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Remember that no matter what happens, the Hufflepuff boy will still come to Harry at a bit after 11:04. This means either that Voldemort will survive this encounter and retain mobility in four hours, or that he set up this message in advance (or that Harry is wrong about the source of this message).
In response to
Harry Potter and the Methods of Rationality discussion thread, February 2015, chapter 104
In response to
comment
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on
Harry Potter and the Methods of Rationality discussion thread, February 2015, chapter 104
I understood it to be implied that the message was actually set in advance to mislead Harry into believing time travel was involved.
Saying that this is what the formula intrinsically does, amounts to saying that field lines are more fundamental/"real" than action-at-distance forces on point particles.
Yep :-). I don't know enough the physics to back that up, but that's what my gut tells me. A more educated version of me might be able to say something "the vocabulary of forces is 'shallow'; the vocabulary of fields is deeper; the vocabulary of group symmetries is deeper still." I certainly do not have the depth of understanding to make that sort of statement with any authority. If you know enough physics to correct me or clarify, please please do.
why not better go for simplifying Einstein's equation and including 8π in G
If somebody who groks relativity told me that this is the right thing to do, I would believe them (ETA mentioned on Wikipedia). I'd be curious where the factor of 2 comes from in the Newtonian approximation.
I'd be curious where the factor of 2 comes from in the Newtonian approximation.
I can take a stab at explaining this. Both the Poisson equation and the Einstein equation have the general form
- 2nd order differential operator acting on some quantity F = Constant * Matter source
In the Newtonian case, F is the gravitational potential. In the Einstein case, it is the spacetime metric. This is a quantity with a simple, natural, purely "mathematical" definition that you cannot play with and change redifining constants; it measures the distance between events on a four-dimensional curved spacetime. "Matter source" in the Poisson equation stands for mass density, and in the Einstein equation it stands for a more complicated entitity that reduces to exactly mass density in the limit when Newtonian physics holds. So the ratio of the constants in each equation is determined by the ratio of how "spacetime metric" and "gravitational potential" are related in the Newtonian limit of GR.
In Newtonian physics, the gravitational potential is that whose first derivatives give the acceleration of a test particle:
- gradient of potential = acceleration of particles
This is considered a phyiscs law combining both Newton's law of gravity and Newton's second law of motion. In GR, the spacetime metric also has the (purely mathematical) property that (in the limit where velocities are much smaller than the speed of light, and departures from flat space are small) its gradient is proportional, with a factor 2, to the acceleration of geodesic (minimum length) trajectories in spacetime:
- gradient of metric = 2 acceleration of geodesics
So if we make the physical assumption that test particles in a gravitational field follow geodesics, then we can recover Newtonian gravity from GR. (The whole reason why this is possible is the equivalence principle, the observation that all forms of matter respond to gravity in the same way.) Since small perturbations to a flat metric have to be identified with twice the Newtonian potential, this is where the extra 2 in the Einstein equation comes from.
The current definition of the gravitational constant maximizes the simplicity of Newton's law F = Gmm'/r^2.
Absolutely, and Planck's constant maximizes the simplicity of finding the energy of a photon from its wavelength, and π maximally simplifies finding the circumference of of a circle from its diameter. But in all those cases, it feels to me like we're simplifying the wrong equation.
ETA: To be explicit, it feels like there should be a 4π in Newton's law. The formula is calculating the gravitational flux on the surface of a 3-dimensional sphere, and 3-dimensional spheres have a surface area 4π times their radii.
The formula is calculating the gravitational flux on the surface of a 3-dimensional sphere, and 3-dimensional spheres have a surface area 4π times their radii.
Saying that this is what the formula intrinsically does, amounts to saying that field lines are more fundamental/"real" than action-at-distance forces on point particles. But in the context of purely Newtonian gravity, both formulations are in fact completely equivalent. (And if you appeal to relativity to justify considering fields more fundamental, then why not better go for simplifying Einstein's equation and including 8π in G?)
