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Mathematical Jargon Failures (plover.com)
111 points by weinzierl 18 days ago | hide | past | web | favorite | 71 comments

> That's right, ellipses are not elliptic curves, and elliptic curves are not elliptical. I don't know who was responsible for this idiocy, but if I ever meet them I'm going to kick them in the ass.

The referenced Wikipedia page contains a perfectly valid explanation for the term "elliptic curves", and a little googling reveals that it was Legendre who's responsible for "this idiocy".

Well, if I ever meet this Legender guy, I'm gonna kick his ass.

You can tell him I said that.

Well, he's dead, so there's that.


Not to disciples of Noah Webster. (-:

Legendre-y pokémon

Just in case somebody else wonders about a reference, its here: https://en.wikipedia.org/wiki/Elliptic_integral -- as the WP page on elliptic curve says: "An elliptic curve is not an ellipse: see elliptic integral for the origin of the term."

The confusing fact which Mark Dominus means is however, probably the fact that the term "Elliptic curve" seems to be a merger of the name "algebraic curve" and the defining equation

     y^2 = x^3 + ax + b
which is however not the defining equation of an ellipse. That would be instead, in its simplest form

     1 = (x/a)^2 + (y/b)^2
That's in fact confusing.

The Type I and Type II errors is especially hurtful to me: I am totally unable to remember which is which and each time I read an article containing them I think: well, I am probably going to get it wrong again but I cannot bother to check the definition one more time... who cares?

You know the story of the boy who cried wolf? The villagers committed several type I errors first, and then a type II error second.

(Yes, the terminology is stupid and should be changed. But as long as we're stuck with it, this helps.)

Wonderful mnemonic, thank you!

I don't understand why they need to be numbered at all. What's wrong with "False Positive" and "False Negative"? They even take less time to say.

I have trouble with those too: they're a composition of false/true with positive/negative to denote whether a finding of yes/no is right/wrong, but I can never remember whether false/true corresponds to yes/no or to right/wrong.

Just say things like "right yes" or "wrong no" and I'll understand. The only problem with that way of speaking is that it doesn't sound fancy.

> Just say things like "right yes" or "wrong no" and I'll understand.

OK. So s/false/right/ and s/right/true/ and s/negative/no/ and s/positive/yes/.

Does that work for you? Positive and negative are about the outcome of the test - did it report whatever or not? True and false are about if this result corresponds to reality or not.

It might just be me, but "wrong yes" sounds like it's claiming something very specific about the test. It's claiming that test said something was present and it wasn't. It's possible that this might not align with how the test works. Calling it a false positive would seem to make it clear that it's positive from the test's perspective.

But I may be wrong! This is clearly just opinion.

I'm not sure I get what distinction you're making. Are you saying that the standard terms don't commit to what we mean by a test's positive/negative, and this generality is more valuable than concreteness? It would be bad to imply too generally that we're talking about a test that says yes or no, a thing is present or absent?

I'm saying that in my opinion, the standard terms are pretty clear and yes or no create exactly the kind of confusion you're hoping to avoid.

Huh. Positive and negative are sort of notorious in medical tests for creating a confusion: positive is often bad!

There are actually three dichotomies here: was the test mistaken, what was its boolean value, and which boolean value means which thing in the world. Saying yes/no still requires a decision about the latter; though it seems clearer to me about this (both the need for interpretation and on suggesting a default), but it is subjective. And of course, any of these are better than Type I/II.

I do kind of insist that right/wrong or correct/mistaken clearly means the first question, where true/false is more ambiguous. To really resolve things maybe a better idea is like wrong/present and right/absent.

I've found that the pronunciation of English tends to dissociate the words "positive" and "negative" from their proper meaning, which has led to all sorts of misuse of the words. The following pronunciation isn't 'correct' English pronunciation, but try 'mispronouncing' it that way a few times (out loud) and see if that flips a switch in your head:

Po‑si–t—ive & Ne‑ga–t—ive.

po‑si–t—ing & ne‑ga–t—ing.

Po‑si–t—ed & Ne‑ga–t—ed.

Po‑si–t—ive‑ly & Ne‑ga–t—ive‑ly.

Gives a whole new meaning to the idea of 'positive' and 'negative' numbers, doesn't it?

> Just say things like "right yes" or "wrong no" and I'll understand.

