Chapter 8       What Is Bayesianism Saying?

Part A 

What is a straining individual who is really searching for truth to conclude at the end of a careful analysis of the problem of epistemology? The pattern is there; records of centuries of fruitless seeking for a model of "knowing" are there; the conclusion is clear.

Rationalism and Empiricism are both hopeless projects. It appears that whatever else the human mind may successfully cognize and manipulate – in purely symbolic forms such as philosophical theses or in more material-world oriented ones such as computer programs – the mind will never define itself.

A human mind is much richer, larger, and more complex than any of the systems it can devise, including systems of ideas that it assembles to try to explain itself. It contains, and makes, systems of symbols for labeling and organizing its thoughts: the symbol systems cannot, in principle, contain it.

Fujisu "K" world's most powerful computer, 2012

The model of the human mind and how it works called "Bayesianism" is workable enough to allow us to get on with building the further philosophical structures that we will need in order to arrive at a modern moral code for all humans. Bayesianism contains some difficult parts, but it does not crack and crash in the way that Rationalism and Empiricism do. Bayesianism will do what we need it to do. It can answer its critics. It will serve as a base upon which we may construct a universal moral code. We will just have to agree to gamble on rational gambling as being the best way of getting on with life.

Under this model, even human consciousness is built on arbitrary and temporary foundations. For example, my concepts of "red", "round", "sweet", "crisp", and "tangy" are descriptor-organizers that help me to recognize and react to things in the real, material world, some of them being apples. Such descriptors are not built into some other dimension of perfect forms as is posited by Rationalism. They aren’t even built into the physical universe in some permanent way as is posited by Empiricism. Even our ways of stating what we think are the laws of the physical universe are constantly being updated.

Once apples did not exist. Nor did the organic chemicals that make sweetness. Even "round" is a constructed concept that exists only in the human mind, only for now, and only because it helps humans whose minds contain it to sort data, make decisions, and get things done. The cave man who could count could think: “Were there five wild apple trees in this valley or six? I know I saw six.” Knowing the difference meant he fed his kids, and they survived to teach the concepts used in counting to their kids.

At bottom, the shifting nature of reality defies all categories, even "here", "now", and "stuff". (Matter, Einstein showed, is really only a form of energy.) A mind (consciousness/sanity) is built up on concepts, a few of them acquired from our genetics (babies fear heights and snakes, but grasp language), some from the conditioning that is programmed into us by our cultures, and some that each of us has built up by spotting patterns in banks of memories gathered in his or her personal experience.

The "I" that is most deeply what I mean by "I" is a program that runs on brain tissue and that is constantly reviewing sense data, trying to decide whether they signify hazard or opportunity or are just more familiar, non-threatening, non-promising, background drivel. A mind looks for patterns in data.

But sanity is a construct and like any construct it can be “deconstructed”, an idea that deserves a bit of digression. If a sanity really is deconstructed, as happens when a person's perceptions are distorted by drugs or sensory deprivation or mental illness so that her/his programming becomes so incoherent that some of interactions with reality get beyond that person's ability to sort, and respond to, real world events, then s/he has a "nervous breakdown". Real deconstruction of a human’s mindset, i.e. the set of programs that a person uses to organize her/his perceptions of reality, can happen, but it is not much like the Deconstructionists’ way of analyzing a work of literature.

Deconstructionism as a philosophy is a kind of playing at mental illness. It is correct in asserting that every sane human cognition is part of a "text" and as such can be deconstructed into its constituent parts, most of which are culturally imprinted and so can be shown to be culturally biased. But complete deconstruction of any "text" - or "context", to put it more accurately - would require the deconstructer to deconstruct the constituents and then the constituents of the constituents. S/he would have to continue until s/he had deconstructed her/his own mind as part of the total context being analyzed. In short, to go mad. Deconstructionists are too cautious to actually use their method to its logical limit. Mental illness, they well know, is not clever, sophisticated, illuminating, or fun.

But let us set regrets about Deconstructionism aside and return to our main line of thought. 

The thrust of Bayesianism is this: all of my sensory experiences and memories of experiences would seem to be jumbled, meaningless gibberish without concepts by which I can organize them. The crucial problem is that these concepts are not built into a supra-real dimension of ideas (Rationalism) nor into material reality itself (Empiricism). Our minds' thinking systems are based almost wholly on concepts that exist only in our minds and only for the time being, be it seconds or centuries.

