So topology studies shapes. When you have such a shape you can construct an algebraic thingy that corresponds to each shape called the fundamental group Basically then if you can show that the shapes have different fundamental groups they're different shapes in the sense that one cannot be smoothly deformed into the other. So in topology a square and a circle are the same shape because if you think of it like playdough you can reshape one into the other.
@@micayahritchie7158 Im so glad I got to play with "dough" as a kid because now in geometry and topology I often ask myself "but what if this thing were made of dough?" To better understand what s going on
The two rings together have a different fundamental property than the two rings apart, so there is no "real" (read 'magic' or 'trickerx' here) operation that can transform one to the other It would break a sort of mathematical conservation law (like energy conservation in physics)
@@IIIztosee topology is one of the hardest if not the hardest topics in mathematics. source:- took a topology course during my bachelors. almost messed up my grade lol
the rings have tiny gap that allow rings to be connected easily. but to make sure those gap not seen by audiences, magician hands play a big role in making sure it work smoothly
Yes, the point is that if the magician was being honest with us, it would be impossible. We can mathematically prove it. So it's clear through mathematical logic that the magician is not being honest with us.
@@anthonyfaiell3263 The whole point of magic is defying physics. If someone claims to be able to alter the laws of physics at a whim, you can't use physics to debunk their claims. No, I do not think magic is real, but you can't prove it's not.
Exactly... mastering sleight of hand is difficult... and the mechanics of a magic trick really isnt the magic... the magic is the magical experience you get from witnessing a very crafty and skillful magician. Magicians create experiences. They allow you watch and see things that optically are indistinguishable from real magic.
The goal is to show that the two spaces are not homemorphic, which, in layman's terms, means that one cannot be transformed into the other by continuous deformations (stretching, twisting etc, but tearing is not allowed). In general it can be difficult to show that two spaces are not homeomorphic, so invariants are considered. If two spaces are homeomorphic, their corresponding invariants are necessarily equal. Equivalently, if the invariants differ, the spaces must be necessarily non-homeomorphic. The fundamental group that the dude is talking about is one such invariant.
Anywhere there are graphs applications of algebraic topology are lurking nearby. Logistics and networks are whole industries that use them constantly. They have working groups and stuff.
At lower levels, maths is a language that makes things in life easier to understand. At higher levels, maths makes things in life harder to understand.
So one magician called me on the stage and he asked me to do it. I gave the exact same reason and he made the whole crowd laugh at me. He asked my college name. I said. I studied Applied Mathematics from IIT Roorkee. And what a joke he made on me. He said that it's something that is beyond mathematics.
Understanding requires effort, something most people don't want to apply. And the way they rationalize being ignorant is by belittling people who are more intelligent or who have put more work in than them.
damn, as a magician myself, that is a dick move. You shouldn't make a single person feel bad even if it makes a lot of people heppy. I'd give you a hug but i can't cause magic aint real :(
The videos that show the separation of the two episodes from each other on UA-cam collect millions of like. , the videos that show the impossibility of that:-....🙄
Magicians often preface their act by pointing out everything you see is a trick, employing suggestion, distraction and other devices, some of them ancient. Derren Brown does it all the time.And he would be the first to admit that there is no such thing as Magic. The whole world is a marvel but not a miracle. R, 😎❤️👹🤩🥸😍👍.
@@Grizzly01 You misinterpreted a person saying it only now seems obvious to them that objects usually cannot pass through each other as an attempt at humor. Are you 1?
@@Grizzly01 You most certainly did. There's no way thanking a person for explaining something could be misconstrued as a joke. You haven't spent enough time on earth, my friend.
What is bad about highschool math tricks? I mean if you want to learn advanced mathematics, then I think reading a book and trying to solve some problems from that topic is better than watching a video about it.
We have several lecture series on the channel that may be of interest - graph theory, knot theory, differential geometry, advanced linear algebra, metric spaces, etc.
