Wikipedia:Reference desk/Archives/Mathematics/2024 April 15

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April 15

Does anyone use the word "cathetus" anymore?

I'm trying to read this article translated from a 1934 article in Swedish by B. Berggren. The word "catheter" is mentioned several times, and I gather it should be "cathetus" meaning a leg, or side other than the hypotenuse in a right triangle. I don't think I've heard of a cathetus before, nor a catheter with reference to a triangle. Is this term still used by anyone now? --RDBury (talk) 20:25, 15 April 2024 (UTC)

It makes it into wiktionary: cathetus, but there are no quotations. This says it's fairly rare, but some prefer it over the term "leg". -- Jack of Oz ^{[pleasantries]} 20:47, 15 April 2024 (UTC)

Thanks. I've mostly heard and used "side", but that's wrong if you think about it; triangles have three sides. I didn't think to look at NGram Viewer before, but I did just now and it seems that "cathetus" had about a 10 year window of popularity between the mid-1920's and mid-1930's, but still only about 3% as common as "hypotenuse". Perhaps it's more common in Swedish. --RDBury (talk) 06:44, 16 April 2024 (UTC)

The Swedish Wikipedia uses it in its article on the Pythagorean theorem. It did not help the translator that in Swedish the form kateter is both the word for "catheter" and the plural of katet, which means "cathetus".  --Lambiam 06:14, 17 April 2024 (UTC)

1,000 random editors

There's a room with 1,000 people, each with a computer. Their task is to access Wikipedia, and click Random article, editing whatever they see needs fixing each time, before repeating the same process endlessly. They're well paid. They do this for 8 hours a day, 5 days a week, until they either quit out of sheer boredom, kill themselves, or ascend to some higher plane of consciousness.

What are the chances that 2 or more of the people could be editing the same article simultaneously, causing an edit conflict when the second or later ones press Publish? And how long might it take for the first such conflict to occur? -- Jack of Oz ^{[pleasantries]} 23:20, 15 April 2024 (UTC)

This is essentially the same as the birthday problem for a set of $n=1000$ randomly chosen people on a planet in which a year takes $d$ days, where $d$ is equal to the number of Wikipedia articles (currently 6,829,684). Assuming all are in the same time zone, working 9 to 5, the probability that any article is being edited simultaneously by multiple persons, using the square approximation, equals approximately

${\frac {n^{2}}{2d}}\approx {\frac {10^{6}}{2\times 6.813{\times }10^{6}}}\approx 0.073\,.$

A slightly better approximation is given by the formula

$1-\exp \left({\frac {n^{2}}{2d}}\right)\approx 0.071\,.$

How long it will take for a conflict to arise (assuming that all simultaneous edits are conflictual) depends on how long editors stay within the same article, which may be characterized by individual-dependent probability distributions and hard to impossible to tackle analytically. If they are synchronized, each editing one article per time slot in equal time slots, the expected number of time slots until conflict is approximately

${\frac {1}{0.071}}\approx 14.1\,.$

 --Lambiam 03:31, 16 April 2024 (UTC)

Thanks. The first answer is about what I expected. But the time till the first conflict is rather counter-intuitive. If the time slots were 5 minutes, that means a conflict would occur after only a bit over an hour. I don't question your maths, but that is amazingly short for such a huge database. Thanks again.

But then, I guess the number of editors does make a rather significant difference (* cough), since the number of possible conflicts with 1,000 editors in each time slot is half factorial 999, a number with c. 2,565 digits, and about 10²⁴⁸⁵ times the number of atoms in the universe. Compared to this, a mere 6-odd million articles is infinitesimally small, so having to wait an hour for a conflict does seems a bit tardy, on reflection. If it were only 4 editors, there are only 6 possible conflicts and the expected time would increase massively, to about 500 days. Very nice. -- Jack of Oz ^{[pleasantries]} 23:56, 16 April 2024 (UTC)

Yes, at first glance it is counterintuitive, which is why the problem in its birthday suit setting is also known as the "birthday paradox".  --Lambiam 05:41, 17 April 2024 (UTC)