Do Dice Play God? Ian Stewart on Fortune Telling and Bayesian Brains

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Do Dice Play God? Ian Stewart on Hepatomancy, Fortune Telling, and Bayesian Brains

Babylonian kings and priests

Before monotheistic religions and the modern establishment, animalism and other micro-religions flourished everywhere. Mythmaking and storytelling helped our ancestors to explain their world and develop local institutions.

In Do Dice Play God?, mathematician Ian Stewart recalls a particular passage in The Bible that tells of a Babylonian king who shook arrows and consulted with household idols to invoke divination (Ezekiel 21:21). The Babylonians also trained their priests in hepatomancy. Careful interpretation of sheep liver, they believed, would reveal the future to them.

But hepatomancy was not all. Our ancestors devised all manner of rituals and superstitions to make predictions. Some of the less messy ones—like horoscopy (star reading), palmistry (palm reading), tasseography (tea leaves reading), nephelomancy (cloud reading), and cromniomancy (onion sprouts reading)—survive to this very day.

A clockwork universe

However, some people began to realize that their belief systems and practices did not help them to understand the world or the future. These individuals preferred instead to rely on logical inference and empirical evidence. Galileo Galilei, for example, studied the motion of falling bodies, while Johannes Kepler investigated planetary motion. Building on their work, Isaac Newton came along in the seventeenth century and developed the classical laws of motion and gravitation.

Slowly but surely, discovery upon discovery unravelled the inner workings of our world and universe. The early pioneers of science began to attribute uncertainty not to divine spirits and gods but to ignorance. The newfound laws of physics suggested, perhaps, that everything ran like clockwork—that life and the cosmos was part of a grand deterministic machine. To the Newtonian folk, the future appeared predictable, at least in principle. What they needed, however, was not tea leaves or sheep liver, but a supreme calculator and the foreknowledge of the relevant physical laws and state of every particle.

Enter quantum and chaos

Dreams of a clockwork universe, however, collapsed in the early twentieth century when development of quantum physics—following the work of Niels Bohr, Max Planck, Werner Heisenberg and other great physicists—took center stage. They learned that “a quantum particle isn’t a particle at all, just a fuzzy cloud of probabilities”, Stewart explains. 

Here, “science morphs from dictator to oddsmaker”, says Tom Siegfried. It is more than just present ignorance or simple observer effects. “Quantum math tells only [of] probabilities for different possible outcomes. Some uncertainty always remains.” And “the structure of our observed world”, according to Sean Carroll, “arises as a higher-level emergent description” of quantum behavior at tiny scales. 

Fundamental uncertainty, however, is not confined only to quantum physics. We’ve also learned that many nonlinear systems are sensitive to initial conditions. And because we cannot measure anything with perfect precision, even the smallest of errors can compound mightily over time. This is why it is so difficult to make long range forecasts of day-to-day weather patterns or stock market prices. In the world of living things, complexity and chaos abounds.

“We can know the laws of a deterministic system perfectly but still be unable to predict it. Paradoxically, the problem doesn’t arise from the future. It’s because we can’t know the present accurately enough.”

Ian Stewart. (2019). Do Dice Play God? The Mathematics of Uncertainty.

Astrologers at the White House

So we live today under a humbler realization that the dices of nature may indeed, in a poetic sense, play god. But while our sum knowledge has improved over the last two thousand years, it’s fair to say, I think, that our attitudes to uncertainty as a collective are not dissimilar to that of ancient times. For starters, most people are not familiar with the consequences of quantum and chaotic phenomena. Our schools, likewise, do not train us to think about the nonlinear nature of our social and economic world.

In politics and business, we’ve simply traded our soothsayers and shamans for financial gurus and management consultants who practice their own brand of arcane language and crystal-ball gazing. Even former U.S. President Ronald Reagan consulted with an astrologer to schedule events and election announcements. Perhaps all we want is somebody to tell us what to do and think.

Bayesian brains and science

Notice, however, that “many of these methods”, from hepatomancy to astrology, “depend on the same presumption—that “to understand something large and complicated, [we tend to] mimic it with something small and complicated”, Stewart writes.

Our thinking apparatus, you see, is not dissimilar to a “Bayesian decision machine”. We formulate ‘degrees of beliefs’ about things that happen based on our limited knowledge and a simplified conception of the world. As events unfold and new information emerges, we revise, reinforce, or rationalize our preconceived assumptions.

The scientific method is similar in this regard. The difference being that a scientist’s confidence or degrees of belief in any given theory depends on testable predictions and an accumulation of observations. Our best theories in science are simply the ones that survive the test of time and falsification.

In this way, we can also see where beliefs might trip us. As the mathematician George Boole writes: 

“It would be unphilosophical to affirm that the strength of expectation, viewed as an emotion of the mind, is capable of being referred to any numerical standard. The man of sanguine temperament builds high hopes where the timid despair, and the irresolute are lost in doubt.” George Boole. (1854).

An Investigation into the Laws of Thought.

What are the chances?

Indeed, let’s say, for example, that I am more optimistic than you are about our prospects for contact with extra-terrestrial life. As Stewart points out, “there’s no way to work out who’s right…, even if the aliens turn up.” So while my guess might seem more accurate upon seeing the alien, “neither of us is demonstrably correct.” We simply do not have the data or methods to build a reasonably objective model of meeting aliens before and after this peculiar fact. We just cannot know.

The same is similarly true of many beliefs in everyday life. They are simply untestable. And even when they are, self-interest and psychological denial may push us to ignore and deny the facts. In a world as diverse, uncertain, and distrusting as ours, the emergence of extreme and nonsensical beliefs are not at all surprising. Some amount of Babylonian affinities, I think, rests inside all of us.

“How does the brain foretell the future? It builds simplified internal models of how the world works… It feeds what it knows into the model, and observes the outcome… Most of us stick pretty closely to what we were brought up to believe… You catch your beliefs from parents,… teachers, and authority figures in your culture… [Beliefs are] wired into your Bayesian decision-making brain, and it may become impossible for you to disbelieve, no matter how contradictory other evidence might appear.”

Ian Stewart. (2019). Do Dice Play God? The Mathematics of Uncertainty.

Sources and further reading