Ants, Instincts and Vectors

I happened upon an article in Plus about the vector analysis that ants seem to be using to find their way home.  Studies exploring insect navigation tools are relevant, not only to building robot navigation tools, but also to understanding the extent to which cognitive structures exist in other living things (and, perhaps, how they exist).  Unlike what we can do with other primates, or other mammals, we can’t participate in much more than the travel patterns of an insect.  But a careful look at these travel patterns has revealed some very mathematical instinctual behavior.

The article in Plus does a nice job of explaining what studies have shown about how a foraging ant finds its way home.  A kind of vector analysis of the path home is created by the ant.

Ants use a mechanism called path integration, which requires them to measure distances and direction.

The sum of the first $i$ vectors gives you a vector which points from the origin $(0,0)$ to the current location. The negative of the vector points from the current location straight back to the nest. So to know your way back home, you don’t need to remember all the vectors you travelled along — you simply add the current one to the last total and take the negative.

The vectors are built by neural circuits that can register distance and direction information.

Ants can approximate distances by counting their steps and use the position of the Sun as a compass to keep track of the direction of each segment of an outward foraging route. Through evolution, ants have developed neural circuits in their brain which can take information about distance and direction and produce an output which is an approximation of the appropriate vector maths. The result is a continuously updated home vector.

The path is built and corrected in an iterative way. The ant can repeatedly correct small errors using visual information about its surroundings.  The ant’s vision does not have enough resolution to use actual objects in its field of view (the way we do when we use landmarks), but it makes a different kind of use of visual data.  Apparently it can take a snap shot of its view of home and has a way to quantify the changes in subsequent views that were caused by the ant’s movement.   It can determine the difference between two views and then move in the direction that reduces the quantitative value of this difference.  When the difference is zero, the ant is home.

There is a website that collects papers and news on insect and robot navigation.

It may be unexpected that such complex circuitry governs ant travel. But it’s probably just our attempt to outline or model aspects of something we can’t quite grasp (namely the way a creature belongs to its world) that makes it look that way.  What I find noteworthy is that this mathematics is biological.  And it suggests to me that there may be a way to recast the persistent mind/body dualism, or even the debate over whether mathematics exists outside of us, in the world somehow.  Without our translation, modeling or formalization of it, it exists, at the very least, in interaction, of the body with the world.


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