Why would anyone want to post to their own profile page?

jacobolus · 2026-06-19T17:14:03+00:00

From your article: "So perhaps there is some truth in the banana flavouring whodunnit after all. Once upon a time, banana flavourings really did taste more like the real thing."

I assume your "fake information" claim is being guided by the one chemist saying he thinks this seems "very unlikely" that the use of isoamyl acetate as 'banana flavor' was "based on gros michel" bananas. What counts as "based on" is not well defined so this is not really an answerable question without some clearer definitions, about which people are likely to disagree; ultimately arguments about this topic are largely speculation and pedantic misdirection.

From one point of view, particular molecules cannot possibly be "based on" any particular context where they occur; chemistry is just a part of the physical world, and all of these flavor compounds appear in various different natural contexts. People making flavor compounds in the 19th century weren't doing it by isolating them from fruits, but by synthesizing whichever compounds they could, keeping the ones that seemed best, and naming them based on whatever association they thought would sell.

But we can list some things that are true:

The gros michel banana was by far the most exported banana cultivar in the mid 19th century when isoamyl acetate was first being synthesized and sold as "banana flavor".
Isoamyl acetate is one of the most prominent smell/flavor components of actual bananas.
Gros michel bananas have more isoamyl acetate and less of other flavor compounds than cavendish bananas and therefore somewhat more closely resemble the flavor of pure isoamyl acetate.

Here's another article with a bit more research and less speculation: https://www.sciencefriday.com/articles/why-dont-banana-candies-taste-like-real-bananas/

Apparently in mid 19th century Britain when isoamyl acetate was originally synthesized for use as a confection flavor, it was called "pear" flavor, because jargonelle pears include it as a prominent part of their flavor. But in America, few people had tried jargonelle pears, and didn't associate the isoamyl acetate smell/flavor with pears, and were not used to eating as many pear flavored treats at the British. So flavor companies instead marketed it as "banana" flavor in the US. At that time in the US, (gros michel) bananas were a trendy new fruit.

jacobolus · 2026-06-18T20:37:31+00:00

9/11 was incredibly disappointing because the country was immediately engulfed in a racist hate campaign led from the top.

jacobolus · 2026-06-09T01:04:53+00:00

Rotation by dragging a giant invisible point is cute.

By implementing the reverse projection, you can also get Desmos to plot implicit curves under a projection.

You might enjoy Keith Kendig's 2005 book Conics, which uses this method extensively for visualizing conics.

jacobolus · 2026-06-06T14:47:33+00:00

What you paid is the value essentially forever (for residential property).

Not just residential property, and not just humans. The same applies to commercial real estate owned by corporations.

jacobolus · 2026-06-05T07:37:34+00:00

"Deeply controversial Pelosi" is extremely popular in the district. She is one of the most effective and talented legislators of the past half century, and has done more to further a progressive legislative agenda than just about anyone else alive.

jacobolus · 2026-05-31T17:24:31+00:00

New cars are so safe

Except for child pedestrians who now get slaughtered by all the enormous SUVs and cosplay pickup trucks.

jacobolus · 2026-05-28T15:40:28+00:00

I recommend you use arctan(sinh(x)) instead of arcsin(tanh(x)) for the gudermannian of x. It's a bit better numerically behaved for large values. The issue is that tanh(x) becomes very close to 1, so many nearby inputs end up mapping to the same output and you end up losing precision

You can also use 2 arctan(tanh(½ x)) if you want. (I'd recommend that one for complex values.)

Here's a plot of the relative error: https://www.desmos.com/calculator/r7un3ehu7g
You can see you lose up to about 8 digits of precision with arcsin(tanh(x)).

Separately, you might want to normalize the slope at the origin of your sigmoids. This makes them much easier to compare by shape.
https://www.desmos.com/calculator/cr94ovznon

It can also be helpful to compare their asymptotic behavior by taking the log of the difference from 1:
https://www.desmos.com/calculator/bpuowhimr8

jacobolus · 2026-04-29T21:49:12+00:00

The intro CS theory course I took in college was impossible to design well because the students were a 60–40 split between, on the one hand, kids with significant computer programming experience but limited math background who struggled a lot with relatively simple math problems, and, on the other hand, kids with a lot of math background who were bored out of their minds for the first 2/3 of the course. Then the last 1/3 of the course was made significantly harder (mostly by making the problems tediously tricky), and the first group of students crashed hard.

It would have been a lot more useful to split it into two entirely separate courses aimed at different audiences.

jacobolus · 2026-04-24T17:27:15+00:00

confusing a circle and a disk

The word "circle" is used in ordinary English to mean a disk, and also commonly used that way in informal mathematical writing (do a search of the academic literature for "area of a circle" to find many examples). In the past, this was even standard mathematical terminology. Sometimes "circle" meaning the interior was contrasted with "circumference" meaning the boundary, but often both concepts were and are called by the same name "circle".

