All right now that you know what a vector is we can talk more about dimensions. In the exercise we did yesterday you were using a 3 dimensional coordinate system. There were 3 axes each corresponding to a different dimension. And we needed 3 different numbers, an x component, a y component and a z component, to specify exactly where your vector end was located. If you only had one dimension you would only need one component to tell where your vector end was located. And the same holds for five dimensions. You may not be able to draw a graph like that but you still only need 5 numbers or components to specify a location in 5-D space. I've included a picture of some objects in 2, 3 and 4 dimensions. String theory and now M-theory suggest 10 and 11 dimensions, respectively. Why so many?
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