ℝolliℵg M∀th Thr∑a∂

I don't know how much higher math you really use to understand music or music theory, the article I was talking about basically says that he thinks a lot of mathematical research on music is sort of bogus, drawing a picture or creating blinking lights that sort of looks like what music is doing. To him the most interesting thing seemed to be the way the similar processes of collaboration jazz improvisation and mathematical research.

i teach high school math but im an econ undergraduate and yall are simply adding fuel to the fire that rages inside me that i shd not be teaching math

plus I didn't always like the Eloi vs. Morlocks setup of formal grad school,

what does this mean?

xp would u rather be teaching econ? my first major was in econ, then i was like ah fuck it and turned my math minor into a full major

The few mathematical ideas I use to think about music are:
*Thinking about the twelve semitones as the Abelian group Z12. (supposed to be a subscript)
*Looking for least common multiples when counting out polyrhythms
*Realizing that the names of the intervals are Ordinal Numbers and
*Realizing that sometimes there are Fencepost Problems in either counting out beats or even in that the octave is the same as the one, which is why some people talk about a heptatonic scale

*Thinking about the twelve semitones as the Abelian group Z12. (supposed to be a subscript)

yeah this was basically the extent of my ruminations lol

well hey you know

http://en.wikipedia.org/wiki/Set_theory_%28music%29

Fully funded PhD student with good background (perhaps trained abroad) and famous advisor, who can sail through qualifyings, has good chance of helping advisor push out papers and securing post-doc and just generally burnishing his legacy = Eloi
Rest = Morlocks

hmm, in the humanities the 'fully funded' part of the distinction doesn't really apply anymore at lots of places, programs looking to trim, improve graduation rates/times etc. figured maybe they should only admit those who they could fund

the other part, though…

Someone told me Hindemith was into group or set theory as it applies to music but I couldn't find a reference. Maybe that Wiki page will have.

Telling you, that Fencepost thing saved me some headaches.

Oh yeah, one more thing
*Thinking about musical entities as partitions- triads as partitioning into three (with the fourth being a "generalized, augmented third*), seventh chords as partitioned into four (with the second between the seventh and the octave as a *generalized, diminished third*)

homotopy type theory isn't exactly homotopy theory bear in mind -- its this wild new realization that homotopy theory is precisely isomorphic to that branch of logic known as martin-lof type theory, and this all works only in a constructivist setting. so you have math/logics ppl without much topology background (hi!) and topology people trying to understand type theoretic notation all sort of in the mix together. i have a coworker with some topology so he's good at explaining things like fibrations and fundamental groups etc. oh right and the other part of the hott project is now you have a setting in which the claim is you can do the foundation of _all maths_ as an alternative to set theory, so eventually (tho it may be 6 mos before we get there, if we can keep up the momentum) we'll stop just building up the theory and do applications and use it to do classic results in e.g. actual homotopy theory, set theory, category theory, analysis etc.

the hatcher book is very approachable but it does sort of require someone with a bit of background to explain what he means by certain things, since the geometrical intuitions aren't totally obvious without someone drawing things or waving their hands or etc. to illustrate movement.

sounds cool xp

xp would u rather be teaching econ? my first major was in econ, then i was like ah fuck it and turned my math minor into a full major

― flopson, Saturday, November 9, 2013 4:53 PM (17 minutes ago) Bookmark Flag Post Permalink

there are many things for which i am better qualified to teach. don't get me wrong, i know the hs curricula v well, i just didnt take much advanced math and sometimes feel like i am training my kids for a sport ive never seen or played before. being the good economist, tho, i know my comparative advantage is in the high-need HS math field rather than the social studies or journalism positions i'd have an absolute advantage in.

Now I remember the problem with math, you have to beef up all this apparatus, before you can really understand or prove anything- except for trivial variations on the proofs in the book with slightly different initial conditions- let alone do a calculation, for what seems like an eternity.

Assuming you are an applied mathematician and want to do a calculation.

calculations! what, like with numbers? i thought we were talking about math!

Ha, exactly. I never forget in Group Theory class when Jonathan Rogawski told us "The idea that mathematics is about numbers is false. Mathematics is about the relationship between mathematically interesting objects and other mathematically interesting objects." RIP, Jon.

lmao. had a group theory prof tell me "math is just patterns. that's why group theorists are like the high priests among mathematicians"

I was a chem major bison

Chemists I've known have always been good at math.

