#Math in Common

[necromimetics]

This has caused great debate among my math friends so I think it needs tumblr's input

[trolley-problem-memes]

this is actually a common core math problem

[river-gale]

i think non-STEM people beat themselves up too much for being bad at math. partially i think this bc shame will never help you learn and everyone is capable of improving at math with patience and practice

partially i think this bc i’m still grading these applied calculus exams from a class of 3rd-5th year engineering students and several of them have said 1 - 6 = -4. two of them have said it’s -7

[baddog-nobiting]

i honestly love that the stancest tag is like 8 people all reblogging each other. it feels... incestuous 👀

[yrrtyrrtwhenihrrthrrt]

I live for the dynamic of "Both Goldenloin and Blackheart are very smart and competent in their respective fields but they are also both very fucking stupid"

[bubbloquacious]

How do you guys like this very convoluted proof of the Pythagorean theorem I just made

[goldstargloww]

jimmy: wait– isn't your soulmate.. doing soulmate things, with another person? martyn: yep! i've been cheated on! martyn: they thought i was cheatin, and then they went and cheated, but actually i never did cheat, so actually, they're the cheaters! martyn: [enters drama mode. voice gradually gets louder and thicker with emotion] martyn: look at them buildin their happy little home, and oohhh, i'm in love with scott, and oohh i'm in love with cleo, and– we're best friends, and we have FLOWERS in our hair, and WE BUILD BRIDGES, and– stuff like that! WHEN IS SHE GONNA THINK ABOUT MENDING OUR BRIDGES? jimmy: … jimmy: [amused] bro, i reckon you build like a little bridge connecting– [trails off with laughter]

[antisocialxconstruct]

was there ever actually any proof that socmed sites suppress posts with words like "commission" or "shop" in them, or is that just the boogeyman we all collectively invented to explain away the fact that people simply do not interact as much with posts where you ask them for money

[lipshits-continuous]

I think what annoys me more than saying the Dirac delta distribution is a function is when people say it's 0 everywhere except when x=0, it is infinity. Like that is just not compatible with the fact it's integral over ℝ is supposed to be 1. Suppose we did define an extended function that way:

δ is a Lebesgue measurable since {x∈ℝ:δ(x)<a} is empty for a≤0 and ℝ\{0} for a>0 which are both Lebesgue measurable sets. δ is non-negative so we can calculate the integral via

where the inequality is pointwise.

Now since δ is 0 except at x=0, we require any simple measurable function φ≤δ must also be 0 except at x=0. This leaves us with a constant times an indicator function:

where a>0, and

Then we have

So taking the supremum over a we get

So δ cannot be the Dirac delta distribution. You really need the theory of distributions to talk about the Dirac delta.

P.s. I know this isn't the typical notation for an integral with respect to a measure but this was the notation I had in my lectures

[eulerseverything]

Fucked up that math is so tied to computer science. Wheres the love for those of us who just wanna look at number. No screens. Touch grass (count them perhaps)

[uncanny-tranny]

Whatever skills or knowledge you think is "universal" absolutely isn't, and when you understand this, you can understand deeper how people experience the world. There are so many things that are deemed "common knowledge" that just aren't to some people.

Maybe you think it's common knowledge to know how to eat, for example. But it isn't common knowledge for me; I don't know how to eat because of my disabilities and because of my history. I can physically eat, yes, but the knowledge of how and when is something I never learned. I can absolutely learn, sure, but it is a time and energy investment, which is why I hadn't done so before.

What would help me more: being belittled and demeaned because I don't "know" something like a normal person would or being educated in an understanding way? Now, apply this to other people who struggle with things you think are "fool-proof," and you will start to understand how people operate when they aren't "normal"

[tswwwit]

I was busy fawning over some fictional men and this question suddenly hit me…Has Dipper ever really got into a celebrity or a character or something similar like that? And how would Bill react if he did, would he tease him about it or be jealous?

I think it would be amusing if there was, say, a demon hunter type, a colleague of Ford's, who gained some celebrity! Dipper, when he was younger, would easily be swayed by the 'charismatic heroism' of some Cool Young Guy in the profession he admires.

