arguing with a math PhD friend be like (unscripted, unedited)
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- Опубликовано: 25 июл 2022
- I asked a math Ph.D. @drpeyam to explain the topologist sine circle (topologist sine curve) from the book "Real Analysis" by Charles Pugh. It is the set of all (x,y) so that x=0 and the absolute value of y are less than or equal to 1 or y=sin(1/x) for x belongs to (0,1]. This is a very interesting curve because it is path-connected but not locally path-connected. What exactly does that mean? Well subscribe to @drpeyam for higher-level math and check out his video here: • Topologist Sine Curve
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Check out Dr. Peyam's video here: ruclips.net/video/pi-sS3lgszA/видео.html
The book is "Real Analysis" by Charles Pugh
Oh that's just implicit, its trivial, it forms naturally from the thing it doesn't say. yep yep
@@TheZabbiemaster Like when a math text says in a proof that "it is easy to show" something, but they don't show it, because it is too easy.
@@barence321 'The proof is trivial and left as an exercise to the reader'
Ok sir
conclusion i take from this video:
Topology is the weirdest branch of math
Fact: 99% of discussions between mathematicians ends when one states an really elegant looking argument and the other one just pretend to understand in order to not look dumb.
Physics student here im the second one haha
So true!!! Googles it later to actually understand.
It’s not dumb to not understand! Many people just prefer to figure shit out alone and at their own pace
That is because the unit sphere is only compact in finite dimensional vector spaces.
@@andik70 Offcourse!!!
"You don't need to understand it to teach it, you just have to sound confident enough that it's true"
I felt that
When I was training young sailors in the Navy, "If you can't dazzle them with brilliance,, then baffle them with bull*". And if you have to lie, then lie with CONFIDENCE!!! lol
😆
...mmm... yeah.... you might just get away with a stunt like that at times. But then one day, you push it a bit too far, and a student begins asking relevant questions to which you start mumbling, clearing your throat.... things a going backward now.... "yes sir - madam, but you just said...." ... caught like a rabbit in a spotlight..... The whole thing can fall apart and take your reputation down with it. Most people are quite appreciative if a presenter "confesses" to doubts about certain matters. It is not academic weakness.
@@vaughanwilliamson173 I had a professor like this for my first abstract algebra course lol
in other words, fake it 'till you make it
PhD in mathematics: Do woosh and you have a circle
Absolutely brilliant
LOL
That is one of the true beauties of mathematics. We show exactly what we want to show, and then say 'Somebody else has already done this, trust me it's possible, so we are just gonna skip that.'
@@ahrim_ I love how much in common advanced maths have with severe ADHD. It becomes jazz after the coda.
I have never felt this attacked before. As an algebraist, the number of times I have told my friends to "just identify them" is uncountable.
Your natural numbers are finite?!?😳
Uncountablely many is much bigger than countablely many.
and the number of times teachers have told me something along those lines is uncountable too
Just tell him how to collapse topological spaces. Equivalence relations, projections and then we are all happy. I can understand the point of the question, and NO, that was not "implicit" at all...
I think by "identifying them" or "attaching them together" he means define another map that takes one point to the other, perhaps uniquely and/or continuously (relative to neighborhoods around them). How else are you going to show "donuts homeomorphic to mugs" than finding a continuous and invertible function that maps points to points?
"Take this, do whoosh, and then you have a circle."
Explains so much and yet so little 😂
This video was so fun to watch
That sentence gave me PTSD from Algebraic Topology.
"It's implicit in the definition"
-"Fine, whatever."
Welcome to math!
😆
Soo true 😂😂
You know you've reached the peak of maths when you can explain a concept using sounds effects from a free trial video editing software, some donuts & coffee, and most importantly, CONFIDENCE.
😆
I wish I could do a PhD and keep my happiness just like Dr.Peyam
I think you have to really be into a specific field in order to get a PhD in it while still maintaining your happiness or even sanity :)))
Perhaps the happiness and enthusiasm results from passing a point of no return, and as it turns out it really is beautiful over there.
