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Why Mathematicians and Physicists Should Stop Arguing

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Jan. 29th, 2002 | 11:59 pm
mood: thoughtfulthoughtful
music: Astaire - I Won't Dance

I had this thought while I was doing my calculus homework the other day. (Yes, I know, thinking while doing homework. What a concept).

Mathematicians say that the fourth dimension needs to be a spatial dimension. Yet they use time as a fourth dimension. (Well, technically a third dimension for the purposes of my thought, but since a third spatial dimension exists already and the dimension of time is non-spatial, the presence of it as a third dimension, particularly in a 2-D system such as the one I am about to discuss, can be extrapolated to time being a fourth dimension in a 3-D system).

My calculus homework was parametrics, equations where the x and y coordinates are defined separately in terms of a parameter. When graphing these equations then, the graphs have three components. They have an x componet (width) and a y component (height), the two obvious ones of a cartesian coordinate system. However parametric graphs are special in that they have a specific direction. The graph is drawn in a specific order determined by the parameter, making the parameter a variable in and of itself. The textbook describes this phenomenon by telling us to think of a point whose coordinates are x and y, both functions of t. This point is free to move in space, and a line follows it in the direction of its movement. In this case then, t, of which the point's ordinal components, x and y, are a function, is representative of time, since any given point cannot be in two places at the same instant. Thus, a graph of a parametric equation on a cartesian coordinate plane has a third property, or dimension, that is determined by time.

So time is the third dimension in a 2-D system, and thus can be the fourth dimension in a 3-D system, as 3-D parametric graphs would also all have a direction of motion as well.

So time is used at least by mathematicians as a fourth dimension, though it also has a spatial component to it. Just as length must come before width, and length and width before depth, the temporal dimension depends on spatial components. It is not traceable in terms of mathematics until at the very least a first dimension, length, is present.

So the Mathematicians and the Physicists should stop arguing now. And I have a new pet theory.

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