About Vectors

(written by Lawrence Krubner, however indented passages are often quotes)

I found a math book that has allowed me make better sense of vectors. This should give you the flavor (from page 40):

Let the period at the end of this sentence represent a point P.

Where is the point P? We could say it is right there, at the end of the sentence. But where is the sentence? On page 40 of some book? But where is the book? On a table in a certain room on the Earth? Then where is the Earth?

After pushing this silent dialogue with ourselves a little further, we begin to realize that the concept of “where” is a fundamentally puzzling one.

But suppose we erect a frame of reference by means of 3 base vectors e_x, e_y and e_z. Then, without knowing where this frame of reference is in any deep sense of the word, we can nevertheless ask where a point is in relation to the reference frame; and this relative sort of where is a far more tractable concept.