Even the mathematically averse among us today recognize the basic geometry that Radolph and Ragimbold failed to grasp, for we live in a numerate society, surrounded by countless manifestations of mathematics. Broadly defined as the ability to reason with numbers and other mathematical concepts, numeracy underlies our current information explosion. Its clichés dot popular speech: “do the math,” “crunch the numbers,” “figure the odds.” From birth to death, numbers track our lives institutionally and demographically. Some scorn such customs (think of Mark Twain’s “figures” of “lies, damned lies, and statistics”), but we all acknowledge numeracy as a cultural given, and agree that mathematics fuels the science, technology, and industry of our world.

Still, as the story of Radolph and Ragimbold suggests, it wasn’t always so.

Before the modern era, whose origins we often date from the Renaissance (circa 1250 to 1600), folks certainly counted and measured. But, bluntly put, the abstractions of numeracy and mathematics mattered not a whit in any practical sense.

Instead, literacy—not numeracy—ruled. For our progenitors, it was the invention of writing, probably between 3200 and 3100 B.C., that served the human impulse to order and manage the flux of experience and its “givens” or “data” (from the Latin, datum, “thing given”). Early scripts provided the first information technology, creating the first “information age”—that of literacy. Its apogee occurred with the phonetic alphabet, devised by the Greeks, who correlated the sounds of speech with individual letter symbols so that each symbol stands for a single vowel or consonant.

The alphabet provided the substrate, the symbols for framing nouns and adjectives, and thus the means of creating definitions, which connected thought to the objects and processes of the world. For Aristotle, science would organize and explain data taken in through the senses, abstracted into words, classified into general and specific categories, and bound together with the formal tools of logic.

The medieval world of Radolph and Ragimbold inherited this word-based technology and culture, assimilating the classifying temper into the curriculum of its new universities. Seven liberal arts anchored the course of studies—three linguistic (the trivium of grammar, logic, and rhetoric) and four mathematical (the quadrivium of arithmetic, music, geometry, and astronomy). The latter were taught primarily as stepping stones to contemplation of spiritual realities, for example the divine order that infused numerical proportions, musical harmonies, spatial beauty, and heavenly motion.

Medieval mathematics was everywhere “enchanted,” its numerology animated with allegorical, generally theological meanings. (Witness the bizarre practice of scapulimancy—divination according to the geometry of sheep shoulder blades.) Its categories, nonetheless, remained separate and distinct from one another. Arithmetic, the subject of discrete things, was incommensurable with geometry, which treated continuous things. And so, the topics of “thing” numeracy stayed tucked away in the cubby holes of literacy.

But then came the Renaissance centuries, and two dominant trends that would dramatically challenge the classifying temper and its embedded mathematics.

The first was an information explosion, begun earlier but powered after 1455 by that great engine of learning, the printing press. The mind-boggling proliferation of printed works (roughly 200 million books by the end of the 16th century) leant cheap paper and ink to spreading the humanists’ recovery of ancient texts, the New World discoveries, and the mounting harvest of information gleaned from nature. There was, in the words of Harvard’s Ann Blair, “too much to know,” too much to classify. The surfeit of new information swamped traditional classes, fractured categories, and overwhelmed the classifying temper. The world lay “all in pieces, all coherence gone,” intoned poet John Donne in 1611, gazing rearward at a more intellectually comforting age.

A second trend was intertwined with this overwhelming volume of facts: the advent of a new information technology. Arising largely from practical activities, new ways to encode information brought forth new and different ways of seeing, imagining, and analyzing nature. In each category of the quadrivium—arithmetic, music, geometry, and astronomy—these new means of data collection and processing laid the foundations of modern numeracy.