Bill is obviously jealous, as is his nature.

I can't decide, however, if it's funnier if Ford regrets not introducing Dipper to that guy when he had the chance, or if he's appalled. That man? His scientific rigor is terrible! His results are shoddy! Dipper should find a partner who respects science, damn it.

[friskdistrollerroblox]

I ain't gonna lie, the Numberblocks fandom is scary in some ways, when I joined it I thought it was going to be people admiring how easy this show explains maths, even how they explain advanced math stuff, some silly content here and there, but what I've discovered with the pass of time actually surprises me and scares me too, controversy, inappropriate stuff, drama... I will not let that stop me from enjoying this show, just hope the fanbase could be a bit better!

[starlitmeadows]

I DID IT

I PASSED THE MATH EXAM

LET'S FUCKING GOOO

[sailor-hufflepuff]

My daughter is crying because she can’t do her math homework. I try to help, but she says I’m not doing it the way the teacher said to (which I believe, because the directions make NO SENSE to me).

Why do they change math every generation? I remember my mom not being able to help me with my homework, and telling me that her dad couldn’t help her either, because they KEEP CHANGING it to make it “easier and more logical”.

Which. Even if it IS, if the parents can’t help the kids with homework, how will the kids be able to learn? Because this disproportionally affects disadvantaged kids whose parents don’t have the time to learn it themselves, or the money to hire a tutor, or the socioeconomic status to send their kids to a school where the teacher actually has the time to TEACH everything during the day.

[motherfactorin-pi-face]

In which I describe the maths of how to attack and dethrone God (per Minamimoto)

So in my evergrowing post thread (which I know I'm already gonna have to add to that essay fml) I did make ref to...well, a thing that literally has made my jaw drop since when I played TWEWY the first time (and keeping in mind this was a game friends forcefully insisted I play because "there's a char Sho Minamimoto who's just like you fr", and after I'd nodded "yup" re the SI unit obsessions and the compsci refs to Heaps and Crunching (and later, as I found out, "crashing" in JP), and the aesthetic, and, and...)

Namely: Sho Minamimoto literally uses (or tries to use) a very famous maths formula called Euler's Identity to take out the Composer as an example of Forcefully Applied Mathematics. :D (This may have also been the moment when I was like "Yup, he just like me FR")

So. First off. Euler's Identity.

It's kind of difficult to explain why this particular equation is considered one of the true Chef's Kisses of Mathematics to non-mathematicians, but part of it is elegance, and part of it is that it includes five of the foundational variables that show up in mathematics all the time (and really even more functions if you break it apart): a) the natural logarithm e or Euler's number which is roughly 2.71828182845... and which is zetta important in a lot of fields including finance, biology, medicine, and calculus functions, and (as we'll get into) antennas and field strength measurements and pretty much a Shitload of functions related to growth b) the imaginary unit i or the square root of -1 (which turns out to be extremely useful in a lot of contexts, including electronics (seriously; AC electricity and functions relating to that are *heavily* dependent on the imaginary unit) and graphing and arguably how Cartesian graphs work especially once you get into calculus c) Pi (π), everyone's favourite circle ratio of 3.141592653589793238462643393279 (is pulled away from keyboard before I can draw a Taboo Noise Refinery Sigil in Paint) and which is Important in many, many contexts d) 1 (yes, 1 is considered a constant! Specifically "A quantity exists") , and

e) 0 (yes, 0 is considered a constant too, specifically "a quantity does not exist", and reducing Euler's Identity results in e^(i*pi)+1=0) To make it even more Minamimoto-esque, you can technically also express Euler's Identity as a reduction of "e^(i*x) = cos(pi) + (i * (sin(pi)) (aka Euler's Formula), and cos(pi) =-1 and sin(pi)=0.

And really it's kind of a beautiful way of how things all fit together in a lovely function that is almost a kiss from the Math Gods and if plotted traces a lovely circle.

