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.
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 :(
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.
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.
The videos that show the separation of the two episodes from each other on RU-vid collect millions of like. , the videos that show the impossibility of that:-....🙄
@@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.
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, 😎❤️👹🤩🥸😍👍.
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.
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
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.
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
Wow that explanation was much clearer. Up until now I thought that it was possible to separate two fixed rings that were linked together. 🤔🤔🤔 Never trust a magician to chain your bike up. It just comes loose.
There's a split in those metal rings magicians use... One ring is solid, the other has a break in the metal ring, and when the "illusionist" move the solid ring on that break,it appears to be separating...
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!
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?
But when the two fundamental groups are boungd by inter coalescence then the abilian properties become quasi-miogastonian allowing the molecules to act as a liquid state under pressure allow each molacule to interlace between each other without loosing it's electro cohesion
Most of the people couldn't get the logic though. Because it is one of the hardest topics in pure mathematics . Much difficult than general and differential topology . This is my opinioin though as a master's student of Mathematics . Fundamental group is mind blowing and destructive topic I say in Algebraic topology . The lifting thorem , induced holomorphisms . It is beautiful ❤️❤️.
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
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.
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 :)
