A correspondent has pointed out that my ignorance of maths, and general stupidity, has led me to make a sharp distinction between 'Knightian Uncertainty'- i.e. 'a lack of any quantifiable knowledge about some possible occurrence' or, in my formulation, lack of knowledge of what are possible states of world or what probability distribution is assignable to them- and such Uncertainty as arises out of 'Pontryagin duality'- i.e. situations where, on a locally compact Abelian group (i.e. where commutativity obtains) there is 'conjugacy' or duality such that measuring one variable with less and less error causes its conjugate variable to be knowable only with a bigger and bigger error term. Consider the formula MV=PT- i.e. money stock times velocity of circulation equals price vector times transactions matrix. It is an accounting identity. It says that total money income equals stock of money times its turnover. If you measure Money with increasing precision.... what happens? The answer is you realize that Money isn't precise enough to be measured. Prices may seem precise on open markets- there is an eigenvector- but Transactions aren't at all. If you try to tamper with M so as to affect P or T, you fuck up. Goodhart's Law applies. Whatever previous correlation existed between M and P breaks down because you have tried to instrumentalize M. There is no 'commutativity' and thus no fucking 'Abelian group' here at all.
Option pricing models, based on an assumption of efficient markets and which focus on volatility- e.g. Black Scholes- are looking at the behaviour of the error term or 'volatility surface'. It does not matter how this is modelled so as to match what obtains empirically. What is inevitable is that there will be duality between calculation speed and the resource intensitivity of the simulation. But that is an artefact of the model. There is no conjugacy or self-adjointness in the underlying asset class. In essence, all that is happening is a best guess as to how 'netting out' should be done at any given moment. But it is merely a guess. The fact is, there are good reasons why 'Aumann agreement' may not obtain. In other words even people using the same model and with the same priors have reasons to value options differently because their interests differ- i.e. there is agent heterogeneity and thus 'uncorrelated asymmetries' dictating different 'bourgeois strategies'. This could be explained by different 'hedging' and 'income effects'- i.e. the same reasons General equilibriums without Knightian Uncertainty are 'anything goes'. Thus fintech uncertainty, which is about volatility, is not Knightian. Because of duality regarding calculation speed & complexity, there is something which looks like conjugacy but it is similar to what obtains when deriving supply curves from cost functions or demand curves from implied utility functions. It is merely a matter of the akreibia (grasping after greater precision than the subject matter allows) of the model and has nothing to do with economia- i.e. the proper economic method of dealing with choice under scarcity. No doubt, the dynamics of this type of management, coordinated through the market, has Knightian uncertainty. But this is a coevolved process which is not memoryless. There is a damming up of capacitance diversity. No doubt, there are forgetful functors mapping to any given class of contingent assets. But there are many classes of contingent assets- indeed, by definition, their existence is...wait for it...contingent! If transaction cost and speed is zero, sure, there could be full and faithful functors but, in that case, you would not need language or any type of signaling device. Also evolution would not be a true theory. We would be monads synchronized by an Occassionalist God.
Obviously, no functor which comes under the rubric of 'co-evolution' can be Abelian, or be otherwise 'intensionally' specifiable, save, perhaps, at the 'end of time'- otherwise there is a better than Godel, teleological, not ontological, proof of God.
With reference to 'duality' or 'conjugacy' , what is crucial is the notion of 'naturality' or 'non-arbitrariness' or 'canonicity' or 'normal form'. In other words, either this is a field where everybody, no matter how they approach it, would agree that there is some most efficient and productive manner to define its terms or else it is a playground for incontinent pedants and pedagogues smearing themselves with their own shit.
In other words, either 'intensionality' obtains 'by nature' and we are carving up the world along is joints or as St. Paul puts it 'dividing the word of truth' as God intended or else some stupid Pundits are shitting higher than their arsehole.
