Pronouns and Paper Cuts

Part 1

It’s not about the pronouns. The pronouns themselves aren’t that important, which is why the pronouns are so very important.

When you use masculine pronouns for me, you’re saying, “I see you as a man. It doesn’t matter how much you object, it doesn’t matter how much you don’t want to play the Bucketing Game, I see you as a man.”

I don’t want to be seen as a man. I don’t want to see myself as a man, but the Bucketing Game is so pervasive, so insidious, that I continue to see myself that way, at least on that immediate implicitly biased level where spoken language usually lives.

It’s not that I see myself as some third gender. It’s not that I’m in denial about my genitals or my chin that needs daily shaving or my deep voice or my comparatively flat chest. I’m not deluded. I’m aware of what my body looks like.

It’s also not that I personally want to get rid of most of those things. I like my voice. I’m mostly indifferent to my chest and genitals, although some days I’d like to look curvy in a dress without … well, that’s for part 2.

Shaving my chin every day is tiresome, but the alternative sounds painful, expensive, and time consuming. So I shave my chin every day.

When I see myself as a man, I have a payload of emotions, a collage of behaviors, that I wish to reject. Also, I don’t wish to participate in the entire compartmentalization of perceptions that goes with the Bucketing Game.

And I play it myself. I play it constantly. I fight against it, but even in a room where the majority of people are nonbinary, my brain is still putting people into two buckets.

Including myself.

When I say it’s not about the pronouns, I mean that the pronouns are a proxy. Changing the pronouns but keeping everything else the same won’t dismantle the game. It won’t remove me from it. If that’s all you do, the bucketing will still happen; if that’s all you do, you’ll still see me as a man.

Sidebar:

There are two major cultural wars going on right now, and while they superficially look the same, on one level they’re the opposite. The anti-CRT/BLM agenda is allegedly about erasing the relevance of race (it isn’t really: It’s really about white supremacy and denial of racial privilege, but those are the attempted optics).

The anti-trans agenda is openly about essentializing the relevance of gender-as-sex. While the anti-“woke” rallying cry is that One Sentence from King about judging people by the content of their character, not the color of their skin, the anti-trans agenda is entirely about judging people by the content of their genitals.

This opposition of theme in the conflation of anti-“wokeness”, belies the claim that the first war is about “content of character”.

I digress.

I don’t have pronouns. I reject the game, and I struggle to stop playing it.

I don’t have pronouns because I don’t know what my gender is, which means you should use the pronouns that we have decided to use in situations where someone’s identity is unknown: They/them.

“Hey, someone left their wallet on the counter!”

“There’s someone at the door, I heard them knocking.”

Not everyone who uses they/them pronouns feels the way I do. But this is the way I feel.

Part 2

This has all been said. By me, by so many others, I don’t know what the point of saying it again is.

I’m saying it again anyway. Maybe this time, it’ll sink in for some new people.

Here are my options: When you speak incorrectly of me, I could say something. Or I could say nothing.

If I say nothing, if I ascribe your error to benevolent error, I receive a tiny little paper cut on my soul. I know you, I know that if I say something, you’ll feel remorse. You’ll apologize. You didn’t mean it. It’s all just instinct. I know all this.

Your intent isn’t malice, you’ve just got more important things to worry about than who I am.

My essence, at most moments in time, isn’t that important to you. Most people have more important things to worry about than to carry around “who you are”s for everyone they interact with.

So: Say nothing, little nick on my heart, it’ll heal. Usually.

If I say something and it goes poorly, it’s a gouge on my soul. I can silently ascribe the error to benevolent indifference; if I say something, I risk a lot more. I am no longer solely in charge of the emotional narrative.

Maybe it’ll go smoothly, but even then, I worry: I am now the person who Says Something. I am now the person that needs to be Worried About. I fear that my exertion of my own identity has made me a liability.

And the next time you cut me, the paper cut will be deeper because we’ve had this conversation.

So: Say something, gouge from my heart, and those take longer to heal.

I don’t write this to make anyone reading this feel guilty, but rather in the hope that some of you will reflect on this: It’s not about the pronouns, it’s about what the pronouns represent.

And if I don’t say anything, it’s not because I’m fine even if I say “I’m fine”. It means that, today, right now, I’ve chosen the paper cut over the deep laceration.

To finish my thought from above:

Some days I’d like to look curvy in a dress without feeling like a freak, but those cuts run really deep. Far deeper than the pronouns. I put on a skirt and the intrusive voice is constant: You’re in women’s clothes. Everyone sees that. You’re playing a pointless game in order to get attention. Take that thing off, you freak. Everyone’s laughing at you right now. Just get over yourself and be a man.

That, except with cuss words.

No matter how much jewelry I put on, no matter what clothing I wear, I fear I will always be seen as “a man in a dress”, and I grew up seeing what my society thinks of men in dresses: They’re the butt of jokes. A punchline. I wasn’t weaned on Norman Bates and Buffalo Bill (although they were there), I was weaned on Kip and Henry, on Mrs. Doubtfire and Tootsie.

Ultimately, it’s not that I have a deep need to wear skirts. It’s that I’m tired of wearing pants. I want to have more choices, but that voice keeps muttering inside my head.

But all I’m asking for you to do is to be more mindful of my pronouns.

And that seems so hard for so many of you that I just give up and try to ignore the deep, infected abscesses of shame that you graze with each paper cut.

1/29/23 Audiobooks

My first experience with an audiobook was in elementary school.


I had been labeled EI–Emotionally Impaired–in Third Grade. This was, according to the documentation, because I had thrown a dictionary at another student.

I don’t remember that specific incident, but I do remember throwing a desk at the teacher. This was the teacher that went on medical leave shortly thereafter, and the probably true rumor was that it was related to mental health.

She decided to retire, so I saw her one more time, at the end of the year, at a party thrown at her house. I remember it being on the waterfront, which might be true since these events happened on Marine City, Michigan, which is pretty much all waterfront.

I also remember a girl being furious at me for daring to attend the party because it was my fault her beloved teacher had had to leave part of the way through the school year, and I figure that may well have been the same girl I’d thrown a dictionary at. (I have several other memories of that girl bullying me.)

I had had other problems in school, so the IEP was not entirely unwarranted. Also, the entire concept of IEPs was new to Michigan at the time. I’m not sure I’d qualify for one in 2023, but I did in 1975 or so. I’m also pretty sure that, in 2023, I’d be labeled Autistic rather than Emotionally Impaired, but I’ll never know for sure.


