The Arts and the Age of the Chip

This chapter provides the capstone to this book’s argument that humankind has adopted quantification as a worldview. It describes how quantification has permeated our lives, far beyond just academic formulas to all domains, whether mathematical or otherwise. Examples are given first from the intersection of mathematics and art in da Vinci’s drawings. Next, the connection between mathematics and music is made, with a discussion of J. S. Bach’s The Well-Tempered Clavier and music theory’s circle of fifths. The chapter then provides an elementary explanation of artificial intelligence (or AI, as it is commonly known) with Bayesian logic, and a discussion of Nick Bostrom’s idea’s that the possibility of a computer having “superintelligence” poses a supreme danger to humanity. In addition, the chapter describes Max Tegmark’s innovative work in astrophysics and his belief in a wholly mathematical universe as part of a larger four-system multiverse.

Related to Relativity

This chapter provides the context for the early twentieth-century events contributing to quantification. It was the golden age of scientific exploration, with explorers like David Livingstone, Sir Richard Burton, and Sir Ernest Shackleton, and intellectual pursuits, such as Hilbert’s set of unsolved problems in mathematics. However, most of the chapter is devoted to discussing the last major influencer of quantification: Albert Einstein. His life and accomplishments, including his theory of relativity, make up the final milestone on our road to quantification. The chapter describes his time in Bern, especially in 1905, when he published several famous papers, most particularly his law of special relativity, and later, in 1915, when he expanded it to his theory of general relativity. The chapter also provides a layperson’s description of the space–time continuum. Women of major scientific accomplishments are mentioned, including Madame Currie and the mathematician Maryam Mirzakhani.

Discrepancy to Variability

This chapter describes quantification during the late nineteenth century. Then, most ordinary people were gaining an overt awareness, and probability notions were seeping into everyday conversation and decision-making. However, new forms of abstract mathematics were being developed, albeit with some opposition from Lewis Carroll (Charles Dodgson), who wanted to preserve traditionalist views of Euclidian geometry. The chapter introduces William Gossett, who worked in the laboratory of the Guinness brewery and developed “t-distribution,” which was published as “Student’s t-test.” It also describes his friendship with Sir Ronald Fisher, who developed many statistical hypothesis testing methods, published in The Design of Experiments, such as the ANOVA procedure, and the F ratio. Fisher also developed many research designs for hypothesis testing, both simple and complex, including the Latin squares design, as well as providing a classic description of inferential testing in the thought experiment called “the lady tasting tea.”

Coming to Everyman

This chapter focuses on how quantification began to increase in the everyday life of ordinary people, who are represented in this chapter by the allegorical figure “Everyman” (from the fifteenth-century anonymous morality play Everyman). It discusses the invention of the chronometer and explores the effect that the increasing availability of luxury items such as sugar, as well as the quantifying ideas that were coming into use at that time, had on the general populace. The chapter then introduces Pierre-Simon Laplace, who assiduously worked to bring the newly formed probability theory to Everyman, especially through his efforts on the orthodrome problem in Traité de mécanique céleste (Celestial Mechanics), his ideas on scientific determinism (symbolized by “Laplace’s demon”), and his General Principles for the Calculus of Probabilities. The chapter also introduces Joseph-Louis Lagrange, whose work on the calculus of variations had a great influence on Laplace.

The Bell Curve Takes Shape

This chapter tells how quantification as an idea in spirit is moving across the Atlantic to the new country of the United States, and its relevance to the signing of the Declaration of Independence. Probability theory begins to take off with Abraham de Moivre as he investigates distributions for numbers. He devises a histogram and begins a study of “errors” in a distribution in his Doctrine of Chances. Three terms are explained: “probability,” “odds,” and “likelihood.” What made the advances in mathematics, statistics, and especially probability theory so prominent was both the sheer volume of new ideas and the absolutely torrential pace at which these developments came.

The Patterns of Large Numbers

This chapter advances the historical context for quantification by describing the climate of the day—social, cultural, political, and intellectual—as fraught with disquieting influences. Forces leading to the French Revolution were building, and the colonists in America were fighting for secession from England. During this time, three important number theorems came into existence: the binomial theorem, the law of large numbers, and the central limit theorem. Each is described in easy-to-understand language. These are fundamental to how numbers operate in a probability circumstance. Pascal’s triangle is explained as a shortcut solving some binomial expansions, and Jacob Bernoulli’s Ars Conjectandi, which presents the study of measurement “error” for the first time, is discussed. In addition, the central limit theorem is explained in terms of its relevance to probability theory, and its utility today.

The Sum of It All

This concluding chapter reviews the long road to quantification, drawing especially on ideas introduced in Chapter 1, but also mentioning highlights from the other chapters. It considers two thought experiments, where a thought experiment is defined as an investigation into a scientific question that is carried out only in the imagination. The first is, suppose quantification had not taken place and we had not transformed our worldview to it. The second is, from our current quantified worldview, how we might evolve in the future? The chapter concludes with a quote from Shakespeare’s King Lear is given, describing a state of internal happiness.

Interrelated and Correlated

This chapter describes quantifying events in America and their historical context. The cotton gin is invented and has tremendous impact on the country, bringing sentiments of taxation and slavery to the fore, for state’s rights. Events leading to the American Civil War are described, as are other circumstances leading to the Industrial Revolution, first in England and then moving to America. Karl Pearson is introduced with description of his The Grammar of Science, as well as his approach to scholarship as first defining a philosophy of science, which has dominated much of scientific research from the time of the book’s publication to today. Pearson’s invention of the coefficient of correlation is described, and his other contributions to statistics are mentioned: standard deviation, skewness, kurtosis, and goodness of fit, as well as his formal introduction of the contingency table.

Regression to the Mean

This chapter focuses on two events that started the transformation to a quantifying worldview for the general public: (1) developments in transportation, especially the invention of the train (meaning people and goods could travel further) and (2) the consequent tremendous economic expansion which led to a full-blown industrial revolution, first in England and then in America. Work by Charles Darwin showed the broadening impact of quantitative thinking on the discipline of sociology. The chapter also discusses the accomplishments of Francis Galton, including his landmark work Hereditary Genius, the invention of Galton’s bean machine (“quincunx”), which demonstrated the central limit theorem, and his Anthropometric Laboratory, which he set up at the International Health Exhibition to measure mental faculties. Galton also discovered the concept of correlation and “reversion to the mean,” evolving the latter into “regression to the mean,” and invented many other statistical concepts, such as quartile, decile, and ogive.

Probably a Distribution

This chapter is all about Carl Gauss, his life, and his accomplishments, including his work in plotting the orbits for Ceres, which he did while still a teenager and which set his reputation. The chapter tells, too, how and when he invented and used his method of least squares and of his dispute with Legendre on who invented it first. One of his most significant accomplishments is his devising (and proof) of the normal probability density function, or, more familiarly, the standard normal curve. This is described and its import and application to modern times is discussed. Also, there is a brief discussion of biographical events and details of his life, such as his reclusive nature in his hometown of Göttingen, and his caring for his ailing mother and then his first and second wives. Some details of his impact today and lasting accomplishments are also provided.