Whenever a science reporter uses the phrase “string theory,” it’s invariably accompanied by a sentence about tiny strings vibrating in 10 or 11 dimensions. Huh? How can you have more than three? And what does it really mean to say that that comix villain comes from the 4th dimension? Actually, we live in many dimensions, though it’s not easy to visualize them all at once. Let’s get some practice.
Right now, you’re reading along a line, a one-dimensional path from left to right. Imagine a point drawing a straight line about a foot in front of you. Let that line just hang out there in the air, glowing a gentle green color, with one “edge” (the line itself) and two “corners” (its ends).
As you read down the page, you traverse a series of lines laid out next to each other in the two-dimensional plane of the page. Imagine your green line moving upward, leaving a plane of yellow sparkles behind it. Stop when you’ve got a sparkly yellow square in front of you showing its one face, four edges (one green, three yellow) and four corners (two green, two yellow). Let’s put some red paint on one of those yellow edges.
Stack up enough printed pages and you’re got a 3-dimensional book. Imagine that nice yellow square moving away from you until you’ve got a friendly cube hanging out in the air. Our original line, the green edge, has produced a green face going into the distance. The red edge has built a pink face. All together, the cube has 8 corners, 12 edges and 6 faces. OK, now make your cube disappear.
But we’re not done yet. Time is a dimension. Consider that cube. Before you dreamed it up – nothing. Then suddenly a cube. Then nothing again. During the interval the cube was floating in front of you, the green line was tracing out a green face in time. The pink face was drawing a pink cube. The whole cube, from when it started to exist until it went away, traced out a four-dimensional figure called a tesseract, also called a 4-cube or hypercube. The tesseract was bounded by a cube at the beginning, six cubes while it existed (one from each face of the initial cube), and a cube at the end of its time, for a total of eight.
Just for grins, count up the faces, edges and corners for yourself.
But wait, there’s more. The tesseract doesn’t just sit there, it can spin. Being four-dimensional, it can spin in a surprising way. We’ll get to that next week.
~~ Rich Olcott
4 thoughts on “Dimensional venturing, Part 1 – What’s 4-D?”
And a 4-D Klein bottle would be?
Have patience, Dick, that one’s just about ready to go.
Looking forward to it. (Looking backward to the future gives me a headache.)
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