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the veritasium video where he shows the bifurcation diagram and then turned it on the z axis and you saw the mandlebrot set wan like woah wanna make a clicker game that somehow includes gravity 🤔🤔🤔 thinking out loud - you have a space field and you have some icons that have (manipulatable?) gravity and from one direction (maybe) you have a particulate resource coming from side and the gravity from each icon sucks in the resource but you might have to fine tune the gravity so the early icons don’t suck in too mind compared to the later icons which might be more powerful or have higher multipliers. and the resource might take some interesting to watch trajectory as it passes some gravity icon and moves around OR you’re some passive space debris harvesting machine floating thru space picking up stuff and you have to manage the ships meagre resources to keep the different harvesting parts of the ship efficient. but idle games. love me an idle game
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Jun 25, 2023 20:44
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watched a video last night where a guy was unnecessarily optimizing n64 code, specifically how to calculate sin and cosine values more efficiently and it went into using complex plane
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Jun 25, 2023 21:08
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deeply offended by echis mathpinions itt
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Jun 25, 2023 21:09
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echinopsis posted:the veritasium video where he shows the bifurcation diagram and then turned it on the z axis and you saw the mandlebrot set wan like woah hofstadter had a good reveal like this somewhere in metamagical themas if that's of interest
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Jun 25, 2023 21:16
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rotor posted:deeply offended by echis mathpinions itt phi vs e which is better
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Jun 25, 2023 21:30
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echinopsis posted:phi vs e which is better phi isn't even transcendental, what is this question even
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Jun 25, 2023 22:41
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https://twitter.com/SummerTimeAlice/status/1581900888364707840
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Jun 25, 2023 23:09
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mondomole posted:phi isn't even transcendental, what is this question even you’re lying to yourself
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Jun 25, 2023 23:16
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absolutely in cahoots with pi. you're just minding your own business flipping roughly infinity coins and you want to know how likely you are to have between a third and two thirds of them heads, and well well well not only is e there, but pi just slips in all "oh don't mind me i'm just here to normalize this probability distribution" like it's nbd. except i'm not doing anything with circles, so why are you here? you weren't invited to this, this is between me and my coins and maybe some sums or integrals depending on how fancy i'm feeling
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Jun 26, 2023 07:28
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Deep Dish Fuckfest posted:absolutely in cahoots with pi. you're just minding your own business flipping roughly infinity coins and you want to know how likely you are to have between a third and two thirds of them heads, and well well well not only is e there, but pi just slips in all "oh don't mind me i'm just here to normalize this probability distribution" like it's nbd. except i'm not doing anything with circles, so why are you here? you weren't invited to this, this is between me and my coins and maybe some sums or integrals depending on how fancy i'm feeling um, coins are round dumbass
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Jun 26, 2023 07:30
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echinopsis posted:um, coins are round dumbass hes gotcha there
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Jun 26, 2023 08:07
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here's a proof for you: Volume = (4/3) pi r^3 see, there's p right there in the middle
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Jun 26, 2023 11:52
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the two bits of maths which really blew my mind when i first learnt them were cantor's diagonal proof (it's so simple but it just feels like it must be wrong, the new sequence must already be in the set! you can't have bigger infinities!!!) and euler's identity
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Jun 26, 2023 14:11
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distortion park posted:the two bits of maths which really blew my mind when i first learnt them were cantor's diagonal proof (it's so simple but it just feels like it must be wrong, the new sequence must already be in the set! you can't have bigger infinities!!!) and euler's identity mine was learning that vectors are derivatives and basis vectors (basically the axes of the coordinate system) are partial derivatives
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Jun 26, 2023 15:01
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distortion park posted:the two bits of maths which really blew my mind when i first learnt them were cantor's diagonal proof (it's so simple but it just feels like it must be wrong, the new sequence must already be in the set! you can't have bigger infinities!!!) and euler's identity i remember finding this extremely confusing and unclear rather than mind blowing per se. it was covered fairly early in an intro class where up to that point we had been rigorous about stuff like basic properties of numbers. the part that always bothered me was: a) why are you allowed to define an infinite sequence based on the diagonal, and b) why is the resulting number even well-defined? i didn't have a way to articulate my concern but it seemed like there was a disconnect between how rigorous we were on some stuff while letting other stuff slide, and i couldn't figure out the pattern and as it turns out (a) and (b) aren't even super obviously true. like a small tweak to (a) and you're in axiom of choice territory, and (b) isn't proven until you cover sequences