In arithmetic, from the 13th century forward, the growing presence of Hindu-Arabic numerals habituated Europeans to a new counting system. Employed initially by merchants, bankers, and accountants, it steadily crept into the procedures of mathematicians and natural philosophers, craftsmen and artisans, musicians, and artists. The new system showcased a much simplified, functional notation of nine ciphers, the numerals 1 through 9, in contrast to the cumbersome Greek scheme of 27 alphanumeric letters or to Roman numerals with their vertical strokes and letters. Further, it featured a place-value arrangement of numerals, our familiar decimal system for determining a numeral’s value by its place in the ones, tens, or hundreds column (and continuing). And the symbolic representation of zero as an empty placeholder greatly facilitated arithmetic computations. All these innovations contributed to perceiving numbers as abstract relations, not just collections of things or objects. By Shakespeare’s day, the character of Shylock in The Merchant of Venice was figuring his pound of flesh with the new, more efficient Hindu-Arabic numerals.

In the world of music, a newly invented and abstract notation accompanied the rise of polyphonic singing, which evolved from Gregorian chant. With their longs, breves, semibreves, minims, fusas, and other equivalents of modern musical notes, composers and musicians caged and managed as information the elusive, ephemeral data of rhythm and pitch. For the first time in human history, time itself was measured by means of an independent system of symbols—standardized units of sound (notes) and silence (rests) that corresponded to physical, acoustical reality. Here, too, Hindu-Arabic numerals described the fluid, irrational proportionalities and harmonies comprising the dynamics of musical tone, and gave rise to new tuning systems, including the equalized temperament of modern pianos and other instruments with fixed, musical intervals.

Turning to geometry, the discovery of linear perspective in the visual arts yielded new expression and shape to visual information. Novel geometric techniques offered alternatives to definitions as a means of seeing objects in the world. Perspective grids tied spatial proportionalities to the changing viewpoints of a world in motion. This was a world of the “winged eye” in the memorable phrase of the Renaissance man himself, Leon Battista Alberti. One-to-one mappings between objects and their representations (two-dimensional drawings or three-dimensional sculptures) provided a new context for situating objects in space. Forerunners of modern geometry’s graphs, these techniques led eventually to separating and analyzing the vertical and horizontal axes of motion.

And in astronomy, new technologies brought heavenly motion and eternal time down to earth, enabling the amalgamation of terrestrial and celestial branches of knowledge, physics and astronomy. Before it became money, time became information. Its “inaudible and noiseless foot” (Shakespeare) succumbed to the technological mastery supplied by that “fallen angel,” the oscillating mechanical clock. Pope Gregory’s solar calendar (1582) and subsequent linear chronologies put the capstone on “clock time” writ large. Time’s mystery was converted to time’s problem, at least in part, as time itself increasingly became an abstract variable expressed in mathematical formulas, such as in Galileo’s laws of free fall, pendulums, and projectiles.

Common to all these arenas—commerce and arithmetic, polyphonic sound and music, art and geometry, timekeeping and astronomy—a novel means of creating and managing information made its appearance. The phonetic letters of definitions, which were the foundation of literacy, gave way to numerals, notes and rests, grid lines, and linear chronologies that would undergird a new numeracy.

These were not the enchanted symbols of allegory associated with words and meanings. As new ways of abstracting, encoding, storing, and manipulating bits of information, these empty symbols—curlicue marks and lines on a page—were purely functional. They guided reasoning with their rules of combination and with their algorithms.

Strangely enough, these symbols even captured “nothing” and made it useful. The placeholding zero (null quantity) in arithmetic enabled “borrowing” and “carrying” amounts from column to column, the basis of adding, subtracting, and myriad further computations. The rest (absence of sound) in music made it possible for composers to develop and depict sophisticated, dynamical musical rhythms. The visual vanishing point in the gridlines of artistic perspective provided focus, thereby giving instructions for the spatial arrangements of objects. And in clock time, the instant (point of no time lapse) separated the flow of time past from that of time future, allowing one to plot events, large or small, on a linear continuum. Later, the 18th-century French philosopher Jean le Rond d’Alembert would summarily refer to the empty symbols of numeracy as “phantoms.”

