Littlewood’s law of miracles

The law of truly large numbers holds that with a large enough number of samples (as opposed to a single sample), any outrageous thing is likely to be observed. A particular application of the law of truly large numbers is Littlewood's law of miracles. Cambridge University mathematician John Edensor Littlewood calculated that any one person is likely to see something they think is miraculous, but he described as merely surprising, about once a month. Littlewood defined a "miracle" as an event of special significance occurring at a frequency of one in a million. He then figured that the average person who's paying attention (he made these calculations before people walked around all day with their snoots buried in their smartphones) sees one "event" per second. If we're alert for about eight hours a day, that means we take in 28,800 events per day (8 hours x 60 minutes x 60 seconds = 28,800 seconds/events a day). If a "miracle" is a one-in-a-million occurrence, then we'd all expect to see a miracle every 34.7 days, or a little less than once per month.

I know Littlewood was showing that what we perceive to be miraculous events are actually pretty commonplace. But somehow I see the opposite in his numbers. Be mindful of your surroundings and you'll see an exceptional event once a month. That's pretty darn cool, even if it's not "miraculous." Now look up from your smartphones and start paying attention.

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Two days after my birthday I decided to make myself a birthday cake. Fortunately, I had a new recipe to try. This is a version of an Italian yogurt pot cake. The idea is that you use a 125 milliliter "pot" of yogurt in the cake, then use the empty pot to measure the rest of your ingredients. In this version, you use 1 pot each of yogurt, sugar, olive oil, and chocolate chips, plus 3 pots of all-purpose flour. As it turns out, 125 milliliters comes out to just about ½ cup, so I translated everything into much easier gram measurements. Use a Kitchen Scale™ and you can have this cake in the oven in less than 10 minutes, which is not quite miraculous but still something to celebrate.

Olive Oil and Chocolate Chip Cake

Adapted from Rachel Roddy via The Guardian (June 28, 2021)

Time: 45 minutes (10 active)

 

I used whole-milk (5% milkfat) Greek yogurt, but you should be able to use any type of plain yogurt, and perhaps low-fat as well. I baked this in a 7½-by-3-inch Bundt® pan; other options are: an 8-by-2-inch round cake pan; an 8-inch square baking pan; or an 8½-inch-by-4½-inch loaf pan.

4 large eggs
120 grams (½ cup) plain whole-milk yogurt (see note)
100 grams (½ cup) olive oil
100 grams (½ cup) granulated white sugar
180 grams (1½ cups) all-purpose flour
85 grams (½ cup) chocolate chips
salt
2 teaspoons baking powder

    1. Place a rack in the center of the oven; heat to 350 degrees. Spray a 6-cup baking pan with nonstick cooking spray (see note).
    2. Crack the eggs into a large bowl and whisk briefly to break up. Add the yogurt, oil, and sugar, and whisk until combined. Add the flour, chips, and a pinch or two of salt. Sprinkle over the baking powder. Using a silicone spatula, stir until everything is evenly moistened and very well combined. Scrape the batter into the prepared pan.
    3. Bake until a skewer inserted into the center of the cake comes out clean (except for some chocolate), about 35 to 40 minutes, depending what type of pan you’re using. Transfer the pan to a wire rack and cool for 5 to 10 minutes. Turn the cake out onto the wire rack and allow to cool.