Those have the same problem, don't they? I think you think you're replacing the positive/negative with right/wrong, but you're actually replacing the true/false. So, if you get a "wrong yes" result, is that "yes" supposed to be a good or bad thing? It's still ambiguous.

Maybe "true good" or "false bad" are better...

Then again, if both results are neither good or bad, then which is which? Maybe true/false positive/negative is indeed the less ambiguous. You just need to be clear on the question that's being answered. "Is there cancer?" "positive" means yes, "negative" means no.

We'd have to poll people to really know which terms are more easily remembered.

But here's how I'm thinking of it: a test says yes or no: is the thing present or not? And right/wrong is the correctness of the test. I can't see people easily getting confused and thinking "wrong yes" means that a test correctly said that the thing is not there. Anyone would think it means that the test incorrectly said the thing is there (among all the four possible meanings we're concerned about). OTOH false and negative could each more easily mean either wrong or absent.

But I may be wrong! This is only my best proposal.

In particular when one could just call them "false acceptance of null" and "false rejection of null", and abbreviate it to FAN and FRN, or so. How hard is that.

False {posi,nega}tive Type II? error

just 2 chars...........

Same here, and some definitions named by people's names. I totally understand the need to attribute and respect people's work, but a more descriptive name is almost always easier to remember and talk about.

This one at least has the justification that there often aren't any words. When you're hip-deep in topology, grabbing graph theory with your right hand and algebra with your left, you've left English way behind anyhow.

Now we just need to go back in time and convince Euler and Grothendieck to pretty-please either discover fewer things, or change their names every couple of years or something.

How about including given names with everything named after one of the many Bernoullis?


Descriptive names, even when possible, translate very poorly to other languages.

I remembered them like this:

Type I: True -> False Type II: False -> True

Meaning something was True (H_0) and our results say it's False (Reject H_0), and vice versa.

The concepts and numbers and letters describing them are perfectly ordered.

  H0        H1
  alpha     beta
  Type I    Type II 
Because error is negation of truth, you get H1 result with Type I error.

You say this as though it were helpful.

Too late to edit the above, but this reminded me of the infamous in-joke about category theory use in Haskell: "A monad is a monoid in the category of endofunctors. What's the problem?" [1]

[1] https://james-iry.blogspot.com/2009/05/brief-incomplete-and-...

They interviewed one of the Rust main guys for Linux Format a few years ago. I think he said the exact same thing lol.

On another note, I think I just met someone with both a power systems and functional programming background today. Small world :).

One I hate is sin^{2}(x) meaning "sine squared" and sin^{-1}(x) meaning "the inverse of the sine function".

A nicer, consistent interpretation would be to take sin^2(x) to mean sin(sin(x)) and keeping sin^{-1}(x) as an inverse.

Idk why people dont just keep the exponents after the function as is already the general convention. Sin^{-1}(x)^2 Sin(x)^2 This one annoys me because it's so preventable.

I'm glad to see I'm not alone in my desperation over the fact that names in math don't always mean what they seem to mean. Intelligent programmers have noted more than once that naming things is one of the greatest challenges. In hindsight, it shouldn't be too surprising that math suffers from the same difficulty.

Oh yes. I've a book on dynamic programming (Applied Dynamic Programming, Bellman + Dreyfus, seriously over my head unfortunately) which uses missionaries, cannibals and a boat to cross a river (page 97). The authors talk about M cannibals and N missionaries. Note again: he used the letter M for cannibals, not the missionaries, which I note start with that letter. And he could have called the cannibals C but, no.

I literally can't understand what mental process led them to do this, or not realise.

Another thing I detest is mathematician's fear of brackets. They'd rather use a tower of unstated precedences than just bracketing the fuckers. Fine, I suppose, if you know the subject but I was trying to learn something recently, something with quantifiers and implications nested densely, and was left mentally bracketing the various subexpressions to (try to!) work out what was meant. If I have to fight the syntax I'm already being blocked from understanding the semantics.

Mathematicians really do make things hard sometimes.

