# Probability and Statistics: The Drunkard’s Walk

## Probability and Statistics Impact Our Lives

In his book, The Drunkard’s Walk:  How Randomness Rules Our Lives [Vintage, 2008],  Leonard Mlodinow provides an interesting look at how random events guide so much of what happens to us and the world around us.  Leonard Mlodinow gives numerous examples of “the principles that govern chance … and the manner in which they play out in politics, business, medicine, economics, sports, leisure, and other areas of human affairs” (p. ix).  Mlodinow also traces the history of probability and statistics, including the stories of some of the lesser-known people who advanced the mathematics of these fields.

## Randomness

Mlodinow writes that “random processes are fundamental in nature and are ubiquitous in our everyday lives, yet most people do not understand them or think much about them” (p. xi).  Some of the examples he includes in which decisions are made because of the misinterpretation of random events are the firing of the coach of a sports team because the team does not do well, the hiring of a corporate executive based on past performance, and the lauding of a mutual fund manager because his fund has done well.  All of these phenomena involve random events in which the coach, the executive, and the fund manager have little or no influence.

The “butterfly effect” is the term used to describe how slight, random factors and events can lead to success or failure in our lives.  This effect was first described in the 1960s by Edward Lorenz, a meteorologist, who rounded some values in a predictive weather model and saw how the model made very different predictions than when non-rounded numbers were used.  About such random factors, Mlodinow writes (p. 11):

A lot of what happens to us – success in our careers, in our investments, and in our life decisions, both major and minor – is as much the result of random factors as the result of skill, preparedness, and hard work.  So the reality that we perceive is not a direct reflection of the people or circumstances that underlie it but is instead an image blurred by the randomizing effects of unforeseeable or fluctuating external forces.

The ability to understand randomness is an important skill for all of us to learn.  But, as Mlodinow writes, it is human nature to infer patterns where patterns do not always exist.  Mlodinow discusses how hindsight is 20/20:  It is easier to see how a random path led to an event, such as the attack on Pearl Harbor and the Three Mile Island nuclear reactor meltdown, if one is looking for information to support that.  But before the event happens, there is too much data to be able to determine what the future will bring.  This is the essence of the “drunkard’s walk.”

## History

The Drunkard’s Walk also provides a somewhat unique walk through the history of probability, going back to the ancient Romans, who saw value in understanding probability, including Cicero, who proclaimed that “probability is the very guide of life” (p. 31).  Mlodinow talks about some of the lesser-known players in this history, including Gerolamo Cardano, who, after studying various forms of gambling, wrote The Book on Games of Chance.  One of the most important concepts to come from Cardano was that of the sample space, which basically lays out all the possible outcomes of some event or series of events.  This was an important step forward in the formulation of the rules of probability.

Mlodinow writes about the famous mathematicians Blaise Pascal and Jakob Bournoulli, who set out to explain the seeming randomness (or, in the early days, the “divine intervention”) that they witnessed, particularly in games of chance.  And Mlodinow describes how, in 1733, Abraham De Moivre used Pascal’s triangle of binomial coefficients to be the first to develop the standard normal (“bell”) curve (p. 138).  Then, in the early 1820s, the little-known Adolphe Quetelet applied mathematical tools to large amounts of social data and discovered the standard normal distribution applies to many social situations (p. 155).

If the subjects discussed in The Drunkard’s Walk are of interest to you, you may want to consider pursuing a degree in data science.

A page from The Drunkard’s Walk showing the relationship between Pascal’s triangle and the bell curve.

## Tying Probability and Statistics Together

Turning to statistics, Mlodinow traces the roots to the early 1600s, when John Graunt and William Petty, called the founders of statistics, analyzed England’s mortality bills (p. 150).  Graunt’s work led to the idea that inferences about a population can be made from a sample of data from that population (p. 155).  It was not until 1828, though, that the word “statistics” appeared in Noah Webster’s American Dictionary.

Jumping to the late 1870s, Mlodinow discusses how Francis Galton, cousin of Charles Darwin, discovered the phenomenon of “regression to the mean” (p. 162) and defined the coefficient of correlation.  In the 1890s, Karl Pearson invented the chi-square to test “whether a set of data actually conforms to the distribution you believe it conforms to” (p. 164).  For example, in rolling a single die, do the values conform to a uniform distribution?

Albert Einstein also played a part in the field of statistics.  In 1905, he applied statistical physics to explain Brownian motion, the apparent random motion of atoms.  This was one of the most important developments in physics and eventually led to modern technology.  It also helped to establish the importance of the standard normal distribution in science.  Finally, during the 1920s, R.A. Fisher developed significance testing, which is the core of the application of statistics and led to the modern development of the field.

Mlodinow does a nice job of tying the stories of probability and statistics together.  His examples of applications of probability and statistics, including the randomness involved in these fields, will resonate with the reader.  For the non-mathematically-inclinded, The Drunkard’s Walk will be an enlightening and understandable look at mathematics.

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