Cambridge Mathematician Reacts to 'Animation vs Math'

today I'm going to be reacting to the famous YouTube video animation versus math let's dive straight into [Music] it hi everyone and welcome back to my channel for those of you that are new here my name is Ellie and I'm a Cambridge Mathematics graduate and today I'm going to be reacting to animation versus math I'm very excited it's my first time seeing anything like this I have lived under a rock for the past few years and I haven't seen any of these animation videos so this is my raw reaction and I'm really excited to watch it so let's dive straight into it okay let's go oh wow the music is intense Okay so we've got a a stick person one it's a great number whoa we've got an equals okay oh okay we've discovered addition is this video just going to be doing this for like infinite amount of times okay maybe maybe whoa okay we're just adding numbers here oh okay got some additive laws in there oh we've gotten to the number two now okay oh is this is that going to go until Infinity as well oh we've got bigger numbers okay okay nice nice we're on to the number 100 we're in three three digits okay got some oh are we going to subtract now is that is that a wand or is that it's a subtraction okay we're so we're subtracting n 98 okay so we're just learning about the addition and subtraction laws whoa okay hang on hang on hang on rewind rewind it's using O's identity hang on hang on yeah nice okay so I'm going to pause here O's identity this is basically just saying that e to the I pi equal minus1 it's actually quite funny this ident is a hot topic of conversation between my friend and I because this is his favorite mathematical equation I absolutely love it it's a great mathematical equation but for me my favorite maths formulas and maths equations are the Navia Stokes equations and this reminds me actually of the shot that I saw on Instagram favorite equation I you know I think oil's identity is is the one isn't quite thing is I think Oilers Oilers equation is a bit like the pumpkin spice latte of the maths world right it's like it's like the one that everyone says you know the one that like everyone loves love and then I love to hate right so it's nice that we've got an appearance of this straight away something about this equation and I can see why a lot of people say it's one of their favorite equations it's so simple yet it corresponds to such beauty in mathematics and yeah it's it's one of my favorite equations but like I said the Navia Stokes equations they have my heart so but yeah I kind of concerned that we we've moved from addition subtraction and now we've moved on to Pi which is a trans transcendental number we've got I which is a complex number and E which is also a trans transcendental number so are we are we going to have multiplication in here soon or I mean I guess we've kind of got multiplication with the I and the pie here but we've got a power LW as well before we've even discovered multiplication and and division so yeah okay let's let's keep watching I'm sure that's going to come up soon but beautiful equation nice nice little bit of mat there oh it's moving okay it sounds like a duck watering oh whoa hang on whoa whoa whoa I'm just going to rewind so it multiply because e to the I pi equals minus one and then it's put an i out front so it's complex or imaginary so i multili e to the I Pi is I so that's imaginary and then once it's done that it's it's moved it's it's gone into like a different is that a dimension I don't know how do I describe this it's like in an imaginary world speaking of an imaginary world would you like to learn more about imaginary numbers brilliant.org have a course on complex numbers that dives into the definition of such numbers as well as interactive lessons and questions you'll get to learn all about the discovery of oil's identity as we've already seen in this video and as we'll see later in the video oil's Formula 2 and the consequences of of this in the imaginary world brilliant.org is a platform that offers courses on a range of stem subjects including mathematics science technology and much more the courses are designed to be interactive so that you are continually testing your knowledge but without the pressure of needing to get every single question right you can skip questions if you're unsure and bril provide you with the information so the learning process is as fun as possible for those of you who are a little bit more competitive you can compete in leagues where the more questions you answer and the more courses you complete the more points you earn if that sounds like something you'd be interested in then brilliant.org are offering you watching this video full free access to everything they have to offer for a full 30 days all you have to do is click on the link in the description box or in the pin comment section and the first 200 of you that click on that link will get 20% off brilliant's annual premium subscription sign up today and compete with me in one of the leagues so we're in the real world back with the real numbers we're missing a zero oh no we're missing a minus one there we go okay okay the subtraction the minus sign is stuck okay so we're moving oh okay nice minus time minus minus yeah minus times minus is a plus oh we're going to do multiplication twist it yeah nice okay okay oh wow we're learning all about the uh the laws of multiplication and addition here go do a divide yes nice okay okay six divided by two okay so it's kind of illustrating what we do whoa whoa whoa whoa whoa oh we're dividing