@@trollme.trollmehard.9524 interesting thesis :)
@@trollme.trollmehard.9524 wym? sounds interesting
"but why are those two points the same?"
"because I identify them to be the same point."
I don't know why, but this just cracks me up... maybe because I would have the same exact confused reaction (as a young physics student) before I took some abstract math classes.
It all gets a lot easier once you just identify physics with abstract math. Just identify it.
I identify as an apache helicopter.
@@mahikannakiham2477 Rofl ^^
Dr. Peyam's enthusiasm for math never fails to amaze me 😂
Hahaha woosh!! Thanks for having me 😊
Here’s the man!!
I know I'm a mathematician because I was getting frustrated too I was like "we just mod out by the equivalence relation. the circle is no big deal they're homeomorphic"
Dr Peyam is always the happiest man I have ever seen
I think the problem with drawing a circle to represent identifying the two end points suggests that there are points in the set being graphed which lie on that circle, where in fact when you reach one end point of the graph you "teleport" to the other end point.
Yes, it was confusing until I read your comment. If I understand correctly it's just a form of notation to say they are basically the same point, it very well could have been drawn on top of the graph instead of under it, right?
yea maybe a dotted line instead of a regular line would be more clear ? not that it changes much tbh, the thing is to know what the line means.
@@fili3907 Yeah I would do dotted line of different color and add a comment that this line is to picture those points are equivalent
@@doktoracula7017 i wouldn't draw a line at all 😂 just say it or show it on another graph as explanation
@@sempiedram Yeah, identification of the two points is the same as quotienting the space by an equivalence relation inducing the following classes: each point is in its own class except for the two endpoints, being in the same class.
"Do whoosh and you have a circle" really makes me think what the hell is actually going on in the heads of PhD people
I'm not sure I'm interpreting this correctly, but here's how I'd think of it: Instead of the domain being [0, 2π), think of the domain as being ℝ mod 2π. This way, in a very real sense, those two points are equivalent, because 0 ≡ 2π (mod 2π).
That was smooth mate, thnx!
That is a good interpretation - ultimately, all of this boils down to defining a certain equivalence relation. You don't necessarily need to equate all numbers based on their remainder, as you can simply say that x ~ y if x=y or if x=0 and y=2*pi or if x=2*pi and y=0. You can then look at these equivalence classes as your new mathematical objects and write that 0 and 2*pi represent the same equivalence class, or, by abuse of notation, that 0=2*pi.
@@beatoriche7301 don't be abuse f_ckboy with math
yeah it's something like that.
I felt like establishment of the domain and range here might be helpful to the discussion and thought process. This is something that is sometimes assumed without statement, but is important information.
'YOu kNoW tHE dOnuT eqUALs thE coFfe ThinG' is honestly hillarious.
coffee thing = mug
Note that the function defined by f(x) = x*sin(1/x), a close relative of this one, may be used to construct a simply closed curve that has a point not reachable from the inside using straight lines. By "reachable from the inside using straight lines," I mean that you can use a sequence of finitely many line segments not intersecting the curve to reach a given point on the boundary. But if you consider f(x) = x*sin(1/x) on, say, [0,1] (continuously extending the function through f(0)=0), do the same thing with cosine but rotated ninety degrees (both curves reach the main diagonal of the coordinate system infinitely many times but never shoot beyond it because cosine and sine are bounded by the number 1, and the choice of sine/cosine ensures they only intersect at 0), and then just use straight lines to connect everything as necessary, you get a genuine simply closed curve - there is no self-intersection or anything -, and yet you can not reach the origin from its inside. That is one of my favorite counterexamples relating to the topology of the Euclidean plane.
