We still have a lot to learn

The brilliant mathematician-billionaire Jim Simons and his wife, Marilyn, have donated $60 million to Stony Brook University for a unique research center focused on two of the most widely dreaded subjects on the planet - geometry and physics. For Simons they "are at the heart of understanding the universe, its origins, its basic nature."

That sentiment brings to mind William Blake, who I believe would have agreed in his own way with Simons. In 1824 Blake crafted his famous watercolor etching "The Ancient of Days," depicting the Creator as geometer and physicist - a hoary, cloud-bound, windblown figure, mathematical compass in hand, laying out the cosmos.

Whether wrought by intention or accident, the physical universe is striking for being so wonderfully, rationally put together. "The most incomprehensible thing about the world," remarked Albert Einstein, "is that it is comprehensible."

God or no God, the universe beckons us to understand it and in doing so, to discover our rightful place in it. Thus the newly proposed Simons Center for Geometry and Physics represents an exciting investment in our venerable search not just for academic knowledge, but for meaning and purpose.

Modern physics was born of this quest. Abu Ali Hasan Ibn Al-Haitham (usually known in the West as Alhazen) and Isaac Newton - pious monotheists of the 11th and 17th centuries - performed meticulous, landmark experiments in optics because they believed light was an essential feature of God's nature.

From there, physics has gone on to reveal innumerable breathtaking secrets about energy and matter generally - the two fundamental elements of physical reality - encouraging today's impression, exceeding even Einstein's, that everything about the sensible universe is now within our ability to comprehend.

The affinity between geometry - the mathematical study of abstract shapes - and physics - the experimental study of the material universe - dates to the ancient Greeks, who commonly described nature in terms of idealized shapes. Pythagoras pictured the five known elements of his day - earth, air, water, heat and the divine - as being the points of a pentagram, which for him represented perfection.

[CORRECTION: An Opinion article March 9 by Michael Guillen on the proposed Simons Center for Geometry and Physics at Stony Brook University gave incorrect facts about solid geometry. The tetra- hedron, cube, octahedron, dodecahedron and icosahedron have 4, 6, 8, 12 and 20 facets, respectively. Pg. A15 ALL 4/15/08] Plato saw the elements as material embodiments of the tetrahedron, cube, octahedron, dodecahedron and icosahedron - perfectly symmetric geometric solids having 6, 8, 10, 12 and 20 facets, respectively. In the 16th century, the astronomer Johannes Kepler saw the Platonic solids as being the key to understanding the movements of the planets.

This geometrical way of seeing the cosmos reached a climax early last century, when a young Einstein fretted over Newton's explanation of gravity - over the notion that an invisible force is always drawing objects to one another, even ones that are half a universe apart. From that point of view, gravity seemed too much like "spooky action at a distance."

In 1916, Einstein published a different theory of gravity - the theory of general relativity - at that point the most brilliant and mind-boggling union of geometry and physics ever conceived. In the new view, gravity isn't a force, but a geometrical illusion - the way the sun's movement across the sky is but an impression caused by the Earth's spinning around its axis.

According to Einstein's novel theory, objects warp the shape of the universe wherever they go, and it's this warping that creates the illusion of gravity. Think of it in terms of your walking around in a kids' bouncy house filled with plastic balls. Everywhere you go, you create a noticeable depression or dimple in the elastic flooring, causing all the balls in your vicinity to fall toward you - as if drawn by some invisible force.

A black hole creates such a severe dimple in space and time that any object coming too close will fall toward the dimple's center without any hope of escaping. To someone watching, it gives the impression of the black hole's being the source of an irresistible gravitational force, but in fact, it's the dimpling of the universe caused by the black hole that's at the bottom of it all.

Trying to imagine a universe teeming with objects and their dimples constantly moving and interacting - never mind doing the multidimensional geometrical calculations that go along with that - is enough to give anyone a migraine.

Yet, it appears to have brought us to within reaching distance of the ultimate mystery, "Whence and whither the universe?"

According to what astronomers call the Standard Model of cosmology - the fruit of astronomical observations and Einstein's wedding of geometry and physics - the cosmos exploded into existence from virtual nothingness and will experience a fate that depends, for the most part, on its shape. A universe as flat as a multidimensional ballroom floor (which ours appears to be) will expand forever; one that is saddle-shaped will quickly dissipate and die out; one that is spherical will eventually collapse on itself.

The Standard Model got more complicated 10 years ago with the discovery of "dark energy." No one really knows what it is yet - perhaps the Simons Center for Geometry and Physics will solve the mystery - but it's causing the galaxies throughout the universe to accelerate away from each other, like a Big Bang in overdrive.

Today it appears the powerful partnership between geometry and physics might even be able to deliver up the scientific Holy Grail: a single, unifying mathematical explanation for everything known.

Here's how this might happen. Once upon a time, physics likened the tiniest imaginable whit of matter to a geometrical point that, strange as it sounds, theoretically has no dimension: no width, length or depth. But experimental research into protons, neutrons and other elementary particles led physicists in the late 1960s to argue that a subatomic particle behaves not like a point, but a string - a geometrical line segment, with length but no width or depth.

This stupendous hypothesis was followed by another in the 1990s, when physicists discerned in string theory resemblances to an 11-dimensional version of Einstein's hallowed theory of gravity.



All of this and more has left scientists deliriously optimistic that in string theory - the latest, greatest offspring of geometry and physics - lies the makings of the long sought-after "theory of everything."

It's all rather dazzling, I know, but here's the irony: Whereas the marriage of physics and geometry has proved enormously successful at describing the world of the very large and the very small, science has fared less well at fathoming the all-important, in-between world of us humans and our quirky human ways.

In its 1996 obituary for the renowned cognitive psychologist Amos Tversky, Stanford University noted that his pioneering research had "seriously challenged economic theory by showing that people frequently do not behave rationally to maximize their welfare." The reasons for our irrationality range from the ignoble - being ignorant of the facts, suggestible or greedy - to the noble - being pointedly selfless with our time, talents and treasure.



Even we physicists are not above behaving in ways that logic and science cannot grasp. When I was a kid studying physics and geometry for the first time, my teacher explained it was provably impossible to trisect an angle - to divide an angle into three equal parts - using as tools only a compass and straight edge. Impossible? It didn't matter. My scientifically and mathematically precocious buddies and I spent the entire school year trying (cheerfully but futilely) to prove the teacher wrong!

Maybe that's why I applaud so wholeheartedly the coming of Stony Brook's bold, new Simons Center. The uniqueness of its mission appeals to the theoretical physicist in me - the part of me science has an easy time understanding. The center, I feel certain, will contribute enormously to our knowledge about nature at the smallest and largest scales - and maybe even help to unify it.

Like William Blake and most others, however, I've come to believe there is more to our humanity than what geometry and physics will ever be able to explain. Moreover, I've come to recognize that our irrationality isn't a failing, but is what makes our lives more fascinating even than black holes, parallel universes and dark energy.

For me, then, the center's exciting mission is fundamental to the larger sacred, human quest for purpose and meaning. It's a pioneering effort that appeals to my irrational human side, which science has a difficult time comprehending, but which resonates so deeply with Blake's image of the Creator as physicist and geometer.

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