jacobolus

Plenty of students succeed just fine without owning a graphing calculator (they can spend a few minutes learning the handful of test-relevant features and borrow one for the exam). Thankfully as of this year there is also a Desmos option.

Ideally the tests would not require external tools at all. There's nothing that needs to be tested in the context of a high school course that can't done with pencil and paper.

NEET means "Not in Education, Employment, or Training". The stereotype is an unemployed young adult living with their parents and playing video games all day.

They had different models with different capabilities. As they made minor style changes, they bumped the numbers slightly. The 81–82–83–84 were basically the same concept, as were the 85–86. The 89 and 92 were higher-end models. The 80 and 73 are simpler models intended for middle school.

All of them are basically a multi-generational scam perpetrated against the hapless parents of American high school students who were told that they needed to buy overpriced anachronistic calculators for their kids to succeed in school. In my opinion the calculators have overall caused more pedagogical harm than benefit; the students would be better served by some combination of (a) problems that can be solved without the tedious but trivial numerical calculations these calculators support, or (b) are solved using a real programming language. If someone really wants to assign simple numerical problems, give the kids slide rules.

Calculators of this type used to make sense for an engineer doing work in the field somewhere, but make no sense in the context of a classroom.

You should try to avoid continuous static load on your muscles, especially the smaller ones. So you should find a typing position where that doesn't happen. You also want to use your muscles in the strong and comfortable part of their range of motion, which depends on the entire chain of joints, because tendons have to stretch past several joints to get to whatever bone they attach to – so for fluent finger motions, you want to keep wrists and hands in as neutral a position as you can.

If your wrists are not straight while typing a lot, that's really bad. I constantly see people typing with their wrists either significantly flexed or significantly extended; doing that a lot is a fast road to RSI, and even doing it a little is pretty unpleasant and inadvisable.

If you are going to type a whole lot at a stretch (say, as a programmer or writer), you want your arms to be mostly passively supported from the shoulder. Having your arm bent at the elbow doesn't cause much strain, as long as the upper arm is hanging loosely down with your shoulder relaxed – so bring the keyboard relatively close to your torso. Resting your wrists, palms, or forearms on some surface and then typing generally causes more strain than having your wrists and palms "floating" above the keyboard while actively typing. You can rest the fingertips lightly on the key tops if you want. You can rest your palms on a palmrest or arms on an armrest (or table, or lap, or whatever) while you are taking a break from typing. It's generally a good idea to take regular breaks.

> the monitor should be at eye level vertically

This is slightly misleading advice. The ideal place for the display has the top of the display at roughly eye level, or for a very large display maybe slightly above, which puts most of the display below eye level. Humans actually have great ability to look slightly downward for long periods of time while doing stuff with their hands, even while keeping their head held up straight, and indeed our eyes can more comfortably focus on close objects in the lower part of our field of view than straight ahead. What you don't want to do is slouch or bend your neck too much.

A laptop display attached to the keyboard usually isn't an ideal placement, but it's generally not too bad.

Having the desk low, the chair high, or putting a laptop on your lap is okay. Having the desk or table "high" (i.e. at normal height for writing with a pen or eating a meal) is generally worse but not an insurmountable problem.

In either case, the most important thing is to keep your wrists in as straight and neutral position as possible, with your palms and wrists "floating" rather than resting on anything while actively typing. Having the wrists either flexed downward or extended upward is a really bad idea. Having the wrists turned out to the side isn't great either, but not as bad.

The keyboard should be positioned close enough to your body so that your shoulders can be relaxed with your upper arms hanging loosely. The laptop surface should be roughly parallel to your forearms, so if you have a high desk or table relative to your torso you will need to prop up the far side to tilt it up a bit.

> save our wrists

If your wrist is in contact with the edge of the laptop while you are actively typing, then your typing style has a good chance of giving you RSI. You'd be better off trying to fix that than trying to make the fast path to RSI more convenient.

