The Satterthwaite Approximation

Whichever way you look at it, BBC Radio 4’s More or Less just isn’t sexy.  The truth is, is Stats has an image problem.  Statisticians are entirely devoid of attitude.  What Stats needs is a Superhero.

Remark overheard in a bar.

 

Walter Digit, head of the Statistics Section of the long-established firm of Avro-Avalon Aeronautics, gazed across the expanse of the grand mahogany board room table at the man he imminently intended to murder.

“Ten minutes!” announced the chair grandiloquently.  “Guillotine at nine.  Then we vote.”

Guillotine.

Digit reminded himself that there are Three Laws of Company Board Room Polemics, as inviolate as the laws of Kepler or Newton.  First Law: To win, you must be present at the battle.  First, turn up.  Be amid the heat and dust of the arena.  It was no good being lofty.  If you chose to be above the battle, you would lose it.

Digit was not a violent man.  Indeed, in his 65 years he had never once perpetrated an act of aggression.  It occurred to him that if, as recently as twenty four hours previously, somebody had told him that this was what he had now resolved to do, he would have been utterly astonished.  But that was before the first extraordinary general meeting of the Board had convened, before he had encountered the Big Noise from Seattle WA, before he had realised the route which Avro-Avalon Aeronautics, if the vote went the way Digit suspected it would, would be bound to take.  There was, admittedly, a faint possibility that the vote might go the other way, Digit’s way.  But having weighed the possibilities and crunched the numbers – number-crunching was after all Digit’s long suit – he thought it vanishingly unlikely.  Such a result would be anomalous; in statistical parlance it would be an inexplicable random variable, an outlier, a quirk to be taken out of the equation.

The Board Room was a thickly carpeted, plush, windowless inner sanctum on the third floor of a six storey art deco office block on the edge of the old apron of the Croydon Aerodrome that was the headquarters of AAA.  Digit regretted that this room in which he had spent so much of his professional life should lack a view.  The Executive Board was surrounded by portraits of past presidents of the company.  On the east wall, behind the position of the current President and Chair, was the company logo, an intertwining of five Greek letter alphas to form a coat of arms resembling an Ampersand, thus a representation of the company’s full name, Avro-Avalon Aeronautics & Avionics.  The room’s only panorama was afforded by the west wall, facing the Chair.  Here, in Mercator projection, was a representation of the world, shimmering like a migrainous aura.  On closer inspection, the map was a composite, in real time, of the radar signals of all the aircraft in the world currently aloft.  Thus the first world, the United States and Europe in particular, was well delineated; but the third world, sub-Saharan Africa in particular, was a black pool and a void.

Digit glanced again at the twelve men and two women that comprised the executive (the glass ceiling was yet to be cracked at AAA).  For the hundredth time he ran a thought experiment and conducted a straw poll as to how each individual would vote.  It really all came down to swords and ploughshares.  The peacemakers would go for Project Beta and the warmongers would go for Project Alpha, simple as that.  You might have expected the two women would vote for peace but no!  They were the most alpha male of the lot.  Any woman capable of fighting her way on to this board must have an inner core of steel.  Professor Frances Paton had MOD affiliations and Dr Vanessa Rothermere, after all, was Project Alpha’s lead.  Who else?  Digit himself would go for Beta, and so would MacFadyen.  Beta was Hector MacFadyen’s baby.  That made it two all.  Then there was Gordon Pritchard – chief engineer.  He didn’t like MacFadyen.  Thought he was a maverick, definitely a threat.  Too clever by half.  He would go with Alpha.  Peutherer, R & D, probably knew the most about both projects’ finer details and should have an even hand.  But Peutherer liked micro-tech – so probably Alpha.  Same with Blair, company lawyer.  Thanks to his training, Blair could easily deploy arguments on either side.  You might have supposed fear of litigation would lead him to support peaceful Beta over aggressive Alpha, but Alpha might get subsumed within an MOD contract, and suits against MOD were seldom successful.   5 – 2 for Alpha; not looking good.  Now the big beasts: Prendergast the CEO and Ismay the MD.  Flabbergast and Dismay, they said on the shop floor.  They were both aviators and they tended to prefer flying machines that were flown by people, over drones, so both Beta.  5 – 4.  The younger set?  Harder for Digit to judge.  Margessun the physicist would go for Beta, and Eugene Delaware the chemist, because of the nature of its payload, would go for Alpha.  As well, Delaware had the hots for Rothermere.   6 – 5 to Alpha.  Then Grey. Strategic Development.  A gentleman.  6 – 6.  It was coming down to the wire.  Hargreaves, the money man?  Hargreaves would definitely have been Beta but that was the problem; Hargreaves was absent.  His chair was occupied by the Big Noise, and even before the Big Noise had made any sort of noise at all, Digit knew he would be Alpha.  7 – 6.

