I have recently had a couple of lunches with Paolo Quattrone, a finance professor, and Michael Northcott, a theologian. The focus of our conversations have been around representing value (values). My involvement is centred on my interest in the nature of mathematics. Specifically, is financial mathematics a "truth-bearer" or is it a mechanism of discourse. The dominant philosophical paradigm sees language as being made up of statements that are either true or false and complex statements are valid if they can be deduced from true primitive statements. This approach is exemplified in the standard mathematical technique of axiom-theorem-proof. Habermas, in the Theory of Communicative Action, replaces this paradigm with one that rests on a Pragmatic theory of meaning that shifts the focus from what language says (true or false) to what it does. Specifically, Habermas sees the function of language as being to enable different people to come to a shared understanding and achieve a consensus, this is defined as discourse. Because discourse is based on making a claim, the claim being challenged and then justified, discourse needs to be governed by rules, or norms. The most basic rules are logical and semantic, on top of these are norms governing procedure, such as sincerity and accountability, and finally there are norms to ensure that discourse is not subject to coercion or skewed by inequality. I have come to believe that reciprocity is important in financial mathematics because it is a norm that enables market discourse which seeks the truth (consensus) on value rather than it determining what is true.
Paolo is interested in how company accounts are used. My understanding of his position is that contemporary accounts are presented as a representation of truth, but their genesis was as focuses of reflection: you accounted for your actions. This was exemplified when I recently started reading Neal Stephenson's Baroque Cycle (a trilogy I strongly recommend - it covers some of the same themes as this blog but with more pirates and sex, what more could you want?) where Stephenson describes Isaac Newton writing down, accounting for, his sins one night. When I first read this section it passed me by, but Paolo has enlightened me as to the depth of Stephenson's story.
When we were having lunch, Paolo and Michael were discussing the fact that while today accounts are "annual" the original accounts were an "open book", they never "closed" the account. Michael is interested in this because it represents a theological conception of time that impacts on ethics. Specifically, modern business practice, built on science, rests on the distinction between now and then, here and there, a distinction that does not exist for believers in a transcendental deity.
I was immediately interested in Michael's position, which motivates his interest in environmental issues, because it is very different from mine. The topic that most interested me at school was entropy and how we know time moves forward: because things become disordered. As a teenager I justified my messy bedroom to my mother as a consequence of the indubitable laws of physics. Interest is charged because the lender is uncertain if the borrower will repay in the future: time exists in finance because there is uncertainty. Believers in a transcendental deity see uncertainty as a subjective problem, the deity does not experience it. I think this could explain why mathematical probability was developed by Augustinians (Calvinists/Jansenists) such as: Pascal, Huygens, Bernoulli, Montmort, de Moivre and Bayes; and not by Anglicans (Newton) or Lutherans (Leibnitz). Augustinians believed that, like time and space, there was/is an absolute measure of chance.
While modern physics accommodates uncertainty it does so in a statistical context. for example, Poincaré's recurrence theorem theorem states that any bounded system (i.e. a bounded universe) will eventually return to its original state, and because the laws of physics are deterministic, it will repeat its evolution: while a gas looks random, it can be considered a (statistically) deterministic system. A simple solution to this paradox is if we introduce 'radical uncertainty' and consider the universe as a non-ergodic system. The fact that no one thinks this is the obvious solution probably indicates it will open a much nastier can of worms for physics.
Noah Smith has argued that
Physics intuition is all about symmetry, and about finding elegant (i.e. easy) ways to solve tough-seeming systems. In econ, that rarely matters at all; the intuition is all about imagining human behavior.This is all true and also explains why physics intuition is often unhelpful in an economic setting. When physicists talk about symmetry they are talking about something being invariant under transformation, i.e. there is something unchanging in nature that can be fixed upon and there is something being conserved (Noether's Theorem). The issues I have with economics adopting physicists intuition will evaporate when someone can identify, and justify, what it is in economics that is invariant: what quantity is being conserved. The reason why economists focus on human nature is because human nature is inconstant.
Time is important in theology, finance and physics. I don't understand, or even know, the details of what the current consensus on time in physics is, but my intuition is that time in physics does not generally have a direction, and while there is a thermodynamic arrow of time (entropy; modulo recurrence) at the quantum level, dominated by uncertainty, time is symmetric.
Where I have a real problem with physics is in the area of multiverses, particularly the many-worlds interpretation of quantum mechanics. As far as I can tell, the many worlds interpretation exists because physicists don't like the idea that when a wave function collapses it collapses simultaneously across the universe, information is transmitted at a speed faster than that of light. We mock medeival scholastics for having (apparently) argued about how many angels could dance on the head of a pin: yet we take physicists and their multiworlds, employed to address a technical issue internal to physics, seriously. My issue is that they appear to resolve their problem, of having to deal with a probability distribution, by replacing a difficult issue related to time and radical uncertainty with an "ensemble" interpretation. My frustration with Ole Peters is because physicists believes in the ensemble approach to uncertainty (that there exist an infinite collection of paths and the universe is on one of these paths) and then suddenly realise it is a bit meaningless in economics.
In the aftermath of the discovery of evidence for gravitational waves the theologian Giles Fraser has argued that science is becoming like religion: it argues that asking what came before the Big Bang is a non-question, just as monotheists argue the question who created God is a non-question. A response from the physicist Jon Butterworth is that physicists deal with the nature of the universe while theologians address the meaning: a fact/value dichotomy. While Butterworth acknowledges that there is an interplay between fact and value, I actually think the interplay is far more important than Butterwoth implies. My case in point, time, clearly demonstrates this. The problem Michael, theoretical physicists and I have with time is that, for me at least, there is no clear demarcation between the nature and meaning of time. In fact the nature and meaning of time could well be ambiguous, even within physics, and scientific integrity demands we take this possibility seriously.