### 1/2 idea No. 17: Algebra of history – Historiographical experiment #3

By Jon Agar, on 30 July 2021

(I am sharing my possible research ideas, see my tweet here. Most of them remain only 1/2 or 1/4 ideas, so if any of them seem particularly promising or interesting let me know @jon_agar or jonathan.agar@ucl.ac.uk!)

From my Notebook G (November 2013-September 2014), this one woke me up in the middle of the night and I scribbled it down. I’m not sure it makes sense. I quote verbatim.

-Can form an algebra of history

-level 1 from history books (ie all historiography)

H(actors, causes, …)

this is a finite algebra

-level 2 from reality

R(actors, causes, …)

-> how does H map onto R?

-is R finite?

– if H is aleph 0 and R is aleph 1 then can construct a unhistoriographical event, ie an element of R that does not/cannot be in H by diagonal argument

(**Comment**: there are some obvious problems with the above. But the key idea is that histories (written and capable of being written) can be placed into an order which can be listed against the natural numbers, (1, 2, 3, …) whereas what it describes might be as infinite as the real numbers. The diagonal argument is that of Cantor. Cantor showed that however you listed the real numbers there was always another that wasn’t on the list. To my mind it is one of the most magical mathematical proofs of all time. The application here, if can be made to work at all, which it almost certainly can’t, is that there is always history that escapes history)

I had a second idea, from Notebook J (October 2016 – July 2017), which I seemed to think was related:

What is the 1/f noise of history?

(This question struck me while reading Hal Whitehead and Luke Rendell’s *The Cultural Lives of Whales and Dolphins, *University of Chicago Press, 2014, which just shows how ideas can come from unexpected and apparently unconnected sources)

(**Comment**: ‘1/f^{α} noise’ is a mathematical approach to measuring how predictable something changes. It came from 1920s investigations of electrical noise in vacuum tubes, but has been applied in a bewildering number of fields since, but not, to my knowledge, history. If alpha = 2 then the noise is random, like white noise hiss. The smaller alpha gets, between 0 and 2, the more organised the phenomenon is. Can the contingency of history be measured?)

Both of the above are applications of mathematical ideas to history. Turchin, *Historical Dynamics* (Princeton University Press, 2018) talks about other ways of formulating mathematical models of history. They tend to be sets of differential equations, as if history was treated like computational meteorologists treat the weather and climate, or how macroeconomics treats the economy. Turchin also notes the history of mathematised history, crediting, for example, Walter Bagehot (in 1895), Bertanffy’s General System Theory (1968, but ideas from 1940s), and Rashevsky (1968) as key texts.