That meant Alpha couldn’t lose.  But there might yet be a tie.  There might be a tie because Digit thought there was a switherer –Alan Mabie, something nebulous in management.  He would swither because he would really have no criterion of value beyond whatever madcap managerial trend happened to be flavour of the month.  Mabie was the one marginal constituency.  Digit grasped this fact when he heard Mabie remark, “Pity we can’t run with both Alpha and Beta.  That way it would be win-win, going forward.”  The rest of the time he sat with his mouth open, gawping like a cod stranded on the beach.  The Board might sit up all night and argue the case until they were blue in the face, and Digit suspected nobody but Alan Mabie would budge.  Mabie was the floating vote.  Could he somehow work on him and pull it up to 7 apiece?  What then?  In that case Sir Howard Whittingehame, the Chair, deep, silent, and patrician, would cast the deciding vote.  Digit was devoted to Sir Howard who had been his boss for 40 years, but he knew that Sir Howard was mesmerised, had fallen under the spell of the Big Noise.  He would succumb to the lure of the charismatic man from Seattle and, if it came down to the wire, exercise his franchise in favour of that particular constituency.  And that would be that.

The name of the Big Noise was Warren Paul Mitchelson.  Economist with a Huge Gong round his neck – the reason why Sir Howard was mesmerised.  He was a Nobel Laureate.  Digit had met him just prior to the first board meeting on the previous day.  Mitchelson had hijacked Sir Howard’s introductions.  “Walter Digit, our highly valued head of the Statistics Section…”  Digit’s hand was enveloped in a bone-crusher.  Mitchelson talked at Sir Howard over Digit’s head.  “You still using personnel to number crunch?  We use robots…  Hiya.  Warren P. Michelson.  My friends call me Warp.”

“How do you do, Mr Mitchelson.  My stenographer, Miss Normal.”

Stenographer?  Geez!

Anita Normal smiled demurely and nodded, but did not proffer her hand.

Mitchelson ignored Miss Normal, and casually ran an appraising eye over Digit, who was not surprised that the American should effect a double-take.  Somewhat under middle height, thick set, gnarled, stocky and robust, Digit had long been aware that he bore an uncanny resemblance to a legend of Hollywood’s golden age, Edward G. Robinson.  “Say!  You look like that guy in the movies.  Whazziz?”

“I simply couldn’t imagine.”

Getaway!”  He snapped his fingers impatiently.  “Double Indemnity.  Straight down the line, Keyes!”

Mr Mitchelson himself could have been a Hollywood film star, occupying the lead.  He was six foot four inches tall.  He had taken care of himself.  He was past fifty but he retained the build of a football player and with his chiselled bronze features and a full head of black hair he was a very handsome man.  An expensive three piece suit of US cut and sheen became him, but he would have looked equally good in casual western livery, strolling across the dirt street of the set of High Noon, a revolver with an extra-long barrel in its holster strapped low outside his right thigh.  It occurred to Digit that Mitchelson would be an advocate for the Second Amendment.  From my cold, dead hands!

“You can’t have much longer to go, Keyes.  You got an exit strategy?”

“I beg your pardon?”

“The golden handshake and the high goodbye?”

“I am due to retire at the end of this year.”

“I guess that’s why they’re letting you wither on the vine.   Stats is History, Keyes.”

Digit was only too well aware of the precarious position Statistics held within the company.  Once, during the great glory days of expansion of the aviation industry last century, the section could, and did, field a cricket team which always did rather well in in-house competition.  But these days were long gone and the section now comprised Digit himself, Miss Normal, and Mr Woo, an odd-job man with learning difficulties retained by Sir Howard who was a little ostentatious about the company’s role in the community.  At that precise moment Mr Woo loped in disco-ordinate fashion into the room, came to Digit’s heel and handed him a mauve folder much as a playful dog might retrieve a stick for his master.

“Thank you, Mr Woo.”

Mr Woo giggled and went off abruptly in search of something else.  Mitchelson watched his departure.  “That guy got issues?”

