> "if you've met one person with autism, you've met one person with autism"

Isn't this true for just about any condition? It's not like people with ADHD or depression all behave exactly the same. I understand the urge to avoid categorizing people too broadly, but at the same time making the "taxonomy" of a condition hyperspecific is contradictory to having the label in the first place.

If saying "I have autism" has no descriptive power because this could mean a million different things, it seems like the term needs to be retired or narrowed to a specific set of behaviors/challenges.

Keep in mind that the current state of our knowledge of autism and other neurological conditions is still extremely new. Just 30 years ago, you would have been told that only young white boys exhibit autism.

There is debate within the autism community about ditching the catch-all term "autism", but I don't expect it to go anywhere. Broad labels like that are useful. I can tell a random person that I'm autistic and they generally understand that my "abnormal" behavior is innocuous. It's less useful to give a stranger a 30 minute lecture on my individual needs and challenges.

Read up on the controversy around asperger's and the "high/low functioning" dichotomy. These were standard measures for a long time and have only been dropped in the last ten years or so.

I've heard it used exactly that way for ADHD.

But more widely, there's a bunch of conditions of varying severity that might be caused by being in a car crash. That doesn't make "I was in a car crash" a bad answer to "what happened to your leg/eye/speech", it's just a fact.

Then the spectrum would refer to the magnitude of any vector in multidimensional “autism space”.

Sure, but saying two people are the same magnitude is very different from saying they have the same level of touch sensitivity

Two complex numbers can have the same magnitude & be very far apart. Assuming we stick to the positive/positive quadrant it's not so bad. This metaphor (which, the spectrum itself is a metaphor, making this a metaphor of a metaphor) is to a 2d space tho, complex numbers are much more comparable based on magnitude as a result

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

Only if their magnitude is large; the maximum possible distance between two complex numbers of equal magnitude is double that magnitude.

And this limit is independent of the number of dimensions in the space you're working in; no two equal-magnitude vectors are ever farther apart than opposite vectors are.

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.

"very far" is of course relative: if we have tree vectors, two of length R and one of length 0.99*R, it's not outlandish to call the distance 2R between the two vectors of equal magnitude "very large" compared to the distance 0.01R between two vectors of dissimilar magnitude.

Your last comment is completely incorrect, for a point at (1,1,1,....) each extra dimension adds a constant 1 to the euclidean distance, so that in 500 dimensions a point at (1,1,1,....) is around 22.4 units away from the origin, while in two dimensions it is only 1.4 units away from the origin.

https://www.youtube.com/watch?v=zwAD6dRSVyI 3Blue1Brown on visualizing higher dimensions explains it well

> Your last comment is completely incorrect

How so? Your followup makes no sense.

> for a point at (1,1,1,....) each extra dimension adds a constant 1 to the euclidean distance, so that in 500 dimensions a point at (1,1,1,....) is around 22.4 units away from the origin, while in two dimensions it is only 1.4 units away from the origin.

You're comparing vectors of different magnitudes. You could equally object that (200, 0) is much farther away from the origin than (2, 0) is. That's true, but so what? You're still in a two-dimensional space.

Are you under the impression that the "magnitude" of a vector and its "distance from the origin" are separate concepts? They aren't.

Consider simple two-dimensional space. A point at (1,0) is 1 unit away from the origin, as is a point at (0,1). But a point at (1,1) is approximately 1.4 away from the origin, i.e. sqrt(1^2 + 1^2). See Pythagorean theorem.

Yes, what's your point? Vectors with larger magnitudes have larger magnitudes than vectors with smaller magnitudes do?

If you're going to defend the idea that something I said was incorrect, maybe you should have some idea of what it was?

You keep referring to the magnitude of the vector itself rather than the magnitude of its components.

> Vectors with larger magnitudes have larger magnitudes than vectors with smaller magnitudes do?

Vectors with more dimensions have larger magnitudes than vectors with fewer components, for the same average magnitude of the components. The distance between the origin and (1,1) is less than the distance between the origin and (1,1,1) even though the components in both cases all have magnitude 1.

> 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.

> 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.

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.

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?

The question is whether each dimension is equally clinically significant, or equally impactful to quality of life. Talking about magnitude is definitely taking the analogy too far, as temping as it is.

I think the point is that the magnitude being the same doesn’t necessarily mean their distance is zero. I think the rest isn’t relevant.

Kinda like how color spectra have multiple dimensions as well: RGB, HSV, YCbCr, etc.

Well color spaces, not spectra, technically. Brown isn't in the spectrum.

That name would make for a really interesting bar.