@@sebgor2319 These so called math tricks are just baby gibberish which won't do you any good in any real problem situation. Also when you decide to actually study math you won't be calculating anything at all. I am German and having 3 degrees from German universities and one of those is in pure Math, so let me tell you if you wanna learn what you call advanced mathematics you can forget any "trick" you know as it is not a trick just some useless clickbait.
@@Pommes736 I know that there is like no calculations in advanced maths. Still Im talking about highschool People that learn Basic calculus, or Basic algebra(factoring, or quadratic formula). I mean this math videos might be useful for them.
I love this. It’s a goofy and simple way to explain an aspect of topology/set theory in an intuitive way that doesn’t have the intimidating names attached.
Saw a comedy magician that opened with “I’m gonna start with a classic: The linking rings. As you can see, they’re already linked. That saves us a lot of time” before throwing the rings offstage
Magicians are great entertainers.. that's what they do. They create fun magical experiences and it dosent mater how it's done. The real magic is what you experienced and believed that you saw. We can't perform real magic but Magicians can give you the experience as though you have seen real magic. That's the real magic.
May Abel rest in peace... having died at a very young age and did a significant contribution to the field of mathematics especially in topology and abstract algebra
Did this in my differential topology course last year, but we used the linking number instead of the fundamental group (because differential, not algebraic lol). The Hopf link is not link isotopic to the unlink :)
At least one of the metal rings has a gap in it, so your closed loops have a different topology than that gimmick ring, which is effectively congruent to a wire.
When the two circles are linked the complement of the link is a wedge of a sphere with a torus, and if they are apart it’s a wedge of two spheres and two circles.
What about a Mobius strip.... if you have one with a complete 360⁰ twist (180⁰ will result in a single loop twice the size of the original) and cut it in half along its length you'll end up with two linked but separate loops .... I know that's not quite the same but it does show you can make interlinked loops without the need to rejoin anything
My best attempt to put this in layman’s terms: Given 2 “spaces”, for example, the space of two unlinked rings and the space of 2 linked rings, the fundamental group is a way of classifying all loops in this space. A loop here is a curve that starts and ends at the same point (not the same as the rings themselves). More specifically, we say 2 loops are equivalent if you can continuously deform one into another. If 2 spaces have a different fundamental group, you cannot continuously transform one of the spaces into another. Here, by showing that the fundamental groups are different because one is abelian and the other is not, we can deduce that you cannot continuously transform 2 linked rings into 2 unlinked rings
For circles in a 2D plane, is there a concise mathemical way of determining if the circles overlap, and to what extent they overlap? Specifically on a complex plane. Without measuring radii, distance... if possible. More, "based on principles?"
@@ben_jammin242 How could it be possible to tell if two circles overlap without distance? Overlap is a question of the intersection between two sets of points. Without distance, how do you have a notion of position and hence overlap? How do you even define the circles in the first if you aren't given radii?
The three cardinal, trapezoidal formations, hereto made orientable in our diagram by connecting the various points, HIGK, PEGQ and LMNO, creating our geometric configurations, which have no properties, but with location are equal to the described triangle CAB quintuplicated. Therefore, it is also the five triangles composing the aforementioned NIGH each are equal to the triangle CAB in this geometric concept!
No idea what he's talking about but i admire his enthusiasm.
So topology studies shapes. When you have such a shape you can construct an algebraic thingy that corresponds to each shape called the fundamental group
Basically then if you can show that the shapes have different fundamental groups they're different shapes in the sense that one cannot be smoothly deformed into the other.
So in topology a square and a circle are the same shape because if you think of it like playdough you can reshape one into the other.