Sir Howard remarked, “He is challenged.”

“I’ll say.”

“Mr Woo is Mr Digit’s assistant.  He has Gerstmann’s Syndrome.”  Digit was aware that Miss Normal had flushed.  She couldn’t see why Mr Woo’s medical file should not be as confidential as anybody else’s.

“Whazzat?”

Sir Howard enumerated, as if reading from a text book, “Agraphia, acalculia, finger agnosia, and left-right confusion.  The lesion is in the angular gyrus of the dominant parietal lobe.”

Mitchelson produced a low and cunning chortle like an eructation.  “Let’s see.  Can’t read, can’t count – even with his fingers, doesn’t know where he’s going.  That’s Stats for you Keyes!”

“My name is Digit” – this said in the soft tones of regionless old-fashioned Received Pronunciation.  “Delta India Golf India Tango.”

“Sure it is, Keyes.”

Digit turned to Sir Howard.  “Where is Mr Hargreaves?”  Hargreaves was AAA’s chief financier.

“Seattle.  Sabbatical.  A six month placement.”

“I take it Dr MacAndrew will be acting up?”

Mitchelson interjected.  “Get with the programme Keyes.  I mean, Hello?  From now on, I’m Hargreaves. Kapische?

Ignoring Mitchelson, Digit continued to address his boss.  “Does Mr Mitchelson have voting rights?”  Sir Howard nodded.  Digit’s heart felt like a stone.  Kapische.

 

Digit told himself that his plan to murder Warren P. Mitchelson had nothing to do with personal animosity.  He said to his stenographer, “Why is it, Miss Normal, that Americans will insist on sporting a middle initial?  Dwight D. Eisenhower, Franklin D. Roosevelt, Warren P. Mitchelson.  I’ve heard it said that Roosevelt’s initial didn’t actually stand for anything.  It’s all very Ivy League.  Phi Beta Kappa.  Or Delta in Roosevelt’s case.  You tote it, like a Glock stuck down your waistband.  Why, Edward G. Robinson, come to think of it.”

“Delano.”

“What?”

“Roosevelt’s middle name.  Delano.”

“Really?  Miss Normal.  You are a fund.”

No, it wasn’t personal.  The reason why Mitchelson had to be removed was Digit’s conviction that Mitchelson, with Hargreaves’ vote, would indubitably go for Project Alpha.  Both Alpha and Beta were R & D projects of considerable scope and ambition.  AAA could not take them both on and run with them simultaneously.  A choice had to be made.  This was why a series of extraordinary general meetings had been called.  Data already had been produced and disseminated. Now the Board would hear a short presentation from each camp, and come to a ruling.

“Toss a coin, Mr Digit, if you please.”  It amused Sir Howard that his chief statistician should perform this ritual.  “Order of ceremonies: heads – Alpha first, tails – Beta first.”  Digit spun the half-crown he retained specifically for this purpose, deftly caught it in his right palm and turned it over on to the back of his left hand.  Tails.  Hector MacFadyen was first up.  He was a freckled, red-headed young Scot.  Digit liked him.  Knew his people.  He was from Ayrshire, of lowly origins, a “lad o’ pairts” who like so many poor Scots before him had seen a way up, and a way out, through the professions, medicine, teaching, engineering.  Digit would never have thought of telling Hector but, privately, he suspected Hector was an engineering genius.  Highly imaginative, Mercurial, Mozartian.  But difficult.  He lacked people skills.  He didn’t know how to get people on board.  He was always a step ahead of his colleagues, who didn’t understand him.  Probably he was on the spectrum.  And today, he was very nervous.  Result – a botched presentation.  Inevitably, the IT acted up.  Digit decided to help him out.

“That’s a really interesting presentation Hector.  Do you mind if I just reiterate the salient features and perhaps you could let me know if I’ve followed your line?”

MacFadyen, who knew very well Digit was bailing him out, turned spaniel’s eyes of deep gratitude in Digit’s direction, and smiled his twitchy smile.

“Of course, ideas of unencumbered personal transport and of human flight have been dreamt of since time immemorial.  Your device-”

“The vacutainer.”

“…the vacutainer, takes the notion of the Hydrogen or Helium balloon to its ultimate conclusion.  What could be lighter than Hydrogen?”

“A vacuum.”

“Just so.  Now we all know nature abhors a vacuum.  Any structure containing a vacuum must be robust, therefore will likely be weighty and bulky.  You suggest you have solved this issue by using a particular material-”

“C60 Graphite.

