Despite the advent of relativity, quantum physics, and chaos theory, most scientists, including most physicists, intellectually inhabit the Newtonian Cosmos. In stark contrast to the Aristotelian Cosmos, where plants and animals possess an inner agency that causes them to emulate the Prime Mover, the Newtonian Cosmos is mechanical, where lifeless matter as well as animate beings is moved solely by pushes and pulls. The Newtonian clockwork universe obeys precise, rigid mathematical laws that determine its evolution; consequently, free will in this cosmos is impossible.In his Philosophical Essay on Probabilities, published in 1814, French mathematician Pierre Simon Laplace made explicit the determinism that would dominate the thinking of scientists for the next two hundred years.“We ought then to regard the present state of the universe as the effect of its anterior state and as the cause of the one which is to follow,” he wrote.“Given for one instant an intelligence which could comprehend all the forces by which nature is animated and of the respective situation of the beings who compose it—an intelligence sufficiently vast to submit these data to analysis—it would embrace in the same formula the movements of the greatest bodies of the universe and those of the lightest atom; for it nothing would be uncertain and the future, as the past, would be present to its eyes.”[1]

In the Newtonian Cosmos, if the mass, location, and velocity of every particle is given at a particular time, what physicists call “the initial conditions,” then Newton’s three laws of motion determine the future and the past of the universe. Laplace’s super-intelligent being knows the entire history of the universe, from the Big Bang to the Big Freeze, including the rise and fall of the American Empire and me writing and you reading this paragraph.

Laplace’s super-intelligent being would be banned from playing roulette, craps, and other games of chance in every Las Vegas casino; for such a being, chance does not exist. The outcome of a ball tossed into a spinning roulette wheel or dice tumbling on the crap table can be calculated with infinite precision. Chance is an illusion rooted in human ignorance.

Psychologist Joshua Greene and neurobiologist Jonathan Cohen give an excellent statement of the determinism adhered to by most scientists. “Intuitively, the idea is that a deterministic universe starts however it starts and then ticks along like clockwork from there. Given a set of prior conditions in the universe and a set of physical laws that completely govern the way the universe evolves, there is only one way that things can actually proceed.”[2] In this picture, the current state of the world is completely determined by the laws of physics and by any one of its past states.

Greene and Cohen rightly point out that in the Newtonian Cosmos every event with the possible exception of the Big Bang results from prior mechanical causes. That I would appear in the universe with a small mole on my right temple was in the cards one second after the Big Bang. Yesterday, a long chain of mechanical causes made my wife buy a new, Marimekko dress. The precise attunement of particles in the early universe led Francis Crick and James Watson to discover the structure of DNA, Charles Townes to conceive the laser, da Vinci to paint the Mona Lisa, and Mozart to compose the Requiem Mass in D Minor. The deterministic outlook that permeates all science necessarily proclaims that human beings possess no free will, that we are machines, mere pawns moved about by mindlessly forces in a mechanical universe.

The determinism that is a basic aspect of the Newtonian Cosmos is false, for two reasons—quantum physics and chaos theory. In the twentieth century, physicists discovered individual events on the atomic level are not predictable. Consider uranium 238, a commonly occurring radioactive substance. A gram of uranium 238 contains approximately 2.5×1021 identical uranium nuclei; about 12,000 of those uranium nuclei decay every second into an alpha particle and a thorium 234 nucleus. Quantum physics can predict the probability that a given uranium 238 nucleus will decay but not when it will. The exact moment of decay is intrinsically unknowable. Unpredictability thus is an integral part of nature.

On the macroscopic scale, chaos theory killed determinism. The basic element of chaos theory first appeared in the astronomical investigations of French mathematician Henri Poincaré at the end of the nineteen century, but only in the latter part of the twentieth century with the advent of computers did physicists and mathematicians see the full significance of his work. While investigating a system of three gravitating bodies, such as the Earth, Moon, and Sun, the so-called “three body problem,” Poincaré discovered that unpredictable behavior occurs in deterministic systems, a fact that has startling implications for the mathematical modeling of physical systems. Before his revolutionary work, physicists and mathematicians assumed that small errors in the initial conditions of any dynamical system produced only small errors in the mathematical prediction of the future state of the system. Poincaré’s analysis of the three-body problem is brilliant and highly technical; yet, the basic result can be easily stated, as Poincaré himself did in his popular book Science and Method: “It may happen that small differences in the initial conditions [of a mechanical system] produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. Prediction becomes impossible, and we have the fortuitous phenomenon.”[3]