Magnus doesn't "dictate the rules of the game or the platforms by which it is played", so I'm not sure what your point is.

You think Magnus should be forced to participate in chess events he doesn't enjoy / doesn't like the format of? Or you think organizations like FIDE or chess.com should be blocked from trying to entice Magnus to participate in their events?

Please be more specific and concrete.

Magnus "drives meaningful outcomes" because he's really good at chess and members of the public enjoy watching him play, so various chess-related businesses will pay him money for sponsorship. How do you propose to "not allow him" that influence? Ban all use of people's names in marketing and products?

There are LED lamps which have a "warm dim" feature so that the appear oranger as you reduce the brightness.

Providing a day-like view of the scene should not be the primary goal of nighttime lighting.

The sodium lamps are in fact safer for driving, because they preserve drivers' night vision, which improves visibility into the shadows, and because they cause less glare.

What they aren't good for is LED manufacturers' bottom line, and the lighting industry spent a lot of lobbying money to entice friendly politicians to heavily subsidize them with public infrastructure budgets, with those subsidies then misleadingly sold to the public as "efficient" and "environmentally friendly".

They're also not very good for reading the newspaper or doing critical color analysis. Thankfully such tasks do not need to be done at night in the middle of the street.

It's not especially close to the peak sensitivity of the human eye (in either bright or dim conditions), but that's entirely okay. The goal should be to not affect people's level of dark adaptation.

If you use shorter ("bluer") wavelengths, as happens with white LEDs which consist of a blue LED + phosphor, it causes people's eyes to become bright adapted and effective night vision is ruined, causing people to have much worse vision in the shadows.

Also, if you use bluer light, the lights themselves cause dramatically more glare in peripheral vision, because the shorter-wavelength-sensitive "S" cone cells and rod cells are mostly absent from the fovea (center of the retina), and prevalent in the outer areas of the retina. This is why LED headlamps on cars are so obnoxious for drivers going the opposite direction.

Also, the LEDs clobber people's circadian rhythms and are extremely disruptive to wildlife.

Finally, the light pollution caused by the LEDs is much worse for seeing the stars, which is maybe not as important as the other harms, but still kind of sad.

Yes, that's the point. It will only break down in water when the water is hot. Here's the paper https://link.springer.com/article/10.1007/s11696-022-02286-x

Yeah, I imagine it's considerably slower at ambient ocean temperature. Don't throw your PLA bags in the ocean or a river. Here's a different paper:

> For example, PLA is not biodegradable in freshwater and seawater at low temperatures [32,36–39]. There are two primary reasons for this: (i) The hydrophobic nature of PLA, which does not easily absorb water [40–42]. In aqueous environments, the lack of hydrophilicity diminishes the hydrolysis process, which is crucial for the initial breakdown of PLA into smaller, more degradable fragments. (ii) Resistance to enzymatic attack; the enzymes that degrade PLA are not prevalent or active under typical freshwater and seawater conditions [39,43,44]. The microbial communities in these environments may not produce the necessary enzymes in sufficient quantities or at the required activity levels to effectively breakdown PLA. Additionally, the relatively stable and crystalline domains of PLA can further resist enzymatic degradation.

Also:

> It should be emphasized that neat PLA cannot be classified as a completely biodegradable polymer, as it generates microplastics (MPs) during biodegradation.

My understanding is that cellophane generally does biodegrade in most settings. Polylactic acid (those cornstarch-derived bags) mostly biodegrades in hot enough compost or (after several years) in ambient-temperature soil, but not very well in cooler water (One study: "The half-life period of degradation [of polylactic acid in artificial seawater] is 12 [days at 90° C] or 468 days [at 60° C]").

BART is full of white-collar people who use it to commute and to travel around the area (alongside all sorts of other kinds of people, as you would expect for a broadly used service).

Ridership collapsed in 2020 because of the pandemic, for obvious reasons, but it's hard to really blame that on the service itself, or the riders.

