WILL SOCIETY DEVELOP ARITHMANCY?

Some might say Hermione Granger simply couldn’t make her mind up about the future. She clearly abhorred the school subject of divination, the art of divining the future, or foretelling future events, by various dubious tools and rituals. And yet, she also said that Arithmancy was her favorite subject. Arithmancy was also a magical discipline that studied the future, but the difference between arithmancy and divination was that arithmancy applied a more precise and mathematical approach to predicting the future, which the rationally minded Hermione preferred. (One of her many complaints about divination was that it seemed to be “a lot of guesswork.”)

Arithmancy was all about the magical properties of numbers. And, as predicting the future with numbers was prominent in arithmancy, it had a little in common with the muggle practice of numerology, where people place faith in number patterns and draw pseudo-scientific conclusions from them. Arithmancy was an elective subject at Hogwarts, offered only from the third year on. Students were set essay assignments that involved the consulting and/or composition of complex number charts. Those who practiced arithmancy were called arithmancers.

Among the notable arithmancers in wizard history were Bartemius Crouch Jr., the death eater who made Voldemort’s return inevitable, and Hermione herself. She became a high-ranking official in the department of magical law enforcement. So, it looks as though Harry indulged in a spot of fortune telling himself. He’d bought Hermione a copy of the book, New Theory of Numerology, for Christmas while they were still in school. But can numbers really divine the future?

Numbers Unlock the Cosmos

The link between numbers and nature had been recognized early by the Pythagoreans when the Pythagorean brotherhood of ancient Greece had realized that numbers were the key to comprehending the entire cosmos. The brotherhood tried to synthesize a holistic view of the universe, one which incorporated religion with science, medicine with cosmology, and mathematics with music; mind, body, and spirit as one. The very word, “philosophy” is Pythagorean in origin. When muggles use the word harmony in its wider sense, when numbers are called figures, etc., muggles speak the tongue of the brotherhood. And their approach was epoch-making; through their application of mathematics to the human experience, the Pythagoreans were founders of what the world understands today as science.

The Pythagorean brotherhood was founded in the 6th century BC. And the Pythagoreans were big on the magic of numbers. To them, philosophy was the highest music. And the highest form of philosophy was concerned with numbers, for ultimately all things are numbers. So rather than numbers leading to a reduction of human experience, it was an enrichment. The Pythagorean concept of harmony was typical of the way in which the brotherhood synthesized an interconnected view of the universe. Numbers were not tossed into the world at random. They were arranged, or arranged themselves, like the structure of crystals or a musical scale, according to the universal laws of harmony.

The basic Pythagorean notion of armonia regarded the human frame and body, too, as a kind of musical instrument. Each string within must have the right tension, the correct balance, for the patient’s soul to be in tune. The musical metaphors that are still applied to medicine, such as tone and tonic and well-tempered are also part of the Pythagorean heritage.

Legend has it that Pythagoras found the link between music and math from a blacksmith. One day, Pythagoras was passing a smith at work. Hearing the sweet sound of the blacksmith striking the anvil, Pythagoras realized that such harmony must bear some relation in mathematics. He spent some time with the smith, examining the tools and exploring the simple ratios between tools and tones.

The Pythagoreans took numbers so seriously that they were prepared to kill for them. Tragically, one of nature’s number secrets helped bring about the end of the brotherhood. For the Pythagoreans discovered irrational numbers. These numbers, such as √2 or π, are numbers that cannot be written down as the ratio of two integers, two whole numbers. For philosophers who believed that all of nature could be understood by number-series and number-ratios, this was a major blow.

The proof of the existence of irrational numbers is attributed to a member of the brotherhood, Hippasus of Metapontum. He is thought to have found them while thinking about the geometry of the pentagram, used by the Pythagoreans as a symbol of recognition among members and as a mark of inner health. At first, other members tried to disprove the existence of irrational numbers through logic. They failed, and today we know that almost all real numbers are irrational. Believing in the absoluteness of numbers, the Pythagoreans kept the discovery a secret, dubbing the irrational numbers arrhetos, unspeakable. But Hippasus let the scandal leak, and legend has it he was put to death by drowning,

“It is told that those who first brought out the irrationals from concealment into the open perished in a shipwreck, to a man. For the unutterable and the formless must needs be concealed. And those who uncovered and touched this image of life were instantly destroyed and shall remain forever exposed to the play of the eternal waves.” —Mark Brake, Revolution in Science

Greek drama, indeed.

The Dark Archives

The modern use of numbers is no less dramatic. In the legendary Foundation fantasy trilogy by Isaac Asimov, a mathematics professor named Hari Seldon predicts the future using what Asimov calls psychohistory. Mathematics is used to model the past to help anticipate what will happen next, including the fall of the galactic empire. It may seem like science fiction, but a new field does something similar.

Cliodynamics (named after Clio, the Greek muse of history) claims to enable its scholars to analyze history in the hopes of finding patterns they can then use to map out the future. One of the big questions they aim to answer is, Why do civilizations collapse? Their holistic approach isn’t too far removed from the Empire-mapping forecasts set out by Hari Seldon in Asimov’s Foundation. The technique predicts a wave of widespread violence around 2020, including riots and terrorism.

This mushrooming field of cliodynamics uses the dark archives. These are data banks from the distant past, including historical documents that have only recently come online. The methods include common statistical techniques, such as spectrum analysis, on historical digitized newspapers and public records. So cliodynamics quantifies the past and makes extrapolations based on those data trends.

Experts in the field have found a pattern of social unrest. It applies to many civilizations, including dynastic China, ancient Rome, medieval England, France, Russia, and even the United States. Analysis clearly shows one-hundred-year waves of instability. And, superimposed on each wave is an additional fifty-year cycle of widespread political violence. China seems to escape the fifty-year cycles of violence, but the United States does not.

These cycles of violence have social inequality at their root. Discontent builds up over a period of time until the pressure is violently released. Scholars have mapped the way that social inequality creeps up over the decades, so much so that a breaking point is reached. A little late, reforms are finally made. But, over time, those reforms are reversed, and society lurches back to a state of heightening social inequality. Sound familiar?

The severity of the violent spikes depends on how governments cater with the crisis. For example, the United States was in a pre-revolutionary crisis in the 1910s, but a sheer drop in violence followed due to a more progressive political era. The ruling classes made calls to reign in corporations, and allowed workers vital reforms. Such policies reduced the pressure, and prevented revolution. Likewise, 19th century Britain was able to avoid the kind of violent revolution that happened in France by making amelioratory reforms. However, the usual way for the cycle to resolve itself is through violence.

Much has been made of the dark archives. Cliodynamics shows that muggles can find much value in the reams of non-digitized records that most don’t even know contain prophetic treasure. The world is taking a closer look. And historians are starting to work with mathematicians to embrace the new techniques. Our future may soon be divined from our past.