Solar Eclipse

Southern Hemisphere view. This eclipse was only visible from New Zealand, Australia, and Chile.

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

Phenemonology between Husserl and Heidegger

Cy Twombly, The First Part of the Return from Parnassus (1961)

Regular readers of this blog will have noticed the relatively recent addition of a blog-roll, in the form of a themed list of 'blogs we read.' That list is for active blogs, in my opinion, but I've found an inactive blog that I wanted to highlight because I think it speaks to some issues meaningful to the motivations of this endeavor for communication across disciplines and specializations: some of our themes of open access, vernacular writing on the web, and increasingly, phenomenology.

The blog, Between Husserl and Heidegger, is clearly an outcome of a graduate-level course in phenomenology at an American university, most likely one taught from a philosophy department or a department arrayed around the disciplinary study of philosophy. The posts are all summaries of the readings written by students in the class. I've written these kinds of excursus myself in graduate school, and have asked them of my own students. Writing a careful, detail-oriented account of someone else's argument is a great exercise in close and attentive reading, and hones sensitivity to the craft of constructing concepts.

So, the blog is a fragment of a course that has been left lying around on the web. It's useful in a number of ways for precisely this reason. For a specialist, it's a nice summary of names and books that reflects an interesting and informed syllabus. For non-specialists, it's an insight into how teaching and learning works in the humanities. For anyone interested in phenomenology, it's a great open-access bibliography — a source for the vocabularies, ideas, and contemporary histories of a topic I'm well aware isn't the most accessible out there.

The URL for the blog is erlebnis - the German word for 'lived experience' which acts as a central, motivating concept in all strands of twentieth-century phenomenology — as the blog's author himself notes. In keeping with his excellent taste, I've taken the image for this post from one of my favorite Cy Twombly paintings in the collection of the Art Institute of Chicago.

The scaling of time: ChronoZoom

One of the conversations that is starting to develop here at the blog relates to the concept of scale. In a recent comment, Michelle wrote about an application that aids with the visualisation of time-scales (although the application's designers see it as more of an interactive teaching tool).

Seeing as "Scale of the Universe" is so popular on the internet, I expect that this application, ChronoZoom, should become equally popular one day soon. Scale of the Universe allows you to zoom in and out of distance scales and it shows you the relevant physics, chemistry or biology at each scale. ChronoZoom kind of does the same for time. However it is quite a bit more detailed and much, much more ambitious as a project. Watch the video above, read a recent article on the project, and play with the application itself.

Michelle wrote in her comment that she finds visualising time-scales through this application more difficult than the equivalent for spatial-scales. This is not surprising. We encounter space with our eyes every day, so visualising space is already second nature. Zooming in and out is also something we do naturally every day. Extending this to a need to zoom in and out on a greater range of scales shouldn't be too hard. However, no matter what happens in life, we always proceed forwards in time at a rate of one second per second and we definitely don't "see" time. Despite all of that I think it is also true that the Scale of the Universe application was specifically designed with the aim to give a sense of perspective. Whereas, ChronoZoom has been designed more as a way of organising information. The sense of perspective it can give seems to be much more of a bonus than a feature.

One interesting observation I can make (and have already to a certain degree in this comment) is how in the early stages of the universe, time scales and length scales were intricately related. This relationship arises from two different mechanisms. The first, and more obvious, is the expansion of space with time. As time progresses, things in the universe get further apart. Therefore the relevant distance scales get larger and larger as well. The second mechanism is the growth of structures in the universe. Structures grow hierarchically. This means small things grow first, then larger, then larger. This is actually a distinct effect from the expansion of the universe, but it's aesthetic implication is the same; earlier times mean smaller scales.

Of course most of the ChronoZoom application is devoted to later times. Something that struck me quite a bit when I first realised it is that the Earth is about a third of the age of the universe. Whether this means that the Earth is very old, or the universe is very young depends on your perspective, but whichever perspective you hold, when it comes to time, the universe and the Earth exist on similar scales. You can see this really clearly in ChronoZoom. What is also quite striking, but already appreciated by many people is just how young humankind is. If you go to ChronoZoom and click on "humanity" right at the top of the page you are given quite a sense of perspective regarding how young we are as you watch it take forever to zoom in on our relevant time.

For both those old dudes, Earth and universe, we humans really are just a flicker.

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