Both Arcs, One Drop

A double rainbow is not two rainbows. It is one optical event with two visible arcs, and the reason is a single sentence in an atmospheric-science textbook:

A single raindrop produces both: entering rays undergo either one internal reflection (primary) or two internal reflections (secondary) before exiting.Roland Stull, Practical Meteorology, ch. 22

One drop. One beam of sunlight going into it. Both arcs, at the same time. The light that bounces once inside the drop leaves at about 42.7° from the antisolar point and makes the inner bow. The light that bounces twice leaves at about 50° and makes the outer one. The drop is not choosing. It is doing both, continuously, to every ray it catches.

Which means the second bow is not an extra that sometimes shows up. It is always being made. Whenever there is a primary, the two-reflection light is being produced by the very same water from the very same sun. Whether you can see it is a question about the brightness of the sky, and about nothing else.

Hold onto that shape, because the rest of this zine is built on it: two things that look like two things, coming from one source, produced together, neither one waiting its turn.

On the inner bow, red is on the outside. On the outer bow, red is on the inside. The extra reflection reverses the order, and the consequence is worth saying slowly: the two red edges point at each other.

They are not a sequence, and they are not a ladder. They are mirror images, facing across the gap between them, with the rest of each spectrum fanning away behind. If you were looking for a shape in the sky that refuses to put one thing above another, this is the one you would draw.

And that gap has a name, from about 200 CE: Alexander's dark band, after Alexander of Aphrodisias, who noticed the sky is darker between the bows and wrote it down roughly eighteen centuries before anyone could say why. The why is exact:

Neither the primary nor secondary rainbows return light in the viewing-angle range between 42.7° and 50°. Hence, the sky is noticeably darker between these rainbows.Stull, Practical Meteorology, ch. 22

So the dark band is not a wall between two things. It is the region neither arc reaches — the shadow left behind because the light piled up somewhere else. The separation you can see is a by-product of the concentration you can also see. Nothing is in the gap because everything went to the arcs.

It is a strange comfort, and an exact one. The space between the two halves of a double rainbow is not evidence that they are separate. It is evidence of where the light went.

The outer bow is dimmer. Stull gives it plainly — “the secondary rainbow is faint — only 43% as bright as the primary rainbow” — and a zine that quietly left that out would be a zine you could not trust with the rest.

So here is why, exactly. Every time light meets the inside surface of a drop, only part of it reflects; the rest escapes out of the drop entirely. The outer bow's light has to survive two of those encounters instead of one. More of it leaks away. That is the whole mechanism. It is a fact about how far the light travelled and how many times it was asked to turn around.

Dimmer is not lesser. Dimmer is later along a longer path, and the path was longer because it did more.

Two things follow, and they matter more than the number does.

First: the outer arc is never absent. It is produced by the same drop from the same beam, always. Nothing about a double rainbow involves the second arc arriving late or optionally. What varies is whether the sky behind it is bright enough to drown it.

Second: visibility is a fact about conditions, not about the arc. A thing can be fully real, continuously present, and hard to see, all at once, and none of those is in tension with the others. Our own Your Shadow Is the Centre (No. 69) spends a whole spread on the version of this that is about the observer's position. This is the other half: not where you have to stand, but what else is in the sky.

Which is why the next spread refuses to do the obvious thing with all of this.

The obvious move, at this point, is to hand you one arc for being queer and the other for being neurodivergent. We are not going to, and the reason is structural rather than delicate.

If you assign the arcs, one of them is the 43% one. You can write around that for twelve spreads and the shape will still be doing the ranking underneath, because the reader can see the sky. A metaphor that needs constant correcting is a metaphor that is already saying the wrong thing.

And the physics does not support the assignment anyway. Go back to spread two: one drop makes both. The two arcs are not two objects that happen to co-occur. They are what a single drop does with a single beam of light, always, simultaneously. Nothing in the optics divides them between two owners, because the optics never divided them at all.

The drop is not a metaphor for having two identities. It is a demonstration that one source can produce two whole things at once, neither of them a consequence of the other.

