I give you a bundle of currency notes, let’s say 100, and ask you to count them. You count 99. I re-count and get 100 again, so I ask you to re-count. You still get 99.
Who’s count was correct?
It’s a familiar but hidden dilemma faced in all counting situations, and not necessarily only those involving human beings. For instance, when a pathology laboratory does your bloodwork, they use sophisticated counting machines to enumerate the number of white blood cells, oesinophils, neutrophils, red blood cells, disease antigens, and so on.
How sure are you of the numbers? Would a second pathology laboratory have produced identical counts from the same blood sample?
Even if it did, would a third machine have? What if 10 machines were deployed and only one gave a divergent answer — what are the chances that nine were wrong and the odd-one-out was actually right?
Remember Galileo? He was the odd one out when he asserted that the earth went around the sun, and was persecuted and reviled for his belief. The majority was believed to be right because, well, how could so many people possibly be wrong?
In real life, unfortunately, we tend to side with the majority too. It takes more than some silly philosophical uncertainty to stop us.
Let’s say I’m counting a bundle of 100 notes, and get 99. Since I’m expecting 100, I’d assume this was an error and recount. If that gave me a 100, I’d probably not count again because after all, that was what I had been expecting. But if I got 99 again, then a third count would become necessary. If that yielded a 100, I’d probably count a fourth time, since I’d gotten 99 twice already. I might even count thrice to see if I got 100 more times than I got 99.
The best of many counts is the usual principle we follow.
But what if life and death were involved in getting the count right?
Counting HIV
If you were being tested for HIV, you have a choice of tests, but the rapid test typically does not look for HIV but for antibodies produced by your body to fight HIV. The assumption is that if your body has antibodies, it must have HIV.
However, there are two cases in which this assumption is not valid and the test could yield false results. in one case a false negative and in the other a false positive.
Here’s the first. It takes an HIV-infected person some time to produce enough HIV antibodies for them to be detected by a rapid test. This period could range from a few weeks to as long as three months. What if a person took an HIV test during this window period? He would test negative while a second test a few weeks later would have shown him positive.
Which of the tests should he go by? What if the positive was false and the negative was actually right? In such a situation, many doctors would advise a third test, if only because the psychological, physical and economic implications of being positive are so devastating. If the third test came out negative, then usually that would be taken as definitive. If it was positive, however, the patient might demand a more sophisticated test, such as a Polymerase chain reaction (PCR) test, to be even more certain.
But even a PCR can be fallible — no? When can we be 100% certain? The answer is, I am afraid, never. We always end up going with the best guess, no matter how sophisticated the instrument.
The other instance where a person can have HIV antibodies without having HIV infection is a child born to an HIV positive mother. Nature, in its bounty, makes sure that a newborn child inherits all her mother’s antibodies, and has natural protection against a slew of diseases until its own body becomes adept at producing its own antibodies, a process which takes about 10 months.
I know a couple who had chosen a gorgeous sunny baby for adoption, but were dismayed to learn that he was HIV positive. The prospective mother, who knew nothing about AIDS, educated herself, and when she realized that motherhood would essentially entail being a caregiver to a sick infant who would die soon, she surrendered the child with the deepest regret.
But she was wrong. The HIV test had merely detected the mother’s HIV antibodies in the baby’s blood. Ten months later they had disappeared completely, because the child was uninfected. He is today a healthy teenager in college in Delhi.
Money to be made
Miscounts can be lucrative. Let’s take blood pressure, which is routinely measured as a key vital sign when you go to a hospital. In general, a higher number (called systole) of 120 and a lower number (diastole) of 80 or less is considered ‘normal’. Let’s say your blood pressure hovers near 140/90 now and then. The doctor could declare that you are a borderline hypertensive, and pretty soon prescribe a range of medications (with their own side effects) for ‘normalizing’ your blood pressure. Depending on which medication she prescribes, your kidneys, sex life or sugar tolerance, among others, could be impaired.
However. even two blood pressure readings taken within minutes of each other will not yield the same numbers.
So — just as with counting money — we must ask how many times a person should his or her blood pressure before letting the doctor conclude they need hypertension medication? Blood pressure varies through the day, generally being a little higher during noon and afternoon, and declining towards evening. Within this period, though, stress, excitement, a near miss with a fast driving car, a rough session from your boss, any and all of these could drive your blood pressure up.
In a well-known phenomenon called ‘white coat hypertension’ it has been shown that even the presence of a doctor in a white coat grimly measuring your blood pressure is enough to drive your blood pressure up a little. Measuring blood pressure itself drives blood pressure up.
My doctor made we wear something called a Holter vest, which monitored my blood pressure at fixed intervals as I went about my day. But my skeptical mind asks: would a different Holter vest from a different doctor have given different results?
My simple rule of thumb with any test or measurement that has implications for your health or your wallet is — measure thrice, at different establishments. The family doctor could be wrong. Worse, he could be in the pay of big pharma, no matter how much like Santa Claus he looks.
Enough for a heartache
Cholesterol measurements are another notorious area where the wrong numbers are bad for you but profitable for the doctor and some corporation in another country. Your ideal low-density cholesterol (LDL or bad cholesterol) is supposed to be between 100 and 129, while your high density cholesterol (HDL or the good cholesterol) is supposed be between 40 and 49 for men.
These numbers, from the USA, are, however, arbitrary. The United Kingdom, for instance, judges LDL over 100 as high, and considers a range of 40 to 60 normal for HDL. Risk calculations, apparently, depend on the ministry of health.
If I were a cynic, which I am, I would guess that neither doctors nor big pharma would be particularly interested in you or anyone else testing your cholesterol several times at different laboratories, since they might disprove the need for medication. Neither would they be in favor of you taking a test after a week on a lovely salads and juices only diet, since that would reduce your cholesterol readings. Cholesterol, like the blood pressure, changes through the day and with your food intake.
The bottom line is that these readouts, taken too few times and from too few machines, and with little cross-validation, could put you in line for a lifetime of statins, supposedly to help avert a heart attack by keeping you cholesterol down. Statins have been shown to do little for cholesterol, and come with a list of side effects you do not want in your old age.
So — back to my original question: how often should you count your cholesterol?
Back to the small change
This post started with an observation about the impossible of knowing when you’d miscounted your money. Over the years, I’ve developed my own way of making sure I don’t overpay anyone because of miscounting and it’s based on human psychology. It’s a cynical little trick, but it works very well. It’s based on the assumption that if I overpay you, you might or might not draw my attention to it, depending on your honesty, but if I paid you less that I owed you, then you sure as hell wouldn’t let that slide.
So if I had to pay you, say, 1,000 dollars or rupees or Thai baht or whatever you consider money, I’d count it out first with my own hands. Maybe twice or thrice even, to be surer. Then I’d remove a single note and pocket it, reducing the amount in my hands to 999. This is what I’d give you. There are three ways this could play out now.
Scenario 1. It could turn out that my count was disastrously off, and I had given you 1001 instead of 999. You, being dishonest to the core, say nothing and walk away, richer by an unexpected dollar.
Scenario 2. Your count yields 1,000 — in which case I would ask you to recount since I’m expecting 99. If you get 999, the answer I expect, on a recount I’d give you the dollar hidden in my hand, making it a round 1,000. But if your second count also yielded 1,000 again, I’d assume I had miscounted the first time. Close shave. You get your money, and I avoided paying you an extra dollar by error.
Scenario 3. Most likely — your count detects 999 and you of course point it out at once. I, being a thorough gentleman, nod and give you the missing buck. All is well.
You can make a mistake with counting, but you can’t go wrong if you count on simple human avarice. Nobody likes to be shortchanged.