All basic concepts are illusions in the sense that they metamorph inevitably into and out of one another. Even trees aren't trees; some are giant bamboo, some are bushes grown big, some are former trees in various stages of decay, some are potential trees (e.g. acorns). 

            Dingo (wild dog of Australia) 

Dingoes that kill human children are vicious brutes; dingoes being killed by human children are pathetic victims. Nature is beautiful or horrible depending on what angle it is perceived from. Light is a particle, not a wave; light is a wave, not a particle. Criminals aren't always criminals; if they make war on another ethnic group and lose, they are terrorists, the worst of criminals; if they win, they are freedom fighters, the best of heroes.

Justices mete out injustice. Teachers stupefy.  Physicians sicken. Not always, of course. Not even mostly. But too often for us ever to get smug about our terms. Life is complex and constantly changing. The distinctions that we draw to try to justify our versions of reality get subtler and subtler, but they are never subtle enough. Real life keeps cropping up with situations that leave us and our thinking systems stranded in bafflement and ambivalence. Therefore, we learn to evolve and even improvise.

There is a reality; I am confident of that – at the 99.99 percent level. But it is too fluid and dynamic for our minds to ever get a 100% reliable handle on it. Individuals, families, gurus, philosophers, businessmen, and politicians, in varying ways, appear to get handles on reality for a while, but they all prove inadequate over the long haul. Things, especially humanly-made systems of ideas, fall apart.

On the other hand, life holds together. All throughout the natural world, living things adapt, even individual human living things. Children raised in the Hitler Youth or raised to be Stalin's "socialist beings", incapable of thinking of themselves except as parts of a collective, can grow out of their early brainwashing. 

Men raised to see women as victims to be used and abused can learn not to do the same things to their wives that their fathers did to their mothers. With medications and counseling, even some pedophiles can learn to re-direct their needs into socially acceptable channels. We can learn and adapt; we can re-program. Not perfectly, but functionally, which in the end is what matters to the individual, the community, and our species’ survival. The kids will do better because they will have to.

Mind/consciousness is a program that calculates the usefulness of other programs for enhancing and perpetuating the conditions that will produce more mind.

I am constantly calculating, usually as a mostly unconscious activity, the odds that each of my familiar ways of organizing my thoughts, processing sense data, and formulating action plans is still working and is still adequate for interpreting, and reacting to, the physical situation that I am in right now. Once in a while, I calculate the odds that a different way of thinking, one that I am only considering using, will get me, my children, and my nation good results, i.e. happiness and health, over the long haul. The majority of the time, I check my sensory impressions against my expectations and re-affirm the beliefs and models of reality that have got me this far.

If I conclude that a new way of thinking about reality is an accurate one and that it will enable me to foresee pain and avoid that pain, or to find more pleasure, health and vigor, then I become inclined to move aside some of my old mental gear and move the new ideas in. This is true of nearly all, but not quite all, of the programs that my mind now contains. I become anxious and reluctant when some event or argument challenges my deepest and most general programs: my values. Those I will replace only in dire circumstances or after years of re-programming. Once in a while, if I am very stubborn in refusing to learn life’s latest lessons, I or my family, or even my tribe, will get discarded from the human community of the planet by evolution itself as some new, more efficient and current society replaces us.

 

That picture, "I" believe, is the correct picture of "me".

Bayesianism says about itself that as a model of how humans think it is probably the best model. The odds that we should accept it as the best model of the human mind keep increasing the more that we use it and then handle reality well because we are using it, that is to say, the more we handle reality, individually and as communities, better than other humans using other, less flexible, less resourceful, less effective, less nimble models. 

  

This description, however, has an important caveat attached. I am forced to admit, if I am honest, that sometimes I am not capable of making my odds-weighing judgments astutely, especially when the judgments are about some of the mental gear that is most central in me. This deep, central gear includes the moral beliefs most widely connected to all of the other systems in my mind.

   

I am very reluctant to change my central operating systems, which in plainer language are programs that I engage as I am deciding, second by second, item by item, possible action by possible action, "Good or not?" Those systems are what most people are very reluctant to change. Because of familial and cultural programming, deep emotions are associated with our values. Rather than change their moral values, many people prefer to die fighting to preserve those values, and in fact they sometimes do.

The harshest mechanism by which the values pool of the human race evolves - by wars between nations, rather than by rational persuasion of individuals - is a mechanism that serves a purpose as well, or at least it served a purpose in the past. It cut out of the culture pool what no longer worked. Today it is a kind of mental baggage that we can no longer afford to carry. What it used to accomplish for our species we must learn to accomplish in other ways, if we are to survive.      