For instance, my friend's dad is a retired chemistry professor and he was writing papers on things like statistical mechanics and Brownian Motion and co-wrote an undergraduate math textbook with a super-famous mathematician, well famous in the field, anyway.

plus I didn't always like the Eloi vs. Morlocks setup of formal grad school,

what does this mean?

― flopson, Saturday, November 9, 2013 5:52 PM (1 hour ago)

http://en.wikipedia.org/wiki/The_Time_Machine

i'm good at math but i've never taken like hardcore college classes, i can just do stuff in my head pretty well and am good at algebra, that's basically the math i need or will ever need

I was trying to teach a student synthetic division today and I kept fucking up! So frustrating! Somehow stressing that you don't actually use that in real life isn't a satisfactory explanation!

Fuck you rational root theorem!!!

i actually kinda think hs math should be less about like, finding roots of polynomials or learning division algorithms, and more, like, elementary/discrete probability theory, basic combinatorics & graph theory, just the really easy stuff you can do with elementary methods

ne x86 math topics aside from khaninstitute? trying to set up equasions on x11 in darwin

Isn't that what computer science freshman learn in their Discrete Math course, flopson, iirc?

well how does that help high schoolers?

besides logic, teaching a critical thinking course now that's heavy on inductive logic and probability, for the first time ever, and already (not being super deep into the material) i'm struck by how useful it could be if more people learned this stuff early on. i had a science-heavy math education, and i've spent some time thinking about how science works, but i can see that there's a lot about it that's overly opaque to me because my knowledge of probability/statistics is shallow. especially when it comes to the social sciences.

Yeah, obviously doesn't help high schoolers, you are right.

you know what helps high schoolers DAILY BEATINGS that's what

j/k

the question of what type of math to teach in school is so contentious and political that it makes my brain boil every time the subject comes up, that's why i made the lame joke

isn't the typical college-prep math track basically set up to produce calculus students (then engineers, and the few others who need calculus, like physicists)?

sorry, don't mean to incense you, v, obv. you do the lord's work

There are certain problems about way math is taught-even if you major in it and are good at it!-my old math team coach is still big in education wrote an article about his take on it, maybe I can find it. One thing is overemphasis on proofs- "it was good enough for Euclid"- rather than other kinds of mathematical thinking to develop intuition and visualize or in some other way organize mathematical structures. Another think I've talked to people about, at least as far as applied math, is not enough discussion about the subtleties of units. Little kids learn that if they are given a problem about the perimeter of a triangle with the sides given in feet, they should give the answer in feet and they figure units must be trivial but in fact a better understanding of units can really help you solve a problem more quickly and, more importantly, accurately, even if it ultimately requires calculus. See the book Street Fighting Math, freely downloadable, for a good presentation.

xpost

you are correct j, which is sad because the 95% of kids who don't want to be engineers and physicists just end up getting turned off of the subject by the end of high school, if they're not already turned off by 9th grade (i would estimate about half are by that age)

http://mitpress.mit.edu/sites/default/files/titles/content/9780262514293_Creative_Commons_Edition.pdf

^ this one?

When I was in high school basically they were leading up to teaching Calculus senior year, when you could take it only if you were in the AP class, in which it was gingerly taught at an extremely leisurely pace, as if we had to slooow ourselves down time-lapse style in order to observe the delta-epsilon proofs.

Yeah, that one.

my thinking matured a lot, esp. my proofs, once i took a logic course, which suggests that maybe mathematicians in my hood were not as plain about what we were doing as they could have been.

but abstract algebra was always more elusive for me (even though really interesting), despite having lots of proof-theoretic niceties in its usual u.g. presentation, because i didn't have so many of those intuitions and had trouble learning how to visualize it or play with the structures. never had much of a feel for numbers, compared to many math majors, when younger, which i think would have made a difference. number theory as a gentleman's pastime, say, still has mostly zero attraction for me.

