[tabs tab1=”2MM Rundown” tab2=”From Chaos to Order” tab3=”From Order to Law” tab4=”From Law to Humans”]
Disclaimer: The views and opinions expressed in the Perspectives Series are those of the author and do not necessarily reflect the official policy or position of 2 Minute Medicine.
When’s the last time you thought about statistics?
If you’ve just watched TV or read a scientific article, you might say ‘quite recently’. But I don’t mean statistics in a ‘30% chance of precipitation’ kind of way, or even in a ‘statistically significant difference’ kind of way. When’s the last time you thought about how statistics work and how startling it is that they do in fact work?
We’ve become so accustomed to statistics that we’ve stopped marveling at it, in the same way we ignore light bulbs or complain about the internet speed on airplanes. Statistics has become the informational equivalent of overhead music at the mall: something we idly hum to while thinking about something else. Yet, in its day, statistics was so radical that people talked about it on the street and statistics books topped the bestseller lists. It is a measure of the success of statistical methods that we do not share our ancestors’ astonishment.
As physicians, we deal with statistics on a daily basis, but we focus on how to use statistics rather than on what they really do. We therefore thought it fitting to inaugurate 2 Minute Medicine Perspectives with an exploration of a subject that features so heavily in this site – and yet goes so unnoticed. This week we examine the historical origins of statistics and how several key insights laid the conceptual groundwork for human research. In the next issue we will narrow in on the use of statistics in medicine – both its successes and its failures.
Historically speaking, gambling was the gateway to statistics. Statistical analysis rests on the mathematical description of uncertainty and probability, and we grapple with these concepts most clearly in a pair of dice. It is no surprise, therefore, that just as teachers now ease into statistics with decks of cards and buckets of balls, the mathematics of statistics was invented to explain games of chance. What is surprising and somewhat mysterious is that humans have been throwing dice and casting lots for millennia, but a mathematical description of these activities wasn’t invented until the decade around 1660. It is even more striking that in this decade probability mathematics was invented twice, independently – first by Pascal and Fermat in a series of letters, and second by a Dutchman Christiaan Huygens in the first textbook of probability1.
Around the same time, in 1662, an English haberdasher named John Graunt made another independent contribution to statistics in the first descriptive analysis of human data. In 1603 the City of London had begun reporting weekly lists of deaths and christenings as a way of monitoring the plague, and Graunt thought he could use the lists to characterize his client base. To the modern reader the lists are evocative – causes of death include ‘Affrighted’ (3), ‘Aged’ (32), ‘Winde’ (3), ‘Teeth’ (33), and ‘Grief’ (3)2– but something in the lists must have also caught Graunt’s attention, because his project quickly grew into the first effort to estimate mortality rates and life expectancies, concepts which he also had to invent along the way. Though many of his inferences were likely wrong, Graunt had made a major methodological innovation; as one historian writes, “Fermat and Pascal worked out more mathematically accurate formulae for probability, but it was Graunt who extended it beyond mathematics and games of chance into the real world3.”
It would take another two hundred years, however, for Graunt’s insights to merge with probability theory into modern statistical analysis. This unification occurred in the application of a principle called the law of errors, which was invented to solve a problem in astronomy. Astronomers attempting to chart the position of a star noticed that their measurements were not always consistent. Depending on the degree of moisture in the air or the person taking the measurements, or any number of factors, their data would vary in unpredictable ways. When they tried to plug these data into their equations, they were stuck; they did not know which measurement was correct and which was skewed by these hidden factors.
The solution came from probability theory. Astronomers noticed that when they plotted multiple observations, the values produced a bell-shaped curve with a peak at a particular value. Their insight was to realize that the peak of this curve pointed to the star’s ‘true’ position in the same way that two thrown dice will tend to sum to seven, or the way the distribution of arrows on a target concentrates near the bull’s eye. Calculating this peak value – the mean – was a separate challenge, but once this problem was solved, scientists could actually use the variability in their data to calculate the true value. This was the law of errors: even error and variability can, over enough observations, become predictable and regular.