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...ereh .enalp naedilcuE eht fo ygolopot eht ot gnitaler selpmaxeretnuoc etirovaf ym fo eno si tahT .edisni sti morf nigiro eht hcaer ton nac uoy tey dna ,- gnihtyna ro noitcesretni-fles on si ereht - evruc desolc ylpmis eniuneg a teg uoy ,yrassecen sa gnihtyreve tcennoc ot senil thgiarts esu tsuj neht dna ,)0 ta tcesretni ylno yeht serusne enisoc/enis fo eciohc eht dna ,1 rebmun eht yb dednuob era enis dna enisoc esuaceb ti dnoyeb toohs reven tub semit ynam yletinifni metsys etanidrooc eht fo lanogaid niam eht hcaer sevruc htob( seerged ytenin detator tub enisoc htiw gniht emas eht od ,)0=)0(f hguorht noitcnuf eht gnidnetxe ylsuounitnoc( ]1,0[ ,yas ,no )x/1(nis*x = )x(f redisnoc uoy fi tuB .yradnuob eht no tniop nevig a hcaer ot evruc eht gnitcesretni ton stnemges enil ynam yletinif fo ecneuqes a esu nac uoy taht naem I ",senil thgiarts gnisu edisni eht morf elbahcaer" yB .senil thgiarts gnisu edisni eht morf elbahcaer ton tniop a sah taht evruc desolc ylpmis a tcurtsnoc ot desu eb yam ,eno siht fo evitaler esolc a ,)x/1(nis*x = )x(f yb denifed noitcnuf eht taht etoN
This is such a great video idea XD, do more of these again
So close to 1M!!! Keep pushing through the algorithm, BPRP, keep pushing!
I'm not joking when I say I'm terrible at math, I can't even divide but this was hilarious LMAO especially 2:52 "I'm just going to pretend I understand" then the guy goes "I'm also going to pretend to understand" even though he's the 1 teaching it 😂😂
😂
The wholesomeness of this video was exactly what I needed rn. Thank you!
this is exactly what I needed in my life thank you very much
Good to see Dr. Peyam and BPRP again!
You guys need to do more of these.
"I also just pretend to understand that. Thats the thing about teaching, you dont really have to understand."
That line got me lmao
Had Dr. Peyam as my differential equations and calculus 3 Professor. Really great at teaching!
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...ereh .enalp naedilcuE eht fo ygolopot eht ot gnitaler selpmaxeretnuoc etirovaf ym fo eno si tahT .edisni sti morf nigiro eht hcaer ton nac uoy tey dna ,- gnihtyna ro noitcesretni-fles on si ereht - evruc desolc ylpmis eniuneg a teg uoy ,yrassecen sa gnihtyreve tcennoc ot senil thgiarts esu tsuj neht dna ,)0 ta tcesretni ylno yeht serusne enisoc/enis fo eciohc eht dna ,1 rebmun eht yb dednuob era enis dna enisoc esuaceb ti dnoyeb toohs reven tub semit ynam yletinifni metsys etanidrooc eht fo lanogaid niam eht hcaer sevruc htob( seerged ytenin detator tub enisoc htiw gniht emas eht od ,)0=)0(f hguorht noitcnuf eht gnidnetxe ylsuounitnoc( ]1,0[ ,yas ,no )x/1(nis*x = )x(f redisnoc uoy fi tuB .yradnuob eht no tniop nevig a hcaer ot evruc eht gnitcesretni ton stnemges enil ynam yletinif fo ecneuqes a esu nac uoy taht naem I ",senil thgiarts gnisu edisni eht morf elbahcaer" yB .senil thgiarts gnisu edisni eht morf elbahcaer ton tniop a sah taht evruc desolc ylpmis a tcurtsnoc ot desu eb yam ,eno siht fo evitaler esolc a ,)x/1(nis*x = )x(f yb denifed noitcnuf eht taht etoN
If you have repetition you can represent with a circular repetition, fortunately Fourier already demonstrated the correlation between a discontinuity point and an infinite series (because when you have a discrete format you can just repeat it and only work in the desired interval).
"you can say thing without saying" i did that and my professor didnt give me full marks on my question
I really loved the energy!
