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I read the Iliad once a year, and every time I do, Hector dies at the end and Achilles in an act of compassion gives the Trojan hero’s body to his grieving father. 

And every time I read Moby Dick, Ahab dies tangled in rope to the whale, and the beast sinks the Pequod. Likewise, the Maltese Falcon always turns out to be lead, and Dorothy always returns to Kansas.

These are stories and they have beginnings, middles and ends. We may know that Achilles is destined for an early death, even though it is not in the Iliad, and we may wonder if Ishmael ever gets on another boat or Brigid O’Shaughnessy hangs by that pretty neck of hers or spends 20 years in Tehachapi, or if Dorothy ever gets a Ph.D. or lives to bear children to a dunce. But all this is outside the knowledge of these stories. 

There is self-containment in a story, even one with sequels, in which each sequel is its own story, with its own beginning, middle and end. There is a front cover to the book, and a back cover, and when we close it over, we put the book back on the shelf. 

This seems to work for books about history, too. We know that Cornwallis will surrender at Yorktown and that Lee will surrender at Appomattox. When we read about Abraham Lincoln, we know his story ends at Ford’s Theater. 

Napoleon ends in Moscow, at Waterloo, or St. Helena, depending on the focus of the history book. Hitler will lose the war and the Berlin Wall will come down. No matter how many times we turn the pages, the end is always the same. We know it even before we start. 

So history seems to be constructed of discrete bits, sewn together. Each with a beginning, middle and end. Alexander will die in the palace of Nebuchadnezzar and the Middle Ages will come to an end in the Renaissance. 

So, when we read about Neville Chamberlain, we know he was a failure because we know what happened after Munich. We know in advance that Communism fails and that computers didn’t go all cattywampus after Jan. 1, 2000. 

It is seldom we acknowledge, even if it is obvious, that Washington didn’t know that he would win the battle, that Lincoln didn’t know he wouldn’t return from Our American Cousin, or that anyone living in AD 800 didn’t know they were living in the Middle Ages. Middle of what? They were modern at the time.

We get a false sense of the world when we look at history as a story. One thing follows another in consequence and bingo, Napoleon comes to the end we always knew he would come to. 

History as it happens isn’t history. It is simply the now of back then. Its participants are just as ignorant of the outcome as we are of what will happen in Syria or North Korea. Or the legacy of Trumpism. Eisenhower didn’t know that D-Day would work; Oppenheimer didn’t know if the plutonium bomb would actually explode; Neil Armstrong didn’t know if he would ever get back from the moon. It is all contingent. 

History is not a story. It is a flowing chaos, a million-billion strands floating out into the ether and gathering in unanticipated knots. You might as well stand at the banks of a river and ask, “Where did that water start, where does it end.” 

So, we don’t know where our future is going, where those knots will form. Only afterwards do we go back, pick out the bits that make sense to us at the moment and weave a story out of them, creating coherence where there never was any. Doughboys never called their fight World War I. They had no idea that their suffering was only prelude to a sequel. World War II was the “Good War.” World War I was “the War to End All Wars.” These are tales we tell to ourselves as if we were our own children. 

A story is a pattern. We may call it plot, or timeline, but in essence, a story is designed to fulfill our innate desire for pattern. In fiction, that pattern is engineered from the episodes the author invents. In history, it is created by simplifying the complexity so that we can impose the same sort of pattern we are used to in a story. 

Different eras find different patterns in the evidence, and so history is constantly rewritten to the specifications of a certain time and place. The old guard cries foul and calls this re-organization of data “revisionism,” but history will always be pushed and pulled like clay, into whatever form is needed for the day. 

So, Napoleon was a great man, a monster, an exemplum, or, like Tolstoy claims, an irrelevance. Which was the real Bonaparte? They are each a story fabricated from bits, like a Frankenstein reanimation. 

Reality offers an infinity of possibility and for mere comprehension, we cut and prune to make the whole digestible. To make it a story. 

For years I was a journalist, and I cringed at the idea that what I was writing were newspaper “stories.” Reporters are trained to make the news comprehensible by making them stories: beginning, middle, end. The truth is always muddier, always messier. 

There seems to be a biological need for stories, or why would we keep writing them, writing fictions we know are not literally true, but reinforce the patterns we know. A story is a theater of shadow puppets. 

The pre-Socratic philosopher Heraclitus wrote, “Panta Horein:” Everything changes, or everything flows, depending on your translation. A story petrifies that flow into a single unmoving image, which always distorts the cascading reality. 

fibonacci in blue

Too often, we take what we hear at face value. Facts turn out not to be facts. No one changed your family’s name at Ellis Island. Didn’t happen.

These are not just myths, they are just things that sound like they could be true and so become embedded in our midden of common knowledge. No, Eskimos do not have 30 or 43, or 90 words for “snow.” Human beings do not use merely 10 percent of their brains.

This is all stuff for the Cliff Clavins of the world.

Sometimes this stuff gets caught in our mental wheel spokes because we simply don’t look closely enough.

Take the Fibonacci series. We are told that this interesting pattern of numbers governs much of what appears in nature, including the spiral patters we see everywhere from whelk shells to spiral galaxies. The problem is, observation does not support this idea, at least not as it is usually presented.

The series is created by starting with a zero and a 1 and adding them together, and continues by adding each new number with the previous, making the series: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, etc. The series has many interesting properties, one of which is the generation of the so-called “Golden Section.”

