Group items tagged

“I’m interested in seeing what design principles nature uses,” Dr. Lalvani said. “Math, perhaps; maybe physics, whatever. The whole D’Arcy Thompson-type stuff.” The biologist D’Arcy Wentworth Thompson’s book “On Growth and Form,” published in the early 20th century, was a seminal work on the subject of patterns in nature. Thompson, a Scotsman, argued that growth and the structures that resulted were governed by physical principles and could often be described in mathematical terms. He saw examples throughout nature — in the spiral shell of a nautilus, the branching veins on an insect wing and the scales of a pine cone, to name just a few.

This story of discovery begins a century ago with Albert Einstein, who realized that space is not an immutable stage on which events play out, as Isaac Newton had envisioned. Instead, through his general theory of relativity, Einstein found that space, and time too, can bend, twist and warp, responding much as a trampoline does to a jumping child. In fact, so malleable is space that, according to the math, the size of the universe necessarily changes over time: the fabric of space must expand or contract — it can’t stay put. For Einstein, this was an unacceptable conclusion. He’d spent 10 grueling years developing the general theory of relativity, seeking a better understanding of gravity, but to him the notion of an expanding or contracting cosmos seemed blatantly erroneous. It flew in the face of the prevailing wisdom that, over the largest of scales, the universe was fixed and unchanging. Einstein responded swiftly. He modified the equations of general relativity so that the mathematics would yield an unchanging cosmos. A static situation, like a stalemate in a tug of war, requires equal but opposite forces that cancel each other. Across large distances, the force that shapes the cosmos is the attractive pull of gravity. And so, Einstein reasoned, a counterbalancing force would need to provide a repulsive push. But what force could that be? Remarkably, he found that a simple modification of general relativity’s equations entailed something that would have, well, blown Newton’s mind: antigravity — a gravitational force that pushes instead of pulls. Ordinary matter, like the Earth or Sun, can generate only attractive gravity, but the math revealed that a more exotic source — an energy that uniformly fills space, much as steam fills a sauna, only invisibly — would generate gravity’s repulsive version. Einstein called this space-filling energy the cosmological constant, and he found that by finely adjusting its value, the repulsive gravity it produced would precisely cancel the usual attractive gravity coming from stars and galaxies, yielding a static cosmos