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What would you like to prove or analyse using n-dimensional vectors?
By "expansion and contraction", I assume you are talking about multiplying a vector by a scalar?
+E=>4/3 pi r³-E=<4/3 pi r³
Only expansion and contraction exists in n-dimensional vector analysis?
the size,shape and age of the Universe is n. t=...=nd=...=nx=y=z=n
Quote from: TheBoxthe size,shape and age of the Universe is n. t=...=nd=...=nx=y=z=nx, y, z and t are dimensions. In conventional notation, x, y & z measure distance, while t measures time.n is a number (a scalar). It counts dimensions. So the point (x, y, z, t) has a location in n=4 dimensional space (it is a vector).x, y, z & t are (fairly) independent - you can move along the x axis without moving along y or z.The dimension of time (t) is a bit different from the dimensions of space, in that the speed of light is a limitation on your movement. And while we can do a rotation about the z-axis, we don't know how to do a rotation about the time axis.You can look at points having x=1 mm, or 3.14159 km or -10 parsecs or +10 billion light years.But you can't say "x=n" or "t=n", because the units of x are distance and the units of t are time; the units of n are a count of the number of dimensions. The units aren't compatible. You can't say 3 apples=4 orangutans.
Quote from: Thebox on 29/05/2016 15:02:52+E=>4/3 pi r³-E=<4/3 pi r³I assume that what you mean is that for any given volume of space the positive energy is continually expanding out of the surface while negative energy is compressing into this same volume through its surface. This may well be an apt description of the effects of dark energy.
n-dimensional vector analysis
Quote from: TheBoxn-dimensional vector analysisAccording to the original question, n is a count of the number of dimensions, eg 1 dimension for a ruler, 2 dimensions for a sheet of paper (or the surface of the Earth), 3 dimensions for space (or the volume of the Earth), 4 dimensions for Einsteins's spacetime, etc. n will be a whole number (unless you are describing some ...sorry, you cannot view external links. To see them, please
REGISTER or LOGIN).The units of n are the number of dimensions for whatever space you are discussing.
this says the distance from (a) to ''nowhere'' is (n) any number, zero point source
This notation seems to be representing "d" as a distance vector from point "a" to another point. But this point cannot be nowhere, or the vector will be meaningless.
The length of "d" will in general be a real number
Is anyone sure what Thebox is talking about, or is it horribly unclear?
You could have a vector <x y z L> that records the intensity of illumination at various points in space. In this way luminosity could be a component of a vector.
So scalars can participate as the components of a vector.
I think n-dimensional is another ambiguous meaning, there is many explanations on internet search.
So what would represent any number from 0 to ''infinite'' if not n-dimensional?
I firstly want something that represents any ''length''.
it is any ''zero'' point of space.
this says the distance from (a)
My vector is not a point to point vector of A to B, B is not there.