Simply because it shows how deceptive the globe model is. They have taken a stationary grid and wrapped it around a “globe” and now the majority of sci fi programmed minions gullibly believe it.🙃😹🥂
Jin Jun Liu Bingo. It’s hilarious that humans pretend the other side of the known world exists in the opposite direction below them when it’s so obvious that we all exist upright on a stationary GRID of varying elevations!🙃😹👏🥂
Insanely awesome. Projects like these are why I get up in the morning. I'm getting trained (lectured thrice a week) to work in a hyperbolic geometry lab. Needless to say I'm excited to do this kind of work. Geodesics baby!!!!!
A rotation of the Riemann sphere about a horizontal axis does not represent an inversion of the complex plane. It represents an inversion and a rotation (combined). The true sphere representation of an inversion corresponds to reaching through the sphere, pinching the other side, and pulling it through, i.e. literally turning it inside out (inverting it).
There are two types of inversion. Inversion 1/zbar and complex inversion 1/z. I think you're referring to the first, but complex inversion is what they're illustrating
I saw these inversions for like 5 years in some videos about complex math. I never understood what they actually doing and why. Even in videos about the riemann-hypothesis these inversions were used, but I never saw or understand, that these graphics were meant to be understood as inversions; or what inversion on the complex plain could possible mean. Thank you so much for making that clear to me.
This is one of the first videos I have ever seen on RUclips. I am pretty sure that I remember I had looked this up under recently uploaded on RUclips when my teacher in high school had shown me what RUclips was. Back then, there was not that many videos on RUclips and I think I had watched every single video uploaded around the same time as I saw this? But I had seen the original video by whomever had uploaded that in September of 2005. Lol. I bet against RUclips Gaining Success.. :/ I remember talking about it in class.
Wish there was a video like this showcasing how the conjugacy classes preserve certain fixed points. From what I understand this arises due to a specific combination of translation and rotation of the Riemann sphere.
Beautiful video! However, I think the part about scaling is incorrect, and should be replaced by actually scaling the sphere and keeping its south pole constrained to the plane. Otherwise you can not visualize Möbius transformations like z -> z/a where |a|
The only qualm I have with this version of the video is someone who cannot say "Möbius" ruining the video by reading the captions of the original video aloud, thus ruining the effect of the beautifully fitting music.
First of all: a very enlightening video! I love it. Especially the inversion of the plane, where infinity comes to lay under the sphere with the little light and the points of the square before the rotation of the sphere are send to infinity. One question though. Is the projection of the square (by the light) around the time of 2 minutes and 14 seconds not different from a square but already part of the projection if the spere is rotated around a horizontal axis, so the square is not a square anymore but already a part of the plane inversion? I guess it's not the same figure on the inside, otherwise, the projection by the light would show the beginning of an inversion. Another question. Can we fill up the whole sphere with colors, (the light can shine through them, so the whole infinite plane is colored too), and show how the transformations come about by looking at how the colors change? Rotations of the sphere rotates the colors, moving the sphere around moves the colors all in the same way, lifting the sphere up will enlarge the distances between colors and finally rotating the sphere around any horizontal axis will bring the colors at infinity below the sphere and send the colors under the sphere to infinity. I'm not sure how you must draw the black lines in this case. Any suggestions? Of course, the video is much clearer in this respect, but I was just wondering! And again (I've seen this video already a long time ago and was really impressed by it! Even now I wanted to see it again, with the ensuing thoughts): GREAT VIDEO which shows much more than all the math symbols that go along with it.
Very nice! I really appreciate it when you can increase the intuition of a complex subject with a simple visualization like this. But what about chained Möbius transformations? There is a projective matrix representation of the Möbius transformation that can be used to combine several Möbius transformations performed one after another into a single Möbius transformation, simply by multiplying the matrices corresponding to the individual Möbius transformations with each other. Since that combined Möbius transformation also corresponds to a transformation of the unit sphere used in this animation, is there also a corresponding, simple way to calculate that transformation from the individual transformations of the sphere corresponding to the individual, chained Möbius transformations?
it has a drawback.... in this way we can not visualize mobius transformation as a naturally induced map from sphere to sphere.......... because sphere is displaced in case of translation and dilation.......
The 'infinite plane' used in Geometry is of course a sphere with an infinitely large radius, so the naturally induced spheresphere mapping property still holds true.
you completely missed my point...... I'm well aware of stereographic projection.......... for an example the translation of real plane will induce different kind of map from sphere to sphere as the infinite point is held fixed..... the map can be viewed as a directed flow along circles passing through the infinite point....... hope u'll understand cause I won't argue anymore......
