• Josh

Everything is a Spectrum

Breaking news: Autism isn’t binary (not autistic / autistic), but instead it’s a spectrum (not autistic ⇄ autistic). This, per the description in the fourth edition of the Diagnostic and Statistical Manual of Mental Disorders, the DSM-IV, published in 1994. In the DSM-IV, autism was categorized as a discrete spectrum, with separable levels like “Asperger’s Disorder” or “Pervasive Developmental Disorder.” Since then, the diagnosis has been further expanded to a continuous spectrum, known now as Autism Spectrum Disorder (ASD), per the more recent DSM-V.

One concrete (though unofficial) representation of what the autism spectrum might look like. It’s labeled somewhat confusingly; still, best visualisation I could find.

In the 80s a doctor might diagnose you as autistic or tell you you’re not autistic, but there was no diagnosis for 1/2 autistic or whatever. Now, friends casually say they’re “on the spectrum”, not in a disparaging way, but to point out when some set of observed symptoms match the diagnosis for autism.

More breaking news: Sexuality isn’t binary (gay / straight), but instead it’s a spectrum (gay ⇄ straight). The quantitative version of this is called the Kinsey Scale, based on work by Alfred Kinsey et al. in the ’40s and ’50s, which studied the range of human sexual attitudes. The scale ranges from 0 (exclusively heterosexual) to 6 (exclusively homosexual), with an additional category X denoting no sexual contacts or reactions.

There are 10^6 versions of the Kinsey spectrum online, but here’s one for illustration.

These days, many people still identify themselves with the binary categories of gay and straight, but the middle ground is more generally acknowledged, as people experiment more and are more open to talking about same-sex attractiveness. Kinsey himself says:

Males do not represent two discrete populations, heterosexual and homosexual. The world is not to be divided into sheep and goats. Not all things are black nor all things white. It is a fundamental of taxonomy that nature rarely deals with discrete categories. Only the human mind invents categories and tries to force facts into separated pigeon-holes. The living world is a continuum in each and every one of its aspects.

This is clearly different from gender being a spectrum, but don’t worry, gender is a spectrum too. I’m no expert in this area, so, an anecdote: I met someone recently who described themselves as gender fluid. Since I don’t know what that’s like, I was curious about it and asked some questions; for example, how do they decide whether they’re masculine or feminine that day? I don’t remember their exact words, but it was something like, “I just kind of wake up and feel a certain way, like, ‘this is a fem day’ or ‘this is a masc day’. Although… actually, it’s not really like that. It’s kind of continuous; I feel a little more fem today than yesterday, but it’s not like I wake up suddenly wanting to wear pink bows in my hair.” I found this extremely interesting, and we had a lovely afternoon.

Lots more breaking news: Dawkins says belief in God is a spectrum (believe in God ⇄ don’t believe in God); consciousness is a spectrum (no awareness ⇄ high awareness); and of course, political attitudes are a spectrum (Left ⇄ Right… no wait, you’re telling me it might be multidimensional? *GASP*).

In light of all these stunning revelations, I ask: should we be surprised? In retrospect, it seems kind of obvious to me that all of these things would be continuous spectra.

  1. Rain Man clearly suffers from extreme autism, but many people with autism don’t need caretakers and lead essentially ordinary lives; on a scale from zero to Rain Man there clearly exists a lot of middle ground occupied by many people with very different experiences.

  2. It is also totally intuitive that a person can be more / less attracted to the same / opposite sex. I’m on the straight side of the spectrum, but across different girls I meet, my attraction level is essentially continuous; why would all men be at exactly zero? (Come on, admit it, you’re at least a little attracted to Bradley Cooper (if you’re man) or to Gal Gadot (if you’re a woman).)

  3. Our feelings and attitudes are clearly fluid, so if fluidity of gender is related to a person’s day-to-day experience of their own femininity or masculinity, this is also a no-brainer.

  4. And obviously any belief is a spectrum; we say things like “I believe [A] more than I believe [B], but not as much as [C]” all the time and nobody is confused in the slightest. That’s all well and just and good, especially for a proper Bayesian.

