4D Discussion Thread

[cubinator]

This is a topic that branched out of the Bad Science in Fiction thread, and I feel it appropriate to dedicate a thread to it. While our brains are very stubborn in interpreting shapes in exactly three dimensions, we can learn a lot about how 4D objects would look and behave by looking at their 3D cross-sections and shadows. These are hypercubes:

 

Try to see each cubic cell connected to the others by faces, just like square faces are connected at right angles to form a cube. This is close to what a hypercube would look like from an actual 4D perspective, in which your field of view is a volume rather than a plane. 

[StrandedonEarth]

Next you’ll come up with a 4D Rubik’s cube....

[kerbiloid]

Spoiler

43 minutes ago, StrandedonEarth said:

4D Rubik’s cube

A hypercubic tesserubic

 

Edited July 14, 2018 by kerbiloid

[YNM]

1 hour ago, cubinator said:

Try to see each cubic cell connected to the others by faces, just like square faces are connected at right angles to form a cube.

Amusingly, we'd probably never quite see it.

All the things that we see are actually 2-D projections of the 3-D world in front of us : Because everything can be made of planes, and our view could be reduced to planes as well (this is how perspective drawing works). Depth information are only picked up thanks to parallax and focus.

Think about what a "lower-down" dimension would "see" : In 2-D world for example, all they're going to see are actually just lines.

If we (3-D creatures) ask a 2-D creature to observe a 3-D object intersecting the plane they live in, it's still going to be lines. And when the object doesn't intersect the plane, it's not going to be visible.

So yeah, if a 4-cube (tesseract) were to appear in our 3-D world, it's just going to look like a cube that appears whenever they intersect our 'volume'.

[NSEP]

I like to imagine the 4th Dimension as time, and 4 dimensional creatures are able to see the passage of time like a stack of animation slides, expect the slides are 3D rather than 2D.

I think about the 4th dimension alot when im supposed to do homework and i have come to understanding it better. The hypercube is bassicly a stack of cubes the same way a cube is a stack of squares.

[cubinator]

1 hour ago, StrandedonEarth said:

Next you’ll come up with a 4D Rubik’s cube....

This has been around for some time...

http://superliminal.com/cube/cube.htm

[Gargamel]

1 hour ago, cubinator said:

This has been around for some time...

http://superliminal.com/cube/cube.htm

Dang it, beat me to it.

Matt Parker did a great little talk at the Royal Institute a few years ago, and I picked up his book because of it.  But at the end of his talk, he points out that they have 'made' Rubik's cubes of N-dimensions.

 

[Superfluous J]

I found that my imagining 4 dimensions helped by thinking how a 2-d person would imagine (or experience) 3 dimensions.

Or if you've not got 100 minutes to spare (I watched it at 1.5x, myself, though I also read the book twenty-mumble years ago in college) here's the trailer:

And for completeness, the book:

http://store.doverpublications.com/048627263x.html?gclid=Cj0KCQjwvqbaBRCOARIsAD9s1XAQcsOsZgUEyygGdV2ofNmbdbEd4ypxkZW_mi_BTw_4D66dEHyUiFMaAixVEALw_wcB

 

Edited July 14, 2018 by 5thHorseman

[kerbiloid]

Spoiler

10 hours ago, Gargamel said:

But at the end of his talk, he points out that they have 'made' Rubik's cubes of N-dimensions.

The last step before a Rubik Warp Drive.

 

[NSEP]

13 hours ago, 5thHorseman said:

I found that my imagining 4 dimensions helped by thinking how a 2-d person would imagine (or experience) 3 dimensions.

Or if you've not got 100 minutes to spare (I watched it at 1.5x, myself, though I also read the book twenty-mumble years ago in college) here's the trailer:

And for completeness, the book:

http://store.doverpublications.com/048627263x.html?gclid=Cj0KCQjwvqbaBRCOARIsAD9s1XAQcsOsZgUEyygGdV2ofNmbdbEd4ypxkZW_mi_BTw_4D66dEHyUiFMaAixVEALw_wcB

 

I just yesterday watched that movie, thanks.

[DAL59]

It would be much better to look a a projection in 3-d instead of on a flat screen.  

[Cheif Operations Director]

What is 4D exactly; diagonals?

[cubinator]

7 minutes ago, Cheif Operations Director said:

What is 4D exactly; diagonals?

It's a geometric space with four axes perpendicular to each other.

We can show what it means with this diagram.

With zero dimensions, you can only have a point. In 1D, you can extend that point along an axis to form a line. In 2D, you make another axis perpendicular to the previous one, to form a square. Then you form another axis perpendicular to both the previous ones, and extrude the square into a cube. This can only be shown on a 2D screen with diagonals, but you know quite well what it is like for a cube to have all 90 degree angles. We can keep going, though, and extrude the cube along another axis perpendicular to all three, to form a hypercube or tesseract in 4D. This shape does not fit in 2D or 3D without diagonals. It is like flattening out a box. That is why we see diagonals when looking at projections of 4D shapes - our brains are not willing to interpret them as right angles because we don't know what direction to put the fourth axis in. We've never seen anything from the perspective of anything but a 3D universe, and so don't know how to visualize in 4D.

However...I do think it is possible to begin to "see" how a 4D being would, by visualizing how 4D objects behave in 3D space (cross sections), imagining having 360 degree vision to facilitate finding a direction entirely separate from all directions possible in 3D, and using drawings like those above (which should work just as well as any drawing of an object).

[YNM]

I guess there's a 'better' way to "visualize" higher dimensions.

 

[kerbiloid]

@cubinator's paradise
 

Spoiler

(Knossos palace)