Dimensions - 3: The Fourth Dimension [Pt. 1] 2/2

Dimensions by Jos Leys - Étienne Ghys - Aurélien Alvarez

Chapter 3: Dimension four (pt. 1)
Mathematician Ludwig Schläfli talks about objects that live in the fourth dimension and shows a parade of four-dimensional polytopes, strange objects with 24, 120 and even 600 faces !

More detailed explanation of Ch 3: http://www.dimensions-math.org/Dim_CH3_E.htm

Visit the site to watch online or download free: http://www.dimensions-math.org/

Category:

Education

Tags:

• math
• help
• 4th
• fourth
• dimension
• fractal
• geometry
• projection
• proof
• mathematical
• imagery
• algebra
• calculus
• space-time
• analysis
• multi-dimensional

[Qu35t10n3v3ryth1n9]

So the lines of these geometrical structures are capable of passing through one another as if they are almost non existent or have an ethereal like nature? Otherwise I don't quite understand how this video demonstrates these shapes. The lines are clearly intersecting one another where no vertices exist and are moving through one another like ghosts. Is that just some odd 4th dimensional law where non-localization is making this possible or something?

[KeepGoing11235]

@Qu35t10n3v3ryth1n9 watch?v=UnURElCzGc0 . Notice that the projection (shadow) of the 3D cube consists of lines of different lengths which can intersect in the 2D world as Carl rotates the cube. In 3D, the cube has equal length edges that do not intersect. So what we see in this video is a 3D projection of a 4D object that is being rotated. In the 4D reality, all the edges of the shape are the same length and none will intersect

[TexasHouseofCarnage]

I don't understand, can you explain how the sides of complex structures such as the 600 cell's links between the vertices never intersect each other? What is the universal rule or pattern all these shapes follow in their natural 4th dimension?

[KeepGoing11235]

@TexasHouseofCarnage Please see my comment to Qu35t... The rule of all of these shapes is that in each respective dimension, the shapes have edges of all the same length that only intersect at vertices.

[UltraGameAchiever]

so i was wondering, if u tried to put it on the x y z axis, would it be just another x u z axis on the z axis?

[Qu35t10n3v3ryth1n9]

@KeepGoing11235 ahhh ok ok, makes much more sense now. Thanks for clearing that up. Completely spaced that we can really only perceive the 3rd dimension and below at this point :P haha

[matreyia]

I wonder if 4D objects exist in nature or if they only exist in abstract math.

[TexasHouseofCarnage]

I wish I could comprehend this to it's degree of importance concerning universal geometry and dimensional-space travel. We all just need more elaborate teachings over this subject. It's quite interesting.

[MEMercuryEnigma]

Not a bad video. I would recommend trying to make it more interesting for more views. :P