So after that little tangent, here's how this all relates to W2D7 of TWEWY, and Minamimoto's forcefully applied mathematics. * * * So, first we end up at Pork City (Mark City if you're watching the anime; Tokyu Group liked the TWEWY tourism and by the time the anime and NEO came around decided to take advantage of the advertising), and...Joshua and Neku start having a very interesting conversation on why there's So Much Damn Noise at Pork City anyways:

Neku asks if this is the work of Pi-Face, Joshua notes "Probably" and then goes on to note that it might not all be JUST Minamimoto:

In other words: Pork City is effectively acting as an amplifier or at least an antenna for Noise. (I am not the only one to have noticed it and not even the only one on Tunglr, for that matter; Voice From The Corner also picked up on this as well though I'll freely admit I'm diving a bit more into the STEM portions of this.) TWEWY:tA is even more blatant about this imagery in ep 6, where Joshua explicitly notes that all the emotion in Shibuya collects at Mark City (remember, the animation uses the RL name) and then "crashes into Mark City and shoots up into the sky. That emotion flows back down and keeps building up here." (Shortly afterwards, Joshua also mentions the Imaginary Noise Plane as the inside of Mark City warps, similarly to a sine wave flow--or the flow of energy into, or out of, an antenna. (You do not know how loudly I screamed seeing this, as an aside) So, this is where we get into piece one, e (and where a healthy interest in radio and electronics hobbies helps!)

So antennas, interestingly, have how well they pick up a frequency measured in a logarithmic scale, and basic field strength measurements (and a lot of other "wavey" things, including earthquakes, including, well, literal background noise) get measured on logarithmic scales too. It's rather more common with antennas and earthquakes for this to be measured on log-10 scales (hence the Richter scale for quakes, or decibels for antennas and sound). There's a particular group of measurements (physical field and power measurements), however, that actually uses log-e, aka the natural logarithm, and especially for voltage or current and "root power quantities"--the neper. And, in Euler's Identity, e is taken to powers...and Pork City is basically acting as a huge antenna. Also in info engineering aspects, there's another aspect--the nat, which is considered a unit of information or info entropy...also based on e. (I told you Euler's number comes up a lot of places!)

Let's continue... So now we come to i, the imaginary unit, and that's called out blatantly by Joshua:

This, too, is based on math--from Final Fantasy II, specifically, and how the Flare spell worked. Flare is an area-effect spell and it hit based on (Enemy's HP/Flare level), i.e. enemies that had HP divisible by 2 could be hit by a Flare level 2 spell and could deliver damage based on that spell's level, etc. So a level i Flare, based on how complex numbers work, could hit just about anything (assuming, of course, that the Composer is not a Fractal Bastard and promptly yeets himself into a PokeYugiBeyBladeVerse). But...that's not the ONLY part where things imaginary come into play. So, one of the interesting bits of lore that came out in (of all things) the NEO:TWEWY Field Walk RPG (alas, JP only, but a delightful source of lore, and thankfully the fan community preserved almost all of it) is actual canon on how Tin Pins and Psychs work including the actual formula on how they work in a convo between Minamimoto and Fret:

Fret: Soooo, these psychs and pins and stuff… how does it all work? Minamimoto: The pin is charged by the Imagination of the user. Fret: Uh huuuh. Minamimoto: The pin itself is just a medium. Fret: Mm-hmm. Minamimoto: “Power” is calculated from the numerical limit of the pin, using your will as a coefficient. Fret: Yeah. Minamimoto: But that formula alone means nothing to me!

(Emphasis mine: props to Pavaal on the Dead Bird App for initial translation, and to multiple others for confirmation from the FWRPG script.) So basically how Psychs work is functionally as an athame, using formula Psych=Limit^Imaginatio. (Secret Report 1 in TWEWY also confirms Imagination is important in making a Psych work to begin with; the formula) Of note, Minamimoto also has a canonically high Imagination, as detailed in the Secret Reports. To even become a Reaper to begin with (as noted in SR7) those who survive the week who have enough Imagination become Reapers, and even among Reapers Minamimoto tends to stand out (he is canonically the youngest Reaper Officer ever, and apparently had quite the rapid rise to power). SR15 in TWEWY notes (even keeping in mind that in this instance Hanekoma is being a bit of an Unreliable Narrator in covering his own butt regarding the Taboo Thing):

The sigil Minamimoto drew was one of the undecodable types. Was that a mistake on the Fallen Angel's part? Or was it a transcription error by Minamimoto? Either way, with that design, he stands little chance of reviving himself. However, Minamimoto is driven, and his Imagination strong. Perhaps strong enough to make a Taboo sigil work, even in the Underground... If so, the specific result would be impossible to predict.

