This city would be perfect, just look at the math!

I have been thinking about cities ever since I read Daniel Tammet’s “Invisible Cities.” Tammet is an English essayist who writes with clarity and skill about the unconventional ways his mind works, a product of autism, synesthesia, and savant syndrome. In 2004, from memory, he recited pi to 22,514 decimal places and got it right. Challenged by a documentary crew, he seemed to learn conversational Icelandic in a week. As a child, he began creating his own language, which he calls Mänti; his Mäntish word for tardiness, kellokült, is derived in Mänti from “clock debt,” which I think is lovely.

“Invisible Cities” is included in Tammet’s book Thinking in Numbers: On Life, Love, Meaning, and Math. He begins by observing how mathematicians respond to cities: “Planning a city, or dreaming about one, invites us to think by numbers, to borrow some of the mathematicians’ delight.” Then he gets to his subject, cities that were imagined but never built.

One of Tammet’s examples: Plato proposed that an ideal city would have a population small enough to permit everyone to know everyone else. Knowing thy neighbor, every last one of them, would prevent strife and criminality and other forms of discord. (Well…) Not content with the vague term “small enough,” Plato did some mathematical pondering and concluded that this ideal community would consist of precisely 5,040 landholding families. Those families would comprise 12 tribes of 420 families each. Each tribe would be both self-sufficient and interdependent, which is a bit hard to square, but never mind. Every family would own an equal plot of land, each plot radiating from the city center to the fertile soil of the outskirts. (All very geometric.) He calculated that this city could maintain an ideal population with an annual birthrate of 170.

He called the city Magnesia. He seemed to regard it as inferior to his other exercise in urban planning, prescribed in The Republic. That one, named Kallipolis, would house a rigidly structured hierarchical society governed by unelected, selfless, virtuous philosopher-kings—an imaginary species if ever there was one. Kallipolis would achieve perfect justice and harmony if the rulers owned no property, if every citizen performed their assigned role and didn’t interfere with anyone else, if everyone was educated properly, and if the arts were censored to prevent moral corruption. (Nobody hates an artist like a virtuous philosopher-king.) Everyone would prosper and be happy, provided they stayed in their lane. (Paging Aldous Huxley…)

Given the choice, I’d opt for Magnesia over Kallipolis. Though I’m too old to contribute to the 170 annual births.

I wonder if Plato sensed from the start that on hearing his plans for Kallipolis, most flesh-and-blood humans would tell him to go fish. If he couldn’t create the perfect city by convincing a few thousand people to shut up, line up, and live without art, maybe he could apply math to achieve his goal. Plato the pragmatist: people will lead their silly damn lives in whatever sloppy way they want, but if they’re part of 5,040 families and make 170 babies per year, everything will work out.

A paradox lurks here. Beneath everything in the universe, every single thing, there is mathematics. Perhaps that’s an artifact of human cognition: our mind’s structure renders us incapable of seeing the cosmos in any other way. (Imagine our first physics colloquium with an alien civilization. One of our physicists confidently states that equations govern the universe. An alien physicist, startled, replies, “Where did you get that idea? The universe is governed by asparagus. Everyone knows that.”) But human cognition is all we’ve got to work with, and it has produced equations that tell us how to create a universe. The paradox is that what works so well for creating a cosmos, what seems so all-encompassing, would be hopeless at creating a city anyone would want to live in.

Throughout history, plans for ideal cities have always fallen back on schematics—figures, stats, geometry, shadowy equations, and algorithms. Urban planners imagine if they get their part right, we will each take our place on the grid, have 2.3 kids, and fill all the requisite jobs. If everyone would just get in sync everything would be grand.

But most days people are terrible at getting in sync. Driving cattle is easier than driving people. Driving gerbils might be easier. And those times when masses of people have marched in rank, the outcomes have been awful. Few things are more terrifying than that moment when a mob falls into lockstep.