Thankfully us programmers are so much better (sarc)

Ah yes, you reminded me. There was another piece of jargon I was trying to come up with that really stinks earlier, but I couldn't remember it. And that's what it was: dynamic programming. Terrible name:

"Where did the name, dynamic programming, come from? The 1950s were not good years for mathematical research. We had a very interesting gentleman in Washington named Wilson. He was Secretary of Defense, and he actually had a pathological fear and hatred of the word research. I’m not using the term lightly; I’m using it precisely. His face would suffuse, he would turn red, and he would get violent if people used the term research in his presence. You can imagine how he felt, then, about the term mathematical. The RAND Corporation was employed by the Air Force, and the Air Force had Wilson as its boss, essentially. Hence, I felt I had to do something to shield Wilson and the Air Force from the fact that I was really doing mathematics inside the RAND Corporation. What title, what name, could I choose? In the first place I was interested in planning, in decision making, in thinking. But planning, is not a good word for various reasons. I decided therefore to use the word “programming”. I wanted to get across the idea that this was dynamic, this was multistage, this was time-varying. I thought, let's kill two birds with one stone. Let's take a word that has an absolutely precise meaning, namely dynamic, in the classical physical sense. It also has a very interesting property as an adjective, and that is it's impossible to use the word dynamic in a pejorative sense. Try thinking of some combination that will possibly give it a pejorative meaning. It's impossible. Thus, I thought dynamic programming was a good name. It was something not even a Congressman could object to." - https://en.wikipedia.org/wiki/Dynamic_programming#History

A Congressman may not be able to object, but I do! It's a particular flavor of recursion, and perhaps a flavor of the term "recursion" would be called for, but "dynamic programming" is essentially meaningless. Any addition meaning that phrase may have in your head is almost certainly unrelated to what the term refers to, since we've used "static" and "dynamic" in all sorts of ways since the 1950s.

Heh. That quote is from Richard Bellman. Same guy who was one of the authors of that book I'm criticising.

But please allow me to disagree with you. The term programming/programme predate programming as we know it, and he was free to use it in the sense of 'scheduling', much like a radio or TV schedule. The dynamic also makes sense as the schedule (or whatever) picks its next state depending on a previous/simpler state (hence a 'stage' in multistage, though I can't understand his use of 'time-varying' here). I think it's ok.

I'd rather punch mathematicians who won't bracket over mathematicians who try and protect themselves and their work from over-powerful, deeply stupid people.

i, j, k, l, m ,n suggest that this problem is concerned with an integral number of cannibals and missionaries. Usually these letters are assigned in the order of occurrence. If cannibals were introduced first and missionaries second it would be unnatural to assign missionaries an m. Further a c for cannibals would be counter-intuitive because c is often used for constants.

> Mathematicians really do make things hard sometimes.

Hard for non-mathematicians for sure, hard for themselves often enough too; but not this time.

1, 2, 3... have a natural ordering.

a, b, c...i, j, k...z do not. Alphabetical ordering is convention and no more than that.

To say, let's apply this convention to a problem to which such an ordering has literally no relevance, and ignore their value as a mnemonic, is bizarre beyond my comprehension.

I suspect some ultra smart people like Bellman, and possibly you, can attach completely arbitrary labels to things and immediately use those. I suspect that's what happened here. But I can't, and I'm pretty sure most people can't. To us, it helps greatly if the label has some relationship to the thing labelled

I think programmers care about names more than mathematicians.

Part of that might be the ages of their respective fields (if I wanted to rename "bubble sort" to "triangle sort", I would only be influencing something like 50 years of established work, whereas if you wanted to change the notation we use for derivatives, that's 400ish years).

Part of it might be the relative proportion of time we spend grappling with syntax versus the conceptual domain. While programming languages themselves don't require that much learning, we still need to learn others' APIs etc. Especially in the absence of documentation, good names are extremely valuable. But math is super documented, and most of the thinking can be done in relation to domain concepts without too much regard to syntax. I am guessing that makes good names comparatively unimportant to them.

"Cobordism" is actually more descriptive than he thinks, but it is French derived. "bord" means edge or boundary and a cobordism is something which connects two boundaries.

I can see the point, but I don't think it's a problem as long as the concept is well-defined. It's only a matter of getting used to don't assume, for example, "open" and "closed" to be mutually exclusive. There are other fields that don't have the privilege of this formal setting: I expect the concept of "species" to be very important in biology, but there isn't a clear definition of that (yet) [0].

[0] https://en.wikipedia.org/wiki/Species#Definition

The problem is that it requires extra mental effort for zero benefit. For example if I tell you that cos(x) is a symmetric function and sin(x) is antisymmetric, the meaning is far more obvious than if I tell you one is odd and the other is even. It costs you time looking the words up and energy remembering them.

