Isaac Asimov: What is the fourth dimension?

The word “dimension” is from Latin and means “to measure completely”. Let us try a few measurements, then.
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Isaac Asimov

by Isaac Asimov

The word “dimension” is from Latin and means “to measure completely”. Let us try a few measurements, then.

Suppose you have a line and want to locate a fixed point, X. You make a mark anywhere on the line and label it “zero’’. You then make a measurement and find that X is just ten cm from the zero mark. If it is on one side, you agree to call the distance + 10; if on the other side, it is – 10. Your point is located, then, with a single number.

Since only one number is needed to locate a point on a line, the line or any piece of it, is “one-dimensional” (“one number to measure completely”).

Suppose, though, you had a large sheet of paper and wanted to locate a fixed point X on it. You begin from your zero mark and find it is 5 cm away — but in which direction? You can break it down into two directions. It is 3 cm north and 4 cm east. If you call north plus and south minus, and if you call east plus and west minus, you can locate the point with two numbers: + 3, + 4.

Or you could say it was 5 cm from the zero mark at an angle of 36·87° from the east-west line. Here again are two numbers: 5, 36·87°. No matter how you do it, you must have two numbers to locate a fixed point on a plane. A plane or any piece of it is two-dimensional.

Suppose now that you have a space like the inside of a room. A fixed point, X, could be located as 5 cm north of a certain zero-mark, 2 cm east of it, and 15 cm above it. Or you can locate it by giving one distance and two angles. However you slice it, you will need three numbers to locate a fixed point in the inside of a room (or in the inside of the universe).

The room, or the universe, is therefore three-dimensional.

Suppose there were a space of such a nature that four numbers, or five, or eighteen, are absolutely required to locate a fixed point in it. That would be four-dimensional space, or five-dimensional space, or eighteen-dimensional space. Such spaces do not exist in the universe, but mathematicians can imagine such “hyperspaces” and work out what the properties of mathematical figures in such spaces would be. They even work out the properties of figures that would hold true for any dimensional space. This is “n-dimensional geometry”.

But what if you are dealing with points that are not fixed, but that change position with time? If you wanted to locate a mosquito flying about a room, you would give the usual three numbers: north-south, east-west, and up-down. Then you would have to add a fourth number representing the time, because the mosquito would have been in that spatial position for only a particular instant, and that instant you must identify.

This is true for everything in the universe. You have space, which is three-dimensional and you must add time to produce a four-dimensional “space-time”. However, time must be treated differently from the three “spatial dimensions”. In certain key equations where the symbols for the three spatial dimensions have a positive sign, the symbol for time must have a negative one.

So we mustn’t say that time is the fourth dimension. It is merely a fourth dimension, and different from the other three.

Science Today, April 1968

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