The Size of Human Freedom

Way back in the mid-1970s before the sexy term ‘chaos theory’ had ever driven books onto the best-seller lists, I took a course with a decidedly unsexy title: The Qualitative Analysis of Ordinary Differential Equations. In that course, we learned how to analyze potentially unstable systems such as a planet orbiting the sun so that it never repeated the same path twice, as is true for the earth and its siblings. As it turns out, it’s possible — with a lot of simplifying assumptions — to make statements about the stability of the planet’s orbit given the mathematical techniques available to an undergraduate math or physics major. Ultimately, the field is very difficult and relies on techniques and disciplined attitudes beyond that of most undergraduates and certainly beyond the typical reader of gee-whiz pop-science books. Unfortunately, the field has acquired the title, “chaos theory,” as misleading a name as special or general relativity theory.

Chaos theory deals with imperfectly stable systems just as Einstein’s theories of relativity deal with invariant relationships between entities and geometries of space-time.

Would you like to make a chaotic system in the lab, or in your basement workshop? Take two pendulums of different period, that is, different length of the wire or rod holding the bob. Connect them with a chain or rope and set one in motion. The movement of the two pendulums will be chaotic. It will be unpredictable by human techniques of mathematical physics though that movement will be well-determined so far as we know.

The unpredictability is seen only as shadows, if you will, against the backdrop of what can be rationally stated regarding these systems. If we hadn’t known the Law, we wouldn’t have known (understood) sin. If we hadn’t known the physical laws which give some ordered structure to physical reality, we wouldn’t have understood the disorder studied in ‘chaos theory’. The term ‘disorder’ in the previous sentence is in the context of human mathematics. To say that we can’t predict the future of even simple physical objects isn’t the same as claiming that there is some sort of irrational or mystical elements entering into that future. It is to say that there are facts which don’t fit into current human mathematical and metaphysical structures.

There is a general principle advanced first, so far as I know, by the philosopher Stephen Toulmin in the early 1960s or thereabouts:

Apparent randomness will arise in the real-world when two well-determined and independent systems interact.

At the time he wrote, he was concerned about a simple model of evolution, one reduced to the interaction of two particular systems: the DNA of an organism and its external environment. This is a useful simplification, but the real world is far more complicated and also more complex in basic ways. When we’ve dived into contemplations of this sort of situation, it does become surprising that order can be seen at all even when we know it to be there.

In the mid-1960s, an interesting proposal was advanced independently by the great Russian mathematician, A.N. Kolmogorov, and the American high school student, Gregory Chaitin. The proposal was to actually define a random number in terms of what is now called ‘algorithmic complexity theory’ rather than just taking it as a naive concept which is typically treated as being some invasion from irrational realms. I had a very highly regarded mathematician as my professor for a year of probability theory and stochastic processes, Professor Kempermann, and I remember him saying, circa 1975, that randomness not necessary in mathematics but is useful mostly for pedagogical purposes. All of probability theory can be enfolded into a fully deterministic measure theory. Marc Kac, a highly regarded measure theorist at Cornell, reacted to the early work of Chaitin and Kolmogorov by saying: Now we know what a random number is, a fact.

A fact. Facts are scary in a way, but not because they’re irrational. Anyone who’s read my first published book, To See a World in a Grain of Sand, and some of my subsequent writings on my blog might suspect that facts play a very important role in my understanding of God’s Creation. Facts are more basic than axioms, because those statements and things we regard as ‘systematic’ truths are drawn by God from an absolutely infinite realm of raw facts which would be so unorganized to us that we couldn’t see them if God were to set us down in what I call the Primordial Universe. The Primordial Universe is my effort to speak rationally about some very complex questions raised by these mathematical issues and also by the meltdown of things into elementary particles and then the meltdown of those particles into some very strange and general sort of substance as we travel backwards in time towards and beyond the so-called Big Bang. As I moved forward in these thoughts, I also came to feel we should speak rationally about the human ability to discover higher orders of infinity which seemingly can’t be embodied directly in our physical universe — meaning they couldn’t be embodied directly in any sorts of relationships between human brain-cells.

God is the Creator of that absolutely infinite ocean of facts, which I call the Primordial Universe, and God is also the only entity who can make a true random number or act in a truly random way just because such acts would require an absolutely infinite mind. God is the Master of Facts and the axiomatic systems of most systems of human thought are special sorts of facts. They’re specially shaped rocks selected from a field of randomly shaped rocks. They fit together to form elegant structures but they’re not the foundation of Creation — that absolutely infinite field packed with randomly shaped rocks is the source of the components of specific worlds within Creation.

