Not me, googled, but I think it might be worth it to me, if the scars didn’t fade.
I’ve done amateur scarification to myself of various symbols in not typically visible areas, and it only lasts a year or two. And I don’t think the pain of doing it once ever couple of years would be worth it.
Back in the day it was mostly depression-related self-harm. But I have a couple I actually planned and tried to make permanent and they healed nicely to just faint white spots.
I’m just gonna leave this here:
Well worth the read, and it covers everything I have to say about this topic more eloquently than I can.
well, it’s a good thing that Aronofsky didn’t make Inception, then. that was Christopher Nolan, pal. And even if it was A, he wouldn’t have “gone downhill fast,” as he did Requiem, Fountain, Wrestler, and Black Swan before Inception’s release.
Pi was awesome, and was forcibly shown to me by my first leet computer friend (a second-generation coder) when I mentioned I’d never seen it, shortly after its video release.
OK, this has bothered me since I first saw the subject of this thread, and no one has talked about it yet so I guess it’s up to me: math isn’t an invention. Math exists, and humans are like archaeologists, working to uncover what’s already there.
That’s kind of a philosophical debate, based on whether you think that math is your description of something, or whether it’s the thing that you’re describing.
Language, for instance, is an invention. Using the vocal cords to emit sounds and communicate complex ideas is something that very few creatures that we know of have done, and especially refined to the point that we have. And many, many cultures have come up with their own invented language, with their own invented words, to communicate those concepts.
So, is math the language, or is it the concepts itself?
If you’re saying “if you have a right-angled triangle on a flat (Euclidean) surface, the square of the longest side will always be equal to the sum of the squares of the other two sides,” then yes, that idea isn’t an invention, that’s a concept built into our reality, similar to the concept that the circumference of a circle will always be approximately 3.14159 times its diameter.
However, the use of the equation a2 + b2 = c2 to represent the former concept, and the symbol π to represent the latter: those are both inventions.
So, is math the ideas, or the language? Both? Neither? I don’t have an answer.
ETA: and what about when you extend mathematics to include concepts (like the square root of a negative number) that don’t occur in reality? Are those concepts “inventions?” Okay, I’m going to stop there before I get a headache.
It’s hard to say which mathematical concepts occur in reality; imaginary numbers are critical in describing quantum particles, while even integers are ultimately abstractions. But I do think you have a point there. Pure mathematics is all about assuming particular systems and studying them.
It’s usually most useful to work with axioms inspired by our observed reality, which is where we get our numbers and ordinary Euclidean geometry from. But you can make up ones that seem more elegant, more unusual, more illustrative of some principle. There are other number systems and geometries, and more abstract things that are not so clearly either, and all sorts of constructs that are easily thought of as invented.
But if axioms are your choice, their consequences are not. They may inescapably explode with self-contradiction, or only have simple results, or result in a large body of non-intuitive theorems. People started looking at defining square roots for negative numbers, and then iterating functions over them, without ever expecting the Mandelbrot set. I think it’s fair to say these kind of things are easily thought of as discovered.
So I think it would be better to say something between the two – math is discovering what abstractions can be invented, or that kind of thing.
I wanted to offer my intuition about it, because I’m curious if it actually helps anyone else. The function y = et is unusual in that it is its own derivative, and sometimes that is even taken as part of its definition. More general exponential functions can be written as y = eat, and then we get dy/dt = ay.
In other words, they represent functions where the rate of change is some constant multiple a of the current position. It’s often handy to think of that as a speed, so it’s like an ever-increasing repulsion from zero. Or rather it is when a is positive. When a is negative, it falls asymptotically into zero instead.
And for imaginary a we do something between those. We can look at this in terms of the complex plane. Then multiplying by a positive number scales everything around zero, and a negative number inverts it, but an imaginary number gives a rotation. In particular multiplying by i means turning 1 into i, which we get by rotating everything 90º to the left.
If you appreciate that you can maybe see how dy/dt = iy will act in the plane. The function is not going to travel outward or inward, but instead the rate of change is always going to be perpendicular to the current position. In other words, we are going to be going in a circle. Since y = eit starts from 1, we go to i then -1 then -i and then back to 1.
