Monday, July 12, 2021

When Numbers Lie and When They Don't

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Lucia de Berk, a Dutch licensed pediatric nurse was convicted of seven  murders and three attempted homicide, and subsequently sentenced to life imprisonment in 2006. What was extraordinarily intriguing about the case, if not alarmingly so, was that only in two of the cases were supported by circumstantial evidence in the eyes of the court while the rest was based on what is called chaining-evidence argument by the prosecution.

"This means that if the several attempted or actual murders have already been established beyond reasonable doubt, then much weaker evidence than normal is sufficient to establish that a subsequent eight "suspicious incidents" are murders or attempted murders carried out by the same defendant".


The prosecution used mathematics - more specifically the scope and power of statistics - that argued that the "chance of a nurse working at the three hospitals being present at the scene of so many unexplained deaths and resuscitations is one in 342 million".

As it turned out, in this case, the numbers were misused by the prosecutors while the science of statistics was blatantly misapplied. It was a miscarriage of justice; rectified only after a long process of reviews and re-analysis of the data that were compiled and the methodology used to convict her. The case was re-opened.  In 2007 she was fully exonerated and compensated for by the government.

Why did this miscarriage of justice happen? Did the numbers lie at first and told the truth later? Actually, numbers do not lie. Never. People do. However, numbers can be and had been manipulated, misapplied or selectively abused to favor one conclusion or sway opinions or, as in the case of Ms. de Berk, win a conviction. It is people who lie. 

There is so much about numbers but let's first focus on the Good, The Bad and The Ugly about it

The Good

Numbers, when applied properly, can project unerringly the results of a fair election long before the final tally. While predicting the weather is often made fun of, there is a method to the madness of forecasting rain or no rain.  When we hear the forecast of 70% chance of rain and it doesn't, it has nothing to do with inaccuracy.  You see, what it meant is that given 100 days on past meteorological records with the same set of conditions being observed and measured for the following day or week, in 70 of such days rain occurred while in 30 of those same 100 days rain did not happen. So, when it didn't rain the forecast was still correct. Our brain only considered rain or no rain without taking into account that the forecast actually and clearly said 70% but only so because in thirty of those days with similar conditions there was not a drop of rain.

The birthday paradox works a little bit differently but it is often met with the same incredulity.  It says that in a room of 23 random guests the odds that two people will have the same birthday is 50-50. Quite high, you say. Increase the number of guests to 75 and the odds go up to 99.9%, a near certainty.  It had been proven many times to be true.  You see, we erroneously think of two specific or particular birthdays of two particular individuals.  When we think simply of two unspecified people and two unspecified birthdays, the odds are higher than we intuitively think.

SO, numbers do not lie. That's good.

The Bad

A particular grocery item languished and unbought for sometime at a posted price of $1.50 each.  The store manager one day put all the unsold merchandise in an open bin in the middle of the isle or intersections of the isles, arranged in a disorderly tumbled mound and labeled Two for $3.00 SALE!  Would you believe they sold faster than had they remained on the shelves?  You'd wonder what happened to the discriminating customers who had avoided those same items all along.  Those are not what the store manager counted on.  He targeted those "not-so-discriminating" buyers who were swayed by the 2-for SALE. 

Lottery is the modern day siren song of the unattainable dream. But what about those who actually won?  But then what about those millions and millions who didn't? And what of those who spend an inordinate amount of their meager income on the odds of 1 in 292.2 million?

  • One in 2,320,000 chance of being killed by lightning
  • One in 3,441,325 chance of dying after coming into contact with a venomous animal or plant
  • One in 10 million chance of being struck by falling airplane parts
Feeling unlucky? If one does not believe that any of the three above potential events will happen to them in their lifetime, why does one think 1 in 292.2 million is a good bet?

The Ugly

According to FBI data there were about 10 million police arrests last year.

"Out of those 10 MILLION arrests, there were 1,004 officer-involved fatalities

Out of those 1,004 officer-involved fatalities, 41 were unarmed.

Out of those 41-officer involved unarmed fatalities (now you might find it hard to believe), out of 41 deaths, now hear this.."

 19 were white - 9 were black

Now 1 is 1 too many, but  41 out of 10 million is a pretty small percentage! (.00041%).

Numbers don't lie but politicians may and do it often with nary a moment of encumbrance nor accountability. You see, if we listen to some of them there is an "epidemic of police killing of unarmed black suspects", or according to one congresswoman, "blacks are being hunted down like dogs by police".  One school teacher in a traffic stop for using her cell phone in a no-cell-phone zone near a school berated the policeman and told him that he and others like him (police) "are a bunch of murderers".

In that same period, last year, 89 police officers were killed in line of duty. 

We hardly hear about them nor their sacrifices.

Numbers don't lie.  People do.

Everyone who heard of Lucia de Berk's story and her conviction only had revulsion and anger at what "she had done" at the time. But, how many of us later knew about what really happened?  I didn't know about it until recently listening to a lecture on TV by a renowned physicist as he explained the power of mathematics and the misuse of it.

Numbers are fundamental to the nature of the universe itself.  Humanity cannot claim to have invented numbers, nor can it take credit for inventing mathematics either.  We (humans) merely discovered them. You see, whether we are here or not, one is always less than two, or that our solar system has one sun orbited by eight or nine planets (depending on your definition of a planet), and that a typical galaxy has anywhere from 100 to 200 billion stars and there could be as many as a trillion of those galaxies in the entire universe.

A circle will always have its area defined by its  radius squared multiplied by an inviolable  constant that we also discovered to be pi. We did not invent that either.

Light will always travel at about 186,000 miles per second.  Unfortunately, bad information, gossip, innuendos, politicians' lies and the woke population's ridiculous "ban this, ban that, cancel this or that", also seem to travel at the same speed.  And the worst part is that some of the worst lies travel to much distances that originate from the very few.

Next time you hear it said and you have doubts that it isn't so, remember Numbers don't lie, people do.


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