Life from geometry

One of the things always fascinated me about Escher’s work is his representation of infinity. Infinity plays a big role in many things I do such as in cosmology, and here [Development II] we have a picture in which he has a pattern of hexagons which recedes, or gets small and smaller, until infinity is represented by the infinite crowing at the central point. There’s another feature here where you have this very geometrical structure in the middle...and as you work you way out in the picture out these hexagons become living creatures. Something Escher was always playing with — this life coming out of inanimate geometry if you like.

Roger Penrose The Art of The Impossible: M C Escher and Me

Thanks to LC

Pattern, process and change

In creating [a mathematics of flowing quantities and rates of change] Newton embraced a paradox. He believed in a discrete universe. He believed in atoms, small but ultimately indivisible - not infinitesimal. Yet he built a mathematical frameworks that was not discrete but continuous, based on a geometry of lines and smoothly changing curves... 

Here at Woolsthorpe the night was strewn with stars, the moon cast its light through the apple trees, and the day's sun and shadows carved their familiar pathways across the wall.  Newton understood now: the projection of curves onto flat planes; the angles in three dimensions, changing slightly each day. He saw an orderly landscape. Its inhabitants were not static objects; they were patterns, process and change.

Isaac Newton by James Gleick (2004)


Newton's early papers here.

Both strange and beautiful

I find [synchrony] beautiful and strange in a way that can only be described as religious. And I know I’m not alone in that reaction. When I read the old accounts by sixteenth century voyagers to Malaysia and Thailand, the first Westerners to witness the astonishing spectacle of fireflies flashing in unison for miles along the riverbanks, I hear in them that same sense of rapture... 

For reasons I wish I understood, the spectacle of synch strikes a chord in us, somewhere deep in our souls. It’s a wonderful and terrifying thing. [Seeing] it touches people at a primal level. Maybe we instinctively understand that if we ever find the source of spontaneous order, we will have discovered the secret of the universe.

from Sync by Steven Strogatz (2003)

an Hieroglyphical and shadowed lesson of the whole world

A murmuration of starlings appears to mirror a quantum phenomenon:

[a] new model is mathematically identical to the equations that describe superfluid helium. When helium is cooled close to absolute zero, it becomes a liquid with no viscosity at all, as dictated by the laws of quantum physics.

Image: murmuration at Netivot via TheFabWeb.com