by zero okay yeah that makes sense for those of you that don't know about when you divide a number by zero it's a big no no in mathematics yeah it's it's technically undefined which is why we're having this kind of repet this infinite number number of of zeros here cuz it's yeah it's not allowed so and again go on for Infinity it's broken we're broken okay there you go 6 minus Z okay we're back we're back we we've covered all the division the multiplication addition oh we're on squares now okay cool nice properties of squares I really like this kind of illustration of how you have one I guess equation so we have 6 + 2^ squar and then you have this this other way of representing it in like a very different kind of abstract way so here with all of the ones which which is quite nice the music is also really good and the animations like so cool okay nice yeah cool okay we're doing power we're doing power L again whoa okay I need to rewind there's too much going on what's going on here so oh that's cool it's kind of like Inception this is so cool the animations on this are so cool oh whoa hang on rewind rewind do you know this this just reminds me whenever I see the number 1024 does anybody remember playing the game that was called I think 1024 and it was where you had like a rectangular grid it was like it was a craze in maybe year 11 so when I gosh I don't know how many years ago now that was but it was where you'd have like you'd start with tiles of two and then when you kind of move them into each other it would make four and then six 16 and so on until you got to 1024 and I think it would keep going after that but whenever I see that number I just remember that game and I remember how I just now I can remember my two to the power n tables I don't know and it's because I did this game so if anybody wants to remember what two cubed and two to the fourth and and all those values are I'd encourage doing that game because it was a fun game yeah okay so back we're still doing laws again power laws we're learning about how if you take a number and put it to the power of zero we get one which is nice it's a it's a classic law in mathematics and then we're now taking a number and putting it to a power that's a negative and here we get a fraction nice we're covering quite a lot of maths in this and we're only three minutes in so I feel like there there's quite a lot left okay so we're learning about fractions and division that's cool and a power to a fraction again and now we're learning about square roots nice square root of four is indeed two or plus or minus two depending that's quite interesting I wonder why oh okay I see he's just pulled out a minus two there okay okay yeah that's nice Square Ro T of two is indeed 1.4142 and so on if you want to learn about the proof of why this is an irrational number why the square root of two is an irrational number then I've made a video on it so check it out if you're interested it's on this YouTube channel yeah learn about why hippasus was thrown overboard for proving it square of one is one nice yes okay okay I was wondering when complex numbers would appear again if for those of you that don't know the square root of minus one is an imaginary number and that is denoted by the letter I so whenever you see the letter i that is an imaginary number and that is equal to the square root of minus one the stick person's shot yeah okay we learn oh nice okay so we're learning about so we've gone from learning about the laws of addition subtraction for real numbers and now we're learning it for complex numbers yeah okay nice sorry I'm getting so nerdy about this we we've done the same thing where we've done I * I is minus one which also equals e to the I Pi multipli by I and yeah you get them both equivalent okay we're back we're back to the the complex stuff so oh no oila is scared whoa whoa whoa whoa God this has turned this has turned violent yeah okay wait wait wait wait hang on wait I need to let me just I need to like analyze this it's going too fast okay so we're hurting OA we're hurting e to the iPie for some reason e the IP is running away it gets an i and it moves into this I'm sure this means it's an imaginary world that's what I'm picking up from this so the white side is like the imaginary world and it's moved yeah okay okay so he's picked up an i he's trying to move to the imaginary world because I time e to the I Pi is imaginary but then the stick person has thrown an i which we know if you multiply I by I you get minus one so oer here I'm going to call e to the iPie oer I'm sure he'd love that Oiler is running away from the stick person and he's trying to get into the imaginary world but he can't because the sick person's just thrown an eye at him which means that he is now back in the real world if that makes sense yeah because he's gone out gone back in okay yeah because they whoa whoa whoa whoa there's so much happening this is this is like so stressful it's great animation but I'm just trying to react okay so so now they're okay this is a good place to pause they are fighting each other so now we've turned into some war in mathematics absolutely love that now eat the iPie it was minus let me just check it was e to the I Pi wasn't it when he came back out he was minus E to the I Pi yep and then this turns into minus E to the I Pi was minus cosine of Pi + I sin pi and that just corresponds to oa's formula in this case so this is a glimpse at oa's formula and I'll show an image of what oa's formula is on the screen just so yeah you're aware okay so we're now shooting minus signs