Topology can also be utilized to create evocative imagery and art. As, study of form and associated function can be used to create imagery, film, or architecture which utilizes the forms in different scales in shorthand to denote evocative function, scale, space, and art.
Hmmm. Wonder what makes topological shapes different from each other. Is it just holes? Other ways to tell shapes apart even if they have the same holes?
I keep hearing about the “squishy/rubbery” thing on a lot of topology’s videos but i never understood where in the definition of topology does such intuition come?
I meant to make a video explaining this eventually, and maybe I will one day, but in the meantime: The technical terms for the squishiness are “homotopy” and “homeomorphism”. When we say “You can squish one shape to turn it into another”, the technical way of saying that is either “those two shapes are homeomorphic” or “those two shapes are homotopy equivalent.” (The second statement allows for more intense squishing, where you can squish a ball into a single point, for example.) I don’t know what your background is or whether you’ve taken a topology class, and I’m afraid that may be an unhelpful answer if not, but those are the terms where that intuition connects to technical definitions. Thanks for your question, regardless.
@@AlternatingSum holy shit I didn't think you'd reply lol. I am a math major and I've studied topology before (introductory) i do understand the homomorphism analogy. What I meant in my question is how does the definition of topology makes us see shapes from the perspective of "how many holes there are"
@@هيلة-ع8م Ha sure, I wanted to reply because I initially thought to make a topology series to address exactly the disconnect you’re talking about, between very intuitive introductory videos and rigorous but arcane-seeming topology lectures. Since I only made one video I didn’t get very far towards that goal, alas. Re: number of holes - if two spaces are homeomorphic then they have the same number of holes, the same kinds of holes, and those holes interact with each other in the same way. Really what I mean is: They have the same fundamental group and the same homology groups. Introductory topology classes usually don’t get to homology, and often don’t get to the fundamental group either, which I think is a little unfortunate - they’re kind of laying the groundwork for concepts but never quite getting there. Algebraic topology classes are where you really get into that stuff. I do like actually like a lot of point-set-topology on its own, the weird pathological examples like the topologists’s sine curve are fun. It can be a nice exercise in stretching your intuition about how space can behave, but it’s not everyone’s cup of tea (or donut of tea, I suppose).
There is a video called “outside in” where a lady narrator is explaining to a guy narrator how to turn a sphere inside out. Anyway…. Is that an example of Topology? Miss narrator explained that they were working with an abstract elastic material that can bend and stretch, and pass through itself, but can’t crease sharply. Is that the “squishy” stuff of topology shapes? here is a link to one example of the video: ruclips.net/video/IbGNZQvobkc/видео.html
There not being a difference and not being currently interested in the difference are very different things. But yeah you are basically right.....The triangle variations and circle variations are not topologically similar (ie homeomorphic). And some of those things are "allowed", they just can't be done without qualification. Cartography is probably the best example of a loose application of topology. You are describing the same shape of the planet, but having different ways of expressing it depending on the context.
Oh, when I say “triangle” I mean the boundary of a 2-simplex, and those are homeomorphic to circles. It’s true that my some of my language here was hand-wavy - this is an introductory video, and when I made it I was laying the groundwork for motivating the rigorous definition of homeomorphisms in a later video. I never got to it, but maybe one day.
Gitonga Mwaniki in topology you cant make/mold together holes. in the 1 hole and 2 hole donut example, streching the donut and pulling the middle together to connect counts as making a hole. as such you can conclude that they are not topologically equal. if it was allowed everything would be the same and there would be no point in topology
That's all true except that you can close holes with continuous transformations. You just can't "open" a hole through tearing because those points at the seam/cut will move a different distance than the neighboring points.
You're still right though, these would not be topologically equivalent because while you can close holes technically, the tearing is what eliminates the inverse. Without an inverse function, we can't preserve continuity.
@@benjaminhanson6137 actually I don't think you can close a hole because then you would be making the surface difference, if you just shrunk the hole until it "disappeared" then the hole might not look like it's there, but its inner lining would have to still be there unless I'm completely misunderstanding topology, because there would be no way to manipulate the shape to have the inner lining disappear.
Topological data analysis is a hot topic in modern science. Basically, one imagines that all of the data points had to come off of some topological shape (called a manifold) and then there is some math to try to figure out what type of manifold the data points came from. One of my coworkers did a few years at Sandia Labs and found out that topological data processing methods were much better at figuring out where to put the drill to get oil and natural gas than previous partial differential equations methods were. One reason why this is the case is that the PDE method had to try to figure out the approximate shape of the caves that the oil was in, but the topological method only cared about the topological types of caves that the oil was in.
