Mind Blowing Facts

I happened to read a short paper/essay by a mathematician who cares deeply about this kind of thing (I don’t, particularly), who argued that the belief that repeatedly exponentiating a natural number gives you a natural number is “just that, a belief”. More broadly he took issue with the successor function, arguing, I think, that a “completed” infinity—that is, an infinite object that you can somehow study all at once rather than viewing it as a process or as something that continues—is a concept we should be concerned about.

In that vein, some people studying the foundations of mathematics consider very large (i.e. massively, wildly infinite) cardinal numbers and have amusing names for them:

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Interesting… I think you get this kind of indescribability already with the Ackermann function, which in the general case can only even be written in terms of itself, it’s kind of an object without any sense, one that can only be approached through formal properties. Descartes would have loved it. Anyway I’ll have to think some more about shrewdness. Transfinite stuff in general already boggles my mind :wink:

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My only connection to the Ackermann function is this very cute idea of Hercules vs the hydra, which I know of via its occurrence within group theory, but this article seems like a nice explanation of the idea.

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I find myself sympathetic to but not terribly passionate about a position, related to intuitionistic logic, that I’m probably mischaracterizing as “a proof needs to be computable to be sensible - a proof is a program, and that program had better terminate, preferably in polynomial time”.

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More depressing than mind-blowing :crying_cat_face:

(the US pet tiger population is almost double the world wild tiger population…)

Decided I’d post here rather than Joy in Pictures.

I’ve never watched It’s My Turn (I’m told it’s not a good romcom), but I do love that this scene gives a totally correct proof of the Snake Lemma. Given Hollywood and that relatively few people would have noticed had the math been wrong, I suppose that squeaks in as mind-blowing.

Since we are, in fact, “addressing ourselves to the cohomology of groups” on Monday and hopefully on-and-off thereafter I decided I wanted a set of notes to refer back to when I get rusty, so I made one. Mostly I wanted an excuse to show off how pretty the diagram is xD

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Butter is a milkshake.

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*creamshake.

(Sorry)

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Belva Lockwood was an American badass who made several major gains for women in the law, professions, and education. She was also the first woman to legitimately run for president, in 1884 as a member of the Equal Rights Party. Even though several newspapers refused to advertise her candidacy, and there were reports of states tearing up ballots that voted for her, she officially won 4,149 votes. It’s not in the Wikipedia article on her, but in a petition to Congress she claimed that the electoral college of Indiana changed their vote to be for her after initially casting it for Grover Clevland.

She wrote an article titled How I Ran for the Presidency in this issue of The National Magazine in 1903 (begins on page 728). Very cool to read about it in her own words, and it includes her nomination and acceptance letters, as well as a copy of the petition to Congress asking that they acknowledge her full count of votes.

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This is the most mind-blowing thing I have discovered this year.

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There exists mathematical constants which are uncomputable (ie Chaitin’s constant) — they are definable (they fulfill a certain equation and can be shown to exist), but cannot be determined (there cannot exist a procedure to uncover its value).

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The singular of “spaghetti” is “spaghetto”, i just learned today

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in fact, “most” numbers are like this, in the sense that the computable numbers are countable and thus have measure zero (roughly, take up no space) in the real numbers!

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https://www.mathsisfun.com/geometry/ellipse-perimeter.html

“Rather strangely, the perimeter of an ellipse is very difficult to calculate !”

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Effects can easily sound like pasted-on gimmicks that tend to get dated with time.

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Hey I knew that! :grinning:

The plural of pizza is pizze.

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Va be…con 20caractere di

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Yeah - graffito, panino… English has a pretty loose history of taking Italian plurals and making them either singular or a non-count noun

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At Seattle coffee shops people always ask for “a biscotti.” Saying this would kill me a little inside. But saying “a biscotto” earns me nothing here except either a blank stare or a medal for pedantry. I was ready to swear off these tasty treats until I found the workaround: “I’ll have one of these biscotti.”

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Maybe no minds will be blown, but:

“emoji” comes from adding “e-” to “moji” - the word has nothing to do with emotions or emoting.

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