Tuesday Recipe Blogging: Pi, Phi, Pie, and Apple Pie

Pi Equals

Although I no longer comment at Slacktivist, I still like reading Fred Clark (and am hoping for Tribulation Force Fridays…). I noticed he had a recent post up asking for pie recipes, tips, and other fruity topics.

Pi is the ratio of a circle’s circumference to its diameter. It is an irrational and transcendent number. It cannot be represented or calculated exactly in decimal (or in hex, or any other way except by saying c/d). It is one of the beautiful and useful numbers of the universe.

A German enthusiast Ludolph van Ceulen taught fencing and mathematics, and when he died on 31st December 1610, after spending years of his life calculating pi to 35 decimal places, the number 3.14159265358979323846264338327950288 was engraved on his tombstone. I think that on 31st December 2010, lovers of pi around the world should assemble on the streets and recite pi and eat pie and remember van Ceulen.

Phi is the ratio of a line divided so that the ratio of the length of the longer part to the entire line is the same as the ratio of the length of the shorter part to the longer part. It is irrational, but not transcendent: nevertheless, it is the golden number, because it is shiny: 1.618033988749895….

Pi is the same everywhere and always will be and always has been, wherever there are circles. Phi is a number that exists because we like it: it has human appeal. It is a universal number, yes, and you can see it in the proportions of snail shells as much as in Notre Dame, but just as it would surprise me if we encountered an alien species that did not know pi, it would also surprise me if this alien species knew phi.

(The Fibonacci series, another lovely set of numbers, has a ratio between one Fibonacci number and the next that converges on phi. Try it for yourself, you’ll like it: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233. 377, 610, 987, 1597…)

For me the most obvious use of phi is in art and architecture: a building or a room is pleasing to the eye if its proportions are calculated according to the Golden Section. For you, it may be music, or the way plants grow, or the way our bodies are proportioned. But it’s all phi.

A pie is made with a pastry shell, a filling, and a pastry lid: if there’s only the shell and filling, it’s not a pie but a tart or a flan or a quiche. All of which are good, but there is something especially fine about pie.

Shortcrust pastry is made with low-gluten flour and butter. (If you are vegan, margarine that is hard at room temperature is just as good as butter, though it has less flavour: if you are coeliac, use a mix of at least 3 gluten-free flours (gram flour, buckwheat flour, hemp flour, potato flour, arrowroot, corn flour…) and more fat than the recipe calls for: I am told that lard is better in gluten-free pastry than butter, but as to that, I can’t say. The BBC recommends an egg… I guess the moral is, if you’re coeliac, don’t be vegan. Hm.)

You weigh out the flour, then add half the weight of the flour in butter, and a pinch of salt. Wash your hands thoroughly in cold water, and rub the butter into the flour using the tips of your fingers. If your hands warm up, wash them again in cold water. Do not rub the bits of flour and butter that congeal on your fingers back into the bowl. When the bowl of flour and butter looks like a bowl of fine breadcrumb, mix it into a ball with cold water. Wrap the ball in cling film to avoid hardening and put it in the fridge for quarter of an hour or so.

Bramley apples are best for pies, I say with British patriotism. No, really, they are. But whatever kind of apple you intend to use, cut them into quarters, cut out the core, peel the apples – enough to fill the pie dish in a slightly heaped way. Sprinkle them with lemon juice so they don’t brown while you’re doing the pastry.

Divide the pastry into two balls, one slightly larger than the other. Roll out one half and line a floured pie dish with it. You can blind bake this if you like – but if you do, remember you need to fill it with beans to avoid the pastry rising. And frankly, I don’t think you need to for this kind of pie. The pastry will cook, it just won’t be very crisp.

Fill the pastry shell with the sliced apples. Generously sprinkle with dark brown sugar and whatever spices go well with apple: I like cinnamon and clove.

Roll out the other pastry ball, and make a lid. Cover the apples with the lid, and pinch the lid and the sides together firmly (this is another reason for not blind-baking the lower crust – you never get a proper seal). Use a fork to make holes in the pastry lid, in a pattern if you’re that way inclined. The recipe books of my childhood always used to suggest you use the scraps of pastry to make decorations in leaves and fruit, and this always used to make me feel very inadequate. But you do need the ventilation in the crust.

You can brush the pastry with milk or with white of egg to give it a goldeny shiny look. Or not. It’s all visual.

Bake in the oven for half an hour to 40 minutes. The brown sugar melts and mixes with the apple juice, especially if you use Bramleys, and floods out over the lid of the pie through the little ventiliation holes, and dear sweet Pomona, it is a glorious thing.

Eat hot with thick whipped cream.