Chapter 7   Part C 

  This indifferent reaction to a new theory's handling troubling old evidence is simply not what happens in real life. When we suddenly realize that a new theory/model that we have been testing can be used to solve some old problems that were previously not solvable, we are definitely impressed and definitely more inclined to believe that this new theory or model of reality is a true one.

       In other words, the critics say, Bayesianism, as a way of describing what goes on in human thinking, is obviously not adequate. It can’t account for some of the ways of thinking that we know for sure we use. We do indeed test new theories against old, puzzling evidence all of the time, and we do feel much more impressed with a new theory if it can fully account for that same puzzling, old evidence.

       

        Now the response in defense of Bayesianism is complex, but not that complex. The thing that the critics seem not to grasp is the spirit of Bayesianism. What I mean is that in the deeply Bayesian way of seeing reality and our relationship to it, everything in the human mind is metamorphosing and floating. The Bayesian picture of the mind sees us as testing, doubting, re-assessing, and re-structuring all of our mental pictures and models of reality all of the time.

       In the formula above, the term for my degree of confidence in the evidence, taking only my background assumptions as being true and thus without letting the new hypothesis into my thinking – namely, the term Pr(E/B) – is never 100%. Not even for very familiar old evidence. Nor is the term for my degree of confidence in the evidence if I include the hypothesis in my set of mental assumptions, namely the term Pr(E/H&B), ever equal to 100%. I am never perfectly certain of anything, not my background assumptions and not even any of the evidence that I may have seen – sometimes repeatedly – with my own eyes.

        

       To consider this crucial situation in which a hypothesis is used to try to explain old evidence, we need to examine closely the kinds of things that really happen in the mind of the researcher in both the situation in which the new hypothesis does successfully interpret the old evidence and the one in which it doesn’t. 

        When the hypothesis does successfully explain some old evidence, what the researcher is really considering and affirming to her satisfaction is that, in the term Pr(E/H&B), the evidence fits the hypothesis, the hypothesis fits the evidence, and the background set of assumptions can be integrated with the hypothesis in a consistent and comprehensive way. The thoughts that pass through her mind then include jubilation over the fact that if she does commit to this hypothesis, it will mean that she can be more confident that the old evidence really happened in the way that she and her fellow researchers saw it, that they were observing the evidence in the right way, and that they were not prey to some kind of mass hallucination or some form of mental lapse that might have caused them to misinterpret the old evidence situations or even misperceive them altogether. In short, she and her colleagues can feel a bit more confident that they weren’t deluded or sloppy in recording the old evidence data, a source of error that scientists know dogs all research.

               

        All of these things become even more apparent when we consider what the researcher does when she finds that a hypothesis does not successfully account for the old evidence. Rarely in scientific research does a researcher in this situation simply drop the new hypothesis. What she normally does is she examines the hypothesis, the old evidence, and even her background set of assumptions to see whether any or all of them may be adjusted, using new concepts or new calculations involving newly proposed and measured variables or different, closer observations of more replications of the old evidence, so that all of the elements in the Bayesian equation may be brought into harmony again. 

 

    When I examine the old evidence in light of the new hypothesis, if I discover that the hypothesis does successfully explain that old evidence, my confidence in the hypothesis and my confidence in that old evidence both go up. Even if, prior to this test, my confidence in that old evidence was over 98%, if the hypothesis does successfully explain that old evidence, then I feel more confident that the evidence is as I saw it because I feel more confident that I and my colleagues – even ones in the distant past – did observe that old evidence correctly and did record our observations accurately.

   The value of this successful application of the new hypothesis to the old evidence may seem to be small – perhaps it has only raised the E value in the term Pr(E/H&B) a fraction of one percent. But that is still a positive increase in the value of the whole term and therefore a kind of proof of the explicative value, rather than the predictive value, of this hypothesis. 

  Meanwhile, my degree of confidence in this new hypothesis, namely the value of the term Pr(H/E&B), as a result of the increase in my confidence in the evidence, also goes up another notch. A scientist, like all of us, finds reassurance in the feeling that comes when more of her/his perceptions, memories, and concepts about the world can be brought into a mental harmony by their being made cognitively consonant with each other. Settling a score with a stubborn bit of old data that refused to fit into any of a scientist’s models of reality is a bit like finally whipping a bully who picked on him in elementary school: not really logical, but still very satisfying.

