#81
stalin ate nine and ordered the clouds not to rain
#82
u put the subtracted value into a small box and keep it secret, keep it safe
#83
the farthest i got was understanding trig and seeing fucking everything is waves. completely turned my head. i enjoy that, but i find it hard to put in the work unless its serving a purpose cause it can be so abstract on its own.

reading i like though, some borges shortstories are beautiful narrative explorations of mathematical concepts which makes glimpsing at that mystery more accessible i think?

anyway, in case youve not read them.. smoke a spliff, have a cup of tea, and sit down with one. they are all short. suggested...

- garden of forking paths: quantum mechanics / infinity
- library of babel: infinity / topology
- lottery of babylon: probability / chaos
- the aleph: infinite sets
- blue tigers: cardinality
- book of sand: dense set
#84

dimashq posted:

u put the subtracted value into a small box and keep it secret, keep it safe


...thats division not subtraction

#85

tears posted:

trying to learn maths but having some problems when u do a "subtraction" where does the bit u take away go to? example: 13 - 3, where does the 3 go to?


Google "number line"

#86

toyotathon posted:

kitchen math

experimenting adding gluten to my flour for bread. turned 10% gluten AP flour into 15%. so far, the bread texture is a lot better, going to keep upping the gluten 1% each batch and see what happens.

i hope this 'gluten-free' fad keeps going cuz, right now there's a gluten glut. my pet theory for the mass gluten allergy is, since white people have been eating bread for millenia, to just now diagnose a mass allergy, that's probably not real. BUT-- maybe the chemical processing step that removes gluten (dissolving the starch in water, removing sediment incl gluten, then drying the starch) might be removing the actual causative agent, like a new pesticide or something. someone was tellin me that their friend with celiacs was fine eating european-wheat breads, maybe cuz of different pesticide regimes in europe and US.

the formula to figure out how much of something to add is:

x = b*(c - a) / (1 - c)

where,
x = the amount to add (weight)
a = the original %/100 (from 0 to 1)
b = total original weight
c = target %/100 (from 0 to 1)

if you want to stick with percents you can turn that '1' into '100'.

so if you have 51oz of 10% gluten AP flour, and want to turn it into 15% gluten bread flour,

x = 51oz * (0.15 - 0.10) / (1 - 0.15) = 3oz

if you don't believe the formula: 10% of 51oz is 5.1oz gluten, 5.1+3=8.1, 8.1/(51+3)=15%

started with semigroups/monoids/groups in this number theory book that's supposed to get to the integers eventually. i am very interested in group theory if anybody wants to PM chat cuz of the euclidean group and its relation to kinematics/exact constraint, and why point-symmetry in solid bodies makes 3-DOF, line-symmetry makes 5-DOF, and plane-symmetries and higher give 6-DOF (?). or honestly geometry. vvvvvv shit TG that gives me an idea.



Classic suggestion for group theory, that isn't too hard to find a pdf of online if you want, is Algebra Chapter 0 by Aluffi. The intent is a basic algebra book that builds naturally into category theory needed for algebraic geometry. The way your book seems to go about it, by starting at monoids and working backwards, makes me think that either there is a lot of hand waving or it is perhaps too advanced to be a good introduction to groups. Sorry if I misunderstood and an intro level book is not what you're looking for.

#87
thank you, last night i looked around libgen for a second intro. i actually picked it up to learn quaternions, but it's all over the place, detouring thru groups, to define the set of integers? i'm going to check out aluffi then hopefully revisit.

the quaternions are for cad but another cool thing in this cad. i'm writing polyhedra code to render pipes, and re-writing it to render an outer pipe diameter, from s=0 to 1, then it loops back on the inside, s=1 to 0, to render the inner pipe diameter. to stitch it up, the last points all connect to the first points. i was going to write a second case, for when a solid filled pipe (no inner diameter), links back on itself, like an ouroboros, or: a torus. but the code's identical, don't gotta make a special case for it, because they're both toruses, they both stitch the first points to the last.

i also realized the code's going to be the same for any "spheres" where the first set of points in a circle, all make triangles connected to the same pole, on the first and last sets -- two poles in a sphere. wish i understood more about spheres and toruses and etc cuz there are maybe more general shapes the code could do w/o much addl effort.

edit: reading about quaternions and the multiplication rules and yo, this defines the cross product! that is cool. cross product from out of algebra. friendship ended with Josiah Willard Gibbs, now William Rowan Hamilton is my best friend.

