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why, exactly, I’m not really sure). In that case, Athena would have to be plotted as a point in a five-dimensional space with axes corresponding to age, number of books read per week, average math test score, number of minutes spent reading the newspaper per day, and number of owls she owns. However, I’m having trouble drawing such a graph. It would require a five-dimensional space, which is very hard to draw. Even computer programs only have 3D graphics.
    Nonetheless, in an abstract sense, there exists a five-dimensional space with a collection of five numbers, such as (11, 3, 100, 45, 4), which tells us that Athena is eleven, that she reads three books on the average each week, that she never gets a math question wrong, that she reads the newspaper for forty-five minutes each day, and that she has four owls at the moment. With these five numbers, I’ve described Athena. If you knew her, you could recognize her from this point in five dimensions.
    The number of dimensions for each of the three people above was the number of attributes I used to identify them: one for Sam, three for Ike, and five for Athena. Real people, of course, are generally more difficult to capture with so few items of information.
    In the following chapters, we’ll use dimensionality to explore not people, but space itself. By “space” I mean the region in which matter exists and physical processes take place. A space of a particular dimension is a space requiring a particular number of quantities to specify a point. In one dimension, that would be a point on a plot with a single x axis; in two dimensions, a point on a plot with an x and a y axis; in three dimensions, it would be a point on a plot with an x , a y , and a z axis. 1, * Those axes are shown in Figure 5.
    In three-dimensional space, three numbers are all you ever need to know your precise location. The numbers you specify might be latitude, longitude, and altitude; or length, width, and height; or you might have a different way to choose your three numbers. The critical thing is that three dimensions means you need precisely three numbers.In two-dimensional space you need two numbers, and in higher-dimensional space you need more.

Figure 5. The three coordinate axes that we use for three-dimensional space.
    More dimensions means freedom to move in a greater number of completely different directions. A point in a four-dimensional space simply requires one additional axis—again, difficult to draw. But it should not be hard to imagine its existence. We’ll think about it using words and mathematical terms.
    String theory suggests even more dimensions: it postulates six or seven extra spatial dimensions, meaning that six or seven additional coordinates are needed to plot a point. And very recent work in string theory has shown that there could be even more dimensions than that. In this book, I’ll keep an open mind and entertain the possibility of any number of extra dimensions. It is too soon to say how many dimensions the universe actually contains. Many of the concepts about extra dimensions that I will describe apply to any number of extra dimensions. In the rare cases when that isn’t true, I will make sure that it is clear.
    Describing a physical space involves more than just identifying points, however. You need also to specify a metric , which establishes the measurement scale, or the physical distance between two points. These are the markings along the axis of a graph. It’s not enough to know that the distance between a pair of points is 17 unless you know whether 17 means 17 centimeters, 17 miles, or 17 light-years. A metric is required to tell us how to measure distance: what the distancebetween two points on a graph corresponds to in the world that the graph represents. A metric gives a measuring rod that reveals your choice of units in order to set the scale, just like on a map, where a half-inch might represent one mile, or as in the metric system, which gives us