The square-root law of price deviations was discovered in 1863 and originally framed theologically.

Evidence

The regularity was that the average extent of price deviations is directly proportional to the square root of the length of the time period in question (Regnault 1863, pp. 49-50). Modern random-walk theory leads to the same conclusion, and there are passages in Regnault’s work (especially Regnault 1863, pp. 22-24) that bring to mind the efficient-market hypothesis. However, Regnault’s comments on his square-root law remind us that he inhabited a different intellectual world. For him, the regularity was an ultimately theological warning to “earthly princes … kings of finance” to be humble in the face of what was, at root, Providential order. — Donald MacKenzie, An Engine, Not a Camera, 262

Categorization

• CANDY: The square-root law predating modern finance by a century and being framed as a Providential warning is a delightfully quotable fact.
• XREF: The square-root law connects to random-walk theory and the efficient-market hypothesis treated later in this same book.