Chapter 7              Bayesianism: How It Works

        

                                  Thomas Bayes (credit: Wikimedia Commons)

The best answer to the problem of what human minds and human knowing are is that, in reality, we are all Bayesians. On Bayesianism, I can build a universal moral system.

So, what is Bayesianism?

Thomas Bayes was a Presbyterian minister, statistician, and philosopher who formulated the theorem named for him: Bayes’ Theorem. His theory of how humans form tentative beliefs and gradually turn those beliefs into concepts has been given several mathematical formulations, but it says a fairly simple thing.

Bayes’ Theorem says this: we tend to become more convinced of the truth of a theory or model of reality the more we keep encountering bits of evidence that, first, support the theory and, second, can’t be explained by any of the competing theories our minds already hold. (An accessible explanation of Bayes’ Theorem is on the Cornell University Math Department website.¹)

Under the Bayesian model, we never claim to know anything for certain. Empiricism and Rationalism both aim to provide us with a way of thinking that can lead us to unshakable truths. But Bayesianism does not claim to seek perfect truth. Instead, it says that we hold most firmly a few beliefs we consider highly probable, and we use them as we make decisions in our lives. We then assign lesser degrees of probability to our more peripheral beliefs, and we constantly track the evidence confirming or disconfirming our beliefs. Under Bayesianism, we accept that all beliefs, at every level of generality, need constant updating, even the ones that have been working well at guiding us to handle real life. It is far more akin to Empiricism than Rationalism, but beyond both. Agile. Alive.

For most people, in their daily lives, the more a theory enables them to establish some kind of overall order that covers all their concepts and memories, the more persuasive the theory seems. If the evidence favoring the theory mounts, and its degree of consistency with the rest of the concepts and memories in the mind also grows, then finally, in a leap of understanding, the mind promotes the theory up to the status of a belief and incorporates the new belief into its total stock of thinking machinery. Once I understand how evolution works, I see it in every living thing I pass. The same is true of gravity, respiration, etc..

At the same time, the mind nearly always has to demote to inactive status some formerly held concepts that are not commensurable with the new belief. This is especially true of all mental activities involved in the kinds of thinking that are now being covered by the new theory. For example, once you absorb and accept a theory of how your immune system works, that concept will inform every health-related decision you make thereafter – diet, vitamins, exercise, etc.

In life, examples of the workings of Bayesianism can be seen all the time. All we need do is look closely at how we and the people around us make up our minds.

When I was in junior high school, each year in June, I and all the other students of the school were bussed to the city track meet at a stadium in West Edmonton. Student athletes from all the major junior high schools in the city came to compete in the biggest track meet of the year. Its being held near the end of the school year, of course, added to the excitement of the day.

A few of the athletes competing came from a special school that educated and cared for those kids who today would be called “mentally challenged”. In my Grade 9 year, three of my friends and I, on a patch of grass beside the bleachers, did a mock cheer in which we shouted the name of this school in a short rhyming chant, attempted some clumsy dance kicks in step, crashed into each other, and fell down – all in an obviously mocking style. I should make clear that I did not learn such a cruel attitude from my home. Had they seen this stunt, my parents would have been furious. But fourteen-year-olds with their peers can be cruel.

The problem was that one of the prettiest, smartest girls in my Grade 9 class, Ann, was sitting in the bleachers, watching field events in a lull between track events. She and two of her friends happened to catch our little routine. By the glares on their faces, I could see they were not amused. Later that day, I learned that she had an older brother who had attended our school and earned excellent marks, but she also had a younger brother who had Down syndrome.

I apologized lamely the next day at school, but it was clear I’d lost all chance with her. However, she said one thing that stayed with me. She told me that if you form a bond with a mentally retarded person (retarded was the word we used in those days), you will soon realize you have made a friend whose loyalty, once won, is unchanging and unshakeable – probably, the most loyal friend you will ever have. And that realization will change you.

The idea she was expressing took root. Then, over the next twenty years, it grew into a concept and finally into an absolute conviction.

                                  

               Francis Galton, originator of eugenics (credit: Wikimedia Commons)

It was the proverbial thin edge of the wedge. Earlier, I had absorbed some of the ideas of the pseudo-science called Eugenics from one of my friends at school. I’d concluded the mentally challenged added nothing of value to a community, but inevitably took a great deal out of it. They could, and should, be bred out of the human genome. What Ann said made me question those assumptions.

Over years of seeing movies like A Child Is Waiting and Charlie, and of being exposed to awareness-raising campaigns by families of the mentally challenged, I began to see them in a different light. Over decades of changes in attitudes, they were called mentally handicapped and then mentally challenged or special needs, and the changing terminology did matter. It changed society’s thinking.