Mapped onto various dimensions of experience, the new techniques of information coding framed new understandings of phenomena and transformed our ways of seeing. And they provided the tools for a new, logical layering of abstraction upon abstraction that became the higher reaches of mathematics.

By Galileo’s lifetime (1564–1642) these practices had mushroomed and coalesced into the information technology of numeracy. Henceforth, as Galileo wrote in a passage often cited, the book of nature would be understood increasingly as “written in the language of mathematics.” With his own experiments and investigations, this “father of modern physics” led a new generation of natural philosophers into the mathematical analysis of matter and motion. Fermat and Descartes followed with their analytical geometries, joining the discreteness of arithmetic with the continuity of geometry. A generation later the calculus of Newton and Leibniz united the forces and motions of matter. On the cornerstones of numeracy, laid in the Renaissance, would be constructed the entire edifice of modern science … and with it our numerate culture, our own phantom world.

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Which isn’t to say that my children thought of pi as a list of random digits. I’m a scientist, and I wanted them to understand what pi was because it’s something I’ve actually used at work. We’ve taken string and cut pieces the length of the diameter of our (round) kitchen table. I wanted them to see how many pieces were needed to go around the table edge—just a bit more than three. We’ve tried the same thing with a cake pan. Same result. With a round Tupperware—ditto. With anything circular at hand, the answer was always a bit more than three. Circumference divided by diameter—that is pi.

Why this fascination with pi? And why are so many people talking about today—March 14, 2015—as the Pi Day of the century, and maybe even planning a celebration at 9:26 a.m. and 53 seconds? I can speak only for myself. And personally, pi obsession is not surprising when your last name (Pitesky) starts with Pi (even if it’s pronounced “pih”).

Pi is a number that’s been known for nearly 4,000 years and has been useful to humankind for many reasons, most famously because it allows us to measure things like the diameter of a tree trunk if you know its circumference.

What makes pi special and compelling is the difficulty—in fact, impossibility!—of figuring out its exact value. Pi is what is known as an irrational number because its digits keep changing on to infinity and can’t be neatly represented as a fraction. Ancient Babylonians and Egyptians approximated pi’s value as three and one-eighth and the fraction 16/9, squared, respectively. Brilliant thinkers from Archimedes to Euler devised increasingly accurate methods for calculating pi. Nowadays, cutting-edge computer algorithms have calculated pi out to more than 13.3 trillion digits. People compete to memorize the greatest number of pi’s digits ; Apu of TV’s The Simpsons has memorized it to 40,000 digits. (“The last digit is one,” he says.) Pi is a living, breathing piece of mathematical history.

At NASA’s Jet Propulsion Laboratory in Pasadena, California, where I work, we have a special affection for pi. I help plan the science observations that the Cassini spacecraft will perform as it orbits around Saturn. Saturn’s moons are also orbiting around the gas giant, and both Saturn and the Earth are orbiting around the sun. Consequently, figuring out when the spacecraft will be in a good position to capture images of the moon Enceladus, or when we can send data back to the Deep Space Network antennas on Earth, involves a lot of geometry for our navigators, mission planners, and scientists.

There’s even a special maneuver Cassini’s navigators use known as a “pi transfer,” which involves two flybys of the Saturnian moon Titan at opposite sides of the moon’s orbit around Saturn. The flybys are separated by 180 degrees, and if you’re expressing that in a sometimes more convenient unit to measure angles—radians—you’d need a pi number (3.1415 …) of them. That’s why we call it a “pi transfer.” We also call Cassini’s high-value science activities “Pre-Integrated Events,” or “PIEs,” just because we love the sound of that word (and because we love acronyms).

My work with space reinforces to me that pi isn’t just a bit of mathematical trivia. Pi is something that has real, concrete applications in our lives, whether it’s figuring out how fast a spacecraft is spinning (in order to sample Saturn’s dust and plasma environment in all directions, for example), or calculating how many inflated balloons I can fit in the back seat of my car.

