The One and the Many

Love, Actuary

Seven and a half years ago, I knew with a clear and unswervable certainty that maddened anyone who spoke to me that Donald Trump would win the 2016 American Presidential Election. How did I know? Katy Perry and Pharrell Williams were tangentially involved. We’ll come to that later.

I should say right off the bat that, in a general way, I am nobody’s idea of a prophet. Don’t approach me for predictions concerning stocks and shares, soft commodity futures, declared vintages, racing results, or Booker Prize/Love Island winners. I’m as unreliable in all those areas as you are, as everyone is. Else, casinos and bookmakers would be out of business.

In Le Carré’s Tinker Tailor Soldier Spy, Sam Collins, ex-Circus agent, now manager of a Mayfair casino, tells George Smiley that the house he runs is straight. “We get all the help we need from the arithmetic,” he says.

The arithmetic, ah, the arithmetic.

When I was a small young object, I discovered the Sherlock Holmes stories and inhaled one after the other with all the greedy enthusiasm of today’s teenagers, sucking down capsules of laughing gas in a suburban park. The second appearance of the great detective came in the novel-length adventure The Sign Of The Four.

As he and Watson cruise up the Thames on the trail of murderers, Holmes muses thus:-

Winwood Reade … remarks that, while the individual man is an insoluble puzzle, in the aggregate he becomes a mathematical certainty. You can, for example, never foretell what any one man will do, but you can say with precision what an average number will be up to. Individuals vary, but percentages remain constant. So says the statistician.

I remember being very struck by this despite not having the faintest idea who Winwood Reade might be. A Scottish explorer and secular thinker of independent means, Wikipedia now tells me, who died aged 37, but was admired by figures as varied as Winston Churchill, George Orwell, H. G. Wells, A. A. Milne, Christopher Robin Milne (and, it is to be hoped, Tigger, Piglet and Pooh). But not by William Gladstone, who considered him ‘irreligious’.

Years later, in 1984, I made my first appearance on the West End stage. The Winwood Reade Principle loomed large there in a way I hadn’t imagined, and I tried, and still try, to make sense of it.

Imagine that you are in a moderately successful commercial theatre play. Not so successful as to be sold out every night, but successful enough to make money and keep running. The company manager or producer will soon (if you ask nicely enough) let you have the attendance figures. The percentages refer to how much of the house has sold.

Monday night - 46%

Tuesday night - 60%

Wednesday (matinee) - 38%

Wednesday (evening) - 88%

Thursday - 97%

Friday - 100%

Saturday (matinee) - 100%

Saturday (evening) - 100%

Such figures, week on week, would be approximate but not very approximate – plus or minus 2% at worst.

Over a month, nearly two full houses’ worth of audience come to see the show on Mondays, but at a steady rate of just under half the house’s capacity each time. Why? Let’s zero in on a couple taking their seats in the stalls - Marcia and Nicholas. She’s the one unwinding that Missoni-like scarf that isn’t Missoni, probably Camden Market, but somehow better than Missoni. He has a rather distressing man bun and is holding two plastic wine glasses. But here they are, come to see the play this Monday evening. They might just as well have turned up the next Monday. Or the following Tuesday. As might everyone in the theatre today and that whole week. Why wasn’t the first Monday of the month only filled to 1% while the second Monday completely sold out, with queues round the block? By what magic does it even itself out and find its predictable level? Why 46% one Monday, 45% the next Monday and 47% the Monday after? Why not 91% on the first Monday and 0% on the second? What is the irresistible force that exerts itself on the theatre-going public such that these navigable, knowable patterns are formed each time?

I’m sure Holmes and Reade were right when they suggested that you couldn’t foretell with any absolute precision when Marcia and Nicolas, as individuals, might choose to go to the theatre. Consider all the variables that might have militated for or against their visit: babysitters, weather, tube strikes, other offers, how they’re feeling, sudden preference for Netflix and chill, happening upon a favourable/unfavourable review of the play, did somebody say Just Eat (no they bloody didn’t. No one ever said it, now will you please fuck the very fuck off). Yet despite this unpredictability, susceptibility to outside factors and general human flakiness, it remains true that producers and theatre managers can forecast, with almost exact precision, what the gate money will be for each week and how it is distributed over each separate performance day.

