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Dewi Morgan

Mathematical notation considered harmful.

Mathematical notation considered harmful.

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"Giant zigzag, sitting on two symbols separated by a scarab's butt." - The diagram is three lines high, and displayed as an image. What does it MEAN? How, using the tools available, can we find out?



It means:

FOREACH (o IN O)
x += f(o)

...which is still unacceptable. It's TERRIBLE. It would quite possibly get a programmer fired, but is considered perfectly acceptable for math professors.

Mathematicians think mathematical notation is acceptable in teaching. It is NOT acceptable, for several reasons.

1) It is not copy-pastable.
2) It is not searchable - Google is blind to these things: pasting in an omega will not give you what you want.
3) It is not linkable. So someone seeing a sum or union symbol has literally NO way of finding out what they mean. An arrow pointing to the right... what does that mean? This arrow has two bars. Hrm. Nope. I got nothing.
4) They feel it is sufficient to provide an explanation in these esoteric alchemical symbols; therefore many wiki pages are left incomplete, where otherwise an intelligible explanation might be given; thus they reduce the sum of human knowledge.
5) They choose the world's worst variable names. The above code is NOT acceptable. When they write programs, they write them with global variables 'a' through 'z', then start again at 'aa', 'ab' - this is not a rarity, it is a commonplace amongst math professors in most faculties. It is how they think: without clarity or any need to explain their workings.

eventProbability = 0
FOREACH (outcome IN eventOutcomeList)
eventProbability += probabilityOf(outcome)

Now that's getting closer to the right way to do it. Without esoteric one-letter symbols to represent things, you stand a chance of being able to see at a glance what is going on.

Mathemagical symbols were designed for writing quickly on blackboards. They are the WRONG TOOL for writing on computers.

"But Dewi, we have no better tool" - what, other than English, every other written language, and every single programming language? Well, if you're not willing to use any of those, then perhaps design a better terminology, then, and push for it to be accepted. But I can guarantee there is a clear and concise terminology in most programming languages to represent every one of those concepts, and that this terminology will at least be copyable, linkable, and searchable.

And don't cry that the terminology is unfamiliar and doesn't have global acceptance in the mathematical community: that is an EXCELLENT feature, for it will mean that you will link to somewhere that clearly defines all your symbols in the language of the rest of your article, and you will actually pick decent variable and function names, instead of arbitrary letters!

And in the commons: I'd be willing to bet that more people know C/C++ or PHP than know how to read math markup. There's a reason for that, and it's not because these people are stupid: it's because math markup is more user-hostile than C/C++!




[When I wrote this in a BoingBoing comment, I got the response "So how about a link to your clear and concise universal grammar/language that all can use to do everything. I personally know several gurus who would be totally willing to throw mad mad money in your (that/this) direction for such a solution to this very general problem. Seriously, dude, we're waiting."

However, I'm afraid that I have no intention of linking "English, every other written language, and every single programming language" - if a reader is unable to find references to these languages themselves, they should probably not be writing, period. But, as a hint: you want what we call a "dictionary". They've been around for at least 4,300 years, so you should be able to pick one up quite cheap. For what it's worth, "mad money" has already been spent on the development of these languages. They already exist, and are very well refined and capable of expressing any nuance you might imagine. They don't need further investment from "gurus".]
  • Mathematicians make up new words every day

    (Anonymous)
    I think it's pretty clear you don't do mathematics or know any mathematicians. Mathematicians *invent* new definitions on a daily basis, and the concepts are far more complicated and nuanced than you imagine. They honestly need to invent these new words because there is nothing existing to express what they're talking about. Part of the reason you don't understand that is because you're afraid to actually learn anything about mathematics before judging it as completely nonsensical. The problem is not the notation; a twelve-year-old can learn the notation. The problem is your ability to go outside of your comfort zone to learn something difficult and new.
    • So do programmers: we just do it better.

      I suppose I should respond to this anon, though it feels like they only read the title, rather than the post. Let's not make that same mistake, and instead address each point.

      > "I think it's pretty clear you don't do mathematics or know any mathematicians."

      Ad hom. Also takes the view that I am addressing the use of such symbols between experts in the field, which I think I very clearly am not, so also a little strawmannish.

      Also happens to be false. I'm a programmer: that means that math is a natural part of my life. But I don't call it "f(x)", I use "fourierTransform(signal);" or "quaternion.increaseYaw(angle);". Still some strange symbols, but next person to try to maintain my code would have at least a chance.

      > "Mathematicians *invent* new definitions on a daily basis, and the concepts are far more complicated and nuanced than you imagine."

      The same is true, to a greater extent, of programmers. However, where mathematicians value simplicity, economy, brevity, and terseness; we value readability above all.

      So when a mathematician needs something to represent an item contained within a set, he asks himself "which single symbol should I use for this?" and picks a arbitrary symbol and modifies it with a strike, dash, bar, rotation, or something he personally understands, but nobody else will until he explains it to them. So he picks a scarab's ass, and in his head calls it "element of".

      When a programmer invents a new definition, we ask ourselves "what's the best term to describe this?" We strive not to reuse terms. So if we have code to define a container, what should we call the thing contained? Object and item are already used. Containable? ElementOf? We will give this much thought: we won't simply call it 'o' and be done.

      "They honestly need to invent these new words because there is nothing existing to express what they're talking about."

      Firstly, upward-facing Scarab-butt is not a word, it's a symbol. Secondly, "Element of" is a perfectly acceptable pre-existing English term for it. As I wrote, "I can guarantee there is a clear and concise terminology in most programming languages to represent every one of those concepts, and that this terminology will at least be copyable, linkable, and searchable." - simply claiming "oh no there isn't" is not a valid rebuttal.

      "...you don't understand that ... you're afraid to actually learn ... judging it as completely nonsensical ... go outside of your comfort zone to learn something ..."

      And this passage is why I left off responding to this, and left off this topic entirely, for so long. Armchair psychology by an anon? If that's all I'll get for this, why even bother? It was despiriting that someone could miss the point SO BADLY.

      But looking at it now, it's a perfect illustration of the kind of overweening arrogance and blindness that is used to preserve this particular terrible status quo.

      When I read an article about a chemical, I see stuff written in English: https://en.wikipedia.org/wiki/Paraquat is a fairly typical example. Chemistry information is both shown in a sidebar, and in the body text, but even though the article is about a chemical, the topic remains accessible to a layman.

      In contrast, consider any math page, no matter how popular the topic might be to lay-people: https://en.wikipedia.org/wiki/Klein_bottle. While this is an unusually good page in that it at least makes an effort to explain some of the topics in English as well as symbols, this is far from true of all.

      To me this feels like a selective form of blindness. Chemists know that they are using speicalist terms, and willingly explain them. Mathematicians appear to feel that everyone should understand the notation - no matter how unsuitable it is for their medium - and that explaining it in English is... I don't know. I'm really not sure what their motivation for avoiding being intelligible might be, and I don't want to sink to contemptuous armchair-psychology as the other anon poster did, and suggest that perhaps it's "out of their comfort zone". Pointless? Beneath them? Impossible?

      Even in chemistry, arcane alchemical symbols quickly gave way to better notations: why not in math?
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