Down Under

https://commons.wikimedia.org/wiki/File:La_rotondit%C3%A9_de_la_Terre,_Image_du_monde_(cropped).jpg

How is it with those who imagine that there are antipodes opposite to our footsteps? Do they say anything to the purpose? Or is there any one so senseless as to believe that there are men whose footsteps are higher than their heads? Or that the things which with us are in a recumbent position, with them hang in an inverted direction? That the crops and trees grow downwards? That the rains, and snow, and hail fall upwards to the earth? And does any one wonder that hanging gardens are mentioned among the seven wonders of the world, when philosophers make hanging fields, and seas, and cities, and mountains?

— Lactantius, Institutiones Divinae, 303

| History · Science & Math

Shapes of Things

https://commons.wikimedia.org/wiki/File:Sierra_Leone-Mappa.gif

In 2016, University of Buenos Aires computer science student Gonzalo Ciruelos worked out that the roundest country in the world is Sierra Leone, with a roundness index of 0.934 on a scale of 0 to 1.

He’d been inspired by David Barry, who’d found that the world’s most rectangular country is Egypt (0.955 on the same scale).

Metropolitan France is known as the Hexagon. I suppose each country has its claim to fame.

(Gonzalo Ciruelos, “What Is the Roundest Country?”, Math Horizons 26:3 [February 2019], 26-27.)

| Science & Math · Trivia

The Art of Living

https://pixabay.com/photos/old-stove-hot-fire-flame-2568425/

When I am going out for an evening I arrange the fire in my stove so that I do not fail to find a good one when I return, though it would have engaged my frequent attention present. So that, when I know I am to be at home, I sometimes make believe that I may go out, to save trouble. And this is the art of living, too, — to leave our life in a condition to go alone, and not to require a constant supervision. We will then sit down serenely to live, as by the side of a stove.

— Thoreau, Journal, Feb. 20, 1841

| Literature

In a Word

https://www.pinterest.com/pin/the-chevening-maze-in-kent-is-the-first-multiplyconnected-puzzle-maze-this-means-it-cannot-be-solved-by-the-put-your-left-hand--48624870947902374/

anfractuous
adj. having many windings and turnings

loof
n. the palm of the hand

penetralia
n. the innermost recesses of a building

swither
n. a state of perplexity

It’s commonly said that you can defeat a hedge maze by placing one hand on a wall and carefully maintaining that contact as you advance. If the hedges are all connected, this method will reliably lead you to the center of the maze (and, indeed, to every other part of it before you return to the entrance).

The Chevening maze, in Kent, was designed deliberately to thwart this technique. Its center is concealed in an “island” of hedges distinct from the outer wall, so following either a left- or a right-hand rule will return you to the entrance without ever passing the goal.

| Puzzles · Science & Math

The Erdős–Faber–Lovász Conjecture

https://commons.wikimedia.org/wiki/File:Erd%C5%91s%E2%80%93Faber%E2%80%93Lov%C3%A1sz_conjecture.svg

This figure contains four “cliques” of four points each, with each of the four points in each clique connected to each of the others, and each pair of cliques intersecting at a single point. Four colors suffice to color all the points so that no two linked points share a color.

Is this always possible? If k cliques, each containing k points, are arranged in similar fashion, can the result always be colored properly with k colors? In 2021, half a century after Paul Erdős first posed the question, Dong Yeap Kang and his colleagues proved that, for sufficiently large k, the conjecture is true.

| Science & Math

Noted

“A few precepts to repeat whenever you are in need of comfort,” by Gabriel Hanotaux, French minister of foreign affairs from 1894 to 1895:

  1. Anything can happen.
  2. Everything is forgotten.
  3. Every difficulty can be overcome.
  4. No one understands anything.
  5. If everyone knew what everyone said about everyone, no one would speak to anyone.

“Above all things, never be afraid. The enemy who forces you to retreat is himself afraid of you at that very moment.”

(Via André Maurois’ The Art of Living, 1939.)

| Society