Page:Relativity (1931).djvu/85

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MINKOWSKI’S FOUR-DIMENSIONAL SPACE

The non-mathematician is seized by a mysterious shuddering when he hears of “four-dimensional” things, by a feeling not unlike that awakened by thoughts of the occult. And yet there is no more common-place statement than that the world in which we live is a four-dimensional space-time continuum.

Space is a three-dimensional continuum. By this we mean that it is possible to describe the position of a point (at rest) by means of three numbers (co-ordinates) $x$, $y$, $z$, and that there is an indefinite number of points in the neighbourhood of this one, the position of which can be described by co-ordinates such as $x_{1}$, $y_{1}$, $z_{1}$, which may be as near as we choose to the respective values of the co-ordinates $x$, $y$, $z$ of the first point. In virtue of the latter property we speak of a “continuum,” and owing to the fact that there are three co-ordinates we speak of it as being “three-dimensional.”

Similarly, the world of physical phenomena which was briefly called “world” by Minkowski

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