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Irregular Math Gets Queasy

I was doing some research on a problem in algebra early this morning, and one thing led to another, and before I knew it, I was looking at a paper presented at the American Mathematical Society in 1972 with the purpose “to show that a complete, convex, externally convex metric space is generalized euclidean if and only if it has the euclidean symmetric isosceles queasy four-point property or the euclidean external isosceles queasy four-point property.”

Wow. Okay. Mrs. Washington never taught me that in high school.

I am calling out for help on this one. I tried to read the paper. Honestly, I did, but I can’t make heads or tails of it.

I need a mathematician to tell me:

What is the euclidean external isosceles queasy four-point property?

How is this concept actually used in math, and what are some of its applications beyond theory?

5 thoughts on “Irregular Math Gets Queasy”

  1. Tom says:

    Rowan: I believe your problem is not one of algebra but rather of abstract algebra. The former is taught in high schools the latter in college math and concerns such things as rings, fields and lots of terms like the ones you read about (isomorphism, Eigenvalues, etc). I took the course way back in the 1960’s, so it’s come a long ways since then, and I haven’t kept up with it, so I can’t help. Though theoretical in topic, applications are found every now and then (product design, machinery design, systems applications, physics, biology, chemistry).

    I laughed when I read your article, because that’s the reaction I had way back when I took the course – every day was like “WTF are we TALKING about?” You should also look at topology if you really want some head-spinning experience. The paper was interesting if you’re into theoretical spaces, lie-groups, and things like that, but this stuff wouldn’t even be on the normal persons radar and isn’t encountered in everyday life. I have no idea of a specific application for it either. Most of the words encountered have very specific mathematical implications and meanings that take some time to develop into everyday vocabulary, and most are not easily grasped by your average person. It’s like trying to talk about calculus to someone who’s never heard of it – kinda hard to get ideas across without some background or a LOT of development.

    i’d let it go, because any “explanation” will be mostly theoretical in nature and require YOU to come to grips with these weird terms and what they mean and imply. i’m not sure it will be worth your time.

    What was the original problem?

  2. Rowan says:

    If someone could even explain to me what makes “queasy” queasy in this context, I’d be much obliged.

    The original problem had something to do with slope and intercept. Not advanced. I was just led from one curious link to another, into a very strange land.

  3. Bruce Nappi says:


    If today was April 1, or you were writing an article for the Onion, I’d quickly get your point: what is the relevance of straightening up the deck chairs on the Titanic when the tipping of the ship makes some of them slide out of place? I assume this is just one of many thousands of studies of this kind that academia / society keeps funding, when our nation is crumbling because the media keeps using a measure of unemployment that doesn’t describe the true level of unemployment. Why doesn’t academia steer some of this math talent toward more relevant needs?

    I studied calculus in high school, plus 4 years in college. I became an MIT rocket scientist. Except for two very isolated projects, I never used it during a 30+ year career. So, what’s the justification for pushing such a specialized skill so hard on so many students starting with AP calc in high school, when 64% of STEM capable students graduating from U.S. colleges can’t find STEM related jobs? ( Right! 64% PER YEAR! Do some calculus on that and see what kind of tech worker surplus we’ve built up in the last 20 years! That’s why I wrote LIARS! (

    So let me throw out a relevant challenge. Avoid the subtlety of presenting an obviously absurd example hoping people will see it as absurd, and ask readers to provide examples from their lives of how relevant / irrelevant our education has been.

  4. Rowan says:

    Actually, Bruce, I really am interested in the answer. I want to know in what sense mathematics can be queasy.

  5. Bruce Nappi says:

    OK. I can buy that. It was just such a good opportunity to segue into the relevance of such obscure studies. Stay strong. Follow your curiosity.

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