whoa whoa whoa okay that's cool that's cool back to when I was on about oa's identity and O's formula typically what oa's formula kind of illustrates is this unit circle you can take oa's formula and it essentially represents a circle and I assume this is what they're getting at here so that's where the semicircle comes from okay nice no don't throw another ey don't don't do it oh no he's got the oh okay I get it oh okay okay so he's put he's taken the the multiplication sign and he's used it as like a power up in this sense God I wish math made me good at spot honestly okay so we're currently fighting between the stick person and Oiler okay now we're fighting with swords whoa whoa this is whoa why was there a zero there another zero is it because they're both fighting with the number one and they cancel out when they hit each other whoa let's see okay so if wait we've got OA with a four and stick person with a one this number from four has gone down to three and I assume that's cuz it's taken it from the stick person who had a number one okay and again it's gone down to two and the back to one whoa we got an arrow he's shooting Arrows with a with two twos wow okay okay now we've got e the I pi over four now that's going to this is going to turn into a circle isn't it's going to like yeah it's going to move up I thought so so that was corresponding on the on the circle at which we have pi over four don't shoot him with fours man come on I love how creative this is I don't know how I haven't seen this before okay I don't know what's going on okay he's broken his bow and arrow we've got a DOT okay hang on I are we going to move to decimals now that there's a DOT what else are the dots in ellipses recurring numbers so not3 and so on what else are the dots in matths time derivatives matrices if you have like the dot dot dot decimals I'm going for decimals I feel like this is this is the best bet okay it's a little ball oh okay it wasn't was it no it's not a decimal so he's drawing a number line now okay so he's drawing the imaginary number line so it's kind of like a chalk ball now he's drawing the real number line so he's drawing oh there we go nice okay so this is what I was on about he's drawn he has drawn the equivalent of oil's formula here nice Okay Okay so we've got radians yeah that makes sense because that extra additional part there is the cuz 2 pi is like 6 point something so the additional part is is that okay don't use it as a bow and arrow oh he's fencing now radius yeah nice okay oh wow okay so he's in he's increased the radius of of the circle and Pi Theta R is the definition of an arc that's that's the definition of of an arc in in maths so this is for when yeah okay nice when you increase R this circle is going to increase and likewise if you decrease R it's going to decrease which yeah it makes a lot of sense he's trying to move Thea isn't going to budge that's kind of cool I like that the soundtrack on this is great as well okay so are we back are we back to the unit no we're not oh nice okay nice yep we got Pi there oh this is really this is really like beautiful mats well okay now he's is he fencing is he fighting what's he doing this is a very aggressive stick person and it oh nice it produces the sign is that the sine wave I assume that's the sine wave was that the yeah and then that's the cosine wave so we're getting the wave function basically the correspond in waves that appear when we take oa's oa's formula and O's identity that's really cool nice we're back oh there there Oiler is again we found him and we're fighting with wand again and now we're fencing this is so aggressive it's very one very aggressive stick person we've got the arrow back the arrow is back we're fighting oh whoa okay whoa whoa whoa whoa rewind we've got some we've got some series here right so each the IP e the iPie turned into this power series and this power series typically we can we can represent e to the X as a power Series where it's an infinite sum of x the^ n / by n factorial so here we just substitute X in for IP and that's what we get okay so we have the series and now this is going to start shooting things oh okay it's shooting the term the first term in its equation each time so it's that's why n is increasing okay and then that's getting turned into the real number my gosh it's like a like a robot it sounds like a robot okay nice okay we're using I have no idea what's just happened here now we now we've got a cylinder cool great right so he's okay so this circle this Arc is now increasing massively sick person is trapped inside this animation is actually great fighting again he's going to they're going to jump F that fencing is not going to do you any good okay that was nice that was really nice POA we're back to oas's ah nice okay the amount of times I say nice in this video is ridiculous I keep just going oh yeah nice so Oiler formula this has turned into the equivalent of what these both these terms can be represented as in terms of exponentials yeah we we're doing a lot of like this is a lot of maths I feel like to watch this you need to know quite a bit of math this is stuff that you learn in in further mathematics whoa whoa what just happened there so while Oiler is building this multiplying Oilers formulas and and now the equivalent in exponential he's got this massive Army of of numbers little Stickman has taken Pi okay so we get nine this is nine tan of Pi he's put instead of Pi he's putting an i in there so now that's tan of unless that's just tan of Pi nine tan of Pi and now it's going to shoot it's