Because of my IEP, I qualified to go to the Resource Room. Because it wasn’t related to a Learning Disability or Cognitive Impairment of the traditional sort (Undiagnosed Autistic with misinterpreted meltdowns didn’t count), the Resource Room staff weren’t quite sure to do with me.

I spent most of my time in my regular classroom, but I was assigned to go to the Resource Room on some pattern of time, maybe weekly, maybe daily, I don’t remember. I could also go hang out there anytime I was feeling overwhelmed.

In the Resource Room, they gave me random tasks to do. Sometimes it was what the rest of the kids were doing, because the teachers had the supplies out. Sometimes it was exploring whatever tool an Education Publisher had sent them a sample of.

At the time, I didn’t really grok that last bit. I just figured the teaching staff was buying random stuff and having me play-test it. As a teacher, now, I realize I was the guinea pig: If I couldn’t figure out, the LD and CI kids certainly couldn’t.

One of these was a series of cassettes that allegedly contained the text of “Moby Dick”.


A bit of history: It might seem strange to younger people, but there was a time when audiobooks weren’t widely available. Even now, there’s a component of society that sneers at them as not “real” books.

They began as an accommodation: In 1932, the American Foundation for the Blind began recording books onto vinyl records, at about fifteen minutes per side. For the first few decades, while the number of producers increased, audiobooks were still mainly for the blind (“A Short History of the Audiobook, 20 Years After the First Portable Digital Audio Device”, Alison Thoet).

By the 1970s, education companies were exploring using audiobooks to assist in literacy programs. A 1977 study, for instance, found that “college students who listened to a short story were able to summarize it with equal accuracy as those who read it” (“Audiobooks for Adult Literacy? It’s Not a Myth!”, Jennifer Vecchiarelli).

These days, it’s SOP for major publications to be available as audio recordings for the general population, but that wasn’t the case in the mid-70s.


Anyway, my teacher sat me down with a bulky clamshell containing several cassettes. Most teachers reading this, especially the older ones, will have instantly visualized what I’m describing. Imagine the puffy plastic clamshell that children’s VHS movies used to come in:

An image from Etsy that shows a stack of children’s titles on VHS: Babe, Rugrats, Fantasia, Antz, Casper, The Land Before Time II, Mouse Hunt, and The Muppet Christmas Carol

So, like that, but even bulkier.

I was given Herman Melville’s text to read along with, perhaps a pair of bulky overear headphones (the only kind available at the time; my memory is hazy on whether I had these), and a cassette player. The teacher put the first cassette in, side one, and…

It didn’t match the text. At all. It seemed to be what is called in literary circles “In medias res”: In the middle of the action. Or what everyone else calls “Not the right place.”

The teacher squinted at the cassette, then at the printed text, then back at the cassette. Aha! Somehow this “brand new, never before used by anyone” cassette tape was cued up to side two.

To my naïve fifth grade-or-so self, that seemed legit. To me, now, I’m highly suspicious. But I’m not sure why the teacher wouldn’t just admit that maybe someone else had already listened to it.

Sidebar: Sometimes I wonder how many of the adults in the special education services suspected I was an Autistic child, and regardless of that, how many of them walked daintily around me, often illogically, out of fear of the next meltdown. And now, back to the story.

She rewound it to side one. That took the few minutes it normally takes, especially with the squealing, on-its-last-legs cassette player.

Something like this, but certainly not this specific one. (The photo shows a Califone-brand CAS1500 cassette player/recorder. Photo snared from School Specialty.)

We tried again. This time, it seemed to maybe start at the same place, but the text didn’t quite match the book. Words were missing or changed. More squinting, more confusion, this time the teacher let out a resigned sigh.

And that was my entire first experience with an audiobook.


As far as I can remember, my second experience with an audiobook was decades later. I wanted to work on my German and French, so I tried buying books in both text and audio form in both languages.

The first one I tried was Leonie Swann’s German-language “Glennkill” (published in 2005). I opened the book, put on the audio version, and tried to follow along.

The experience wasn’t anywhere near as bad as it had been with “Moby Dick”, but it wasn’t perfect either. Words were changed. Portions seemed to be missing. I don’t know if there had been edition changes between publication and recording, if the reader made occasional mistakes, if I was not following along correctly, or what the problem was, but the mismatch was just enough to make it too frustrating for me to continue.

The same thing happened with the French book, the title of which eludes me now. I do still have both books in both forms, so it’s not too late to try again. At least there’s that.


Thinking back now about “Moby Dick”, I wonder if either the book or the cassette (or both) was a “children’s edition”, and not Melville’s own words. It’s likely, I think, that that’s why the texts didn’t match.

I spent some time Friday cleaning out my classroom, not because I’m leaving but because I realized I hadn’t touched half the bookshelves since I’d inherited the room seven years ago, and I was tired of pack-ratting someone else’s stuff. In so doing, I was reminded of how atrociously half-assed so much of the material in the education world is.

So “Moby Dick: The Audio Version” may well have been in that category, as edutech companies struggled with carving out territory in new technologies.


I don’t currently like audiobooks much, but I haven’t really given them a solid try yet (as I was typing this sentence, I got stuck on an intrusive lyric: “I don’t really miss you but I haven’t tried yet” [“I Got the Message”, Men Without Hats]).

A few years ago, we acquired an audiobook for the sole purpose of having someone read us to sleep, “The Alchemist” by Paulo Coehlo. We picked it because it was read by Jeremy Irons, and I wanted a soothing voice.

Sidebar: I couldn’t remember who the reader was as I was writing the paragraph above. I could picture his face, but all that came to mind was “He looks like an older Daniel Day Lewis”. So I googled “actor who looks like daniel day lewis”, not expecting anything but getting:

Google prevails: The search “actor who looks like daniel day lewis” yields “Jeremy Irons” with a side-by-side comparison of the two actors

That worked, but it reinforced my concern with audiobooks: Listening to people talking usually has one of two effects on me. It either puts me to sleep or it stresses me out. There are a handful of exceptions, but it’s hard for me to keep the proper focus for processing information when someone’s reading to me.

At the same time, though, my ND brain struggles with lots of printed text. I’m a fairly slow reader, and I also get distracted a lot. And when I’m watching a video with subtitles, my ability to choose my reading speed can get in the way of listening to the voice.