Meteorologist Edward Lorenz called what Poincaré discovered fifty years before his own work the “butterfly effect,” where a flap of a butterfly’s wings in Brazil could set off a tornado in Texas. Because of the impossibility of measuring initial atmospheric conditions precisely the weather cannot be predicted accurately more than a week or so in advance. Vladimir I. Arnol’d, a Russian mathematician, proved, in 1963, that depending upon the initial conditions the motion of three gravitating bodies can be either predictable or chaotic. Advances in computer technology have made it possible to begin to directly address the long-term evolution of the solar system. The results of Gerald Jay Sussman and Jack Wisdom suggest that the solar system as a whole is chaotic, making its long-term behavior uncomputable.[4] In particular, their computer models indicate that the Pluto has a chaotic orbit and that astronomers cannot predict whether the planet will be on this side of the Sun (relative to the Earth’s position) or on the other side ten millions years from now.[5] In his book Newton’s Clock: Chaos in the Solar System, Ivars Peterson concludes, “Long held up as a model of perfection and the symbol of a predictable mechanical universe, the solar system no longer conforms to the image of a precision machine. Chaos and uncertainty have stealthily invaded the clockwork.”[6]

The chaos that Poincaré discovered in the Newtonian Cosmos is often called deterministic chaos to emphasize that in an ideal world with infinite precision and without rounding errors in computations the future behavior of a mechanical system is fully determined by its initial conditions. The Newtonian Cosmos, however, is a map of the physical world drawn with mathematical lines that are breadthless, and points, which are dimensionless. Mathematical lines and points are idealizations that approximate the physical world. In the Newtonian map, the shape and location of objects can be specified with infinite precession. However, no perfect circle exists in nature, and the boundary of a physical object is fuzzy, not a sharply-defined concept as in mathematics. In the Newtonian map, the laws of physics are eternal, abstract, and never fully embodied in actual matter. Such a mathematical map often helps a scientist to understand a system or situation but the real world always differs in significant ways from the map.

The Map Is Not the Territory

Polish-American scientist and philosopher Alfred Korzybski enunciated, in 1931, the general principle the map is not the territory that applies to all maps.[7] Here, map is a representation of an object and can be a guidebook, a history, a novel, or a science. To give one simple example: years ago for three summers in a row, I drove from New Hampshire to New Mexico and often consulted a AAA map and guidebook given to me by a well-meaning friend. The static map, of course, did not indicate unpredictable events such as road construction or detours caused by car accidents. I stopped one night in Springfield, Missouri, and the guidebook directed me to a motel decorated in a Fifties motif and to the Highlander Restaurant. My AAA road map and guidebook necessarily contained only a broad sketch of the roads, motels, and restaurants along my route. What the guidebook did not tell me was that inside the restaurant I would hear Howard, a cool middle-aged, black musician, playing an electric organ and singing love songs from the Fifties, nor did AAA tell me I would see senior citizens slow dancing just as they had during their high school days filled with romance. I was overjoyed to discover that some loves last over fifty years. Nor did the guidebook inform me that I would stumble upon a bartender in the heart of the Bible Belt who made a wicked martini. A tourist goes to see a sight described in a guidebook, while a traveler hopes to encounter the unexpected not given on any map.

In the road map I used, the distance on the map from Springfield to Joplin was less than the distance from Joplin to Tulsa, and the same relation existed in the actual driving distances in the territory. For a map to be accurate, certain structures in it must be identical to the same structures in the territory. Many markings on a map, however, pertain only to the map. Neither I nor any other driver would read a AAA road map literally and then expect to see the Interstate exchanges painted red and blue. The colors made the map easier to read and were not intended to represent anything in the territory.

We should always keep in mind that every map is limited and that very few of the maps we consult for guidance in life are mathematical. For Instance, John Locke’s Second Treatise on Government is a map of political life, one that gave direction to the Founding Fathers of America; Locke’s map does not include anything about philia (friendship) or agápē (Christian love), which bound together the Greek polis and the medieval village, respectively.

