What if, and if so – What Then?

What if Pic

A contender for the shortest quotation in history must surely be – ‘If’. The story goes that, in ancient Greece, Philip of Macedon issued the threat to the Spartans: ‘If I enter Laconia I will raze it to the ground’. Their singular retort – ‘If…’ – with its mockingly fearless gravitas (and from which comes the term ‘laconic wit’), is said to have deterred the vaunted incursion.

‘If’ plays a large role in human thought and behaviour. It facilitates the perception and expression of possibility. It prepares us for action and interaction; every game we play pivots on this pointed conditional.

Game theory is the branch of mathematics popularised by the film ‘A Beautiful Mind’, which portrayed the troubled life of genius mathematician John Nash, who proved that every game (more precisely, every rationally played game) has at least one state of equilibrium in which each player’s gains converge upon a reciprocally optimal value.

So whether you’re shopping for high street bargains, insuring your car, or buying and selling shares in the stock market, you are playing the kind of game to which Nash’s equilibrium applies. You and others are haggling, hedging, or holding out in order to maximize gains and minimize losses. Life can seem a never-ending sequence of games with new rules to learn and old ones to fall back on, and the simplest of strategies invariably begin with the ubiquitous ‘if’: buy if low, sell if high, drive if raining, run if late, wait if early etc.

But that’s not the whole story. ‘If’ would be nothing without ‘then’, ask any computer, better still, ask any computer programmer. Recall the basic number sorting programme in ‘Free Will – The Special Malfunction’, which detailed the consecutive criteria necessary to separate a sequence of numbers into the categories ‘odd’ and ‘even’? Each step required an ‘if…then’ statement and they all worked together to ensure the success of the overarching condition: if the number is odd then store it in ‘odd’, if not then store it in ‘even’.

You may notice the absence of ‘then’ from the original algorithm in that article but its presence is nevertheless implied (as in – ‘if low then buy’, ‘if raining then drive’ etc.). In programming languages ‘then’ is explicitly included in conditional instructions in accordance with the unambiguous requirements of Boolean logic.

While ‘if’ helps us to quantify possibility, ‘then’ enables us to evaluate consequences. Returning to game theory our projected gains and losses are consequences we either aim for or avoid, depending on our strategy, and they range from the trifling to the monumental. So there is a lot to be said for garnering as much knowledge as we can before making a particular decision, lest we overlook seemingly trivial consequences which could subsequently accumulate and thwart our best-laid plans.

If chaos theory has taught us anything (see Brains, Vats, and the Inner Outer Space Race), it is that many – if not all – outcomes involving human behaviour are unpredictable. In the financial markets (where the application of Nash’s work earned him his Nobel Prize) the movement of every share price is fed by, and feeds into, the collective force that is ‘the market’. Nothing is certain and every investment decision is a gamble with varying odds. Traders keep their ears to the ground for timely and relevant information which will inform both their short and long-term strategies. Yet for all their diligence and acumen their successes depend upon criteria that are at best relative: buy if low, sell if high is certainly sound advice – but how high is ‘high’? And how low is ‘low’?

An ‘if…then’ statement either asserts or commands and this means that we ourselves must handle the responsibility of choosing our response to it; if it asserts a particular fact we can immediately defer to its authority without further question, or reject it; similarly, if it prescribes a course of action we can choose to follow it blindly; or ignore it completely. In the words of physicist Richard Feynman ‘In any decision for action, when you have to make up your mind what to do, there is always a “should” involved, and this cannot be worked out from “if I do this, what will happen?” alone’.

‘If’ and ‘then’, therefore, certainly do a lot for us, but they can not tell us what we should do. We’re all familiar with such phrases as ‘rules are made to be broken’, and ‘the exception proves the rule’. They tell us that no course of action is necessarily justifiable, and that no set of rules exhaustively covers consequences and possibilities. Perhaps such limitations are what, paradoxically, make games possible and desirable in the first place. Philip of Macedon, in his classic ‘war game’, never expected his one-word reply; such is the nature of wit. And at the turn of the millennium when the dot-com bubble finally burst many investors had no idea whether to get out or stay in because there was no definitive way to tell if a price was too high or too low.

In summary, it appears the conditional is provisional. And if I’m wrong, then that still proves I’m right! This could be mere wordplay of course; a gamble, even. But I do like my odds.

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