*"God does not play dice." --Albert Einstein*

Since my Jan. 2 post, we've been discussing assumptions that science initially embraced, either explicitly or tacitly, only to abandon later as invalid or unnecessary. These include most of the following: dualism, determinism, reductionism, absolute time, absolute space, the principle of locality, materialism and realism. The last post addressed absolute time and space. Today we ring the death knell for determinism, the collateral damage of two revolutionary scientific developments of the 20th century. Let's review them in reverse historical order.

* * * * *"If I have seen further than others, it is by standing on the shoulders of giants," acknowledged Newton. He didn't name the giants, but it's clear that Galileo and Kepler were among them. Galileo Galilei, the father of experimental physics, laid foundations for the science of motion. Johannes Kepler, the "Protestant Galileo," laid the foundations of celestial mechanics. Both men developed descriptive laws. Galileo described the now-familiar parabolic trajectory of a thrown object; Kepler teased from Tycho Brahe's astronomical data the fact that the planets travel in elliptical orbits. Neither explained *why*.

It took the peculiar genius of Newton to move from *descriptions* of natural phenomena to *explanations*. By combining 1) his three laws of motion, 2) the calculus, which he termed "fluxions," and 3) an inverse-square law of gravitation, Newton proved that the planetary orbits naturally and exactly satisfy all three of Kepler's descriptive laws.

Newton's achievement was monumental. To those of his era, it seemed that Newton had illuminated every scientific corner, leaving nature bereft of secrets. The French mathematician Pierre Simon de Laplace, the "Newton of France," extrapolated beyond Newton to envision the day when science could predict the future "movements of the greatest bodies of the universe and those of the tiniest atom." What was necessary to preordain the future? "An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed." The difficulties with *Laplace's daemon*, as this hypothesized intelligence became know, were practical rather than conceptual. By the 1950s Laplace's daemon was incarnate in the digital computer. Two decades later men stood on the moon, navigated there not by compass but by a digital daemon that could solve Newton's equations of celestial motion in real time.

Just as it seemed that the computer might fulfill the dream of scientific determinism, it turned against Laplace. The year was 1961, the place was MIT, and the person was Edward Lorenz, a meteorologist. While playing with a "toy" weather model on a primitive, vintage, vacuum-tube Royal McBee computer, Lorenz stumbled onto something unexpected: *chaos*.

Lorenz's system consisted of just three simple differential equations. However, the equations were *nonlinear*, a mathematical term indicating that the system's output is not directly proportional to its input. On impulse, Lorenz restarted an old computation at its midpoint in time. The old and new solutions followed nearly the same trajectories for a while, then they diverged dramatically, eventually losing all resemblance. Suspecting a computer malfunction, Lorenz checked and rechecked the Royal McBee. It was in perfect working order.

Pausing to ponder, Lorenz was stunned by the truth. For the original calculation, he had entered the initial data to six significant digits; in the repeat calculation, he had done so only to three. Tiny differences in the input were magnified by the system to yield enormous differences in output, a phenomenon known to mathematicians as *sensitive dependence to initial conditions*, and to the general public as the *butterfly principle*, thanks to James Gleick's bestseller *Chaos* (1988). In a nutshell, nonlinear systems can be extraordinarily sensitive to their initial states. Change the initial data a smidgeon and you'll get a wholly different solution.

Quantum mechanics rankled Einstein, steeped as he was in the determinism of the philosopher Spinoza. Quanta (subatomic particles) are defiantly probabilistic and therefore non-deterministic.

With the discovery of radioactivity in 1895, probability thrust its ugly head into physics. The moment at which a radioactive element decays is inherently unpredictable. One can ascertain the probability of an aggregation of decay events from a lump of radium with sufficient precision to define its half-life spot on. But as to when an individual atom will shed its alpha particle, one is powerless to say.

With the advent of quantum mechanics in the early 1900s, probability was here to stay. Each of the nearly 120 elements that comprise the universe emits a unique fingerprint, its visual *spectrum*, when heated or burned. No one knew why. Niels Bohr's adaptation of Ernest Rutherford's atomic model explained the hitherto mysterious spectral lines, but at the expense of quantizing the orbits of electrons. Each spectral line originates when an electron jumps from one orbit to another, Bohr reasoned. But Bohr's model troubled Rutherford: The leaping electrons seemed "to choose not only the timing of their leap but the destination [orbit] too."

The harder physicists tried to explain away the probabilistic nature of the quantum the more resilient it became. Erwin Schroedinger, a titan of quantum mechanics, grumbled, "If we're going to put up with these damn quantum jumps, I am sorry that I ever had anything to do with quantum theory." Einstein fought amicably with Bohr over the issue for more than two decades, and lost.

Dominating the landscape of quantum mechanics is Werner Heisenberg's *uncertainty principle*, which quantifies what can and cannot be known about quantum objects. Specifically, one can never know precisely and simultaneously the position and velocity of, say, an electron. You can know where it is but not where it's going. Or you can know where it's going, but not where it is. You can even split the difference, accepting some fuzziness in each. But you can never precisely know its complete initial state.

On the shoal of uncertainty, determinism founders. On the reef of chaos, it sinks. By and large, nature has a strong predilection for the nonlinear. Newton's law of gravitation is nonlinear. Maxwell's equations of electrodynamics are not, but they're the exceptions. General relativity is strongly nonlinear. So are the strong and weak nuclear forces. As a result, so is most chemistry. And because life involves chemistry, life's basic mechanisms are inherently nonlinear.

To accurately predict the evolution of events in a nonlinear universe -- in which the flapping of a butterfly's wing in Brazil literally affects Peoria's weather days later -- Laplace's daemon would need absolute precision in its initial data: the position and velocity of every molecule of air and butterfly. Heisenberg's uncertainly principle forbids just that. In the wonderfully pithy summary of Lorenz: "The present predicts the future, but the approximate present does not predict the approximate future."

The universe is contingent, not deterministic. For sentient beings this implies that the cosmos is also participatory. Individual intentions and actions, however seemingly insignificant, shape the cosmic future.

*This blog post is adapted from Chapters 1 and 11 -- "The Clockmaker and the Clockwork" and ''Through the Looking Glass," respectively -- of my recent book "Reason to Wonder".*

*Read earlier articles of the series:*

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