calculating the circumference of the Earth

Calculating the circumference of the Earth is easy to do, and was done already in antiquity. Learned men since antiquity have known not only that the Earth was round, but how far around. The men who advised Columbus not to make his voyage were not afraid that he would fall off the edge of the Earth, but that his store of supplies would not be sufficient for the long voyage.
The circumference of the Earth was calculated in antiquity using the geometry of two parallel lines cut by a transversal (colloquially referred to as ‘sticking a stick in the ground’). It was done by Eratosthenes.
Here is the link to the Wikipedia article explaining how Eratosthenes did it.
And here is my own write-up on it:
Circumference of the Earth
keywords: shadow, measurement, proportionality, 25000 miles

lorem ipsum

“What is real is what has effects.”
— Kurt Lewin
(cf: “That which can affect our senses in any manner whatever, is termed matter.” – Poisson)
keywords: psychology

less versus fewer

Abbreviations are used all the time, and if you don’t recognize that and try to parse an abbreviated expression as it it were a complete expression, you wind up with recommendations that sound false to native speakers, but who are afraid to say so because they can’t put their finger on the theoretical error being made. So, in the supermarket, we see nonsense like ’15 items or fewer’ used to designate the express checkout area. The sign should say, as it did in the good old days before mush-headed hyper-correctness took over in the wake of rampant political correctness, ’15 items or less’. This is correct, because it is an abbreviation for ’15 items, or a quantity that is less than that’.
keywords: life, language, grammar

a mnemonic for emergent structure

“Within 6 square miles there is either a hill or a valley.”
This can be taken as a an allusion to the 6-people theorem, or, more generically, to the phenomenon of emergent structure. It can also be taken as a ‘stylized fact’.
(An analytic mnemonic, if one so prefers, can be given as follows: “If x is greater than or equal to 6, then there exists a y such that |f(x,y)| is greater than or equal to 1.”)
(Note: If you wonder why I spelling out the symbols, such as “is greater than or equal to” instead of just using the symbol, it’s because WordPress does not allow the symbol (replacing it with a little square)).
keywords: Ramsey Theory, within six square miles, emergent order