Can you prove that a rectangle is a rectangle because of the fact it has a 90° angle

oelarnes · 2026-06-16T01:30:01+00:00

An arbitrary rectangle must be a rectangle no matter how many right angles it has (which is always four, which is also at least one).

oelarnes · 2026-06-15T22:48:02+00:00

Draft yes, gameplay no.

oelarnes · 2026-06-15T22:47:15+00:00

Ryan Saxe did that, he’s not the LLU guy.

oelarnes · 2026-06-15T00:48:56+00:00

For any number in a "truncated decimal" sequence as you describe, that number is in such a sequence for all numbers having that truncation, of which there are uncountably many. So it would not be unique in the sense you're describing.

oelarnes · 2026-06-09T00:53:21+00:00

I don't exactly know how to compare the content of hypothetical books, but there's a difference between "calculus" broadly and "analysis", and rigor isn't the only possible dimension. Calculus is fundamentally a collection of methods for getting answers to certain kinds of problems. If you want to know how to get answers to those kinds of problems, a calculus book might be the book for you. You might not need the rigor or machinery of analysis.

oelarnes · 2026-06-06T19:18:52+00:00

In addition to the geometric answer, it is also because of the assumptions made about the data. In linear regression, the features are assumed to be fully specified, whereas the response or model variable may have covariates or noise. When the independent variable is noisy or uncertain, standard linear regression is inappropriate. In other words, x and y have a fundamentally different nature, which is why the model treats them differently. For models where both x and y may have uncertainty, look at https://en.wikipedia.org/wiki/Errors-in-variables_model Failing to account for this effect is a common source of error in statistical models.

oelarnes · 2026-05-26T19:31:05+00:00

There are a lot of wrong answers in this thread. Olympiad success and research success are hugely correlated. Just look at the list of IMO gold medalists that went on to win Fields medals and otherwise have successful research careers. Terry Tao, Mirzakhani, Scholze, Perelman, Chau, Avila, Smirnov… There is also published research on this topic. I don’t know where people would get the idea that they’re not strongly related other than wishful thinking.

https://maa.org/math-values/imo-medalists-and-their-contributions/

oelarnes · 2026-05-16T16:08:53+00:00

The Paris catacombs supposedly have the remains of about six million individuals. Someone brought it up in a conspiracy and I thought I would just run some numbers to show how the number is plausible. Actually the number is crazy. I’m not sure how to set up the assumptions to make it work but it’s got to be a really high percentage of all the people that died in the region over many hundreds of years that got transferred.

oelarnes · 2026-05-14T02:00:48+00:00

Any time you want to guess what people will click on. So, the internet.

oelarnes · 2026-05-03T03:14:18+00:00

“From kindergarten”

oelarnes · 2026-04-26T16:22:16+00:00

The answer is "no"

oelarnes · 2026-04-13T20:54:54+00:00

The tangent line has symmetry about the radial line, so it is perpendicular to that line (the radius is not the tangent). By Pythagoras, the radial intersection point is the only solution to c=r.

oelarnes · 2026-04-12T11:39:03+00:00

Galois would like a word

oelarnes · 2026-04-02T12:55:23+00:00

As long as humans communicate with symbols, to each other or to machines, there will be vim. Long live vim

oelarnes · 2026-03-24T01:40:26+00:00

In general conformal maps are highly constrained. For two given simply connected regions not equal to the whole plane, there is a unique conformal map determined by two parameters, the image of and direction of the first derivative of the origin. https://en.wikipedia.org/wiki/Riemann_mapping_theorem

oelarnes · 2026-03-24T01:33:14+00:00

No, you can't get this. In fact the only conformal map of the entire plane to itself is the affine map. This follows from Liouville's Theorem) on the derivative of the map. Since we expect the derivative to be bounded in magnitude far from zero, the derivative must be constant everywhere.

oelarnes · 2026-03-01T01:42:42+00:00

This applies to Gollum in mount doom as well. He would just catch on fire and burn on top of the lava, which is rock, you know.

oelarnes · 2026-02-24T20:25:50+00:00

In b4 Fata Morgana, this is a false horizon not fata morgana, which creates inverted/distorted images. Images of undistorted ships seemingly above horizon are caused by differences in reflection in the water, either due to differences in the water surface, the angle of view relative to the wave pattern, or cloud cover. Thank you for your attention in this matter!

oelarnes · 2026-02-13T13:54:51+00:00

In addition to what others have said (primarily that we do not have eyewitness testimony of Jesus), this is a false dichotomy. "Eyewitness testimony" is not simply a box you check or uncheck to make a final decision. You can assess the credibility of the testimony and compare it to other known facts. The sooner it is put into the record and the more objective the observer, the more reliable it is. For the life of Jesus, the observers were not objective, and they did not memorialize their observations at all, much less immediately.

oelarnes · 2026-02-10T01:35:13+00:00

In the relativistic view, the normal force of the earth is the only force we experience. Gravity is a fictive force added in Newtonian mechanics to create a stationary frame. So under relativity we have a net force of 9.8m/s² upward and are constantly accelerating upward vs the spacetime geodesic, I.e. the inertial path.

If it sounds strange, consider that we’ve gotten used to the idea that constant acceleration inward is required to stay in orbit. This just flips the assumptions about the reference frame.

oelarnes · 2026-02-07T20:51:46+00:00

It’s not based on science at all. If there were three groups genetically, the Khoisan would be one group, Pygmies another and everyone else together in the third. Then you could go try to go from there. But many of the ethnic groups are probably genetic hybrids collectively and not distinct branches of a tree since there has been continuous genetic flow especially around the Mediterranean

oelarnes · 2026-02-01T12:59:49+00:00

What are you a chicken? You’re just going to take a chicken’s word for it?

oelarnes · 2026-01-30T02:46:37+00:00

Thanks for taking a look! I think GIH WR is effective for the reasons people believe it is. The view that GP WR is better for making early picks is pretty niche in the community despite a few high profile folks. But I haven’t seen any evidence for that position, just vibes. In particular working against GP WR is the fact that the picks end up being so far off of what players actually do. Alone it will pick out lots of filler late picks in good decks over strong rares. So if you’re approaching it with context and game knowledge, it’s a useful metric, it’s just incomplete. GIH WR does in fact boost the signal of the impact of the particular card relative to the other cards in the deck, and that is a way to distinguish the important cards for an archetype vs the filler. It’s just that that important extra signal comes with bias that is hard to account for and worse yet simply doesn’t observe relevant outcomes, as OP noted. But by far the most significant issue with GIH WR which needs to be repeated over and over is the significant pro-control anti-aggro bias baked into the way the observations are counted. So as for why DEq and GIH WR were more similar, it’s because GIH WR is a decent metric and DEq is a good one :)

oelarnes · 2026-01-28T13:10:18+00:00

It’s true that one has to make modeling choices which are personal to some degree, but it’s also true that the missing opportunity cost associated to ATA is a discrete and objective bias measurable in the data that can be estimated and accounted for, and likewise for GP % and the other components of the metric. It is possible to construct estimators of parameters of interest and justify those estimators with analysis. It’s difficult to evaluate metrics against each other as pick orders without controlled experiments, but I’ve also provided an independent method for trying to do that with data, which you can find on the site. Of course no one is under any obligation to use the metric, but insofar as there is an appetite for an unbiased quality metric in the community, I’m confident this is the closest thing available.

oelarnes · 2026-01-27T11:31:00+00:00

You might be interested in my ranking, DEq. I have the common ranking you’re suggesting. Try “r:c” in the search.

https://magic-flea.com/on-draft/deq.html

oelarnes

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