Might one say that Marcia and Nicholas, as individuals, are – in Chaos Theory terms – turbulent and cannot be represented or described by a linear equation, whereas an audience, as a group, can? An audience may be a collection of Marcia’s and Nicholas’s, but it somehow takes on an identity of its own, one in which Marcia and Nicholas have no conscious or governing role. A group.

Groups are weird. They behave in the oddest manner. Predictably, for one. Predictably, like groups of people who come to the theatre, but predictably in weirder ways too.

Imagine you have a group of 20 randomly chosen people. You study this group and discover that differing personality types have emerged. Not surprising. There’s The Clown – a joker who just can’t stop themselves trying to raise a laugh. There’s the quietly charismatic Natural Leader. There’s The Loudmouth who thinks they should be leader. There’s The Shy One. The Complainer who moans about everything. There’s The Kindly Empathetic One. There’s The Bossy One. The Quibbler. The Bickering One. The Know All. The Rebel. The Sneaky Sycophant. And so on. If you’ve seen an episode of Big Brother, The Traitors or similar, you will know what I mean.

To prove these group dynamics, you - the leader of an experiment - create nineteen more similar groups of twenty individuals (the grant to your Behaviorology lab is very generous). Okay? So you now have twenty groups of twenty people, inside each of which has emerged a Leader, a Joker, a Know All, a Quibbler, etc.

Here comes the fun part. You now take The Leader out of each group and make a new group composed entirely of 20 Leaders. You do the same with the other types. So now you have a group of 20 Leaders, a group of 20 Clowns, a group of 20 Loudmouths, another of 20 Quibblers etc, etc, yes? No. No. That’s the fun part.

Guess what happens within the group of 20 Leaders? Why, it settles into a group comprising one Leader, one Clown, one Loudmouth, one Complainer, one Shy One. And the same happens to the group of 20 Clowns, 20 Quibblers and all the other types. Groups have their own rules, their own dynamics, and we puny individuals can no more resist them than we can defy the law of gravity. All the groups will compose themselves in this manner, dividing into the 20 archetypes like crystals forming in a school science lab beaker. For all our apparent autonomy, we individuals take on different characteristics to fit ourselves into groups. Not consciously, but it seems to work.¹

‘Autonomy’? Well, we are individuals. Equipped with our own outboard and inboard motors, we like to think of ourselves as ‘masters of our fate and captains of our souls’, as described by W. E. Henley. Not that anyone credible believes in free will these days, but that’s a whole other cerated sphere. Free will or no, outboard and inboard motors or no, it does feel that we are also helpless pieces in the game of chess that Fate, or Arithmetic, or Group Theory plays. Neither Brownian and random, nor self-directed and autonomous, but somehow flying in a formation controlled by an outside force that we don’t really know or understand.

Then again, take actuarial tables. Actuaries are those people who, for and on behalf of insurance companies, work out risk. They don’t care why; that’s the beauty of their art. If red-haired people are statistically more likely to have car accidents, then red-haired people are charged a higher premium for their driving cover than blonds or brunettes. As someone who prances about on stage and screen from time to time, I know from experience that we actors always have to pay above-average premiums to be able to drive. It’s fun but fruitless to rationalise or ponder why. Is it because we’re naturally ditzy? Because we’re often driving back home at night after gigs? Because we’re all drug-addled sillies? It doesn’t matter; it’s because we are statistically at a higher risk. The actuary couldn’t care less why. I believe Equity, the actors’ union, tried to challenge the insurance industry’s premium policy once and didn’t get anywhere. Facts is facts, figures is figures. If it turned out that being called Geraldine, living in Thirsk and possessing a Ninja Dual Basket Air-Fryer tripled your chance of being burgled, then your house insurance premium would be three times higher than someone called Eileen living in Basildon who crisps her potato wedges with a Chefman TurboFry Touch.

