https://getgoally.com/blog/autism-spectrum-wheel
Along with many comorbidities (adhd, ocd, depression, etc) which are more likely but not requisite
This leads to the saying "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.
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.
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.
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
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.
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.
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.
If you're going to defend the idea that something I said was incorrect, maybe you should have some idea of what it was?
> 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.
The next step is them doing a black knight and pretending they didn't put in the requirement by hand.
> 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?
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.
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'll just quote nih.gov:
> Autism is known as a “spectrum” disorder because there is wide variation in the type and severity of symptoms people experience.
and wikipedia:
> Autism is clinically regarded as a spectrum disorder, meaning that it can manifest very differently in each person. For example, some are nonspeaking, while others have proficient spoken language. Because of this, there is wide variation in the support needs of people across the autism spectrum.
and maybe take a look at this list:
https://en.wikipedia.org/wiki/Spectrum_disorder#Types_of_spe...
From a few random dictionaries:
>2. used to classify something, or suggest that it can be classified, in terms of its position on a scale between two extreme or opposite points.
>a range of different positions, opinions, etc. between two extreme points
?????
The naïve assumption is the spectrum is a binary more/less autistic. It very much is not.
I understand this is just a figure of speech, but this wording suggests that there are "two ends" of the spectrum and (as I understand it) autistic communities are trying to fight that myth.