6 August 2016

Kant, bees, and the brain’s GPS

How do we find our way around? One obvious method is landmarks. Researchers have identified “place cells” which represent locations in our cognitive map of the world. However, that doesn’t explain how we can find out way around in a place we’ve never been before.

In 2005, a second kind of brain cell associated with location was identified in the paper Microstructure of a spatial map in the entorhinal cortex. The new cells were called grid cells:

Unlike place cells, the regularity observed in the firing patterns of grid cells does not appear to be derived from environmental features, or any type of sensory information. Rather, they appear to code a spatial structure that is generated internally within the brain and use it to scaffold the external environment, much in the same manner that Kant had anticipated.

…That’s Immanuel Kant, who argued that physical space as we experience it is an organizing feature of the human mind and dependent upon it, rather than something in the world which we perceive.

The grid cells of the brain are the ones that construct the mental coordinate grid you use to let you know how far you’ve moved in which direction. And here’s the thing I find interesting about this mental grid: it’s hexagonal.

Each layer of grid cells is arranged in a pattern of equilateral triangles, like isometric graph paper. That makes it hexagonal because at any coordinate point, there are 6 coordinate points one step away. Compare to regular graph paper, where at any point you can take a step in only 4 directions.

So if the brain cells which model our movement in the real world are fundamentally based on a hexagonal grid, might we actually be able to find out way around more easily if our cities and buildings were arranged on a hexagonal grid as well?

The idea has been floated by architects and urban planners before, going back as far as the 19th Century. Part of Detroit was built on a hexagonal grid, until the town abandoned the idea in the 1820s. Part of the center of Canberra, Australia is still laid out in a hex grid, and at one point it was proposed that London’s boroughs be rearranged hexagonally. Hexagons make for more efficient use of space and require fewer roads, and by the 1930s there were multiple plans for possible hexagonal grid cities. It was argued that triangular intersections would lead to fewer accidents than four-way intersections, because lines of sight are easier and you only have two possible sources of oncoming traffic. They’d be faster, too, if you had traffic lights, because you’d only need a 3-step cycle.

So could it be that the whole idea of laying out cities on a rectangular grid is fundamentally wrong? Are we wasting space, causing traffic accidents and making it easier to get lost?

Hexagonal grids turn up in Central Place Theory, which hypothesizes that natural settlements will tend to develop a more hexagonal structure. The theory was devised by German cartographer Walter Christaller, and I wouldn’t be surprised if it was part of the thinking behind the game Settlers of Catan.

It seems to me that it would be worth investigating whether navigation is truly easier on a hex grid. It should be possible to come up with video games that require navigation on either a hex or square map, and precisely measure navigation speeds for players dropped in to play from a first person perspective. Some people have done some toying with the math of hex navigation, and apparently you can construct hex grid cities in the game Cities: Skylines.

Maybe the bees have got it right?

© mathew 2017