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Mathematics is hard for mathematicians to understand too

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Re: Mathematics is hard for mathematicians to understand too

#101

Post by gjulianm »

matheme wrote: post #99
gjulianm wrote: post #98

Earlier quoted context omitted.

I know it is a matrix, the notation is not confusing at all. I am saying that the concept of a matrix as a set of numbers arranged in a rectangles and the concept of operations on a matrix are very different things, the confusion will not come from notation.

You must be correct, because this interaction is completely devoid of any confusion between the two people attempting to communicate clearly.

I do not have any confusion with the notation, I am confused about what the argument you’re trying to convey with English words.

Re: Mathematics is hard for mathematicians to understand too

#102

Post by matheme »

gjulianm wrote: post #101
matheme wrote: post #99

Earlier quoted context omitted.

You must be correct, because this interaction is completely devoid of any confusion between the two people attempting to communicate clearly.

I do not have any confusion with the notation, I am confused about what the argument you’re trying to convey with English words.

Ceci n'est pas une pipe.

Re: Mathematics is hard for mathematicians to understand too

#103

Post by matheme »

gjulianm wrote: post #100
matheme wrote: post #96

Earlier quoted context omitted.

I was calling you a gatekeeper rather than notation, but feel free to keep stuffing that man with your straw. The sentence I called out, independent of the article's content: "You expect the players of the game to learn the rules before they play." Is you explicitly stating your goal is gatekeeping.

The only thing that sentence says is that it’s impossible to understand math without understanding the language of math and how it is constructed. Not sure how that is controversial or gatekeeping. If you are annoyed at that comment saying “learn” instead of “be taught”, I think that’s a pedantic argument because the argument wasn’t about that at all.

"Can I enter your gate?"

"In order to enter this gate you must know what this symbol means."

"I am unfamiliar with that symbol."

"Well, I expect you to learn what it means before I allow you to enter this gate. Now go away."

Re: Mathematics is hard for mathematicians to understand too

#104

Post by kragen »

bmacho wrote: post #91
kragen wrote: post #65

Earlier quoted context omitted.

Probably not. The conventional math notation has three major advantages over the "[n]o superscripts or subscripts or [G]reek letters and weird symbols" you're proposing: 1. It's more human-readable. The superscripts and subscripts and weird symbols permit preattentive processing of formula structures, accelerating pattern recognition. 2. It's familiar. Novel math notations face the same problem as alternative English…

AsciiMath makes easy equations read easy. 1 and 2 would be 1) d/dx e^y = e^y dy/dx = 1 2) d/dx e^y = d/dx x = 1 edit: edited, first got them wrong

When you render it for proper typesetting, do the parentheses around dy/dx disappear? (Oh, I guess you've removed them in your edit.)

If they do, it seems like an error-prone way to write your math.

If they don't, it seems like it will make your math look terrible.

Supposing that the parentheses aren't necessary, as implied by your edit: how does AsciiMath determine that e^y isn't in the numerator in "e^y dy/dx", or (worse) in the denominator in "d/dx e^y"?

It seems somewhat less noisy than the LaTeX version, but not much; assuming I can insert whitespace harmlessly:

  \frac d{dx}e^y = e^y\frac{dy}{dx} = 1
        d/dx e^y = e^y      dy/dx   = 1

  \frac d{dx}e^y = \frac d{dx}x = 1
        d/dx e^y =       d/dx x = 1

Re: Mathematics is hard for mathematicians to understand too

#105

Post by aleph_minus_one »

matheme wrote: post #94
assemblyman wrote: post #89

I find software engineers spend too much time focused on notation. Maybe they are right to do so and notation definitely can be helpful or a hindrance, but the goal of any mathematical field is understanding. It's not even to prove theorems. Proving theorems is useful (a) because it identifies what is true and under what circumstances, and (b) the act of proving forces one to build a deep understanding of the phenome…

> If the idea is that the right notation will make getting insights easier, that's a futile path to go down on. I agree whole heartedly. What I want to see is mathematicians employ the same rigor of journalists using abbreviations: define (numerically) your notation, or terminology, the first time you use it, then feel free to use it as notation or jargon for the remainder of the paper.

> What I want to see is mathematicians employ the same rigor of journalists using abbreviations: define (numerically) your notation, or terminology, the first time you use it, then feel free to use it as notation or jargon for the remainder of the paper.

They do.

The purpose of papers is to teach working mathematicians who are already deeply into the subject something novel. So of course only novel or uncommon notation is introduced in papers.

Systematic textbooks, on the other hand, nearly always introduce a lot of notation and background knowledge that is necessary for the respective audience. As every reader of such textbooks knows, this can easily be dozens or often even hundreds of pages (the (in)famous Introduction chapter).

Re: Mathematics is hard for mathematicians to understand too

#106

Post by kelipso »

matheme wrote: post #103
gjulianm wrote: post #100

Earlier quoted context omitted.

The only thing that sentence says is that it’s impossible to understand math without understanding the language of math and how it is constructed. Not sure how that is controversial or gatekeeping. If you are annoyed at that comment saying “learn” instead of “be taught”, I think that’s a pedantic argument because the argument wasn’t about that at all.