Ridership has been gradually recovering since then. Total trips are now up to something like 70% of 2019 levels, and continuing to rise. Number of unique riders is actually above the 2019 level now.

Maybe you haven't tried riding BART again within the past several years?

The speed of spoken Spanish varies significantly from one place to another.

"To reduce human errors in his experiments, Wu opted to use a scoring machine to accurately fold the origami patterns."

For a bit of context, the Phaenomena was a book by Eudoxus (c. 400 BC) explaining the then-current knowledge of astronomy; unfortunately there are no extant copies. A poem (also called Phaenomena) by Aratus (c. 300 BC) made the content more accessible, and was extremely popular. The only surviving work by Hipparchus (c. 150 BC) is a critical commentary on these two books, and it only survived because it was bundled together with several other commentaries on Aratus' poem which were copied as a group. Hipparchus synthesized Mesopotamian astronomical observations and measurement techniques with Greek spherical geometry, founding the subject we now call trigonometry. All of his other works are lost, but much of the content of Ptolemy's Syntaxis (a.k.a. Almagest, c. 150 AD) was taken from Hipparchus' astronomical and mathematical works.

Any additional fragments of Hipparchus' works is of great interest to the history of mathematics and astronomy.

The only way anything ever changes in a volunteer project is if someone feels motivated and makes the effort. Please contribute changes to German Wikipedia articles (or English ones) when you notice possible improvements. If you are not personally capable of improving an article about a topic you don't know about, please try to contribute to the articles about topics you do know something about. Or you can try to leave a talk page message asking for help.

> the challenge is all the gatekeeping

I'd say there's significantly less gatekeeping on Wikipedia than most parts in academia. YMMV.

But: there are a bunch of random clueless people trying to promote their obscure papers to boost their citation counts, push weird nationalist POVs, add fringe pseudoscience, make "fixes" that turn out to be wrong, add vague explanations which they find personally helpful but nobody else can make sense of, remove clarifications and explanations in the name of rigorous purity, change the wording of sentences that have been subject of years-long dispute and careful compromise, and so on. Wikipedia maintainers are constantly fighting against these agents of entropy (or when an article is not actively maintained, it tends to get a lot worse over time), which unfortunately can sometimes also negatively color interactions with helpful contributors. They're also part-time volunteers, and fallible humans; try to cut them some slack.

To the extent that there is "gatekeeping", it is mostly along the lines of: you can't use Wikipedia primarily for self promotion, you can't add your own new claims that have no published source, and you have to abide by existing norms of project/community engagement. In general, people are judged by their contributions and behavior, not their credentials (though editors also include a bunch of world-class experts in the topics they contribute about, and it does have some pull when someone can say "I literally wrote the top cited paper about this" or whatever).

But beyond that, the difficulty is that there's no one correct way to explain difficult topics, no single audience for Wikipedia articles, a lot of strong opinions about how things should be one way or the other. Trying to satisfy everyone takes discussion and compromise and sometimes a minority is still unhappy with the resolution. The biggest problem though is that there are not enough active participants (including in mathematics) to write great articles about every topic, and writing a really excellent article about something takes a huge amount of work; there are many mediocre articles that have never really had the time put in to make them great.

When someone new to the project gets into a heated dispute about a minor point, they routinely get extremely frustrated and occasionally then run around the web complaining about how awful the people on Wikipedia are. Several times times in the past few years I have asked such complainers for specifics, and remarkably I have gotten a reply ~4 times. In all but one case, when I went to investigate further it turned out that they were clearly in the wrong. In the last example there was a misunderstanding and I fixed the issue. If you want to provide a specific article and error, I'm happy to go take a look.

Alternately, when people run into an unresolvable dispute on one local article talk page, they can seek opinions from wider groups of Wikipedia editors, e.g. on the math "wikiproject" talk page https://en.wikipedia.org/wiki/Wikipedia_talk:WikiProject_Mat.... If you make a post there about your issue, you will get more eyes on your problem, and it will likely be resolved correctly.

