Date: Sat, 16 May 1998 19:19:12 -0500
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.
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
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.
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