And then there’s NPR. I have friends who love love LOVE “Fresh Air”. I struggle because I need to hear every word and I can feel panicky if I miss something, but at the same time I feel like it’s all so intrusive. I don’t like having the pace chosen for me; I want to process information on my own terms, in my own time, which might be faster or might be slower than it’s given.

This is a challenge of aurally presented material, but on the other hand, I struggle with visual-only material. I think that first experience with an audiobook, the gross mismatch between written text and audio text, soured me in a very deep way.


Now that I’m thinking about it, this pacing issue is also a struggle for me for e-books, of which I have quite a few. If I’m reading a print book and find myself confused about what’s happening, I can easily flip back a few pages to remind myself of events. I have a pretty decent memory for how long ago (in pages) something was mentioned, and then I can quickly flip back to where I was in the book.

I don’t have to remember where stopped reading because I can put my finger there. But with an e-Book, I have to either go through the process of putting in a bookmark, or I need to hold the page number in one of the limited number of memory slots we all have in our brains.

Anyway, no real conclusion here, just meandering thoughts. This seems to have fizzled into chaos, so I’ll stop for now.

Coloring Vertices

The other day, I came across this problem on Twitter: How many distinct ways are there to color the vertices of a cube, such that exactly four are one color and the other four are a second color?

I played around a bit first. My first task was to list all the possible combinations, and then I tried to remove rotations. Assuming I didn’t make any mistakes, I came up with seventy combinations of eight dots with four red and four green (this does happen to be the central number on the eighth row of Al-Karaji’s Triangle, so I’ll assume I’m right).

As I started to work through the duplicates, I noticed some patterns, so I decided to try to figure out the possibilities more systematically.

I realized we could see the cube as a “front” and a “back”; ultimately, we could rotate a cube so that any of the six faces would be the “front”. A front face has four vertices, any number of which could be red.

However, if the front face has zero reds, all of the reds would be on the back, and we could rotate the cube to reverse front and back. So we can reduce the possibilities by requiring that the front has 4, 3, or 2 reds (1 red on the front means 3 on the back).

For four reds on the front, there is only one possibility.

For three reds on the front, we can orient the cube so that the upper right is green. The back side would have one red, and there are four logical possibilities for where to put it.

For two reds on the front, there are two possibilities: They are along the same edge or they aren’t. Taking the case that they’re along the same edge, neither of the two reds on the back can share a face with that edge, or there would be a face with three reds, which is covered in the last paragraph. Removing those cases, there’s only one possibility (the middle top image above, the third image in the second row below).

Taking the case that they’re not along the same edge: If the two reds on the back share an edge, they’ll form a three-face with one of the front reds. If the two reds are on the same diagonal as the front, this will be a rotation of the situation in the previous paragraph. So that leaves the situation that they’re on the opposite diagonal (the lower right above, the lower left below).

So that leaves us with just seven to consider: All others will be orientations of these. The question is whether any of the four three-faces will be orientations of the others.

The answer to this is no: These seven configurations (red is solid in my diagrams) are all distinct, and an exhaustive list.

The seven possible distinct configurations.

Extension questions:

  1. How many distinct ways (where different orientations are the same “way”) can we color vertices red and green, with any number of reds? Zero and one red (and hence seven and eight reds) are trivial, one distinct way each. That leaves two and three to examine (five and six would be the same).
  2. How many distinct ways can we color the vertices with up to eight colors, given any number of each?

EDIT: For the first extension question above, the values are three for two (or six) reds and four for three (or five) reds. In the diagram below, a solid dot represents a fixed red, circles represent distinct reds, and ex’d vertices (in the last two rows) represent duplications. The third row represents four reds, generating the same set as above. This means if you wanted a set of dice such that you could orient it to any possible distribution, you’d need 25 (1 + 1 + 3 + 4 + 7 + 4 + 3 + 1 + 1) distinct dice for the 256 possible red/green distributions.

Two, three, and four reds, with three, four, and seven distinct distributions, respectively.

Star Trek: The Last Bigotry

Last night I had a dream about a new Star Trek show under development. This morning, I was thinking about why people are bigoted against transgender people. Within a few minutes, I realized I was thinking about the same thing.

Part 1: The Dream

In my dream, NBC had originally developed a spin-off to Star Trek called The Romulans. According to my dream, in 1970, there had been three full episode scripts written and a pilot made. This was a sympathetic view of the Romulans, and depicted the Federation as barely relevant to their existence.

NBC had originally pulled the plug because they decided viewers weren’t ready for that sort of progressivism. But now, in 2023, as Paramount Plus was casting about for novel ideas, they had assigned a creative producer named Michael Ivens to the task of taking those three scripts and that one pilot, revamping them to the current Star Trek aesthetic, and creating a full season of episodes.

I was working somehow with Ivens, because in the dream I was sitting with him in his broom closet of an office discussing his plans and his perspective. I don’t know if I was his assistant or a journalist interviewing him for an article. Or a prospective writer, or some other creative attached to the show.

In many of my dreams, my identity isn’t particularly relevant. I am usually an active participant, but I am often just watching my dream as if it’s a TV show, occasionally inserting myself just to remind my brain of the dream’s relevance to myself. This was the case in this dream.

Part 2: Bigotry

Brushing my teeth this morning, I found myself thinking about why people are so opposed to people being transgender. This wasn’t a long thought process, because I came to: This is too simple a question for such a complex answer.

I am active in several marginalized online communities, particularly the transgender and Autistic communities. Ask what it means to be transgender, and you’ll get a complex answer: It’s different for everyone, nobody has the same path, we’re all unique individuals. Ask what it means to be Autistic, and you’ll get the same complex answer.

Ask why people are hostile to individuals in either group, and the answer will dwell on hatred, bigotry, closedmindedness, and so on. If we’re at all generous, we’ll include that many people are ignorant and misinformed.

We are multidimensional and complex; in our minds, our opponents are one-dimensional. It appears not to be possible for well-meaning and informed people to be opposed to someone presenting as transgender; it simply must be hatred and ignorance.

Part 3: Star Trek‘s Progressive Stumble

The original Star Trek series was lauded for its progressiveness. For 1960s TV, it was indeed progressive in several ways: There were multiple ethnicities in the regular cast, including one alien; money was rarely mentioned; the goal was exploration, not domination; the default was to see foreign races as benevolent until proven otherwise.

