[SiempreViernes]

I think their point boils down to the fact that you can require that all vectors have the same magnitude, irrespective of the dimensionality of the space, which is of course true.

The next step is them doing a black knight and pretending they didn't put in the requirement by hand.

[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?