I became a teacher, and then, in the middle of my career, mentally challenged kids began to be integrated into the public school where I taught. I saw with increasing clarity what they could teach the rest of us, just by being themselves.

Tracy was severely handicapped, mentally and physically. Trish, on the other hand, was a reasonably bright girl who had rage issues. She beat up other girls, she stole, she skipped class, she smoked pot behind the school. But when Tracy came to us, Trish proved in a few weeks to be the best with Tracy of any of the students in the school. Her attentiveness and gentleness were humbling to see. In Tracy, Trish found someone who needed her; it changed everything for Trish. As I watched them together one day, it changed me. Years of persuasion and experience, by gradual degrees, finally, got to me. I saw a new order in the community in which I lived, a new view of inclusiveness that gave coherence to years of memories. We are all siblings caring for each other.

Today, I believe the mentally challenged are people. But it was only grudgingly at fourteen that I began to re-examine my beliefs about them. At fourteen, I liked believing my mind was made up on every issue. Only years of gradually growing awareness led me to change my view. A new thinking model, gradually, by accumulation of evidence, came to look more correct and useful to me than the old model. Then, in a kind of conversion experience, I switched models. Of course, by gradual degrees, through exposure to reasonable arguments and real experiences, I and a lot of other people have come a long way on the mentally challenged from what we believed in 1964. Humans can change. By Bayesian kinds of steps, I learned a new way of looking at the mentally challenged.

                      

   

                           Doberman Pinscher (credit: Wikimedia Commons) 

In a more scientific example of Bayesianism working in my own thinking, I will also mention our Doberman Pinscher–cross pup. Rex was basically a good dog, but he was a mutt, a Doberman cross we acquired because one of my aunts couldn’t keep him. People often remarked that he looked like a Doberman, but his tail was not docked. This got me curious. I learned that most Dobermans had had their tails bobbed for many generations, and I wondered why the tails, after many generations of docking, had not simply become shortened at birth. I asked a Biology teacher at my high school, but his answer only confused me. Actually, I don’t think he understood the key concepts in Darwinian Evolution Theory himself.

                        

                     

                               Jean-Batiste Lamarck (credit: Wikimedia Commons)

Once I got to university, I took several Biology courses. Gradually at first, and then in a breakthrough of understanding, I came to realize that I had been thinking in terms of the model of evolution called Lamarckism. At first, I did not want to let go of this cherished opinion of mine. I had always thought of myself as progressive, modern, scientific; I did not believe in Creationism. I thought I knew how evolution worked. I thought I was using an understanding of it in all my thinking. It was only after I had read more and seen by experience that docking dogs’ tails did not cause their pups’ tails to be any shorter that I came to a full understanding of Darwinian evolution.

Evolution for all species proceeds by the combined processes of genetic variation and natural selection. It doesn’t matter how often the anatomies of already existing members of a species are altered if their gene pool doesn’t change. If the species’ gene pool doesn’t change, then the next generation will, at birth, basically look pretty much like their parents did at birth. Chopping off a dog’s tail doesn’t change the tail genes it carries in its sperm or egg cells.

Under Lamarckism, by contrast, an animal’s genes are pictured as changing because the animal’s body has been stressed in some way. Lamarckism says a chimp, for instance, will pass genes for larger arm muscles on to its young if the parent chimp is forced to use its arm muscles a lot.

But Darwinian evolution gives us what we now see as a far more useful picture. For example, in nature, individuals within a species that are no longer well camouflaged in the changing flora of their environment become easy prey for predators and so they never survive long enough to have babies of their own. Or ones that are unable to adapt to a cooling climate die young or reproduce less efficiently, while their thicker-coated, or smarter, or better camouflaged cousins flourish.

Then, over generations, the gene pool of the local community of that species does change. It contains more genes for short, climbing legs or long, running legs or short tails or long tails or whatever the local environment is now paying a premium for. Gradually, the anatomy of the average species member changes. If short-tailed members have been surviving better for the last sixty generations and long-tailed members have been dying young, before they could reproduce, the gene pool changes. Eventually, there will be many more individuals with short tails, a now-normal, genetically transmitted trait of the species.

Pondering Rex’s case helped me to absorb Darwinism. My understanding grew and then, one day, through a mental leap, I suddenly “got” the newer, better model. A model I hadn’t understood became clear, and it gave deeper coherence to all my ideas about living things. Lamarckism became just an interesting footnote in the history of Science for me, occasionally still useful because it showed me one way in which my thinking, and that of others, could go wrong.

