Alien Scientist 48: Globes and Bagels
Stephen Marshall, a former resident of Tsukuba, has been writing Alien Scientist articles for the Alien Times since 2001. Even though he no longer lives in Tsukuba, he is still a regular contributor to the magazine. Here is his latest intergalactic report.
When we look at a city map, we tend to assume the Earth is flat, extending infinitely in each direction. That is, we tend to regard the streets going off the edges to the north, south, east and west, as if going to different places in different directions, indefinitely. This is because our planet is so large compared with the size of a city, that the question of where those directions would eventually take us does not arise. But what if we had a city-sized planet – or a planet-sized city?
Let us imagine a hypothetical alien planet covered entirely by a single city. The city-planet has three main streets. The first is the equivalent of our Equator. The second is a great circle at right angles to this, like our lines of longitude 0 degrees plus 180 degrees, that together go right round the circumference of the planet. The third main street is another great circle – like our longitude 90 degrees plus 270 degrees – lying at right angles to both of the other two. This gives us a global city where each main street intersects with the two other main streets twice each.
Although each intersection is right-angled, there are no rectangular blocks: the streets divide the planetary surface into eight curvy triangles. In fact, if you had a ‘planetary city map’ spread flat, the streets would form a trefoil shape – like a Venn diagram of three intersecting circles (simple, after all, once you grasp it).
Or, we could imagine an alternative alien planet, this time the size of a region or nation, with three main highways and six cities, one at each intersection: the equivalent of four cities along the Equator, and two at the poles.
At the north pole city, the street map shows all roads in four directions heading south. The reverse applies at the south pole: you can choose any direction, as long as it is north. Although this orientation may seem alien, it is not so different from a normal city where all roads head either ‘out’ or ‘in’; from the centre you have no choice but to go ‘out’.
And, having a road eventually curve back on itself is really no different from a normal city that has an ‘orbital’ highway round its circumference, where you know that if you keep going you will come back on yourself. It is just a matter of how we define things: where ‘inward’, ‘outward’, ‘clockwise’ and ‘anti-clockwise’ are the relevant cardinal directions.
It may seem curious in a way, to our terrestrial minds, that a city with right-angled streets extending to cover a planet should end up with a trefoil shape streetmap, rather than a rectangular grid. But this is not to say it is not possible: it all comes down to the shape of the planet.
Let us imagine an alien planet whose entire surface is covered by a rectangular city grid – like New York’s Manhattan. The Manhattan grid has a handful of long main avenues heading north-south, and a multitude of shorter east-west cross streets. Now what if each long avenue and each short cross-street curved back on itself? This could work, if the shape of the planet was not spherical, but toroidal: that is, not like a globe, but more like a doughnut, or bagel.
So let’s imagine the central ‘north-south’ avenue goes round the outside circumference of the bagel and so curves back on itself. Running on either side will be a series of parallel avenues, that also run ’round the hole’. At right angles to these run a series of ‘east-west’ streets, which run ‘into’ (and back out) the hole. (Note how our terrestrial language fails to easily describe the directions on a toroidal world – there is no easy way of meaning ’round this way’ as opposed to ’round that way’).
So here we have a system where every avenue and street curves back on itself; every avenue intersects with every street and vice versa. And this time, all the blocks are four-sided. (This suits an alien civilisation whose uptown residents favour roughly rectangular buildings.) For an extra touch of authenticity, we could add in a Broadway: a route that cuts diagonally across the other streets; it too eventually curves back on itself.
Because the streets – and the subways beneath them – would clearly connect up in a finite, three dimensional way, the inhabitants of this Cosmic Bagel City would not think of their city as flat. But they could be forgiven for believing – like the stereotypical New Yorker – that the world does not go beyond ‘Manhattan’.