Beyond the Third Dimension--Chapter 6

Like Anya, I find it very interesting that movement around an object or representation is what exposes perspective as the illusion that it is. I'm taking VA10 this semester, and we worked a little with perspective. One of the most important aspects of this process (which our professor stressed as being very mathematical) is that the illusion only will work from the one single vantage point that you create it to work for. If the veiwer looks at the art from any other point, it will look grossly distorted- the illusion is broken. In fact, a cool phenomenon is that people automaticallyadjust their position so that they are looking at the picture from that certain point. I just think it's amazing how our mind and sense of sight are so well trained to interpret the lines and shapes that we are used to seeing.

It's amazing, but also frustrating for people like us who are striving to visualize some kind of object (a hypercube, for example) that no person has ever really seen. We must use our extremely refined sense of visual perception- refined, that is, for the conventional 3D shapes we encounter every day. I begin to wonder if a 3D being could ever really understand 4D objects. So much of visualizing seems to be knowing instinctively which information to pay attention to and which to ignore (the top of the printer beside me actually looks like a trapezoid, but I see it as a rectangle). Like Professor Banchoff said about his movie, every time you view it you can notice something new about the way a hypercube appears as you "walk around it" in 4-space. Can we ever really know how to look at a hypercube?

It seems that the sense of sight has its conventions in each respective dimension. In Flatland, they relied on their sense of touch to understand how something "looked". Here, we rely on the convention of perspective to make up for objects getting smaller in the distance and other such distortions. What about the way a four dimensional creature would "see?" How do we know that it isn't an entirely different process for them?

I feel as if I'm drifting speedily away from thoughts relevant to Chapter 6, so I'll stop now. It was a good chapter.