@@micayahritchie7158 Im so glad I got to play with "dough" as a kid because now in geometry and topology I often ask myself "but what if this thing were made of dough?" To better understand what s going on
Yeah, and the rings have a slot, you just have to keep your fingers over it at all costs
Definitely needs to work on his sleight-of-hand. 😅
He seems to be having an asthma attack
that's why we need algebraic topology
Ok but I don't even know how you'd compute the fundamental group of two interlocked rings
@@micayahritchie7158you compute it on the complement
@@micayahritchie7158 It is the fundamental group of the complement of (a neighborhood of) the links. See the full lecture linked in video for details.
@@MathatAndrews A neighborhood as in sunset of Euclidean space it's embedded in?
@@micayahritchie7158 You can just think that we are finding the fundamental space of 3-dimensional space, drilling out the links.
I could study for abelion years and still not understand this.
It's pretty simple, grab 2 rings that are linked and try to unlink them. Boom, you understand.
Bravo. Well done. The guy above has zero sense of humor or perception.
@@CLove511 😂🤦♂️
I think Abelian means = symmetrical!
The two rings together have a different fundamental property than the two rings apart, so there is no "real" (read 'magic' or 'trickerx' here) operation that can transform one to the other
It would break a sort of mathematical conservation law (like energy conservation in physics)
Abelian. I thought he said a billion at first jeez. 😂
a single word that sets apart the math chads and the virgin engineers
@@g_rr_ttthe burn~~
@@g_rr_tthell yeah!
If it’s any consolation so did I.
*_" I thought he said a billion"_*
Me too!
{:o:O:}
Glad he cleared that up.
I so hope he’s going to make a video debunking the tooth fairy using eggplants. We need it.
😂
@@carebear2883😂
Real life application haha
Where is sin cos tan
@@gameseeker6307in trig
@@gameseeker6307engineering
@@gameseeker6307In your computers to function at all, and planes to fly, and electricity to work.
Who said math is useless 😅
The real magic is that someone in the class learned that magic isn't real.
Next week debunking Santa and the Easter bunny.
Don't leave out the tooth fairy
@@jacquesroche7654I did leave out the tooth, and dont call me a fairy! 😂
@@ifireatwill2225surely, you cant be serious
Man teaching the hardest topic in mathematics just so casually.
By far not the hardest topic in mathematics
@@IIIztosee topology is one of the hardest if not the hardest topics in mathematics. source:- took a topology course during my bachelors. almost messed up my grade lol
@@vincentchan4777proof qed 😅
@@vincentchan4777that's like saying "biology is the hardest topic in the study of life"
@@kokid312kokidactually, the hardest topic in the study of life is defining what a woman is ☝🏻🤓
They say earning your first Abelian is the hardest one.
Love the girl in the back that groans in disbelief after the teacher says he has just proven that magic isn’t real! Hilarious 😂
the rings have tiny gap that allow rings to be connected easily. but to make sure those gap not seen by audiences, magician hands play a big role in making sure it work smoothly
And that's why you probably fail math.
@@abrammedrano4392What do you mean?
Yes, the point is that if the magician was being honest with us, it would be impossible. We can mathematically prove it. So it's clear through mathematical logic that the magician is not being honest with us.
@@anthonyfaiell3263 The whole point of magic is defying physics. If someone claims to be able to alter the laws of physics at a whim, you can't use physics to debunk their claims. No, I do not think magic is real, but you can't prove it's not.
David Blaine checking in lol
It's amazing how magicians are able to undo that connector and put it back together so fast we don't see it 👍
They disguise reality a different way.
Exactly... mastering sleight of hand is difficult... and the mechanics of a magic trick really isnt the magic... the magic is the magical experience you get from witnessing a very crafty and skillful magician. Magicians create experiences. They allow you watch and see things that optically are indistinguishable from real magic.
You can tell he's dedicated to his profession. The little smile of accomplishment on his face. Teacher by choice
We certainly don't do it for the pay! 😃
Now I understand even less the reason why that's not possible. 😬
The goal is to show that the two spaces are not homemorphic, which, in layman's terms, means that one cannot be transformed into the other by continuous deformations (stretching, twisting etc, but tearing is not allowed).