   Normally, testing a new hypothesis involves performing an experiment which will generate new evidence. When I do the experiment, if the experiment delivers new evidence that was predicted by the hypothesis, but not by my background set of concepts, then the hypothesis, as a way of explaining the real world, seems more likely or probable to me. The new evidence “confirms” the hypothesis.

   But I may also decide to try to use a hypothesis and the theory or model that it is based on to explain some old, problematic evidence. I will be looking to see whether what the hypothesis and its base theory predict did in fact occur in the old evidence situations. If I find that the new hypothesis and the theory that it is based on – this theory that I am considering adopting as one of my background concepts and thus accepting into my regular thinking patterns – do successfully explain that problematic old evidence, what I am actually confirming is not just the hypothesis/theory, but also the consistency between the evidence, the hypothesis, and even my background set of assumptions and concepts.

    And no, it is not obvious that evidence seen with my own eyes is 100% reliable, not even if I have seen a particular phenomenon repeated many times. Neither my longest held, most familiar background concepts nor the ordinary sensory data that I see in everyday experience, are trusted that much. If they were, then I and all humans who trusted gravity and light and human anatomy would be unable to watch a good magic show without having a nervous breakdown. Elephants disappear, men float, and women get sawn in half. By pure logic, if my most basic concepts were believed at the 100% level, then either I would have to gouge my eyes out or go mad. 

   But I know, and I confidently tell my kids, that it is all a trick of some kind. And I choose, for this one night, to suspend my desire to connect all of my sense data with my set of background concepts. It is supposed to be a night of fun and wonder. If I did figure out how the trick is done, I would ruin my kids’ fun ...and my own.

  It is also worth noting here that even the idea behind “H&B” is more complex than the equation can capture. “If I integrate the hypothesis into my whole background concept set” is how this part of the term  should be read. It is an expression that is trying to capture in symbols something that is almost not capturable. This is so because the whole point of positing a hypothesis, H, is that it does not fit neatly into my background set of beliefs. It is built around a new way of seeing and comprehending reality, and therefore, it will only be integrated into my background set of concepts and beliefs if some of those old background concepts and beliefs are removed, by careful, gradual tinkering and adjusting.

  Similarly, in the term Pr(H/E&B), the “E&B” part is trying to capture something that no formula can capture. “E&B” is trying to say something like “if I take both the evidence and my set of background concepts and beliefs to be 100% reliable”. But that way of stating the “E&B” part of the term merely highlights the whole point with problematic old evidence. This evidence is problematic because I can’t make it consistent with my set of background concepts and beliefs, no matter how I push them.

   Thus, all that the whole formula really does is try to capture the general gist of human thinking and learning. It is a useful approximation, but we can’t get confident or complacent about this formula for the Bayesian model of human thinking and learning any more than we can get complacent about any of our concepts. And that thought is consistent with the spirit of Bayesianism. It tells us not to become too blindly attached to any of our concepts; any of them may have to be radically updated and revised at any time.

   In short, this whole criticism of Bayesianism — which says that the Bayesian model can’t explain why we find a fit between a hypothesis and some problematic old evidence so reassuring – this whole criticism, on closer examination, turns out to be not a fatal criticism but more like a useful tool, one that we may use to deepen and broaden our understanding of the Bayesian model of human thinking. We can hold onto the Bayesian model if we accept that all of the concepts, the thought patterns, all of the patterns of neuron firings, in the brain – hypotheses, evidence, and assumed background concepts – are forming, re-forming, aligning and re-aligning, and floating in and out of each other all of the time.

     And what of the spirit of Bayesianism? What Bayesian thinking requires of us is this willingness to float all of our concepts, even our most deeply held ones. Some are more central and we can stand on them with more confidence, more of the time. A few we may believe almost, but not quite, absolutely. But in the end, none of our concepts is irreplaceable. 

      For our species, the mind is our means of surviving. It will adapt, if it has to, to almost anything. I just choose to gamble most heavily on the concepts that I have been using to organize most of my sense data and memories most of the time.

  I use my concepts to organize both the memories already stored in my brain and the new sense data that are flooding into my brain all of the time. I keep trying to acquire more concepts, including concepts for organizing other concepts, that will enable me to utilize my memories more efficiently so that I can make better and better decisions and do more and more effective actions. In this constant restless, searching mental life of mine, I never trust anything absolutely. If I did, a simple magic show would mesmerize and paralyze me. Or reduce me to catatonia.