There were several ways in which it stumbled, some of which were addressed in later series: The women all wear miniskirts and are in supporting roles (at one point, Kirk complains that a competent woman officer will someday find her man and will leave his ship; in the final episode, Kirk comments that women can’t be Captains, by Starfleet policy). While the Prime Directive is recited as Starfleet Policy throughout the show, it’s also routinely violated when Kirk needs to save his own ship. And while Starfleet is shown as being ethnically diverse, both the Klingons and the Romulans (as well as most of the single-episode races) are ethnically monotone.

That is to say, all the Klingons look like Klingons (with the exception of “The Trouble with Tribbles”, where it’s a plot twist), and all the Romulans look like Romulans. More importantly, in the original series, all* the Klingons ACT like Klingons, and all* the Romulans ACT like Romulans. (* I wouldn’t be surprised if “In episode x of season y, this one character…” because I don’t have encyclopedic memory of the show, but nobody immediately stands out.)

In the Cold War climate that the show was made in, the Klingons were thinly veiled Russians, and the Romulans were thinly veiled Chinese people. But here’s a reality: Even in the height of the Cold War, many Russians hated the Soviet Union, and many Chinese people hated the Chinese government.

Star Trek’s plots routinely allow for members of the Federation to be opposed to their basic ideals. Indeed, Kirk himself pushes against direct orders multiple times.

Naturally, the focus of the stories is not on the complexities of what’s happening on Klingon or Romulan ships; the story is generally about “these bad guys are threatening us, how are we going to respond?”

Plus I’ll grant that having all the Klingons look the same (right down to the facial hair) and all the Romulans look the same makes things easier for the viewer at home. The show is about the Federation, and the Bad Guys are background information.

At the same time, though, the Klingons and the Romulans are more one-dimensional than they need to be, as shown on the later Star Trek shows’ treatment of, say, the Ferengi and the Borg.

Part 4: The Red Pill (the estrogen metaphor, not the MRA perversion)

For the most part, people who are opposed to transgender rights present a fairly one-dimensional perspective of us: They see us as broken, as perverts, as dangerous. And I’ll be honest, I’ve interacted with one or two transgender people who are dangerous, broken perverts. That’s out of the hundreds of transgender people I’ve interacted with, but they do exist, and any of our claims that they don’t is a disservice to the truth and ultimately to our own goals.

Until I started seriously exploring my own gender, I had a simplistic view of transgender people. Now that I’ve crossed the breach, I find myself resisting the pull in my community to simplify my view of cisgender people, and of anti-trans bigots in particular.

Ron DeSantis, JK Rowling, Dave Chapelle, and Piers Morgan are four distinct humans. They have different views on a variety of subjects. There are places where they are likely in full agreement, and there are places where they disagree, even on transgender rights.

They are not a monolith of thought, even on transgender issues.

What absolutely matters most is that they are all actively working to make the world more dangerous for me and my transgender siblings. That is absolutely, unquestionably the primary issue.

Also what makes them differ from us is that we want to live our lives in peace, and they want to control us.

Well…

That’s certainly true if we see them as a monolith of misinformation and malice. Seeing them as multidimensional means we should at least take the time to consider the aspects of their perspective that contradict our claim that we don’t want to control others.

Part 5: Bathrooms

One of the things that many transgender people want is the right to use gendered lavatories that match their gender.

One of the things that many women (including trans women) want is the right to have gendered spaces, including lavatories, that are free from the threat of men.

So what to do with a trans woman? The woman sees herself as a woman, because she’s a woman. The anti-trans bigot sees her as a man, especially if she has a penis.

(The irony that the bigot is thinking invasive thoughts about a trans woman’s genitals while fretting about the possibility that a trans woman is only going into a woman’s bathroom to get her jollies thinking about cis women’s genitals should not be forgotten.)

It is easy for me to declare that the trans woman’s right to pee safely trumps the cis woman’s right to pee… safely?

And therein sits the problem:

A trans woman has a legitimate reason to fear for her safety in a men’s bathroom. Transgender people are still killed in the United States at a disproportionately high level (once a week in 2021, three a month in 2022, according to the HRC), and assault levels are similarly disproportionate. Statistically, the risk that a given trans woman will be physically assaulted in a public bathroom on a given day is very low, but it’s not zero. And the risk of verbal assault is far higher than that; my friends have numerous stories of mockery and gatekeeping at the bathroom door.

So it’s statistical fact that a trans woman is overall safer from both verbal and physical assault in a woman’s bathroom than in a men’s bathroom. And safety aside, it just plain makes sense that a woman should be using women’s bathrooms, if we’re going to have gendered bathrooms.

At the same time, though, all women have a legitimate reason to fear for their safety from men, and there have been a handful of incidents involving both men claiming to be women and trans women proper assaulting women in bathrooms. The statistical likelihood of that happening is likely lower than the risk of trans women getting assaulted in men’s bathrooms, but it’s not zero.

Standard debate points apply here: Sexual predators will find ways to predate (but that doesn’t mean we should make it easier for them); cis women assault cis women (but at much lower levels); bathroom “guard” policies hurt cis women who look “suspicious” and get blocked, while rewarding stealth trans women who pass; these arguments are low-hanging fruit in the debate and often hide a deeper distrust of transgender people.

That aside, though, I would agree that it’s important for everyone to feel safe. And if my position is that those cis women who fear that trans women are just perverted men looking for their jollies need to “just get over it”, then I’m indeed seeking to control them.

And since such women typically see me as a man, as part of the patriarchy that is constantly seeking to strip them of their hard-won rights, I can completely understand why they wouldn’t want me being part of the decision-making of who gets to use their bathroom.

Part 6: Pronouns

The other major “you’re trying to control us!” talking point is pronouns and other gendered language.

I do not consider myself a man. As a result, I do not like having male-oriented language used for me.

I am aware of my body. I know what my genitals are. Statistically, I am most likely to have XY chromosomes, especially since I “sired” a child. These are facts that I have no interest in changing.

It is hence inevitable that, in 2023 in the United States, the majority of people will just automatically assign “male” as my gender and slip into male-oriented language about me.

If I want it to change, I need to say something. I need to assert my desires.

Some people do this gently: “I prefer ‘they/them’ pronouns. If you want to show your respect for me properly, please use those.” But then, if someone slips or, worse, maliciously uses the wrong pronouns, they just keep any complaints themselves.

Some people do this aggressively: “My pronouns are ‘they/them’. Anything else is wrong and will not be tolerated.” And then, if someone slips or, worse, maliciously uses the wrong pronouns, there’s an air horn at the ready and a trip to HR in the offing.

And no, I’m not kidding about the air horn.