Sanger was originally hired to edit Nupedia, a web encyclopedia project with a strict peer review process, and only worked for Wales for about a year. Wikipedia was started as a side project (with Sanger contributing to the concept and some early organizing), but Wikipedia quickly became much more successful while Nupedia basically never got off the ground. My impression is that Sanger wanted to impose his own vision on Wikipedia, but couldn't because the community of volunteer editors disagreed, and when Wales stopped paying him as a full time Nupedia editor (Wales's company was tight on cash at that time), he stopped any involvement. This was long before most of the actual work of Wikipedia happened, and that should have been the end of the story.

But ever since, Sanger has been trash talking Wikipedia as a project and community ("broken beyond repair") and trying to undermine it. A few years later he started a competing project (which was predictably a total failure). For two decades he has been promoting himself as "cofounder of Wikipedia". Interviewer after interviewer asks the same lazy questions about the subject, without ever adding any new insight. (You can see that Sanger's ghost is chasing Wikipedia even into this discussion.)

It's beating a dead horse, and entirely off the topic of what the interview was supposed to be about. Answering the question clearly and accurately takes a lot of time and finesse, which is wasted on the interviewer and most of the audience. Wales clearly screwed up in that interview, but it's not hard to see where he's coming from, psychologically.

The articles about Fourier series and Fourier transform currently begin with:

> A Fourier series is a series expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series. By expressing a function as a sum of sines and cosines, many problems involving the function become easier to analyze because trigonometric functions are well understood.

and

> In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input, and outputs another function that describes the extent to which various frequencies are present in the original function. The output of the transform is a complex valued function of frequency. The term Fourier transform refers to both the mathematical operation and to this complex-valued function. When a distinction needs to be made, the output of the operation is sometimes called the frequency domain representation of the original function. The Fourier transform is analogous to decomposing the sound of a musical chord into the intensities of its constituent pitches.

It's extremely difficult to write math articles for a general audience which are both accessible and accurate, and the number of excellent writers working on Wikipedia math articles is tiny.

Please get involved if you want to see improvement. There are some math articles which are excellent: readable, well illustrated, appropriately leveled, comprehensive; but there are many, many others which are dramatically underdeveloped, poorly sourced, unillustrated, confusing, too abstract, overloaded with formulas, etc.

There are some flowers which produce tiny amounts of caffeine in their nectar, apparently to give the pollinators a buzz.

> What is this [Greek notation] about?

The Greeks "notation" was a diagram full of points labeled by letters (Α, Β, Γ, ...) with various lines connecting them and a list of steps to do with an unmarked ruler and a compass, some of which added new points. But those tools alone can't be used to describe cube roots of arbitrary numbers (or, equivalently, trisections of arbitrary angles).

> What is this [statisticians' function]?

The integral of the bell curve (normal distribution) is called its cumulative distribution function (CDF). The CDF of the normal distribution is closely related to a special function called the "error function" erf(x).

> Is there a good intro to [the symmetry interpretation of the quadratic formula]?

There's some discussion at Wikipedia's article about the quadratic formula: https://en.wikipedia.org/wiki/Quadratic_formula#By_Lagrange_...

> foreign government maintain 40 colonies within your boundaries with ~200,000 of their colonists?

Instead of speaking in riddles, can you be more explicit? Which foreign government are we talking about, and who are "their colonists?"

> no other war [besides WWII is] ever used to belittle and degrade any other people [than Germans]

This is an absurd claim.

How many do you think were killed then, over those centuries of conflict? Several hundred thousand? What if we include deaths due to famine? How many were forced to migrate? Also several hundred thousand?

As I said, I'm not an expert; and you are right, it's not easy to find good sources for numbers about this. As far as I can tell were quite a few individual events with tens of thousands of people killed at a time. There were hundreds of recorded major battles.