I only took up to Calculus II in undergrad, so I understand NOTHING of what he is saying, but goddamn, that was a hilarious interaction
I had Charles Pugh as my real analysis teacher when he was visiting our math department that year. It was a very challenging but enjoyable experience.
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...ereh .enalp naedilcuE eht fo ygolopot eht ot gnitaler selpmaxeretnuoc etirovaf ym fo eno si tahT .edisni sti morf nigiro eht hcaer ton nac uoy tey dna ,- gnihtyna ro noitcesretni-fles on si ereht - evruc desolc ylpmis eniuneg a teg uoy ,yrassecen sa gnihtyreve tcennoc ot senil thgiarts esu tsuj neht dna ,)0 ta tcesretni ylno yeht serusne enisoc/enis fo eciohc eht dna ,1 rebmun eht yb dednuob era enis dna enisoc esuaceb ti dnoyeb toohs reven tub semit ynam yletinifni metsys etanidrooc eht fo lanogaid niam eht hcaer sevruc htob( seerged ytenin detator tub enisoc htiw gniht emas eht od ,)0=)0(f hguorht noitcnuf eht gnidnetxe ylsuounitnoc( ]1,0[ ,yas ,no )x/1(nis*x = )x(f redisnoc uoy fi tuB .yradnuob eht no tniop nevig a hcaer ot evruc eht gnitcesretni ton stnemges enil ynam yletinif fo ecneuqes a esu nac uoy taht naem I ",senil thgiarts gnisu edisni eht morf elbahcaer" yB .senil thgiarts gnisu edisni eht morf elbahcaer ton tniop a sah taht evruc desolc ylpmis a tcurtsnoc ot desu eb yam ,eno siht fo evitaler esolc a ,)x/1(nis*x = )x(f yb denifed noitcnuf eht taht etoN
This is by far the most accurate video of my mathematical experience
This is the equivalent of showing a child a magic trick and then trying to explain it to them without revealing the trick.
I absolutely love this session 🤣
The book actually answers your question. You can read it at 3:58, "The topologist's sine circle is shown... it is the union of a circular arc and the topologist's sine curve..."
So, the rigorous definition given is the one for the topologist's sine curve; the circle has a different definition which is only described.
Never doubt Charles Chapman Pugh
So, in reality, there is nothing to identify. Because the definition and the graph are not directly related.
@@DjesonPV ahhhhh. makes more sense.
this comment should be pinned
Sine circle is graphed as "woosh". Makes sense. I dont see why BPRP was confused.
This was really a beautiful video.
U can think of it as a circle of length 2pi, and the startpoint and endpoint of the circle are 0 and 2pi respectively, which are one next to each other, or one over the other
the person recording's reaction at 0:51 basically summarizes any proof heavy class past advanced calculus
"Take this and do *whoosh*"
Flawless victory!
"Topology! It's the donut equals coffee thing." 2:20
My best math lecturer in uni. Nice to see him randomly pop up on my recommended page.
I think the problem here is conflating the topologist's sine curve (the object he defined and drew initially) and the warsaw circle (the object derived by identifying the points he mentioned, i.e. connecting the circle). The topologically interesting part is the same so it's an easy mistake, but technically they are slightly different.
The set is how it is written but the topological space is not standard euclidean :) This is where from confusion arise. It is connected in the sense of topology on this set.