The question that now arises is this: how would the Bayesian way of choosing between the Lamarckian and Darwinian models of evolution or of reshaping one’s views on the mentally challenged compare with the Empiricist way or the Rationalist way of dealing with these same problems?

The chief danger of Empiricism that Bayesians try to avoid is the insidious slip into dogmatism. In the history of Science, many Empiricist-minded scientists have worked out and checked a theory so thoroughly that they have slipped into thinking they have found an unshakeable truth. For example, physicists in the late 1800s were in general agreement that there was little left to do in Physics. Physics, for these people, was complete. Newton and Maxwell, between them, had articulated all the truths of the physical world, from the atomic to the cosmic. Then, Einstein’s Theory of Relativity overthrew the Old Physics.

                        


                   

                              James Clerk Maxwell (credit: Wikimedia Commons)

Today, Physics is in a constant state of upheaval. A few physicists still show a longing for certainty, but most modern physicists are tentative and cautious. They’ve been let down so many times in the last hundred years by theories that once had seemed so promising, but that later were shown by experiment to be flawed, that they have become permanently wary of all “truth” claims.

It is regrettable that a similar caution has not got into more of the physicists’ fellow scientists, especially the biologists. Darwinism explains all aspects of the living world that we currently know about. But it is still only a theory; it should be viewed as tentative, and very likely, but not final or irrevocable.

The larger point for our purposes here, however, is that while Empiricism may present the Theory of Evolution to us as final, Bayesians never endorse any one model as the last word on anything, and they never throw out any of the old models or theories entirely. Even those that are clearly proven wrong have things to teach us, and of the ones that are currently working well, we have to say, simply, that …they are currently working well.

In contrast to Empiricism, Rationalism has other problems, especially with the whole Theory of Evolution and what was going on with my dog, Rex.

For Plato, the whole idea of a canine genetic code that contained the instructions for the making of an ideal dog would have sounded appealing. Obviously, the code must have come from the dimension of the forms, the pure Good. 

But Plato would have rejected the idea that back a few geological ages ago no dogs existed, while some other animals did exist that looked like dogs, but were not imperfect copies of an ideal dog “form.” We know now these creatures can be more fruitfully thought of as excellent examples of canis lupus variabilis, another species entirely. All dogs, for Plato, should be seen as poor copies of the ideal dog that exists in the pure dimension of the Good. But the fossil records in the rocks don’t so much cast doubt on Plato’s idealism as belie it altogether. With regard to gradual, incremental change in all species, Plato’s commitment to “forms” would have led him to totally reject Darwin’s Theory of Evolution.

In the meantime, Descartes’s version of Rationalism would have had serious difficulties with the mentally challenged. Do they have minds/souls or not? If they don’t get Math and Geometry and they can’t discuss “clear and distinct” ideas, are they human or are they mere animals? The abilities of the mentally challenged range from slightly below normal to severely mentally handicapped. At what point on this continuum do we cross the threshold between human and animal? Between the realm of the soul and that of mere matter, in other words?

Descartes’s ideas about what properties make a human being human are disturbing. But his ideas about how we can treat other creatures are revolting.

To Descartes, animals didn’t have souls; therefore, humans could do whatever they wished to them and not violate any of his moral beliefs. In his own scientific work, he dissected dogs alive. Their screams weren’t evidence of real pain, he claimed. They had no souls and thus could not feel pain. The noise was like the ringing of an alarm clock – a mechanical sound, nothing more. Generations of scientists after him performed similar acts: vivisection in the name of Science.²

Would Descartes have stuck to his definition of what makes a being morally considerable if he had known then what we know now about the physiology of pain? Would Plato have kept preaching his form of Rationalism if he had been given access to the fossil records we have? These are imponderable questions. It’s hard to imagine either of them would have been that stubborn. But the point is that they didn’t know then what we know now. 

In any case, after considering some likely Rationalist responses to the test situations described in this chapter, it is certainly reasonable for us to say again that Rationalism’s way of portraying what human minds do when they think and know is simply mistaken.

And now, we can put aside for good our regrets about both Rationalism and Empiricism and the inadequacies of their ways of looking at the world. We can go on to a more detailed and comprehensive discussion of Bayesianism.

Notes

1. Bayes’ Formula, Cornell University website, Department of Mathematics. Accessed April 6, 2015. http://www.math.cornell.edu/~mec/2008-2009/ TianyiZheng/Bayes.html.

2. Richard Dawkins, “Richard Dawkins on Vivisection: ‘But Can They Suffer?’” BoingBoing blog, June 30, 2011.

http://boingboing.net/2011/06/30/richard-dawkins-on-v.html.