To see Actuary as Hero, you need to look no further than at Hollywood’s first great film noir, Billy Wilder’s Double Indemnity. Edward G. Robinson features as an insurance company investigator. Barbara Stanwyck, aided by her lover, Fred MacMurray, has murdered her husband. The pair arrange to have his body found on railway tracks as if he’d taken his own life by jumping from the back of a train. There’s a clause in his insurance that pays out big for his death, even if it’s suicide. A perfect murder and swindle.

This is what Edward G says:

Come now, you’ve never read an actuarial table in your life, have you? Why they’ve got ten volumes on suicide alone. Suicide by race, by color, by occupation, by sex, by seasons of the year, by time of day. Suicide, how committed: by poison, by firearms, by drowning, by leaps. Suicide by poison, subdivided by types of poison, such as corrosive, irritant, systemic, gaseous, narcotic, alkaloid, protein, and so forth; suicide by leaps, subdivided by leaps from high places, under the wheels of trains, under the wheels of trucks, under the feet of horses, from steamboats. But, Mr. Norton, of all the cases on record, there’s not one single case of suicide by leap from the rear end of a moving train. And you know how fast that train was going at the point where the body was found? Fifteen miles an hour. Now how can anybody jump off a slow-moving train like that with any kind of expectation that he would kill himself? No.

In all the excitement about autonomous motorcars, I think we overlook how the future of motoring will be decided not by techies or business leaders, not by politicians or glorious gifted and entertaining Substack contributors, nor even by lawyers and ethicists, but by actuaries tapping at their calculator buttons. The moment the numbers reveal that it is less safe to drive a car by the human operation of steering wheels, brakes, gears and conscious decision-making than it is to be driven by an autonomous system, then up will go the premiums for drivers, and down they will go for those happy to let the tech do it all for them. The arithmetic, ah, the arithmetic.

Groups. The set of people called actors must pay more to drive. The set of people called theatre-goers will divide themselves predictably across the weeks. We are puppets pulled by strings that are operated by … chance? Quantum waves?

The fact that I am still so baffled and beguiled by this, to me, almost paradoxical oddity in the reading of humans going about their business may strike you as ridiculous or – if you are a mathematician or philosopher – naive and mournfully ill-informed. I have to confess that I am not fluent or even basically literate in statistics and the mathematics behind it. I know almost nothing of Poisson or Gaussian curves, Bayesian priors, standard deviations or discrete and continuous normal distribution within stochastic time sets. I know enough to know that I know nothing, or as statisticians themselves might put it, I know enough to be confident that my epistemic capacity approaches zero. For all my ignorance, I am at least aware that statistics is a branch of mathematics and thought that describes much of our world and that the field is concerned with far more than the petty lists of figures that politicians brandish, often prefaced by phrases like “the vast majority”, to shame opponents or crow great achievements: that low usage would come under Mark Twain’s (or was it Benjamin Disraeli’s?) quip: “there are lies, damned lies and statistics”.

It has been true for some time that the algorithms that (should) frighten us out there seem to be getting closer and closer to knowing not just how my demographic and my age group will behave but precisely how I, the individual Stephen Fry, will behave.² Will the Bayesian logic that underlies much of Artificial Intelligence make a leap from Winwood Reade and the West End producer such that we will be able to say that the individual is now as precisely predictable as the group or mass?

Jonathan Swift wrote in a letter to Alexander Pope:

I have ever hated all nations, professions, and communities, and all my love is toward individuals … principally I hate and detest that animal called man, although I heartily love John, Peter, Thomas, and so forth. This is the system upon which I have governed myself many years, but do not tell...