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Jun 26, 2023 15:33
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mondomole posted:i remember finding this extremely confusing and unclear rather than mind blowing per se. it was covered fairly early in an intro class where up to that point we had been rigorous about stuff like basic properties of numbers. the part that always bothered me was: a) why are you allowed to define an infinite sequence based on the diagonal, and b) why is the resulting number even well-defined? i didn't have a way to articulate my concern but it seemed like there was a disconnect between how rigorous we were on some stuff while letting other stuff slide, and i couldn't figure out the pattern welcome to intuitionism comrade
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Jun 26, 2023 16:26
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if you like your number system, uh, you can keep it
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Jun 26, 2023 16:27
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echinopsis posted:um, coins are round dumbass ...gently caress
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Jun 26, 2023 16:39
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it's both math and computer science, and it's not a fundamental thing, but i remember going "woah" when i learned how you can solve for all the zeros of any polynomial iteratively without dealing with poo poo like getting stuck in minima or missing some of the zeros. since there's already iterative algos to get the eigenvalues of a matrix, and eigenvalues are the solutions to the characteristic polynomial of that matrix, you just build a matrix that has the polynomial you want as characteristic polynomial and you find the eigenvalues of that. it feels kind of obvious once you learn about it, but when you first learn about this in linear algebra you pretty much always start with a matrix, then build the polynomial, then solve for that, so you never really think of going in the other direction
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Jun 26, 2023 16:48
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Deep Dish Fuckfest posted:it's both math and computer science, and it's not a fundamental thing, but i remember going "woah" when i learned how you can solve for all the zeros of any polynomial iteratively without dealing with poo poo like getting stuck in minima or missing some of the zeros. since there's already iterative algos to get the eigenvalues of a matrix, and eigenvalues are the solutions to the characteristic polynomial of that matrix, you just build a matrix that has the polynomial you want as characteristic polynomial and you find the eigenvalues of that. it feels kind of obvious once you learn about it, but when you first learn about this in linear algebra you pretty much always start with a matrix, then build the polynomial, then solve for that, so you never really think of going in the other direction this sounds kinda like how when u graph functions like z = y^2 * x or whatever you always do it that way. but if you flip it around and subtract z from the right side and set the equation equal to 0 then you basically have a field that approximates the distance from the n-dimensional surface you just graphed. you can make it more exact by dividing that by the derivative of the function, which is essentially the vector field that defines the gradient of the distance from the surface. the direction of the derivative vector field at the surface itself is the same as the direction of the surface normal, which defines the angle at which light will bounce off it. you can then use all that garbage for computer graphics it’s basically just plotting a function but sorta flipped around a bit
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Jun 26, 2023 17:05
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fart simpson posted:if you like your number system, uh, you can keep it based 10
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Jun 26, 2023 18:00
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fart simpson posted:this sounds kinda like how when u graph functions like z = y^2 * x or whatever you always do it that way. but if you flip it around and subtract z from the right side and set the equation equal to 0 then you basically have a field that approximates the distance from the n-dimensional surface you just graphed. you can make it more exact by dividing that by the derivative of the function, which is essentially the vector field that defines the gradient of the distance from the surface. the direction of the derivative vector field at the surface itself is the same as the direction of the surface normal, which defines the angle at which light will bounce off it. you can then use all that garbage for computer graphics signed distance fields you mean? yeah they're pretty neat. i was a graphics programmer for a number of years in another life so i've dealt with them before. you can use them for collision detection, fluid dynamics constraints, and a whole bunch of other stuff. really nice when you want to compute stuff in parallel, eg on a gpu, since a lot of times you can update each discrete sample of your field independently. they're a case of a "dirichlet problem" where you have a partial differential equation, and you want to solve it in a way that the values on a boundary (the surface in this case) are equal to some condition you set (being the surface normal in this case). it shows up over and over in physics; everything from heat transfer to electromagnetic fields to quantum mechanics
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Jun 26, 2023 19:19
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OzyMandrill posted:here's a proof for you: that equation was actually my aha moment where I wanted to study math, when we did an acial rotation integral on a semicircle and simplified it down to that and I realized that all the bullshit I had been forced to memorize had poo poo backing it up. i was all in