  When I see elephants disappear, ladies get sawn in half, and men defy gravity, and all come through their ordeals in fine shape, obviously some of my most basic and trusted concepts are being violated. But I choose to stand by my concepts in almost every such case, not because I am certain that they are perfect, but because they have been tested and found effective over so many trials and for so long that I am willing to keep gambling on them. I don’t know they are “sure things”, but they do seem like the most promising of the options that I have available to me. 

 Harry Houdini with his "disappearing" elephant, Jennie

   Life is constantly making demands on me to move and keep moving; I have to gamble on something. I go with my best horses.

   What this mental flexibility on my part means is that the critics of Bayesianism simply haven’t grasped its spirit. What Bayesianism is telling us is pretty much what Thomas Kuhn was saying in his very influential book “The Structure of Scientific Revolutions”. We are constantly adjusting all of our mental constructs to try to make our ways of dealing with reality more efficacious, all of the time. 

   And when a researcher begins to grasp a new hypothesis, and the model or theory that the hypothesis is based on, the resulting experience is like a philosophical or religious awakening – profound, all encompassing, and even life-altering. Everything changes when we accept a new model or theory because we change. In order to “get it”, we have to. We have to cut some of our old beliefs out of our familiar background set.

   And what of the shifting nature of our view of reality and the gambling spirit that is implicit in the Bayesian model? Most of our instincts, along with the general tone of all of our experience, tell us that this overall view of our world and ourselves, though it may seem scary, or perhaps for some more confident individuals, challenging ...it’s just life.

   We have now arrived at a point where we can feel confident that Bayesianism does give us a solid base on which to build further reasoning. It can answer its critics, decisively as it turns out, both the ones who attack it with real world counter-examples and the ones who attack it in the abstract world with pure logic.

     For now then, let us be content to sum up our points so far in a new chapter devoted solely to that summing up. 

Chapter 7.   Part B 

One of the ways by which a new hypothesis gets more respect among the experts who are interested in the field that the hypothesis covers is by its being able to explain old evidence that no other theories in the field have been able to explain. For example, physicists all over the world felt that the probability they assigned in their minds to Einstein’s Theory of Relativity took a huge jump upward when Einstein used the theory to account for the changes in the orbit of the planet Mercury - changes that were familiar to physicists, but that had long defied explanation by the old, familiar Newtonian model.

representation of the inner solar system 

The constant, gradual shift in that planets’ orbit had baffled astronomers for decades. This shift could not be explained by any pre-Relativity models. But Relativity Theory could describe this gradual shift and make predictions about it that were extremely accurate. Instances in other branches of Science of hypotheses that worked to explain old, anomalous phenomena could easily be listed. Kuhn, in his book, gives many of them. (1.)

  

What is wrong with Bayesianism, then, according to its critics is that it cannot explain why we do give more credence to a theory when we realize that it can be used to explain pieces of old, anomalous, evidence that had long defied explanation by the established theories in the field. When the formula given above is applied to this situation then, critics say, Pr(E/B) has to be considered to be equal to 100%, or certainty, since the evidence (E) has been accepted as having been accurately observed for a long time. After all, it has been replicated many times. 

Similarly, Pr(E/H&B) has to be thought of as being equal to 100%, for the same reasons, because the evidence has been known and has been known to have been reliably observed and recorded many times since long before we ever had this new theory to add to our stock of usable ideas. When these two quantities are put into the equation, again according to the critics, it looks like this:

Pr(H/E&B) = Pr(H/B) 

               

     This new version of the formula emerges because Pr(E/B) and  Pr(E/H&B) are now both equal to 100%, or a probability of 1, and therefore, they can be canceled out of the equation. But what the new version of the formula means is that, when I realize that this new theory or hypothesis that I am thinking about accepting and adding to my mental programming can be used to solve and explain some old and nagging problems in my field, my overall confidence in this new theory is not raised at all. The degree to which I now trust the theory - after seeing it explain some old, troubling evidence - is equal to the degree to which I trusted it before I realized that it might apply to, and explain, that same old evidence.

This is simply not what happens in real life. When we suddenly realize that a new theory/model that we have been testing can be used to solve some old problems that were previously not solvable, we are definitely impressed and definitely more inclined to believe that this new theory or model of reality is a true one.

               

    In other words, the critics say, Bayesianism, as a way of describing what goes on in human thinking, is obviously not adequate. It can’t account for some of the ways of thinking that we know for sure we use. We do indeed test new theories against old, puzzling evidence all of the time, and we do feel much more impressed with a new theory if it can fully account for that same puzzling, old evidence. 