Unlike painters and sculptors, who never mistake the guidebook for the museum, most biologists, neuroscientists, and physicists confuse the maps drawn by their respective sciences with the territory. One reason scientists take the map for the territory was hinted at by Laplace when he visited Napoleon Bonaparte at his country estate, in 1802. The mathematician entertained the French political leader by relating the nebular hypothesis, Laplace’s scientific explanation of how the solar system formed from the revolving atmosphere of the primitive Sun. When Napoleon asked Laplace about the place of the Creator in his mechanical account of the solar system, he replied, “Sire, I have no need of that hypothesis.”[8] If the universe is deterministic, then a mathematician or a physicist approximates an all-seeing, super-computing god. A mathematician or a physicist, marooned inside his skull contemplating the Newtonian map, believes that he borders on the super-human, for he too can calculate the future and the past of the universe.

Another reason scientists take the map for the territory is that if the limitation of every map is acknowledged, then we humans necessarily have to accept our scientific and philosophic theories will always be incomplete. To do this requires humility on our part and an acceptance of limits to science itself. No map or theory can capture the concreteness of real life, and any map of the total cosmos, such as the Grand Narrative of Science that fashions a story about our place in the cosmos must fall short in significant ways.

In the Newtonian map, most, if not all, non-chaotic dynamical systems have counterparts in the territory. The Newtonian map by mathematical design is drawn with infinite precision, and thus future behavior of any mechanical system in this map, even if chaotic, is fully determined. But in the territory, no digital clock records time to an infinite number of decimal points and every meter stick has fuzzy, ill-defined endpoints; thus the precise initial conditions of a physical system are a fiction and chaos is real. Nature is not a gigantic clockwork mechanism; the cosmos is not deterministic. The infinitely precise attunement of particles in the early universe is part of the myth of determinism instilled by the habit of taking the Newtonian map for reality. No arrangement of elementary particles ten seconds after the Big Bang led Francis Crick and James Watson to discover the structure of DNA, Charles Townes to conceive the laser, da Vinci to paint the Mona Lisa, and Mozart to compose the Requiem Mass in D Minor. No human being is a machine; Crick, Watson, Townes, da Vinci, and Mozart were creative minds exploring nature and human life.

When biologists, neuroscientists, and physicists argue 1) the brain is the mind, 2) the brain is determined and thus the thoughts that arise from the brain are determined, and therefore 3) free will is an illusion, those scientists are describing the map, not the territory. The real, physical world is not a determined machine. Chaos demands indeterminism, which in turn allows for the presence of chance and mind.

On my part, the principle the map is not the territory liberated me from materialism, Marxism, capitalism, nationalism, and every ideology that constrains the human spirit and denies that one glory of human life is the spontaneous discovery of the unexpected. In the territory, we should be intellectual travelers, not ideological tourists. We humans are mere mortals, incapable of understanding the totality of being, although virtually no physicist, neuroscientist, biologist—or philosopher or political thinker, for that matter—can resist the temptation to be God, to claim he or she captured the whole show in three equations or in one intellectual insight or in a clever political slogan. We must rely upon multiple maps to guide us in our pilgrimage through life. Plato and Aristotle, Augustine and Aquinas, Sophocles and Shakespeare, Machiavelli and Marx, Newton and Heisenberg, every profound mapmaker reveals to us a partial glimpse of the territory, yet profound mysteries always remain.

Freedom: A Prerequisite for Science

To convince ordinary people and fallen away believers in materialism like me that “the combined effects of genes and environment determine all [their] actions,” Greene and Cohen hope in the future to possess “extremely high-resolution scanners that can simultaneously track the neural activity and connectivity of every neuron in a human brain, along with computers and software that can analyze and organize these data.”[9] Then a person, such as you or I, could watch a film of his or her brain choosing between soup and salad. The analysis software would highlight the “neurons pushing for soup in red and the neurons pushing for salad in blue.”[10] The film would show “the tipping-point moment at which the blue neurons in [the] prefrontal cortex out-fire the red neurons, seizing control of [the] pre-motor cortex and causing [the person] to say, ‘I will have the salad, please.’”[11]

Greene and Cohen imagine this sort of brainware in every future classroom, so “people may grow up completely used to the idea that every decision is a thoroughly mechanical process, the outcome of which is completely determined by the results of prior mechanical processes.”[12] (See Figure 1.)