Species doesn't have an exactly bounded definition because it is not an exactly bounded thing. It's like trying to define "life". This doesn't really have anything to do with bad jargon though so I'm not sure why you brought it up.

It can prevent the concepts from being used outside of experts in a particular academic field. A personal computer's "file system" is a nice concept tech-illiterate people can understand and use, and it's unquestionably proven a useful metaphor. Even though it falls apart in certain cases, it works pretty well for most.

A confusing vocabulary kills the curiosity of casual observers — those who'd gain the greatest joy from seeing how seemingly separate concepts coalesce.

The world is an endless adventure in ever-expanding tendrils of interest, if not gated by rote.

The referenced article, https://blog.plover.com/lang/jargon-failures.html, on jargon failures is a nice read as well!

IT is full of jargon as well. Where else would it make sense to cherry-pick commits into a branch and then ask others to pull that branch into their repository? :)

My German team has a running gag where, when a sentence turns out especially jargon-riddled, we translate all the jargon words into German, as literally as possible. The result is always hilarious.

Sometimes IT and biology share some jargon, or at least they share the words but not exactly the meaning.

Both in IT and biology a collection of trees is called a forest. In IT, if you take a tree and remove the root, the result is a forest. Biologists don't agree.

Don't forget the nut metaphor.

* https://superuser.com/a/329479/38062

By the way, did you know that broad-leaved trees are infinitely large during winter? The proof is really easy to do for yourself: In winter, those trees don't have any leaves, so all nodes must be inner nodes, and you can easily show by induction that the height of the tree must be infinite.

Well, the biological angle kind of makes sense if you think of it as taking the branches from a big tree, without the roots and successfully planting them in the ground individually. It doesn't quite work that way in practice, but if it did, you would get a small forest.

> In IT, if you take a tree and remove the root, the result is a forest. Biologists don't agree.

Unless it's Pando:


> Often brought up as an example are the topological notions of “open” and “closed” sets. It sounds as if they should be exclusive and exhaustive — surely a set that is open is not closed, and vice versa? — but no, there are sets that are neither open nor closed and other sets that are both

For a rant on this see "Hitler Learns Topology" [1].

[1] https://www.youtube.com/watch?v=SyD4p8_y8Kw

That video is funnier than it had any right to be.

In spherical coordinates, the Physicists use Phi for the azimuthal angle, and Theta for the equatorial angle. While the mathematicians use the opposite. That was always fun trying to switch between for the various classes.

Additionally, the physicists use 'i' for electrical current, while the electrical engineers use 'j'. Again, very fun trying to remember what is what during finals week.

>Additionally, the physicists use 'i' for electrical current, while the electrical engineers use 'j'.

Sir William Rowan Hamilton would like to have a word with you. I think he mumbled something about some bridge or something?

Oh Jesus. Yes, then you have quaternions and octernions.

Never mind all the indices of Taylor Series.

The most beneficial thing that Einstein ever did was getting rid all the Sigmas. He did other things too, of course, but nothing really compares.

Even and odd functions don't form a partition of the space of all functions, but they do span it as a vector space. What's more, the vector space of functions is the direct sum of the even and odd functions: every function has a unique decomposition as a sum of an even and an odd function. So the problem there is that vector spaces don't behave the same way as sets.

I find the terms eigenvector and eigenvalue to be especially opaque, it does not give any hint as to what it means at all to me.

The general case of eigen-things has no other term to describe it. One might want something that hints at the geometrical meaning of eigen{values,vectors} when they learn about them in the context of multiplying vectors by matrices, but ultimately the concept is a mainly algebraic one. Accepting this it becomes easy to deduce what should be meant by "eigenfunction of the differential operator". So I think, somewhat retroactively, "eigen" is the best word to use there.

A field of sets is neither an algebraic field nor a collection of sets.

A wonderful related talk and discussion: https://news.ycombinator.com/item?id=15473199

The function f(x)=1/x is continuous, but its graph is not connected. It's an interesting one to explain to people.

You've edited your comment so many times my other reply just gets more and more off-topic lol

Wait what? I thought f(x) = 1 / x is continuous iff x != 0 since 1/0 == undefined.

Few things bother me more in life than the prevalence of Pi over Tau

I wonder, could a font have a ligature for the sequence "2π" that rendered it as τ?

Amen, brother!

(I am the author of The Tau Manifesto.)

I love you, I really do

That manifesto should be on the front page of the NY Times

lol, my cat needs clopen doors all day...

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