Edited by toyotathon ()

#88
saw this shape in Blanding, 4 right-angle tetrahedra connected at tips, to form a regular tetrahedron in the center:


the way this regular tetrahedra is balanced on an edge, if you take a cross section level to the sea, it forms rectangles:


it's a cube where every rectangle is braced with a crossbar, in a certain way. and every bar is held in at least 6 places (but many are over-constrained)

edit i knew i fucked up the stairs... it's like a double mobius and in the middle you're on em upside down oh well

Edited by toyotathon ()

#89
i live in a fucking trash can
#90
like 2 make little hand-drawn math anti-memes. unshareable unlikeable unsubscribeable. on but not of the internet

Edited by toyotathon ()

#91
boring

Edited by toyotathon ()

#92
ive been learning all about the weak force (quantum flavourdynamics), and the best bit is when all the physicists go "welp, maybe theres like a secret mirror dimension", when they cant explain pariety violation
#93
i'm trying to write a CAD program, and am re-writing the triangle mesh generator today to fit new requirements. realized it'd actually be cheap to find the global optimum solution.

probably the longest function description i've written in my life:


Description:
Determines how to mesh two sets of points. The mesh is
a set of triangles between the points. This finds all
possible triangle combinations, and finds the set with
the smallest sum of triangle perimeters, which is closest
to the analytical model.

This is an interesting math problem -- given two number lines,
with n and m points, how many ways are there to connect the
points to each other, such that every point is connected at
least once, and no lines cross? It makes a ribbon of triangles.
It helps to draw two lines, dot them irregularly with points,
and try out some solutions. Remember, no lines cross, and first
connects to first, and last to last. Number the points 0, 1, 2...

Like this: (ASCII's no good for drawing the triangle lines tho)
0----1--2--------3----4-------5---6-----------7 n=7
lines = n+m+1
0--1------2---3-----4-----5--6-----7---8------9 m=9

One trick is to note that, one side of each triangle is on the
number line, and the other two sides are between. So that, when
the points are numbered 0 to n or m, as you draw triangles from
one side to the other, each triangle drawn advances one of the
number lines by one.

If you then draw an ordered list of how the points connect, like
[n,m] = [0,0], [0,1], [1,1], [1,2], etc, you'll notice that the sum
of both point ID's increases by one (since one side of each triangle
lies on one or the other number line). The sum goes 0, 1, 2, 3...
It is the set of natural numbers (with zero), up to n + m,
the number of triangles between the number lines.

There are many ways to draw the triangles, so we're trying to figure
out which, and how many. You can draw the first line, between 0,0
exactly one way, [0,0]. The second line (first triangle) can be
drawn [0,1] or [1,0]. The third [0,2], [2,0], [1,1]. See the pattern?
Given a natural number c, and two natural numbers a and b (<= n), there
are c+1 ways to sum to c.

Does that mean we've figured out how many ways there are to draw
these triangles? That'd be nice if this were the formula: adding up
all combinations to c, you get 1 + 2 + 3 + ... + c+1, which is always
a triangular number. Then the product of the triangular numbers, up
to c, would be the number of ways to draw the triangles. But because
we have the condition that no lines can cross, and because a and b
max out before c, the actual solution set is smaller.

Let's visualize all combinations in a triangular pyramid:
[0,0]
[0,1] [1,0]
[0,2] [1,1] [2,0]
[0,3] [1,2] [2,1] [3,0]
[0,4] [1,3] [2,2] [3,1] [4,0]
[0,5] [1,4] [2,3] [3,2] [4,1] [5,0] etc

And let's restate the condition that no lines can cross: no number
in a set can go backwards, only forwards by 1, to draw the next line.
So you can't go [0,1], and draw the next line at [2,0]. That means
the path, from top of this pyramid to the bottom, must be either down
and right, or down and left, zigzagging or hugging an edge.

When you add up how many ways you can reach each number in the pyramid,
it becomes the Staircase of Mount Maru (or, Pascal's triangle). That's
useful for knowing the rough probability of reaching each number.

To apply the other condition (n and m maximums), we can truncate the
pyramid into a diamond shape. So for [n,m], if n_max=4, m_max=3,
[0,0]
[0,1] [1,0]
[0,2] [1,1] [2,0]
[0,3] [1,2] [2,1] [3,0]
[1,3] [2,2] [3,1] [4,0]
[2,3] [3,2] [4,1]
[3,3] [4,2]
[4,3]

Now we know the full solution space, and all paths thru it, and the
rough probability of reaching each one. And using the Staircase of
Mount Maru, we can calculate the number of ways to draw the triangles:

1
1 1
1 2 1
1 3 3 1
4 6 4 1
10 10 5
20 15
35 <---ways to draw the triangles


i dunno had fun going thru it, thought it was fun how much triangle shit came out of a triangle-drawing problem. triangular numbers, pascal's triangle. altho like so much else in white culture, pascal didn't discover it first, indian and chinese mathematicians did, by hundreds of years. some white just claimed the territory. one of its first names is The Staircase of Mount Maru.

edit: really glad i saw this was a binomial problem b/c the internet's filled with pseudocode that goes, 'for a traveling salesman starting in the top left corner of a grid, who can only move right and down, here are all his possible paths to get him to the bottom-right corner'. like this https://xlinux.nist.gov/dads/HTML/allPairsShortestPath.html flip the diamond on its side and this problem becomes that problem. math: it's great

Edited by toyotathon ()

#94
can sum physicist explain to me why interger spin particles dont follow the pauli exclusion principle. basically why can multiple bosuns occupy the same quantum state while multiple femions cant. do i need to know Bose–Einstein and Fermi–Dirac statistics?
#95
yes
#96

tears posted:

can sum physicist explain to me why interger spin particles dont follow the pauli exclusion principle. basically why can multiple bosuns occupy the same quantum state while multiple femions cant. do i need to know Bose–Einstein and Fermi–Dirac statistics?


Bose-einstein and fermi-dirac statistics are consequences of what you're describing. The reason half-integer spin particles cant occupy the same states has to do with symmetry properties of the wave function. Essentially, half-spin particles require (for reasons that are somewhat formal) that the wavefunction is antisymmetric under exchange of particles. That means that when you swap an electron for a "different" one the wavefunction picks up a minus sign. A consequence of this is if the two swapped particles were in the same state the wavefunction there would be equal to minus itself, meaning it must be zero, so the probability of that happening is exactly zero.

#97
thanks, so let me see if ive got this straight - they cant occupy the same state because they would cancel each other out - like wave interferance - and thats impossible right, two particles cant just disapear each other. But when bosuns occupy the same quantum state its like additive interferance which is just +1 + +1. they would appear industinguisahble/identicle to each other just +n - hence the bose-enstein condensate where you get them to all do it at the same time and bring quantum wave shit into real life

with femions where its +1 + -1, which is impossible for particles, though possible for particle anti-particle interactions? idk, i feel like im missing something

i dont understand this bit though:

c_man posted:

symmetry properties of the wave function. Essentially, half-spin particles require (for reasons that are somewhat formal) that the wavefunction is antisymmetric under exchange of particles.



why do half spin particles require that the wavefunction is asymetric under exchange of particles? is it a maths thing?


tryna get my head round the higgs mechanism next, wtf is mass?

#98
Because you touch yourself at night
#99
there's the understanding you can get in a paragraph, which'll lead to question fractal. and there's the revelation-level event you get from the math. gotta learn the language of creation!

i'm sure that math teaching is part of the bourgeoisie's big school con. nobody leaves school feeling the way they do about math, discouraged, from their gentleperson's C in art class. nobody sees that C and gets scared to ever pick a marker up again. after a con's done and the money's gone, and the victim starts getting wise, there's always a cool-down where the con-artist makes em feel like it was a game that they lost fair and square. it helps prevent blowback or revenge. was math class a fair game? there are only so many well-paid technical jobs. math class is more for sorting than learning. not a lot of people are turned off by reading forever from english class. maybe its closest analog is phys ed, another naked sorting system. i had a facebook data scientist one time tell me math was like harry potter magic. really embarrassing thing to say. but that's part of the harry potter ideology, that there's a special privileged race of man that's destined for advantage. math's not like that but the ideology around it is, so don't let all that turn you off.
#100
maths is for harry potter nerds
#101

The Higgs mechanism is therefore also called the Brout-Englert-Higgs mechanism, or Englert-Brout-Higgs-Guralnik-Hagen-Kibble mechanism,[8] Anderson-Higgs mechanism,[9] Anderson-Higgs-Kibble mechanism,[10] Higgs-Kibble mechanism by Abdus Salam[11] and ABEGHHK'tH mechanism [for Anderson, Brout, Englert, Guralnik, Hagen, Higgs, Kibble, and 't Hooft] by Peter Higgs.[11]