@@darwinvironomy3538 I was thinking about it for a scifi concept but I dont think there are real world applications, and the names are just me having fun
Ok these r rlly interesting concepts but also what’s the point of studying this? Like how can this be applied to real life? (Would u need to know this for engineering or physics or smth?) Or is it just studied for fun?
Various concepts have several different applications. Here is the one application of topology. So in topology you have topological spaces, some topological spaces are very useful and they're known as manifolds(basically surfaces in higher dimensions). In general theory of relativity, spacetime is a 4 dimensional manifold that allows one to understand gravity and how a lot of things in the universe work. This is just one application. It even has application in quantum computing.
And then when you have some topology classes in college it's all closed\open sets and other set-teoretic stuff with little to no visualizations of the objects 😅. I'm probably biased because I've only ever had topology courses in the context of other classes.
Eventually! I decided to make the "Distance, Dimension, and Space" playlist first, since that material is a prerequisite for the next topology video. I'll release a video on 4-dimensional space soonish, then one on distances in high dimensional spaces. Then I'll be ready to resume the topology series. :)
You have convinced me that topology is a subject that I have zero interest in, so thank you. BTW I have a distant relative who was a fairly well-known topologist: Oswald Veblen. I never understood what interested him about this subject, and I still don't.
The problem is there does not exist a way to truly convey the intrigue of pure math to laymen who have not learned any of it. You can try explaining it at a very basic level like this video does, but its missing so so much of the greater context and richness that makes the subject actually interesting to learn.
"But it's not a very funny one" You can clearly hear the topologist who feels totally targeted
holy shit linux tech tips
@@eliaswenner7847 me 😭
okay so basically geometry play doh
This may be the best simple description.
Except it's a play doh statue and the police are watching to make sure you don't break or glue it.
That statement is stupid... but whatever.
play doh but you can’t make or remove holes
you summed up topology in 6 words
After 8 years RUclips recommend me this video. I like the video.
Same here
your voice + topology is extremely soothing to me
Your narration, explanation, and animation work so great together! It was so clear to understand and also very fun. Thank you for this video!
Topology; studying surfaces in reference to holes
Bottomology; studying holes in reference to surfaces
This deserves an award!!
.
thank u for beautiful, concise explanations of TOPOLOGY concepts to persons who dont understand it! Much Thanks!
The topologist is the only one who will bite into his/her coffee mug, because it looks to him/her like the donut in his/her other hand
I wished there were edible coffee mugs made out of donut dough.
If you make them, I will buy them, lol.
@@wynstansmom829 if buy then i will it them
This is the exact video that I needed.
Well I was looking for this topic for my optimization course. And this video is equally informative and soothing 😌💙💙
I really love your videos, keep it up!
This is really well done, thank you.
Great hand-drawn homeomorphism animation!
Very concise introduction of what topology is. Thank you very much!
my geometry took a topology class to fill space in his schedule when he was in college😭😭
Topology can also be utilized to create evocative imagery and art. As, study of form and associated function can be used to create imagery, film, or architecture which utilizes the forms in different scales in shorthand to denote evocative function, scale, space, and art.
This is awesome! We need other topology videos! :)
this is the actual which I have been searching for long time 😊 thank u next part of this video pls
i dont think this channel is reviving back any time soon :cc
Hmmm.
Wonder what makes topological shapes different from each other. Is it just holes? Other ways to tell shapes apart even if they have the same holes?
the only inaccurate part about this video is that it is a very funny joke
Ok buddy topologist
I keep hearing about the “squishy/rubbery” thing on a lot of topology’s videos but i never understood where in the definition of topology does such intuition come?
I meant to make a video explaining this eventually, and maybe I will one day, but in the meantime: The technical terms for the squishiness are “homotopy” and “homeomorphism”.
When we say “You can squish one shape to turn it into another”, the technical way of saying that is either “those two shapes are homeomorphic” or “those two shapes are homotopy equivalent.” (The second statement allows for more intense squishing, where you can squish a ball into a single point, for example.)
I don’t know what your background is or whether you’ve taken a topology class, and I’m afraid that may be an unhelpful answer if not, but those are the terms where that intuition connects to technical definitions. Thanks for your question, regardless.
