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Superstring theory describes a world comprised of at least 10 dimensions. For most of us—with our way of thinking and the way in which we experience the world—it's difficult to imagine more than three spatial dimensions. In mathematics, however, working in more than three spatial dimensions poses no problem at all and helps solve problems not solvable otherwise. Here's a simple example that shows why.
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Dimensionless point
A point has no width, no height, and no depth. It has no dimensions and so no numbers are needed to describe it. We could describe a location where a point exists with numbers if we wanted to give its position, but right now we're only concerned with the point itself.
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One-Dimensional Line
A one-dimensional line can be described by one number, which describes the line's length. Length can be measured in any of a number of units—inches, centimeters, finger widths, etc. This one is measured in pixels.
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Two-Dimensional Rectangle
The rectangle can be described by two numbers. One number is length (the first line), and the other is height. By multiplying these two numbers, you can find the area of the rectangle.
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length
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height
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=
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area
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100 pixels
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50 pixels
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=
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5,000 square pixels
(or pixels2)
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Three-Dimensional Box
This box can be described by three numbers: length, height, and depth. By multiplying these three numbers, you can find the volume of the box.
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length
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width
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*
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depth
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=
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volume
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10 pixels
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20 pixels
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55 pixels
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=
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125,000 cubic pixels
(or pixels3)
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Four-Dimensional Hypercube
A hypercube is created by pulling the box into a fourth dimension—into a space that we cannot experience. It is difficult to imagine a four-dimensional object (and to depict one on the two-dimensional surface of a computer screen), but in this case focus your attention on the mathematics involved. The formula (expression?) below describes the total volume—hypervolume—of an object that exists in four spatial dimensions.
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length
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height
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*
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depth
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hyperdepth
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=
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hyper volume
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10 pixels
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*
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20 pixels
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15 pixels
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60 pixels
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=
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7,500,000 pixels4
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Is the Expression Meaningful?
Although it's difficult to imagine a four-dimensional object, the "pixels4" resultant of the equation is meaningful. If there was another four-dimensional box just like the one shown here, but was deeper into the fourth dimension, the hyper volume measurement of the object would be larger. This number would be useful for comparing the "size" of the object to that of another.
Likewise, the math involved with string theory is meaningful (at least in the mathematical sense), although the objects it describes are much more complex and much more difficult to imagine. Shown here is an attempt. This is a rough representation of a so called Calabi-Yau shape. Its six dimensions, along with the three familiar spatial dimension and the dimension of time, account for the 10 dimensions of string theory.
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