To the Greeks, the golden section was the ratio ”AB is to BC as BC is to AC.” It also generates the Fibonacci series and is said to define how nature makes spirals.

golden overlap

Look at the end of a whelk shell, they say, or the longitudinal section of a nautilus shell, and you will see the Fibonacci series in action.

whelk

Yet it is not actually true. When you look at whelks, you find spirals and the Fibonacci series creates a spiral, but the two spirals are quite different: the mathematical spiral opens up much more rapidly. The shellfish has a tighter coil. The whelk’s spiral makes roughly two turns for every turn the Fibonacci spiral makes. Math is precise, but nature is various.

fibonacci whelk

What I am most interested in here is not just the agon of conflicting beliefs, but rather the faith in mathematics, and the sense that math describes, or rather, underpins the organization of the world.

I cannot help thinking, in contrast, that these patterns are something not so much inherent in Creation, as cast out from our brains like a fishing net over the many fish in the universe.

Take any large string of events, items or tendencies, and the brain will organize them and throw a story around them, creating order even where none exists.

Consider the night sky, for instance, a rattling jostle of burning pinpoints. We find in that chaos the images of bears and serpents, lions and bulls. Even those who no longer can find the shape of a great bear can spot the Big Dipper. The outline seems drawn in the sky with stars, yet the constellations have no actual existence outside the order-creating human mind.

Ursa major

Our own lives — which are a complex tangle of events, conflicting emotions and motives — are too prodigal to fit into a single coherent narrative, even the size of a Russian novel. Yet we do so all the time, creating a sense of self as if we were writing autobiographies and giving our lives a narrative shape that makes them meaningful to us.

We usually believe the narrative version of our lives actually exists. Yet all of us could write an entirely different story by stringing events together with a different emphasis.

The question always arises: Are the patterns actually there in life and nature, or do we create them in our heads and cast them like a net over reality?

The issue is central to a brilliant movie made in 1998 by filmmaker Darren Aronofsky called Pi. In the film, a misfit math genius is searching for the mathematical organizing principle of the cosmos.

His working hypotheses are simple:

”One: Mathematics is the language of nature.

”Two: Everything around us can be represented and understood through numbers.

”Three: If you graph the numbers of any system, patterns emerge.

”Therefore: There are patterns everywhere in nature.”

Pi movie scene 3

The movie’s protagonist nearly drives himself nuts with his search until he cannot bear his own obsession anymore.

But the film also questions in a roundabout way whether the patterns exist or not.

When different number series — each 216 digits long — seem to be important, an older colleague warns our hero that, once you begin looking for a pattern, it seems to be everywhere.

It’s like when you buy a yellow Volkswagen and suddenly every other car on the road is immediately a yellow VW. Nothing has changed but your perception.

Mathematicians find patterns in nature, yet math itself is purely self-referential. It can only describe itself.

As mathematician/philosopher Bertrand Russell put it: ”Mathematics may be defined as the subject in which we never know what we are talking about nor whether what we are saying is true.”

In other words, ”one plus one equals two” is no different from saying ”a whale is not a fish.” You have only spoken within a closed system. ”A whale is not a fish” tells us nothing about whales but a lot about our language.

It is a description of linguistic categories, rather less an observational statement about existence. Biology can be organized as a system of knowledge to make the sentence false — indeed, at other times in history a whale was a fish.

Before Carl Linne, who created the modern biological nomenclatural system, there were many ways of organizing biology. In his popular History of the Earth and Animated Nature, from 1774 and reprinted well into the 19th century, Oliver Goldsmith divided the fish into “spinous fishes,” “cartilaginous fishes,” “testaceous and crustaceous fishes” and “cetaceous fishes.” A mackerel, a sand dollar and Moby Dick were all kinds of fish.

Plate from Goldsmith's "Animated Nature"

Plate from Goldsmith’s “Animated Nature”

Let’s face it, although the Linnaean system is useful, it is kind of arbitrary to organize nature not by its shapes, or where it lives, but rather how it gives birth or breathes.

”One plus one” likewise describes the system in which the equation is true.

It is possible to cast other patterns over reality. For instance, artists understand perfectly well how ”one plus one equals three.”

That is, there is the one thing, the other thing and then the two together: one sock, the other sock, and the pair of socks. That is three things.

Three things

Three things

 

In art, we constantly put one object up against another object and observe the interaction between them. In that sense, one plus one can equal three.

When mathematicians say that numbers describe the world, they are speaking metaphorically. Numbers do not, in fact, describe the world. The patterns of numbers seem to mimic the patterns we discern in nature and bear an analogical relation to them.

The fact that this seems to happen so often may be little more than the yellow VW effect.

For experience is large and contains multitudes, even infinities. In any very large set, patterns can be found.

That is the trick behind numerology. If the name Ronald Wilson Reagan can be turned numerologically into the symbol for Satan because each of his names has six letters, making the “666” or “mark of the beast” from the book of Revelations, well, looked at another way, it can be turned into a recipe for Cobb salad. All it takes is a system ingenious enough to do it.

Our hero in Pi believes in the Fibonacci spiral: ”My new hypothesis: If we’re built from spirals while living in a giant spiral, then is it possible that everything we put our hands to is infused with the spiral?”

He begins to sound more and more paranoid.

And paranoia has been defined as a belief in an invisible order behind the visible world.

Paranoia and idealism thus are siblings.

There seems to be hard wiring in the human brain that makes us cast patterns over the world. That hard wiring seems to bring forth what Carl Jung called archetypes, that is, the narrative patterns our brains spin out and the shape we then jigger all of actual experience into.

And when forced to choose between the coherent pattern and the incoherent reality, we always choose the pattern.

Perhaps we could not live otherwise. But it makes me mistrust idealism just as I mistrust mathematics.