If I see myself as a genderless (not sexless) person and you see me as a man, then we have a difference of perspective. Me forcing you to accept my belief about myself is me trying to control you, even if it’s in a ludicrously basic way.

I could write screeds on the complexities of this topic, but the relevant point is: Me telling you how to speak when addressing me, to the point of assault (air horns are assault, says the Autistic) or threatening your job, is me controlling you. At the same time, though, I have the right to not be in a hostile work environment, and someone maliciously misgendering me at work is creating a hostile work environment.

Part 7: The Romulans: The Undiscovered Series

The relevant point is: Some of these topics are complicated, and they can be greatly simplified by “we’re complex and diverse, and our opponents are one-dimensional groupthinkers”.

Rather than accept the complex nuances and having mature discussions, it’s easier to just say, “Y’all are hiding your true agenda, which is total control.”

This river flows both ways, too. Which is why Twitter, the land of simplistic takes, is filled with “Y’all are hiding your true agenda, which is total control.” From all sides of every topic.

Which is why social media in general is filled with insults and dismissiveness towards opposing viewpoints.

To be clear, to be absolutely and totally clear: Some viewpoints aren’t worth serious consideration. The idea that Drag Queens are categorically seeking to sexualize children is absurd on its face; Drag Queen Story Hours are mostly just men* in overdone dresses and makeup reading fun children’s stories to children. Not my thing, but not sexual perversion, either. (*Most-not-all Drag Queens are men having fun or exploring their gender perspectives.)

But even those viewpoints are connected to, even evolutions of, more reasonable positions. When we dismiss more reasonable positions without at least arguing through their reasonableness, we leave them to fester into inanities.

Also to be clear, to be absolutely and totally clear: I am not asking any victim of bigotry to “rise above” and to take the time to see the opposition as reasonable. On the topic of transgender issues, there is a very clear side that started the hostility, and I do believe the bulk of the onus for finding peace in this debate is on them.

What I’m pointing out, though, is that whether we want to admit it or not, our opposition, whoever that is, is no more of a monolith of thought than we are. It may feel like we’re facing the Borg, but we are not.

Postscript: Trump Supporters

The other day, I was talking to my boss about politics. He lives in a “red” part of the metro area, meaning that in the fall of 2020, most of his neighbors had “Trump” signs on their lawn. Most of my neighbors had “Biden” signs on their lawn.

Over the last half-decade, I’ve fallen into the habit of saying that anyone who would vote for Trump is a terrible human being. Don’t they know what Trump supports?

Don’t I know what Biden supports?

We discussed, my boss and I, how the majority of people just vote for whatever party they’ve always voted for. A single “Trump” sign on the lawn during Presidential election season may mean a steadfast support of bigotry, but it more likely means “I’m a Republican, I’ve always been a Republican, and this is the Republican candidate this year”.

I pointed out that the Wall of Trump Signs is different. That people wearing Trump 2024 shirts in 2022 are different. Those people are advertising a depth of commitment that we have good reason to be concerned about.

But as the low attendance at an average Trump rally in recent months indicates, those people may be loud, they may be dangerous, but they’re not the majority of the 74 million people who voted for Trump.

Not even Trump voters are a monolith.

I have seen it claimed on social media that Biden and the DNC enforce singularity of thought, that disagreement is not possible.

I will say without fear of reprisal: Biden has a lot of terrible policies. Biden is continuing a long tradition of militarism and colonial attitudes around the world. His weakness on student loan forgiveness is appalling. He has failed to make any clear comment on the mess that SCOTUS has become. I would rather have him as President than Trump, but I struggle to believe that in a country of a third of a billion people, he’s the best we can do. Not even in the top 100.

There. Come at me, Jeffries. Let’s go, Schumer. You want a piece of me, too, Harrison?

(The current chair of the DNC is Jaime Harrison. I had to look that up.)

It’s not happening. Democrats are allowed to publicly disagree with Biden. Republicans are allowed to publicly disagree with Trump. Yes, I do think that Trump is propped up by a dangerous Cult of Personality, but that doesn’t mean that the majority of his voters in 2020 were monolithic groupthinkers. Just the loudest. Just the most dangerous.

It is easy to see our community members and allies as complex. It is important to remember that our opposition is also complex.

1/8/23: Platonic limerence

The first time I was exposed to the word “limerence”, some decades ago, it didn’t really register. It felt like a fancy, dismissive word for “New Relationship Energy”, and though the two concepts are tangential, they’re not the same.

Today I ran across it being used in a (potentially) Platonic sense, in terms specific to Autistics:

A meme about limerence, with a graphic of Pearl from “Steven Universe”

The text of the image says, “One of the reasons Autists isolate is to mitigate the risk of future Limerence. Many Autists see a profound pattern of abandonment in their lives and they can never seem to break the cycle… and suffer more with each additional person they lose.”

Having forgotten the term, I looked it up again, and found this on Wikipedia: Limerence is a state of mind which results from romantic or non-romantic feelings for another person, and typically includes intrusive, melancholic thoughts and/or tragic concerns for the object of one’s affection as well as a desire to form or maintain a relationship with the object of love and to have one’s feelings reciprocated. Limerence can also be defined as an involuntary state of intense desire.”

Key concepts include intensity, intrusiveness of thoughts, a potential lack of reciprocation, and the idea that it can apply to both romantic and non-romantic feelings.


I have reflected on the past, and would like to reflect more in the future, on my struggles with interpreting any sort of affection as romantic interest. However, in my life right now, I can and do generally interpret attention from others as being friendly, not romantic.

Even so, I still struggle with intense feelings when someone new notices me. Internally, these feelings can seem “clingy” and even “obsessive”, and I feel high levels of anxiety about abandoned, yet again, by the people who have caused them.

Today I’ve been wondering about the interplay of these feelings of intense need to be around someone (which often have the effect of scaring them away) and rejection sensitivity: The cycle is obvious. Meet someone, decide they are the greatest human ever, cling to them, get upset and pushy when they don’t fully reciprocate, scare them away, get rejected.

Wash, rinse, repeat.

One advantage to knowing that this cycle is something that I do, that other people do, that is attached to some manifestations of neurodivergent brains, is that I can then acknowledge it. I can step back and remind myself: This is okay, this is the way my brain works sometimes, but let’s adjust our interpretation so that it’s not beholden to the dysfunction.


I saw one Autist suggest that limerence was a form of special interest, one where the target of that interest is another person. I’m more inclined to think that it comes from damaged emotional attachments in early childhood: In Freudian fashion, I read a suggestion that Platonic limerence comes from seeking a missing emotional mother, and while that feels a bit blindered, I think the abstract gist is solid.

