jacobolus

Grandmasters absolutely make mistakes, and you could learn to notice them with a few months of guided practice.

For a low-discrepancy sequence you are usually trying to generate one point at a time, up to some arbitrary number. Here the goal is to generate (roughly) a specific number of points that fill a whole region.

So you probably could figure out a way to use this method to make a low-discrepancy sequence but it's probably not going to be particularly suitable compared to alternatives.

Also fun: https://observablehq.com/@jrus/spheredisksample

Folks may find https://observablehq.com/@fil/poisson-distribution-generator... useful

That's not at all about fine detail, but is about relative amounts of absorption/reflection of the light between skin vs. vein.

See https://en.wikipedia.org/wiki/Metamerism_(color)

People always feel like that to a certain extent, but both quantitatively and qualitatively there have been very dramatic shifts in the past few decades in the USA.

I'd recommend reading the Federalist Papers. A large number of them are more or less explicit warnings that Trump-style actions and attitudes should not be tolerated, and explanations about how they should be prevented and countered.

The Federalists were extremely familiar with the way monarchies functioned, spent a lot of time thinking about government strucutre, and the US presidency was quite explicitly set up to be something else.

If the leaders of all of our institutions decide to shrug when the president treats national powers as a tool for organized crime, and voters don't do anything about it, that's a people problem, not a problem of institutional structure. Any institution is only as powerful as our collective willingness to support and protect it.

Politics doesn't work if a significant part of the leadership is constantly acting in bad faith, and behaving essentially sociopathically.

Voters' and citizens' (and some judges') willingness to support sociopathic behavior by leaders is a profound failing at their basic social duties, and is deeply shameful.

The so-called "Tea Party" was not a "populist movement". It was a billionaire-funded (notably by the Koch brothers, but also by fossil fuel and tobacco companies) astroturf operation.

This is one variant of the 3-d analog of the "shoelace formula" for area:

https://en.wikipedia.org/wiki/Shoelace_formula#Generalizatio...

The 2-d version is from the 18th century. I'd expect the 3-d version was probably known in the 19th century, but I haven't searched for a reference.

Some authors use a ton of dashes, while others never use dashes.

Spaced en dashes – like this – are a correct and accepted typographical choice. Whether to use spaced en dashes or (spaced or unspaced) em dashes is a matter of taste or local convention, and varies from one publication to another. Other than a typo or two where the space was left out on one side of a dash, the dashes in this linked document are just fine. See https://en.wikipedia.org/wiki/Dash#En_dash_versus_em_dash

It sounds like you want a return to a time before a lot of the government research money coming to institutions like MIT was gutted.

That's why they didn't design an entirely new font. Instead they made semi-automated modifications to a free font, and then tweaked a few specific characters afterwards.

The result is not as good as what they had before, and not as good as it would have been if they hired a professional to design a new font from scratch, but it was cheap and solved their problem.

There's no inherent issue with it. It just requires doing a bunch of additional design work, which is not free.

You are misunderstanding. The Nebula people were previously using the Whitney typeface. The organization that produced/sells Whitney changed ownership and the licensing became prohibitively expensive overnight.

They wanted something that could be a drop-in replacement for Whitney with the same letter sizes and spacing, so that they could put it into all of their products without needing any other redesign.

They couldn't find anything like that available off the shelf, and fonts they found that were close to Whitney in appearance were still also somewhat expensive, so their alternative was to take Source Sans, which has a free license, and make some quite significant but semi-automated modifications to it.

Making changes to just the typeface was presumably cheaper than making changes to all of their other designs.

From your OCW link, you can see the Spring 2006 version of the course has syllabus, lecture notes, readings, lab assignments, and 2 quizzes available, but no videos. Separately, videos of the 2020 version of the course are on YouTube: https://www.youtube.com/playlist?list=PLrw6a1wE39_tb2fErI4-W...

This use of "logging" comes from the "logbook", a book recording what happened on a ship, which was called that because a literal log (i.e. part of a tree) attached to a rope was used to measure the ship's speed.

See:

https://en.wikipedia.org/wiki/Chip_log

https://en.wikipedia.org/wiki/Logbook_(nautical)

In the modern computing context, "logging in" does involve adding entries to a kind of (digital) record-keeping tool.

Some OCW courses have lecture videos, while others do not.

Personally I like books, but there are also many, many lecture videos on YouTube, some of them excellent (though I think they could still be better with bigger production teams and higher budgets). For college-level technical subjects, there are also e.g. many MIT lectures on OCW. If you have a specific topic in mind, I urge you to search around. (Making a long list of my own book/website/video recommendations about various topics here seems a bit off topic and out of scope.)

