

Visualizing the Fourth Dimension Using Color - adbge
http://www.rdrop.com/~half/Creations/Puzzles/visualizing.4D/

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ragle
Those that enjoyed this may also enjoy the film "Dimensions".

A brief guide for the film that gives an overview: [http://www.dimensions-
math.org/Dim_tour_E.htm#guide](http://www.dimensions-
math.org/Dim_tour_E.htm#guide)

Watch online (Deutsch, English, French, Spanish, Italian, Japanese, Russian
and Arabic subs available): [http://www.dimensions-
math.org/Dim_regarder_E.htm](http://www.dimensions-
math.org/Dim_regarder_E.htm)

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vixin
Great link!

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yzzxy
Better cache:
[https://web.archive.org/web/20130601110834/http://www.rdrop....](https://web.archive.org/web/20130601110834/http://www.rdrop.com/~half/Creations/Puzzles/visualizing.4D)

(Includes images)

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jakebian
OR you can simply project the fourth dimension into 2D, much like how we
project 3D pictures onto 2D screens. Here's an example
[http://jakebian.github.io/hypercanvas.js/](http://jakebian.github.io/hypercanvas.js/)

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Houshalter
It's a cool idea but I don't know how to comprehend what I'm looking at.

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heeton
What would your response be to a child who said something similar when you
drew a cube?

It does take practise to be able to visualise 4d objects, and I agree that 2d
projection example isn't helpful. I find it interesting to think of the 3d ->
2d problem that some people have, and extend it to 4d.

~~~
Houshalter
I mean that there is no description on how these projections are even created.

A child would recognize a cube since we naturally see 2d projections of 3d
objects as it is. Likewise a 2 dimensional being could recognize a 1d
projection of a 2d object (looking at the 2d object on it's side.) But would a
3d object projected to 1 dimension make any sense?

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xtacy
I've thought a lot about visualising higher dimensions in 3D. Colour is a
fantastic way to start, and it infact is adding 3 more dimensions
(hue/saturation/lightness). If you could add other senses, e.g., touch, taste,
pain, etc., you can sense even more dimensions.

However, one thing does strike you that no matter how many senses you
incorporate, you will always navigate a particular 3D projection.

EDIT: Cached page:
[http://webcache.googleusercontent.com/search?q=cache:http://...](http://webcache.googleusercontent.com/search?q=cache:http://www.rdrop.com/~half/Creations/Puzzles/visualizing.4D/)

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j2kun
> no matter how many senses you incorporate, you will always navigate a
> particular 3D projection.

How do you mean? I can think of visualizations that do not.

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swift
Could you describe the visualizations you're thinking of?

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j2kun
An animated visualization, for example.

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elnate
Can someone give a two dimensional analogy to the unknotting example?

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mirosam
Nontrivial knots don't exist in 2D, so not really.

Something almost analogous is if you imagine two circles: one smaller and one
larger in 2D. Let's say the smaller circle is inside the larger. It's
impossible to move the smaller one outside smoothly without intersecting the
larger.

In 3D of course this is trivial, just move the smaller circle up away from the
2D plane, then over the larger one and down on the plane again.

~~~
ragle
I think your circles analogy is good.

To tie it in a bit tighter with OPs article, I would just add that if we could
only perceive two dimensions, the inner circle would disappear as we "move the
circle up and away from the 2d plane".

It would only reappear to us once we moved it back down into our plane of
perception, safely outside of the other circle.

The relevant bit from OPs article that this is analogous to is:

> " _What would we see if you watched this happen in real life? Since we can
> 't see anything outside our 3D slice of 4D space, from our perspective the
> moving (green) loop would disappear, to reappear later in the unknotted
> position_."

