If the flap of a butterfly’s wing can trigger a tornado months later and thousands of miles away, could a tiny force of will change a person’s life?
In the last blog we looked at the first 2 of 5 answers that attempt to reconcile free will with a firm theory of causation. The 1st answer, to name the problem as a paradox, does not work as an answer at all, but instead abdicates the search for an answer. The 2nd, an appeal to “levels in the hierarchy of matter” (physics, chemistry, biology, and psychology/sociology according to Paul Nunez), describes limits on calculable predictability that bar real-world reduction of human choosing down to the level of particle physics. However, this appeal does not remove human choosing from the realm of scientific explanation, because science still works within each hierarchical level.
Now we continue with a look at two more proposals that emerge from scientific investigation. Potential answer #3 to reconcile will and causation goes by the catchy name of chaos theory. It is a new explanatory paradigm for natural systems. On the surface chaos theory resembles the appeal to levels in the hierarchy of matter, but it’s actually quite different.
Chaos theory can be demonstrated with computers. It arose when computer simulations of natural phenomena became powerful enough to exhibit what Edward Lorenz in a pathbreaking 1963 paper called “deterministic nonperiodic” behavior. Think about computer simulations of atmospheric weather which often exhibit random-appearing (nonperiodic), but completely determined fluctuations. We know that the simulation results are completely determined because the rules built into the computer program are known, and running the program any number of times will always produce the same result.
The key to understanding chaos theory is to recognize that tiny changes in the initial startup conditions set for the computer simulation can produce widely different and unpredictable results as the program runs its course in virtual time. Not every computer program exhibits this kind of behavior, but some do. Examining how this happens and how it behavior applies to natural phenomena constitutes the essence of chaos theory.
Lorenz described chaos theory memorably and poetically with the well-known example:
A butterfly flaps its wings in the Brazilian rain forest, and months later the result is a tornado in Texas.
It’s important to remember that this example is not derived from scientific experiment involving an intrepid team of jungle explorers measuring the movements of an actual butterfly’s wings and following the consequences in real time and space. That experiment is from every practical viewpoint impossible. Instead it’s an example based on analogy to a sufficiently powerful and cleverly designed computer program.
Chaos theory properly belongs to the field of mathematics, but it is applicable to descriptions not only of weather, but also of certain physiologic or pathologic responses, earthquakes, forest fires, epidemics, biological evolution, financial markets, social unrest, and many other kinds of phenomena.
One of clearest conclusions we can make about chaos theory is that mathematicians really enjoy it and perform useful service as well. Philosophers dealing with chaos theory get a chance to show that they, too, can think mathematically, before branching off to speculate on the consequences for scientific realism or the like.
As suggested above, one might think that philosophical application of chaos theory merely repeats with a spiffy title what we examined already as the hierarchy of matter (our 2nd answer examined in the prior blog). However, chaos theory, when it is turned around to look backward, say, at the causes of hurricanes and tornados, does not necessarily try to examine a class of phenomena beneath the level of atmospheric physics. It is not a question of differing layers of scientific knowledge. Instead, atmospheric physics itself is sufficiently complex to give rise to “deterministic nonperiodic” behavior, which complicates our usual notion of experimentally confirmable causation.
Thus chaos theory might seem to be a new kind of wormhole through which the human sense of free action might sneak into our consciousness, while not contradicting at all the dictum that all events are caused and determined by particle physics.
Unfortunately everything said previously about the attempt to define a pragmatic pair, using the concept of differing major levels in the hierarchy of matter, also applies to chaos theory. Chaos theory is completely within the sphere of science. It also fits within positivism, which asserts that nothing is known meaningfully unless it is known scientifically. I shall not repeat the argument about positivism, but refer the reader back to earlier blogs in this series.
The 4th proposed answer to explain the inward testimony of free will in a world based on causation is the concept of true randomness. Randomness has an origin at the interface between philosophy and mathematics. Mathematics (especially statistics) and natural science (especially quantum physics and evolutionary biology) incorporate and use randomness in essential ways. By definition, a random event is one that is not predetermined as a singular occurrence. However, a series of random events will exhibit a predetermined probability distribution. If neither the event nor the probability distribution is predetermined, then we do not use the term “random” but instead the term “arbitrary.” Arbitrary events have no place in science.
