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That is, if one dimension adds two possible directions to move in, would a half a dimension add only one direction to move in? That is - one way in time.

The number of dimensions is the number of integers required to uniquely located a particle. Thus it takes one integer to determine where a particle is on the x-axis, one integer to determine where a particle is on the y-axis, one integer to determine where a particle is on the z-axis and one integer to determine what time it is - that gives 4 integers.

Of course, dimensions are not limited to "integers", but rather "numbers" which would include rational, real, and perhaps imaginary numbers.

would it make sense to think of space-time as 3.5 dimensional instead of 4? That is, if one dimension adds two possible directions to move in, would a half a dimension add only one direction to move in? That is - one way in time.

would a half a dimension add only one direction to move in?

dimensions are not limited to "integers", but rather "numbers" which would include rational, real, and perhaps imaginary numbers.

A point X in a manifold is a set of numbers X = ( x^{1}, x^{2}, .... , x^{n}) where the x^{k} is either a real number or a complex number.

a half a dimension

Can you give a example of [partial dimensions]?

What is your definition of a dimension there Evan? I'm not following it as you present it? presently some single malt might limit my understanding, but I still hope you will find a description that works, even so

presently some single malt might limit my understanding

What is your definition of a dimension there Evan?

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.

3) Assume the spacetime is not flat and the 4-force is zero. Define S as where (This is merely called the integral of the interval. Some people call it the "length" of the world line. That is a widely used misconception.)While S is not necessarily the smallest possible value, it is a stationary value.

Quote from: PmbPhy on 05/01/2015 20:36:233) Assume the spacetime is not flat and the 4-force is zero. Define S as where (This is merely called the integral of the interval. Some people call it the "length" of the world line. That is a widely used misconception.)While S is not necessarily the smallest possible value, it is a stationary value. What about calling S the proper (interval of) time? 😊--lightarrow