I posit the following general rule: everything is a spectrum. Ahhhh, doesn’t it feel good to just say that? We spend so much time categorizing everything into two clean categories only to “discover” that our classifications aren’t clean at all. I think spectrums should be, by now, the null hypothesis; if we discover something that is truly discrete or binary, that’s what is worth explaining. (Kinsey apparently figured this out long ago, as did Tim Minchin.)

Why is everything a spectrum? Because when you actually look at one of these binary classifications and ask “what precisely are we trying to distinguish here?”, a spectrum rears its head. It seemed to make sense to call autism binary, but when we define autism by the severity of particular symptoms, it’s clearly a spectrum. It seemed to make sense to call sexuality binary, but when we define sexuality by people’s behaviors or desires, it’s clearly a spectrum. As soon as you replace the binary label by a specific, concrete variable, that variable gets to take whatever value it takes and we find ourselves with a spectrum. This is increasingly true throughout human history as the world population increases, because more people implies more variation implies filling up more of the space between discrete classifications along every axis.

Everything is a spectrum, at a more biological level, because genes matter, and they don’t operate in a one-to-one way with phenotypes that we care about (though back in the day, many people thought they would). There’s no “gene for [X]”, where X is IQ, autism, conscientiousness, homosexuality, or anything else we care to mention. Genes matter quite a lot for all of these things, explaining as much as 50% of the variance in these traits. But given that there are a small number of genes controlling a very large number of outcomes, we should expect by now that each gene contributes to many many things. The result is a combinatoric explosion of complexity, which looks to us like a spectrum of outcomes.

Obligatory physicist aside: The analogy to quantum mechanics is actually pretty good here. QM tells us that, for example, the set of possible energy levels of electrons orbiting a nucleus is discrete (“quantum” literally means “discrete”); when I add one more electron to the system, it can’t go just anywhere, but must land in an orbit which is nontrivially separated from the others. This kind of discreteness is a law of Nature. This is in principle true for the Earth’s orbit around the Sun too, but in that case there are so so many electrons and atoms in the Earth that, though it’s a quantum (discrete) system at a fundamental level, it effectively behaves classically (here, meaning continuous or not quantum). The cumulative effect of so many quantum choices is something that doesn’t appear quantum at all.

Similarly, if you dig deep enough, many brain functions are binary: neuron #3957329 either fires or it doesn’t. But at the level of things we are aware of and actually care about, all these many discrete operations add up to something that is essentially continuous. Just as your computer screen is formed from red, green, and blue (RGB) pixels, but to your eye produces an effective continuum of colors, the vast world of quantum, neuronal, and genetic discreteness add up to produce the effective continua of autism, sexuality, etc.


Let’s apply our new rule in some more controversial cases. Cancer is a spectrum. You don’t merely “have it” or “not have it”; it’s a complicated condition with degrees of severity. We have stages of cancer (Stage 0 to Stage 4), but I’m pretty confident an experienced oncologist would tell you that not all Stage 3s are the same. There is a spectrum of treatability; there is a spectrum of negative symptoms; there is a spectrum of number or size of tumors. Look closely, and on any particular axis, there exists a range of possible outcomes and given enough cases, people will fill the spectrum in a more or less continuous way. (By the way, it’s totally fine to have a “cancer=0” endpoint to the spectrum.)

Race is a spectrum–or, actually many spectra. We have demarkations of Native American, African, German, Japanese, etc., but these are all just classifications originating in our individualized, complex genetic makeup, which forms an effectively continuous spectrum of ancestral genetic heritage. This is more clear than ever today, as everybody and their mother is using 23 and Me or another similar gene-analysis test. (Actually, I haven’t done it yet, but my mother’s side of the family has!) You can take the test and find out that you’re ancestry was 6% Japanese, or 13% Jewish, or whatever. Who knew! In retrospect, probably all of us. Lineages are complicated; genes get passed around generation after generation, and the vast majority of us are complicated mash-ups of all sorts of complicated genetic heritages. People aren’t “Japanese” or “Not Japanese”; they’re 0%-100% Japanese, somewhere on a continuous spectrum.

