Finding Common Ground/Doubt and our Bayesian Brains

When you first wake up each morning it is likely you are unsure about what to expect for the day’s weather. You might expect rain, snow, sun, a warmer day, perhaps a colder day, or have no specific expectation. You are largely indifferent in your expectations and beliefs about today’s weather until you look out the window, step outside, or consult a weather report.

In contrast, you do expect the sun to rise each morning, even if you can’t see it through the clouds. Rarely will you have some urgent need to see the sunrise to be confident the sun did rise again today.

These examples illustrate how we use Bayesian reasoning in seeking out information, evaluating evidence, choosing beliefs, and making decisions. We have little or no prior expectations regarding the day’s weather until we gather up-to-date information about today’s weather. We may prefer sun over rain, and to hope for sun and discover it is indeed raining may be disappointing, but it does not challenge our belief system. We easily assimilate the new information and readily accept the fact that it is raining. In contrast, we have a strong belief that the sun will rise each day. Discovering the sun has not risen would shake our belief system to its core. We might double check the time of day, suspect a solar eclipse, carefully examine the cloud cover, talk to friends, interpret this as some omen, and perhaps become confused or even fearful that some catastrophe has occurred.

In the language of Bayesian statistics, the likelihood we hold before seeing new evidence is called the Bayesian prior or simply the prior probability. In the case of weather, the prior is the probability we estimate (before looking out the window) that it will rain or that it will be sunny. In the sunrise example the prior is the probability we estimate that the sun will rise. The evidence we begin to gather, for example by looking out the window, stepping outside, or listening to a weather forecast, is called the new evidence or simply just evidence. We combine the new evidence with our prior expectations to update our current expectation, also known as the posterior probably.

Bayesian approaches to brain function investigate the capacity of the nervous system to operate in situations of uncertainty. These promising models of our brain describe our decision-making processes as largely Bayesian. Bayesian decision making begins with a prior probability (the probability we estimate based on our assumptions about the outcome before gaining new evidence) and then updates the likelihood based on subsequent evidence. If the Bayesian prior is allowed to become either 0 or 1, reflecting a prior certainty, then subsequent evidence becomes moot and is ignored. This is what we mean by “having a closed mind”. Our decision-making processes are most active when we need to resolve an uncertain prior assumption. This is the importance of embracing doubt—doubt keeps our decision-making process open to evaluating new evidence. Both faith and prejudice begin with certainty and skip over doubt as they depart from reality.

Because our brains continuously maintain a predictive model of the world, Bayesian priors play an important role in sustaining our belief systems. In fact, Bayesian priors may be the primary manifestation of our belief systems.

Is the sun rising or is the earth turning? How do you know?

Both Galileo and the Pope were fascinated by observing daybreak. They noticed as the sun appeared bright in the sky each morning and disappeared each evening.

Pope Paul V had no trouble interpreting this observation. The earth was the center of the universe and was surrounded by a celestial sphere. The sun was attached to that celestial sphere as it circled the earth.

Galileo was told that the earth was the center of the universe, but he had his doubts. Galileo was aware of a different story, told by Copernicus, that the earth circled the sun. He was curious and kept an open mind as he adopted a scout mindset , and turned his simple telescope toward the sky to investigate. He observed craters on the moon, the phases of Venus, and the moons of Jupiter. These observations cast doubt on the geocentric model of the universe and provided support for a heliocentric model. Galileo challenged, and eventually superseded, the dominant paradigm.

The Pope allowed his investment in the geocentric story to determine his interpretation of the observation. His Bayesian prior reflected his certainty that the earth was the center of the universe. Subsequent contrary evidence was discarded because it was preempted by his prior certainty. Learning could have replaced conflict if the Pope began with the observation, escaped the ideology, adopted a less than certain prior probability, and considered a wide range of possible interpretations before becoming attached to any single interpretation. The Pope’s allegiance to the geocentric ideology preempted the search for alternative explanations of the observation.

Our Bayesian brains work to minimize surprise by accurately predicting the future. Because unexpected events elicit surprise, creating and constantly updating an accurate model of the world minimizes surprise. Doubt is uncomfortable because continuing to compute Bayesian outcomes is hard work for our brains. Closure—a feeling of certainty—is comfortable because it seems to resolve doubt. Furthermore, we rely in certainty to get through our day. We rely on the certainty that the sun will rise, we will have air to breath, the floor will support our weight as we walk, the breakfast cereal is safe to eat, we can open the door, the car will start, and the store will almost certainly have milk we can buy.

Henri Poincaré cautions us: “To doubt everything or to believe everything are two equally convenient solutions; both dispense with the necessity of reflection”. There is a time for doubt, and a time for closure; we can seek the wisdom to know the time for each. We can learn to manage our doubt and seek true beliefs.