The Mathematical Murder of Innocence

by Michael Carter

  “Who needs facts when opinions and prejudice are much more fun?” I joked. “Just look at the Brexit referendum or Trump’s election. Or worse, look at what has happened since. I don’t know if they’ve already made up their mind – if so, my job will be to get this Professor Goodwin to admit he’s made a mistake and so convince them otherwise. I think the real problem is that they don’t like a young upstart like me getting above his station, so to speak. The French have a wonderful and rather crude expression for that, which I could roughly and slightly more elegantly translate as ‘breaking wind above your rear posterior’.”

  “I’m a nurse, used to some very crude language. You don’t have to put any gloves on for me!”

  “OK, the literal translation is ‘farting above your ass’.”

  “I like it. I’m going to remember that one! You seem to refer to the French rather a lot. Why?”

  “I did a three-month summer internship for a French offshore engineering company in Paris.”

  “I didn’t know they had any oil in France.”

  “They don’t really. They just follow Total around the world. They also do a lot of work for the American oil companies. They like the excuse to come to Paris for technical meetings. It was part of my job to look after some American clients when they came over and accompany them to the Moulin Rouge for the second part of the meetings.”

  “Too much information!” she said, laughing. “So, what did you all get up to in the Moulin Rouge?”

  “Nothing too untoward. The American clients were all shocked at the dancers’ bare breasts. No, I think thrilled would be a better word. We did almost lose the next stage of the contract, though.”

  “How?”

  “I’ll tell you once I refill our glasses.” Which I did, and paid for again, being the perfect gentleman with only a few ulterior motives.

  We tucked into our second pints.

  “So, was it the bare breasts that almost scuppered your contract?” she asked.

  “No, I’m sure that encouraged them to stick with us!” I said. “What happened is that we made our client look a fool, literally. We’d booked well ahead and had paid extra for one of the best tables, which means we were right next to the central stage that sticks out into the dining area. This comedian comes on between two dances. He says he needs volunteers. But he selects the volunteers himself, and there he is pulling our client’s top man up onto the stage. He gets another two victims from other tables and sets the three of them up as ventriloquist dummies. It’s all done in English for the tourists. Whenever he squeezes one of them on the arm, that person has to open and close his mouth, while the comedian adds the words. Well, the other two were staged as having an argument, and every now and then they would ask our guy for his opinion. He opens and closes his mouth a few times, but all that seems to come out of are the grunting sounds of a mentally challenged idiot. It was actually very funny, and our client’s colleagues were rolling about laughing to see their boss that way. But our man did not appreciate it at all.” I took another swig of my beer.

  “Anyway, next day we won him back,” I continued, “not so much with all our brilliant technical presentations, but more in the company restaurant.”

  “What, the gourmet French food?” she asked.

  “No, something a bit more down to earth,” I said. “You see, the ground floor of our office building was an in-house self-service restaurant, together with a couple of VIP rooms where you actually get served, the food’s more upmarket and there are some pretty good wines. Well, to begin with, this same VIP, he’s shocked we serve alcohol on the premises. He explained how this would be a firing offence in the States: any alcohol consumed at work, and you’re out. But after his second glass of Saint-Emilion he was actually coming around to the idea that maybe France wasn’t such a heathen place after all. But what really made him delighted was when one of the French team explained to him how to impress his friends back home by becoming an instant wine expert.” I paused to de-ballast my glass a little more. Why does it go down so fast?

  “And how do you that?”

  “It’s very easy, as my colleague explained to him. If French wines are being served – he should make sure the wines are French and not from some other country – he should check if the bottle has shoulders on it. If so, he should pour a little into his glass, swirl it around, hold it up to the light, deeply inhale the delicate bouquet, sip it and swirl it around the mouth, make some rather rude sounding slurping noises, swallow, nod sagely, and then he should calmly announce to his friends that this wine must come from Bordeaux. The friends will of course be impressed by his expertise but wouldn’t necessarily believe him. So, they all look up ‘Chateau Haut-Paullac’ or ‘Saint-Emilion Cru Bourgeois’ on Google Maps, and are astonished to find it right next to Bordeaux.”

  “OK,” she said, “but there are so many different wine Chateaux in France, how is he supposed to know which ones come from Bordeaux?”

  “It’s simply the shoulders on the bottle.” I explained. “In France, only the Bordeaux wines come in bottles with shoulders, as opposed to bottles with a smoother more rounded curve for the other regions. There are some exceptions, Côte de Provence, which is further East, that also comes in bottles with shoulders, but you’d be unlikely to find this exported to the USA. Anyway, people love to imagine they are wine snobs, and they love even more to be able impress their friends. So, this wonderful pearl of wisdom won back the head and heart of our client. He spent the rest of the meal happily swirling wine around in his mouth and shouting, ‘It’s Bordeaux!’”

  “I’m going to try that one with some of my nursing friends!” said Stephanie, laughing.

  “Anyway, after our boozy lunch, he approved the funding for the next part of our project. As he was signing, he was proud to tell us that his company strictly forbade anyone to sign contracts after having been taken out to a meal with alcohol served – can’t think why – but then, he said, we wouldn’t tell, would we?

