Have you ever noticed that laughter and fear are basically the same? (Up to, or modulo something that has the discursive structure of an ambit, at least.)

This idea came to me as a counterintuitive reversal of what’s implied in the actual dynamics of these processes; but as it turns out (you can research this yourself, the referencespace is huge) the physiology bears what earlier on was a radical hypothesis — a false concept on whose marrow to suck. So this raises a follow-up question: if the physiology of laughter and fear is roughly comparable, what’s the quotient here? To spell out unusual terminology: in the phrase “laughter and fear are the same modulo X”, what’s X?

The beautiful theory of algebraic topology, quickly shaping into one humanity’s great achievements, is concerned with the classification of spacelike objects (here I’m glossing over with great violence the meaning of “topology”) up to X. What’s ultimately desired is to classify objects up to homotopy. Homotopy equivalence between two objects means that a continuously-varying family of intermediate objects can be found: in the following picture, we can imagine a continuous thickening of shape A that ultimately leads to shape B.

A or B

(Image source: Google Image search, but concretely this)

The better-known illustration is that, up to homotopy, a donut and a coffee mug are the same. Mathematicians love their counterintuitive truths, but from a broader theoretical standpoint this undersells the radical ambition of this program: to upheave naïve metaphysics of identity (implied, for example, by the analytical geometry according to which A and B are rigorously distinct) while establishing a process view of identification: A and B are “like” each other because they can be deformed into each other. In broader terms: there’s a path that A can undertake to become B, and symmetrically a path that B can undertake to become A. This is an ethical program.

(motu propio)

The following is a slightly less violent restatement of homotopy — still meant for broader theoretical and philosophical usage; you can’t learn math by reading. (1) A set is a collection or family or otherwise box of nonduplicate items, often called “points” for coolness. (2) A function f: U->V between sets U and V is a pairing that associates points u1, u2,… of U to one point f(u1), f(u2),… of V each. (3) A space is a collection of points with a vicinity structure. The vicinity structure tells you when two points u, v are close together: it’s a collection of closeness-concepts. (4) A function is continuous if whenever u, v are close, then f(u), f(v) are close. (5) The cartesian product U x V is the set of all pairs of elements of U and V; particularly, the cartesian product U x [0,1] is a set that stacks many copies of U, as many times as there are real numbers between 0 and 1. (6) A homotopy from U to V is a continuous function from U x [0,1] to V. Note that this function is both continuous in U (you can’t tear apart points that were close together) and in [0,1] (there can’t be leaps between adjacent versions of U, even if each is untorn). (7) U and V are the same up to homotopy if a homotopy can be obtained: if a path that obeys the axioms (which in the limit are undistinguishable from moral laws) of topological continuity can be found.

We had just declared that homotopy equivalence was an ethical program. This was something of a rhetorical overreach; it’s sometimes necessary to pause on key turning points so we can appreciate the madness in them. The better formula is: homotopy is a model for an ethical program. Humans act, in the general case, following a mashed-up conflation of is-nesses and ought-nesses. The radical distinction between is-nesses and ought-nesses, which has really been long established by men like Hume, is a minimorum prerequisite for being able to speak in-and-about axiologies at all, let alone General Axiology. If this distinction doesn’t “stick” in how people act, it’s because our ought-nesses are parameterized by is-nesses.

An if-then-else routine (or its homotopy equivalent) tells us what to do if we find a person lying face down on a sidewalk: is this a man or a woman? does he look homeless? does she look middle-class, similar-enough-to-me? Uriel Alexis’s “reality rules!” speaks to this fundamental is-ness: have you noticed that middle-class women are more attractive than poor panhandling ones? Did we help the former because of their looks, because of tribal belonging, or because our is-ness model of the world tells us we can’t help panhandlers anyway? Uriel’s Razor says these reasons are all the same.

Neoreactionaries go further and tell us there’s one specific vicinity structure that makes the human population-space topological. This is how axiomatics and morality are indistinguishable: they’re both concerned with rigor that will preserve true knowledge (mathema). But indistinguishability doesn’t quite entail “the same”. Remember, a homotopy is continuous not only “space-wise” (arbitrarily close points mapping to arbitrarily close points), but “path-wise” (in [0,1]; an uninterrupted transition going forward smoothly). There’s no homotopy path between the if-then-else that leads one to ignore the homeless-looking dude and the one that leads one to dismiss him as someone who can’t be helped. There’s morality here, not ethics.


It’s somewhat distressing to google for the “difference between morality and ethics” and discover how widespread is the misunderstanding that there’s none. This is an incredible obstacle to the diffusion of axiological thinking. It does a lot to explain the emergence of professional ethicists who, profiting from the decline in religious spirituality, portend to speak from a place of lived-in wisdom (in the jargon, from truth-rain), through contemplation and towards action — three quick desiderata, a.e. non-exhaustive, that come up when imagining a newspaper column about ethics. The distinction between morality and ethics, much like the is-ought rift by Hume, has long been established by Spinoza and convincingly revived in the 20th century by Deleuze. But you needn’t be aware of these philosophical doctrines to have an under-the-skin feel for the distinction: a priest is someone who trains in morality but, when asked for advice, speaks in ethics.

It would be similarly distressing to learn that the distinction between laughter and fear had been forgotten. In all likelihood, there’s a deeper sense in which these are in equivalence — a homotopy-like path spanning a continuum of unintelligible human emotion. But there’s an obvious nonmoral view in which laughter and fear have positive and negative valences, respectively. The equivalence is obtained modulo some physiological generalities. Does this mean you should never scare someone for a laugh? People do this, it’s often fun for the victim too. Yet there’s a basic ethical choice to be made — in this frivolous example, one that’s not really that complicated — a path to traverse, in concrete action, through a pseudohomotopy class. The grand program of ethics — if it’s at all something that can even be squeezed like olive oil from the raw stuff of existential choice — is to classify all such scare-laugh-fright-fun situations.

All of this takes place in a fairly low-level axiology, mind you. As GPT-2 once said after ingesting a few of my writings:

At present we have no choice but to become stronger and do all of this in order to make the promise of General Axiology true: infinite wealth, infinite bliss, and unlimited freedom from our thought and actions – infinite power. We must also realise how to get stronger, stronger, stronger. As such, we can also gain the experience of developing new ways of living – and learn more when our efforts go ahead.

This also means we have to get the very basics right.

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