It’s the start of your twelfth summer as a parent. And you haul your kids to the pool and slather them with sunscreen. And as they trot off one by one to the diving board (as briskly as they can without earning a whistle from the lifeguard), none of them so much as glance back at you. And you realize that the long-awaited day has finally come: your children are all strong and independent swimmers. Which means you don’t have to be quite as vigilant. Which means you’re free to read a book, or doze in your chair, or listen to a podcast, or chat with the moms and lifeguards who’ve been admiring your awesome swimsuit.

You open your book, chiding yourself that you’ve had it for a month but are still only on page 190 (though in fairness, it’s not exactly light reading, and you DO read every endnote as it appears). And as you learn that the capital/income ratio is equal to S/G where S is the savings rate and G is the growth rate – though this is an asymptotic law that is valid only in the long run – the delighted laughter of your children keeps creeping into your consciousness. It’s laughter that you’re not really experiencing. And though they’re fine and having a great time, it nevertheless leaves you strangely wistful.

And moments later, you deliver an epic cannonball equal to C x J, where C is the number of children impacted and J is their joy. And unlike Thomas Piketty’s equation, yours is valid in both the short and long run.

Happy Summer everyone!