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
dimashq posted:u put the subtracted value into a small box and keep it secret, keep it safe
...thats division not subtraction
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"
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.
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.
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 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
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.
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.
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
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.