The symmetry of the Four again (set to the music of Bumba’s harmonica fourths if you click).

The Quatro: the tesselations of the square, the grid. Everything laid out on graph paper, a world made of little boxes.
The usefulness (to humans, not so great for all the other species) of patterns based on the four has been astounding. Pyramids, temples, and skyscrapers arise square and straight from their cornerstones. Roads and cities laid out on grids. Brick by brick, square by square. Maps of distant lands, maps reaching to the heavens.

Analytic geometry, the great bridge between algebra and geometry – so kindly revealed to us four hundred years ago by the Frenchman Descartes – allows us to visualize patterns and mathematical functions. Equations are made manifest in two or three dimensional space. Functions come to life. Newton’s calculus arises. Motion is finally described via a set of laws. The scientific age, the Industrial Revolution follow. All thanks to poor Rene Descartes, who, lying on his back in bed watching a fly walk across the ceiling, suddenly conceived of the grid defined by the two dimensions we now call the x and y axes. What a guy that Rene Descartes. Here’s to Rene Descartes and the symmetry of the four.

Thanks. Compared to the 2, the 3, the 5, and the 6 (and all their patterns), the 4 seems a bit dull, but it is quite useful and agreeable. I suppose I should do posts on those numbers.

Which question do you want me to answer first? (Also a Groucho Marx line).
I hope that Robert De Niro doesn’t get confused and challenge Rene Descartes to a boxing match.

strange how sudden thoughts enter a brain, Bumba, and a whole world of possibilities open up. Inspiration, where would we be without it? xx

Inspiration: the breath, the spirit. Without it, well, we would be spiritless?

Here’s to a quadro symmetric post very agreeable to the senses [hearing first]! 🙂

Thanks. Compared to the 2, the 3, the 5, and the 6 (and all their patterns), the 4 seems a bit dull, but it is quite useful and agreeable. I suppose I should do posts on those numbers.

Is it just me, or does he look like Sylvester Stallone?

Which question do you want me to answer first? (Also a Groucho Marx line).

I hope that Robert De Niro doesn’t get confused and challenge Rene Descartes to a boxing match.

And here’s to you, Bumba, for writing such a fine post. Elegant is the word for it. I loved it and I’m not hot on math.

Thank you for your kind words. Don’t encourage me. i’m already thinking of writing about the three, the two, and the five. And maybe the six.

thank you for the music!

Very welcome, Frizz.