# The Surface World

Cartographers hold a special affinity for spatially anomalous regions such as the territory of Kaliningrad Oblast. Between the wars it was the East Prussian exclave of Germany, surrounded by Poland and Lithuania. Annexed by the Soviets in World War Two, after the collapse of the Soviet Union it once again became an isolated exclave, this time of Russia, leaving mapmakers throughout history recurrently puzzled as to the minimum number of colors a map of the Baltics requires if no two adjacent regions share the same color yet individual nation states remain homochromatic. Ironically, despite Kaliningrad’s territorial separation, Russia’s compulsion to control this small piece of Baltic waterfront is driven by questions of connectedness and continuity. Because Kaliningrad is home to possibly the world’s most dangerous cult, The Teutonic Order of Topologists.

The humble origins of the Order can be traced to the mid-19th century. Students joining the Mathematics department at the Universität of Königsberg faced a set of seemingly unsolvable examination questions; for instance, “Find a route from the University crossing each of the city’s seven bridges once and once only before returning to the University”. Ostensibly no-win scenarios, Hohenzollern precursors to the Kobayashi Maru, designed to determine how prospective candidates coped when faced with the impossible. Capable students, familiar with Leonhard Euler’s theories, enumerated vertices and incident edges, formulating mathematical proofs of the problem’s unsolvable nature. One failed student adopted a more unorthodox solution, attempting to detonate a gunpowder bomb under one of the bridges after the exam.

Many of those that passed the test on entering the Mathematics department soon joined the Biertrinker Bruderschaft, known formally, for respectability’s sake, as the Teutonic Order of Topologists. A philosophical crowd, they embraced the enlightenment of Immanuel Kant, adopting the motto “Have courage to use your own understanding” as their own. The legend of the failed student’s dynamite solution also entered the Order’s folklore, a heroic model of enlightenment thinking that so nearly rendered the impossible possible.

Gradually over time this lighthearted grouping evolved. Mathematics advanced too, Möbius with his endless strip, Cantor and his sets, Felix Hausdorff’s axioms defining disjointed neighborhoods, leading to topologist jokes about Königsberg being housed off. Mathematics, it seemed, was constantly advancing, improving, refining, like an endless progression towards some infinitely distant point of perfection.

The world around changed too, but not in a positive direction - wars, hyperinflation in the Weimar Republic, repeated financial crises. Problems unresolved by conflicting ideologies; Marxism, Fascism, Communism, one disastrous ism after another. Then after the ism’s had faded into the discredited past, a succession of Neos: neoliberals feeding the globalized über-wealthy, neo-Marxists pontificating on late capitalism, neo-Keynesians shafting the common man with their fiscal stimulus. Nothing had changed, peek behind the curtain and Neo reveals itself as a prefix denoting mutton dressed as lamb. Mankind in the real world was locked into a recursive loop without progression or exit, the antithesis of the advances realized in Mathematics.

After the Soviet invasion, the Order of Topologists became more secretive, akin to a resistance movement, vowing to use their mathematical knowledge to release the world from the cycle of repeated failure. They vanished into the vast system of secret underground tunnels and passages hidden below Kaliningrad, remnants of 12th century forts built by Prussian knights. A new life under the utilitarian reinforced concrete structure of the Haus der Räte, a monstrous building dumped in the reconstructed Soviet city landscape like some gigantic defunct cubic robot. Now they inhabited a subterranean world of passageways, marked with geometric cyphers comprehensible only to those familiar with the symbology of topologists. Complex Eulerian circuits linking Nazi underground bunkers, sewer hatches providing openings into the surface for communication, an interconnected graph of tunnels in three dimensions supporting a concealed separate existence.

The Order’s entrance exam was replaced by ritualistic initiation of discreetly selected brethren. Candidates were dressed in nothing but a waistcoat, blindfolded with hands bound. Those that could turn the waistcoat inside out and put it back on with the lining showing were raised to the order. The ritual symbolizing that, having found a function to map the outside to the inside, the candidate was indeed worthy of life in the topologist’s world.

A harmless topological magic trick, not the markings of a subversive sect you may think. Yet topologists have long known a simple truth. You can’t comb a hairy ball. Take a continuous tangent vector field on the surface of a sphere, attempt to comb it flat. There will always be a point somewhere where the vectors all flow away, somewhere that they all converge. To a topologist the Earth is just a ball, the vector field perhaps magnetism, wind or tide. There are always singular points, where the wind is still, where you can’t travel north, oceanic points where there never is a tide. Yet at all times somewhere there is wind, so Mathematics proves that somewhere on Earth there must also always be a rotating cyclone, with a singular still source or sink point at its center.

Deep beneath the city streets, over cups of coffee and bagels, a momentous meeting of the order once took place. One of the topologists held up his bagel, (or perhaps it was his coffee cup, but that detail is irrelevant, they’re homotopic - any torus will do), and announced a geometric solution to the economic woes of the world. Money, he declared, is just another continuous vector field flowing over the surface of the earth. The fundamental problem with the world’s financial system was obvious. Humans subsist upon a Platonic solid. Money could never flow smoothly over Earth’s surface without disappearing into some unscrupulous sink, or being constantly printed at some state bank’s point source. The neo-Marxists are wrong; capitalism is not late, it’s being continuously sucked into a vortex. The inevitable consequences of these financial singularities within the vector field over Earth’s great sphere are obvious; erratic fluctuations in money supply, spiraling maelstroms of debt, boom and bust, financial meltdown, chaos and human misery. There could only be one mathematically correct solution to this conundrum. No monetary policy would ever be stable on Earth unless the world was balanced topologically and the Teutonic Topologists understood how to achieve this. They must have the courage to use their own understanding, and blow a fucking hole right through the Earth.

Yes folks, the Russians are right to fear the day when the Teutonic Topologists return to the surface world.