The hypersphere
ฝัง
- เผยแพร่เมื่อ 27 ก.ย. 2019
- A hypersphere is a 4D sphere. How does such a strange shape look like ? To answer we must first have an idea how to represent the fourth dimension in our world. The hypesphere can be built with a set of 3D spheres. We discover that the 3S sphere is open in the hyperspace. We can figure the hole by enlighting the sphere with a spot light.
my left ear is really enjoying this
Blame the platform at this point
I’m glad I saw this because I was so confused for a few minutes trying to figure out what went wrong
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
One thing though. If that was possible, no human or anything would be any longer protected. Anything could be attacked through the fourth dimension.
Another thing. Humans or anything in the universe dont have 3d surfaces i think? So how would anything be approached from the fourth dimension?
@@littlyshippy4999 it really can't. Unless there actually *is* an accessible 4-dimensional object somewhere in the universe sticking into 3d space, we as 3d beings have no way of touching the 4th dimension with anything 3-dimensional.
That is a cool idea!
Maybe that's how they performed operations in Star Trek (Bones once lamented in one of the season's finale "The City on the Edge of Forever" that people back then used to tear them open and sew them back together like garments. To describe surgeries. Quite a visual.)
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.
Yup. This is what I'm currently obsessed with.
So the universe might not be expanding after all. It could be just an optical illusion. Keep thinking in the direction of proving this, and you folks might shutter the world of science once again!
this video and channel is so underrated, deserves a million more subs and views
This is the best hypersphere video I've ever seen
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!
Thanks. I know my accent is so bad. I just hope it is understandable....
@@somecoolideas No, your accent is really cool, I understood almost everything you said even though I'm not a native speaker myself. And the subtitles helped a lot as well. Actually I think your way of telling things is unique, a phrase like "The whole world is a tangle of spaghetti" has an enormous memetic potential, in my opinion =)
The only weird thing is the audio going only to the left ear. Everything else, your accent, your way of putting words together, make you a very interesting and a rather unique TH-camr. I think you have a potential of gaining a LOT of subscribers if you keep posting.
So don't let people discourage you!
@@VasilyMusic Thank you very much for your support. I Really appreciate :-)
@@somecoolideas You're doing a great job, keep posting if you have ideas for videos
By far the best demonstration of 4D -> 3D projection I've ever seen. Bravo!
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.
play with chat cpt about dimensions and dragons...
uh-jeahh !!
One of the best videos explaining 4D projections I’ve ever seen.
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.
Merci, pour l'instant c'est bcp de travail pour peu de résultats. Il va falloir que je publie d'autres vidéos...
@@somecoolideas l'accent est comme hercule poirot :) un peu comique mais tres comprenable.
Thank you, I love only-side audio
This was a very nice video, explaining things at a decent pace without getting boring or too confusing.
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 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.
Wow, thanks!
@@somecoolideas you still make videos
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!
Fantastic video! Loved it! I especially liked your animations depicting projections, by showing an object 'flattening' as it passes through a viewing plane.
Understanding topological features of 4d space with hyperspheres is useful in understanding gravity.
why does a French person explaining things make it seem much more casual and relaxed
ur brain links 2 unordinary things as normal ironically
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!
Best treatment of this subject I have ever seen. Thank you.
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.
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.
Muy BIEN explicado, Gracias por el vídeo.
👏👏👏
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!
Thank you. For my last vidéo, I used AI to translated directly from French. Less work, better accent. I hope so.
This is an amazing video, and it should have a milion views
NightWng120 thank you
Best video of this type I’ve ever seen. My 4D friend even likes it apart from the accent.
Brillant explanation!
Thank you for this video. Really helped me understand the mathematical model spaces that I use for my research.
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...
Je trouve ça très intéressant. Dommage que la video n'est pas plus "percé" bien que le travail fourni soit enorme ! Bonne chance.
This is an amazing video that helped me greatly ! Look forward to more . Subbed . 👍
This video actually helped me process 4D. Also the narrator's french accent was funny and brightened my day :)
👏👏 thank you for the video
Great Introduction! X
my left ear really enjoyed this
Please ignore the comments making fun of your pronunciation of SPHERE. I LOVE IT!!! DON'T CHANGE IT!!
This was the best explanation of the 4D space ever
Not sure if I am able to 'see' the 4d shape in 3d but I did certainly enjoy the different accent.
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
I hit subscribe after about 1.5 seconds. I took one look at the animation, one listen to the voice, and I just knew.
one of the best videos explaining this , very well done ; kudos =]
That part about having no surface let me connect some more dots on other concepts and google queries. Thanks.
Cools video man, I'm gonna refer your video in one of my blogs to explain the curvature of space.
The best❤
It’s kind of like looking at a semi transparent balloon very cool demonstration
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.
Impressive! Great quality video! Where are your other 1 million subs?
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
Interesting, but the audio being stuck panned fully left made it a chore to listen to.
Thank you for this!
Amazing video, subbed!
I love this channel!
this is the video that finally did it
I LOVE INTELLIGENCE. THANK YOU SUPREMELY MUCH, GOD-TEACHER.
whoever this magical French man is, he isn't being paid enough.
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.