  “Let’s talk about your job,” I said, changing the subject. “Do you enjoy intensive care?”

  “Yes,” she said. “It’s full of action. Never a boring moment. Hardly a shift goes by without some emergency to handle.”

  “You said they were mostly heart patients?”

  “Yes, in my ward. The most critical time is of course the heart surgery itself, but the next most critical is the intensive care while they recover afterwards.”

  “Do you ever lose any patients?”

  “We try not to. I have found myself ripping open the sutures and pumping a stopped heart with my own hands, while the alarm goes for the crash team to arrive.”

  “Wow! Did you save him?”

  “Yes. But some of the others I couldn’t,” she said sadly.

  I placed my hand on hers. “I don’t know how you live with such a stress. I admire you.”

  “Thanks,” she said as she gently pulled her hand out from under mine. “Of course, it’s heart disease that’s the killer, just as bad as cancer. We do our best, but it sometimes just isn’t enough.”

  I tried to lighten the mood with a rather macabre joke. “Well, if you’ve had two or more die on you, I promise not to tell Professor Goodwin. He’ll have the whole lot of you in court!”

  We finished our beers.

  I rather nervously asked her if I could invite her out to dinner, maybe grab some pub food here? She said it was very sweet of me, but that it had already been a full day, and she had better be going since she had things to do back in her flat.

  “May I have your phone number?”

  “Yes.” She smiled, and gave it to me.

  I typed it into my phone and rang her. “Now you’ve got my number, too,” I said as her phone buzzed.

  “See you tomorrow,” she said as she pecked me on the cheek. I liked that.

  We went our different ways once
outside. I wondered where her flat was. Wishful thinking! She probably has a steady boyfriend.

  Sitting on the tube, images of Stephanie faded from my two-pint mind, to be replaced by the vision of Professor Goodwin humiliating me the next day and then the judge throwing me out of court. I like a challenge, and in the face of problems, I look for solutions; that’s the way I’m wired! At least, that is what I told myself. It seemed to do the trick, by the time I got off at Tooting Bec Station, I already had some ideas to follow up.

  While nibbling some stale bread and cheese, doubtless with Montignac turning in his grave, I checked some ideas by surfing on the internet. I considered that I was not committing a crime, firstly because they specifically wanted me to ask questions that were correct, and secondly, I was not researching the case, just revising mathematical probability concepts. I also pulled out Taleb’s book The Black Swan, to check on the section where he writes about random causes and random results. I found quite a few other ideas in there too.

  I noted some angles of attack for my questions the next day. I hoped the ushers would let me take the paper into the courtroom. Although the ideas were pretty well imprinted in my mind, I knew from experience that when standing up to give a presentation to clients, if I did not have written bullet points to remind me, the sheer nervousness of talking to a room full of people leads you to forget half of what you want to say.

  I did not sleep very well that night. Sometimes fully alert, sometimes in the neverland between consciousness and sleep, I was already continuing my cross-examination. Twice I sat up and added some more ideas to my list for the next day. At one point I had to will myself to calm down in order to get to sleep, just like I used to do before exams. The fact that you cannot sleep makes you even more worked up, so that then you certainly cannot sleep. You just have to tell yourself that it’s actually not that important, that whatever happens the next day, even if you don’t sleep at all, it really doesn’t matter, you’ll still do OK. It worked; I finally slipped off into a fitful sleep.

  Chapter Eight

  Next morning, at ten minutes to ten, all the jurors were in the jury room, all feeling distinctly naked without any mobile phones, but ready to go. Despite my lack of sleep, it seemed my adrenalin was keeping me wide awake and alert, at least for the time being. So at least I did not have to drink too much coffee; can you imagine having to ask the judge for a loo break?

  “Did you see the newspaper headlines this morning?” asked one of my fellow jurors. “‘72 million to one its murder, says expert’ – that was in The Times.”

  “The Sun has a picture of our young would-be Einstein and the girl, coming out of the courthouse,” said another. “The caption says, ‘Mad judge lets young juror cross-examine’. It goes on to say that the British justice system must be scraping the bottom of the barrel if any Tom, Dick and Harry can interrupt critical expert testimony, or something like that.”

  “We must not read or be influenced by the press,” said Hilary. “I avoided buying or reading any papers exactly for that reason. I did not look up any reporting on my phone either. I suggest you all do the same.”

  The jury keeper came in, smiled, and then filed us out into the courtroom for the second day of questioning witnesses.

  As I was taking my place in the jury box, Stephanie whispered to me, “Go for it! You can do it. Break wind!” I could not suppress a giggle at the thought of some embarrassing sound happening just as there was perfect silence in the courtroom.

  We all stood up as the judge came in. He looked carefully around the courtroom, first at the jury box, then to the public seats; he smiled.

  “Good morning,” he said, as we all sat down with him. “Let’s get to work. Please bring in Professor Goodwin.”

  Once the usher had installed him in the witness stand, the judge continued. “Good morning, Professor Goodwin, I remind you that you are still under oath.” He turned to me. “Mr Fielding, please do stand up and carry on with your questions. And I ask you not to get out of line. If you do, I will stop you. Is that clear?”