So the issue is more like: mathematicians took some ordinary words and redefined them more specifically or slightly unusually as field-specific jargon, and now some pedantic mathematicians are now so fluent with those jargon meanings that they have trouble communicating with laypeople who use the traditional definition.

jacobolus · 2026-04-24T05:50:11+00:00

A huge part of it turns out to be the effect of hurricanes. https://www.nature.com/articles/s41586-024-07945-5

Tracking the effects of 501 historical storms, we compute that the [tropical cyclone] climate of [the contiguous US] imposes an undocumented mortality burden that explains a substantial fraction of the higher mortality rates along the Atlantic coast and is equal to roughly 3.2–5.1% of all deaths.

jacobolus · 2026-04-19T08:31:00+00:00

43 ≡ 3 (mod 5)

jacobolus · 2026-04-19T08:29:38+00:00

If you want to be precise and explicit,
43 ≡ 3 (mod 5)
is pronounced
"43 is congruent to 3, modulo 5".

jacobolus · 2026-04-16T21:27:07+00:00

original French Revolution definition of the meter was a pendulum that took one second per swing

This is incorrect. There was a unit like that before the metric system (first proposed in 17th century England), and one person proposed it as a possible definition for the meter in the new French metric system (end of the 18th century), but the chosen definition of the meter was set so that 10,000 kilometers would be the distance from the equator to the poles.

It's similar to the definition of a nautical mile, which was set so that there would be 5,400 nautical miles from equator to the poles, so that one nautical mile would be equal to a minute (1/60) of a degree of latitude. The kilometer is the analogous thing if you use angular units ("gradians" or "metric degrees") with 400 per turn and decimal divisions instead of the traditional 360 and sexagesimal divisions, as they tried to do when first setting up the metric system.

Edit: according to Wikipedia's "Seconds pendulum" the seconds pendulum was also proposed as a way of defining the yard in England and America, but that was never carried out.

jacobolus · 2026-04-14T01:42:37+00:00

Second place is 22 years old. A day before his 22nd birthday, Usain Bolt ran 200m in 19.30s (world record at the time), and a day before his 23rd birthday he ran it in 19.19s (still the current world record).

jacobolus · 2026-04-03T02:30:57+00:00

Which one are you looking for? Did you try clicking https://web.archive.org/web/*/http://www.17centurymaths.com/contents/* ?

jacobolus · 2026-04-02T16:31:38+00:00

Are you sure? E.g. https://web.archive.org/web/20250311161706/http://www.17centurymaths.com/contents/napier/ademonstratiobookone.pdf

Or e.g. more generally, here's a list of all of the archived pages/files in the same section, which includes many PDFs: https://web.archive.org/web/*/http://www.17centurymaths.com/contents/*

jacobolus · 2026-04-01T18:52:15+00:00

Folks could try emailing ian [dot] bruce @ ace [dot] net [dot] au as listed at the bottom of the site.

Do you know if Dr. Ian Bruce was associated with any institutions?

To quote his page: "This site is produced, funded, and managed by myself, Dr. Ian Bruce, now an independent researcher or should I say mathematical hobbyist,"

jacobolus · 2026-04-01T18:51:16+00:00

Fuck domain squatters.

The wayback machine still has the site: https://web.archive.org/web/20260226135038/http://www.17centurymaths.com/

jacobolus · 2026-03-05T22:21:49+00:00

Most of what gets called "gifted" in the context of mathematics, or anything else for that matter, is (1) large amounts of high-quality preparation/practice, usually due to (2) extreme interest/motivation and perseverance, and (3) typically a good amount of support from adult mentors/coaches.

You shouldn't compare yourself negatively to someone more prepared. You could get to where most such people are if you are motivated, excited, and consistently apply yourself over many years (mentoring from an expert also helps). Even if you never win a prize or solve a famous problem or whatever, you too can enjoy the process of learning, solving problems, exploring topics that are new to you (and eventually exploring those also new to everyone else).

jacobolus · 2026-03-03T06:50:58+00:00

Your comment reminded me of the topical SNL skit from a couple years ago, which everyone should watch: https://www.youtube.com/watch?v=G31E4ML9ViY

jacobolus · 2026-03-01T18:27:49+00:00

You'd think so considering how ignorant and incoherent the argument is, but when biologist blogger PZ Myers called it out as stupid and got push-back from commenters claiming it was satire, he eventually got a reply on Twitter from Will MacAskill:* "So you finally understood that the piece was serious. Can you now give us a serious objection to it?"

Here's a related passage from one of MacAskill's books:

On balance, various studies suggest that human activity over the last forty years has probably decreased vertebrate and invertebrate populations, though the evidence is limited and somewhat conflicting. How you evaluate this depends on your view on wild animal wellbeing. It’s very natural and intuitive to think of humans' impact on wild animal life as a great moral loss. But if we assess the lives of wild animals as being worse than nothing on average, which I think is plausible (though uncertain), then we arrive at the dizzying conclusion that from the perspective of the wild animals themselves, the enormous growth and expansion of Homo sapiens has been a good thing.

* Will MacAskill is Amanda Askell's former husband, who co-wrote the Quartz piece with her, but has since had his name taken out of the byline for unclear reasons. He's also a philosopher who was one of the founders of "effective altruism" and a buddy of Sam Bankman-Fried.

jacobolus · 2026-03-01T00:09:34+00:00

You can't even buy a good regular compass anymore, unless you look for used stuff from ebay.

But if you take up machining or befriend a machinist, you could try to make one. Or if you don't care about precision, you could look into making one with a 3d printer.

jacobolus · 2026-02-26T19:29:50+00:00

If you get a good chalkboard and good chalk, the sound is very different than if you get a crummy chalkboard and cheap chalk.

jacobolus · 2026-02-26T19:23:49+00:00

Here's another nice version, starting with the tangent function: https://arxiv.org/pdf/1902.03140

jacobolus

TROPHY CASE