One of the great joys of a holiday in France is the early morning trip to the boulangerie, in my case the Ti Ar Bara in Audierne. The baker has been up since 3.00am, working hard for your sybaritic pleasure. And what a true pleasure it is. As that gorgeous smell of freshly baked bread steals into the still morning air, you feel a rushing lift of the spirits. Yes, any day with such a blest beginning will surely bring all manner of wondrous things later.
Not just ‘your daily bread’
It’s not just the smell of the bread, it’s the glorious range of different things on offer. It is a mark of true civilisation to take a so pedestrian a concept as ‘daily bread’ and turn it into this transcendent cornucopia of golden joy. There are croissants and pan chocolat, flaky and light as a cherubim’s kiss, the eggy richness of the many different styles of brioche and, here in Brittany, the dense layers of caramelised butter in the kouign amann and the far breton. But even in the simplest things there is still a riotous diversity. ‘White bread’ in the Anglosphere is a simile for bland and unimaginative mediocrity. In France, white bread comes in dizzying array of forms; boules, epis, plats and rondes. Even the quintessentially French baguette comes in many different formats. There is the Ficelle, thin as the string it is named after, the shorter Batard, the pointy ended Festive, the double sized Parisienne and the giant Pan Ordinaire, which is not ordinary at all but a massive truncheon of crusty extravagance.
Surface area to volume ratio
Where does the catataxis come in? Well, it’s to do with this variety of forms. Why so many different types of baguette? If you want more bread why not just buy two normal sized ones rather than one big one? Two Ficelles weigh the same as one Batard so in ‘volume of bread’ terms they are identical. But mathematicians know that they are not the same thing at all. This because surface area and volume don’t scale up in the same way. Surface area scales in proportion to the radius but volume scales with the square of the radius. Gourmands know this difference too, but they put it a different way: you get a lot more crust with two Ficelles. A Ficelle is all crust; it’s so thin that there is very little doughy interior. So if you like the crust then get two Ficelles. By the time you get up to the monster Pan Ordinaire there is relatively little crust and a huge expanse of doughy interior. You can easily slice it and put it in a toaster.
This surface area to volume issue is a key factor in catataxis, and one of the main ways that ‘more of the same is different’ when you try to change the scale of something. For another example, consider the reason why no insect is ever bigger than a foot long: its exoskeleton design cannot support the interior mass at bigger scales.