physicists are fucking morons

#102
you're thinking of alchemy
#103
i dont think youre properly taking into account differences in learning styles - mathematical explainations just dont stick for me, i need conceptual stuff. so baninging on about how i just need to learn maths is stupid and irritating - i can do plently of maths already, it just doenst make sense conceptually when it comes to particle physics. id say if you are incaplable of explaining it to me without maths, you dont know it very well - and ive never met a physicist who could explain it without just pointing to numbers and going ta da. they might me "smart", but theyre absolutly crap at teaching. and they cant even come up with proper standardised naming conventions - how am i ment to teach this to children
#104
if you are receiving lots of common advice, that math is how QM concepts are communicated, and is the only discovered way to communicate them in full, then you can choose to put the intellectual energy you're expending now into learning the language, or you can expend it in another way. the advice tho is to take the easier route, thru the math, instead of the harder one, reading a million papers w/o understanding. check twitter for what class analysis looks like as performed by people who've never studied the 5 heads. thousands of hours they've engaged there w/o very much improvement, and how irritated they get when someone suggests they study one book, like it's an insult. maybe 200 hrs studying Lenin vs thousands in twitter fights fronting.

i went thru school intimidated by dy/dx and limped thru the courses, but have since changed my mindset during self-study and am finally allowing myself to learn it. calculus isn't that hard, it's how one thing relates to another thing, like space and time or energy and distance or posts per hour. i was over at my buddy's recently, in the last few months he's filled notebooks w/ math problem sets in self-study. film major cuz he got intimidated in college by the weed-out calc courses. we're gonna co-study linear algebra next month out of Halmos. it's what i'm saying. there's a whole ideology around STEM built by the profiteering class, standing in our way, existing for the mass-acceptance of high-paid, male mental laborers. 'of course they get paid more, they know magic and teacher told me i don't'
#105
im telling you i cant do it - physically - my brain wont do it, no matter how hard ive tried - i could waste years trying to "understand maths" or i could just use a model, which I can probably pick up in a few weeks - why cant you understand that?
#106
tears you're teaching physics to children? that's dope. ganbatte!
#107
im teaching "science", and since most people even in the core leave school not knowing what electricity is, let alone maths, i think its pretty rude that every time i ask for simple explainations for complex things in the realm of "physics" so i can translate them all i get told is learn maths - thats gonna go down a treat in the classroom isnt it lol
#108
as probably the only professional mathematician (at least currently, i'm not quite sure i'll stick around in academia) on these boards, i just a have a few comments that i hope won't be misunderstood as being dismissive.

firstly, from both myself, and from talking to my colleagues, none of us imagine we have some special innate talent in mathematics, and probably more than any other discipline, it's mastery is the product of time, patience, and focus, but little else. during my time in graduate school, i had found that most of my friends were not terribly successful in math during their regular schooling; in fact, a couple of them had failed math classes in highschool. i have had many friends that showed much more promise than myself when i was younger who ended up burning out. i didn't finish my phd because i had a special talent for math, i finished it because i didn't want to do anything else.

secondly, i am suspicious of the individuality of learning styles. i have been teaching college math for about 7 years now, and have read a bit of the empirical research on pedagogy. my understanding is that individualizing teaching for students has not shown to be effective. we don't really learn concepts in ways that are that much different than each other on aggregate. obviously, there are certain concepts that take longer to click for some students than others, and as a teacher you try to show different contexts to the students, so perhaps one way of approaching a problem will click faster than the other; however, ultimately, i do not think this is a difference in types of learning, but rather the specific educational histories of various students. if a student has never learned to add fractions (as many of my college intro students struggle with), teaching them about rational polynomial functions becomes a problem. furthermore, memory can be a stupid thing, most students only remember pieces of their studies, and they try to bridge those pieces of knowledge into a piecemeal system of understanding, which can cause particular difficulties for mathematics due to the very cumulative and unforgiving nature of it.

thirdly, i do think the "intellectual class" nature of it is more pronounced in highly capitalist countries. i do not buy into the complete cynicism some of you may have towards "western" education; however, i do think that schools everywhere serve as sorting system in addition to a education system. this is not necessarily a terrible thing in and of itself. even in communist countries, students were tracked to what they showed interest and "talent" in. however, in communist states, there was generally a much more even playing field that children started off with. most elementary schools were relatively uniform in quality, and with a (more) leveled class structure, you didn't have students in one school coming from asbestos apartments competing against students in another school who all had private tutors and full stomachs. my mother, a social academic from yugoslavia, went on a social sciences and languages track during highschool, and never considered herself good at math; however, she never had this fear of mathematics i've seen in the united states. talking to friends and family from eastern europe, they might be amazed that i am a mathematician, but they're always eager to ask me what i'm studying and aren't afraid to have me sit down and show them at least the schematics of my research topics. americans on the other hand just say "dude, i always sucked math, i don't understand how you do that shit" and back off.

