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NUMERACY

Our journey begins with the story of Edmond Halley (1656-1742). Son of a wealthy soap maker, he studied mathematics at Oxford and became a respected astronomer. The question of how gravitational force influences the shape of celestial orbits led him to travel to Trinity College, Cambridge, to seek help from the reclusive Isaac Newton.

Upon their meeting, Halley recognized the scope of Newton's astonishing genius. The young astronomer pressed his hero to publish thoughts in a book that came to be titled Mathematical Principles of Natural Philosophy, which has my vote for the most significant scientific book ever written. Among other things, Newton demonstrated that the sun holds a planet in an elliptical orbit.

Halley then used this principle to review past observations of comets. These bright, fleeting objects have attracted attention since biblical times. The Bayeux Tapestry shows a comet streaking through the sky before the Norman conquest of England in 1066. Halley reasoned that comets follow the same laws of motion as other celestial objects.

Armed with Newton's inverse-square law, Halley studied records of past comet observations and attempted to infer orbital periods. He concluded that a comet he observed in 1682 was the same object identified in the tapestry and then seen by Peter Apian in 1531 and Johannes Kepler in 1607. In 1705, Halley predicted that this object would return to view in 1758.

Sixteen years after Halley's death, stargazers turned to the skies to search for the returning comet. On Christmas Day in 1758, an astronomer in Germany spotted the object that would become known as Halley's Comet.

This anecdote illustrates numeracy in action. Halley identified a pattern buried within data and then used this pattern to make a bold prediction outside of the domain of the original data set. This was some trick because the gravitational pulls of Jupiter and Saturn give the comet an irregular orbital period. What's more, this object is visible for just a few weeks out of each orbit. Halley crafted a successful prediction from thin data.

Halley's story leads to the summary idea of this book:

Numeracy is the craft of statistical reasoning.

Permit me some ink to unpack the four key words in this short sentence.

Numeracy. I first came across the term numeracy as a college student, when I read a paper written by the statistician Andrew Ehrenberg (1977). He railed against colleagues at the prestigious Royal Statistical Society who amassed gobs of data and then did little with it. Educated math whizzes, surrounded by rich data sets, often show little skill at extracting meaningful information and then presenting it clearly. A useful statistician - for whom Ehrenberg bestows the label of numerate - identifies a cool "so what" and then presents the finding in a way that communicates it clearly.

I cannot begin to list all the horrifically bad presentations I have endured in my career. Time and again, well-trained people gushed waterfalls of data without providing any meaningful insight. Apparently, the presenters were saying, I worked so hard on this analysis, and I want you to see evidence of how much time was spent on the project. Ugh.

Occasionally, however, I watch a presentation or read a paper where the presenter distills hours of work into a simple summary that builds a bridge between evidence and conclusion. When I'm blessed to receive the work of a numerate person, I feel enormous gratitude for the gift of information delivered in a concise, pleasing manner.

Halley showed numeracy by distilling his work on comets into a breathtakingly simple conclusion: the celestial body in question would again be visible in 1758. Simplicity is a foundational idea of this book.

Craft. A typical U.S. university has a school of arts and sciences. Disciplines taught there, ranging from soft humanities to hard physical sciences, expose students to two broad categories of scholarship. The softer arts encourage expression of individual points of view while the sciences emphasize agreed-upon answers.

No two classics students will draw identical conclusions about the role of Achilles in the Iliad, but every chemistry student should agree on how to balance a reaction equation involving sodium and hydrochloric acid. Scientific statements may be disproven, while those in the humanities may be argued without end.

Falling between arts and sciences are crafts, pursuits requiring a type of thinking rarely taught in higher education. An example of a craft is metalworking. Grades of steel have chemical properties that lend themselves to scientific study. Other factors, however, influence a metalworker's ability to cut a certain piece of metal to meet required specifications.

On a particular day, the air has a certain temperature, humidity, and pressure. The grinding machine is at a certain stage in its maintenance cycle. The steel blanks have idiosyncratic properties associated with the production lot made at a point in time at a particular mill. I doubt that any scientific model will ever be able to incorporate how these and dozens of other variables influence the shaping of metal.

When I was in college, I worked in a factory that made transmission assemblies. An unshipped unit in final assembly needed roller bearings with dimensions specified to a couple ten-thousandths of an inch - a ridiculously tight tolerance in an age before the spread of numerically controlled machines. My job was to deliver steel blanks to a master machinist who was "voluntold" to cut the bearings immediately. A baseball analogy would be asking a player on his scheduled day off to step out of the dugout in the bottom of the ninth inning to hit a home run.

A crowd formed around the machinist, who examined the blanks, inspected the grinding machine, and took note of myriad factors that were lost on me. He set up his equipment and began cutting. A quality control professional used precise calipers to measure the dimensions of the output. The first few bearings failed quality control. The machinist made adjustments and then produced a series of bearings that each met the required size standards. The rest of us watched in awe.

In that moment, this craftsman garnered more respect among colleagues than any investment banker, management consultant, university professor, or business executive I've ever met. None of us present that day could come close to doing what he just did. I considered dropping out of college to become his apprentice.

This machinist - whom I remember as Yoda - worked a craft, a discipline that straddles the domains of art and science. The science of metallurgy informs us of processes used to transform steel. However, the scope of this science is not sufficiently developed to tell us how to handle every situation we may face. At that point, a craftsman blends individual judgment with formal training to accomplish a desired task.

This judgment is not easily codified or documented, hampering the ability of a master to pass along know-how to an apprentice. The master offers coaching, but the apprentice assumes responsibility for finding their own way while learning from the master.

Numeracy is a craft. There is some science embedded in the tools used to reveal patterns buried in data. However, this science is not sufficiently robust to instruct people what to do in all cases. Simply buying a computer loaded with statistical software gets one nowhere fast. Numerate people use their wits to sort through quirks embedded in unfamiliar data sets. An effective craftsman blends school-taught technique with hard-won experience to sort through the problem at hand.

The little science given in this book merely repeats what many other reference books on statistics share. Any decent teacher may explain the dozen or so concepts discussed here. The real magic comes from you using your judgment to apply them to circumstances associated with data sets in your life. The art of numeracy is learned but not taught, and I hope that the storytelling in this book serves as a catalyst to help you cultivate this skill faster than what would have been accomplished if you had not read these pages.

Halley's prediction required blending the science of Newton's inverse-square law with the art of estimating masses and distances of significant bodies within the solar system using incomplete astronomical data available at that time.

Statistics. Statistics, a subset of mathematics, studies how one may make uncertain inferences about a broader (and often unobservable) population from the study of properties of a small sample. A classic example is when your grandmother prepared homemade soup. After combining and heating the ingredients, she undoubtedly stirred the liquid and sipped a spoonful to assess the mixture. She was able to draw conclusions about the entire pot from a small taste.

Statistics may be viewed as the opposite of probability, the study of the likelihood of future events occurring based on known frequency distributions. We know that a fair, flipped coin has a 50% chance of landing as a head. Since fair coin flips are independent events, we may conclude that there is a one-in-four chance that this coin will land as heads in two consecutive trials.

The field of probability arose in the seventeenth century as gamblers sought to understand how much money should be wagered in games of chance. Use of probability theory requires...