@@AlternatingSum holy shit I didn't think you'd reply lol.
I am a math major and I've studied topology before (introductory) i do understand the homomorphism analogy. What I meant in my question is how does the definition of topology makes us see shapes from the perspective of "how many holes there are"
@@هيلة-ع8م Ha sure, I wanted to reply because I initially thought to make a topology series to address exactly the disconnect you’re talking about, between very intuitive introductory videos and rigorous but arcane-seeming topology lectures. Since I only made one video I didn’t get very far towards that goal, alas.
Re: number of holes - if two spaces are homeomorphic then they have the same number of holes, the same kinds of holes, and those holes interact with each other in the same way. Really what I mean is: They have the same fundamental group and the same homology groups. Introductory topology classes usually don’t get to homology, and often don’t get to the fundamental group either, which I think is a little unfortunate - they’re kind of laying the groundwork for concepts but never quite getting there. Algebraic topology classes are where you really get into that stuff.
I do like actually like a lot of point-set-topology on its own, the weird pathological examples like the topologists’s sine curve are fun. It can be a nice exercise in stretching your intuition about how space can behave, but it’s not everyone’s cup of tea (or donut of tea, I suppose).
I’m going to dig a hole in the Earth
I am so evil I am topologically changing the earth
So the human body is equal to a donut :)
Yep! A donut with a few fluid-filled internal compartments, but still. :)
nolifeonearth a three-holed donut, I think, since the nasal sinus connects to the mouth.
no there is more than one hole
nolifeonearth فوزي موزي
@@malcomthonger more than one hole? that's the ULTRA DELICIOUS donut!
So is it geometry at scale but shapes are only grouped together based on characteristics they may have in common rather than equivalency?
Yeah sort of
There is a video called “outside in” where a lady narrator is explaining to a guy narrator how to turn a sphere inside out.
Anyway…. Is that an example of Topology? Miss narrator explained that they were working with an abstract elastic material that can bend and stretch, and pass through itself, but can’t crease sharply. Is that the “squishy” stuff of topology shapes?
here is a link to one example of the video: ruclips.net/video/IbGNZQvobkc/видео.html
что означает ваша картинка 2:46?я частично понимаю в топологии,но не пойму что означает человек,разделенный на двух шарах.)???
сферическая геометрия
Who’s here after seeing that ad on Instagram? My mind was blown I had to do more research on topology 😂😂😂🤔🤔🤔🤯
Thank you for making this video. It was very helpful.
Great intro ❤
There not being a difference and not being currently interested in the difference are very different things. But yeah you are basically right.....The triangle variations and circle variations are not topologically similar (ie homeomorphic). And some of those things are "allowed", they just can't be done without qualification. Cartography is probably the best example of a loose application of topology. You are describing the same shape of the planet, but having different ways of expressing it depending on the context.
Oh, when I say “triangle” I mean the boundary of a 2-simplex, and those are homeomorphic to circles.
It’s true that my some of my language here was hand-wavy - this is an introductory video, and when I made it I was laying the groundwork for motivating the rigorous definition of homeomorphisms in a later video. I never got to it, but maybe one day.
This is amazing.
Why are holes so important in topology?
Gitonga Mwaniki in topology you cant make/mold together holes. in the 1 hole and 2 hole donut example, streching the donut and pulling the middle together to connect counts as making a hole. as such you can conclude that they are not topologically equal. if it was allowed everything would be the same and there would be no point in topology
( ͡° ͜ʖ ͡°)
That's all true except that you can close holes with continuous transformations. You just can't "open" a hole through tearing because those points at the seam/cut will move a different distance than the neighboring points.
You're still right though, these would not be topologically equivalent because while you can close holes technically, the tearing is what eliminates the inverse. Without an inverse function, we can't preserve continuity.
@@benjaminhanson6137 actually I don't think you can close a hole because then you would be making the surface difference, if you just shrunk the hole until it "disappeared" then the hole might not look like it's there, but its inner lining would have to still be there unless I'm completely misunderstanding topology, because there would be no way to manipulate the shape to have the inner lining disappear.
Who invented topology has a strange fetches about holes.
You're Awesome.
This was good!
Well done! Good Job!
What are application of topology in moder era
Topological data analysis is a hot topic in modern science. Basically, one imagines that all of the data points had to come off of some topological shape (called a manifold) and then there is some math to try to figure out what type of manifold the data points came from.
