Cake math

Say it’s Friday after a long week, a week that was more of a rollercoaster than you’d anticipated¹, and a Friday that itself had some unexpected twists to it. You’re driving home after picking up some medication from the vet (or some other similarly “oh yes, the realities of life” type errand), and passing a Dairy Queen.

Because you’re an adult who knows when you need to treat yourself, it’s a no-brainer to hang a right and pull in. The $6-off coupon your driving companion brandishes doesn’t hurt, either.

This coupon, though, it’s only for a purchase over $30. Which brings you, inevitably, to the ice cream cake section of the store.

Now, a wave of responsibility may wash over you. You may think to yourself, “Okay, getting an ice cream cake on the spur of the moment—this feels a bit indulgent. So we should just get a small one.”

For good reason, you should push through that wave.

Small ice cream cakes at DQ are 8 inches diameter. The next size up is 10 inches. The price difference is small, less than a 10% increase from the 8-inch to 10-inch cake.

Because of the beauty of cake math (or, for the less sugar inclined, “geometry of circles”—this applies to pizza and other round delights!), that 2-inch increase in diameter is not a mere 25% increase in the amount of cake you’re getting—it’s a more than 50% increase. (To compare the size of two cakes, use r^2, where r is the radius, or half the diameter, of your cake.)

So for less than 10% more in price, you’re getting more than 50% more in cake. Indulgent, sure, but it’s economically efficient indulgence—and all the sweeter for it.

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• The best thing I listened to / read this week was Krista Tippett’s 2021 interview with the late Joanna Macy and Anita Barrows. It’s a discussion of Rilke, especially his Letters to a Young Poet, by three women for whom Rilke and his work have played a large part in their lives (Macy and Barrows translated Rilke). “Live the questions now”, what a stirring call!
• Another interesting listening / reading experience this week was Simon Collison’s “afternoon of advanced sound discovery”, with a number of tracks recorded during a walk through Greenwich. Neat to see what the different equipment picks up, and the details in Simon’s “listening notes”.

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• CSS keeps getting better. I’m only slowly learning of features that’ve been added in the last ~5–10 years (!), but the :has selector (pseudo-class) sounds amazing.
• An illuminating articulation of how LLMs work, extending from just “next-word generator” to “next-word generator operating in a given ‘area in personality space’”.
• And the price / risk of rampant AI use in development? Enabling the creation of services (apps) run by people who have little interest in whether people are well-served by them.

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• An account of how to intelligently “shrink a government department”. Refreshing to see writing like this from a sitting MP! (via Ryan)
• A lively response by Jim Mitchell on different ideas on organizing government. I’d missed Canadian Public Administration’s largely open-access issue on “Re-Setting the Public Service of Canada” (Mitchell is responding to a few articles from that issue), but have saved a number of articles to settle into over tea (or some other beverage).

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All the best for the week ahead! Eat some cake, and be logical about which size you pick!

Lucas