[thaumasiotes]

> Vectors with more dimensions have larger magnitudes than vectors with fewer components, for the same average magnitude of the components.

Is this related to something that's been said so far?

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

Obviously, I didn't. It was already there before I made my first comment. Look up:

>>> Two complex numbers can have the same magnitude & be very far apart.

The only thing we've ever been discussing is what can happen between vectors of the same magnitude. But if you want to discuss what can happen between vectors of different magnitudes... everything I said is still true! It's easy to construct low-dimensional vectors with high magnitudes, and in fact the construction that I already gave, of interpreting large vectors within a space defined partially by themselves, will do the job.

[AnthonyMouse]

> Is this related to something that's been said so far?

Are you considering what all of this is supposed to be an analogy for?

Suppose autism has different components, something like this:

https://getgoally.com/blog/autism-spectrum-wheel/

You rate someone on each factor using the same scale, e.g. a real number from 0 to 1, or a scale of 1 to 10. The scale is arbitrary but consistent.

Then someone whose "average" rating is 0.5 on a scale of 0 to 1 can be farther away from someone else whose "average" rating is 0.5 when there are more factors. On a linear scale two people both at 0.5 have distance zero. On a two dimensional scale, you could have one at (0, 1) and one at (1, 0) and then each of their averages is still 0.5 but their distance is ~1.4.

That's what we're talking about.