"Can I enter your gate?" "In order to enter this gate you must know what this symbol means." "I am unfamiliar with that symbol." "Well, I expect you to learn what it means before I allow you to enter this gate. Now go away."

That’s a very good gate to keep. Some things are just meant to be gatekept so that the cranks and dilettantes that wastes everyone’s time can stay far outside.

Re: Mathematics is hard for mathematicians to understand too

#107

Post by kragen »

kragen wrote: post #84
zozbot234 wrote: post #81

Earlier quoted context omitted.

We do often find add(a, b, c), just written as Σ(a, b, c). Similar for mul and Π. The binary sub operator can be simply rewritten in terms of add and unary minus; the fact that we write (a - b) instead of (a + [-b]) or perhaps Σ(a, [-b]) is ultimately a matter of notational convenience, but comes at some cost in mathematical elegance. Considering operators that are commutative yet not associative is not very useful;…

Usually you'd have to write that as \sum_{v \in \{a, b, c\}} v; one of the ways I think conventional math notation could in fact be improved would be by separating the aggregate function of summation from the generation of the items, allowing you to write \sum \{a, b, c\}, at the minor cost of having to write \sum_{i = 1}^N i^2 as something like \sum |_{i=1}^N i^2. It's not conventional to write commutative-but-not-a…

A thing I didn't appreciate the first time I read Spencer-Brown's book is that he actually cites Sheffer's 01913 paper, and proves Sheffer's postulates within his system in an appendix. This situates him significantly closer to the mathematical mainstream than I had thought previously, however flawed his proof of the four-color theorem may have been.

Also, the axioms I cited above are written in his notation on his gravestone: https://en.wikipedia.org/wiki/G._Spencer-Brown#/media/File:G... but I have evidently reversed left and right in my rendering of the DNF rewrite rule above. It should be:

    ─────┐   ────┐────┐
    ─┐──┐│ → ─┐─┐│─┐─┐│
    a│bc││   a│b││a│c││
His first statement of the first axiom in the book is a little more general than the version I reproduced earlier and which is inscribed on his gravestone; rather than his "form of condensation"

    [][] = []
his "law of calling" is general idempotence, i.e.,

    AA = A
although the two statements are equipotent within the system he constructs. Similarly, before stating his "form of cancellation"

    [[]] =
he phrases it as the "law of crossing", which I interpret as

    [[A]] = A

Re: Mathematics is hard for mathematicians to understand too

#108

Post by kelipso »

matheme wrote: post #102
gjulianm wrote: post #101

Earlier quoted context omitted.

I do not have any confusion with the notation, I am confused about what the argument you’re trying to convey with English words.

Ceci n'est pas une pipe.

This is funny. “Mathematics notation is confusing to me because I refuse to learn it. I refuse to learn it because mathematics notation is confusing to me.” Okay sure, be happy with yourself.

Re: Mathematics is hard for mathematicians to understand too

#109

Post by bmacho »

kragen wrote: post #104
bmacho wrote: post #91

Earlier quoted context omitted.

AsciiMath makes easy equations read easy. 1 and 2 would be 1) d/dx e^y = e^y dy/dx = 1 2) d/dx e^y = d/dx x = 1 edit: edited, first got them wrong

When you render it for proper typesetting, do the parentheses around dy/dx disappear? (Oh, I guess you've removed them in your edit.) If they do, it seems like an error-prone way to write your math. If they don't, it seems like it will make your math look terrible. Supposing that the parentheses aren't necessary, as implied by your edit: how does AsciiMath determine that e^y isn't in the numerator in "e^y dy/dx", or…

Here is an online renderer and the description: https://asciimath.org/

The rules are basically the same as LaTeX, with saner symbol names, support for fractions, \ is not needed before symbols and () can be used instead of {}.

> Supposing that the parentheses aren't necessary, as implied by your edit: how does AsciiMath determine that e^y isn't in the numerator in "e^y dy/dx"

It seems to me that dx,dy,dz,dt behave like numbers, single letter variables and symbols (probably they are symbols, but not listed for some reason). Just as LaTeX doesn't need {} parentheses for numbers, single letter variables and symbols, AsciiMath allows omitting them too.

So `/` captures a single number/symbol/variable left to it, and that is `dy`. But if there was `du` for example it would only capture u, and you would need to put du between parentheses.

Re: Mathematics is hard for mathematicians to understand too

#110

Post by auggierose »

assemblyman wrote: post #89

I find software engineers spend too much time focused on notation. Maybe they are right to do so and notation definitely can be helpful or a hindrance, but the goal of any mathematical field is understanding. It's not even to prove theorems. Proving theorems is useful (a) because it identifies what is true and under what circumstances, and (b) the act of proving forces one to build a deep understanding of the phenome…

Understanding new math is hard, and a lot of people don't have a deep understanding of the math they use. Good notation has a lot of understanding already built-in, and that makes math easier to use in certain ways, but maybe harder to understand in other ways. If you understand something well enough, you are either not troubled by the notation, because you are translating it automatically into your internal representation, or you might adapt the notation to something that better suits your particular use case.
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