Eh pretty much, a 2d man can enter a 3d guy
Wow, mind-blowing thought. That was what I thought at first... But now that I have had another thought about it, I think it's not really right... (Even if my alternative isn't complete and might be entirely false)
That's what I thought: Let's take a Circle with a radius of one and keep the radius always at one for the next figures. So the Circle has a circumference and a surface. The Sphere has the same circumference as the Circle (spheres have circumferences, yes), a different surface than the Circle as well as a volume, which the Circle doesn't have at all. Now the Hypersphere should have the same circumference as the Circle and the Sphere, the same surface as the Sphere, a different volume than the Sphere as well as another measurement unit which the Circle and the Sphere don't have at all.
If this would all be true than the length of a line (The Line is the 1D figure of a Circle, yes) would be its circumference. So the circumference of 1D is the diameter of 2D.
However I am quite certain that there is no 4th SPACIAL Dimension, there are many other Dimensions you encounter daily, but no other spacial dimensions than the three x, y and z.
@@SoulofRilus It's been a while since I wrote this comment and researched 4 dimensional shapes so I don't fully understand my original point. Maybe I should rewatch the video :) . I do wanna know about the other dimensions you believe we encounter daily.
Well, when we talk about dimensions we almost always mean the spacial dimensions. There are three known spacial dimensions (x, y, z) and some also debate about more.
What my great-uncle told me half a year ago is that in physics dimensions actually are nothing but "criteria" that varies depending on the problem you have to solve. So the spacial dimensions are needed in problems where you need to know where a certain object is. Temperature would be the dimension that you need when you face a problem regarding, for example, cooking. Anything like mass, temperature, force, work, amount of rays, volume and density is a dimension and time is one as well.
Although this is a completely different approach than what we are used to I quickly accepted this concept. I am quite a sceptical person, but as my great-uncle is a very, very smart, experienced scientist and physicist I am convinced that it is right.
No, a perimeter is just a 2d surface. A 2d being cannot pass through, but a 3d being can. A surface is just infinite perimeters stacked on top of each other so that neither a 2d nor 3d being can pass through, but to a 4d being a 3d surface is not fully closed like it is to us. A volume, however, cannot be passed through by anything in or under the 4th dimension. A 3d volume can basically just be walked around by a 4d being, though, just like you could just step around what is an impassable obstacle to a 2d being.
well done!
The accent is cool and clear, Thank you! great visuals!! Make more!!!
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.
what
can you extend this taught? im able to imagine this but im not able to get into those points within to feel outside them from 4d to 3d space.. could the spacetime be seamless?
So in 4D you can see the inside & outside of 3D objections at the same time or big & small at the same time?
yeah, as like we can see the skin and organs of a flatlander (basically the inside and outside of a square □)
This person is so smart!
I HAVE VISUALIZED IT, THUS PROVING DIVINE EVOLUTION.
@cool ideas. May you please share with us many more videos just like this. How to Invision hyper cubes and other shapes.
Thanks for your comment. I will try. Don't expect it soon, I've a lot of other videos in mind, especially my series on General Relativity.
@@somecoolideas take as much time as you need, best of luck.
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?
Why is this the only video in the channel. I need to learn more from you!!
Sound resonates in higher dimensions, that’s why speakers don’t sound like real instruments. It’s resonant a different in the higher dimensions
What if you made the hyper sphere clear like glass could we maybe see the inside of it?
Wouldn't be just easier to explain hypersphere as an expanding ball? Like a balloon inflated with a liquid metal.
I think no. The hypersphere I describe here is in a pure space, not in a space-time. When you consider space-time, you have to change the way you compute lengths. Basically, you have two possible lengths : space or time. So, in space-time you have two possible "hyperspheres" : one with its the radius expressed in meters and one with a radius expressed in seconds.
The shape of the hyperspheres are hyper-hyperboloids, single sheet or two-sheets.
As you propose, these two "hyperspheres" look like an deflating then inflating balloon. With a "space radius", the size of the balloon will decrease down to its spatial diameter and inflate again. With a time radius, the ballon will completely disappear during its "time diameter".
My left ear enjoyed this
my left ear enjoyed this
Please make more videos in future ...
Fantastic video, I hope you haven't given up and are just busy!
Busy... I have to find time to translate my French videos.
This stuff is so mindblowing, hard to grasp
4D shapes are so cool
when your conclusion kicks in, my 2d(igit) iq transcended to 3d. very nice video sir.
left ear loves this
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.
This video is so good
Like illusion in Shakespeare's.
My left ear loved this video
So is a 4D sphere the same as 3D of curved space?
This is a very thought-provoking video, very different and novel compared to the others available on TH-cam. 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
I'm not sure to be able to answer your questions properly, especially in the complex quaternion space.
I don't understand why you say that an axis (straigtht line) could be a meridian (arc of a circle).
When's the next Upload?
...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 !
My left ear somewhat enjoyed this.
my left ear really liked this video
Good
- 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.
For the moment I thought my headphones is broken because its only playing in left ear
My right ear really likes this video
You're wearing your headphones the wrong way around.
Firstly, is this unity?
Secondly, such a beautiful accent.
Thankzs. This is Blender
hmmm while i am watching this channel on a 2D space while my eyes saying that this is 3D
Let's summarize: I have a sausage shape in 4D space.
question to the channel admin:can a normal person like me truly understand 4 dimension and all that complicated geometry or is it just for special brains like the scientists?
I'm sure everyone is capable of great wisdom and can understand complex physics and geometry . it just takes lots of discipline to take time to study harder than you ever in your life..
It only plays on the left channel.
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