It’s hard for us now to appreciate the enormity of this insight. In the early 19th century, when the law of errors was developed, astronomers weren’t the only ones trying to fit data into equations. Natural laws were everywhere. An object in motion stays in motion; offspring inherit an allele from each parent; the pressure of a gas varies inversely with its volume. Scientists prized these and other natural laws as the ultimate form of explanation because they described the hidden regularities that silently governed the chaotic world around us. In practice, however, as the astronomers had discovered, these laws were difficult to discover and difficult to apply due to the impenetrable variability of measurement. Before the law of errors, scientists had assumed that this variability was a permanent obstacle, a kind of natural static that blocked our ability to hear the law. The law of errors transformed this static from random noise into something that itself was predictable, a scrambling code that, with the key, could be decoded to reveal the underlying regularity. Error was no longer insurmountably random, and its predictability was itself a tool to help us access natural laws.
This insight has forever changed our approach to scientific data. However, the full significance of the law of errors was that it extended beyond the natural world. The man who best understood this was Pierre-Simon Laplace. A brilliant scientist and an ardent determinist, Laplace had helped develop the method to calculate the statistical mean, and was famous for describing the universe using only Newtonian principles (coining the phrase ‘celestial mechanics’). He also had the intuition that the law of errors could extend beyond heavenly bodies and inanimate objects. If, as the law of errors predicts, all things that vary are likely to vary in a way that can be measured, then the law should apply to everything – including humans. Building on the work Graunt had started 200 years prior, Laplace showed how a range of human behaviors – whether someone lies in court; death rates and marriage rates; the number of female and male babies born each year; the number of letters sent to the Paris dead-letter office – all vary around a calculable mean. Adophe Quetelet, one of Laplace’s most zealous successors, showed that Scotsmen’s chests and even murder methods follow this rule. We may not know who will kill whom, but we can estimate how many will die by gunshot rather than stabbing, caning, stoning, drowning, strangulation, or fire4.
When Laplace and Quetelet published these findings, their books became instant bestsellers. It astounded the citizens of 19th century Europe and America to think that something as personal and seemingly random as getting married or grabbing a knife for murder is as predictable as the movement of planets. The lurking implication – that even human behavior is governed by social laws analogous to natural laws – challenged our self-understanding of our own behavior as deeply as Darwin’s law of evolution and Freud’s later discovery of the unconscious. Our contemporary preoccupation with the social determinants of behavior is the product of this insight.
Our thinking about health and disease also bears the imprint of these ideas. Prior to statistics there was no systematic way to extrapolate from the variety of experiences that constitutes human illness and therapeutic response. Because human health and disease arise at the intersection of biology (natural law) and human behavior (social law), we needed both the scientific and the social implications of the law of errors to conduct medical research on humans. Put simply, these findings created and validated the ‘human subject’ of human subjects research – an entity that we now forget was made rather than found.
So, the next time you come across a statistic, take a moment to appreciate it. Statistics has helped us make sense of the world and the people around us, and it has done so with such success that, like the weather, we can no longer imagine the world without it. But, like a surprisingly radiant sunset, it’s worth noticing.
 Hacking, I. The Emergence of Probability. Cambridge University Press: Cambridge, 1975.
 Strathern P. Dr. Strangelove’s Game: A Brief History of Economic Genius. Penguin (England), 2002, p 20.
 Strathern P. Dr. Strangelove’s Game: A Brief History of Economic Genius. Penguin (England), 2002, p 21.
 Menand, L. The Metaphysical Club: A Story of Ideas in America. Farrar, Straus & Giroux. New York: New York, 2001.
© 2013 2minutemedicine.com. All rights reserved. No works may be reproduced without written consent from 2minutemedicine.com. Disclaimer: We present factual information directly from peer reviewed medical journals. No post should be construed as medical advice and is not intended as such by the authors or by 2minutemedicine.com. PLEASE SEE A HEALTHCARE PROVIDER IN YOUR AREA IF YOU SEEK MEDICAL ADVICE OF ANY SORT. Content is produced in accordance with fair use copyrights solely and strictly for the purpose of teaching, news and criticism. No benefit, monetary or otherwise, is realized by any participants or the owner of this domain.