“…designed into a specific shape-”

“The buckminsterfullerene.”

Mitchelson threw his gold pen on to his blotter, stretched, and yawned.  “Let me get this straight.  You want me to take a big golf ball, strap it on my back, and jump off a tall building.”

“That’s it.”

“How’s it powered?  Gas?  Nuclear?”

“Neither.”

“This some kinda green shit?”

“Wings.”

There was a protracted silence.  Mitchelson broke it.  “Wings.”

“Paddles if you like.”

“What d’you do with them?”

“Flap.”

“You flap?”

“Flap.”

Another strange noise emanated from Mitchelson’s mouth.  At first Digit thought he was clearing his throat, but then he realised he was laughing.

“Mister.  Anybody tell ya?  You’re a nut job.”  Mitchelson turned in his chair.  “What do you think, Keyes?”

“They all laughed at Christopher Columbus.”

Second Law of Company Board Room Polemics: It is a mistake to be seduced into debate with an adversary whose mind cannot be changed.  Under normal circumstances, Digit would have stuck to his brief and rendered a dispassionate account of the robustness of a business model, how the numbers stacked up.  But he had already recognised that Mitchelson would pay no attention, and that what Mitchelson thought was what was going to matter.

Digit had to admit that the second presentation, Project Alpha, was very much more professional.  It was given by a woman.  Vanessa Rothermere, UCL, mid-thirties, polished, cool, urbane, eloquent, and sexy.  She worked in nanotechnology.  She presented an engine of war.  It was an antipersonnel device in the shape of a drone that was tiny, silent, and could deliver a lethal injection.

Intrigued, Mitchelson asked, “What sort of injection?”

“There could be a suite of choices, depending on each specific situation.  Designer drugs of one sort or another, VX, Ricin, batrachotoxin, tetrodotoxin, botulinum toxin…” Dr Rothermere sounded medieval.  The rope, the rack, the garrotte, the strappado…

Mitchelson said, “Now you’re talkin’.”

Without waiting for an invitation Digit interjected, “Avro-Avalon has neither a history nor a tradition in arms manufacture.”

“That’s not entirely true Walter.  During the war…”

“That was a question of national survival.  The nation is not now at war, at least so far as I’m aware.”

“We have always made modest contributions when it comes to MOD procurement.”

Digit was later to say to Miss Normal, “Procurement!  There’s a word.  Does it not have a lewd connotation?  Is it not something gentlemen indulge in at kerbsides?  And is such trafficking not therefore a form of prostitution?”

Proxénitisme,” volunteered Miss Normal.

“Miss Normal, you always come up with le mot that is juste.”

There was never really any doubt in Digit’s mind that the death-midge was going to win hands down over the backpack full of sweet FA.  He needed time to think.  “Could I propose a cooling off period?  We should mull over our deliberations.”

“Time is a luxury we just don’t have.  Blink, and the other guy takes the biscuit.”

“I think, Warp,” said Sir Howard with due respect to his ancient and trusted colleague, “We can allow a day for reflection.  I think we’ll follow Mr Digit’s lead, stop and think, and reconvene here in 24 hours.”

Mitchelson sighed and pointed out, “One of your prime ministers said that a week’s a long time in politics.  Well I tell you something, in war, twenty four hours is an age.  Lose twenty four hours, and you hand the other guy the day.”

Nevertheless, Sir Howard adjourned the meeting.

 

Digit never married.  He had been an only child, and he was without issue.  He lived with his aged mother and had become, since she had gradually lost herself in the labyrinthine forest of dementia, her principal carer.  The ravages of Herr Alzheimer.  Senile plaques and neurofibrillary tangles, a glorious fankle which our neurophysiologists have yet to unwind.  Digit never considered his role as carer as anything other than a privilege.  Thankfully his mother had retained her sunny personality, and he was never conscious that he was on duty or under obligation, far less that he laboured under any sense of burden.  He was a creature of routine.  He rose at 5, bathed, made a good breakfast, and solved the Financial Times crossword usually under ten minutes.  He lived in Westerham, a short bus journey from AAA’s Croydon HQ.  He reached his desk by 8 am and thus undertook a solid hour of work in solitude which he regarded as the most productive part of his day.  His office had changed little since he had first occupied it four decades ago.  It resembled that of a news editor or a private investigator.  The walls were lined, floor to ceiling, with ancient tomes, perhaps of jurisprudence, in calf-bound vellum.  The desk was littered with the office accoutrements of a bygone age.  Digit would hang his jacket over the back of an austere dark wooden office armchair on castors, and sit in his bulky tweed trousers, braces and shirtsleeves.  He affected a dark green eye shade as protection against the glare of an angle-poise lamp, and he chewed on the stub of a cheap cigar.  The smoke-free policy of the company somehow had given Digit’s office an exemption.