Almost 100% sure that this is how You should think about it, but took topology class some time :P
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...ereh .enalp naedilcuE eht fo ygolopot eht ot gnitaler selpmaxeretnuoc etirovaf ym fo eno si tahT .edisni sti morf nigiro eht hcaer ton nac uoy tey dna ,- gnihtyna ro noitcesretni-fles on si ereht - evruc desolc ylpmis eniuneg a teg uoy ,yrassecen sa gnihtyreve tcennoc ot senil thgiarts esu tsuj neht dna ,)0 ta tcesretni ylno yeht serusne enisoc/enis fo eciohc eht dna ,1 rebmun eht yb dednuob era enis dna enisoc esuaceb ti dnoyeb toohs reven tub semit ynam yletinifni metsys etanidrooc eht fo lanogaid niam eht hcaer sevruc htob( seerged ytenin detator tub enisoc htiw gniht emas eht od ,)0=)0(f hguorht noitcnuf eht gnidnetxe ylsuounitnoc( ]1,0[ ,yas ,no )x/1(nis*x = )x(f redisnoc uoy fi tuB .yradnuob eht no tniop nevig a hcaer ot evruc eht gnitcesretni ton stnemges enil ynam yletinif fo ecneuqes a esu nac uoy taht naem I ",senil thgiarts gnisu edisni eht morf elbahcaer" yB .senil thgiarts gnisu edisni eht morf elbahcaer ton tniop a sah taht evruc desolc ylpmis a tcurtsnoc ot desu eb yam ,eno siht fo evitaler esolc a ,)x/1(nis*x = )x(f yb denifed noitcnuf eht taht etoN
Love every single word of this video! 😆
"You don't need to understand it to teach it, you just have to sound confident enough that it's true"
I laugh so hard with this haha gonna use it
"it's implicit in the definition". Best line.
Hi, blackpenredpen. I've never left any comments under your videos on RUclips. This time I want to say that you are super nice guy! Your videos are very interesting and informative! You are a good teacher! And the last thing. I've seen Q&A video with you and dr. Peyam it was funny, you are good friends. But it was made many years ago and I didn't find many common videos with you and dr
Peyam. So, I just wanted to say that I am glad to see you are still friends!
Thank you so much for your nice comment. It is just that peyam has moved to the east coast while I am still on the west. That’s why it much harder to collaborate with him in person. This clip was taken when I was visiting him 😃. Thank you again. Wishing you the best!
esrever ot txet epyT
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...ereh .enalp naedilcuE eht fo ygolopot eht ot gnitaler selpmaxeretnuoc etirovaf ym fo eno si tahT .edisni sti morf nigiro eht hcaer ton nac uoy tey dna ,- gnihtyna ro noitcesretni-fles on si ereht - evruc desolc ylpmis eniuneg a teg uoy ,yrassecen sa gnihtyreve tcennoc ot senil thgiarts esu tsuj neht dna ,)0 ta tcesretni ylno yeht serusne enisoc/enis fo eciohc eht dna ,1 rebmun eht yb dednuob era enis dna enisoc esuaceb ti dnoyeb toohs reven tub semit ynam yletinifni metsys etanidrooc eht fo lanogaid niam eht hcaer sevruc htob( seerged ytenin detator tub enisoc htiw gniht emas eht od ,)0=)0(f hguorht noitcnuf eht gnidnetxe ylsuounitnoc( ]1,0[ ,yas ,no )x/1(nis*x = )x(f redisnoc uoy fi tuB .yradnuob eht no tniop nevig a hcaer ot evruc eht gnitcesretni ton stnemges enil ynam yletinif fo ecneuqes a esu nac uoy taht naem I ",senil thgiarts gnisu edisni eht morf elbahcaer" yB .senil thgiarts gnisu edisni eht morf elbahcaer ton tniop a sah taht evruc desolc ylpmis a tcurtsnoc ot desu eb yam ,eno siht fo evitaler esolc a ,)x/1(nis*x = )x(f yb denifed noitcnuf eht taht etoN
Honestly one of the best vids I’ve seen. Should totally show some more of these unedited clips 🔥🤓
Actually understood this too haha
I think they are missing something and bprp is right. The topologists sine circle is the Union of what is on the board (known as the topologists sine curve) with a circular arc connecting 0 and 1. This is also called a Warsaw Circle.
The idea is that the space is globally path connected (every point lies on the same path component) however the space is locally not path connected (taking a neighborhood around any point will show that this curve is not connected in that neighborhood).
