[thaumasiotes]

Here's what you said:

> Your last comment is completely incorrect, [random gibberish]

Here's what you were referring to:

>> If you stick to the first quadrant / octant / whatever n-dimensional division of space where all coordinates are positive... I don't think the number of dimensions makes any difference there either? Any two vectors define a plane (or a line, or, if they're both zero, a point), so two vectors in a 500-dimensional space can't be farther apart from each other than is possible for two vectors in a 2-dimensional space. Those 500-dimensional vectors are already embedded in a 2-dimensional space.

All of those statements are, obviously, true. What did you think was incorrect?