And since our absolute distance from zero stays 1, the magnitude of our rate will stay 1 as well – we’re circling with constant speed. At which point it’s not so surprising that a full circle needs t = 2π. Or, if you want to travel to -1, you only go half the circumference; we plug in t = π and so end up at eit = -1.
So writing that out, I see it relies on a lot of other concepts to try to form a picture, though for me it gives a more satisfying one than just a numerical proof. Does any of it work for you?
That was actually quite helpful. Thanks.
That’s a literally insane way to count. Why unhook your language from the base you count in just to say “four twenties”? Like, I could imagine a child doing that, but why would everyone think that’s neat?
You ever come across shepherd’s counting? Goes back a fair way and 20-based numbers might tie into it.
Gonna go look now. 
ETA: Someone with better languages than me would be able to tell, but there might be something to do with the Breton/Brythonic stuff? Way outta my league with this, lolz.
According to the wiki, most of those shepherd counting systems are base-20, but don’t have a distinct word for 20 beyond the equivalent of “score”.
But beyond that, the French have standardized their language. They have an official dictionary with “all the words”. Nearly all of their counting is done in base ten except for that little “four twenties” bit where they decide to go off into nonsense for a little while. The rest of their counting system is base ten, so what’s the point of keeping the base 20 bit at all?
Personally, I’m a fan of the Japanese counting system.
When you get to eleven, you just say “Ten-one”, “Ten-two”, “Ten-three” and so on. When you get to 20 you say “two-ten”, “two-ten-one”, “two-ten-two” etc, it works all the way up to 10,000 then it does get a little funky with orders of magnitude jumping by four places though.
I am of the mind that Math is less Invention and more us delivering the ways the universe goes together.
Came for meth, left disappointed.
Someday I will get my spectacles out of hock
Nice. Found some stuff about Aboriginal maths, too. Might be of interest?
http://aiatsis.gov.au/collections/collections-online/digitised-collections/ethnomathematics-australia/introduction
Any chance you rock the soroban?
Nah, I’ve used an abacus once or twice, but never seriously. Mostly abacus counting on my fingers in marching band.
ADHD makes simple tasks like remembering two numbers simultaneously really hard, eg remembering which bar I’m on while I’m actively counting beats. So I had to count rests and stuff on my hands in ASL so that I’d not get distracted and lose my place.
The hand gets the current bar I’m at, and I count the beat internally. That way I can keep track of the two related numbers I’m counting.
My impressions.
First, math is logic. It’s interesting in the theory and in the practice, but not everyone needs the theory and all of us need the practice.
Second, I ought to pick up a new copy of Refiguring Anthropology.
Third, in my experience, math was usually badly-taught. I get that we’re supposed to show how, but writing that much hurts. I get that reading math books is supposed to teach us both how and why, but it never worked that way for me; many of them present formula - what the fuck am I supposed to do with formulae? - and/or pure derivations without textual explanations. I don’t get the logic of spending the first 40 minutes going over the previous night’s pain-drills, and the last 10 minutes “we’re out of time so read chapter 5 and do these 30 drills.” [And also explanations that rest on understanding stuff I never learned, like anything using cross-multiplication.]
That actually happens a lot when you play Tuba.
In an orchestral setting, most of what you’re doing is counting rests so that you can blow one long note, or do some oompah, then “shutup let the fancy stringy bass do everything else.”
Ah yes, I play my part, then rest for three bars, play a doot, rest for 27 bars that I have to count exactly, play some wind-sucker contrabass doots, and then I rest for 11 bars and that’s the song!
Also, whoever arranged that score doesn’t know much about wind instruments. Typically you write the Flat equivalents for the key signature for a low brass instrument, instead of leaving all those sharps in the signature.
Who doesn’t love tuba / sousaphone?
Mandarin Chinese too (so probably Cantonese as well).
The opposite also happens. One of my best teachers ever was a community college lecturer teaching math. The man was a genius at overhead projector examples, with color coding, and multiple explanations of why common formula solving methods worked - from different viewpoints.
Sometimes community college instructors are actually better at actually than 4 year college professors. The community college instructors I had actually taught their own courses and were there as teachers not as publishing academics who sometimes had to teach a class. Granted, I’ve had good and bad teachers in both 2 year and 4 year colleges (and, at least once, the exact same teacher, moonlighting), but there seem to be some huge impediments to good instruction built in to graduate and post graduate academics.