In general it can be difficult to show that two spaces are not homeomorphic, so invariants are considered. If two spaces are homeomorphic, their corresponding invariants are necessarily equal. Equivalently, if the invariants differ, the spaces must be necessarily non-homeomorphic.
The fundamental group that the dude is talking about is one such invariant.
Loved the excitement, never expected it in a maths class😂😂👍
The best professor I had in college was my differential equations teacher. He clearly loved the subject.
Thanks man, here I was, thinking they were stuffing 20 bunnies in a hat and chopping people in half
The only real life application of algebraic topology
Clueless
Anywhere there are graphs applications of algebraic topology are lurking nearby. Logistics and networks are whole industries that use them constantly. They have working groups and stuff.
I guess you don't know about topological data analysis
At lower levels, maths is a language that makes things in life easier to understand. At higher levels, maths makes things in life harder to understand.
Pretty apt description.
@@MathatAndrews 🫡❤️
Ah good old group theory. 😂
In this case we should be using ring theory lol
@@deananderson7714HAHA good one
@@deananderson7714nicest joke ever award goes to you, sir
No idea what I just witnessed
Me too
it was the second coming
Proof that magic is real
I don't think it was proof that magic doesn't exist 🙄
Abelian
Magic is precisely about doing something impossible. It's about pretending to do something which is yet impossible.
you mean like the theory of human creation?
@@GarnetDart ?
@@LightKnight_Age_Of The theory that God made man. You summed it up perfectly. Impossible
I say this professor is worth abelian
Yet I don't even get paid half that!
I always wanted to know the mathematic formula behind those 2 rings to know if it’s possible or not
Yeah, good thing he was there cuz everybody thought it was actual magic 😲
So one magician called me on the stage and he asked me to do it.
I gave the exact same reason and he made the whole crowd laugh at me.
He asked my college name.
I said. I studied Applied Mathematics from IIT Roorkee.
And what a joke he made on me.
He said that it's something that is beyond mathematics.
Super villain origin story
@@sirpomegranate2446literally
Understanding requires effort, something most people don't want to apply. And the way they rationalize being ignorant is by belittling people who are more intelligent or who have put more work in than them.
Sounds like you need a mathematical support group! *hug*
damn, as a magician myself, that is a dick move. You shouldn't make a single person feel bad even if it makes a lot of people heppy. I'd give you a hug but i can't cause magic aint real :(
Imagine him on a first date in the audience of a magic show 😂😂😂
Them: you'll never need algebraic topology in the real world
This guy: took this personally
This is one of those "no math required" type problems!
Glad he's having fun though!
When math creeps up in your UA-cam feed like tests on Friday in school ...
The videos that show the separation of the two episodes from each other on UA-cam collect millions of like.
, the videos that show the impossibility of that:-....🙄
Yeah
Thank you for keeping my social science classrooms filled homie!
What is the “real-life application of algebra??
I was captivated the whole time.
Probably because you were abelian
Next time I am at a magic show:
*_”haha … tHaT rInG’s NoT aBeLiAn!”_*
And the magician will answer ‘dang ! He knows I’m not doing actual magic 😩´
How did I ever get this far in life without knowing that??
When you ask your math professor for real world application of algebraic topology
You can't call something a fraud when it was never claimed to be true in the first place.
Magicians often preface their act by pointing out everything you see is a trick, employing suggestion, distraction and other devices, some of them ancient. Derren Brown does it all the time.And he would be the first to admit that there is no such thing as Magic. The whole world is a marvel but not a miracle. R, 😎❤️👹🤩🥸😍👍.
Niels Abel is really proud 🎉
Correction, you have proven a case where your math doesn’t work!
Lol😂
The excitement in the class is so MIT
Thanks, now you say it it appears obvious 😅 wasn't so sure before
You weren't sure if it's possible for objects to pass through each other? Are you 3?