So many of us are lacking a history of healthy emotional bonds. This is more true for Autists, who are traditionally stigmatized, marginalized, and misunderstood, so it makes sense that we’d be more vulnerable to getting overwhelmed by a new bonding, romantic or otherwise. Indeed, Autism as a medical disability is related to a difficulty properly managing stimulus responses, and human relationships involve stimulus responses.

The challenge is managing that response in a way that doesn’t harm another person. Seeing limerence as a special interest manifestation is objectifying: Trains and comic books don’t have feelings (something we objectively know, even if we Autists are prone to anthropomorphizing them). People do. Infatuation rising to obsession is problematic, and can bring emotional discomfort to both the target and the obsessed one.

Anyway, I was also going to reflect on rejection sensitivity, but this is already long enough, and the concept is still new to me. I hope I’m not completely botching it up. This is my perspective, today, and subject to change.

InferKit Test 1: Medusa

Note: I seeded InferKit with the first sentence and let it generate text until it ended on the end of a sentence. So everything after the first sentence was AI-generated.

I have a ceramic bust of Medusa.

You know, the woman with snakes for hair.

The one who turned all of Phoenicia to stone when Ganymede turned to stone and Medusa laughed.

That one.”

We were silent for a minute.

“Do you want to know what my first thought was?

Is that too much to ask?

Okay.

That’s how I was thinking, okay?

I was thinking-did you ever look at the Medusa in the original painting?

I think it’s a stone gargoyle.

So you know, stone and stone and more stone and that’s why she turned to stone.

That’s a stone gargoyle.

So, what if I bought a ceramic Medusa, and I decided that it wasn’t worth much money, so I broke her head off and hid it.

After all, she only does what I want her to do, doesn’t she?

I think that maybe she only destroys things that are worthless.”

I was not surprised to see Julia shiver.

Her hand had flown to her mouth.

She looked down at the table, breathing through her mouth.

“Is it, do you know, obscene to talk like that?”

I asked.

“Isn’t it?

Is this the kind of conversation we should have with people in the art department?

After all, we have to be familiar with all of the many styles of sculpture and painting that this college has produced over the years.

Right?

So, if I told the art history department that I had a friend in the janitor’s closet who threw away some of their garbage, and he’d brought me a marble sculpture that he’d found in a dumpster, I don’t think that they’d tell me that was lewd and filthy.”

I had never said anything so obscene.

I could feel my face going hot.

And then I said, “It’s because you’re a woman, isn’t it?

You can’t make these jokes.”

“Well, that’s just it, Christian,” she said.

“What you think that this university is, what it is-what it was.

It’s not.

It’s not so much a university as it is a place for cultivation and improvement.

It’s not a place for my jokes.

It’s not a place for your jokes.

It’s an academy, and it wants students who have the ability to follow rules.”

“It doesn’t want my jokes?”

“Christian, that’s not what I’m saying.”

“You think this is some kind of place, some kind of position in life, that you can say any word you want and you’re protected?

All of us-the servants, the janitors-we don’t have the ability to say anything that we want and think that we’re protected?

Do you think that maybe when we got here, we signed on to do a job?

Do you think that maybe we’re here to study?

So we don’t think the way the artists think, or the philosophers, or the anthropologists, or the historians?

Because there’s this school of thought that we have to pick one culture to study, because that’s all we’ve got.

Do you know what that feels like, to go from being an Indian to being the servant?

To go from being a Mexican to being the servant?”

“I’m sorry,” she said.

“Don’t be sorry.

It’s not your fault.

I shouldn’t have said it.

I apologize.”

And then she touched my hand.

She had very pale hands.

They were warm, but they were cold.

On Comorbidity

Dyscalculia is highly comorbid* with Autism.

Hypercalculia is highly comorbid with Autism.

Dyslexia is highly comorbid with Autism.

Hyperlexia is highly comorbid with Autism.

Many Autistics struggle with sensory overload and seek to minimize external stimulation.

Many Autistics love sensory overload and seek to maximize external stimulation.

Many Autistics prefer to live in households that are tidy to a museum level.

Many Autistics prefer to live in households that are cluttered and barely navigable.

Many Autistics are completely consistent–they always avoid stimulation, or they always seek stimulation.

Many Autistics have reactions which vary–they avoid stimulation in some contexts, and seek it out elsewhere.

Why?

Because Autism is about being outside the parameters of “neurotypicality”. Hyper- and hypo- are both outside those parameters.

It means that different Autistics can look and act VERY different, and that if you know one Autistic, you know… one Autistic.

* “Comorbid” is such a bleak word. It just means that the two things tend to co-occur.

1/4/22: Hyperlexia

I recently learned the word “hyperlexia”, which is “when a child starts reading early and surprisingly beyond their expected ability.” The second type of hyperlexia is highly associated with autism; while only about 10% of Autistics are hyperlexic, about six out of seven Hyperlexics are autistic. (Source: WebMD)

At 54, it’s hard to definitively diagnose myself as being hyperlexic, but I was definitely advanced for my age.


My father used to talk about how my parents tried to keep my from reading before I got to school.

It starts with this story: My older brother, born three years before me, was going to be held back in Kindergarten. The teacher’s reason was that he had trouble staying focused, especially during reading time.

My father said it was because he wasn’t interested in the stories, having already read them. The teacher would let the students look at the book before she read it, and he would read it to himself.

In my father’s version of the story, each child was given a copy of the book to take home to get familiar with the pictures. That part of the story strikes me as strange, but possible. My own memory of having books read to us in elementary school is that there was a single copy of the book, not enough for the entire class, but it’s been a long time.

Anyway, however it happened, the argument was that my brother wasn’t paying attention during reading time, and the teacher didn’t believe it was because he could already read.

So near the end of my brother’s Kindergarten year, my father had a meeting with the teacher, during which my brother proved that he could read by reading a book that had just arrived from the publisher.


Allegedly afraid that I would experience the same issue, my parents refused to let me see the page while they read books to me. Nonetheless, I was also able to read when I entered Kindergarten.

My parents blamed my brother, and said he’d taught me to read. That’s possible, but hyperlexia could also have been a factor.

I remember in Kindergarten, sitting on a piano bench during naptime, reading to the other children. My father insists this never happened, but I don’t know how he could know. He wasn’t there, I was. (It may have been in daycare, I suppose, but I know it happened.)