I don't have a problem with Khan's site existing, but it's disappointing that often answers to requests for learning materials/ideas begin and end with Khan Academy. My personal opinion is that Khan's videos are roughly comparable to an average-quality classroom teacher lecturing about a typical mediocre curriculum.

They have some significant advantages compared to (just) a classroom: (1) They set a quality floor – sometimes a teacher can be really incomprehensible, or mean, or whatever, but Khan's videos are consistently okay. (2) They are available from anywhere, without need for special social/technical infrastructure, like enrollment in school or access to a university library. (3) They are self paced, which means they can better accommodate the various interest level, motivation, and speed of different students. (A typical classroom also has some advantages: it gives social setting, a consistent schedule/structure, and human feedback.)

I'm also disappointed though, because it seems like, given production resources, there would be potential to make widely available materials that were much better than average lectures. With significant production effort (a team of subject experts and content creators doing a lot of dedicated work on each topic) I think it would be possible to make something truly great, but Khan's videos fall so far short of my imagination. For any particular topic, there are typically other freely available resources which I think are better.

I've also been disappointed because many people have hyped the site as being extraordinarily amazing, but when I have looked at it, what is there doesn't match the hype.

For what it's worth, the linked article has only en dashes. (I have no idea whether LLMs use en dashes.)

> The radians became popular in the 19th century

Something akin to radians was widely used in ancient India. That is, sine tables constructed for a circle with circumference 360·60 (angular minutes) and radius 3438 ≈ 360·60/2π.

In Europe, radians per se developed in the early 18th century. What is true is that the name radian came about in the late 19th century.

> trigonometric functions with arguments in radians are harmful

Trigonometric functions are not inherently "harmful", but they are sometimes cumbersome. Changing the units doesn't make all that much practical difference.

Avoiding transcendental functions in favor of vector methods is often a good strategy though, especially in code.

Dickens is full of extremely theatrical scenes. The characters are often a caricature, but the caricature is so finely drawn that it is tremendous fun.

(Nobody should be ashamed for having read or not read some work though, or for having enjoyed or not enjoyed one.)

For more: https://en.wikipedia.org/wiki/User:Jacobolus/HalfTan

You might enjoy the much longer and more detailed article https://en.wikipedia.org/wiki/Geodesics_on_an_ellipsoid which discusses the context.

If you want a single number (e.g. you are trying to serialize a lot of data), in many contexts you can replace the coordinates (cos θ, sin θ) with the stereographic projection h = tan ½θ = sin θ / (1 + cos θ). Converting back and forth between these representations is cheap and easy: cos θ = (1 − h²) / (1 + h²) and sin θ = 2h / (1 + h²).

The biggest problems were various supply shocks associated with the pandemic and its aftermath and the Russian invasion of Ukraine.

The Biden admin brought down inflation much faster than even optimistic economists predicted, while maintaining full employment and avoiding a recession. The US economy during that period significantly outperformed most other wealthy countries. (As one indicative example, the cover story of The Economist from October 2024 was titled The American economy: The envy of the world.)

Since then we've had a wide range of completely self-inflicted policy faceplants, including notably several rounds of illegal tariffs and a war with Iran.

I hate that people keep trying to add LLM spam to Wikipedia, imposing extra work on the volunteers trying to write articles. I hate that people keep posting LLM spam on social media sites that at some point in the past mostly consisted of human-generated comments. I hate that many students are now using LLMs to do all of their homework, resulting in a significant part of the next generation being incompetent at basic scholarly tasks and unprepared for more serious work. I hate that lawyers are using LLMs to write legal briefs, not bothering to check that their cited cases say something exactly the opposite of what their briefs say. I hate that government officials are using LLMs to write public statements that get basic facts wrong. I hate that graphic designers are losing their jobs because their bosses would rather "just use AI, it's cheaper". I hate that Google Search results are now overwhelmed with LLM-generated slop which ranges from dubious to outright wrong, and it's now much more difficult than it used to be to find the information I'm looking for on the open web. I hate that researchers are now publishing LLM slop in journal articles, making it significantly harder to tell the difference between careful scholarship and someone lazily phoning it in. I hate that friends and neighbors now ask ChatGPT as their first source of information about any topic and it frequently tells them something completely misleading or wrong, but they don't bother double checking.

Am I "ideologically motivated"? I guess, where my ideology is: I want to have myself and other people get accurate information, and I want people to actually do their work instead of trying to cheat their way out of as much of it as possible, no matter what the downsides might be.

The Antikythera mechanism is 4 centuries after Thales, during which time there was extensive additional study done by Greek astronomers. Evidence of old solar eclipse predictions seems pretty sparse; I can't figure out when the first successfully predicted solar eclipse was that we are certain about.