And in SR19 (again, covering up just a bit for his own helping hand):

I've detected an energy spike here. It would seem Minamimoto has returned. I judged his revival unlikely after spotting his Taboo refinery sigil on the first day, but it appears Minamimoto's Imagination is much stronger than I'd anticipated. The Fallen Angel must have completed the array for him. A troubling thought. Who can say what impact this will have on the Composer and Conductor's Game?

And even in the NEO Secret Reports it's noted his second trip through Coco's version of the Sigil actually ramped up his Imagination even more (in NEO SR 7):

Minamimoto, on the other hand has all but vanished from the proxy’s side. His Noise refinery sigil drastically heightens his Imagination, which may be why he can clearly recognize the proxy’s abilities. I have an idea of what he’s planning. It’s dangerous, but I have no way of stopping him.

And again, TWEWY:tA also makes it more blunt that Minamimoto was selected explicitly because of his Imagination and his connections to Shibuya as Hanekoma's Plan B. So there's imaginary units (in the sense of literal level i flare), and imaginary units (in a Reaper whose Imagination is already in the stratosphere). And in regards to pi? Well, Pi-Face, he has very much a rep of being....numbers- and math-obsessed even BEFORE he throws 156 digits of pi in the Composer's face:

But pi (as a number) is actually meaningful as HELL to Minamimoto, he engages in saying pi to himself drawing the Taboo Noise Refinery Sigil (goroawase in Japanese which relates to literally an obstetrician going to a foreign country and a woman giving birth at night as insects make a lot of noise which can almost be seen as a minor ritual to Make It Work, a little happy pi rhythmic thing in English in the game, actual spoopy sounding pimetry in the anime that sounds very sorcery-y). Looking (for far too long) at the Taboo Noise Refinery Sigil, pi is encoded in it in at least four or five places (multiple times as functionally a magic binding circle, at least once where he draws the symbol for pi in such a way that when it's turned upside down it literally spells "pi"). It's important. It's meaningful. It's His Number and transcedential and irrational and beautiful and unrestrained :D So now y'all are wondering, "OK, smartass, where's the -1 at?" As I noted, another way you can write Euler's Identity is specifically as "e^(i*pi)+1=0", so that can be expressed as a way to null the Composer (who is probably the 1 in question). Euler's Identity would be used to subtract 1 from the equation, in other words (as Minamimoto was intending to come back from Erasure by literally integrating himself via Taboo Noise Refinery Sigil). There's one other interesting bit of symbolism, one that's deep enough that I'm not even sure the writers of TWEWY intended, but if so...it's such a chef's kiss that I have deepest admiration.

So Euler's Identity can be expressed in terms of a formula, and as a reduction of sine and cosines involving pi and i, but it can also be mapped as motion--specifically as how a function evolves. (I tend to be a pretty visual thinker, and there's an extremely good discussion on Euler's Identity here that goes into the whole "mapping the function" aspect to show how Euler's Identity works in practice.)

So typically when you're doing a non-negative function or a zero function, generally there's an assumption of "right-hand" rotation or movement. Complex functions, you get into fun things like circles, and curves, and even some very beautiful fractals (like with the Mandelbrot set) with the right iterative formulas. Euler's Identity...is literally a left-hand-path function:

(And those of you who were writing about the Cyclic Nature of Minamimoto are probably all screaming right now) Anyways, wanted to share in full one of the things that was a jawdropper for me in TWEWY back when I found the game at a glorified skateshop that sold games in 2011. Thank you for coming to my TED talk, zeptograms :3