by Dilip D’Souza
It didn’t really surprise me that someone has worked out the mathematical laws I have been reading about of late. It did surprise me that it’s taken me till the ripe old age I’m at now, when the laws have been known for over a century, to find out about them.
I refer to Lanchester’s Laws of combat. These are, of all things, mathematical equations that describe war. That most chaotic and unpredictable of human endeavours, and mathematicians have tried to model it. These laws were worked out during World War I, independently by Frederick Lanchester and Mikhail Osipov. (After learning about them, I find that a mathematician I am proud to call a friend, John Allen Paulos, wrote about the Laws here on 3QD a few years ago.)
I won’t get into the actual (differential) equations here. Think for now of two armies that confront each other and begin fighting. Let’s assume the soldiers of each army are about equally competent (or otherwise) fighters, meaning all of them can kill opponents at about the same rate. Their opponents’ competence, of course, may differ – and that difference will obviously have some bearing on how the battle proceeds. Also remember that the size of the two armies steadily decreases, because soldiers are dying as the battle progresses.
Started with this rate of mortality in each army, Lanchester sought to describe how they would fare in battle. After all, how quickly an army loses soldiers is determined by the number of opponent fighters, and by their competence in battle.
In wars in ancient times, soldiers confronted each other one-on-one, and the war as a whole was made up of all these individual fights. How quickly an army loses soldiers is then described by the numerical strength of the enemy multiplied by their competence – which is, in fact, the enemy’s overall fighting power. That is, one army’s fighting power describes its opponents’ rate of mortality. You might also think of it this way: the death rate per capita in one army is the ratio of enemy numbers to friendlies, multiplied by the competence of the enemy soldiers. This is Lanchester’s Linear Law of combat.
But as weapons became ever more powerful, war itself evolved away from those frantic one-on-one battles. Read more »


Sughra Raza. Dancing On The Esplanade. Boston, August 2026.



Why am I reviewing in Autumn 2026 a book that came out in Spring 2024? Because of what else is happening this Autumn; all the political events that I describe here took place during August and September this year.
When Mark Carney
AI safety has what I would call a “last mile” problem. This summer, AI safety suddenly and very unexpectedly went mainstream. Whether it was the appearance of 
The iconic Aretha Franklin performance of (You Make Me Feel Like) A Natural Woman came across my feed the other day. You can watch it 


The other day I heard that
Bhen Alan. Three Hundred Thirty Three, 2022.