going to use the function it's going to use the function as a as a gun okay sure and it's shooting okay so it's shooting Tans why are zeros appearing there so much going on I feel like I'm missing everything so hang on so zero are appearing I mean I suppose that makes sense cuz if if e to the I Pi goes into tan of Pi then that's going to be tan of minus Pi which is zero so I guess that's maybe why there's a zero appearing here but then again I didn't know why the zero was appearing last time so there's so many Oilers okay so the the circles increasing notice how R's getting added on here notice it's at 39 now and 40 it's just getting bigger and bigger stick person is probably going to die okay we're now Crossing higher oh how where have they come from where did they even appear from oh poor little stick person it's not going to stand a chance oh it's stolen the infinity sign okay oh nice okay so it's the function of infinity and it's yeah it's making it's doing it an infinite number of times so it's it's killing all of the ease whoa hang on we've got the span oh who that takes me back to my first year of uni okay I keep rewinding this so so we've got oh are we moving into a higher Dimension now cuz we had r one are we going to move or is this going to be is this going to turn multi-dimensional Okay so we're in R to the four r four dimensions okay so time's going to play a part in this surely oh resume positions resume positions oh my gosh right there's just so much going on okay now we have a Transformer so we've got a war in mathematics this is great this is this is fantastic I'm not sure how stick person is going to defeat that got Theta powerful symbol in mats okay so it's adding nine I so it's moved up nine and it's continuing to do that it is it is it going to drop on the Transformer drop on it no we're just going to use the gun again oh whoa Okay so we've moved okay the dimensions moved and now this this beam's been created using the amplitude of the S and cosine waves I assume and it's become like a three dimensional thing because of the change in dimension I assume I I kind of missed that but this Transformer does not sound a chance now increase the beam make it bigger and kill the Transformer is that an integral I only just noticed that oh my God there's a log there as well W it was using an integral as like as a a stick I don't even know can't believe I missed the integral I love doing integrals right stick person no it's making the beam bigger transform me you don't stand a chance okay so so now oa's moving to an imaginary into the imaginary world I think I'm I hope I've picked up on that correctly go quickly move go they're both going to go to the imaginary world aren't they yep okay so we're in the we're in the imaginary world now whoa no we're breaking oh it must be the imaginary world cuz look at all the numbers that are it's like the square root of negative numbers which obviously are imaginary so we are in the imaginary world okay that's nice that's nice we're breaking it though so the the imaginary world oh he's swimming stickman's swimming I'm just going to assume it's called Stickman cuz I've been referring to it as stick person but then calling it he so we're just going to s with Stickman oh be friends again oh he's apologizing okay a do you reckon oers realized that the imaginary world is broken so he can't go back there now so he has to make friends with people in the real world which is Stickman that's what I get for doing an English literature a level so just ignore the analysis there okay so they're talking about something now oh my gosh wait they looking for an eye yeah okay so now they're going to go into the imaginary world oh oh I actually don't know what's going on right now I think are they trying to find a way for Stickman to get into the imaginary world or to fix the imaginary world there's a there's a circle now whoa okay the gamma functions appeared out of nowhere oh whoa so is Stickman now in the imaginary world whoa so he's in the imaginary world now I think hang on hang on I feel like I don't actually know what just happened there so that's the end of Stickman okay and now e the IP is equals minus one we know that nice we've learned that okay okay whoa we're getting some more Greek symbols nice a are they their friends a what's that in the background what is that the thing that's moving along with them oh that was the end I still want to know what that is though to the left that's moving let me know in the comments what that is cuz I can't quite my brightness on my laptop can't it just showed me something that's slightly moving oh okay that was really cute I like that it's also not I wasn't I don't know what I was expecting for some reason I thought it was going to be like the stickman explaining math as though he was the teacher and I was not expecting a full-on war in mathematics so that was quite a nice refreshing thing to watch different from someone teaching on a whiteboard but I I really enjoyed that I really want to watch all the other ones now so I'm quite tempted to just make some separate videos on me watching like the physics ones this is so cool I've really enjoyed that thank you to everyone who asked me to do this it's a little bit different than teaching maths but I really enjoyed it and I'm excited to make this maybe a little series thank you for watching and I'll see you all in the next one

Channel: Ellie Sleightholm

Views: 308,080

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Id: g0NQ7x8PFfM

Length: 28min 34sec (1714 seconds)

Published: Sun Feb 18 2024