PM 2Ring

I like oregano, the ancient Italian art of pizza-folding.

@watchme The electric field isn't exactly non-material. But anyway, the field has some potential energy due to the spatial arrangement of charges. There can be a potential difference (i.e., a voltage difference) between different locations in the field. The lamp converts that potential difference to light (electromagmetic radiation). This is analogous to a water wheel converting gravitational potential energy of water in a dam to kinetic energy of the wheel.

@peterh Sorry, I don't quite understand what you're trying to say. There are a lot of great pop-sci books & videos, but they can only go so far. Pop-sci tends to avoid mathematics, but that doesn't work very well for physics.

Fair point. But I can't see obvious AI signs in most of her posts, apart from the high quality of her English.

She's also been prolific on Astronomy.SE. Her 1st question initially got a couple of downvotes, possibly for being too sci-fi, but then it got a great answer from ProfRob, and scored a pile of rep via the HNQ. astronomy.stackexchange.com/q/61407/16685 So I don't blame her for posting prolifically, attempting to get another HNQ hit. ;)

I agree with John. I think Anushka wants to be a good member of the community. She does jump all over the place, but I think that's just a combination of her enthusiasm and an excess of pop-sci & YouTube over proper textbooks. I don't think she's using AI to farm rep, but she may be using it to polish her English.

So it's kind of appropriate to define the Planck length in terms of the circumference or area of the event horizon. Also see en.wikipedia.org/wiki/Bekenstein_bound

@SiddharthKuchimanchi Note that the Schwarzschild r coordinate is defined in terms of the area or circumference of a sphere centred on the BH. The spacetime curvature is constant on such a sphere, so the definition avoids the difficulties of measuring distance with a rod oriented in the radial direction, where the spatial distortion increases as you get closer to the BH.

@SiddharthKuchimanchi Note that John Rennie didn't think your question needed closing. If you'd simply asked why is hbar rather than h used in the Planck length equation, then your question probably wouldn't have been closed.

@naturallyInconsistent Well, Eddington eye-balled it. He didn't have the equipment to fully justify his conclusions, even though he was correct.

@SiddharthKuchimanchi That close reason is supposed to be used to close questions that lierally ask us to check the OP's arithmetic or algebra, especially when the question looks like a solution to a homework assignment. However, some regular close voters use it on anything that looks vaguely homework-like that contains calculations. Our homework policy permits questions that are primarily about the underlying concepts, and sometimes it's appropriate to include some calculations in such questions.

> A modern reanalysis of the dataset, though, suggests that Eddington's analysis was accurate, and in fact less afflicted by bias than some of the analyses of solar eclipse data that followed.[41][42] Part of the vindication comes from a 1979 reanalysis of the plates from the two Sobral instruments, using a much more modern plate-measuring machine than was available in 1919, which supports Eddington's results.[43]

@Slereah It was less than ideal. ;) And Eddington's analysis was possibly a little biased. However, from en.wikipedia.org/wiki/Eddington_experiment

Repeating the Experiment that Made Einstein Famous

@naturallyInconsistent :D By way of comparison, "for light grazing the surface of the Sun, the approximate angular deflection is roughly 1.75 arcseconds". It's possible for an amateur with an excellent telescope to measure the deflection of starlight during a solar eclipse (by comparing eclipse photos to photos taken 6 months earlier), but it's not easy.

@naturallyInconsistent It's actually good that we aren't exactly in the galactic plane. A lot of dust accumulates in the plane, making it harder to see stuff, especially at optical wavelengths.

For my plot, I used data for the J2000.0 epoch, that is, 2000-Jan-1 12:00 Terrestrial Time. The modern ICRF frame (defined in reference to a bunch of quasars) was chosen to align as close as possible to the old J2000 frame, which is defined in terms of the equatorial & ecliptic planes. The alignment isn't exact due to some sloppiness in the old definitions. ;) But the error is only a couple of milliarcseconds. See ssd.jpl.nasa.gov/horizons/manual.html#frames

I don't know if birds grok the number line, but they understand pecking order. As long as the total number of chickens in the flock isn't too large, each bird can remember which birds are superior to it in the order, and which are inferior. But if the flock size is too large (around 100 or so), they get bewildered, and chaos ensues.