@@jaycee9153 ımagine a periodic function(sinx, cosx or a square step function). Mean of these functions are on x=0 axis. Imagine mean of these periodic functions on a function like y=x^2 or on y=e^(-x^2) or on any other big wave-length periodic function. How can we build such a function?
Translations of sphere = 2 real degree of freedom. Up/down translations of sphere to make dilations=1 real degree of freedom. Rotations of sphere = 3 real degree of freedom. Total= 6 real degree of freedom. BUT a Mobius transformation is defined by 4 complex numbers = 8 real degree of freedom. The Mobius transformations you showed must be only a subgroup of all Mobius transformations, I think.
@@ChristopherKing288 ¡Exacto! Yo llegué a la misma conclusión haciendo un cambio de base. En lugar de que sean 8 dimensiones reales tomé cuatro dimensiones complejas tomando cuatro matrices (no recuerdo si eran las de Pauli o i veces las de Pauli, o algo parecido) y una de ellas, que es, de hecho, creo que la matriz identidad, no contribuye a la representación matricial de una transformación de Mobius. Así que la acción de una de esas matrices no contribuye a la transformación de Mobiusv. It's like a quotient subgroup, i think. ¡Of course! Las matrices identidad conmutan con cualquier matriz, so the "clases laterales izquierda y derecha" son la misma. Where I come, people is used to say. Cámara carnal, ahora pásame tu número, princhecha mosa. :kiss:
Mobius transformation has only 6 degree of freedom. since multiplying any complex k (2 degree of freedom) to a,b,c,d does not change the transformation. 8-2=6
i had an intuitive idea about this but I do not even know where this came from...I am not a fundamental mathematician. Maybe knowledge is a wave the collides with us
Title of this video: Möbius Transformations Revealed [HD] Quality of this video: 720p Date of this video: 10 years ago My response to these stats: Don't tell me you call this [HD], son. You must be a grandpa by now who fought in the military and gives his grandchildren ice cream. My friend standing next to me: u got dem big brains man (>-_-)>
The connection between the riemann sphere and mobius transformations just became alot more clear thanks
They're both related to stereographic projection
cool video, but I still cannot solve my complex analysis problems
What I did understand is that you need a ball, a flashlight and a marker.
@@neh1234 in what order
Haha same
as someone who was there...
*git gud*
lmao same
10 years old yet the best video on this topic :/
Simply because it shows how deceptive the globe model is. They have taken a stationary grid and wrapped it around a “globe” and now the majority of sci fi programmed minions gullibly believe it.🙃😹🥂
@@MonsieurDrobot Yeah the thing inside the globe isn't a square if you flatten it out, but it's about the projection
Jin Jun Liu Bingo. It’s hilarious that humans pretend the other side of the known world exists in the opposite direction below them when it’s so obvious that we all exist upright on a stationary GRID of varying elevations!🙃😹👏🥂
Insanely awesome. Projects like these are why I get up in the morning. I'm getting trained (lectured thrice a week) to work in a hyperbolic geometry lab. Needless to say I'm excited to do this kind of work.
Geodesics baby!!!!!
Thrice
What's a hyperbolic geometry lab? Sounds cool.
Simply amazing, that sphere visualisation blew me away.
Beautiful, simple and elegant. Thank you.
A beautiful way to connect the Riemann sphere to Möbius trasformation. Very intuitive.
A rotation of the Riemann sphere about a horizontal axis does not represent an inversion of the complex plane. It represents an inversion and a rotation (combined). The true sphere representation of an inversion corresponds to reaching through the sphere, pinching the other side, and pulling it through, i.e. literally turning it inside out (inverting it).
There are two types of inversion. Inversion 1/zbar and complex inversion 1/z. I think you're referring to the first, but complex inversion is what they're illustrating
I saw these inversions for like 5 years in some videos about complex math. I never understood what they actually doing and why. Even in videos about the riemann-hypothesis these inversions were used, but I never saw or understand, that these graphics were meant to be understood as inversions; or what inversion on the complex plain could possible mean. Thank you so much for making that clear to me.
Morbius Transformations Revealed [HD]
Wow! What an elegant video
THANKS FOR RECOMMENDING THIS TO ME AFTER I GOT STUCK AFTER TRYING TO SEARCH IT
Thank you so much.
that was absolutely lovely!!!
I am really speechless. What a wonderful educational content and the way you explained it is totally amazing
Got my complex analysis final coming up, thanks :)
morbin time
Wow ! This was really helpful. Thank you so much.
Pure gold! Bravo!
