Elements of surprise

Reading Vera Tobin’s Elements of Surprise for New Scientist, 5 May 2018

How do characters and events in fiction differ from those in real life? And what is it about our experience of life that fiction exaggerates, omits or captures to achieve its effects?

Effective fiction is Vera Tobin’s subject. And as a cognitive scientist, she knows how pervasive and seductive it can be, even in – or perhaps especially in – the controlled environment of an experimental psychology lab.

Suppose, for instance, you want to know which parts of the brain are active when forming moral judgements, or reasoning about false beliefs. These fields and others rest on fMRI brain scans. Volunteers receive short story prompts with information about outcomes or character intentions and, while their brains are scanned, have to judge what other characters ought to know or do.

“As a consequence,” writes Tobin in her new book Elements of Surprise, “much research that is putatively about how people think about other humans… tells us just as much, if not more, about how study participants think about characters in constructed narratives.”

Tobin is weary of economists banging on about the “flaws” in our cognitive apparatus. “The science on this phenomenon has tended to focus on cataloguing errors people make in solving problems or making decisions,” writes Tobin, “but… its place and status in storytelling, sense-making, and aesthetic pleasure deserve much more attention.”

Tobin shows how two major “flaws” in our thinking are in fact the necessary and desirable consequence of our capacity for social interaction. First, we wildly underestimate our differences. We model each other in our heads and have to assume this model is accurate, even while we’re revising it, moment to moment. At the same time, we have to assume no one else has any problem performing this task – which is why we’re continually mortified to discover other people have no idea who we really are.

Similarly, we find it hard to model the mental states of people, including our past selves, who know less about something than we do. This is largely because we forget how we came to that privileged knowledge.

“Tobin is weary of economists banging on about the ‘flaws’ in our cognitive apparatus”
There are implications for autism, too. It is, Tobin says, unlikely that many people with autism “lack” an understanding that others think differently – known as “theory of mind”. It is more likely they have difficulty inhibiting their knowledge when modelling others’ mental states.

And what about Emma, titular heroine of Jane Austen’s novel? She “is all too ready to presume that her intentions are unambiguous to others and has great difficulty imagining, once she has arrived at an interpretation of events, that others might believe something different”, says Tobin. Austen’s brilliance was to fashion a plot in which Emma experiences revelations that confront the consequences of her “cursed thinking” – a cognitive bias making us assume any person with whom we communicate has the background knowledge to understand what is being said.

Just as we assume others know what we’re thinking, we assume our past selves thought as we do now. Detective stories exploit this foible. Mildred Pierce, Michael Curtiz’s 1945 film, begins at the end, as it were, depicting the story’s climactic murder. We are fairly certain we know who did it, but we flashback to the past and work forward to the present only to find that we have misinterpreted everything.

I confess I was underwhelmed on finishing this excellent book. But then I remembered Sherlock Holmes’s complaint (mentioned by Tobin) that once he reveals the reasoning behind his deductions, people are no longer impressed by his singular skill. Tobin reveals valuable truths about the stories we tell to entertain each other, and those we tell ourselves to get by, and how they are related. Like any good magic trick, it is obvious once it has been explained.

Maths into English

One to Nine by Andrew Hodges and The Tiger that Isn’t by Michael Blastland and Andrew Dilnot
reviewed for the Telegraph, 22 September 2007

Twenty-four years have passed since Andrew Hodges published his biography of the mathematician Alan Turing. Hodges, a long-term member of the Mathematical Physics Research Group at Oxford, has spent the years since exploring the “twistor geometry” developed by Roger Penrose, writing music and dabbling with self-promotion.

Follow the link to One to Nine’s web page, and you will soon be stumbling over the furniture of Hodges’s other lives: his music, his sexuality, his ambitions for his self?published novel – the usual spillage. He must be immune to bathos, or blind to it. But why should he care what other people think? He knows full well that, once put in the right order, these base metals will be transformed.

“Writing,” says Hodges, “is the business of turning multi?dimensional facts and ideas into a one?dimensional string of symbols.”

One to Nine – ostensibly a simple snapshot of the mathematical world – is a virtuoso stream of consciousness containing everything important there is to say about numbers (and Vaughan Williams, and climate change, and the Pet Shop Boys) in just over 300 pages. It contains multitudes. It is cogent, charming and deeply personal, all at once.

“Dense” does not begin to describe it. There is extraordinary concision at work. Hodges covers colour space and colour perception in two or three pages. The exponential constant e requires four pages. These examples come from the extreme shallow end of the mathematical pool: there are depths here not everyone will fathom. But this is the point: One to Nine makes the unfathomable enticing and gives the reader tremendous motivation to explore further.

This is a consciously old-fashioned conceit. One to Nine is modelled on Constance Reid’s 1956 classic, From Zero to Infinity. Like Reid’s, each of Hodges’s chapters explores the ideas associated with a given number. Mathematicians are quiet iconoclasts, so this is work that each generation must do for itself.

When Hodges considers his own contributions (in particular, to the mathematics underpinning physical reality), the skin tightens over the skull: “The scientific record of the past century suggests that this chapter will soon look like faded pages from Eddington,” he writes. (Towards the end of his life, Sir Arthur Eddington, who died in 1944, assayed a “theory of everything”. Experimental evidence ran counter to his work, which today generates only intermittent interest.)

But then, mathematics “does not have much to do with optimising personal profit or pleasure as commonly understood”.

The mordant register of his prose serves Hodges as well as it served Turing all those years ago. Like Turing: the Enigma, One to Nine proceeds, by subtle indirection, to express a man through his numbers.

If you think organisations, economies or nations would be more suited to mathematical description, think again. Michael Blastland and Andrew Dilnot’s The Tiger that Isn’t contains this description of the International Passenger Survey, the organisation responsible for producing many of our immigration figures:

The ferry heaves into its journey and, equipped with their passenger vignettes, the survey team members also set off, like Attenboroughs in the undergrowth, to track down their prey, and hope they all speak English. And so the tides of people swilling about the world?… are captured for the record if they travel by sea, when skulking by slot machines, half?way through a croissant, or off to the ladies’ loo.

Their point is this: in the real world, counting is back-breaking labour. Those who sieve the world for numbers – surveyors, clinicians, statisticians and the rest – are engaged in difficult work, and the authors think it nothing short of criminal the way the rest of us misinterpret, misuse or simply ignore their hard-won results. This is a very angry and very funny book.

The authors have worked together before, on the series More or Less – BBC Radio 4’s antidote to the sort of bad mathematics that mars personal decision-making, political debate, most press releases, and not a few items from the corporation’s own news schedule.

Confusion between correlation and cause, wild errors in the estimation of risk, the misuse of averages: Blastland and Dilnot round up and dispatch whole categories of woolly thinking.

They have a positive agenda. A handful of very obvious mathematical ideas – ideas they claim (with a certain insouciance) are entirely intuitive – are all we need to wield the numbers for ourselves; with them, we will be better informed, and will make more realistic decisions.

This is one of those maths books that claims to be self?help, and on the evidence presented here, we are in dire need of it. A late chapter contains the results of a general knowledge quiz given to senior civil servants in 2005.

The questions were simple enough. Among them: what share of UK income tax is paid by the top one per cent of earners? For the record, in 2005 it was 21 per cent. Our policy?makers didn’t have a clue.

“The deepest pitfall with numbers owes nothing to the numbers themselves and much to the slack way they are treated, with carelessness all the way to contempt.”

This jolly airport read will not change all that. But it should stir things up a bit.