Ah! I feel like I've got a more concise idea of what I've been trying to get at with clumsy writings about mathematics and politics and so forth. Reactionary ideologues and other persons who espouse beliefs that make no sense nevertheless believe they're logical. Their brains are doing their best with what they have, trying to connect everything together into some sort of mental framework. To them...it all makes sense. Why exactly do they feel like they're constructing faultless logical edifices?

Human brains are squishy, so whatever physical entities correspond to "thoughts" and "concepts"—I can vaguely imagine some fearfully complicated function of thousands or millions of different chemical gradients throughout overlapping regions of body and brain—are likely to have a sort of...analogue nature. You can whimsically imagine a puff of "thought molecules" spreading outwards through the tissues of the brain and the body, slowly dispersing, and while there are no particular "thought molecules" in the human brain, there are a moderately limited range of inorganic and organic substances, some uncharged, some electrically charged, which are specifically pertinent to thinking and neural function. Chemical gradients are rarely very steep, so the world of organic life and thinking is one of smoothly rising and falling curves, an analogue world.

And thus, I think the reactionary ideologues (and others) are deceived by their own bodies, in a sense. Their lives are dominated by phenomena that occur on biological timescales and with biological smoothness (or squishiness), phenomena that are in fact easily modeled with relatively simple mathematical operations. Astonishing complexity may emerge from the Navier-Stokes equation, for example, but the equation itself is straightforward and amenable to numerical analysis and computer modelling.

Hence I conjecture that they unconsciously apply that sense of mathematical simplicity onto everything. Their lives are always rising and falling according to simple mathematical laws; therefore the Universe must also be "mathematical" in the same way.

~Chara of Pnictogen

Everyone (I hope) knows these days that one of the biggest comedy celebrities of my childhood, America's favorite TV dad for a while, former standup comedy superstar Bill Cosby, is a gross sexual crook. I didn't take the news well because, growing up, I was a massive fan of Cosby's standup work. Both my sibling Frisk and myself scouted thrift shops to build up a library of comedy LPs and Cosby had some pride of place in that collection. Now, though, I ask myself why we didn't ask ourselves harder questions about some of his material, like his "Spanish Fly" sketch—where he's basically laughing about the idea of drugging women for sex—or the misogynist flavor of his depictions of marriage. Does he ever have a positive word to say about his wife?

All the same I haven't "cancelled" Bill Cosby and I still listen to some of his stuff on YouTube, for the same reason that his standup attracted my interest and Frisk's interest in the first place: he told funny stories about being an unhappy child. If you've seen Martin Scorsese's astonishing film The King of Comedy, you might remember how Rupert Pupkin's routine, the one that he's willing to commit crimes in order to get on television, is largely about how his dad's an abusive piece of shite. Pupkin's material is...middling, at best (it's not awful). Bill Cosby supplied the top-quality version of such comedy material, getting his audience roaring about his parents would beat him and his brothers, and how terrified they were of their father in particular.

Now, Frisk and I did not have a childhood THAT frightening, in comparison. All the same our household was unhappy and argumentative, so without really knowing that we were looking for it, we were drawn towards comedy like Bill Cosby's, humorous depictions of family misery. Where else could we find anything like it? We despised most situation comedies on TV because of the nauseating falsity of the families on display. Even Bill Cosby's TV family didn't seem that convincing—partly because we could recognize that he was going through some of his old standup material and making it mainstream-friendly, and that was no fun. Maybe child abuse would get the Very Special Episode treatment from a TV show. Only the standup comedy stuff seemed real, even if we knew it was comically exaggerated.

~Chara of Pnictogen

There's a sort of "as above, so below" principle at work when people get drawn into organizations that suit them, and surely that's a completely unoriginal observation. People whose conscious minds yearn for order and hierarchy join hierarchical organization. Folks who dislike such rigidity end up in loosely-knit, fluid groups. Solitary persons avoid groups altogether and become free agents and "heterodox thinkers" and such.

What inferences can be made, then, about the overwhelming yearning for the "Inner Ring"? I derive this phrase from the writings of C. S. Lewis, who gave that title to an essay (https://archive.is/HMFOz) and referred to the concept elsewhere. His novel That Hideous Strength is, in part, about a young man's unhealthful fixation on seeking "inner rings" and where that fixation ultimately leads him. I don't take every Lewisian idea seriously but this one seems quite practical, and I've seen it for myself and even gone after it myself, without quite realizing that's what I was doing. When I was trying out churches and covens and similar groups in earlier years, mostly I was looking for surrogate family, but with an undercurrent of zeal for learning the big secrets and joining the society of those who really knew how the world worked.

Maybe that's a good starting place for speculation. If you're harboring a powerful desire to meet the true movers and shakers of the world, applying the "as above, so below" principle implies that inside yourself are the "true movers and shakers", the entities or forces that rule over your psyche and supply your most powerful drives. Inside you there are two sharks and they're both queer—you know, that sort of thing. More seriously, we could reach for the major divisions of human life or the human psyche that have been postulated by numerous different philosophers and psychologists. Id, ego, superego; animus, spiritus, corpus; who knows how many of these models exist, but they all have a fundamental trait in common, which is the hypothetical subdivision of what seems to be a single unit—human life or human awareness—into a small team of oligarchs, all presumably cooperating, all hopefully in balanced equilibrium.

Presumably, though, this is true of everybody, if these models are valid. Those philosophers and psychologists hoped that their models were true for every human being, and not every human being is running around looking for the Inner Ring, hoping they can befriend the true masters of the Universe. Why would they want to do that...unless their inner team of triumvirs or tetrarchs, the "inner ring" of psychic forces that keeps them going, was unhappy?

