## Horsekicks, Celebes and (no) bunnies

EPFL, the Swiss polytechnic institute I am visiting, is not far from Lake Léman (aka Lake Geneva) – just a few hundred meters away.
This is a photograph taken from the port of Ouchy, not from EPFL. In many cities that have long absorbed their ports, people still speak of the port as a distant separate entity. This here may be an extreme example – Ouchy is a short walk (1.6 km) down a slope from the very centre of Lausanne.

It is tempting to underestimate a body of water where one can see the other shore. How many accidents, fatal and otherwise, have there been each year for the last fifty years, say? Either this turns out to be the sort of question for which it is not trivial to get an answer in a few seconds through a web search, or my search skills are subpar. I’ve heard (thanks, Mom) that one of the most classic examples of a Poisson distribution (namely, the distribution of the number of soldiers killed each year by horsekicks in the Prussian cavalry) may actually be a negative binomial distribution. I wonder what the distribution for drowning accidents would be here?

Then the naturalist went home, and Stein, having no home to go to, remained with an old trader he had come across in his journeys in the interior of Celebes – if Celebes may be said to have an interior.

Joseph Conrad, Lord Jim

What are your favorite instances of mathematical humour in serious non-mathematical literature? Both intended and unintended instances count. The above must be a rare example of a remark whose somewhat mathematical humour is certainly intended, but has also become richer as a result of later developments in the field (viz., point-set topology).

Almost later: Poincaré’s Analysis Situs predates Lord Jim by five years. I doubt Conrad was reading Poincaré, and, at any rate, some of the basic terminology did not stabilise right away.

For non-mathematical readers: let $X$ be a metric space, i. e., something for which the notion of “distance” makes sense; for example, let $X$ be the earth’s surface. (It is also possible to discuss the notion of interior without using the notion of distance, but we do not need to do that here.) Let $S$ be a subset of $X$. (Example: let $S$ be Celebes.) The interior of $S$ is defined to be the set of all points $x$ in $S$ such that one can find a small disc around $x$ such that the disc completely contained in $S$. In standard notation:

$\text{Int}(X) = \{x\in S: \exists \delta>0 \text{\; such that \;} \forall y\in X\; |y-x|<\delta \Rightarrow y\in S\}.$

The point is that this technical meaning of the word "interior" does not subvert its day-to-day usage; in fact, it corresponds very neatly to how Conrad is using the word.

(Of course, Conrad's joke relies precisely on the fact that he and his readers are forced to think technically, in a very loose sense, for an instant: speaking of the interior of Sulawesi presumably seems more counterintuitive only if one has a map in mind.)

If anything, the aside in Lord Jim can be seen as a remark on constants and effectiveness. (The interior is non-empty, but there $\delta$ will always be rather small.)

I’ve been asked (in French) to explain the reason for the name of this blog. As some readers will have noted, it is a pun that works in English but not in French (or Spanish): “the value of the variable” can mean both “la valeur de la variable” (el valor de la variable) and, on second thought, “la valeur du variable” (el valor de lo variable) – the value of that which is variable. I thought it apposite as a title for something that is about many passing thoughts in and outside mathematics.

Oh well. At this point I wanted to say that, at least, that had taken me much less time than explaining the structuralist joke implicit here, but the crucial paragraph on bunnies is hidden somewhere behind the LRB’s subscription barrier. How sad.

I am a number theorist with side interests in combinatorics and group theory.
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### 3 Responses to Horsekicks, Celebes and (no) bunnies

1. Fede says:

The first part of your post made me think of Ben Orlove’s book Lines in the Water: Nature and Culture at Lake Titicaca, in the first chapter of which he does a review of novels that involve lakes, in particular Theodore Dreiser’s An American Tragedy, where someone drowns/is killed in a lake. Like you, Orlove argues that lakes tend to be underestimated.

• valuevar says:

It is a funny thing. I would not be surprised if most people were more aware of danger in a deep pool than in any lake in which you can see the other shore.

2. Fede says:

I wonder if other Indonesians make fun of Sulawesians for the shape of their island the way people make fun of Chileans for the shape of their country (i.e. about their feet getting wet when they sleep).