Відео

A story as old as time itself.

Any infinite-dimensional object will be like a sphere in our dimension?

3:47 This is actually pretty misleading. Rotations are a 2d phenomenon, meaning it can only happen within a 2d plane. When you rotate in 2d space, there is only a single point that does not rotate. In 3d, you still fundamentally only rotate along a single plane, but that plane is extruded along the 3rd axis, rotating the whole object with a line being stationary. You can also add another plane to rotate along, but it only ends up rotating the original plane along a non-parallel plane. You can verify this yourself by grabbing an object, imagining a plane slicing through the middle, and arbitrarily rotating the object. You can rotate it however you want, but it will still rotate along the imaginary plane that is itself rotating. However, in 4d, you can create a plane and still have 2 more axes to create yet another plane. If you rotate one of those planes, the other is unaffected. Assuming the first plane is still rotating, there is no reason to assume the 2nd plane can't. Rotating both at the same time (or in sequence to get from one 4d rotation to another) is called a double rotation.

I also use PyGame for such animations, nice work. Can I ask are you doing anything special for increasing the floating point precision?

Could this be how an atom looks like?

very cool ty tucan

I've just tried to implement gravity simulation in rust (8 cores, simple n**2 algorithm with Euler's integration) and got ~55 ms per step (18 fps) for 10k particles. After that re-implemented the sim using pytorch tensors. On 4090 10k ~ 5 ms sim + 3 ms rendering. Managed to push it up to 35k, before running out of mem, got 60 ms per frame (16 fps). P. S. Measurements were collected for 3D sim.

I can never understand 4D. But now I understand

:D

My brain hurts I think Zeppeli got a little out of hand

loved the discussion of projection of the trig unit circle to unit sphere and unit hypersphere, that "exchange of values" in rotations

"unlike humans their lack of purpose is Very obvious" frickin legend hahaha

particle life shit posting

ARE YOU MARK？

Did you use raymarching

i support you!

Null 0, crawl points.

3:50 NOO!!! All rotations happen inside a plane! in 0D and 1D you can't rotate because there aren't any planes, in 2D there's one plane of rotation so 1 value to describe rotations. in 3D there are 3 planes, in 4D there are 6 and so on with the formula of planes = (d * (d - 1)) / 2. It's a common misconception that rotations happen in d-2 (axis for 3D, point for 2D, plane for 4D) but that's not true. The reason we use planes in 4D for rotations is that you can't get away with using axes. in 3D you can get away with it by saying Y axis instead of XZ plane because that's the only plane perpendicular to the Y axis. but in 4D, the Y axis is perpendicular to the XZ, ZW and XW planes. edit: saw someone else said the same thing. Sure, its technically different ways to say the same thing but its still kind of misleading. like if you use use planes in 4D rotation and points in 2D, then rotating *around* the XY plane in 4D means rotating *in* the ZW plane. anyway I liked your video!

tbh I understand where you come from I've been doing similar things my entire life, replace cult with broken healthcare and educational system and you got my vector into this thing. Ever read about Leibniz and relational space, monads, etc? A lot of our understanding of spacetime is taught with absolute space and absolute time, but relational is so interesting. I am trying to imagine an n-dimensional relative space defined by matter that freely associates on any number of dimensions, who all count their own time, or times. The monadic(I prefer duadic so could also be duadic) matter relates to what it considers local/neighborhood through a set of polar coordinates, sorta creating manifolds or something like that. It is hard to put into language, its just this ever transforming ever non-linear place that can throw my own imagination in an endless loop. Try to imagine that, it blows my mind to think of so I wanted to give it to you.

Dude you need better glasses

THANK YOU FOR THE UPDATE!!!!!!! I’m so happy someone on UA-cam actually cares about what I ponder about before I go to sleep ❤️

Nice!

1:00 If you use the Minkowski hyperboloid model, then you can use rotations to perform translations as you say, but I think Hyperbolica actually uses the Poincaré disc model, and instead uses something known as gyrovectors, which instead of performing 4D rotations to achieve translations, perform 3D Möbious transformations to achieve the same thing.

🫂

Great video, keep it up <3

Very well made

Support to you man. <3 At least math is always here when me need it

Who would've know 4D would be the best way to escape reality. Hope to see your channel get the love it deserves

:D

This couldn't have been easy to share! Your previous videos have been very interesting to me, I'm really surprised to hear how you started. Hope you're doing well!

What do you mean by "all the points are the same hyperbolic distance away from each other"? I can sense that this sentence makes sense someway, since for normal rotations all points remain the same distance from each other (it's an isometry), but what is this distance that you are talking about?

The first thing that come to mind is 4D Marble Marcher

Is that poop

You say someone wrote some papers about this? Non-linear time is something that gives me life so I'd love to know the name of said papers

underrated channel

cringebased

are these not just 3 dimensional spaces? how is this 4 dimensional?

calm down there i barely understand 2d fractals 😭

wow at 1:03 you can hear him actually getting comfortable with the void around him!

Your channel is one of the coolest recent yt discoveries

This is not a 4d sphere. This is a 3d sphere. An ant walking on a circle (the boundary; not inside the disk) can't tell the difference between that vs. walking on a line, which is why the circle should properly be called 1d. The fact that one might draw it in 2d doesn't make it 2d. If I draw a point in the plane it's a 0d object, despite sitting in the plane.

they have significance in future for voxel worlds probs i wanted to build an Minecraft city in one first time I saw these things!

He's telling about fractals but can't edit an audio properly And the video is not smooth at all

Dimensional beings are living in my home and physically harming/torturing me every single day. I need help immediately please. There are lots of people in my house that reside in the 4th,5th and 6th dimension. Some are friendly and some are extremely violent. I communicate with them on a closed circuit v2k set that I can take off if I want to. Most of them are reptilians but there are arachnids humans and shapeshifting demons as well. They can all can time travel in the second dimension as they have been created to run really fast through time and space. For a human to experience the dimensional world, you need a creator residing in the 4th dimension and a human in the 3rd dimension who will have (often by force) terrestrial technology installed in their brain. 4th dimensional beings eventually connect to said brain via nano robot technology and their consciousness can then be placed into a shapeshifting nano robot. They feed off your blood, brains and spinal fluid. I am a victim of dimensional human trafficking and am currently being held hostage in the 3rd & 4th dimension while 2-3 creators & 20-50 reptilians use me for bodily resources and sex slavery. I have run out of ideas and ways to resume to a normal life. I can no longer have regular relationships in my life. if my friends come over, they put terrestrial gear on them and follow them home for blood etc. If I go out they follow me. I can’t talk about this to any human and even if I did they wouldn’t understand, care or believe me. They quite literally drain me of blood every single day for resale amongst their community. I wake up weak and sick every single day. They torture me with needles for fun everyday. Despite the knowledge I convey regarding blood loss, they continue to use their regular blood consumption habits without any evolutionary change to benefit me.

I hope I would see this in my dreams

1:02 TVTropes:DiedDuringProduction

Most based take on fractals

In my novel, Above Dark Waters, fractals play a main point at the very end. One character basically has an NDE and the 'other world' is massive and infinite like a fractal. I also imagine a Mandelbox like you visualize at 2:21

I still have no idea what Im looking at! My mind simply can't understand the hypersphere... Maybe I can understand the hypercube - I have 2 videos on my channel about it - but the hypersphere might forever elude me.