Actual systems meant to order human affairs (and we all live under one kind or another) end up as crufty and slapdash social jalopies that lurch along and, in the best cases, leave room for people to improvise solutions to whatever confronts them. The sleek, orderly systems created by earnest thinkers and ideologues contain a trap, a sort of siren’s song, once anyone tries to enact them: Making them work turns out to be messy and frustrating and halting and disorderly. It’s much more fun to come back to the model and tinker with it.

Start with a smaller example: personal productivity programs. We in Western corporate culture have been trained to fret constantly that we should be accomplishing more. Conned into embracing productivity as the secret to prosperity and fulfillment, by the thousands we sign on to systems, be it David Allen’s Getting Things Done, or Ryder Carroll’s Bullet Journal, or Merlin Mann’s 43 Folders system. To reform all of our bad habits, we read the book and print out the forms and buy the notebook (our BuJo!) and dive in with the fervor of new acolytes. Feels good for a while. We congratulate ourselves. We’re life hackers! We draw up the prescribed lists, lay out our new productivity journals, set up our hanging folders, and feel on the road to redemption. Yes! Yes! Yes!

Then we hit a snag, a roadblock, a bit of resistance. At our desks we poke at the problem for a few hours with no result. Maybe we need to step away for a bit and tinker with our system? What if we create some nested lists in our personal GTD setup? What if we make up new icons for our Bujos, or redo our Future Log so that it’s really pretty and shows off our creativity? Maybe recolor all of our computer folders. Time spent tweaking the system proves much more satisfying than staring at our problem, and it’s not time wasted because the improvements to the system will pay dividends the rest of our days. Right? Oh, and look, there’s a website devoted to uploaded pictures of everyone’s Bujos! Here’s mine!

Fascination with and devotion to the system takes over our minds. The people who create the systems know this aspect of human nature and capitalize on it. David Allen has registered “GTD®” and Ryder Carroll has registered “Bujo®.” These are not dumb guys. They know how to make a buck from our weaknesses.

In corporations and other institutions, why do the hard, sometimes unsettling work of chancy improvisation that is actual life when you can work on the business model, the statement of core values, and the annual performance goals?

People who devise political programs and social theories and economic blueprints have the same weaknesses as the rest of us. At a certain point, they forget that there’s no such thing as perfecting human nature and become obsessed with the theory, the system, the model. Look how perfect it is! How sleek and elegant!

The stakes are not small. The forced imposition of “perfect” models since 1917 has extinguished hundreds of millions of lives. But what price perfection?

Plato was a smart fellow. But I think that at some point in his work on his perfect city of Magnesia, he lost himself to Tammet’s mathematician’s delight. We’ll never know how he landed on 5,040 as his ideal number of families, but I think the number took on a mystical aura for him. Mathematicians call it a highly composite number because it has 60 divisors. It is divisible by all numbers from 1 to 12 except 11, which made it practical for Plato’s purpose. (Mathematicians also classify it as the eighth “colossally abundant number,” which is too complicated to get into.) Start with 7 and multiply by descending numbers—7 × 6 × 5 × 4 × 3 × 2 × 1—and you arrive at 5,040, which makes it feel significant in some cosmic way. (The proper equation for this is 5,040 = 7!) You arrive at the same result with 10 × 9 × 8 × 7. Do you want more? Start with 23 and add up 42 consecutive prime numbers—5,040.

I don’t know how much of this was known in Plato’s day, but I think 5,040 exerted a sort of gravity that pulled Plato in. That the number had no meaning regarding human behavior didn’t matter. Look at how perfect it was for the model! Plato was deeply moved by mathematics. He believed geometry illuminated eternal truths and was the foundation of the universe. He saw harmony and order inherent in mathematics, as well as justice and moderation. All of that virtue could not be an accident, and only good could come of applying it to society.

If only people didn’t behave like people.

Were I a citizen of Magnesia, I know what I’d want to do. I’d want to run the dairy. It’s name, of course, would be Milk of Magnesia.

[rimshot]