I did those tabletop exercises with my kids because I wanted them to know that when they saw that funny-looking Greek symbol in their textbooks, it was something tangible, something they could actually work out themselves. Math often seems entirely disconnected from people’s lives. Explaining pi and measuring it show that math can be a shorthand way to describe the world. Pi is something you can rely on, even if it’s called “irrational.”

Reminding people about the centrality of this constant, and mathematics, to our everyday lives is the reason Larry Shaw, of San Francisco’s Exploratorium, organized the first Pi Day on March 14, 1988, and why even Congress has approved its commemoration.

What makes this year—’15—special is that we can add two more digits to the date, which only happens once a century. It’s conceivable that there will be an exact moment on 3/14/15 when the time will exactly match the 30-trillion-plus digits of pi that are known now. But without clocks that can count milliseconds or microseconds, most of us humans have to be happy with stretching it out for only a few more digits.

I can’t remember exactly when I started celebrating Pi Day. Maybe it was from an old-style Usenet forum, in the days before web browsers became ubiquitous. Maybe it was from work colleagues. I’ve seen Pi Day grow from something that was only mentioned among fellow math and science enthusiasts to an event that allows even math haters to get excited about numbers And as a baker and a nerd, I’m always happy to celebrate Pi Day with a pie. In this year of Ultimate Pi(e) Day, my husband and daughters—both home on college spring break—are ramping up for 9:26 p.m. and 53 seconds tonight. We’ve invited a couple dozen coworkers and friends to bring over one pie each to our home. Or a tart, or a galette, or a quiche. And yes, pizza is a member of the pie family.

If you’re looking for recipes, I’m making the Momofuku crack pie, a peanut butter pie, lemon angel pie (really, a pavlova—also a pie family member), derby pie, and maybe a vegetarian smoked cheese tart. We’ll be showing a YouTube playlist on the TV featuring some great pie fights (if you’ve never seen Jack Lemmon, Natalie Wood, and Tony Curtis in The Great Race, watch this). It will also flash up pi humor—like “My PIN is the last four digits of pi”—which would be of absolutely no help in remembering your PIN because pi’s digits stretch on to infinity, so there are no last digits. By the end of the evening, I’m hoping everyone will be able to proudly wear this T-shirt.

But our family doesn’t limit our celebration of pi just to Pi Day. Because my husband will sometimes refer to me as Dr. Pi, he once tried to surprise me by ordering a cake with the inscription, “Happy Birthday Dr. 3.1415—our true constant.” (How adorable is that?) Of course, not everyone is so pi-obsessed: The cake decorator apparently didn’t recognize the joke because the icing said “Happy Birthday Dr. 3.1415—our true contestant.”

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I remember that it was supposed to have been different. My generation of schoolkids was told that we didn’t need to bother learning the number of inches in a foot or the number of ounces in a pound, as a switch to the metric system was imminent. The popular narrative holds that this 1970s conversion movement failed, and that Americans have never gone metric because we are too obstinate or patriotic or just plain stupid to do so. This tale is wrong, or at least wrongheaded. It is also faulty in its basic assumption.

News flash: The United States is metric, or at least more metric than most of us realize. In many areas, the 1970s effort to fall in line with the rest of the world did succeed. American manufacturers began putting out all-metric cars, and the wine and spirits industry abandoned fifths for 750-milliliter bottles. The metric system is, quietly and behind the scenes, now the standard in most industries, with a few notable exceptions like construction. Its use in public life is also on the uptick, as anyone who has run a “5K” can tell you.

Our hybrid system of measurement can surely be confusing, so why is it that America hasn’t gone full-on metric? The simple answer is that the overwhelming majority of Americans have never wanted to. Ditching all of our old measures is an extreme act that would require forcing citizens to change their daily habits and culture. The gains have always seemed too little, and the goal too purist.

