FLEAS, AD INFINITUM

I’ve always been enamored of the couplet that contains the words “little fleas have lesser fleas, and so ad infinitum.” I always thought the author was Ogden Nash, or perhaps Lewis Carroll (“mimsy were the borogroves”) and was surprised to find the couplet has a
much longer history.

The couplet is from the great British mathematician Augustus De Morgan (1806-1871), who adapted it from the Anglo-Irish satirist, essayist and author Jonathan Swift (1667-1745).

De Morgan:

Great fleas have little fleas upon their backs to bite 'em,
And little fleas have lesser fleas, and so ad infinitum.
And the great fleas themselves, in turn, have greater fleas to go on;
While these again have greater still, and greater still, and so on.

Swift:

So, naturalists observe, a flea
Has smaller fleas that on him prey;
And these have smaller still to bite ’em;
And so proceed ad infinitum

[Added Note]: The phrase “mimsy were the borogroves” is from Lewis Carroll’s Jabberwocky. It’s also the title of a science fiction book written by Lewis Padgett (aka Henry Kuttner and Catherine L. Moore), published in 1943, which I read - and enjoyed - as a teen sci-fi addict.