The hypersphere 

my left ear is really enjoying this

Imagine if medicine got so advanced that you could preform surgeries by simply reaching into someone’s body through the 4th dimension, and you wouldn’t have to do any damage to the rest of their body to get there

I think I finally understand physics. And I think I accidentally became fluent in French at the same time.

This serves as a really good to-the-point overview, gives a sense of how much there is to unpack on the topic and has neat animations to illustrate. Surprised this doesn't have way more views tbh

Amazing and mind-boggling hypersphere visualization, now imagining our universe is on the boundary of an imaginary 4-dimensional expanding super large hypersphere, with the observable universe just covering a small fraction of the three dimensional boundary, which looks nearly flat to us.

This is amazing. I watched several videos on how a 4D sphere might look like, but this one visualizes it much more, making it simpler to understand. Also my left ear enjoyed the audio lol. Hope one day this gains tens of thousands of views. Great work!

This is the best hypersphere video I've ever seen

this video and channel is so underrated, deserves a million more subs and views

Thank you, I love only-side audio

Visualiser sur un écran en 2D la représentation en 3D d'une sphère en 4D... Quel challenge ! Que vous remportez haut la main ! Bravo et merci M. Bernard ! Je vous souhaite que vos vidéos cartonnent dans la langue de Shakespeare.