Awesome video, thanks! It's amazing how simple it becomes.
amazing , Thanks !
Amazing video❤❤
The most beautiful video on RUclips.
Thanks for this beautiful explanation
He reposted it from the actual creator. Original: ruclips.net/video/JX3VmDgiFnY/видео.html
This is one of the first videos I have ever seen on RUclips. I am pretty sure that I remember I had looked this up under recently uploaded on RUclips when my teacher in high school had shown me what RUclips was. Back then, there was not that many videos on RUclips and I think I had watched every single video uploaded around the same time as I saw this? But I had seen the original video by whomever had uploaded that in September of 2005. Lol. I bet against RUclips Gaining Success.. :/ I remember talking about it in class.
Such a great video.
Astonishingly well done -- congratulations !!!
Not his creation. Read the description. Original: ruclips.net/video/JX3VmDgiFnY/видео.html
cant believe this is a video made 10 yrs ago. eggcellent video
if i'm being honest, a light that travels to infinity in an infinite plane just sounds unsettling to me
Beautiful
terence tao mentioned this video in his 2009 induction ceremony speech, which is why i came here. i like how simply this is explained.
Wish there was a video like this showcasing how the conjugacy classes preserve certain fixed points. From what I understand this arises due to a specific combination of translation and rotation of the Riemann sphere.
This is sooo cool!! ♡
When it inverts, the empty space almost looks like a silhouette of Tweety Bird. :P
love it man, thanks for sharing.
I'm from MathPath! Cool video
Yo
Hello there
MORBIUS
thanks! simple and enlightening;
So cool, thanks for the vid :)
Very helpful to see. Because this kind of stuff is hard to understand from a book with just proofs and notation.
Learning these for smith charts, neat
beauty at its peak
Wow! Mind-blowing!
Amazing Video
Beautiful video! However, I think the part about scaling is incorrect, and should be replaced by actually scaling the sphere and keeping its south pole constrained to the plane. Otherwise you can not visualize Möbius transformations like z -> z/a where |a|
Complex analysis is great study.
and Riemann had made a gretest achievement!!
really great video! ty!!
So great!!!!
Morbius 😥
The only qualm I have with this version of the video is someone who cannot say "Möbius" ruining the video by reading the captions of the original video aloud, thus ruining the effect of the beautifully fitting music.
Notice that the colors are invariant under the transformations depicted.
does this apply to all elliptic, parabolic and hyperbolic cases?
This is beautiful
I am SCREAMING this is so cool
Awesome...
Amazing
First of all: a very enlightening video! I love it. Especially the inversion of the plane, where infinity comes to lay under the sphere with the little light and the points of the square before the rotation of the sphere are send to infinity. One question though. Is the projection of the square (by the light) around the time of 2 minutes and 14 seconds not different from a square but already part of the projection if the spere is rotated around a horizontal axis, so the square is not a square anymore but already a part of the plane inversion? I guess it's not the same figure on the inside, otherwise, the projection by the light would show the beginning of an inversion. Another question. Can we fill up the whole sphere with colors, (the light can shine through them, so the whole infinite plane is colored too), and show how the transformations come about by looking at how the colors change? Rotations of the sphere rotates the colors, moving the sphere around moves the colors all in the same way, lifting the sphere up will enlarge the distances between colors and finally rotating the sphere around any horizontal axis will bring the colors at infinity below the sphere and send the colors under the sphere to infinity. I'm not sure how you must draw the black lines in this case. Any suggestions? Of course, the video is much clearer in this respect, but I was just wondering! And again (I've seen this video already a long time ago and was really impressed by it! Even now I wanted to see it again, with the ensuing thoughts): GREAT VIDEO which shows much more than all the math symbols that go along with it.
Very nice! I really appreciate it when you can increase the intuition of a complex subject with a simple visualization like this.
But what about chained Möbius transformations? There is a projective matrix representation of the Möbius transformation that can be used to combine several Möbius transformations performed one after another into a single Möbius transformation, simply by multiplying the matrices corresponding to the individual Möbius transformations with each other. Since that combined Möbius transformation also corresponds to a transformation of the unit sphere used in this animation, is there also a corresponding, simple way to calculate that transformation from the individual transformations of the sphere corresponding to the individual, chained Möbius transformations?
This is like salvia, without the humiliating RUclips videos after.
Look up Stereographic Projections, the mathematics of maps which project a sphere onto a plane.
wtf how cool is that
How is 2c) going everyone
Is rotation in Z-direction possible ? Suppose Z- is into the screen.