Basically I think Peyam is missing the union and what is written is simply the unconnected sine curve
when your in class and ask your teacher a question and he somehow dodges it and doesnt answer anything at al
This argument was the perfect definition of how to turn a straight line of a topic into a circle 😂
‘I don’t understand but sure’ LITERALLY
In topology, it's called equivalence class to "attached points".
That hand-waviness. I love it!
you need to say 'glue together' and he'll understand
I think the part really missing from the definition is the metric space x is from. If you had that, you'd see that the distance between x and 0 goes to 0 as x goes to 2pi, which means that you're supposed to be graphing this on a cylinder.
This is probably the funniest video about maths I've seen so far xDD
It took me hell a lot of time to get comfortable with ideas of quotients and equivalent classes (but even then I still do really bad at Algebraic Topology)
"Topology. You know, the donut equals coffee thing." That is exactly what I think when I hear topology lol.
esrever ot txet epyT
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oga skeew 3
...ereh .enalp naedilcuE eht fo ygolopot eht ot gnitaler selpmaxeretnuoc etirovaf ym fo eno si tahT .edisni sti morf nigiro eht hcaer ton nac uoy tey dna ,- gnihtyna ro noitcesretni-fles on si ereht - evruc desolc ylpmis eniuneg a teg uoy ,yrassecen sa gnihtyreve tcennoc ot senil thgiarts esu tsuj neht dna ,)0 ta tcesretni ylno yeht serusne enisoc/enis fo eciohc eht dna ,1 rebmun eht yb dednuob era enis dna enisoc esuaceb ti dnoyeb toohs reven tub semit ynam yletinifni metsys etanidrooc eht fo lanogaid niam eht hcaer sevruc htob( seerged ytenin detator tub enisoc htiw gniht emas eht od ,)0=)0(f hguorht noitcnuf eht gnidnetxe ylsuounitnoc( ]1,0[ ,yas ,no )x/1(nis*x = )x(f redisnoc uoy fi tuB .yradnuob eht no tniop nevig a hcaer ot evruc eht gnitcesretni ton stnemges enil ynam yletinif fo ecneuqes a esu nac uoy taht naem I ",senil thgiarts gnisu edisni eht morf elbahcaer" yB .senil thgiarts gnisu edisni eht morf elbahcaer ton tniop a sah taht evruc desolc ylpmis a tcurtsnoc ot desu eb yam ,eno siht fo evitaler esolc a ,)x/1(nis*x = )x(f yb denifed noitcnuf eht taht etoN
I love that the Math PhD know how silly everything sounds. It probablyt stems from his comment, when the producer says:
"I'm gonna pretend I understand it, otherwise I sound like..."
And the Math guy says: "I'm also gonna pretend I understand it".
I agree with the camera guy, there should be an equivalence relation to mod out by, even if the relation itself is implied, it should be notated at least in the definiton of the things
"take this, do WOOOOSH and then WHOAAAAAAA you have a circle"
When I watched this video for the first time I had no idea but now I think I can tell that it is not just a subset of R2 but a quotient set given by a relation of equivalence where classes are singletons {(x , y} for 2pi /= x /=0 or y /= 0 and a pair {(0,0), (2pi,0)} or something similar depending on whether you IDENTIFY the right end with the entire line segment or just a point at the origin.
Omg we have the exact same analysis book! I took the class under Pugh! I saw the inside of it and was like... that looks a lot like Pugh's book. And then I saw the iconic yellow cover
2:28 ‘I see three circles btw’
one, two, three(0)
Sometimes you gotta run before you can walk!!
"You know that Donut equals Coffee thing?" that's offensive...
1:33 lmao I thought for sure Dr Peyam just went 'Oh the audacity!' and kept going
He actually makes absolutely perfect sense. But I am not smart enough to grasp it.
From his explanation about 0=2π, I gather that it is at least similar to that of polar coordinates, where x=0 and x=2π are the same point.
