Infinitesimal calculus and renal calculus

By | October 11, 2013

I ran across the phrase renal calculus, another name for a kidney stone, and wondered whether it was related to the calculus you learn in a math class. It turns out that it is, and the link is limestone.

Calx is the Latin word for limestone; it comes from the Greek word khalix, or pebble. The diminutive form of calx in Latin, calculus, was originally used to refer to a pebble used for counting and simple calculations. The Latin word calculus thus forms the basis for the English word calculate

Calculus can be used in English to refer to any system of calculation using symbols, although it is used primarily for the indispensable mathematical tool developed by Leibniz and Newton in the 17th century to describe and study change. This was originally called the calculus of infinitesimals, later shortened to infinitesimal calculus; I think this is why you sometimes hear people talking about, for example, the history of the calculus instead of simply the history of calculus.

It’s obviously a short step from the pebbles used to reckon your accounts to the pebbles that cause such misery in the urinary system or in the gall bladder. Calculus is now used to refer to any type of accidental accretion in the body. Now that I think about it, I have vague recollections of puzzling over the thought of calculus on the teeth, perhaps when I was the target of a dental health campaign in grade school. Dental calculus is essentially hardened plaque, perhaps the first step on the road to gum disease. I will generously share all of what I remember learning about it: Brush! Floss!

The Latin root calx also made it into English in the name of the element calcium, which is a major constituent of limestone (and coincidentally is also found in some kidney stones). Renal, by the way, comes from the Latin word for kidney, ren.

Learn more:

  • Why Do We Study Calculus? gives a brief history of calculus and its applications and explains why it’s worth learning
  • Free online math courses at Open Culture
  • French composer Marin Marais wrote “A Description of the Removal of a Stone” in 1725, which is thought to depict the horrors of an operation to remove a bladder stone (the first gallstone operation didn’t occur until later). This article lists the brief descriptions in the score, which are worth reading, but note that the article identifies the operation, apparently incorrectly, as a gallstone removal. 
  • [Added October 23]: A friend sent links to an analysis and a performance of the Marais piece.