finally, i am not a physicist, but when understanding anything, it's important to not mistake the metaphor from the propositions themselves. there's a difference between understanding that gravity is a force that pushes things together, and actually being able to get actual scientific statements from it. the mathematics is the concept you are trying to learn.
#109
try teaching a class of 30 14 year olds who hate school and maths
#110

tears posted:

thanks, so let me see if ive got this straight - they cant occupy the same state because they would cancel each other out - like wave interferance - and thats impossible right, two particles cant just disapear each other. But when bosuns occupy the same quantum state its like additive interferance which is just +1 + +1. they would appear industinguisahble/identicle to each other just +n - hence the bose-enstein condensate where you get them to all do it at the same time and bring quantum wave shit into real life

with femions where its +1 + -1, which is impossible for particles, though possible for particle anti-particle interactions? idk, i feel like im missing something

i dont understand this bit though:

c_man posted:

symmetry properties of the wave function. Essentially, half-spin particles require (for reasons that are somewhat formal) that the wavefunction is antisymmetric under exchange of particles.



why do half spin particles require that the wavefunction is asymetric under exchange of particles? is it a maths thing?


tryna get my head round the higgs mechanism next, wtf is mass?


The first bit is exactly right, interference is precisely the concept to be invoking here. As for why fermions require this antisymmetry, im not of a way of understanding this that doesnt go into the guts of quantum field theory which requires a decent amount of sort of esoteric math, at least as far as i understand it. There could be a more straightforward explanation of why that should be the case but i dont know it. Thats really what math can help with the most, precision and dealing carefully with abstract concepts in regular ways.

I also agree with most of what elemenop said. I was never particularly gifted in mathematics, i just spent a lot of time on it and i found it more or less enjoyable, and eventually i developed some kind of fluency. Imo the process is similar to learning a language or musical instrument, and it can be easier or harder for various people for various reasons. Institutional preparation is a big one and any one those is a fairly daunting task to tackle without the active pedagogical action of some institution, which leaves a lot of people behind when they dont match the institutional vision of the desired students.

#111

tears posted:

try teaching a class of 30 14 year olds who hate school and maths



i have...it's difficult, and i certainly empathize with your struggle

#112
thanks
#113
science as a whole, but especially biology are a complete clusterfuck in the english education system - the amount which has to be taught in so little time is absurd. like in the average class if i cant explain something quickly and effectivly its not gonna get explained - if i want to include advanced and interesting stuff in an syllabus that is total shit i need to be able to do it quickly and effectivly around my professional obligations. as elementop said, memory is a funny thing, were absulutly crap at remebering anything. what a mess. this whoule thing is falling apart
#114
tears, if youre interested in a minimally mathematical explanation of some of these topics in particular you could read "qed: the strange theory of light and matter" by feynman (as much a pos as he was, he wrote on these topics pretty clearly). It doesnt address this particular question but it goes into a lot of interesting phenomena and is realistic about what sorts of calculations one needs to do, without sweeping too much under the rug.
#115
if i learned the maths what proportion would i find that was simply descriptive rather than explainatory?
#116
as a rule of thumb (i don't know QM) if it's got a differential equation, weird aspects of reality will fall out of the math. if it is an extremely simple formula, like gibbs phase rule, or exact constraint, then same, it holds hidden truths. if it's algebraic with lots of variables, it is probably a curve fit.
#117

tears posted:

if i learned the maths what proportion would i find that was simply descriptive rather than explainatory?


Iirc he describes the processes of doing the calculations in detail either in detail in simple situations where the answer can be understood in the correct way or heuristically in terms of the procedure you would carry out to arrive at the quantitatively correct answer. So i think it would be both descriptive and explanatory.

#118
sorry i didnt explain that very well - is the mathematics (in general) behind quantum mechanics primarily a (imcomplete) descriptive model or does it provide explaination of what is actually happening?
#119
Im not sure how to answer that beyond saying that it allows very precise predictions to be made. A lot of work has to be done to prepare the matter that we see every day in a way that allows phenomena that are normally averaged out into nothing to leave a measurable statistical trace, so our intuition in these matters is really reduced to understanding regularities about the formalisms that are borne out statistically by experiment. If a certain formalism is seen to be consistent with these highly specialized experiments we can then try to develop an intuition for what could be "actually happening" by observing limiting cases of these mathematical formalisms. But this is complicated by the fact that so many different ways for the microscopic dynamics to work could all potentially lead to very similar results at the length and time scales that we're most familiar with, and have well grounded intuitions for. I would say that they provide valuable and intuitively meaningful approximations of whats actually happening but thats hard to "prove" i guess.
#120
Edit: i misunderstood part of the question