Sex–that is, biological sex, as distinct from gender and sexuality–is also a spectrum. Most people have either XX or XY chromosomes, and similarly most people are born with either a vagina or penis, typically denoting biological female and male (respectively). But there are other cases. Intersexuality is typically associated with ambiguous genitalia (there’s a spectrum for that too, the “Quigley Scale”, with a NSFW picture). A person with Swyer syndrome is born with XY chromosomes, but is by literally any other measure biologically female. There are plenty of other cases besides. (And of course, gender and biological sex are often closely related, but not perfectly correlated, as in the case of people who are transgender.)


Ok, so now that we’re all getting used to thinking about spectra, let’s walk it back a bit; let me tell you what “everything is a spectrum” doesn’t mean. It does not mean that our discrete terminology is useless. It also does not mean that there are no natural demarkations between things, as the existence of a continuum does not imply a flat distribution of outcomes. This can be made clear by an example. The distribution of incomes (you know, the income outcomes!) in the world is basically continuous, spanning the range from the poorest villager with nothing, up to Jeff Bezos. Yet the distribution is very far from flat; it is rather peaked at low or middle incomes.

Bezos is way, way, WAY to the right of the figure

Wow, income is a spectrum! As a result, “rich” and “poor” are not unambiguous binary classifications. Yet, I’m very comfortable calling Jeff Bezos “rich”. He’s rich, and so are Bill Gates and Elon Musk. “Rich” is a shorthand for “pretty far to the right on the income spectrum” and it’s useful to have a label for that. If you made me give a precise number for an income that qualifies for “rich”, I’d hesitate. I dunno, maybe $1 million? Who cares. Bezos is rich.

We might even introduce new terminology to distinguish different parts of the spectrum. There’s “rich”, and there’s “really rich”, respectively at $1 million and $1 billion or something. That’s fine, sounds good to me. We can keep chopping up the spectrum further if you want, and I won’t complain: $10 billion is “super duper rich”; $100 billion is “ultra mega rich”; nobody has $1 trillion dollars, so a category at that benchmark is kind of useless. Even if our category contains only a handful of people, or only the possibility that people might someday fall into that category, I have no objection to it. But we should remember that we are the ones drawing the lines and assigning the names, not Nature.

The spectrum also doesn’t have to be single-peaked, as evidenced by the case of political attitudes. Apparently Republicans and Democrats in the US are becoming increasingly ideologically divided, which implies a two-peaked structure on the spectrum of Left ⇄ Right political opinion.

Note that the data set excludes people in the Center by construction.

“Republican” and “Democrat” are useful terms to the extent that they distinguish groups that are different from each other in some way. But still, the axis itself is continuous, and there is a large purple area where the attitudes overlap. There’s nothing puzzling about any of this.

See, we have a bias towards seeing discrete levels, but that doesn’t mean the discretization is necessarily an error. Remember that the categories were made for man, not man for the categories. We draw lines to make distinctions where we think they exist, but we have to go and test whether the distribution of actual outcomes adheres to our separation: is what I call a Republican different in some way from what I call a Democrat? The answer, and how people might stack up on one or another end of the spectrum (or in the middle part), is an empirical question that we can answer by studying it.


I’m a little worried that this post will end up looking like it’s about gender issues, which was not my intention when I started writing; I really do mean to be making a general, Meta Level point here. But let me lean into it for a minute anyway.

I hope the recognition that everything is a spectrum might put some things in context. I do think it’s great, really great, that we move away from the assumption that everyone is precisely “male” or “female”, biologically or in terms of gender. People who are e.g. intersex or transgender are left out when we chop things up that way. As a culture we seem to be working on this problem.

This is fine. Why are people mad?

Yet, biologically and in terms of gender, “male” and “female” remain the most common classifications, representing peaks in the apparent distribution of outcomes. They are useful terms and totally refer to real things in the world, just like “rich” is real and useful to talk about Bezos, Gates and Musk.

At the same time, whenever we give labels to parts of a spectrum, we leave things out, and we should be aware of what we’re doing; we’re chopping up something that is actually more continuous than the resulting pieces might suggest. One solution is to chop more finely, but in doing so, we likely end up with pieces that apply to only a small fraction of the population. What we gain in inclusion, we lose in simplicity. So I’m fine with 32 genders, with the caveat that we acknowledge the underlying spectrum and the fact that we are still the ones choosing how finely to chop.