@@josh8584 You were unable to detect the obviously humorous intent of the opening comment? Are you 2?
@@Grizzly01 You misinterpreted a person saying it only now seems obvious to them that objects usually cannot pass through each other as an attempt at humor. Are you 1?
@@josh8584 I misinterpreted nothing. You, however...
@@Grizzly01 You most certainly did. There's no way thanking a person for explaining something could be misconstrued as a joke. You haven't spent enough time on earth, my friend.
Finally some real math, not this high school gibberish from youtubers who not even having a math major or even could hope to get one in a mio years
What is bad about highschool math tricks? I mean if you want to learn advanced mathematics, then I think reading a book and trying to solve some problems from that topic is better than watching a video about it.
We have several lecture series on the channel that may be of interest - graph theory, knot theory, differential geometry, advanced linear algebra, metric spaces, etc.
@@MathatAndrews Thanks for letting me know.
@@sebgor2319 These so called math tricks are just baby gibberish which won't do you any good in any real problem situation. Also when you decide to actually study math you won't be calculating anything at all. I am German and having 3 degrees from German universities and one of those is in pure Math, so let me tell you if you wanna learn what you call advanced mathematics you can forget any "trick" you know as it is not a trick just some useless clickbait.
@@Pommes736 I know that there is like no calculations in advanced maths. Still Im talking about highschool People that learn Basic calculus, or Basic algebra(factoring, or quadratic formula). I mean this math videos might be useful for them.
Next, he’ll use Euclidean geometry to prove that Santa’s sleigh could never cover the whole globe from his starting point in the North Pole. 🎅
We need spherical geometry for that!
How really smart say, “I don’t know how they do the trick.”
Want to learn algebraic topology 😢
Shhh
We will be posting a series of lectures introducing algebraic topology in the upcoming months!
You must be the life and soul of the party . Next week’s lesson for the kids is Santa doesn’t exist
Topology was soo long ago...
Is the difference between the fundamental groups the number of holes?
Essentially! We have a lecture on the fundamental group on the channel you can watch.
I love this. It’s a goofy and simple way to explain an aspect of topology/set theory in an intuitive way that doesn’t have the intimidating names attached.
Thanks! That was the goal!
My five year old daughter and I were just discussing this the other day.
Today's lesson:
How to make mathematics seem even more ridiculously pointless than it already seems.
I love people who pour so much passion into their jobs
He's so cute 😭
And yet the rings still somehow come apart.
I came to see a magic trick and got an Algebra lesson instead... Now I know what's a billion and what's not a billion.
Saw a comedy magician that opened with “I’m gonna start with a classic: The linking rings. As you can see, they’re already linked. That saves us a lot of time” before throwing the rings offstage
Is there a video of that ?
It's Amazing Jonathan.
@@carebear2883lookup Amazing Jonathan
Magicians are great entertainers.. that's what they do. They create fun magical experiences and it dosent mater how it's done. The real magic is what you experienced and believed that you saw. We can't perform real magic but Magicians can give you the experience as though you have seen real magic. That's the real magic.
SMH! The dude doesn't even know how much a billion is! 🙄
Thanks Kermit the Frog!
I thought he was saying "not a billion"
12k likes on this video wow! Good to see Topology getting the spotlight it deserves!
When is a knot not a knot. I find it fascinating that a knot displaces more negative space than a not knot
Will start topology soon. Good explanation of what it studies
this is abstract algebra.
"Why did the chicken cross the mobious strip??"
- "To get to the same side...Bazingaa!"
May Abel rest in peace... having died at a very young age and did a significant contribution to the field of mathematics especially in topology and abstract algebra
Did he explain how it works? I didn’t get the explanation
He did not explain how to perform the magic, but he did explain it is impossible to do so without some tricks like "break the rings very quickly".
That girl saying “ewwww” got me rolling 🤣
Magicians are smart . They came up with an attractive application of science and called it magic.
Wish I had an abstract teacher like that.
