Adventures in the 4th dimension. Posted on March 11th, 2010 by

“The perception of existence by human beings is entirely different from existence itself.” This is how Paul Humke, St. Olaf math professor and the American liaison for BSM, concluded his amazing colloquium lecture on the 4th-dimension today. Chalk in hand, he asked us to investigate the numbers behind higher dimension. We counted vertices, edges, faces, solids, hyper-solids, etc, finding the patterns within the chart and relating these to what actually happens when you stretch an object into a new dimension. He then showed us a video that graphically portrayed the progression of a cube, which appeared to be rotating, through the first four dimensions. Many scientists and scholars claim that viewing the fourth dimension is not within the range of human perception. The other side of that argument, however, is that we’re simply not trained to see in the fourth dimension. As evidence of this second point of view, he told us this really interesting story about a man who had been blind from birth and through a new medical procedure was able to regain his eyesight at the age of 23. But even though his eyes functioned perfectly, he was still never able to see the same way that the rest of us do. This is because our eyes only give us the raw data from our surroundings while it is our brain that perceives what is going on around us. By the time he had the procedure, he had already lost his ability to learn how to perceive faces, edges, depth, and colors. Thus it stands to reason that we simply can’t see higher dimensions because our brains are not trained to do so. Before showing us the video again, he informed us that although our brains perceived the cubes as rotating in space, the “rotation” is actually the movement of some higher dimensional object through our dimension. As the object moves through a lower dimension, we only see cross sections of the object. The illusion of rotation is caused when the object is twisted, therefore appearing to rotate as the cross sections progress. Here is Paul Humke’s more concrete example:

Imagine a 3D ball passing through a 2D plane. As the ball moves through, someone living in this 2D space perceives it as a series of circles gradually increasing then decreasing in size until the ball passes all the way through and vanishes. Now put a red ribbon vertically through the middle of the ball. When you pass this new object through the 2D space, it is perceived as the same series of circles, but with a red line segment always in the middle. Now here comes the interesting part. Take that ribbon and twist it around a couple of times before attaching it inside the ball. This time as the ball moves through the plane, instead of staying still, the red line segment appears to be rotating according to the twists in the 3D ribbon. Cool, huh.

The crazy thing is that someone living in that 2D space has no idea about the existence of the 3D ball. S/he simply sees a bunch of circles and line segments without the ability to comprehend the shapes in any sort of higher dimension. So who’s to say that the objects we perceive in our world aren’t just the circles and line segment cross sections of some object in a higher dimension? I think Professor Humke summed it up perfectly when he said that given the complexity of the universe and of existence, we should consider ourselves lucky to be in possession of even a small portion of this knowledge.


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