Suppose such imaginary equipment that Greene and Cohen fantasize about had been available to record the most famous conversations in modern physics, Niels Bohr trying to convince Albert Einstein that quantum physics is true and the founder of relativity attempting the opposite. Using a high-resolution brain scanner, we watch the neurons pushing for the truth of quantum physics in red and the neurons pushing for its falsity in blue. The heated debate ends with two tipping-moments, the red neurons in Bohr’s brain out-firing the blue and the reverse occurs in Einstein’s brain. Mechanical processes cause Bohr to mumble, “Nature is indeterminate,” and Einstein to shout, “No! God does not play dice!” In this scenario, the combined effects of their genes and environments determine the actions of the two great physicists; Bohr and Einstein were simply mouthpieces for their differing genes, say numbers 26 and 27 on chromosome 12, and the cultures of their youth, Danish and German.

We have arrived at the Great Contradiction of modern science. If scientists are, as their science proclaims, nothing but a pack of neurons, and their joys, sorrows, memories, and sense of free will are in fact no more than the behavior of a vast assembly of nerve cells, then intellectual insight is an illusion.[13] If the thoughts of scientists are determined by neurophysiology, action potentials, and the endocrinology of neurotransmitters, then physics, biology, and psychology are meaningless. If every decision in science, as in ordinary life, is a “thoroughly mechanical process…determined by the results of prior mechanical processes,” [14] truth is an illusion.

Science, in the twenty-first century, fired a bullet into its own brain; the Grand Narrative of Science imploded.

Let me restate the logical contradiction of the Grand Narrative of Science in the simplest possible terms. Suppose my interior life is determined wholly by the motions of atoms in my brain. One day, the atoms in my brain jostle around and what arises is the ancient Irish belief that leprechauns store their gold in a pot at the end of the rainbow. Such a belief clearly pertains to the atoms in my brain, not to an objective world. But this is true for all my beliefs, and hence I have no reason to suppose that any of them are true, including the one that the motions of atoms in my brain cause my interior life. From this contradiction, we can safely conclude that mind cannot be a mere byproduct of matter.[15]

In every physics colloquium I attended in my youth, when there were virtually no female physicists, a researcher at the front of the room attempted to persuade his colleagues seated in front of him that his theoretical ideas illuminated nature or his experimental results were free from error. In the colloquium room where truth was pursued in public, an unstated premise was that each one of us had the freedom to judge whether something is true or false.

For science to be possible the human will must be free. A denial of free will renders the whole of science absurd. Physicist Carl von Weizsacker states unambiguously, “Freedom is a prerequisite of the experi­ment. Only where my action and thought are not determined by circumstances, urges or customs but by my free choice can I make experiments.”[16] Cosmologist George Ellis argues that free will is a requirement for any theoretical science to exist: “The enterprise of science itself does not make sense if our minds cannot rationally choose between alternative theories on the basis of the available data, which is indeed the situation if one takes seriously the bottom-up mechanistic view that the mind simply dances to the commands of its constituent electrons and protons, algorithmically following the imperatives of Maxwell’s equations and quantum physics. A reasoning mind able to make rational choices is a prerequisite for the academic subject of physics to exist.”[17] Neuroscientist John Eccles concurs: “There are thus no sound scientific grounds for denying the freedom of the will, which ironically, must be assumed if we are to act as scientific investigators.”[18]

What holds for the scientist also applies to the layperson: Every human has the capacity to make free choices. Genes and environment do not determine all our decisions. Thus, two core human experiences are not illusions: we can choose one course of action over another, and we can apprehend the truth. Certainly, we often act from mindless habit, and we often accept unexamined opinion as true; nevertheless, we have the capacity to grasp the truth and to choose good over evil.