Awesome! Do mobius transformations preserve the shape of regular polygons ?
no as u can see the color square becomes weird
So right angles stay true. Does that imply that möbius transformations are conformal in general?
yes
it has a drawback.... in this way we can not visualize mobius transformation as a naturally induced map from sphere to sphere.......... because sphere is displaced in case of translation and dilation.......
The 'infinite plane' used in Geometry is of course a sphere with an infinitely large radius, so the naturally induced spheresphere mapping property still holds true.
you completely missed my point...... I'm well aware of stereographic projection.......... for an example the translation of real plane will induce different kind of map from sphere to sphere as the infinite point is held fixed..... the map can be viewed as a directed flow along circles passing through the infinite point....... hope u'll understand cause I won't argue anymore......
You're right
I don't disagree necessarily, but ..... can ...... you ..... calm ..... down ..... with .... the ..... misuse .... of ..... dots?
@@IsomerSoma It's over 4 years now and I am calm enough. Bdw I typed from laptop and I pressed "." to my heart's content.
awesome
nice video
Nice video.....I think, it is created in 'BLENDER'....right?
Which software did you use to make this..?
I also wanna know. I'm thinking it's POV-ray
He didn’t make it. It’s not his original content. The creator: ruclips.net/video/JX3VmDgiFnY/видео.html Read the description for all info.
Nihal hocam izledik ama ben konuyu yine anlayamadım.
the music is distracting, too staccato and cheery
How did you guys figure this out?
Can we draw sinx function on x^2 curve or generally on any curve?
what do you mean?
@@jaycee9153 ımagine a periodic function(sinx, cosx or a square step function). Mean of these functions are on x=0 axis.
Imagine mean of these periodic functions on a function like y=x^2 or on y=e^(-x^2) or on any other big wave-length periodic function.
How can we build such a function?
Translations of sphere = 2 real degree of freedom.
Up/down translations of sphere to make dilations=1 real degree of freedom.
Rotations of sphere = 3 real degree of freedom.
Total= 6 real degree of freedom.
BUT a Mobius transformation is defined by 4 complex numbers = 8 real degree of freedom.
The Mobius transformations you showed must be only a subgroup of all Mobius transformations, I think.
The 4 complex numbers defining a mobius transform aren't unique, so it doesn't utilize all 8 dimensions.
@@ChristopherKing288 ¡Exacto! Yo llegué a la misma conclusión haciendo un cambio de base. En lugar de que sean 8 dimensiones reales tomé cuatro dimensiones complejas tomando cuatro matrices (no recuerdo si eran las de Pauli o i veces las de Pauli, o algo parecido) y una de ellas, que es, de hecho, creo que la matriz identidad, no contribuye a la representación matricial de una transformación de Mobius. Así que la acción de una de esas matrices no contribuye a la transformación de Mobiusv. It's like a quotient subgroup, i think. ¡Of course! Las matrices identidad conmutan con cualquier matriz, so the "clases laterales izquierda y derecha" son la misma. Where I come, people is used to say. Cámara carnal, ahora pásame tu número, princhecha mosa. :kiss:
¡Eh, hermano! No te pases de verga con una dama. Sorry, Samantha.
@@luisalejandrohernandezmaya254 I don't speak Spanish, but "sin problema" I'm guessing.
Mobius transformation has only 6 degree of freedom. since multiplying any complex k (2 degree of freedom) to a,b,c,d does not change the transformation. 8-2=6
I want to see this is 4d
Sweet!
Wow...
man I have no idea what just happened.. awesome tho
I viewed your channel mate, really love the content. Liked straight away, We should connect!
Body building and mobius transformations will be a very interesting collab...
Real ASMR
Was that fractals or a cartoon head?
Nonconcensusical Rotating along the Z axis produces a rotation in the plane.
i had an intuitive idea about this but I do not even know where this came from...I am not a fundamental mathematician. Maybe knowledge is a wave the collides with us
awesomee
divide p by its square magnitude ;)
Great video! Would it be possible to use your graphics in one of my videos? I would place a link to your original video!
ıt's morbin tıme
morbius strip
2:08
I like more Moebius for Wilson Colorines
tereographic Projection
Wooow wooooowwww
wat dis?
Cool vid.btw im on my moms account.
Title of this video: Möbius Transformations Revealed [HD]
Quality of this video: 720p
Date of this video: 10 years ago
My response to these stats: Don't tell me you call this [HD], son. You must be a grandpa by now who fought in the military and gives his grandchildren ice cream.
My friend standing next to me: u got dem big brains man (>-_-)>
What are u saying?
Noice
lel
i'm the thousandth like :P
awesome