# The Curious Link Between Parked Cars and Perched Birds

Could an uncanny resemblance between the statistics of parked cars and perched birds help us understand the relationship between mathematics and physics?

At first sight, parallel parking may not seem to have much to do with the way that birds perch on electricity wires, but Petr Šeba at the Czech Technical University, in Prague, begs to differ.

He has measured the gaps between parked cars and says that the statistical patterns in the data bear an uncanny likeness to those in the distances between perched birds. (Note that distances are by no means random.)

That’s kind of interesting, but perhaps not for the reason that Šeba gives. His argument is that the mechanisms that birds and humans use to judge distances are essentially the same. He says that this is because both species evolved from a common ancestor that also perceived space in the same way. Perhaps.

A more interesting explanation is that Šeba has stumbled across a deep connection between the statistics of seemingly unrelated phenomena. It has been known for some time that the statistics associated with the gaps between parked cars can be described by a branch of mathematics known as random matrix theory.

This theory also describes the distribution of peaks in the way that neutrons scatter off heavy nuclei, the zeros in the Riemann zeta function, and the statistics of the bus system in the city of Cuernavaca, in Mexico (as Šeba knows all too well: he went to Mexico to study the buses).

In fact, random matrix theory seems to be remarkable in its effectiveness at describing not just the physical world but the mathematical world too.

In 2006, Percy Deift from the Courant Institute of Mathematical Sciences, in New York, even went so far as to say that random matrix theory may play the same role in mathematics as thermodynamics does in the physical world. In other words, random matrix theory is a manifestation of some fundamental universal property of mathematics.

That is a profound idea that leads to many fascinating questions. For example, if seemingly unrelated phenomena can be linked by the mathematics of random matrix theory, are they also linked in some physical way?

And if so, what then links the real world governed by physical laws and the nonphysical world of mathematical patterns?

Perhaps the way that birds and humans line up offers us a clue.

Ref: arxiv.org/abs/0907.1914: Parking and the visual perception of space