I have a couple different ways of visualizing it coming to mind.
1) Imagine a helix (like a spring or a slinky). In 3d space, you can clearly see that the circle is constantly being redrawn. However, if you visualize that in 2d space, you don't see the "helix" extending out front to back. So, in 2d space, the values of x=0 and x=2π are the same.
It's like a sine or cosine wave if only viewed from the y-axis with no respect to the x-axis. You would only see a vertical line.
2) I also was reminded of the classic *simple explanation of wormholes*, where you connect two points on a paper by folding it and sticking the pencil through it.
Of course, we don't want to have two outputs that mean the same thing (double-counting possible outputs), so we constrain the function as you mentioned, (0,1]. That way, only one of the points exists.
Long story short, the circular part of the graph illustrated in the book doesn't actually exist, but is instead illustrating that those two points are the same, thereby completing the loop/circle.
*The line is more pointing to the two points than connecting them using the line. The line doesn't actually represent values that are found in the equation.
If you open the book, though, you will find out that the circular part does actually exist and is a part of the definition of the topologist's sine circle.
"Just Identify It!"
Not sure if it's an air duct or some other mechanical thing, but that constant banging in the background added a lovely percussion element to the whatever the hell this was. It added to the tension of the situation and I hope it never gets fixed (the mechanical thing, not your complex relationship with the math weirdo). Peter Gabriel would be smiling down from heaven right now if he were dead, which I hope he's not, because he's still alive and fuck you for suggesting otherwise. Anyway, gotta go zink the rest of this pinot you guys are literally the future don't die otherwise we'll all have to rely on elon musk to kill us all on mars or die trying wait that's the same also great vid keep it up.
The way he casually says..."You know the coffee equal doughnut thing"....just a lot to unpack there i thought
used to work in a place to tutor kids, parents sometimes ask about our degrees. this video proves why degrees doesnt matter if you cant make other people understand, so teaching/tutoring is a whole thing to learn when u are in the job, just like most jobs
A degree doesn’t make the holder an expert, but it just gives some evidence the holder received more training on his area of specialization.
He's a physicist at heart.
*gestures vaguely with hands* "topology where the donut equals coffee thing"
lol, love the Goku instant transmission hand symbol at 3:30
this is just Abbot and Costello "Who's On First" but with math instead of baseball
well in any epsilion neighborhoud of 0 the function oscillates an infinite amount of times bewteen 1 and -1 so while the fucntion technically doesnt converge to a single point it kinda converges to the line from -1 to 1. If you squint both eyes really hard
His circle thing actually made sense to me though.
Definition of perodic function: a function returning to the same value at regular intervals.
[0 , 2pi] is the interval and sin(1/x) is the value
My problem is if you follow the X axis portion of the graph while mapping the parabola on top youre tracing the sin of that circle up to 180° at 270 then 360 the parabola underneath the x axis in the negative territory is formed. Why is it graphed this way as its an oval when both ends are reconnected.
Wow, I finally got the point in math where this makes sense!
"What branch of math is this?"
Vigorous hand waving
"Topologgggggyyyyyyy"
I think, it is just for completeness, even though with 0
He doesnt know what he's confused about. Wildly accurate.
"Identify"
what
"you can identify"
Now you're thinking with portals!
Never know that Math can make one so happy
I love his energy :D Funny guy haha
Reminds of my programming teacher from the 80’s - whoosh
Oh, the donut equals coffee thing, now I get it! You just have to whoosh them together!
It literally rebooted my computer when he started to explain the donut thing. It was probably a coincidence, but it seemed like he was trying to take the video to another dimension causing the computer to crash.
Best math video ever.
When a concept is that abstract I think implicitly gets thrown out the window haha
That is exactly how I feel whenever I have to deal with topology in my research xD
You're the one kept following me in dream.. "this man"
Well, you got a point.
Teacher: "It's implicit in the definition"
Me: Ooooh that makes sense *nods confidently*
"It exists, therefore, I'm done"