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Applications of Stochastics to the Debate between Free Will and Predestination

            There has long been a debate in the Christian community between two competing models of the universe: free will and predestination. What is often lost in this debate is a middle position: a God created universe that exhibits both qualities of randomness and determinism. It may surprise many that I would refer to theological concepts in such a manner, but this debate is not simply theological; it is also scientific. Guidance in answering this great doctrinal question may thus come from a surprising source: science.

            I have always enjoyed pondering great theological mysteries, but I have done these with a special tool, scientific understanding. Though many have attempted to separate theology and science into different realms, there is a great overlap between them. Theologians analyze special revelation (mostly in the form of the Bible) to understand the world around them, while scientists analyze general revelation (in the form of the Universe around us).  As a Chemistry Education major brought up in a Christian background, I naturally attempt to derive my worldview from both sources. Though these two sources of knowledge sometimes conflict, more often they provide unique insight into the amazing nature of reality when utilized together. The debate between free will and predestination is one of those cases.

            The debate between free will and predestination centers on seemingly competing verses in the Bible. Free will arguments stem from verses such as Genesis 2.16: “And the LORD God commanded the man, ‘You are free to eat from any tree in the garden…’”1 and Deuteronomy 30.19: “This day I call heaven and earth as witnesses against you that I have set before you life and death, blessings and curses. Now choose life, so that you and your children may live”1, while predestination arguments center on Paul’s writings; such as Romans 8.29-30: “For those God foreknew he also predestined to be conformed to the likeness of his Son, that he might be the firstborn among many brothers. And those he predestined, he also called; those he called, he also justified; those he justified, he also glorified”1 and Ephesians 1.4-5: “For he chose us in him before the creation of the world to be holy and blameless in his sight. In love he predestined us to be adopted as his sons through Jesus Christ, in accordance with his pleasure and will”1. Problems exist in using only one of these models: free will brings with it the idea of an out of control God who lacks omniscience, while predestination brings with it the connation of an unfair God who chooses to send people to hell. In the scientific world, however, it is not unusual to have two different working models. For example, while chemical bonding is often thought of as either completely ionic or completely covalent, most compounds are best described as partially ionic or partially covalent.2 In the Bible, Exodus has Pharaoh hardening his own hard ten times[a] and God hardening Pharaoh’s heart ten times[b],1 which points to the biblical combination of these two ideas into one model.

Scientists already use a combination approach for these kinds of problems: stochastics. Stochastics comes from the Greek word “stocházesthai” meaning to “to aim at”. It is defined as “of or pertaining to a process involving a randomly determined sequence of observations each of which is considered as a sample of one element from a probability distribution.”3 In other words, it is anything related to a process that forms a probability curve. In even simpler words, stochastics is the scientific use of probability; it is the tool scientists use to make sense of an ordered yet chaotic universe. The usefulness of stochastics is a testimony to the fact that events can be predicted but only with a limited level of certainty. It indicates the universe is not a place where every single event has an equal chance of occurring, but it also indicates the universe is not a place where only one event has any possibility of occurring. Stochastics is thus a scientific balance between complete randomness, which would translate to no influence of God over our lives, and determinism, which would translate to God being indirectly responsible at creation for every aspect of our lives and as a result no real choice existing.

The history and current use of stochastics speak to the balance between randomness and determinism that exists in our universe. The use of stochastics is traced to an eighteenth century experiment performed by Georges Louis Leclerc.4 Leclerc repeatedly tossed a needle at random on to a board ruled with parallel straight lines.4 He derived from this experiment the probability that a needle would intersect a line.4 Pierre Simon de Laplace used this experiment later to get a statistical estimate of pi.4

In the early 1930’s, Enrico Fermi used stochastic modeling to answer problems related to neutron diffusion.4 Later on, while working on the Manhattan Project, Stanislaw Ulam, John von Neumann, and Nicholas Metropolism rediscovered and used Fermi’s method, turning it into formal methodology; they dubbed it the Monte Carlo method after the European gambling city.4

Today stochastic modeling is used even in matters not theoretically considered probabilistic.4  Stochastic modeling is now used in economics, medicine, traffic flow, biochemistry, the physics of matter, and the list goes on.4 In one example, stochastic modeling was used to model the atomic randomness for an axon based on its length.5 Creating models for quantum randomness is very demanding, however, and the author overshot the length where “significant numbers of spontaneous action potentials occurred”.5 In another example, in an experiment examining the cyclical timing of lighting in the Zebrafish, a bioluminescent capable fish, researchers were surprised to find cloned cells demonstrating significantly different cycles of light.6 They found that the randomness of the light pulses were even larger when the fish were immersed in complete darkness, depriving them of their natural cycle resetting mechanism, the sun.6 This randomness was made more strange by the relatively static luminosity when the fish were immersed in the complete darkness compared to the normal cycle of luminosity.6

Particularly significant is the use of stochastics in explaining widely differing structure among planets.7 Stuart Ross Taylor in an article in the journal Nature notes that unlike stars, which are modeled using the Hertzsprung-Russell diagram, no model currently exists for planets.7 He states in the beginning of the article:

Planets are diverse individuals formed by stochastic processes. In our Solar System we have eight planets, all of which are distinct from one another in mass, density, composition, rotation rates and angle of inclination (obliquity). Their only common properties are near circular orbits and low inclinations to the Earth–Sun plane, characteristics that enabled Pierre-Simon Laplace to conclude in 1796 that they had originated from a rotating disk, the solar nebula.7

For example, he explains that Venus and Earth are different despite their similarities in mass, density, bulk composition, and the abundances of heat-producing elements due in large part to water but also likely due to the random behavior of impacts by bodies such as asteroids.7 Thus even at the macro level we can see a balance between randomness and determinism. This pattern is even the same one we see on the atomic level. We see more order as we progress from the electron level to the molecular level to nature around us, and in the same way, we see more order as we move from the chaotic behavior and structure of asteroids to the more orderly behavior and structure of the planets to the mostly predictable behavior and structure of stars.

Even though most Christians will be quick to point to this kind of article as scientists appealing to chance to explain the creation of the universe as we know it, we must not neglect the importance of randomness in shaping the universe around us. One needs to look no further than London dispersion forces, a major force of attraction between molecules caused by random shifts in the locations of electrons, to see the importance of randomness to our universe. Randomness in the universe does not diminish the argument for the existence of God. After all, I recognize that stochastic processes naturally lead to a zero sum game. Thus, without a designer, I would expect to see a static universe on the macro level even with random fluctuations on the micro level. Beyond that, I feel the whole universe is based on the character of God. God is the basis of the Christian’s unifying “theory of everything”. While scientists struggle to find a unifying “theory of everything”, I see the character of God as the basis of the universe. I see God creating the universe, and with it, knowledge itself, which explains how He can be eternally omniscient without planning the entire universe from the beginning of time. I may not understand how God came to be or understand the existence of infinity, but based on the anecdotal evidence of Occam’s razor, a principle stating that the simplest solution is usually the best, I feel that believing in the God of the Bible is the best explanation for the universe as we know it. While a significant amount of Christians may rather have a simple “black or white answer”, I find the balance we see between randomness and determinism to be a beautiful aspect of the universe. This idea of two opposites working in tandem is not foreign to Christianity. God is merciful yet just, protective yet testing, loving yet vengeful, personal yet universal. Surely, we as Christians can admire randomness working to form order in the universe around us.

As prevalent as randomness is around us, scientists have found it difficult to create the complete randomness that would suggest a chaotic universe absent of God’s control.4 The first simulators of stochastics used dice tosses or card throws. While these systems, in theory, obey Newtonian mechanics, in reality they exhibit randomness due to their chaotic dynamics.4  Computers are now used to generate “pseudorandom” numbers, but are incapable of generating truly random numbers.4 Even coin tossing, a staple of unpredictability, is biased towards one side due to the different designs on the two sides of the coin.4 We thus find science pointing to a balance between randomness and determinism. This would also point to a balance existing between free will and predestination. As Gregory Chaitin, who in the 1960’s pointed out the impossibility of a computer generating a truly random set of numbers, stated, “The world consists of the tension between order and chaos. When simulating physical phenomena, order is supplied by the laws of physics and chaos is supplied by random numbers”.5

            In a stochastic model for free will, a probability is assigned to our chances of committing any action.  If a probability over 50% exists for performing an action than that action is predestined, but not inevitable. God is omniscient in that He understands all the mechanisms; He understands how we will act based on the probability of us doing anything. God understands all that can be known. In this model, the chance aspect of reality is why God had to exert influence over Pharaoh in Exodus. This model, based on current scientific understanding, may hold the secret to this age-old debate over free will and predestination.

 

References

 

1. The Holy Bible, New International Version. Zondervan Bible Publishers.

2. Silberberg MS. Section 9.5 between the extremes: Electronegativity and bond polarity. In: Chemistry: The molecular nature of matter and change. 4th ed. Boston: McGraw-Hill; 2006. .

3. Dictionary.com [Internet]: Lexico Publishing Group, LLC [cited  2008 Apr 9]. Available from: http://dictionary.reference.com/search?r=2&q=Stochastic.

4. Malescio G. Predicting with unpredictability. Nature 2005 04/28;434(7037):1073-.

5. Jones R. Biophysics: Signals and noise in tiny axons. Nature Reviews Neuroscience 2005 08;6(8):589-1.

6. Carr AF, Whitmore D. Imaging of single light-responsive clock cells reveals fluctuating free-running periods. Nat Cell Biol 2005 03;7(3):319-21.

7. Taylor SR. Why can't planets be like stars? Nature 2004 07/29;430(6999):509-.

 

 

©2008 Jorge Eduardo Fernandez



[a] Exodus 7.13, 7.14, 7.22, 8.15, 8.19, 8.32, 9.7, 9.34, 9.35, 13.15

[b] Exodus 4.21, 7.3, 9.12, 10.1, 10.20, 10.27, 11.10, 14.4, 14.8, 14.17