Suppose such 'naturality' or 'canonicity' actually obtained. Then any 'blind' Darwinian process would hit upon it within a few iterations and this would be a 'robust' solution. In other words, even if the thing is 'non-deterministic', we could 'in silico' get 'black boxes' to verify valid solutions very quickly even if the actual proof is in a higher time class. Put another way, though we would not have a 'gnosis' or 'light-box' or 'substantive' theory, still, for any practical purpose, we'd have cheap and cheerful almost 'zero-knowledge' proofs for anything we needed. Category theory would be the final incarnation of Left Hegelianism. William Lawvere's Canada would have led the world out of that Slough of Despond into which the American and French and Bolshevik Revolutions precipitated us, back into the sunny uplands of a truly Tory- i.e. non agon (or antagon)-istic- 'Kingdom of Ends' where there would be no 'scarcity' because genuine 'needs' would be the conjugate of 'wants'. Alternatively, if the Canadians- by reason of having no souls- couldn't step up to the plate, perhaps a Mochizuki could have put Ninomiya General Equilibrium (which makes 'giri' conjugate to 'ninjo'- i.e. deontics to empathy- in a manner perfectly 'Hegelian') on a sound basis of pragmatics and 'piece-meal social engineering' such that us boomers needn't have a bad conscience about the diminishing demographic horizons of our sons or (if we have any) grand-kids.
Obviously, what I am really saying here is that Canadians have no souls because they- being so fucking determined to being so fucking super-nice all the fucking time- permit themselves no equivalent to Jap nohonjinron discourse.
Why isn't there some easily understandable Wikipedia article which quickly captures all the essential aspects of the not elite 'Laurentian' but D.H Lawrence type, bottom up, psycho-sexual Canadian ipseity vs the World's perverse alterity or, its masochistic, reverse conjugacy or kategoros?
Lawvere wasn't actually Canadian. Orrell is. I urge him to seek a Canadian kokugaku rather than some Quack Quantum Econ. Otherwise he is merely the uglier and more obviously ignorant anti-particle to the not entirely useless Jordan Petersen.
To conclude, guys who actually do useful stuff- as opposed to stupid pedagogues or book-keepers or whatever- deal in mimetic, not mathematical, certainty. Indeed, for anything multiply realisable, it generally makes more sense to appeal to mimesis not mathesis.
Thus Orrell- a gelding bleating to be accorded the kudos accorded a Karan Barad- who had the good-sense to retain 'her' as her favoured pronoun- is but a 'convergent evolution' type mimesis of my own illiterate, utterly innumerate, Socioproctology which, however, represents the only utile way forward. Why? Canadians do too have souls. But, in accordance with that 'parhessaic' and univocally Soteriological formula first articulated in 'Team America- World Police'- they need to be dicks about it, not assholes or pussies.
I will now briefly dispose of my correspondent's objection that I was wrong to see Knightian Uncertainty as wholly distinct from such as might arise from a Mathematical formalism.
Here is my argument. Frank Knight- being an Econ Prof- had shit for brains. Seriously. Read his stupid shit for yourself. I only appeal to 'Knightian Uncertainty' coz the thing is funny. Also it's a bit M. Night Shyamalamadingdong- i.e. initially looks smart, builds narrative tension, but then just turns to Pico Iyer level narcissism, solipsism and faux-Sufi, self-regarding, shite.
I'm not saying Evolution aint making every relevant e.s.s Hannan consistent. I'm just saying Iyers not actually paid money to do useful or soteriological stuff are almost infinitely smarter than Canadians who decide to 'shit higher than their arseholes' without actually becoming either Mounties or such Moose as might mount them.
But this is only because acharabrashta Iyers like me are shit. Canadians aren't at all. Like the vast majority of Tamils or Transylvanians or whatever- they iz gud peeps.
Fuck u Orrell! U r trying to compete with genuinely stupid Iyers and fucking up nevertheless coz u r shitting on Math.
This is funny when Bengalis do it. But u iz Canadian= elder sister of Commonwealth! Mind it kindly. Aiyayyo.
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