Randomness itself was a hard pill for science to swallow. Remember that science is built on reproducibility. And reproducibility requires at least some degree of determinism. Albert Einstein was famously resistant to the notion of randomness. He wrote in a letter to the physicist Max Born in 1926, “I, at any rate, am convinced that He does not throw dice.” This later took the form we are accustomed to remember, “God does not play dice with the universe.”
Quantum physics, for reasons that I do not time or space to explore here, requires randomness. Stephen Hawking, the English physicist, explained it well in a lecture worth reading. Hawking’s lecture describes the acceptance of randomness into science in terms of the wave function of particles, which turns out to be a kind of probability distribution. Reproducibility is retained, as is necessary for science, but it is a probabilistic reproducibility. Randomness accentuates the wobble factor in a way at least superficially similar to chaos theory. The wobble factor in quantum physics has a noble heritage in the Uncertainty Principle discovered by Werner Heisenberg in 1927, based partly on Max Planck’s prior finding that energy and mass are not divisible without limit, but occur in discrete quanta.
Didn’t we already discuss randomness in terms of chaos theory? No. There is a critical difference philosophically between chaos theory and true randomness. Remember that a computer program which exhibits the wild gyrations of chaos theory will reproduce exactly the same wild gyrations if the computer program begins with exactly the same inputs as previously run. True randomness will never (beyond any stated degree of statistical certainty) produce exactly the same result.
What about “random number generators,” widely used in computer simulations and statistical science? That’s a fair question. A digital computer will not exhibit true randomness. Nevertheless, a computer can produce a very satisfactory simulation of randomness in the following manner: (a) Start with a program that delivers chaotic behavior. (b) Keep track of the inputs for the program, and be sure that the inputs for each new run of the program differ from those of previous runs. This condition can satisfied if one of the inputs simply counts 1, 2, 3, …. (c) Check to see that the output of a very large number of computer re-runs produces the desired probability distribution. This could be defined, for example, as an equal likelihood of representing any real number, within some stated small interval without a lower limit, between zero and 1.
Ah. We seem to have a satisfying answer. True randomness, ultimately found in quantum physics, defeats determinism. Somehow in the interaction between quantum randomness and neuronal chemistry, consciousness arises and free will has space to maneuver.
Unfortunately, a leading investigator in the field does not endorse the idea that free will might emerge from quantum interactions in the brain.
In his remarkable book on the relations between mathematics, computers, minds and consciousness, and the laws of physics, titled The Emperor’s New Mind, Roger Penrose chiefly focuses on the questions of what is required to have a mind, how mathematics itself may be as real as moving particles and waves, and how consciousness might arise. He waits until the very end of book to broach the term “free will,” although previous chapters addressed something akin to it in terms of a “suggestion that there is an essential non-algorithmic aspect to the role of conscious action.” In discussing free will near the end of his book, he points toward quantum interactions in the brain as follows:
The R ‘quantum-jump’ is not deterministic, and it introduces a completely random element into the time-evolution. Early on, various people leapt at the possibility that here might be a role for free will, the action of consciousness perhaps having some direct effect on the way that an individual quantum system might jump. But if R is really random, then it is not a great deal of help either, if we wish to do something positive with our free wills.
Penrose hits the nub of the difficulty with randomness. Randomness gives the conscious person no more a sense of ownership and responsibility for her actions than does fate. Randomness fails to solve the Free Will Problem.
Upcoming blogs will look at will and willpower as medical questions and then address the phenomenon of consciousness, including cosmic consciousness or God as the 5th proposed answer to the Free Will Problem.
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Photo: Butterfly in Ecuadorean jungle. (c) Jrg Hackemann – Fotolia
 Lorenz E. Predictability: does the flap of a butterfly’s wings in Brazil set off a tornado in Texas? Presented at the American Association for the Advancement of Science, Washington, D.C., 1972.
 Albert Einstein, letter to Max Born, 4 December 1926.
 It is theoretically possible to engineer a computer to make “mistakes” based on the inherent randomness of quantum physics, but actual computers today perform amazingly accurate and reproducible calculations.
 Penrose, R. The Emperor’s New Mind. Oxford University Press, Oxford, 1989. Reprinted by Penguin, New York, 1991. P. 431.