Regardless, at that time (1973), most people thought that typical children entering Kindergarten weren’t capable of reading. These days, it seems to be an expectation that they can, at least for many schools, but back then, it was seen as an aberration. Even a party trick.

After only a few weeks, I was transferred into first grade.


Rewind: Another story my father used to tell involved my “first words”.

I lost my eye when I was just over a year old. According to my ocularist’s records, I got my first prosthetic eye when I was sixteen months old, so I had to have lost my real eye not long before that.

I was late to speaking. My father blamed the trauma of losing my eye: I had been progressing normally on language development, but I stopped after my surgery.

Months passed and my family tolerated my grunts and pointing. One day, the story goes, my father got sick of it. I pointed at the ketchup, and my father said I couldn’t have it unless I used my words. I grunted and pointed a few more times, then finally relented with, “Please pass the ketchup.”

Many of my father’s stories have a Big Fish taint to them, with an underlying element of truth. Even so, they had a remarkable consistency to them, right down to it always being ketchup that I was asking for, so either it was true or my father was just a consistent liar.

Late speech development is a common-not-universal trait of Autistics.


I wanted to be a writer from a young age. I remember that I was going to write a story called “The Mysterious Monster”, but I didn’t know how to spell, and I gave my father a sheet of paper with the title written on it. He looked awkwardly at it, then asked me what it was about.

I told him, and he laughed in that way that parents laugh condescendingly at children, thinking the child won’t remember or will laugh along, that Art Linkletter “Kids Say The Darnedest Things” laugh.

I’d written “The Mistress Monster”.

After my father gave the paper back, I hid it or threw it out and never pursued that story. And I still remember that laugh.


When I was in the upper grades of elementary school, I was in a spelling bee. I was one of the representatives of my school. We drilled spelling words over and over, and I was caught up on “lavatory”, which I insisted on spelling to match “laboratory”, that is, as “lavoratory”. Or maybe it was the other way around; I don’t remember for sure.

Regardless, the word I consistently confused with the other one was the word I got in the spelling bee. I got it wrong. My father scolded me because we had practiced over and over, and I still got it wrong.

A few years later (this was in Berkley; the spelling bee was in Marine City), my father asked me how to spell “hors d’oeuvres” because he couldn’t find it in the dictionary and he was writing up a menu for the church. I guessed, but I didn’t know about the “h” so I didn’t get it right.

He did figure it out eventually; his secretary managed to find it in print somewhere, I think. This was before the internet, so there was no way to just Google it.

I felt like I’d let him down.


This memory is from Kindergarten or so, I think. Maybe second grade. I was being tested for my intelligence because I was overachieving in school.

It’s strange to read that WebMD website I linked before, acting like hyperlexia in itself is something to be “fixed”. That reinforces how much Autism is pathologized: Reading “too early”, having “too large” of a vocabulary, is seen as something that needs fixing.

Anyway, I had an IQ test. My father said I scored a 165 or a 185, I forget which. The only part of the test that I remember is reading words from a list, with the instruction that I should stop when I didn’t recognize one. The examiner had to skip a few pages because I just scanned quickly through the first one she showed me.

So much has been written on the education system continues to struggle with the proper treatment of students who “overachieve” in schools. Maybe at some point I’ll write something more focused about my own experience as a “gifted” child, but it’s tangential to this.


A memory from around twelve years old: I’m in the car with my mother, the front seat. I think we were going to my therapy, and I’m reading a book. I ask her what the word “eh-pee-tohm” means, so she has me spell it. I do, and she says it’s “epitome”, and proceeds to define it.

It’s the clearest memory I have of having seen a word but not knowing how to pronounce it, while at the same time knowing a word but not knowing how to spell it.

That and “The Mistress Monster” occupy adjacent spaces in my memory, even though they happened years apart.

A memory from high school: My English teacher and I are discussing some student-written poems. One, written by a student whose name I remember but won’t share, is called “Hyperbole”, which is a word I don’t know but which reminds me of a word I do know, “Hyperbola”. So I’m confused, because the poem is about a squirrel and has nothing to do with mathematics.

I suppose the point of these memories is that, as advanced as my reading skills were at a young age, I had gaps. English is a robust language, gaps are not surprising. I know there are words that other people see as quotidian but which I’m unfamiliar with.

(Yes, that was a joke. Autistic humor.)


Also interesting, though, is how my brain has clung to the memories of “words I didn’t know” as moments of personal shame, like I felt like I was expected to have known them.

Okay, so, yeah, that’s the bit about being labelled “gifted” that I wasn’t going to go into, but I’ve changed my mind. It’s the Platonic expectation that all learning is remembering, and that gifted children already know everything about whatever it is they’re gifted at.

The autistic tendency to infodump certainly doesn’t help with that.

Another memory, this one as an adult and the owner of an MA in Linguistics: My father tells me that Korean is written in Chinese characters, and that he knows this because he spoke to a Korean person, and so I better not argue with him about it.

It isn’t true, at least not as stated. Korean is written in its own writing system, a phoneme-based one like most of the world’s writing systems, not an ideographic one like Chinese. It’s true that Korean contains occasional Chinese symbols, but they’re hardly the bulk of the writing system.

It seemed, and seems, strange that my father was so adamant that I not correct him. I imagine part of it is my tendency to infodump, which has been taken throughout my life as being a Know-It-All.

But there’s no such thing as someone who truly knows it all. For instance, while I know the basics of the Korean writing system (as well as many others), I don’t know the basics of every writing system in current use, let alone that’s ever been used. And I don’t know how to read Korean, I just have a general sense that it’s written in syllabic clusters of phonemic marks.


Relevant point being: Once I was identified as being “gifted” and having a “large vocabulary”, the expectation was that I’d simply know how to spell any random word, and so it was a point of shame for me when I didn’t. Those are the memories that stuck with me, not the ones where someone asked me to spell a word and I did so correctly.

For instance, I know that someone who tries hard is a “trouper” and not a “trooper”, and that people get their “just deserts”, not their “just desserts”, and that people have “piques” of anger, not “peaks” or “peeks”. I find it interesting that playwrights can copyright plays they write.

I struggle with keeping my displays of knowledge like this somewhat suppressed, because I don’t want people thinking I’m trying to shame them. I just happen to know the prescriptive spelling of a lot of words, including many confused ones.

