Subject: Question
Date: Sat, 16 May 1998 19:19:12 -0500

Name: Whitney
Question Level: Secondary (10-12)
Asked by: Student (I'm really in sixth grade, but I beleive the question highly advanced. My parents don't understand it. That is why I put it in the secondary level)

Okay, here goes all my effort to try to explain shat I'm trying to ask of you. It's about something I read in a book called A WRINKLE IN TIME, by Madeline L'Engle. It's called tesser, or tesseract.

It talks about first diminsion, a straight line, second diminsion, a flat square, and third diminsion, a square with sides, front and back, top and bottom.

I can picture all of that. Then it says that fourth diminsion is when you square the three diminsional square. It also described the fourth diminsion as time. I can't figure out how that can be. Then it says that you get fifth diminsion by squareing the fourth diminsion. Okay, then you have tesser. And then it says that tesseract is going between a long distance in a short distance of time. Like : a line is not the shortest distance between to points. It gives an example of an ant on one side of a string wanting to go to the other. It would be faster just to bring the ends together. I still couldn't understand anything. I would really like a better way of understanding all of this.

Thanks.
Whitney

 Hi Whitney I'm not familiar with the book you describe, but it sounds confusing. Perhaps you might enjoy FLATLAND, by Edwin A. Abbott (which is whimsical and charming, but a bit old-fashioned: it was written by a Victorian cleric!).   These days, the four-dimensional version of a cube is usually called a hypercube. (The name tesseract sounds old-fashioned to me, and I've never heard it called a tessera.) Here is the way I visualize it:   Start with the corner of a room; label as the x-axis the line where the side wall meets the floor, the y-axis where the back wall meets the floor, and the z-axis where the two walls meet. A point in the corner is the "0-dimensional cube." Move that point one unit in the x direction and joining the original point to its final position you get the "1-dimensional cube" (or line segment). Move the 1-dimensional cube one unit in the y direction and join the original two endpoints to the points in their new position to get the "2-dimensional cube" (or square). Move the 2-dimensional cube one unit in the z direction and join the four initial corners to the points in their new position to get the "3-dimensional cube." In the abstract world of mathematics one can imagine a direction that is perpendicular to all of the x, y, and z directions. (Since we live in a 3-dimensional world, we cannot point a stick in a direction perpendicular to our world, but we can certainly imagine it, and we can draw its shadow.) So move the 3-dimensional cube one unit in that new direction and join the 8 original corners to the points in their new position to get the 4-dimensional cube (or hypercube). You don't have to quit with four dimensions, but that's enough for today.   As for allowing time to be the fourth axis, it doesn't help visualize four dimensions, but it is convenient trick to help investigate the laws of physics -- part of the problem is that time and space seem to be different and incomparable ideas. Among other difficulties, you can't walk backwards in the time direction! Nevertheless, you can imagine a simple example. Drop a stone in a still pool of water and you will see a wave pattern that begins as a small circle and grows ever larger. To draw the corresponding space-time graph, place the pool at time zero in the xy-plane, and draw the time axes perpendicular to that plane. The wave at each successive time t will be drawn in the plane parallel to the xy-plane that is t units above, with the center of the circle directly above the point where the stone entered the water. The graph will look like an empty ice cream cone.   As for a line being the shortest distance between two points, that's true in every dimension -- in fact it's the definition. You make it sound as if Madeline L'Engle is suggesting that the ant is able to move backwards in time, but that's against the rules. I would call that "science fiction", not science. Cheers, Chris

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