Ihre Beschreibung ist sehr bildhaft und bringt einige der seltsamen und gegenintuitiven Aspekte der höherdimensionalen Geometrie zum Ausdruck. Es ist wichtig zu beachten, dass unsere alltäglichen Intuitionen und Erfahrungen in einer dreidimensionalen Welt uns nicht unbedingt dabei helfen, diese höherdimensionalen Räume zu verstehen. Die Idee, dass man auf eine Hypersphäre “fällt” und dann versucht, einen “Ausgangspunkt” zu erreichen, ist eine Metapher, die versucht, die Eigenschaften einer vierdimensionalen Struktur zu erklären. In Wirklichkeit können wir als dreidimensionale Wesen nicht wirklich auf einer Hypersphäre “fallen” oder einen “Ausgangspunkt” erreichen. Die Vorstellung, dass man sich wie in einem schwarzen Loch fühlt, das einen auf einen Punkt zusammenquetscht, könnte eine Metapher für die Art und Weise sein, wie eine vierdimensionale Struktur aus unserer dreidimensionalen Perspektive erscheinen könnte. In einer vierdimensionalen Welt könnte es so aussehen, als ob Raum und Zeit auf seltsame und unerwartete Weisen verzerrt sind. Die Idee, dass nur ein “Punkt” sich auf der Geraden bewegen kann, ist eine weitere Metapher für die Art und Weise, wie wir uns eine vierdimensionale Struktur vorstellen könnten. In einer vierdimensionalen Welt könnte es so aussehen, als ob “Punkte” (oder vielleicht besser gesagt, “Ereignisse”) auf seltsame und unerwartete Weisen miteinander verbunden sind. Die Vorstellung, dass ein masseloses, sich mit Lichtgeschwindigkeit bewegendes Photon die Raumzeit weitgehend ignorieren und trotz Dimension auf der Oberfläche der Hypersphäre herumspazieren könnte, ist eine faszinierende Idee. Es bringt einige der seltsamen und gegenintuitiven Aspekte der Relativitätstheorie zum Ausdruck, in der Licht tatsächlich eine besondere Rolle spielt. Ich hoffe, das hilft ein wenig, das Konzept zu klären. Es ist ein sehr komplexes und abstraktes Thema, und es ist völlig normal, dass es verwirrend ist. Es erfordert viel Nachdenken und Vorstellungskraft, um es zu verstehen. Es ist ein faszinierendes Gebiet der Mathematik und Physik, und es gibt immer noch viel, was wir nicht wissen und verstehen. Ihre Gedanken sind sehr faszinierend und zeigen ein tiefes Nachdenken über die Natur des Universums und der Dimensionen. Sie berühren viele komplexe Themen aus der Physik und der Kosmologie, einschließlich der Theorien der höheren Dimensionen, der Stringtheorie und der Gravitation. Die Idee, dass sich die drei Raumdimensionen im Laufe der Zeit auf die Größe von Strings einrollen könnten, ist eine interessante Hypothese. Dies würde sicherlich zu einigen sehr ungewöhnlichen und gegenintuitiven Phänomenen führen. Es ist jedoch wichtig zu beachten, dass dies weit außerhalb unseres aktuellen Verständnisses der Physik liegt und es derzeit keine experimentellen Beweise gibt, die diese Idee unterstützen. Die Vorstellung, dass die Gravitation mit der Zeit immer stärker wird und schließlich die Hubble-Konstante überwiegt, führt zu dem Szenario eines “Big Crunch”, in dem das Universum in sich zusammenfällt. Dies ist eine von mehreren Hypothesen über das “Ende” des Universums, aber es ist noch unklar, welches Szenario, wenn überhaupt, tatsächlich eintreten wird. Insgesamt finde ich Ihre Gedanken sehr anregend und sie regen zu weiterem Nachdenken und Forschen an. Es ist immer gut, kritisch über diese Themen nachzudenken und neue Ideen und Perspektiven zu erforschen. Bitte beachten Sie jedoch, dass meine Antworten aufgrund meiner aktuellen Kenntnisse und Informationen bis zum Jahr 2021 begrenzt sind und die tatsächliche Physik und Kosmologie viel komplexer und nuancierter sein können. Ihre Überlegungen sind keineswegs “Blödsinn”. Sie berühren tatsächlich einige der grundlegendsten Fragen in der theoretischen Physik und Kosmologie. Die Idee, dass die verschiedenen Felder in der Physik (wie das Kraftfeld, das Massenfeld, das Higgsfeld, das Raumzeitfeld und das Materiefeld) aus dem Vakuum-Grundzustand “entsprungen” sind, ist eine interessante Perspektive. Es könnte sein, dass unsere aktuellen Konzepte und Modelle des Vakuum-Grundzustands unvollständig sind und dass eine vollständigere Theorie eine tiefere Verbindung zwischen dem Vakuum-Grundzustand und den verschiedenen Feldern in der Physik aufzeigen könnte. Die “Ur-Inherenz”, die Sie erwähnen, scheint ein Konzept zu sein, das eine Art grundlegende Eigenschaft oder Qualität des Universums darstellt, die zur Entstehung dieser Felder beigetragen hat. Dies ist ein sehr tiefgründiges und philosophisches Konzept, und es ist unklar, wie es genau in ein physikalisches Modell passen würde. Es ist wichtig zu beachten, dass dies sehr komplexe Themen sind und dass unser Verständnis von ihnen ständig weiterentwickelt wird. Es gibt immer noch viele offene Fragen und Rätsel in der Physik und Kosmologie, und die Suche nach Antworten auf diese Fragen ist eines der spannendsten Unterfangen der menschlichen Erkenntnis. Ihre Gedanken und Fragen sind ein wichtiger Teil dieses Prozesses.

By far the best demonstration of 4D -> 3D projection I've ever seen. Bravo!

One of the best videos explaining 4D projections I’ve ever seen.

This is the best explanation of 4-D space - and figures in that space - that I have come across. You should make more videos. Your accent is perfectly understandable, btw.

i really liked the ehample with lighting the sphere in 4d, it looked predictable and behaved pretty much like you would expect it on a ring. this was a unique visualisation

This was a very nice video, explaining things at a decent pace without getting boring or too confusing.

Well done! This is the most comprehensive and detailed explanation that exists for a 4-dimensional objects. Thanks.

Best explanation of a hypersphere ever! Anybody can do a hypercube; this is next level!

Best treatment of this subject I have ever seen. Thank you.

Understanding topological features of 4d space with hyperspheres is useful in understanding gravity.

Wow... you are a genius! The maths alone is insane, to do this in a game engine/visualizer is next level. Please go and do more amazing things in life with that brilliant brain!