I did spend a lot of my life sneering at people who made mistakes, like using “they’re” when they mean “their”, and sometimes I do still slip and wind up joking about that. Yes, spelling is important; yes, vocabulary is important. But if I know what someone means, maybe I can keep the need to be “correct” to myself.

And all this aside, there are still words that I don’t know. I’m currently reading a book that uses the word “absquatulate” to illustrate how to teach new vocabulary. It was effective for me: I certainly don’t recall having encountered the word before. (It means “leave in a hurry”.)


This expectation got in my way earlier in my life: Just as being seen as a math genius kept me from challenging myself more in mathematics (lest I hit walls and prove myself human), I also avoided reading books that were too far outside my comfort zone.

A mitigating issue: I’m a slow reader. I can read complex texts, but I do so at a snail’s pace. This is another common trait of Autistics, particularly AuDHDs (which I may also be). The expectation was that, as an early reader with a large vocabulary, I would quickly devour anything I encountered. But the reality is that I struggle with longer texts, both because of attention issues (I’ve stopped writing this several times mid-sentence to go look something up and found myself back on social media, vapidly scrolling) and because of a need to read every word, even the ones I’m not familiar with (and if too many clutter up my working memory, I get frustrated and give up).

So this all gets into the issue of proper support of “gifted children”. I may be both hyperlexic and hypercalculic, a rare combination. Research by Wei et al suggests that hypercalculia occurs twice as often in Autistics as hyperlexia, but I wonder how much of that is because the mathematical Savant stereotype of autism leads to a higher rate of diagnosis.

“Gifted children” receive a persistent message that they’re expected to excel, which can lead to feelings of shame when we struggle with some aspect. This is a threat to our identity: A “mathematical genius” isn’t supposed to struggle with math; a “lexical genius” isn’t supposed to struggle with reading.

So when I did, I was embarrassed (at 54, I still misspell “embarrass” on my first attempt, and that’s okay) and avoided disclosing that. In more extreme situations, I avoided topics entirely. My biggest mistakes in mathematics are consistently when I’m rushing to show off how “smart” I am, something I know objectively is silly but which years of training programmed me to believe.


This has now gone on longer than I expected or initially planned, and morning has progressed into afternoon, so I think it’s time for me to self-defenestrate. Pardon my absquatulation.


Sources:

Brennan, D. (reviewer). (2021) “What is Hyperlexia?” Accessed via WebMD 1/4/23

Wei, X.; Christiano, E.; Yu, J.; Wagner, M.; and Spiker, D. (2015) “Reading and math achievement profiles and longitudinal growth trajectories of children with an autism spectrum disorder”, Autism 19:2, accessed via Sage Journals 1/4/23

On Cognitive Load Theory and Story Problems

I’m currently reading “Sweller’s Cognitive Load Theory in Action” by Oliver Lovell, specifically the section on reducing extraneous load during education (ca. p. 32; I’ve got the e-book). This leads me think about story problems, such as those on the SAT, which often contain information that’s irrelevant to the problem. For example:

Carrie invites some friends to a party. For every two friends who bring snacks, there are five who bring nothing with them. If the number of friends who bring nothing is 15 more than the number of friends who contribute snacks, how many friends in total arrive at the party?

SAT Math: Word Problems, Anika Manzoor

The first sentence has nothing to do with the underlying math; it’s meant to contextualize the problem, to make it less abstract. But this puts information in our working memory, which is finite, and hence takes up room that we could be using for other things (such as actually solving the problem).

The second sentence has important information, but it also has some irrelevant information: We are going to have two groups of friends, “snack-bringers” and “non-snack-bringers”. The nature of these groups is irrelevant; this could be “people who watch TV” and “people who don’t watch TV”, and they could be gathering at a shopping mall. This could be “Democrats” and “Republicans” and they could be filling out a survey. But “snack-bringers” and “non-snack-bringers” are particularly clunky groups to have, cluttering our memory more.

The mathematically relevant part of this is just:

\[A + B = C \\ B/A = 5/2\]

For a mathematician, that’s where we are. For a non-mathematician, we’re also at: Who is Carrie? What’s the party about? What kind of snacks? Was everyone supposed to bring a snack? Are we to infer that there are no friends who brought, say, a game but no snacks? And the first two questions (completely irrelevant!) are loaded into working memory before any math can happen, taking up room.

Then we have the painfully confusing “if” clause. In mathematical notation, it’s:

\[B = A+15\]

with the “how” clause being:

\[\text{Find } C\]

But we have all this other language, including the unnatural structure of the “if” clause, to muddle through. So teaching a student to solve a story problem means teaching them to FIRST find the mathematical parts, THEN clear out working memory to focus just on the math, THEN solve the math.

The underlying math, meanwhile, is not as straightforward as it seems to a fluent mathematician, and requires checking back against the convoluted scenario it’s provided in. So it’s little wonder that many students, once they’ve gotten some sort of mathematical problem (right or wrong) out of a story, simply discard the story entirely and go with whatever number they wind up with as “the answer”.

Let’s solve this problem according to how we’d usually teach it in Algebra class.

\[A + B = C \\ B/A = 5/2 \\ B = A+15 \\ — \\ (A+15)/A = 5/2 \\ 5A = 2(A+15) \\ 5A = 2A+30 \\ 3A = 30 \\ — \\ A=10 \\ B=25 \\ C=35 \]

This is likely not how a fluent mathematician would solve it: More likely, we’d hazard a guess for the snack-bringers, noticing that for every two, there are “three more” non-snack-bringers. We might jump immediately to that “three more” and realize that every 7 people represent three “extra” non-snack-bringers (and hence there are 15/3 = 5 groups of 7 people involved).

So first we overload working memory with irrelevancies, then encourage students to discard those irrelevancies when solving, then encourage an inefficient-but-universal algorithm for solving, all while the clock is running.

I’m not saying that we shouldn’t have story problems. The common mantra in mathematics education is that the purpose of what we’re learning is so that we can apply it to real world scenarios.

The underlying process is an important one:

  1. Convert from natural language to mathematical notation
  2. Solve the mathematical problem
  3. Convert back to natural language

However, the first step requires extra time, and importantly, there is the need to release working memory between the first and second steps and then recall between the second and third steps, something which students often struggle with.

Just some thoughts as I’m reading through the book.

Addendum: I asked my 13-year-old about this question, and he wondered whether Carrie was meant to be counted at any point. I had given him a paraphrased version, and I think the question itself is phrased in a manner that says she’s not included at all. But given that many of my students have been trained to look for trick questions, this is a fair observation, something else that muddles up cognitive load.