Former Bank of England Governor Mervyn King’s excellent book The End of Alchemy is inevitably noticed mainly for its views on the future of banking regulation and the outlook for the Eurozone.  But for me the most important message of the book is its emphasis on radical uncertainty.

That emphasis reflects parallel intellectual paths we have each taken since we were young dons at St John’s College (he at Cambridge, me at Oxford) forty years ago.  In a book published in 1976 Milton Friedman disparaged an older tradition which ‘drew a sharp distinction between risk, as referring to events subject to a known or knowable probability distribution, and uncertainty, as referring to events for which it was not possible to specify numerical probabilities’.  Friedman went on ‘I have not referred to this distinction because I do not believe it is valid.  We may treat people as if they assigned numerical probabilities to every conceivable event’.

This is what we were taught, and what we passed on to the next generation of students.  It seemed an exciting time for young turks in finance; insider trading within an old boy network was to be superseded by a new generation of quants and rocket scientists. We had the mathematical tools to revolutionise investment banking. Our theory came to underpin the risk models used within financial institutions and imposed by regulators.

But Friedman was wrong.  There really are limits to the range of problems susceptible to the mathematics of classical statistics.  Friedman was, erroneously, rejecting the concept of radical uncertainty described fifty years earlier by John Maynard Keynes and Frank Knight, the concept memorably described twenty-five years later by Donald Rumsfeld as ‘the things we do not know we do not know’

   ‘By uncertain knowledge’ Keynes wrote in 1921, ‘I do not mean merely to distinguish what is known for certain from what is only probable.  The sense in which I am using the term is that in which the prospect of a European war is uncertain, … or the position of private wealth owners in the social system in 1970.  About these matters there is no scientific basis to form any calculable probability whatever.  We simply do not know’.

While the long term future of interest rates or copper prices, about which Keynes also speculated, might be approached probabilistically, (how), questions about the nature of the social system fifty years hence are too open-ended, and the outcomes too varied and insufficiently specific,  to be described  in probabilistic terms.  Philip Tetlock’s recent book on superforecasters illustrates the point well.  By trying to turn multi faceted questions into ones precise enough to enable those who proffer answers to be assessed for their accuracy, he makes the questions narrow and uninteresting: ‘how will the Syrian war develop’, and ‘how will Europe manage its refugee crisis?’ become ‘how many Syrian refugees will land in Europe in 2016?’

But more fundamentally, there are things we do not know because we cannot imagine them. If you had described your smartphone to Milton Friedman in 1976 he would not have understood what you were talking about, far less been able to speculate intelligently on the probability that it would be invented or bought.  These are the ‘black swans’ that Nassim Taleb has described. The reader who once wrote to me asking which ‘black swans’ were most likely to materialise in the next five years could not have missed the point more comprehensively. 

  There is a world of difference between low probability events drawn from the tail of a known statistical distribution, and extreme events which happen but had not previously been imagined.  And it is usually the latter, not the former, that give rise to crises – and opportunities.

The references are to Friedman’s Price Theory, 1976, and Keynes’ Treatise on Probability, 1921  (and Knight’s Risk Uncertainty and Profit 1921)