In response to
Stupid Questions February 2015
A lot of math and physics definitions feel like they have weird dross. Examples:
- The Gamma function has this -1 I don't understand
- The Riemann Zeta function ζ(s) negates s for reasons beyond me
- cosine seems more primitive than sine
- The gravitational constant looks like off by a factor of 4π
- π seems like half the size it should be
After years of confusion, I was finally vindicated about π. That π is not 6.2831853071... is mostly a historical accident. Am I "right" about these other definitions being "wrong"? What are other mathematical entities are defined in ugly ways for historical reasons?
The current definition of the gravitational constant maximizes the simplicity of Newton's law F = Gmm'/r^2. Adding a 4π to its definition would maximize the simplicity of the Poisson equation that Metus wrote. Adding instead 8π, on the other hand, would maximize the simplicity of Einstein's field equations. No matter what you do, some equation will look a bit more complicated.
In response to
Bill Gates: problem of strong AI with conflicting goals "very worthy of study and time"
Here the question is raised again to Gates in a Reddit AMA. He answers:
I am in the camp that is concerned about super intelligence. First the machines will do a lot of jobs for us and not be super intelligent. That should be positive if we manage it well. A few decades after that though the intelligence is strong enough to be a concern. I agree with Elon Musk and some others on this and don't understand why some people are not concerned.
Edit: Ninja'd by Kawoomba.
This could either show that the topic isn't mindkilling, or that it is very mindkilling, if the Less Wrong consensus happens to be simply mistaken.
My understanding of the use of "mindkilled" is that people who can be so described are incapable of discussing the relevant issue dispassionately, acquiring an us-vs-them tribal mentality and seeing arguments just as soldiers for their side. I really don't think that this applies to the topic of abortion on LW, which can be discussed dispassionately (much more so than in other places, at least). This is quite compatible with the possibility that the LW consensus is biased and wrong, which is what you are suggesting.
In response to
What topics are appropriate for LessWrong?
There was just an astonishingly civil examination of the most mindkilling topic I could think of in Discussion. I've criticized people for violating the LessWrong politics taboo in the past, but I'd be happy to chat about anything from particular elections to the merits of Marxism if it was always done so painstakingly in the articles and so thoughtfully in the rebuttals.
I'm not sure how to achieve that, though. "Everybody can talk about politics carelessly" isn't any better an idea than it was before, and trying to enforce "only talk about politics carefully" might just add tone arguments without actually improving the tone.
Abortion is a strongly mindkilling topic for society in general, but it is not one for Less Wrong. According to Yvain's survey data on a 5-point scale the responses on abortion average 4.38 + 1.032, which indicates a rather strong consensus accepting it. As a contrast, the results for Social Justice are 3.15 + 1.385. This matches my intuitive sense that discussions of social justice on LW are much more mindkilling than discussions of abortion.
In response to
Open thread, Dec. 29, 2014 - Jan 04, 2015
I answered "not at all", even though I was for some years very shy, anxious and fearful about asking girls out, because I never felt anything like the specific fears both Scotts wrote about, of being labelled a creep, sexist, gross, objectifier, etc. It was just "ordinary" shyness and social awkwardness, not related at all to the tangled issues about feminism and gender relations that the current discussion centers on. I interepreted the question as being interested specifically in the intersection of shyness with these issues, otherwise I might have answered "sort of".
In response to
PSA: Eugine_Nier evading ban?
You are the fourth or fifth person who has reached the same suspicion, as far I as know, independently. Which of course is moderate additional Bayesian evidence for its truth (at the very least, it means you are seeing a objective pattern even if it turns out to be coincidental, instead of being paranoid or deluded)
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I've had an experience a couple of times that feels like being stuck in a loop of circular preferences.
It goes like this. Say I have set myself the goal of doing some work before lunch. Noon arrives, and I haven't done any work--let's say I'm reading blogs instead. I start feeling hungry. I have an impulse to close the blogs and go get some lunch. Then I think I don't want to "concede defeat" and I better do at least some work before lunch, to feel better about myself. I open briefly my work, and then… close it and reopen the blogs. The cycle restarts. So Lunch > Blogs, Work > Lunch, and Blogs > Work.
(It usually ends with me doing some trivial amount of work--writing a few lines for a paper, sending an email, etc--and then going for lunch with an only half-guilty conscience.)
Has anybody else experienced circular-like preferences, whether procrastination-related like these or in a different context?