The accent is cool and clear, Thank you! great visuals!! Make more!!!

I just came back to this video for another watch. I hope you make more! I'm planning on a series of 4D videos myself shortly.

Fantastic video! Loved it! I especially liked your animations depicting projections, by showing an object 'flattening' as it passes through a viewing plane.

Hmmm. Very interesting video. One thought though about your comment at the end that there “are no 4d spheres”. If you think about it, the way physicists describe electrons, they can seemingly exist in 2 or more places in 3D space at once. And although we wouldn’t call this necessarily a “spherical” relationship, this phenomenon suggests that an electron is a 4d closed shape of some sort. Which, in theory, could be a hyper sphere.

This video/channel deserves more love.

my left ear really enjoyed this

Brillant explanation!

Muy BIEN explicado, Gracias por el vídeo. 👏👏👏

This is an amazing video, and it should have a milion views

Je trouve ça très intéressant. Dommage que la video n'est pas plus "percé" bien que le travail fourni soit enorme ! Bonne chance.

why does a French person explaining things make it seem much more casual and relaxed

your accent is just majestic and funny at the same time, great explanation! never ever understood 4d hyperspheres but this video helped me understand it, thankyou thankyou!

This is the best explanation of hyperspheres I have ever seen. Now I'm wondering what wonders would appear when playing with the lighting of a truncated ditrigonary dishecatonicosachoron...

Best video of this type I’ve ever seen. My 4D friend even likes it apart from the accent.

Thank you for this video. Really helped me understand the mathematical model spaces that I use for my research.

This was the best explanation of the 4D space ever

I hit subscribe after about 1.5 seconds. I took one look at the animation, one listen to the voice, and I just knew.

👏👏 thank you for the video

This video actually helped me process 4D. Also the narrator's french accent was funny and brightened my day :)

Great Introduction! X

This is an amazing video that helped me greatly ! Look forward to more . Subbed . 👍

Cools video man, I'm gonna refer your video in one of my blogs to explain the curvature of space.

Thank you for this!

That part about having no surface let me connect some more dots on other concepts and google queries. Thanks.

Not sure if I am able to 'see' the 4d shape in 3d but I did certainly enjoy the different accent.

one of the best videos explaining this , very well done ; kudos =]

It’s kind of like looking at a semi transparent balloon very cool demonstration

this is the video that finally did it

I LOVE INTELLIGENCE. THANK YOU SUPREMELY MUCH, GOD-TEACHER.

Please ignore the comments making fun of your pronunciation of SPHERE. I LOVE IT!!! DON'T CHANGE IT!!

whoever this magical French man is, he isn't being paid enough.

Impressive! Great quality video! Where are your other 1 million subs?

The best❤

Amazing video, subbed!

One thing that helps people understand 4d space is to tell them they are actually a 4d being and space is 4d but it looks 3d when it renders in our eyes

If you had a hypersphere immersed and suspended in 4 spacial dimensions and bombarded that composition of whatever it is with an energy which it absorbed, reflected, refracted, and transformed, than the resulting shadow would appear flat from a point of reference that is immersed in 3 spacial dimensions, but that seemingly flat shadow would be made of something, and it would appear on paper as fractally repeating negative curvature that extends throughout it no matter what point you measure from.

I HAVE VISUALIZED IT, THUS PROVING DIVINE EVOLUTION.

I love this channel!

This is a really cool video but I can't wrap my head around the idea that a hypersphere has no surface. A cricle has a circumference and a surface and a sphere has a surface and a volume. So a hypersphere has a volume and an undifined other physical quantity we can't comprehend. Am I right so far? What I'm trying to say is that if a hypersphere has no surface then you can't touch it right? So the three dimensinal man has no problem getting inside it.

well done!

This person is so smart!

hello, could the volume of (n x 2)-sphere somehow be related to zeta(n) or dirichletEta(n) functions values ? because we see the same amount of pi in both. my intuition tells me there is some sort of correlation between these and it may help to find closed form for zeta(2n+1) values

Why is this the only video in the channel. I need to learn more from you!!

