mathematical desire

(c) Randall Munroe (2010)

Model of romance for you. Say there are two functions:

• A(y) – how attracted person x is to person y, and
• R(y) – x's respect for y.

Then, two composite functions with each other:

• R(A) - how much respect x has given a degree of attraction, and
• A(R) - how much attraction x has for a given level of respect.

If we assume that they aren't symmetrical (that people can have non-monotonic functions), then romantically active people all fall into 2 or more of 8 exhaustive romantic functions:

SUPPLY-SIDE [If A(y) goes up --> R(y) goes up]. R(A) is proportional: x is ruled by beauty's halo. (X is shallow.)	More eye pop, swell chest
[If A(y) goes up --> R(y) goes down]. R(A) is inverse: The mind's revenge. (X is sadistic.)	More eye pop, shrink chest
[If A(y) goes down --> R(y) up]. R(A) negatively inverse: Hm! (X is maybe insecure?)	Less eye pop, swell chest
[A(y) goes down --> R(y) down]. R(A) negative proportion: Reverse halo. (X is nasty-shallow.)	Less eye pop, shrink chest
DEMAND-SIDE [If R(y) up --> A(y) up]. A(R) is proportional: A just and rational desire. (X is blessed.)	Swell chest, more eye pop.
[If R(y) up --> A(y) down]. A(R) inverse: The mind's disdain for the body. (X pedestalises.)	Swell chest, less eye pop.
[If R(y) down --> A(y) up]. A(R) negatively inverse: Masochism.	Shrink chest, more eye pop.
[If R(y) down --> A(y) down]. A(R) negatively proportional: Dignity (or purity).	Shrink chest, less eye pop.

Quelle surprise, those that have attraction determining respect (5&8) are the humane ones. But there are more perverse strategies than healthy ones, and can you say you’d be surprised if this were borne out empirically?

James points out the need of a reflexive self-respect variable, R(x), to really see the shape of an ordinary relationship (since we're drawn to people who are in some respect better than us). [If R(x) > R(y) --> A(y) down.] and [If R(x) < R(y), A(y) up.]

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It is equally fatal to the spirit to have a system and to not have a system. One will simply have to combine the two.
- Novalis

Now, the exercise is laughably incomplete, missing as it does dozens of salient variables* as well as the internal poetic significance - what feels to be the whole point. (For any given individual, I would guess the above R-squared of the above at less than 0.3.) In fact just adopting this nasty economic-sociobiological posture dissolves the thing's poetry. But nothing can talk about everything.** The model’s as simplistic as can be and still illuminating, and that's the interesting bit; how much of us can you show up, how surprising can you be, with just two quantities and four relations. To me the options seem to be: entertain theories***, or settle for courageless commonsense (in which I include intuition). Aporia – the aseptic procedure for handling the debilitating pathogens, ideas – is a rare talent. Its opposite, human dogmatism, is the default but it's our failure, not theory’s.

When is a model unacceptably distorting, though? (Can we model that?) People who take the above line must be clear with themselves about when models become liabilities. This happens when: the class of mathematics used is too restrictive for the class of problem (generally true of human affairs, though do note Nate Silver-style stats); when the use of precise maths implies we have solutions where we have none or can have none; and above all when the model obscures more of the phenomenon than it uncovers. There could be good theories we wholly lack the maths for. People who think formally about people should remember they are heuristics: we use theory as a conditional reminder of the complexity of people, rather than a predictive or exhaustive encapsulation of them.*****

* e.g. The interval between the two's self-respect, simple proximity, parental influence, inverse parental influence, y's place in local pecking order, degree of shared interests, romantic anosognosia (or the whole subsystem of casual criteria)...

** You might say that theoretical silence preserves more than any theory can state, but I think you'd do silence too much honour. It doesn't mean anything to mean everything, and implying anything's the same.****

*** This claim is close to ludicrous fiat, saved from it only by my saying ‘theories’ rather than ‘a theory’.

**** What about Tractarian silence? Sure it's a peerlessly beautiful thought, but people divorce it from the properly hellish mathematical world that gives it its punch and significance. No-one is a Tractarian (except the very ill), because life would be intolerable without the nonempirical kinds of meaning the Tractatus shoves out of language and almost out of life.

***** All right, all right, let's say you've justified precise theorising about fuzzy humans. Why cloak it in maths, a rhetorical device that repels 80% of even the educated world?******

****** Look, it's a joke, A JOKE I TELLS YA!

XKCD (2000)