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Jun 26, 2023 19:56
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what pisses me off about integrating areas and volumes of disks and balls (heh) is that it makes it obvious that whatever moron decided that pi should be 3.14 instead of 6.28 hosed up big time and now we're stuck with all of those 2 factors everywhere for no goddamn reason. half of the time whenever i'm trying to solve something that has trigonometry or anything periodic in it, just replacing 2*pi by its own variable makes things so much easier to think about kinda like how physics people crunching hard equations just go "yeah assume all physical constants are 1 we'll just retcon it later when we clean this up"
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Jun 27, 2023 01:39
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Deep Dish Fuckfest posted:signed distance fields you mean? yeah they're pretty neat. i was a graphics programmer for a number of years in another life so i've dealt with them before. you can use them for collision detection, fluid dynamics constraints, and a whole bunch of other stuff. really nice when you want to compute stuff in parallel, eg on a gpu, since a lot of times you can update each discrete sample of your field independently. they're a case of a "dirichlet problem" where you have a partial differential equation, and you want to solve it in a way that the values on a boundary (the surface in this case) are equal to some condition you set (being the surface normal in this case). it shows up over and over in physics; everything from heat transfer to electromagnetic fields to quantum mechanics yah i just used them to make this donut last week 
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Jun 27, 2023 01:47
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fart simpson posted:yah i just used them to make this donut last week don’t show us your hairy donut
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Jun 27, 2023 01:49
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comb that doughnut
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Jun 27, 2023 03:47
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George posted:comb that doughnut nut in the dough comb
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Jun 27, 2023 04:24
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rotor posted:deeply offended by echis mathpinions itt he is a complex pain
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Jun 28, 2023 22:38
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Deep Dish Fuckfest posted:what pisses me off about integrating areas and volumes of disks and balls (heh) is that it makes it obvious that whatever moron decided that pi should be 3.14 instead of 6.28 hosed up big time and now we're stuck with all of those 2 factors everywhere for no goddamn reason. half of the time whenever i'm trying to solve something that has trigonometry or anything periodic in it, just replacing 2*pi by its own variable makes things so much easier to think about my friend what you need in your life is τ
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Jun 29, 2023 01:59
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big scary monsters posted:my friend what you need in your life is τ you're not wrong, except that τ is 100% the wrong symbol for those "circle constant" guys to have chosen. A main audience for this is EEs / signal-processing folks, because we have 2π bullshit everywhere. But τ is widely used to represent time-constants in that domain, so it's not open for reclaiming. They should have picked 🍑 instead of τ if you ask me
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Jun 29, 2023 07:35
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Poopernickel posted:you're not wrong, except that τ is 100% the wrong symbol for those "circle constant" guys to have chosen. extremely good av for this opinion
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Jun 29, 2023 09:21
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Just make it happen. Pick a symbol and start using it. Make it one syllable and fun to write with a pencil. The Greek letter Xi is pretty dope.
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Jun 29, 2023 20:03
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I propose 麤
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Jun 29, 2023 20:06
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Poopernickel posted:you're not wrong, except that τ is 100% the wrong symbol for those "circle constant" guys to have chosen. it also looks sort of like half a π, which seems backwards
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Jun 29, 2023 23:17
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wide pi
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Jun 29, 2023 23:53
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pipi (pronounced like modern greek)
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Jun 29, 2023 23:54
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using τ probably does make more sense, but the community of people pushing it are the most insufferable bunch imaginable. they really give off the vibe of nikola tesla fanboys or dvorak keyboardailures who have to make it their personality and work it into everything
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Jun 30, 2023 00:07
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Sweevo posted:using τ probably does make more sense, but the community of people pushing it are the most insufferable bunch imaginable you do realize where you're posting, right???
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Jun 30, 2023 00:16
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huh. never heard of the τ thing before. shame about both the choice of symbol and the people pushing for it, though i'll settle for just considering 2pi a single symbol and making it an error to split it or cancel the "2" in an assignment or exam or peer-reviewed paper or anywhere else. or if not an error, then at the very least rude and not socially acceptable unless in the company of the most reckless, notation-abusing, and frankly depraved physicists around
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Jun 30, 2023 00:22
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