Does Randomness Really Exist?

On January 11, 2016

Is randomness real? Discussions of this topic are often confusing because the word “randomness” does not enjoy a univocal definition—it denotes a number of concepts bearing a family resemblance. For mathematicians, randomness refers to uncertainty, for statisticians to a property of a selection process, for computer scientists to an absence of pattern in bit strings (I’m oversimplifying in saying that), for quantum physicists to absence of cause, and for biologists to the independence of variations in offspring from their environment. Popular usages also include notions such as lack of purpose or meaning, absence of control, and gratuitous occurrence. However, even though the scientific definitions vary, there is nothing in them that suggests that randomness necessarily lacks purpose, meaning, or control or that it is gratuitous.1 Here’s a typical confusion—someone points to a phenomenon in quantum mechanics or evolutionary biology and says that it exhibits randomness in the scientific sense. The speaker then shifts to a popular definition and asserts that the phenomenon is without purpose or meaning. Neither conclusion is warranted. So in talking about God and randomness, I’m going to stick to the scientific definitions.

From a mathematical point of view, randomness clearly exists. The prime number theorem is well-established and shows that the distribution of primes among the natural numbers is random. Theoretical computer scientists have recently shown that if we think of numbers as infinite decimals, for almost all numbers, their digits are random in the sense mentioned above. From a theological perspective, there are only two possibilities—either numbers have existed in the mind of God from eternity or they were created by God prior to the creation of this universe. Either way, the conclusion is inescapable—randomness originates in God and has existed from eternity.

But that’s abstract mathematics. Does randomness exist in the physical world? Just to make the discussion concrete, I’d like to address a specific example of randomness—the arrival of cosmic rays at a detector. “Cosmic rays” are actually particles—protons or atomic nuclei that come from interstellar space and pass through our solar system. They can be easily detected on earth or on satellites with the right equipment. Such arrivals follow a Poisson process—a well understood form of randomness. The underlying mathematics of Poisson processes rests on two assumptions—that arrivals are equally likely to occur at any time in the interval and that arrivals are independent of each other. The arrival patterns predicted from these two assumptions fits the actual arrival of cosmic rays astonishingly well—they follow a Poisson distribution and in aggregate are quite predictable even though no individual arrival is predictable.

In the light of this example, let’s examine the question of whether or not randomness is real. If we use the mathematical definition of randomness as unpredictability, it certainly is real—it is impossible to know of the existence of a particle until it is detected. So for human beings the randomness can never go away—there is no way for humans ever to acquire the knowledge that would make the process predictable at the individual particle level. Note that the particles all move according to well-known deterministic laws of physics but as a system, their behavior is random. So saying that looking at particles closely, as some bloggers here have suggested, there is no randomness, neglects the fact the randomness is a property of systems not just a property of individual events.

But is this process random from God’s perspective? The answer depends on how one looks at it. Presumably God knows the location of every particle in the universe and can therefore predict the arrivals. So in that sense the process is not random to God. But the randomness in this situation rises from two properties of these particles—they’re part of a complex system containing enormous numbers of particles and each is independent of the others. This is why they arrive with equal likelihood at any time in a fixed interval and why they can be detected individually. So from God’s point of view the process is still a Poisson process and in that sense is still random. An occasionalist (those with the highest possible view of God’s sovereignty over creation) might object by saying that God is in direct control of every particle, so it’s not appropriate to apply the word random to such particles. Thomists (those who follow theologian Thomas Aquinas) would agree that God was the prime mover of the particles but see God as allowing each entity in creation to be a (secondary) causative agent in its own right. So God can know both what is happening and observe its random behavior. I lean toward Thomism, so I have no trouble asserting that, for God, a process can be both predictable and random.

I would go so far as to suggest that most of the randomness that we commonly experience arises from these two factors—complexity and independence. Even the commonly used dice example—something that appears random but when looked at closely enough can be seen to be deterministic—is the result of a complex interaction of multiple independent factors. So its randomness need not be dismissed. Randomness is nothing strange or fearful—it’s a necessary part of living in a complex world in which there are many independent entities. Furthermore, as other writers here have pointed out, biological processes use randomness. Also mathematically, the most important theorem in statistics, the Central Limit Theorem, proves that even the most disorderly sets of numbers necessarily follow a highly ordered pattern when aggregated appropriately. Putting all this together, it seems that randomness originates in God and that God has built the world both to incorporate and to manage randomness.

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