# The parable of the perfectly symmetric ass

I would like to introduce a phrase into the lexicon of science and everyday life, based on the following ridiculous story that was taught to me at the CERN summer school.

Imagine a perfectly symmetric ass, standing atop a perfectly symmetric hill (…I’m talking about a donkey here, folks). Placed on either side of the hill, at perfectly equidistant locations, are two perfectly identical piles of hay.

The ass is hungry, but it feels itself pulled toward each pile of hay with exactly equal and opposite forces.

Given the staggering symmetry of the setup, the only logical conclusion is that the ass is doomed to inaction and will eventually starve.

As it turns out, this silly story is a famous satire of the assertion by the French philosopher Jean Buridan that

Should two courses be judged equal, then the will cannot break the deadlock, all it can do is to suspend judgement until the circumstances change, and the right course of action is clear.

The poor starving donkey above is thus called “Buridan’s ass.”

(As is often the case, the original version of this satirical argument actually belongs to Aristotle.)

Since hearing this story, there have been a large and increasingly frequent number of times when it has seemed like a good depiction of myself or someone else. So I would like to suggest using the phrase “to be a perfectly symmetric ass” as a description of someone who is being paralyzed into inaction by symmetry. In particular, I see two good targets for this phrase:

### 1. Scientific arguments that invoke symmetry at the expense of energy minimization

For example, suppose someone asked you to predict what will happen if you apply a large voltage between a small inner sphere and a large outer sphere that is filled with a weakly-conducting plasma. Most of us who had Gauss’s law arguments trained into us would immediately say that an electrical current will flow out from the inner sphere in a radially-symmetric way, and consequently that the total current flow will be very small. But most of us would be wrong, however, because what actually happens is this:

[Just watch from the 0:09 mark until 0:12 or so.]

In short: the system figures out very quickly that there is a much lower-energy way to move its current from inner to outer surface. Namely, by creating sharp (symmetry-breaking) pathways with intense current, which produce dielectric breakdown of the plasma and allow the current to flow easily.

If you allow symmetry to fool you into thinking that the current will flow slowly and radially, then you are “being a perfectly symmetric ass.”

### 2. Everyday situations in which opportunities are missed because of an inability to choose between two good options

Suppose, for example, that you are at an ice cream shop and you are standing at the counter, unable to make up your mind about which of the various fantastic flavors you will get. As the line starts to build up behind you, you eventually get flustered and say “never mind, I’ll just get chocolate.”

In that situation, you are “being a perfectly symmetric ass.”

Or, maybe, you have “made a perfectly symmetric ass of yourself.”

I say it lovingly, of course, because I make a perfectly symmetric ass of myself all the time.

I like to say that, in Buridan’s ass type situations, the symmetry requires only that the two outcomes be equally probable. In other words, the symmetry of the situation is preserved, but in the probability distribution over the outcome space rather than in the actual outcome. It’s the same thing with the plasma ball. A narrow, localised pathway is possible, just as long as the probability distribution over its locations is spherically symmetric.