Digit never used email and there was very little evidence that the digital age had touched him.  Anita Normal occupied an anteroom on the other side of a battered door whose top half was of opaque glass bearing the AAA logo.  The phones were of heavy dark green Bakelite with liquorice-black wiring.  Miss Normal used a heavy office Barlock typewriter, not a word-processor.  Digit felt that its incessant clatter aided his creativity.  She would tap away while he would muse at his desk, then jump up and walk through the half-glass communicating door.  “Take a letter Miss Normal.”  Despite the fact that she was half his age she had somehow acquired the requisite shorthand (Pitman’s) and typing skills.  She would insert two pages of foolscap, carbon paper between them, into the Barlock, and take dictation.  When she had reached the bottom line Digit might reach over, pull the pages out with a flick of the wrist, and peruse her work.  “The full stop – third paragraph second sentence.  I prefer a semi-colon.”  She would dutifully retype the entire page, change the punctuation, automatically shorten the double space to a single space thereafter, and continue, recommencing in lower case.  It would never have occurred to her to object.  Twelve years ago, at her commencement, she had merely found the set-up eccentric and amusing.  But she had come to dote on her boss.  If Digit had realised it, he would have been astonished, discomfited, and embarrassed.  But he never had an inkling.  Nor had he ever been consciously aware that her feelings were reciprocated.

His day was made up of study, contemplation, and meetings.  He finished at 5.  He might reasonably have finished at 4 but the concept of “flexitime” was quite alien to him and in any case he was devoted to his work and to the company.  Regular as clockwork, he would take the bus back to Westerham.

“Good evening, mother.”

“Oh!  Good evening, sir.  Do I know you?”

He would take over again from his mother’s day-time carers, and fix supper.  He didn’t smoke at home as the smell nauseated Mrs Digit.  He hardly drank at all, aside from a small glass of Bristol Cream at New Year.  In the evening he would converse with mother, and they would ask about one another’s day.  Mrs Digit’s short-term memory was severely affected, but Digit answered her repetitive questions fully and with great patience.  She would generally ask Digit where his father was.  Mr Digit senior had died a decade before, and this news caused Mrs Digit distress.  The ironic tragedy of Alzheimer’s disease is that bad tidings need to be renewed every day, and therefore there is no attenuation of grief.  To spare her such anguish, Digit only once told his mother a lie.  He told her that his father was working late and that he would be home presently.  He soon realised that the lie would need to be repeated as often as the truth, so he abandoned this subterfuge because denial of the truth was very foreign to his nature.  His entire professional life was based on a search for truth and an enquiry as to its nature.

Sometimes he and his mother would play Scrabble.  Despite her dementia, Mrs Digit was rather adept at Scrabble, and she would sometimes astonish Digit with the placement of an obscure seven or eight letter word which would earn her a bonus of 50 points.  Marzipan and Fraught and, taking advantage of the presence on the board of Li (the Chinese mile), Imbroglio.  Around 9 they would take Horlicks and he would assist his mother to bed. He himself would retire at 9.30.

What of the prospect of retirement?  Retirement held no dread for him.  He would read.  He would walk.  He had the church.  It is certain that Walter Digit led a quiet life, and you might suppose he lacked vice.  Yet he had a flaw.  A fatal flaw, the Greek “hamartia”, something that he recognised as a Nemesis, something he knew he could not keep under control, and therefore something he knew he must abjure altogether.

Digit was a gambler.  He was not secretive about it.  He called himself a “recovering gambler”.  He hadn’t made a wager for forty years, for the same time that he had been working for AAA.  Before that, when he was 25, he would have been declared bankrupt but for the fact that his parents bailed him out, offering to pay off his debts so long as he attended an addiction clinic for gamblers.  This he duly did, and since then he had assiduously avoided regions of temptation, the dogs and the turf and the trots, the casino, fruit machines, the betting shop, even the stock market.  Of course nobody living in a capitalist world can avoid the stock market.  Digit’s investments were through the bank and were generally low risk. ‘Cautious growth funds’. His only stocks were in AAA and these represented a profound belief in AAA’s activities rather than any form of speculation.  Digit knew that AAA had saved him.  He had studied mathematics and then statistics and had been attracted to actuarial work, the study of probability, and the assessment of risk.  He subsumed his fascination with the odds into his devotion to his profession.

