/sci/ - Science & Math » Thread #12965468

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4d

Anonymous Mon 12 Apr 19:09:23 2021 No.12965468 View Reply Original Report

Quoted By: >>12965828 >>12965867 >>12965902 >>12965908

brainlet here.. I thought this would be a good start to try to understand 4d... nope. Wtf is that? How do I visualize 4d?
I don't understand 2 cubes connected to each other.
Pic very related.

Anonymous

Anonymous Mon 12 Apr 2021 20:25:04 No.12965828 Report

Quoted By:

>>12965468
4d, like 3d, 2d and 1d is an infinite vector space.
The 1d infinite vector space is an infinite line. The 1d object in your image is an object embedded in the line.
The 2d infinite vector space is an infinite plane (the cartesian plane). The 2d object in your image is an object embedded in the plane.
The 3d infinite vector space is an infinite space. The 3d object in your image is an object embedded in the space.
The 4d infinite vector space is an infinite 4-space. The 4d object in your image is an object embedded in the 4-space.

Anonymous

Anonymous Mon 12 Apr 2021 20:33:10 No.12965867 Report

Quoted By: >>12965885 >>12965927 >>12966405

>>12965468
you dont visualize geometric stuff in >3D
you gather experiance and intuition working with 1D and 2D, generalize it and use 3D as a final sanity check before generalizing to nD and finally have a look at edge cases like infinityD, 1.5D, (-3+2i)D..

Anonymous

Anonymous Mon 12 Apr 2021 20:36:32 No.12965885 Report

Quoted By: >>12965913

>>12965867
There's no such thing as complex dimensional vector spaces. D is a positive integer (or positive real) quantity.

Anonymous

Anonymous Mon 12 Apr 2021 20:40:46 No.12965902 Report

Quoted By:

>>12965468
ITS FUCKING TIME
ITS THE SAME SHAPE BUT APPEARING AT A DIFFERENT FUCKING TIME

Elon Musk Fanboy

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Elon Musk Fanboy Mon 12 Apr 2021 20:42:04 No.12965908 Report

Quoted By: >>12966227

>>12965468
You need about 500 micrograms of LSD, a linear algebra book and good music, it'll come to you eventually.

Anonymous

Anonymous Mon 12 Apr 2021 20:44:10 No.12965913 Report

Quoted By: >>12966237

>>12965885
havent encountered it myself (and im glad about that) but im pretty sure there are some ugly PDEs out there describing relativistic plasma vortices or whatever, where some quantity scales with a complex dimension
Kinda like the imaginary time or the complex index of refraction

Anonymous

Anonymous Mon 12 Apr 2021 20:47:35 No.12965927 Report

Quoted By: >>12965950

>>12965867
but why do they go through the trouble of making 4d visuals if nobody can understand them?

Anonymous

Anonymous Mon 12 Apr 2021 20:51:22 No.12965950 Report

Quoted By: >>12966031

>>12965927
you need to first understand 4D theoretically so that you know what you're looking at

Anonymous

Anonymous Mon 12 Apr 2021 21:04:56 No.12966031 Report

Quoted By:

>>12965950
speaking of that... if we look at 4(a^3)b
it implies there are 4 objects of equal "4d" volume (orange cube and 3 orange cuboids). The pic shows 3 orange cuboids are identical in shape while the 4th (cube) one looks bigger. What gives?

In (a+b)^2 and (a+b)^3 examples, "2ab" and "3a^2b" show are 2 and 3 (respectively) equal parts by volume/area and shape. Why does that logic fall apart in (a+b)^4?

Anonymous

Anonymous Mon 12 Apr 2021 21:50:52 No.12966227 Report

Quoted By:

>>12965908
No, you would be sitting there spinning

Anonymous

Anonymous Mon 12 Apr 2021 21:52:53 No.12966237 Report

Quoted By:

>>12965913
you are likely thinking about using complex spatial coordinates, which find use in numeric simulation for implementing perfectly matched layers

Anonymous

Anonymous Mon 12 Apr 2021 22:23:29 No.12966405 Report

Quoted By:

>>12965867
>generalizing to nD
only special cases generalize. for anything useful, everything changes each time you add a dimension

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