@leslietownes Clearly, you need to include ducks in the number line. :)

What leslie said. The |x| stuff is a level of abstraction that you get to after you understand what's happening on the number line. And when working with absolute value it's always a good idea to test results (eg, on a number line or graph), to check that you haven't made a sign error.

Then solve x^2 = 4, plot the solutions on the number line and look at the 3 intervals on the number line created by those two points. Investigate how x^2 compares to 4 in those three intervals.

IMHO, it's a good idea to use number line diagrams.

@cybersecurityattacker First, the student needs to understand what happens to an inequality when you multiply both sides by a negative number.

I actually wrote a little Sage script to draw 3 mutually tangent circles given their radii, and to fit inner & outer tangent circles to them. But I don't want to post a partial answer in the comments of a closed question. So I guess I'll just post it here. :) sagecell.sagemath.org/?q=glzmle

On a simpler note, there was a question on the main site last week about fitting 3 circles inside another circle. math.stackexchange.com/q/5083878/207316 In a comment, I suggested exploring Descartes theorem, but the question is closed for lack of clarity & details. I was hoping my suggestions would help the OP to add some details to their question, but they seem to have abandoned it.

But yes, FFT tends to be the fastest way to do big multiplication when the number of digits is on the order of 10^5 or so. Of course, it can be wasteful if your data size isn't a power of two.

@anankElpis Hmmm. I'm not sure how well FFT would work for this. Sure, it's fast, but I think it will chew up a lot of RAM, since you're basically replicating the generating function algorithm, so you need a slot for every coefficient in the final polynomial. I think. ;)

The +/- stuff is just inclusion-exclusion counting. I suppose there's a clever way to avoid it that's not too slow. But when you're doing big number arithmetic on this scale, it's usually better to go for speed & simplicity than to worry about a few thousand extra digits in your terms. ;)

BTW, 10^5 takes around 17 seconds, depending on traffic on the server. The result has 75934 digits.

Sane people don't try to calculate probabilities involving 100,000 dice. :)

Neither of those algorithms can do 10^5 dice using SageMathCell: there are time & RAM restrictions. And the generating function version must consume an awful lot of RAM for 10^5 dice. But here's an optimised version that can do 10^5. sagecell.sagemath.org/?q=cegkne

Interestingly, with large numbers of dice, it seems to be faster to do the calculation using the generating polynomial, rather than using the simple sum of products of the binomial() function. I assume that's because all the binomial() coefficients have to be computed from scratch. sagecell.sagemath.org/?q=bdpggy

@anankElpis You can share Sage code via SageMathCell. The short "Share" link is supposed to be temporary, but they seem to have a very long lifetime these days.

@leslietownes He also worked on a nice movie about various mathematical topics. dimensions-math.org/Dim_E.htm It was pretty cutting-edge in 2008. I guess it's a bit tame these days.

Jos Leys did some lovely work using stereographic projection. See josleys.com/show_gallery.php?galid=363 He also did a series of videos debunking Flat Earth, until he realised it was a lost cause. Link at top left of josleys.com

People aren't necessarily as stupid as they may appear. They might just be misguided. Eg, by religion. ;)

Because we're standing on top of the world. Why don't you guys fall off?

Maybe, although Flat Earthers are notoriously thick when you try to explain geometry to them.

@leslietownes Yes, it seems on-topic, and fairly innocuous, until he starts responding in comments. OTOH, he's not a new member, and his profile "about me" is a bit disturbing...

IMHO, thousands of years of institutionalised religion has selected for people capable of sustaining a fair amount of cognitive dissonance.

Some Christians are science deniers, but it's not required. ;) And it seems to vary, depending on region, and denomination.

And yet there are many people who consider themselves to be Christians who don't believe in flat earth.

@leslietownes Yes, eg

I suppose so, if you're a strict scriptural literalist.

There's a current HNQ on Christianity.SE where the OP claims that it's heresy to not believe in the flat Earth. christianity.stackexchange.com/q/108073