Gregory Chaitin worked on exploring the meaning of randomness from his high school years in the mid-1960s until 1990 or so. He found that all numbers are random.

What could this possibly mean? Following standard mathematical procedures, we can discuss only numbers between 0 and 1. A non-random number is one that has a pattern that allows a shorter encoding than a simple listing of all its digits. For example, 0.1111… can be encoded as either (1/9) or by the words: “An infinite number of 1s after the decimal point.” Either encoding is clearly shorter than a listing of an infinite number of 1s. The number 0.1111… isn’t random. It’s somewhat amazing that all numbers with patterns, including those which can be ‘built’ from axiomatic systems, form a set which is infinitesmally small compared to the set of random numbers, those without patterns.

Let’s make a stab in the dark at the possible meaning beyond mathematics. What lies outside the realm of entities with elegant patterns? Our moral lives? Our creative lives, including our creative corporate lives by which we form useful collectives of various sorts? Our very lives? Maybe even life in general? Or at least the higher forms of life which exhibit some sort of moral and social characteristics?

Don’t those aspects of our lives have the feel of factuality? To be sure, we don’t operate with total freedom.

Only God can make a random number and only God can act in a truly random way.

The most random act we know of is the ‘selection’ of the extraordinarily unlikely initial conditions of our universe. I’m not sure if we can even try to describe God in His transcendent and necessary being which is His own Act-of-Being, the supreme Act-of-being, but God as Creator acted freely in creating. He acted randomly, factually and not according to any possible logic or axiomatic reasoning.

Factuality, metaphorically drawn from the set of numbers between 0 and 1 which have no pattern, may be our way of understanding and describing God’s freedom as Creator. I’ll provide a short outline of what might be involved in dealing with reality from this angle:

  1. God, as Creator of this world, works in the domain of absolute infinity.
  2. God, in His transcendence, is pure existence — His own Act-of-being — and it might not make sense to speak of such matters as infinity with respect to the transcendent Lord.
  3. Creatures move around in domains restricted by the lesser infinities associated with that elegant realm of mathematics.

Factuality bursts into this creaturely realm. That is, freedom shows itself but we have trouble seeing it. After all, pure freedom doesn’t belong to creatures, can’t belong to us, and we shouldn’t wish for it,

God can be absolutely free because He’s pure existence. He has no structure as such, no substance or body parts. He is the source of all that we as creatures can know about by the efforts of our own minds: the truths of a philosopher and those of a mathematician. He is the source of the substance of our bodies and that of the perfected bodies of the resurrected.

The movement from a view of Creation built from that elegant subset of the foundations of Creation to the entirety of the foundations would seem to me to be analogous to the movement from the Law as tabulated and elaborated by men to the Law who was a Person, the Son of God.

In that case discussed with such energy by St. Paul, there’s a movement from the skeleton necessary for helping men to behave a little bit like God towards the reality of Christ-like being. In the other case, there’s a movement from the scaffolding necessary for elementary thought to the more complete realm of factuality which includes that scaffolding. When we make that latter transition, the possibility arises of seeing God’s world, in principle, in a way similar to the way that He created it. We learn to imitate God in this way, just as a child watches her mother and then cares for her doll as she sees Mommy care for the new baby in the family.

In both cases, knowing the greater reality exists doesn’t negate the value of the smaller reality. It doesn’t even necessarily help us to see the greater reality with any clarity. Grace still completes nature in this way of viewing our mortal world and the entirety of God’s Creation. Grace completes the Mosaic Law into the Sermon on the Mount and grace completes the mortal bodies of those who belong to Christ into resurrected bodies with the same freedom as the Lord’s resurrected Body.

2 Comments

  1. Paul Boire

    Hi
    Thanks for the wonderful read. It will take a couple more wonderful re-reads to mine the treasures, but I’ve been in discussions with some atheistic philosophers and was primarily interested in Thomistic treatments of pragmatism, and through Prof A. Rizzi in “The Science Before Science”, I’ve been looking for argumentation refuting the idea of acausality.

    Thanks beaucoup

    Paul

  2. Hi Paul,

    If you’re interested in William James’ version of pragmatism vs. Thomstic existentialism, you might want to read the entries with a major title of “What is Mind?”, found under the category of ‘Brain sciences’.

    Loyd

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