You know we just had an argument about that last night.
Leave it to math to settle an argument!
Did this in my differential topology course last year, but we used the linking number instead of the fundamental group (because differential, not algebraic lol). The Hopf link is not link isotopic to the unlink :)
At least one of the metal rings has a gap in it, so your closed loops have a different topology than that gimmick ring, which is effectively congruent to a wire.
My abstract algebra teacher in college was not like that
Where is the full video of that?
What's purple and commutes? . . . An abelian grape.
Penn and Teller should just shout 'Abelion' at every trick!
who said magic couldnt be boring?
Mathematicians. Spoiling magic since 1665
is this part of a full lecture I can watch somewhere?
Go to his channel. He put an entire course online.
Where can i watch the full video?
Here is the full lecture: ua-cam.com/video/aaRGgsmo70Q/v-deo.html
I guess he doesn't believe in Santa Claus either...🎅
I’m already lost. Can we see the card trick now?
How does rank from linear algebra even go into this topic
I thought that's the reason it was called magic in the first place 😂
“Eureka!”😂
Super cool something to near 0° K and they can suddenly have objects phase through them.
0 K, no ° please
No way UA-cam could have known I know what an abelian group is when recommending this short, but they got lucky this time.
When the two circles are linked the complement of the link is a wedge of a sphere with a torus, and if they are apart it’s a wedge of two spheres and two circles.
What about a Mobius strip.... if you have one with a complete 360⁰ twist (180⁰ will result in a single loop twice the size of the original) and cut it in half along its length you'll end up with two linked but separate loops .... I know that's not quite the same but it does show you can make interlinked loops without the need to rejoin anything
one of those rare applications of algebraic topology that everyone understands:
Suddenly I have the courage to relinquish my foolish belief in magic.
Algebraic topology is indeed magic
"A billion? No sir" .... "Oh, abelian! I definitely didn’t need to Google that"
My best attempt to put this in layman’s terms:
Given 2 “spaces”, for example, the space of two unlinked rings and the space of 2 linked rings, the fundamental group is a way of classifying all loops in this space. A loop here is a curve that starts and ends at the same point (not the same as the rings themselves). More specifically, we say 2 loops are equivalent if you can continuously deform one into another. If 2 spaces have a different fundamental group, you cannot continuously transform one of the spaces into another. Here, by showing that the fundamental groups are different because one is abelian and the other is not, we can deduce that you cannot continuously transform 2 linked rings into 2 unlinked rings
Math is like magic, but real (& imaginary... it's a complex idea)
can't wait to see you on pen and teller
Thank goodness for math to explain in the most convoluted ridiculous way what anyone can figure out in 3 seconds of hands-on experience
If math does not account for the exceptions to the rule, what good is it?
This guy must be fun at p̶a̶r̶t̶i̶e̶s̶ math lecture.
Started off as a joke, culminated in an idea for a project. Thanks!
For circles in a 2D plane, is there a concise mathemical way of determining if the circles overlap, and to what extent they overlap? Specifically on a complex plane. Without measuring radii, distance... if possible. More, "based on principles?"
@@ben_jammin242 How could it be possible to tell if two circles overlap without distance? Overlap is a question of the intersection between two sets of points. Without distance, how do you have a notion of position and hence overlap? How do you even define the circles in the first if you aren't given radii?
What! You’re telling me that this magic trick was FAKE all along????? I’m devastated.
I hate mathematics for this reason as chemistry major ( typology is really important in chemistry unfortunately 😢)
The three cardinal, trapezoidal formations, hereto made orientable in our diagram by connecting the various points, HIGK, PEGQ and LMNO, creating our geometric configurations, which have no properties, but with location are equal to the described triangle CAB quintuplicated. Therefore, it is also the five triangles composing the aforementioned NIGH each are equal to the triangle CAB in this geometric concept!
I got to the same answer, that they can't be pulled apart but more so by gut feeling.