sometimes i wish i could just chill and enjoy math instead of stressing about mathematically illiteracy

let's just like, do some problems

"A farmer has some rabbits and some cages. When he puts 2 rabbits in each cage, there are 2 rabbits left over. When he puts 3 rabbits in each cage, there are 16 cages (but no rabbits) left over. How many rabbits and how many cages are there?"

lol i swear the cover of that book practically reads like 'the art of fucking shit up and guessing about things' to me

number theory is ridic ... as far as algebra goes i learned groups rings and fields to pass a test and promptly forgot everything. i know nothing about topology or real analysis.

this course was about as far as i got in math before i gave up (i passed!)

http://www.amazon.com/Foundations-Higher-Mathematics-Peter-Fletcher/dp/053495166X

i just tried to solve that rabbits and cages problem and got six cages and eighteen rabbits

hm

ahem

http://math.arizona.edu/~savitt/GTM.html

okay, fixed

apparently i am

You are William S. Massey's A Basic Course in Algebraic Topology.

You are intended to serve as a textbook for a course in algebraic topology at the beginning graduate level. The main topics covered are the classification of compact 2-manifolds, the fundamental group, covering spaces, singular homology theory, and singular cohomology theory. These topics are developed systematically, avoiding all unecessary definitions, terminology, and technical machinery. Wherever possible, the geometric motivation behind the various concepts is emphasized.

so this test has really revealed something about my self to me

Awesome. I have a copy of that book somewhere that I can give if you want, if I can find it and you are in NYC.

Tried to do that caged rabbit problem in my head but suspect it's broken meaning non-integral solutions. But maybe it's my brane that's broken will solve properly when I get home.

nah there's a simple integer answer

posting quean

!

Do we know whether she was also posting the questions? Seems perhaps a bit too convenient that people just happened to ask about some rather contrived integrals that just happened to have neat and tidy solutions that one poster knew the answer to.

Certainly seems possible.

i enjoyed this thread about zero:

This meme is very very funny, but it is also inviting a serious explainer 🧵 from yours truly about 0 in Sinitic languages (there'll also be something funny later on). 😂 Let's go! 1/ https://t.co/I3vEGnNS7Z

— Egas Moniz-Bandeira ᠡᡤᠠᠰ ᠮᠣᠨᠢᠰ ᠪᠠᠨᡩ᠋ᠠᠶᠢᠷᠠ (@egasmb) May 21, 2023

also have enjoyed videos recently from math youtuber @Domotro

That was good, thanks.

as solved by "anonymous 4chan poster and anime-fan":

https://www.quantamagazine.org/sci-fi-writer-greg-egan-and-anonymous-math-whiz-advance-permutation-problem-20181105/

(courtesy max read so others will have seen this)

The Unabomber has died. Here is a famously good footnote to him in a mathematics paper.

Citation: Pudwell, Lara. “Digit Reversal without Apology.” Mathematics Magazine, vol. 80, no. 2, 2007, pp. 129–32. JSTOR, https://t.co/IpyzPWc0AA. Accessed 10 June 2023. pic.twitter.com/xCwNbMtQmf

— Alex von Tunzelmann (@alexvtunzelmann) June 10, 2023

i love Greg Egan's short stories. he is better versed in math than more recognized literary writers like Borges, Calvino, et al

Subscribers to this thread might enjoy the novella a short stay in hell by this guy https://en.wikipedia.org/wiki/Steven_L._Peck

There’s something annoying about Greg Egan but some of his stories are indeed mindblowing.

https://www.youtube.com/watch?v=ArADlJx7SlU
I love that she has a Penrose tiling tattoo.

https://www.youtube.com/watch?v=_ZS3Oqg1AX0

https://cs.uwaterloo.ca/~csk/hat/

https://www.youtube.com/watch?v=FUHkTs-Ipfg

thought this bump would be about terry tao's formalized proof of the Polynomial Freiman-Ruzsa conjecture using Lean4 proof checking language

https://terrytao.wordpress.com/2023/11/18/formalizing-the-proof-of-pfr-in-lean4-using-blueprint-a-short-tour/

(this post was written while it was still ongoing but they finished it the other day)

super interesting stuff. i don't think s clover still posts but would be interested to hear his thoughts on the significance of this. seems like it was cute niche a few years ago but is now catching on

I watched that coin rotation video the other day, pretty cool - especially solar vs sidereal year.