Visualizing 4D Geometry - A Journey Into the 4th Dimension [Part 2]

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This is part 2 of the series. We take a look at Hyperspheres, Hypercones, and Hypercubes (tesseract).

Graphics:
"Cono y secciones"

Music:
Aspire (piano)

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Imagine chilling in your room an suddenly a random floating shape appears out of nowhere morphing into different random shapes until it dessapears...

Mikelaxo

Imagine what geometry tests in the 4th dimension are like

xaio-xen

This is by far the best visualization and explanation of 4d dimension

infoteka

*meanwhile in flatland . . .*

Visualizing 3D Geometry - A Journey Into the 3rd Dimension [Part 2]

xxseyroxx

I've never felt so scared by watching a cube rotate.

This is, I don't know what this is...

arattactician

Alternate title idea: “Where lost nerf darts go”

infinity

If our reality was extrapolated to 4 dimensions...

- Round earthers don't make sense, but flat earthers would make even less sense.
- One of the simplest musical instruments would be the tetrahedron.
- When you roll dice, any one die will display a number from 1 to 8 instead of 1 to 6; you can have regular dice that have 5, 8, 16, 24, 120, or 600 different results.
- Intersections between three streets are commonplace; apart from going straight, turn lanes can go left, right, up, or down (hyper-up and hyper-down are the 4D directions and those are reserved for hyperflying).
- In addition to widescreen and ultrawide, hypermonitors can also be deepscreen or ultradeep; hypermonitors that are widescreen are usually also deepscreen with an aspect ratio of 16:9:4, an upgrade from 4:3:2; a 1080p hypermonitor would have a screen resolution of 1920*1080*480, an ultrawide equivalent 2560*1080*480, an ultradeep equivalent 1920*1080*1920. A hypermonitors that is both ultrawide and ultradeep may require a GTX 1166400-T2 to run.
- A 4K hypermonitor would have the same number of voxels as eight 1080p hypermonitors.
- Cars have eight tires and would have 4 turn signals instead of 2.
- A piano would have 7744 keys. (I have no good reason why.)
- An MTG hypercard would have as much text as a deck of MTG cards in 3 dimensions.
- You can draw a cube with absolutely no distortions on a piece of hyperpaper.
- Painting is like reverse sculpting; instead of subtracting material from a 4D medium (like a block of hypermarble), you're adding pigment to a 3D canvas.
- Elevators have to go hyper-up and hyper-down instead.
- Klein bottles don't self-intersect like they do in 3 dimensions.
- Hyperprinting is basically 3D printing.
- People have a hard time learning octonions; quaternions and complex numbers are straightforward; 7blue1brown would also have a video on octonions.
- There are speedtessing communities, not speedcubing communities.
- This video would be titled "Visualizing 5D Geometry - A Journey Into the 5th Dimension [Part 4]"

ganaraminukshuk

4 dimensional creatures: _theyre getting smarter_

wyntryx

This absolutely helped me understand 4D. It was like a sleeping part of my brain waking up. Thank you.

prouddad

Science videos
Vsauce
Experiments

*I sleep*

Visualizing 4D Geometry - A Journey Into the 4th Dimension [Part 1]

*Real shit?*

Visualizing 4D Geometry - A Journey Into the 4th Dimension [Part 2]

*A S C E N D E D*

helpme

You're watching someone explain the 4D dimension in a 2D screen.

herculean

This is one of the best videos about 4D I’ve found on YouTube.

btipton

me all video :

*shows* *it* *on* *4D* *to* *3D*
what the *** what is going on ?!!?

*shows* *it* *on* *3D* *to* *2D*
ohh right now I get it

robot-sensei

Very cool, thank you so much for this

Makes me wonder if the electrons that "pop in and out of existence" arent projections of 4 dimensional spheres or something...

danable

One thing that’s caught my attention is that in lot of videos and sources (NOT this one, though), especially about 4D knots and links, one might get the idea that you could link two spheres in a 4D-space. This is simply not true. You can only link a sphere and a circle (or a hypersphere and a point) in a 4D-space, and to link two spheres (or a hypersphere and a circle), you need a 5D-space. Generally, the combined dimension of your linkable components must be precisely 1 less than the dimension of the surrounding space. In other words, you can link an l-sphere and an m-sphere in an n-space, iff l+m=n-1. If l+m>n-1, the components will intersect; and if l+m<n-1, the link will be trivial. Keep in mind that a sphere is actually a 2-dimensional manifold (2-sphere), and a circle is a 1-dimensional manifold (1-sphere).

PC_Simo