Explanatory gaps in the Grand Narrative of Science, such as neuroscience not being able to explain consciousness solely in terms of brain function, can be tolerated; scientific hope, even if blind, can keep the Grand Narrative on life support, seemingly forever. Logical contradiction, however, destroys any theory; for it cannot be quarantined to a tiny domain. If we admit that A and not A are simultaneously true, then the abandonment of logical contradiction bores wormholes throughout the entire theoretical structure—B and not B can also be true, for any B—and the theoretical structure collapses. Such a logical disaster is traditionally called ex falso quodlibet (from the false anything follows). Everything is equally true and false at the same time.

If we are free as doing science demands and not free as the Grand Narrative of Science proclaims, then every decision is the result of mechanical processes and every decision is not the result of mechanical processes; then materialism is true and materialism is not true; then everything arises from matter and not everything arises from matter. The Grand Narrative collapses into in the worst kind of theoretical failure, a jumble of contradictory nonsense. Consequently, the grand pronouncements of science — “the human race is just a chemical scum on a moderate-sized planet;”[19] Homo sapiens is “a more-or-less farcical outcome of a chain of accidents;”[20] “human beings are lumbering robots manipulated by genes;”[21] “evil and good, are built into our brains by millennia of Darwinian evolution;”[22] and, “when we die, we die and that is the end of us”[23] — have no credibility.

Only a young child, an inveterate drunk, or a one-eyed scientist can believe in the Grand Narrative of Science that simultaneously declares that a person is free and not free, that truth is possible and not possible. The great hope of modern science to prove through the experimental method that matter is the ultimate source of everything terminated in nonsense.

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[1] Pierre Simon Laplace, A Philosophical Essay on Probabilities, trans. F. W. Truscott and F. L. Emory (New York: Nabu Press, 2010), p. 4.

[2] Joshua Greene and Jonathan Cohen, “For the law, neuroscience changes nothing and everything,” Philosophical Transactions of the Royal Society London B (2004) 359: 1781.

[3] Henri Poincaré, Science and Method, trans. Francis Maitland (Mineola, NY: Dover, 2003), p. 68.

[4] See Ivars Peterson, Newton’s Clock: Chaos in the Solar System (New York: W.H. Freeman, 1993), Ch. 11.

[5] Gerald Jay Sussman and Jack Wisdom, “Numerical Evidence that the Motion of Pluto Is Chaotic,” Science 241 (1988): 433-437.

[6] Peterson, p. 270.

[7] See Alfred Korzybski, Science and Sanity; an Introduction to Non-Aristotelian Systems and General Semantics (Lakeville, CT: International Non-Aristotelian Library, 1958), Ch. IV and Supplement III.

[8] See Ronald L. Numbers, “Science without God: Natural Laws and Christian Beliefs” in When Science and Christianity Meet, ed. David C. Lindberg and Ronald L. Numbers (Chicago: University of Chicago Press, 2008), p. 271.

[9] Greene and Cohen, pp. 1780, 1781.

[10] Ibid., p. 1781.

[11] Ibid.

[12] Ibid.

[13] Francis Crick, The Astonishing Hypothesis, (New York: Scrib­ner’s, 1994), p. 3.

[14] Greene and Cohen, p. 1781.

[15] A similar argument was given by J.B.S. Haldane, a British geneticist and a committed Marxist. See J.B.S. Haldane, Possible Worlds: And Other Essays (London: Chatto and Windus, 1927; reprint, London: Transaction Publishers, 2002), p.209. Page reference is to the reprint edition.

[16] Carl F. von Weizsacker, The World View of Physics (Chicago: University of Chicago Press, 1949), p. 203.

[17] George F. R. Ellis, “Physics and the Real World,” Physics Today 58 (July 2005): 53.

[18] John Eccles, Facing Reality: Philosophical Adventures by a Brain Scientist (Berlin and New York: Springer-Verlag, 1970), p. 120.

[19] Stephen Hawking, quoted by David Deutsch, The Fabric of Reality (New York: Viking, 1997), pp. 177-178.

[20] Steven Weinberg, The First Three Minutes: A Modern View of the Origin of the Universe (New York: Basic Books, 1977), p. 154.

[21] See Richard Dawkins, The Selfish Gene (New York: Oxford Univers­ity Press, 1976), p. 21.

[22] Dawkins, “Let’s all stop beating Basil’s car.”

[23] William Provine, “Evolution and the Foundation of Ethics,” MBL Science 3 (Winter 1988), p. 27.


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