One of my coworkers did a few years at Sandia Labs and found out that topological data processing methods were much better at figuring out where to put the drill to get oil and natural gas than previous partial differential equations methods were. One reason why this is the case is that the PDE method had to try to figure out the approximate shape of the caves that the oil was in, but the topological method only cared about the topological types of caves that the oil was in.
Thank you. Where can i find the next part?
Thank you very much, it was very useful!
I am wondering when will the new video on Topology be released?
I've been trying to figure out, what would you consider the opposite of topology? Like the study of making holes and changing data in space.
hmm
@@darwinvironomy3538 Poke-ology, Advanced Concepts in Void
@@ryangunnison38 you made it up or that's real?
@@ryangunnison38 it's a cool subject but i don't get the application and if you define something consistent
@@darwinvironomy3538 I was thinking about it for a scifi concept but I dont think there are real world applications, and the names are just me having fun
Ok these r rlly interesting concepts but also what’s the point of studying this? Like how can this be applied to real life? (Would u need to know this for engineering or physics or smth?) Or is it just studied for fun?
Various concepts have several different applications. Here is the one application of topology. So in topology you have topological spaces, some topological spaces are very useful and they're known as manifolds(basically surfaces in higher dimensions). In general theory of relativity, spacetime is a 4 dimensional manifold that allows one to understand gravity and how a lot of things in the universe work. This is just one application. It even has application in quantum computing.
Very nice Video :D Thank you for this good explanation ^^
The super donut we call it a pretzel😊
this is more algebraic topology than basic point set topology
Well yeah but algebraic topology is what topology is actually “used” for, “in the wild” so to speak
And then when you have some topology classes in college it's all closed\open sets and other set-teoretic stuff with little to no visualizations of the objects 😅.
I'm probably biased because I've only ever had topology courses in the context of other classes.
If you take an algebraic topology class you start seeing the shapes
basicly topologicy is math of holes?
wow. you're a good explainer. thanks for a great intro.
Excellent
Thanks for this!
the three holed donut looks sad
thanks for the video
Next lectures in this series?
when is this taught
undergraduate math programs usually have topology as a 3rd or 4th year subject, mandatory or elective depending on the university
@@lordspongebobofhousesquare1616 thank u spongebob
Is a blackwhole a whole?
Hole*
There’s definite answer yet, mostly the scientific consensus is it’s just a really dense ‘object’ not is wormhole
wait....this has nothing to do with 3d modeling right?
pstuddy Might have something to do with meshes.
Topology is useful in animation
next part?
Eventually! I decided to make the "Distance, Dimension, and Space" playlist first, since that material is a prerequisite for the next topology video. I'll release a video on 4-dimensional space soonish, then one on distances in high dimensional spaces. Then I'll be ready to resume the topology series. :)
Great, thanks for replying, subbed!
good overview
So topology is the study of holes. No wonder the word itself is full of Os.
Damn i need a donut right now😂
amazing !!!
I have more questions than answers now...
So basically topology is the study of holes?
Interdimentional geometry
I love dmt
… and then there’s point set topology which is way more generalized and we stop caring about all the properties in a metric topology.
should i be learning this at 7th grade?
Absolutely! Start off young!
No
notable notes of topology.
shavan
merja
Ayo why am I here rn
HOLES!!!
I’m tired of hearing this joke
I be studying holes
And i have to define dis
You have convinced me that topology is a subject that I have zero interest in, so thank you. BTW I have a distant relative who was a fairly well-known topologist: Oswald Veblen. I never understood what interested him about this subject, and I still don't.
The problem is there does not exist a way to truly convey the intrigue of pure math to laymen who have not learned any of it. You can try explaining it at a very basic level like this video does, but its missing so so much of the greater context and richness that makes the subject actually interesting to learn.
Nice
thank you so much
This video would greatly benefit from a de-esser. Otherwise - informative and well made video.
Voice beatifull!
simp
69 dislikes????
👏👏👍
I'm still confused
i dont get it...
Holes (:
Im in year 8 and im tryna learn how to do this (;´༎ຶٹ༎ຶ`)
call it symbolic logic and be done
God loves you ❤
Topology is the ultimate difference between men and women
Clarify?
2:05 uhh...ok
Is anyone more confused?
Too immature for the holes examples
This is a horrible and misleading intro to what topology is.
Stop saying holes. 🤤
you describe it horribly
not very funny? come on..
so Topology is nonsense thanks