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Please explain what the fourth dimension is and how it can be visualized

Date: Tue Jul 15 22:20:21 1997
Posted by Kate
Grade level: nonaligned
School: graduated a long time ago
City: San Francisco State/Province: CA
Country: US
Area of science: Physics
ID: 869023221.Ph

Message:

Please explain what the fourth dimension is and how it can be visualized.


When I was in high school, I was fascinated by the fourth dimension, and thought a lot about it. I never found any really good books describing it, although there is one fun one called "The Fourth Dimension Simply Explained". It has essays written by people as part of a contest with the same title as the book. Many of the descriptions are pretty good, considering that the contest was held about 60 years ago! Maybe your local library can find a copy of it.

Anyway, on one level there is nothing mystical about the fourth dimension. It is simply another dimension like the familiar three of length, width and height. However, since we live in three dimensions, it is difficult (some say impossible) for us to visualize a fourth dimension. For example: take a line (the first dimension) and draw a second line perpendicular to it to make a right angle. You now have a two dimensional drawing. Now draw a line at a right angle to both lines, going up: now you have three dimensions. The fourth dimension would be if you could draw a line perpendicular to all three lines. Of course, we can't do that, any more than a two-dimension creature could draw that third line. We are stuck in the third dimension, and can't draw outside of it.

On another level, you can think of dimensions as something with which you measure other things. In this sense, time can be a fourth dimension. That way, any object has a position that can be defined by the three normal dimensions and the fourth dimension of time. Some people call this the space-time continuum, because you can define this object in space and time (for example: at 7:00 o'clock this morning I was at longitude 75 degrees west, latitude 38 degrees north, four meters above sea level-- this defines my position in three spatial dimensions and one in time). So time can be a fourth dimension, but not necessarily the one. It depends on what you are measuring.

If you want to try to visualize the fourth physical dimension, I suggest trying to think of an example in three first. For example: imagine you were floating at the center of a large sphere. All points on the surface of the sphere are at the same distance from you. Now suppose you move around a bit. When you do, you will always move a little towards one side of the sphere, and away from another, right? In other words, some points on the surface will now be closer to you than others. However, if you could move in the fourth dimension, and not just three, you could move in such a way that all points on the sphere would recede from you by the same amount! How is this possible?

To visualize it, take this example down a dimension. Think of it this way: draw a circle on a piece of paper, and place your pencil tip at the center. Now move your pencil a bit. The tip will get closer to one part of the circle and farther from the other, right? Now matter how you move your pencil in the plane of the paper you will always approach one part of the circle and recede from another. Ah, but now put your pencil tip at the center of the circle and lift it straight up, into the third dimension. All points on the circle are now receding from your pencil tip at the same rate! This is exactly the same as when you were floating in the sphere. If you could move in the fourth dimension, you could go straight out from the center of the sphere, receding forever, but never actually touch the surface. Weird, eh?

Maybe it's a good thing we don't have access to the fourth dimension. You could walk into locked rooms, untie knots in secure ropes without unfastening the ends and all sorts of other unsavory things. Of course, you could also operate on people without breaking the skin, and remove diseased tissue without leaving a scar! And people say abstract math has no useful purpose!



©2008 Phil Plait. All Rights Reserved.

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