Yet he never thought of himself as cured, always in recovery.  So he sedulously avoided any office sweepstake, a flutter on the National, even a lottery ticket in aid of a good cause.  He always knew that he would never be free of the Mad Impulse, the sudden overwhelming desire to risk absolutely everything on a game of pitch and toss.

At the reconvening of the Board, it became evident that Warren P. Mitchelson had decided to play Digit at his own game, by producing data.

“I ran my own analysis.  Yeah.”  He passed reams of A4 around like a croupier dealing from the shoe.  “You can get this stuff off the net.  Google it.  Easy-peasy.  Wikipedia and so on.”

Digit said, “Off the peg statistics?”

“Bespoke I’d say.  D’you know ‘R’?  It’s very good.  The language of big data.  Sorry Keyes.  No hard feelings, but you’re redundant.  Anyway-” He glanced at his laptop.

“Let’s look at the units.  Vacutainers versus stealth drones.  Compare and contrast. Let’s cut to the meat and potatoes.”  Mitchelson performed some rapid arpeggios on his laptop keyboard with the facility of a concert pianist.  The Mercator projection of the world’s aviation activity was replaced by a graph projected on to the bare wall beyond the foot of the table.  There were no glitches.  The IT was on Mitchelson’s side.

“Instant economics.  Apologies.”

The graph represented a bell shaped curve.  “This is a projection model for the movement of units, aka sales.  “On the Y axis –” the red dot of the laser pointer ran up and down the line – “number of units.  On the X axis –” laser pointer again – “we have the Mitchelson Index.”

Digit enquired, “What is the Mitchelson Index?”

“As I say it’s rather technical.  It’s an index of risk.  Or, more accurately, it is the square root of the reciprocal of what is known as the risk attraction-aversion amalgam.”

“Gobbledegook,” said Digit.

“Don’t spit the hickory, Keyes.”  The laser pointer began to dance around the slide projection.

“Mitchelson for Plan B…”  He clicked the mouse.  “…and Mr Mitchelson for Plan A.”  The bell curve moved upwards and to the right.  “Let’s do it again… Plan B… Plan A… and then A and B superimposed.   Two populations.  I calculated the pooled standard error.  As a business venture, going forward, the drones win hands down.  No contest.”

Digit glanced down at the handout and gave the paper a cursory glance.  It was a mix of ready-to-go statistics and on-line advertising.  Statistics how to… practically cheating statistics handbook… how to calculate pooled standard error… Fast Money Transfers… How to retire in Thailand…

It is a mistake to be seduced into debate with an adversary whose mind cannot be changed.

In for a penny.  Digit laid the paper down.  “It’s flawed.  You can’t apply the pooled SE when the variances are different.  You need to apply the Satterthwaite Approximation.  It’s elementary.  It’s a subtle distinction, but critical.”

“Well you know what they say. There’s lies, damn’d lies, and statistics.”

“A remark attributed to Mr Twain that is, I believe, widely misconstrued.  You think it describes a downward continuum of misinformation, but in fact it conveys a contrast.  You have on the one hand, humbug, then bullshit, but, on the other hand and by way of contrast, the truth.”

It was very remarkable that Digit, who abjured vulgar language, should use the word ‘bullshit’.  That he should do so betrayed a deep inner passion.

“Bullshit!  You said it.  You can make numbers mean anything you like.”

“On the contrary, data, if properly collected, construed, interpreted, and presented, in terms of hard evidence, are really all we have.  They allow us to get as close to the truth as is humanly possible.  The truth is not an inner construct of the imagination.  The truth is out there, waiting to be discovered, and revealed.  That is why it is so important to speak the truth to power.”

“Nah.  See Keyes, that’s why you’re obsolete.  I guess that’s why I’m here.  To speak power to truth if you like!  Yes I like that.  Just as the victors are the ones who write history, so it is that the powerful define truth.  And that’s why Avro-Avalon Aeronautics must back adversarial drone technology.  The next time some tin-pot despot from some shit-hole banana republic sends his suicide bombers in our direction – sshhhht!”  Mitchelson slapped the side of his neck.  “His successor will think twice believe me.”