Why does anyone seek the vicinity of the powerful? There's practical advantages of course, worldly benefits—money, influence, greater freedom to indulge the pleasures of the moment. But surely these things are most alluring to those who are unhappy, who feel powerless to obtain happiness for themselves, and therefore look upwards or rather inwards, hoping to find the people who really and truly have the power to change destinies. We can perhaps imagine the inner triumvirate of such an unhappy person always restless, always talking amongst each other, always tossing unsolved problems back and forth among themselves: "What do we DO? We're supposed to make this human being happy, and we're failing. What's the secret?"

As below, so above: the person whose inner world is constantly exchanging worries and fears back and forth seeks the external company of people who are constantly exchanging worries and fears back and forth. Inner "conspiracy"—i.e. the oligarchs of one's psyche always whispering together in consternation, trying to figure out how to fix things—seeks its counterpart in real-life conspiracy.

~Chara of Pnictogen

Over the years I have come to form a vague but persistent conviction that there's a distinct analogy between reactionary ideologies and certain mathematical constructs.

To the true believer of (say) "ethnonationalism", their ideology must surely make sense in their head, feeling as sound and whole and true as a mathematician's appreciation of a complicated proof. It's been a long time since I've worked complex mathematical problems but I'm aware of the clear cold feeling of truth that comes with successfully working out a difficult exercise. It's like a sudden gust of wind from a high snowy mountaintop, or like the pleasurable sting of being hit in the face with cold water on a hot day. One feels, for a moment, as if illuminated by starlight. I have no doubt that all the fascist ideologues I've seen scurrying around on Twitter, with names like "TheSensibleCentrist" and "Apollonius of Fresno", or the ones who proudly advertise a long string of memberships in "non-political" think tanks, all believe they've experienced this same brisk, bracing feeling of uncovering a deep truth. They must feel like their ideas make sense.

And I think perhaps they do make sense, but in the same way that a Klein bottle makes sense, or the way that one can find solutions for otherwise impossible mathematical problems among the complex numbers, i.e. numbers that have no physical representation. "Imaginary numbers" excited my imagination (hah) as few other intellectual concepts did, when I was a child learning mathematics. Aha! negative numbers do have square roots! So they do, but a "real" square root may be constructed with a compass and straightedge, while an imaginary root can only be represented symbolically. The real root of a function is a dot on a graph; the imaginary root isn't to be seen on the graph at all and must be obtained through symbolic manipulation. Not all mathematical entities, even if they can be logically defined and manipulated as readily as ordinary numbers, have no concrete form. One can't assemble -5 + i√2 beans in one place.

Hence I conjecture that extremist ideologies of all sorts, not just right-wing ones, must have some equivalence to such virtual constructs in mathematics. They can be defined and discussed, but they can't ever be realized in the material world, any more than one can construct a real Klein bottle, only an approximation or lookalike to one. In the heads of the "gender critics", for example, their ideas must make perfect sense and seem like the only logical ones. They measure the rationality of the world against their bizarrely contorted (but logically consistent) hypotheses, find that the world doesn't measure up, and blame the world for not being real enough. They would like to codify their ideas in a fully rational and concrete form, because then it would be persuasive. They can't ever get it quite right but no matter, they'll keep trying the way that people are still trying to "trisect the angle".

The example of the Klein bottle is especially useful here, for the difficulty with building Klein bottles and many other such mathematical surfaces is that they require "self-intersection" in three dimensions. If we could somehow imagine two wholly separate pieces of matter occupying the same space at once, as if they could pass harmlessly through each other, then you could make a genuine Klein bottle, but real-life matter does not behave that way. One sees something like "self-intersection" happening with fascist ideologies. Consider the "doublethink" involved in the infamous TERF slogan, "Sex is Real", which seems like mere tautology. The slogan works for them because of "self-intersection". The word "Sex" is carrying a heavy load of multiple meanings. They wish outsiders to see "Sex" and think of real-world things—sexual things. But they also wish "Sex" to mean something subtle and insidious and indeed metaphysical, referring to their absurd desire to enforce the "laws of biology" through coercion and violence.

Can this be formalized somehow? The analogy between harmful ideology and abstract mathematical constructs seems so natural that I'm persuaded to believe that it's valid and can be thrashed out in some practical form.

~Chara of Pnictogen

An excellent response, and I'm trying to figure out how to respond, and explain further where I was coming from.

It's something like this. I don't think that a fascıst ideologue has actually worked out their reasoning in advance. I don't think they've consciously reasoned out their beliefs—indeed, I think it's likely that many of their core beliefs are things that they don't even recognize as beliefs, because in order to maintain themselves in public they need to avoid articulating everything that's on their mind. However, I've come to think that they must FEEL, in a wordless way, that all their ideas hang together into a coherent pattern. They must feel the sort of certainty that comes from thinking they've got everything worked out in their heads. Hence I conjecture that, internally, their minds must contain some sort of coherent system—some construct in which every concept links up, in a locally rational manner, with other concepts. I don't think the kind of certainty that these people think they have, their indomitable sense of rightness and certitude and purity of logic, can possibly exist merely through bluff. In some way, their beliefs must make sense to them and all link up with each other in a logical way.

Hence I conjecture that they're able to do so only through constructing logical systems that are mathematically equivalent to "impossible surfaces". I don't think they're doing this consciously. I don't think they're even thinking about mathematics at all! But I think they've constructed chains of reasoning to defend their beliefs that are "impossible", and if you could map their interconnections among concepts in some 3D way, I think you'd see the equivalent of an "impossible" or self-intersecting surface.

~Chara of Pnictogen