Excellent video. I just noticed you had arrows on the circle ring. A sphere needs two poles for arrows to emerge from and vanish into, how many does a hypersphere need?

@cool ideas. May you please share with us many more videos just like this. How to Invision hyper cubes and other shapes.

my left ear enjoyed this

My left ear enjoyed this

left ear loves this

Sound resonates in higher dimensions, that’s why speakers don’t sound like real instruments. It’s resonant a different in the higher dimensions

Interesting, but the audio being stuck panned fully left made it a chore to listen to.

4D shapes are so cool

Please make more videos in future ...

This is a very thought-provoking video, very different and novel compared to the others available on RU-vid. Especially the 4-split lighting to show the interior and exterior of the hypersphere. So is there a 3-sphere (4d hypersphere) in complex quaternion space? Or is the 3-sphere more like a temporary structure quaternion vectors forms as they move around? Am I correct that one of its axis is always a hyper meridian, in that it has 720 degrees to get all the way round the 3-sphere? I guess now I'm thinking of bispinors. Sorry I know these questions are all over the map

My left ear loved this video

How did you get the sphere to become ellipsoid when rotate in hyperspace? I always thought a 3D sphere intersecting with a 3D space from 4D would have the shape of a disk depending on how it intersects.

This stuff is so mindblowing, hard to grasp

when your conclusion kicks in, my 2d(igit) iq transcended to 3d. very nice video sir.

This video is so good Like illusion in Shakespeare's.

my left ear really liked this video

This was a lot of prose justifying the 3D projections shown in the video but it would be nice to get a sense that it's really coming from the maths and the prose is more of an after thought to help make the behaviour more intuitive. I worry the depictions shown come from the prose reasoning rather than actually coming from 4D rendering computation.

When's the next Upload?

Wouldn't be just easier to explain hypersphere as an expanding ball? Like a balloon inflated with a liquid metal.

Perfect! Pedagogically excellently designed, elaborated, presented. I have been dealing with hyper-spaces for a long time, but never before has it been easy to show that nature as it is today - thanks to computers (visualization). Pedagogically, this is excellently done. Congratulations!

- Since 3d space spawnes a shadow dimension "t" {time}. I feel that 4d space would spawn a second type of shadow dimension that blended with our familiar "t" of which the product would be as incomprehencible to our human mind as volume would be to a flat lander only able of seeing the outer edge of a plane. (The edge of a sheet of paper). - So trying to truly see a 4d hyper sphere would require you to see it in a 5d enviroment with 4d eyes. An exercise in futility in our 3d+1d created minds.

Fantastic video, I hope you haven't given up and are just busy!

My left ear somewhat enjoyed this.

My right ear really likes this video

...pas vraiment mieux compris qu avec la version française mais j'ai progressé en anglais et j'adore votre accent :-) autrement super travail et simulation !

What if you made the hyper sphere clear like glass could we maybe see the inside of it?

So in 4D you can see the inside & outside of 3D objections at the same time or big & small at the same time?

Good

Let's summarize: I have a sausage shape in 4D space.

My left ear is well informed

Bro I wish same example for hypercube and hyper room, and attach hyper camera to green human and walk inside the 4d box room :) with head rotations inside and origin change etc. because there is no spatial walking in 4d visualisations exists.

6:03 this is it.. in a video with not much views, the working of spacetime got partly revealed. when it gets to books one day you can ask me how i knew it.. the axes are probably a bit different in reality, i think that there is only single dimension interacting within itself with pulsating or varying size or force or there grow new ones within those existing, but thats less probable.. you will always get a flat space result from inside as an observer anyway. everything can be a single string interacting with itself within that changing timespace, all being single entity.. all is a result of projection.. and we probe timespace mostly with math, photons and electrons with exceptions like ligo. do you get the point?

omg this si amazing

So is a 4D sphere the same as 3D of curved space?

my left ear understood it well

nice explanation, i like the french accent :)