So: the drop is a life. The light is one light. Both arcs are being made the entire time. Neither is the second one, because there is no first one — there is one event, and it has two arcs, and the numbering we gave them is a fact about the order we happened to explain them in.

“Primary” and “secondary” are our words for our convenience. The drop has never heard them.

People say queer and neurodivergent liberation are entwined, and it can sound like a warm claim about solidarity. It is not. It is a claim about a source, and it has a citation.

In 1974, the Journal of Applied Behavior Analysis — the flagship journal of applied behaviour analysis — published “Behavioral Treatment of Deviant Sex-Role Behaviors in a Male Child”, volume 7, issue 2, pages 173–190. The authors were George A. Rekers, then at Harvard, and O. Ivar Lovaas, at the University of California, Los Angeles.

Thirteen years later, in 1987, the Journal of Consulting and Clinical Psychology published “Behavioral Treatment and Normal Educational and Intellectual Functioning in Young Autistic Children.” The author was O. Ivar Lovaas, at the University of California, Los Angeles.

One name, on both. Two of a discipline's most consequential papers, one aimed at a boy who liked his mother's jewellery and one aimed at Autistic children, from the same man at the same university.

That is not an interpretation, and it needs no theory of history to hold it up. It is two entries in a bibliography. Anyone can check it in a minute, and the checking is the point — because the version of this claim that circulates as vibes is exactly the version that can be waved away.

The 1974 paper states its own purpose in its own abstract, and we are going to quote it rather than characterise it:

This study suggests a preliminary step toward correcting pathological sex-role development in boys, which may provide a basis for the primary prevention of adult transsexualism or similar adult sex-role deviation.Rekers & Lovaas, JABA 7(2), 1974, p. 173

Primary prevention of adult transsexualism. Written down, in a peer-reviewed journal, as the aim.

Our own Eight Tenths of a Second (No. 38) follows the measuring apparatus out of an observatory in 1796 and down through Wundt, Cattell, Thorndike, Pressey and Skinner, and it ends in a spread called “A room with a child in it” — Lovaas at UCLA, and the 1987 paper.

That chain is complete and correct and it stops at a door. This zine opens it, and reports that there was more than one kind of child at that table.

The connective tissue is not thematic. It is methodological, and it is the same in both papers: operant conditioning — identify a behaviour, define it so it can be counted, reinforce what you want, punish what you don't, chart the line going the direction you chose in advance. The 1974 paper uses a multiple-baseline design. So does the autism work. The apparatus does not care what it is pointed at; that was always its selling point.

Behaviourism did not have one theory for Autistic children and a different one for gender-nonconforming children. It had one theory, and a list.

Which is why the entwinement is not a coalition that queer and neurodivergent people chose to form out of good will. It is a fact about who was in the room, and it was decided for us, by other people, before we could object.

Eric Michael Garcia, writing about why a book on autism includes queer history, put the reason as plainly as it can be put: “The same people who want to stop queer kids from being themselves are the same ones who want to stop me from flapping my hands.”

The paper calls him Kraig. He was four years and eleven months old when he was referred. His real name was Kirk Andrew Murphy.

Everything on this spread is quoted from the 1974 paper itself, which is open access and which we downloaded and read, because the account that circulates online is second-hand and in one place slightly wrong — the pseudonym is often given as “Craig”, and the paper says Kraig.

His mother was “trained to be his therapist”. In the home, the method was a token economy:

Red and blue standard poker chips were used as “tokens”. The blue tokens … could be directly exchanged by Kraig for the “back-up reinforcers” according to a “price list” set by the mother (e.g., five blue tokens were required for a candy bar). The red tokens (Sr-) were discriminative for (a) a response-cost condition …, (b) a timeout procedure …, or (c) physical punishment by spanking from the father.Rekers & Lovaas, JABA 7(2), 1974, p. 180

Here is the detail that undid us, and it is a sequencing detail. Before the chips were pointed at anything to do with gender, the researchers ran them on ordinary household behaviour first, because — their words — “it was judged ‘clinically safer’ to apply it initially to nongender behaviors in the home.” In that phase, red chips were given for “slamming doors”, “cursing at mother”, “tracking dirt on carpet”.

