There's also an overlap in traits.
I'm AuDHD (autism + ADHD). You can read about my ADHD side if the experience (with memes!) here:
Don't ask me what's normal about normal subgroups¹, for example (or what's weird about other ones, especially given that it's the normal ones that are special in some way, and the "abnormal" ones didn't even get a name).
Or why mathematicians came up with other, alternatively stupid ways to refer to them, when saying kernel subgroups (or simply kernels) would communicate the idea exactly (normal subgroups are simply kernels of morphisms, i.e. the subgroups that could be sent to identity by a map that preserves group relations).
Better yet, call them divisor subgroups (or just divisors), because the reason we care about them is that we can use them to divide a group into equally-sized pieces which also form a group.
Which we naturally call the quotient group.
So, to be clear:
* You have M=12 apples. You put them on the table in rows of N=3 apples, and get exactly 4 full rows of 3 apples each, which line up with each other:
•••
•••
•••
•••
Math speak: you divide M=12 by N=3, its divisor, to get M/N=4, the quotient.* You have a group G of remainders mod 12 . You pick three of them, H = {0, 4, 8}, and write them down in a row.
If you add 1 to each number in H, you get another, new, row of 3 remainders: 1, 5, 9. You write that down; same thing works for 2 and 3.
With modular arithnetic, adding 4 or 8 just shuffles numbers in any row that you wrote down. So adding 5 is the same as adding 1; you get only 4 rows that don't overlap.
Math speak: H is a subgroup, and H acts on each row by a shuffle. The rows correspond to remainders modulo 4.
0 4 8 = H + 0 (= H + 4 = H + 8)
1 5 9 = H + 1 (= H + 5 = H + 9)
2 6 10 = H + 2 (= H + 6 = H + 10)
3 7 11 = H + 3 (= H + 7 = H + 11)
Addition mod 12 preserves these rows too.For example, if you pick any number from row 1 and add any number from row 2, you always get a number from row 3.
Adding two numbers from row 3 yields a number from row 2. We can write this like this:
[1] + [2] = [3]
[3] + [3] = [2]
[3] + [2] = [1]
...
(Here, [2] stands for "row which has 2 in it", i.e. H + 2).You can see how the rows not only correspond to remainders mod 4 (as a set), they are related in the same way (add like numbers mod 4):
(H + a) + (H + b) = H + (a +b)
= H + ((a + b) % 4) (since H + 4 = H).
So we've divided our group G=Z_12 by the action of H=Z_3 into parts which also form a group with the same structure as Z_4 (remainders mod 4).Math speak: by analogy with the division of numbers, we say that we get a quotient group G/H=Z_4 with elements [0], [1], [2], [3].
We could use the same naming logic to say that to get the quotient group G/H, we divide G by its divisor group H....
...hahaha, who am kidding, that makes too much sense. If you saw the word divisor, you'd think of getting a quotient right away. Come on. Can't have that.
To get the quotient group G/H, you quotient G by its normal subgroup H.
Yes, mathematicians straight up verbed the word quotient, and called the operand H something that is in absolutely no way connected to it.
To recap,
Numbers: divide a number M by its divisor N do get the quotient M/N.
Groups: quotient a group G by its normal subgroup H to get a quotient group G/H.
... I'm not going to complain about "comorbidity".
It could be that autism really is, exactly as we describe it and conceive of it, in some meaningful way defined by actual reality, a thing.
It could be that it's ten different things that aren't actually connected at all, but happen to look kinda similar. Some of which either are a variant of ADHD (or vice-versa, doesn't much matter) or just happen to include similar symptoms and behaviors that respond well to the same drugs and therapies we use to tread ADHD.
(now, to some degree we do have real tests we can do to pick up e.g. genetic markers of certain disorders, but these largely remain just another clue, not exactly solid proof, with some exceptions)
To illustrate: imagine we couldn't ever see the inside of a human body and just had to guess at what was going on when something went wrong. We'd probably have something we just called "bad kidney" that was actually several different problems, and we'd just throw drugs and other therapies at it until (often, but not always) some set of those relieved the symptoms. Meanwhile, sometimes it's a kidney stone, sometimes it's cancer, et c. And maybe we even have a whole step that's trying to figure out if it's "bad kidney" or "bad bladder" and sometimes we'd get that right, but sometimes wrong, but also some of the same medicines work for either (depending on the actual cause) so we might incorrectly diagnose "bad kidney" then accidentally correctly treat "bad bladder", and think we were right all along.
The lack of executive function is overlapping, but this particular post might be more of an ADHD simulator.
The very first "Follow the morning routine" or not is where this veers off my experience of the spectrum.
"Changing plans because of situations internal or external" is hard.
The option should've been "Spend 20 minutes making eggs again, because the yolks weren't the right kind of runny", miss the train, take a cab to work, but tell the driver that you've now got a system for eggs which you didn't have today (yeah, fun fact, the recipe was off because they don't refrigerate them over in France).
It is not "pop-psych", it is reality.
These are just labels we apply to buckets of symptoms. The underlying problems and biological differences that can cause these buckets of symptoms probably will be found, and then we can re-categorize things quite a bit. My bet is we do this within the next couple decades.
What causes difficulty is that actual symptoms of one of these buckets can cause behaviors and coping strategies that look like other ones.
Another issue is that these symptoms are not specific. What one neurodivergent person means by "I have sensory issues" is vastly different from another neurodivergent person, and your psych health provider will dig into those specifics and try and tease out which label fits the best, or whether it's even an example of that symptom. How those symptoms affect you is the entire point.
>I'm still hesitant that "autism" these days may describe either someone who's completely nonverbal and living in assisted living, or someone who's a successful academic/engineer/entrepreneur.
And you have that same feeling towards "blind" or "deaf" right? Since a lot of blind people struggle to lead "normal" lives but there are accomplished blind software devs right here on HN
Consider how many people live life with some sort of mild delusion and yet are perfectly functional 99% of the time. The brain is complicated and cannot ever be reduced to single dimensions like that, and it is weirdly good at still functioning when part of it is broken in some way, like with Broca's area or Phineas Gage.
Yes, "syndrome" and "disorder" are vague labels that don't have hard cutoffs or any test you can objectively run. That's the point of those words. When you have a hard test you can run, it becomes a "disease".
With Autism, as noted elsewhere in this thread, a general social understanding of it is required to help normalize environments that don't exclude autistic people. Having specific labels could, on the one hand, help bring focus towards the specific needs of those people. On the other hand, it's harder to convince people of a 100 different neurodiverse profiles than one...
EDIT: I misread your comment earlier, ignore the above paragraph. I definitely get how exhausting it might be to list off everything. I suppose I feel the Autism label is too big at the moment to communicate effectively though. See the following, I think it still applies.
It also helps people on the other end. If someone says they have "Misophonia, Aural sensitivity, and Rejection Sensitivity" I would understand a lot more about their situation than if they simply said they're mildly Autistic.
It's called comorbidities. It's very common in mental health conditions.
I know it feels nice to be able to craft a simple narrative, but this narrative feels more harmful and misconstrued than useful.