The measurement debate actually goes back to our nation’s very beginning. The original metric system was developed in France during its revolution, and was so radically decimal that it divided the day into 10 hours. As our first secretary of state, Thomas Jefferson was charged with deciding which set of measures would be best for the country to use. He had been instrumental in creating the dollar—the first fully decimal measure any nation ever used—and was in favor of a universal system of decimal measurement. Jefferson rejected the metric system, however, because in origin he found it to be too French—which was saying something coming from the nation’s foremost Francophile. His beef was that the meter was conceived as a portion of a survey of France, which could only be measured in French territory. How universal in spirit was that?

Other Americans didn’t share Jefferson’s concerns. President George Washington repeatedly asked legislators to look at adopting the metric system, while John Quincy Adams considered it the greatest invention since the printing press. Adams couldn’t, however, recommend that the United States adopt a measurement system that nearly vanished after the demise of the French Empire, with which it had first spread.

The meter’s fortunes would soon rebound, however. A new wave of revolutions in the 1830s would see France and Belgium re-adopt the system, while the second half of the 19th century would see it become a truly international system. The reasons for its adoption were various. Italy and Germany were unified out of dozens of statelets, duchies, and principalities, and a neutral system of measurement helped soothe parochial jealousies. Decolonization in Eastern Europe and South America created new nations keen to adopt modernity and standards that would align them with Western Europe. In all these cases, however, conversion was dictated by democratically deficient governments bucking the will of the people. The 1880s imposition of the metric system in Brazil led to a full-scale uprising that lasted months.

The strongest push in the U.S. actually came at the start of the 20th century, Alexander Graham Bell, Lord Kelvin, and other notables testified at congressional hearings on metric conversion. The hearings were shepherded by Samuel W. Stratton, the head of the new Bureau of Standards, who put forth the metric system as a vital national interest. Thinking they were joining a winning cause, lawmakers jumped aboard the metric bandwagon. But they were in for a rude awakening. Charges of elitism and wasting money came their way from a public that increasingly believed the U.S. should be the leader in global affairs and not just another follower.

Lip service was always paid to idealism and science as the reason for change, but politics and economics were the real incentives to go metric. The world’s most anti-metric nation—Great Britain—grudgingly began to ditch its Imperial system in the 1970s because it was the only way to gain access to the markets of continental Europe. Most of the rest of the world adopted the measures in order not to fall behind in the global economy, and that anxiety also fueled our own push toward it.

Americans were perhaps never more anxious than in the 1970s, and the Metric Conversion Act of 1975 is partial proof of that. American society turned unusually introspective in those post-Watergate days, even leading us to elect Jimmy Carter, the president who told Americans about their shortcomings like no other.

Ronald Reagan’s election sprang from a more familiar American attitude—that our problems were caused not by questioning our core values, but by drifting away from them. And it was Reagan’s axing of the U.S. Metric Board during his 1982 budget cuts that was seen as the deathblow to American metrication.

The notion that Reagan killed the metric system makes for a satisfying narrative, but it is spurious. The effort had already encountered stiff public resistance under Carter. And, Reagan actually signed a bill that required the federal government to go metric, a conversion achieved under George H. W. Bush.

Love it or hate it, there is no question that a uniform global system of measurement helps cross-border trade and investment. For this reason, labor unions were among the strongest opponents of 1970s-era metrication, fearing that the switch would make it easier to ship jobs off-shore. (Which it did.) The meter has never been a clear left-right political issue in this country, one more reason it has never gained traction.

Is global uniformity a good thing? Not when it comes to cultural issues, and customary measures are certainly a part of our national culture. But our measures are more than that. The metric system reinforces the idea that the world is ordered by tens. Base-10 math, however, originated in an accident of the hands. Ten is a poor choice, particularly when it comes to dividing. Thirds, quarters, sixths, eighths, and twelfths are all important fractions that are handled better in inches and ounces than in centimeters and grams. To have brains trained in such fractions as well as the relentless decimals of the metric system can only be beneficial, in the same way that learning a second language is better than knowing only one.

That ours is a dual-measurement country is part of our great diversity. We are the only republic on earth that predates the metric system, and that’s a major reason why we never fully joined the party.

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