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On Mon, 5 Feb 2007, Spurling, Shannon wrote:
But distance is a scalar quantity. Dimensionally, you are still 1/4 of
the way closer to the truth, even if your half way only along one
dimension. Right?
There are many kinds of distance, but Euclidean distance is the square
root of the sum of squares of the distances on every dimension. So if you
are 4 units away on X and 3 units away on Y, you are 5 units away in
Euclidean distance. If you move halfway closer on X (2 units) you are
still sqrt(13) = 3.606 away which is more than 1/2 of 5. It's even worse
with more dimesions or if you are already very close on the one dimension
on which you change -- it has very little effect on overall distance.
Mike
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