Think about it

Letters

Vol. 15 No. 6 · 25 March 1993

From Paul Taylor

John Allen Paulos (LRB, 11 March), explains how psychologists can devise situations which lead unsuspecting subjects to make supposedly irrational choices. This must be entertaining for lovers of practical jokes, but it is not clear what it reveals about human rationality. We are told that, when asked whether ‘r’ occurs more often as the first or the third letter of a word, people answer on the basis of the words readily available to memory. Does this show that people are irrational, or merely that they don’t think hard enough about the question? How hard should a rational being try, when answering such a pointless question? Research into irrationality requires a ‘gold standard’ of rational behaviour. Much of the work Paulos surveys adopts a mathematical theory of rational decision-making which indicates the correct choice when all options and their outcomes are known. However, such a theory cannot tell us how seriously to take a problem, whether to mistrust the evidence or to stop and look for other solutions.

The Imperial Cancer Research Fund is developing computer systems to assist in medical decision-making. We have found that the models used by mathematically-minded decision-theorists are of little use in complex situations where evidence is ambiguous and data may be missing. Much better results are obtained from models based on understanding what people actually do when confronted with a dilemma.

Paul Taylor
Imperial Cancer Research Fund,

Vol. 15 No. 7 · 8 April 1993

From David Pimm

John Allen Paulos’s odd non-review of the unfortunately-titled Irrationality: The Enemy Within by Stuart Sutherland (LRB, 11 March) did nothing to assuage my concerns about mathematicians’ imperialist meddling along the interesting borderlines between rational thought or behaviour and this ‘Other’ of ‘irrationality’, apparently to be reviled. There was a widely-differing range of ‘examples’ Paulos mentioned in his piece, though with no discussion of what each contributed to identifying or understanding irrational thinking. He generally cited studies by others rather than discussed what Sutherland had to say about them – assuming they even were from his book. At times, it was quite unclear whether what we got was just Paulos telling us about a motley collection of studies (e.g, the Wason experiment on cards) that he knew about.

Paulos informed us that a sequel to a great movie being not as great as its original may ‘simply be another instance of regression to the mean’. Eh? Pretty implausible, I thought but how to defend against such a claim? Does ‘regression to the mean’ explain anything – or merely explain away? What on earth could ‘the mean’ mean here, where there is at best a highly finite, underlying (and only potential) distribution (with the possible exception of the Rocky collection of films)?

The situation he reported with regard to the two different sums of money won with different probabilities shows a similar problem. The fact that mathematical comparison fails to distinguish the two scenarios may actually be a criticism of mathematics for not reflecting or attending to salient distinctions. The point is surely with the stage scenario that you can make the decision at stage one – and it depends on your gambling nature whether you take the then certain £30 or continue on for a second risk. The situations are not equivalent to me! His discussion certainly suggests that probabilities are things of this world that can be known or discovered. But probability is not part of the material world. It is not observable. Everything that happens, happens with 100 per cent probability every time. And I am often not interested in average expected gain. I am interested in the actual outcome when I carry out an action – and probability has almost nothing to say to me about that singular occurrence that has never happened before nor can again.

Consider the following situation. I have to decide whether or not to inoculate my child against whooping cough. I am told that the statistics about the vaccine causing brain damage are 1 in so many. I am also told that the statistics on child deaths from whooping cough are 1 in some other many. What do I do? My decision cannot be just to compare the two rates. That is to compare unalike things. My vaccination decision is now – and at the end of it I will either have a brain-damaged child or I won’t. The statistics on death from whooping cough only refer to a future possibility – once my child catches whooping cough. So I am trying to compare a present about-to-be-actual state with a possible future state. And these apparent probabilistic ‘facts’ fail to make important distinctions – the rates are not uniform geographically, nor across social class, to name but two. I can continue to make distinctions, until I get down to the actual circumstances of our life, even the genetic make-up of my child. Because that is what I am interested in – not average rates and likelihoods.

Paulos in passing mentions QALYs. On a TV programme a while ago, the sociologist inventor of QALY (the Quality-Adjusted Life Year) was interviewed and asked the pertinent question: is this a helpful way to think about the value of human life? In the telling subtitle to his book Computer Power and Human Reason: From Judgment to Calculation, Joseph Weizenbaum identifies precisely my major area of concern: namely, the way in which human judgments are being devalued and eventually ignored in preference to calculations – as if the latter were somehow preferable.

I end by offering a more interesting form of ‘irrational’ thinking, Gregory Bateson’s spectacular pseudo-syllogism:

Grass dies;
Men die;
Men are grass.

I think Bateson is onto something fundamental about how humans think creatively (and the implicit role of metaphor). But Bateson had no need of clothing such a style of creative argument (known pejoratively as ‘affirming the consequent’) in the virtuous trappings of ‘rationality’ and ‘logic’. There is much work to be done on the development of human rationality. I think it also worth exploring the concomitant fear of irrationality, one which I felt lurking beneath the surface of Paulos’s piece. He seems to see rationality as objectified with rules and procedures of its own – so I imagine that current discussions with regard to whose rationality, discourse and rules and procedures (e.g. Women’s Ways of Knowing by Belensky et al, or Gillingan’s In a Different Voice) will leave him cold.

I have not yet read Sutherland’s book. But if Paulos is giving an accurate reflection of the tenor and range of examples, it seems to offer a far from full account of thinking, which is a far more interesting phenomenon than certainly Paulos would have us believe. Richard Noss has written: ‘the belief that mathematical thinking is genuinely superior to practical thinking is deeply embedded in Western culture; it forms part of the ideology of what it means to think abstractly, perhaps even what it means to think.’ I claim mathematics actually plays a far smaller and less significant part in rational thinking about the material world around us. What’s more, I bet Paulos believes people wouldn’t gamble if they understood probability theory a bit more.

David Pimm
Faculty of Mathematics,

John Allen Paulos writes: Mr Pimm raises the spectre of mindless cretins churning away at scientistic and inadequate algorithms and in the process oppressing us all. Unfortunately, this vision is at best tenuously related to the contents of Mr Sutherland’s fine book or my review of it. On a more positive note, he has discovered that any situation can be analysed in greater depth, with more attention to nuances and complications. This is a remarkable insight and he should be proud of himself.