  “Yes, my Lord.” I cleared my throat, and looked at my notes that the jury keeper had indeed allowed me to take in. “Professor, first I would like to understand your figure of one in 8,500 as the average for cot deaths. You said this was from a study of 400 cot deaths over three years, and this figure applies to families that are non-smoking, have a wage earner and the mother is over twenty-seven?”

  “Yes, that is correct,” he answered.

  “What are the odds if some of these conditions don’t apply?”

  Goodwin shuffled through some papers he had brought with him. “Yes, as we said, for the case where none of the aggravating factors are present – smoking, unemployment, young mothers – the probability is indeed one S.I.D.S. for every 8,543 live births. If one of the factors is present, this reduces to one in 1,616 live births.”

  “What?!” I exclaim. “If there is either a smoker in the house, or if both parents are unemployed, or if the mother is young, suddenly the odds of a cot death are – what…” I did some quick mental calculations, “…more than five times more likely?”

  “Yes, about that.”

  “What happens when there are two, or all three, of these factors present?”

  “With two aggravating factors present, the odds are one in 596,” said Goodwin looking at his paper. “If all three factors are present, the odds are one in 214.”

  “One in 214 compared with one in 8,500?!” I did another bit of mental arithmetic. “About 40 times more likely to happen than your statistic for the defendant?!”

  “Yes,” said Goodwin, “but none of those aggravating factors were present. I repeat, none. So, the one in 8,500 is the correct figure to use.”

  “But if we use the one in 214 figure instead, the probability of a random succession of two cot deaths would be one in 214 squared…” in my mind I squared the 2 and then added two lots of two zeros, “a bit more than one in only 40,000 – a lot less than one in 72 million! Then, if there are 400,000 second or more births each year, and if, just for the sake of argument, all parents were smokers, unemployed and young, then 400,000 divided by 40,000 would give us 10 double cot deaths per year. Mrs Richardson would never be in court. Is her crime simply because she doesn’t smoke, she’s over twenty-seven and that she or her husband have a job?”

  “Don’t be flippant!” Goodwin shot back at me angrily. “The figures for her category are clearly one in 8,500, not one in 214.”

  I also caught a look of disapproval from the judge.

  “But just look at the variability,” I countered. “You just change one or more small variable in the baby’s environment, and your figure comes tumbling down to much higher odds of cot deaths. What was the aim of this study?”

  “To identify families at higher risks than others,” answered Goowin. “Once warned, we can use better baby surveillance methods, like apnoea alarms and so on.”

  “So, it’s descriptive to identify risks,” I said. “Since when does descriptive become prescriptive? The defendant does not have the right to have more cot deaths simply because her husband works?”

  Unsurprisingly, Goodwin chose not to answer my rhetorical question.

  I decided to change tack slightly. “This is based on an analysis of 400 cot deaths, you say?”

  “Yes.”

  “What defines a cot death?”

  “When a young infant dies of no known cause,” replied Goodwin.

  “No known cause… or perhaps a cause which is known but that is just not visible?” I asked.

  “Well, yes. That would apply as well.”

  “So,” I said, “it’s a bit arbitrary. Some well-known natural cause is not found, because the body hides the symptoms, or because the pathologist does not have enough experience in baby post-mortems, so it gets qualified as a cot death. If on the other hand, the cause is
visible, it gets qualified as something else. I suppose the full number of infant deaths is much higher.”

  “If you include infections, known pathologies and so on, yes,” he replied.

  “So, if we said, ‘death by all natural causes’ and not just ‘cot deaths’, we would have more deaths, so more than one in 8,500 in your extreme best-case environment, and more than one in 214 at the other extreme for the worst-case environment?”

  “Er, yes,” he concurred.

  “So, you’re penalising Mrs Richardson, using harsher odds against natural deaths, not only because of no smoking, having jobs and being over twenty-seven, but also, perhaps, because the pathologist didn’t do his job well enough?”

  Again, no reply.

  I decided to open yet another door of weakness in his arguments. “In your opinion,” I said, “is 400 cases over three years a big enough sample, and a big enough time span, to get accurate probabilities?

  “Yes, I think it’s pretty good.”

  “Wait, you identified three variables,” I countered. “That means you have three squared, that’s nine possible combinations of each variable – none of them, one of them (but which one?), two of them (again which two?) or all of them. That’s 400 divided by nine, about 44 cases of cot death for each combination of variables. That’s not enough data to identify clear trends. A few unusual happenings could corrupt events – maybe there was temporarily milder weather, so less flu virus going around at that time, just as an example. And who says that what happens in one period of three years is representative of what happens a few years later?”

  Liking the sound of my own voice, I ploughed on. “Let’s take an example from my own experience – my company designs offshore oil platforms. We did hundreds of thousands of wave height measurements where a platform was to be installed in the North Sea. We extrapolated the data to get the so-called one-hundred-year wave – the big one that comes on average every hundred years, so that we can design the platform to withstand it. But once the platform was installed, lo and behold, waves bigger than the hundred-year-wave hit the platform twice in the first five years and did extensive damage. In your opinion what went wrong?”