Approximately speaking

Physicists are notorious for making approximations.  This character trait is the subject of many jokes – for example, one rather rambling one involving a physicist advising a punter on which horse to put his money ends with the line "Oh, didn’t I tell you – my calculations assumed a spherical horse rolling through a vacuum."

But approximations are useful things. The general idea is that a physicist will want to consider something in all necessary detail, but no more.  All necessary detail is obvious – for example it is very hard to adequately describe static electricity without talking about positive and negative charges. But physicists don’t like going the other way either – for example the reason why the earth orbits the sun can be explained without invoking General Relativity. It just adds in extra complication that is not necessary.

In my research on the electrical nature of the brain I make a lot of approximations – for example one that occurs a lot in computer modelling of the brain is that the brain is two-dimensional and square. Moreover, I assume ‘toroidal’ boundary conditions. This means that, if a pulse of current flows off one edge of my square, it will flow in again on the opposite edge. (The square ‘loops’ around on itself in both the horizontal and vertical directions – this is why it’s called toroidal – after the ‘torus’ (doughnut) shape which has two ways of looping around – either round the ring of the doughnut or from the outside, through the hole, and back to the outside.)

Obviously these approximations are wrong – my brain is not square, nor does it have toroidal conditions, but, for the explanation of some electrical brain phenomena, this does not matter. The model is adequate. We use it because it is a simple way of encompassing the necessary details. (Toroidal conditions are used a lot in many different areas of physics – such as simulating molecules moving in a gas or liquid.)

But, imagine my surprise when on Monday I stand in front of a cuttlefish tank at Melbourne aquarium and read that, amongst other strange features like three hearts, the cuttlefish has a brain shaped like a doughnut!  So my approximations are maybe closer to the mark than I thought – at least for cuttlefish brains.

Which leaves me wondering, are there any creatures out there that are spherical and live in vacuums?