Thursday, April 19, 2012

The phenomenology of a fourth spatial dimension.

A hyperdimensional cube, known as a tesseract...

Part of the motivation for this blog was to open up a dialogue between working artists and working scientists. One of the conversations that is starting to develop relates to the (artistic) field of phenomenology and whether it does/doesn't have anything to say when it comes to the more abstruse sciences. Of course phenomenology is the study of the things humans experience (at least according to my rudimentary understanding of it) and scientists are human beings who experience abstruse science so phenomenology must have something to say about science, by definition. But what?

The discussions which began this conversation concerned two online applications that aid in the visualisation of the scales involved in time and space. See this post and this post and the comments in each for a discussion of the apps. In that discussion and in the comments to a later post I expressed a sense of disappointment in what these apps were managing to express. I should clarify that I think the apps are great and interesting, but if one is looking for a phenomenology of science I don't think this is where the most interesting phenomenology is (of course the app creators aren't looking for a phenomenology of science, so they are completely forgiven). The scale of space and time are very ordinary, everyday, Earthly things. The most interesting discoveries science has made, at least in the world of high energy physics, are not well described in such terms - this is almost precisely what makes them so interesting.

As Rhys pointed out in one of those comment threads a huge part of this problem is that many of these discoveries rely heavily on mathematics. And, to a very large degree, to understand the discoveries, you need to have a grasp of the maths. The fact that the very abstract structures and symmetries and patterns that lie hidden in the mathematics are then actually exhibited in the real universe is one of the more wonderful things experienced by a scientist. And that is not easily captured simply through pictures, videos and sounds (or even smells) of the universe.

However, I came across an app today that really does try to bridge this gap. If someone were to be looking for a true phenomenology of the more interesting and wonder inducing aspects of theoretical physics then this is the sort of thing one should be looking for. It is an app that simulates a hyper-dimensional cube. OK, so what on Earth does that mean?

Well, a dot exists in zero dimensions, it has no length, width, nothing. A line exists in one dimension, it has simply a length. A square exists in two dimensions, it has a length and a width. Next, a cube, exists in three dimensions, it has a length, a width and a depth. Now, just imagine there was a fourth spatial dimension. Mathematically this is an easy thing to write down. Then, just as one can form a cube by extending a square into a third dimension, one can form something known as a tesseract by extending a cube into a fourth spatial dimension.

Now, we creatures who exist in just three spatial dimension can't visualise a fourth spatial dimension (I certainly can't). But, just as we can look at a two dimensional surface (a TV screen) and see a projection of a three dimensional object, so can we do the same for an imagined four dimensional object projected onto three (or two) dimensions. And this is precisely what this app does for a four dimensional tesseract. [Edit: Or, as Rhys said in this comment "it shows what a 4D painter would paint on a 3D canvas..."]. And the brilliance is that the app even allows you to manipulate the tesseract, to move it, to spin it (in any of the four dimensions) and while manipulating it you see how that three dimensional projection changes on your two dimensional screen. Here's a video preview...

This app came to my attention as a consequence of minutephysics covering extra spatial dimensions in his latest video - which you should watch for a quick overview of higher dimension. There is even, apparently, a game in construction that requires you to move into and around a fourth spatial dimension to solve puzzles (for example using it to navigate one's way around obstacles and put keys into locks).

I actually think that a phenomenology of abstruse science can go even further and get even more interesting than this. A fourth spatial dimension is one of the simplest ideas I can think of that is not directly understandable from an Earthly perspective, but easily described by maths. It also has the unfortunate position of quite possibly not actually being reality and certainly not yet being testably true reality. However, it is here, with this sort of application/idea that I would think a phenomenology of the interesting bits of high energy physics should start.

Twitter: @just_shaun


  1. I wanted to write a comment in the post itself about how the phenomenology presented in the Scales of the Universe and ChronoZoom applications was one dimensional, when compared to this newer app... but... well... I temporarily had more discretion.

  2. Looks neat. When I read 'projection' I though of a linear projection from 4D to 3D, but of course that's not what's going on; instead, it shows what a 4D painter would paint on a 3D canvas...

    1. Yeah, that's a good point. I like your description. I wondered a little bit what the most appropriate word to use there was. My first thought as to what "projection" means is the same as yours, but when I saw that the app description itself wrote projection I took the path of least resistance.

      Wikipedia does seem to suggest that the word has a large breadth of meanings, one of which is relevant to this.

    2. "...the word has a large breadth of meanings, one of which is relevant..."

      Absolutely! I meant only to flag a possible point of interest, not to suggest that the wording was wrong.

  3. Gentlemen, if you are interested in 4D, it would be worth your while to check out Zometool. A simple but profound building "toy" that is the golden standard for building physical 3D models of projections from 4 (and higher) dimensions.

    I hope you find this useful!

    1. Thanks cneumann. That does look really interesting.

      If you send me a sample of zometool I'd be happy to write a review of it here.