It used to be that hard leftists were often notable for how much they could weep and shake their fists on behalf of the masses while being off-hand, mean, rude, and treacherous towards individuals. Howard Kirk, the antihero of Malcolm Bradbury’s classic novel of 70s campus life The History Man was a brilliantly drawn exemplar of this type. Across the divide, hard rightists are often notable for their worship of the individual and either contempt for or disbelief in “society”. Their high priest is, I suppose, Ayn Rand. Her most popular work, Atlas Shrugged, is a dramatisation of her libertarian prizing of the achieving individual over the state-supported scrounging, unachieving masses. The Austrian School economist Ludwig von Mises wrote her an admiring letter:

You have the courage to tell the masses what no politician told them: ‘You are inferior, and all the improvements in your conditions, which you simply take for granted, you owe to the efforts of men who are better than you.’

Wow. And they say soft progressive centrists are “elitist”!

But whatever our political stripe today, don’t we feel what Swift feels? Haven’t we all noticed the startling disconnect between the mass — as encountered in social media and crime statistics, for example — and the individuals we bump into in the street, sit next to on the bus, and chat with in the supermarket queue? How we hate and detest that race called humanity, but how lovely and trustworthy and honourable are Benny and Penny, Karen and Darren, Rita and Peter, Erroll and Beryl (that’s enough rhyming first names, Ed.), Marcy and Darcy, Nate and Kate, Bill and Jill, Rudi and Trudie (you’re fired, Ed.).

The number of conversations I’ve had with taxi drivers, baristas and make-up artists in which we puzzle over this problem. Yes, I live a gilded life; people are ‘nice’ to me, and I live in neighbourhoods compounded of ‘nice’ people. I mentioned, you’ll have noticed, being in conversation with baristas and make-up artists, not doner kebab carvers and probation officers. But I don’t think that’s relevant here. I think it is probably true that most people, regardless of class or prospects, chatting over garden fences, under the dryer in the salon, having a smoke on the pavement, at some point wonder aloud to each other how it can be that the mass of humanity seems so monstrous when the average person you meet is pretty much ok.

But whatever the power of arithmetic to predict the group or even the individual, there are areas of human judgement that I think it will take machines a very long time to approximate.

Eight years ago, with the American election reaching fever pitch, no one truly believed that Donald Trump would defeat Hillary Clinton. I certainly didn’t. But then the Clinton team decided to publish her playlist –

Rock out, Hillary 2016 style, with the official campaign playlist

(I’m embarrassed just to type that). In one flash, I knew that Trump would win. Not because Clinton’s playlist was lame, obvious, safe, uninspiring … I’m not judging her taste in music, or lack thereof, nor would I count myself qualified to do so. I knew instantly she would lose because it was so clear that no one on earth would ever want to see her playlist. Let alone listen to it. No one on earth would want to know that such a playlist existed, much less care a raspberry fuck what was in it, what genre, what generation, what anything. For all the negative feelings I may have entertained concerning Trump’s personality, moral and ethical nature, honesty, decency etc., etc., I had to confess that I was fascinated to know what might be in his playlist. For all I knew, it could be polka music, soft rock, clawhammer bluegrass, death metal, light classical, Nu-folk, Tesco³, psychedelic funk, Tijuana brass. It didn’t matter. What mattered was that I was interested. And I knew with a certainty that might be regarded as deeply arrogant that my belief – that a Hillary Clinton playlist was among the least interesting ideas ever proposed – would be a belief shared by most people, whatever their political leanings. It’s not fair on Hillary Clinton that this should be the case, but the case is what it is. We smell it at once. Hillary Clinton’s playlist? No. Therefore, somehow, Hillary no.

Statistics and group theory can take us a long way, but smell takes us further.

1. Obviously, the experiments, results, personality types and so on are not as clear-cut and absolute as I’ve described. But the principle of Group Dynamics remains the same.

2. Though I’d be grateful if it stopped offering me various types of showerheads. Yes, I searched for a new one a couple of years back when the old, lime-scaled showerhead started to corrode, but I replaced it, and I don’t need any more. I’m good for Cialis, too, thanks very much.

3. Tesco, as a branch of dance music, does, or at last briefly did, exist. It’s a blend of techno and disco. You knew that.