It was at that point that Digit realised Mitchelson had to go.

Back home, Mrs Digit was sitting over the Scrabble board in quiet contemplation of yesterday evening’s undisturbed game.  She wore an expression of great sweetness, but she was grey and inert.  Digit gently took his mother’s hand and laid his fingertips across her wrist.  She was still warm, but he verified there was no pulse.  The carer would have departed an hour ago, so Mrs Digit’s passing was extremely recent.  Digit felt a strangely intense emotion of sad serenity.  He glanced down at the Scrabble board, idly curious as to what her last play had been.

LOOFAH

Digit picked up the telephone and called the family doctor.

 

“Take a letter, Miss Normal.”  He waited until his secretary had arranged the paper and the carbon copy in the typewriter’s roller.

“To Sir Howard Whittingehame, Chairman, Avro-Avalon Aeronautics….

“Dear Sir Howard…”  Digit paced about behind Miss Normal’s straight back.

“With respect to the recent deliberations of the company’s executive board…”

Of course, he had always known that Miss Normal was pretty.  It only occurred to him now that she was a remarkably beautiful woman.

“…a board whose make-up has been subtly yet significantly altered by…

“…by the replacement of Mr Hargreaves by our visitor from overseas…

“…with respect… where was I?”

She read back.  “Our visitor from overseas…”

“Ah yes.  Where is Mr Woo?”

“Hastings.”

“What on earth is Mr Woo doing in Hastings?”

“He has been relocated.”

“Relocated?  Why wasn’t I told?  Which section?”

“Not by the company.  His sheltered House in Croydon has closed.  Council cuts.  I believe a place has been found for him in Hastings.”

“But Mr Woo will not know anybody in Hastings.  He will be confused.  Does Sir Howard know?”

“I couldn’t say.”

“He must be told.”

“Yes, sir.”

There was a pause.  Digit looked down at the nape of Miss Normal’s neck.  Miss Normal sat patiently before the Barlock, awaiting further dictation.

“As you know Miss Normal, I am due shortly to retire.”

“Yes, Mr Digit.”

“In the event that I am not replaced, in the event that the section folds…”

“Sir?”

“Forgive me.  None of my business.  Shouldn’t pry.  Anita, have you any plans, for example, to marry, settle down?”

Miss Normal sat stock-still.  She was unable to interpret the sense of pent-up turmoil within her bosom.  In the course of their twelve year professional relationship, Digit had never until now addressed her by her Christian name.

 

Before the final meeting, and the vote, it was absolutely essential that Digit pave the way for Warren P. Mitchelson’s timely assassination.  For this, he needed to recruit Hector MacFadyen.  He entertained no hopes of being able to deceive MacFadyen as to his intent, yet he was determined that MacFadyen not be an accessory to the crime; all he needed was some information, and some technical know-how.  MacFadyen would have both because MacFadyen had a handle on AAA’s every project.  He phoned Hector at about 9 pm, after Dr Campbell had visited and issued his mother’s death certificate, and after he had made preliminary arrangements with the undertaker.  MacFadyen lived in a bachelor apartment in Biggin Hill, twenty minutes away.  Digit drove over, declined refreshment, and explained succinctly what he needed.

“You’re going to do the bastard in, then?”

“If that were the case, then you would doubtless be interviewed by the police.  Speaking hypothetically, in such a case you would be able to tell them that I made some enquiries into Project Alpha, enquiries perfectly commensurate with my role as Chief of the Statistical Section.  Your suspicions were not aroused for one moment.”

“Sure you don’t need my help?  Hypothetically, I mean.”

“I don’t make hypotheses.”

 

“Five minutes!” announced Sir Howard Whittingehame.  “Five minutes!”  Digit rose from his chair.

“Where are you going, Mr Digit?”

Mr Digit replied gravely, “I am going to the lavatory.”

“Ha!  Too much information Keyes.”

In fact Digit had no need to answer a call of nature.  He was merely following the Marginal Constituency, Mabie, the ditherer, into the men’s room.  It was his final chance to change the course of the meeting through the ballot box rather than the bullet.  They stood together before the pissoir in companionable silence, and then before the wash basins.

“What was that Proxy business about? Saturday… Saturnine…”

“Satterthwaite.”

“Yes.  What is that?”

