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Isn't it remarkable however that no matter how far you've progressed on
the one path, switching to the other doesn't force you to 'start from
scratch' ?
Mike Miller wrote:
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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