On alphabets and dinosaurs

rob

Dec 15, 2018 14:53

On the subject of homework-like questions (he said to an empty room): I had to spend about five solid hours this week explaining to my ten-year-old the difference between his arithmetic class, which he hates and struggles with, and mathematics, which he finds amusing and is good at.

I read him the "musician's nightmare" section of Lockhart's Lament, without reading him the title of the essay, and he recognized immediately which academic subject was being parodied.

I also used that essay's examples of real math questions as ways to get him to experience the "oh! aha!" sensation of actually understanding something interesting about the way that logic works, and told him that that's what mathematics is like.

Since I've been helping him with long division, I've stumbled on a question about the repeating decimal expansions of fractions with prime denominators. I was able to explain that question to him, and to talk about how I might go about looking for an answer, but that I hadn't yet. And he got that, and agreed that the question was interesting.

And I pointed out that, even though he's having a hard time dealing with his arithmetic class, he knew enough long division to appreciate this thing that I was asking. I told him that long division is like an alphabet that he needed to be able to have the conversation with me.

And long division, like the alphabet, is stupid and boring. Nobody talks about the alphabet as an interesting object with students who are older than about age eight. Instead, you use the stupid and boring alphabet to read clever and interesting books about dinosaurs --- or literally anything else.

The trouble with low-level homework questions on a website like ours, in my opinion, is that they come primarily from people who haven't yet figured out this distinction between "alphabet" questions and "dinosaur" questions.

I joined this community because I had a "dinosaur" question --- something counterintuitive about the correlation between density and redshift in the WMAP data set.

But if I had been looking for a place to ask that question and the front page here had been full of questions about coefficients of friction and inclined planes, I would have expected not to find an answer and left, forever, unsatisfied.

Anonymous

Dec 15, 2018 15:12

@rob Very well summarized :)

Loong

Hello Sir, I am currently writing a research paper on Planar Bus platform Rotation for Optimum Commuter Comfort, and this is a small component of it. So is it still classified as a homework problem? — Steve Gordan 24 mins ago

Anonymous

Anonymous

@Loong Lol, I was just looking at that. I must say - Good luck writing a research paper with that kind of diagrams :P

Loong

Such diagrams seem to work for that xkcd guy.

rob

@Blue That's a picture of an alphabet.

@Loong That's a joke about a dinosaur.

Exhibit A.

Semiclassical

Dec 15, 2018 15:35

i'm not familiar with the alphabet/dinosaur distinction

Anonymous

43 mins ago, by rob

On the subject of homework-like questions (he said to an empty room): I had to spend about five solid hours this week explaining to my ten-year-old the difference between his arithmetic class, which he hates and struggles with, and mathematics, which he finds amusing and is good at.

Anonymous

Starts there ^

Semiclassical

ah, now I see it

the funny thing is that, while the alphabet is boring, the history of how the alphabet came to be can be plenty interesting

Anonymous

That reminds me. Someone once showed me that that numbers, as we write them in English (rather ancient Arabic iirc), originated because they had the same number of angles as the value they represented. Like 1 has one angle, 2 has two angles, and so on

Semiclassical

huh

Anonymous

Dec 15, 2018 15:40

But it gradually evolved

rob

@Semiclassical Sure. I have successfully read texts (of varying lengths) in five different alphabets. Their similarities, differences, and common histories are interesting. That complexity is absent from "the alphabet song."

Semiclassical

yep

which is understandable, to a point

Anonymous

Semiclassical

hah, that's cute

though that's a very specific way of writing 7,8,9 :P

Slereah

yeah it's bullshit

Anonymous

Dec 15, 2018 15:43

The person who told it to me, also said that was the initial way of writing it. But it gradually changed according to the convenience of writing

Anonymous

Sounds like a question for Skeptics SE

Slereah

I have a whole book on the topic of the history of mathematical notation

Anonymous

@Slereah Damn. A Google search says that it's a rumour.

Semiclassical

this is an interesting table from wikipedia: en.wikipedia.org/wiki/Arabic_numerals#/media/…

"The evolution of the [Arabic] numerals in early Europe is shown here in a table created by the French scholar Jean-Étienne Montucla in his Histoire de la Mathematique, which was published in 1757"

Anonymous

goodmath.org/blog/2015/07/21/…

Anonymous

Dec 15, 2018 15:46

@Semiclassical Nice!

Anonymous

Semiclassical

the 8 and 9 in there are interesting to me

Anonymous

> Some popular myths have argued that the original forms of these symbols indicated their numeric value through the number of angles they contained, but no evidence exists of any such origin.

Anonymous

Ah. I did expect they earlier used something like a tally chart.

Anonymous

Dec 15, 2018 15:52

But then there were too many lines and they had to think of shorter symbols.

Semiclassical

the 4 as + sorta makes sense--- 2-by-2

the rest make you wonder, though

rob

@Semiclassical Which is interesting, since modern research suggests that four is the largest number of things that most people can recognize without counting. The research I read reported that chimps recognize numbers up to about nine without needing to count. I'm not optimistic about finding a link, though.

ACuriousMind

@rob How do you tell whether a chimpanzee needs to count?

rob

@ACuriousMind That question is why I'm looking for a link. But I think it was about the amount of time that it took to respond.

Anonymous

Maybe it was an experiment with bananas

Anonymous

Dec 15, 2018 15:57

:P

Anonymous

(Don't ask how)

ACuriousMind

1 banana, 2 bananas, 3 bananas, ::gulp:: 2 bananas, 3 bananas...

3

Loong

@ACuriousMind thunder and lightning

rob

@ACuriousMind This one is close, but I'm not sure that's it. Linked from here.

> The numeric working memory of young chimpanzees is astonishing: Flash a random scattering of numerals on a screen for just 210 milliseconds — half an eye blink — and then cover the numbers with white squares, and a numerically schooled young chimpanzee will touch the squares sequentially to indicate the ascending order of the numbers hidden beneath.

> Don’t bother trying to do this yourself, Tetsuro Matsuzawa, a primatologist at Kyoto University, said at the scientific meeting in London on which the themed journal was based. “You can’t.”

Loong

Sesame Street: The Count - Mailbags 1 to 12

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rob

Dec 15, 2018 16:08

@Loong I remember being a kid and watching a skit where the Count announced that he was going to count all the way to one hundred. It was a big production. And when he got to the end, in addition to the usual thunder and lightening, it actually rained.

Semiclassical

@rob reminds me of nothing so much as how counting works for the rabbits in Watership Down

"Notable traits include... the fact that cardinal numbers only go up to four, with any number above that being called hrair, "many", although the runt Hrairoo's name is translated into English as "Fiver" instead." (from Wikipedia: en.wikipedia.org/wiki/Lapine_language)

rob

@Semiclassical Yes, although I assume that Adams invented that for his book. (It's a favorite of mine.)

Semiclassical

yeah, it's a good book. I can see it on my bookshelf, though I haven't read it in a good while

Loong

Three shall be the number thou shalt count, and the number of the counting shall be three. Four shalt thou not count, neither count thou two, excepting that thou then proceed to three. Five is right out.

Anonymous

Monty Python-Holy Hand Grenade

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The h Bar

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