What we don’t want to do is make distinctions where there isn’t any difference; this is my best steel-man of the argument against 32+ genders. If you chop up a spectrum too finely, it’s possible to end up with pieces so small that they don’t apply to anything. I’m of the opinion that low-occupancy categories are fine, but let’s try to see just how fine the pieces are. I tried to figure out what percentage of the population does not identify as either “male” or “female”, and there are various surveys giving all kinds of answers: somewhere between 1-19% within LGBTQ+ respondents surveyed in Canada, and 35% of transgender respondents in the US identified as non-binary. It was hard to find good general data about this.

At the population-wide level, the best I could find was this study in the UK which finds 0.4% of respondents who identified as neither “male” nor “female”. We can cross reference that with the Gender Census, which tries to determine the subfraction of each of the 32 genders above just by asking people what they identify as (sampling bias suspected in both sources). If both are totally accurate–I have concerns (below), but let’s try anyway–and choosing a random example of “demiboy” from the list, we have roughly (population of the UK)*(0.4%)*(8%) = about 21,000 demiboys. Assuming homogeneity across the globe, that’s about 2 million demiboys in the world. This implies that while they’re out there, unfortunately it’s very unlikely that I’ll ever meet one.

I’m very skeptical of my own calculation, because: (a) The UK study finds 0.4% non-binary classification. but statistically one needs very large sample size to justify any survey finding <1% representation (the error goes like 1/sqrt(N), where N is the number of respondents); and (b) I have spent my adult life studying and working in universities in liberal Western countries, where there is sure to be a higher-than-average chance of meeting people who openly identify as non-binary, but I know almost none (could be a fluke or fluctuation, or it could be that my society is not as non-binary-friendly as I think it is… I don’t know). Whatever: even if it’s not 0.4% but rather 0.04% or 0.004% my conclusion is the same: we’re talking about a very small fraction of the population at most, but if it’s a question of asking whether it’s a real thing I err on the side of accepting what people tell me about themselves.

A last caveat is that the goal of most terms is to identify differences where we think they exist, so that we can treat different cases differently. When the genome was mapped, nobody found That One Cause of gender differences hiding in any particular gene; similarly, once we’ve mapped the brain, there won’t be a single neuron for X, Y, or Z. Is there some pattern of neuronal structure that will one day distinguish demiboys from males? Maybe. Do I care about such differences? Not really. I’m happy to use your pronouns for the same reason that I’m happy to call you by whatever name you tell me you prefer; I don’t need deep brain analyses to just be kind to people.


But anyway, back to the point.

Autism is a spectrum, which makes it more complicated and difficult to figure out than doctors in the 80s could have appreciated.

Sexuality is a spectrum, yes, which makes everybody a little gay. This does not mean that every point on the Kinsey scale is equally occupied. The distribution of outcomes, and the question of who is more gay and who is more straight and who is close to the middle, is an empirical one. If we care to know the answers we have to go out and test it. But I’m still comfortable calling myself “heterosexual.”

Gender is a spectrum, but are there such things as “male” and “female”, or as “masculine” and “feminine”? Yes, absolutely there are. They’re partly biological and partly cultural, like everything else. I’m comfortable calling myself “male” nonetheless; this term is useful insofar as it points out a particular region on the spectrum. And it does! “Male” and “female” are useful categories, just like “poor” and “rich”. If you ask me precisely which traits make someone “male”, I’ll hesitate. I dunno, [such and such] masculine behaviors? I have no idea. But I’m male like Bezos is rich.

So my starting point is: Everything is a spectrum. Beyond that, we can chop up these spectra in all kinds of ways. Binary, two-piece chops are a common choice, but they often exclude large groups of people. On the other side, in the limit of ultra-fine chopping, we may find ourselves distinguishing each possible quantum or neuronal state, losing all the convenience of using words for different regions of the spectrum at all. We should talk about how to optimize, balancing both the inclusion of people and the usefulness of language with the fineness of our chops. Just remember that the chopping is done by us, not by Nature.

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