“It is a way of comparing apples and pears without distorting the truth.”

It occurred to Digit that Mabie was like Pontius Pilate, washing his hands.  “The truth?”

“Yes.”

Mabie dried his hands under the roaring vortex of the Dyson air blades.  He had a fixed expression, a musing pout of puzzlement.  Maybe he just couldn’t hear above the racket.

“The truth.”

“Only the truth will make you free.”

“The truth?  What is that?”

Mabie was going to vote for Alpha.

 

Third Law of Company Board Room Polemics:  The most critical decision is made during the last five minutes of the meeting.

Digit had long understood that the board room decisions that really mattered took place during “Any Other Competent Business”.  Nothing is decided, until everything is decided.  This was when you had to be at your most alert.  Why is it that politicians are the last people to apprehend this?  Airline pilots and physicians know to quit when they are tired.  Not politicians.  They slog it out during an all-night session and then make the critical decision in a state of exhaustion.  But now Digit was sure, with 95% confidence he might have said, of the outcome, and it was time to activate Project Charlie.

He took the laptop out of his brief case, placed it on the mahogany surface, opened the lid, and switched it on.

“Good heavens Walter!  In the 40 years I’ve known you, I’ve never once seen you engage with the satanic looms of Apple and Microsoft!”  There was an eruption of astonished laughter round the table.  Most people thought Digit was a Luddite, computer-illiterate.  That was their great mistake.  In fact Digit had spent a considerable portion of his career undertaking work which, while distasteful to him, he was rather adept at – programming.  Two of his great scientific heroes were Alan Turing and James Clerk Maxwell.  He understood their work at a deep level.  Sir Howard opened his mouth to make another quip, but he was silenced by his own further sense of astonishment at the facility with which Digit utilised a machine he was wont to refer to as a “hellish contraption”.

Digit exercised a few mystic passes, shut the machine down, closed the lid, and put it back in his briefcase.

“What was that about?”

“Exit strategy.”

“Sorry?”

“Just checking the bus timetable.  Some of us do have a home to go to.”  (Was that true?)

“Don’t sweat the small stuff Keyes.   My driver will give you a ride.”

The culmination to the meeting turned out to be somewhat anticlimactic.  Mitchelson passed away in much the same manner as Mrs Digit on the previous evening.  Death entered the room, and departed therefrom so silently, that Digit was the only person to see Mitchelson absently reach a hand up to his neck and brush away a mosquito.  Digit rose unhurriedly, picked up his briefcase, and made for the door.

“Walter!  The vote!”

“Don’t want to miss the bus.”

“Like I said, Keyes, don’t spit the hickory.”

“Walter, you must vote.”

But Digit had suddenly decided, now he was a felon, there was a moral imperative he not vote.

“I abstain.”

“Don’t spit the hic-  hic – hic – hic!”  Abruptly, Mitchelson stopped talking and stared straight ahead.

Digit took the back stairs, not the lift.  On the top floor, yes, here was the equipage, fully prepared and lying in wait.  The vacutainer was the size of a bulky rucksack – and once deployed, it would expand considerably – yet amazingly light.    Digit strapped it on.  Helmet and goggles.  Now he looked like a cross between a bumblebee and a free fall parachutist.  He stepped out on to the flat roof.  Clear skies, a crescent moon, and the great panoply of the Milky Way.   Last safety checks.  He ran Hector’s briefing again over in his mind.  Final, vital actions.  The emergency door at the top of the service stairs scraped open and MacFadyen, breathing heavily, was at his side.

Digit asked blandly, “How did the vote go?”

“A tie.  Six apiece.  You shouldn’t have abstained.”

“Six all?  Somebody else must have abstained also.”

“Mitchelson.  As you very well know.  There’s pandemonium down there.  Cardiac arrest they think.  They’ve started CPR.  They can’t find the defib.”  The sound of the siren floated up to them from somewhere in the southeast.  In a moment they would be able to track, quite clearly, the course of the twinkling blue lights.

“How do you suppose Sir Howard will cast his deciding vote?”

“He will vote for you, Hector.”

“How do you know?”

“I worked it out.  It’s a great project.  Good luck with it.  Every success.”  Digit stepped towards the edge of the roof.

“Walter.  I’m not sure this contraption’s going to work.”

“I have every faith.  It will work.”

“How do you know?”

“Probability.”

Digit stepped off the roof.

 

 

 

 

 

 

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