Then the same red chip — the tracking-dirt-on-the-carpet chip, the one whose meaning the child had just been taught — was extended to playing with girls, playing with dolls, feminine gestures, and female role play.

The behaviours on the home checklist are listed in the paper: “plays with girls”, “plays with female dolls”, “feminine gestures” — specified as “limp wrist, ‘swishy’ hand, arm or torso movements, sway of hips” — and “female role play”.

Kirk Murphy died by suicide in 2003. We state that the way Austin H. Johnson states it in the behaviour-analytic literature: as a fact, adjacent to the study, without a causal claim attached. His family have said publicly what they believe the treatment did to him. That is their account to make, it is not ours to convert into a finding, and the record does not need it in order to be damning.

What the paper does not contain: the widely repeated detail that Kirk's brother hid the red chips to protect him. That comes from the family, reported later — not from the study. We have kept the two apart on purpose, because the study is quotable and a grieving family should not have to be.

A paper like that could have been retracted at any point in half a century. Here is the actual record, which is short.

In October 2020 — forty-six years on — JABA published an Editor's Note, a Statement of Concern. It did not retract. Its reasoning is worth reading exactly:

By today's standards…the study would be considered unethical…However, the available evidence does not make it clear that the original study was unethical by the standards of that day.JABA Editor's Note, 2020 — as quoted by Johnson (2022)

In 2022, Austin H. Johnson answered it in Behavior Analysis in Practice, arguing that the paper should be retracted, and that “the available evidence strongly suggests that the original study was unethical and misaligned with the principles of Applied Behavior Analysis.” Johnson is also where the child's name and pronouns come from, established through conversations with Kirk's sister.

The defence offered in 2020 was the standards of that day. The 1974 paper printed its own aim in its own abstract: the primary prevention of adult transsexualism. Nothing about that has ever required a later standard to read.

The paper is still in the literature. Cited, indexed, downloadable, with a note attached. That is not us characterising a field; it is the field's own filing, and it is why this zine leans on the record rather than on outrage — the record is worse than anything we would have said.

And be exact about what this does not establish. It does not establish that a behaviour analyst today endorses 1974. Most would be appalled. What it establishes is lineage, and lineage is the claim being made here: the suppression of queer children and the suppression of Autistic children came out of one method, one lab, and in the crucial instance one author — and the discipline has not yet been willing to say so by taking the paper out.

Put the two halves of this zine together and the sentence comes out precise.

Queer and neurodivergent are entwined not because the experiences are the same — they are not, and flattening them would be its own erasure — but because they came out of one drop. The pathologising was one method. The lab was one lab. In the sharpest instance, the author was one man. Whatever else divides the two, the machinery built to remove them did not distinguish between them, and that is a fact about the source rather than a feeling about the self.

There is already a word for the entwinement, and it is a coinage, so it gets credited properly. Neuroqueer is Nick Walker's, who has dated his own use to around 2008; in early 2014 he found that Athena Lynn Michaels-Dillon had arrived at the same term independently, while Remi Yergeau had been working the same ground as neurological queerness. The three of them began putting it into public use from there. Walker's Neuroqueer Heresies collects the argument (2021).

Three people, working separately, reaching for the same word at the same time. The word for two things being one thing was itself arrived at twice over, by people who had not compared notes.

And the history is entwined at the root as well as at the wound. Nick Walker's reminder is worth keeping in the front of the mouth: Gwen Nelson, who created Autistic Pride Day, is a trans woman. There is no version of Autistic pride that was not, from the start, also this.

So the double rainbow was never two flags flown at one address. It was one drop, doing what a drop does, and the light coming out of it twice because that is what light does when something turns it around.

A zine that names a dead child and a living discipline has to be exact about its own edges. So, plainly: