocking ratio if you haven't thought about it before, or at least that was my reaction.
One other thing that I thought was interesting about these calculations is that the water floating around near the top of the reservoir carries much more extractable energy than the water floating around near the bottom. Simply because it's higher up. So if the reservoir is low, that might be when you most desire incoming water from a scarcity perspective, but incoming water actually brings with it the most extractable energy when the reservoir is nearly full. This is related to how it takes more energy to add charge to a capacitor the more charge it already has on it so that stored energy goes as the square of the stored charge.
One thing this means is that if you're digging out a reservoir to make it larger, you should mostly focus on increasing the volume just underneath the maximum water level of the reservoir. I.e. you should shallowly dig a large area rather than deeply digging a small area.