          Notes 

1. Kuhn, Thomas; "The Structure of Scientific Revolutions"; University of Chicago; 1996

Chapter 7 

Bayesianism:  A Major Theoretical Criticism And A Response

Part A

The Bayesian way of explaining how we think about, test, and then adopt a new model of reality has been given a number of mathematical formulations. They look complicated, but they really aren’t that hard. I have chosen one of the more intuitive ones below because I intend to use it to discuss the theoretical criticism of Bayesianism which I mentioned in the last chapter.

The Bayesian model of how a human being’s thinking evolves can be broken down into a few basic components. When I, as a typical, modern human, am examining a new way of explaining what I see going on in the world, I am considering a new hypothesis, and as I try to judge just how true – and therefore how useful – a picture of the world this new hypothesis may give me, I look for ways of testing the hypothesis that will tend to show decisively one way or the other whether this new hypothesis and the model of reality that it is based on really work. What I am trying to determine is whether or not this hypothesis will help me to understand, anticipate, and respond effectively to, events in my world.

When I encounter a test situation that fits within the range of events that the hypothesis is supposed to be able to explain and make predictions about, I tend to become more convinced that the hypothesis is a true one if it does indeed enable me to make accurate predictions. (And I tend to be more likely to discard the hypothesis if the predictions that it leads me to make keep failing to be realized.) I am especially more inclined to accept the hypothesis and the model of reality that it is based on, if it enables me to make reliable predictions about the outcomes of these test situations and, if also, in the meantime, all of my other theories and models are silent or inaccurate when it comes to explaining my observations of these same test situations.

It is worth noting again here that this same process occurs in a whole nation when some citizens become convinced that a new way of doing things, that is making the rounds in their society, and is starting to push some old ways of doing those same things aside, is effective, and is a way that is better than the status quo practices for achieving the desired results. In other words, both individuals and societies as wholes do learn, grow, and change by the Bayesian model. 

In the case of the whole society, the clusters of ideas that the individual sorts through and tries to work into a more coherent system are simply replaced by clusters of citizens, arguing as members of factions within society for the way of thinking that each faction, in its turn, favors. The leaders of each faction search for reasoning and evidence to support their positions in ways that are closely analogous to the ways in which the various biases in an individual mind struggle to establish their hegemony. The difference is that the individual usually does not settle very heated internal debates by blinding his right eye with his left hand. 

In societies, factions sometimes work out their differences, reach consensus, and move on without violence. But sometimes, of course, as noted above, they seem to have to fight it out. Then violence between factions within society, or violence with the neighboring society that is perceived as being the carrier of the threatening new ideas, settles the matter. But Bayesian calculations are always in play in the minds of the participants, and these same calculations almost always eventually dictate the outcome. One side gives in and learns the new ways. The most extreme alternative, one tribe’s complete and genocidal extermination of the other, is only rarely the final outcome.

But back to the so-called theoretical flaw in the formula for Bayesian decision-making.

  

Mathematically, the Bayesian situation can be represented if we let Pr(H/B) be the degree to which we trusted the hypothesis before we observed a bit of new evidence,  Pr(E/H&B)  be the degree to which we expected the evidence if, for the sake of argument, we briefly assumed that the hypothesis was true, and Pr(E/B) be the degree to which we expected this evidence to happen based on what we knew before we ever met this hypothesis (using our old, familiar background models, in other words).

Note that these terms are not fractions in the normal algebraic sense at all. The term Pr(H/B) is called my “prior expectation” and should be read “my estimate of the probability that the hypothesis is a correct one if I base my estimate just on how well the hypothesis fits together with my whole familiar set of background assumptions about the world.” 

The term Pr(E/H&B) should be read “my estimate of the probability that the evidence will happen if I assume just for the sake of this term that my background assumptions and this new hypothesis are both true”. Finally, the term Pr(E/B) can be read “my estimate of the probability that the evidence (the event that the hypothesis predicts) will occur if I base my estimate only on my ordinary set of background assumptions and do not use the new hypothesis at all”.

The really important symbol in the equation comes now, and it is Pr(H/E&B). It stands for how much I now am inclined to believe that the hypothesis gives a correct picture of reality after I have seen this new bit of evidence, while taking as a given that the evidence is as I saw it - not a trick or illusion of some kind - and that the rest of my background beliefs are still in place.

Thus, the whole probability formula that describes this relationship can now be expressed in the following form:

Pr(H/E&B) =  Pr(E/H&B) x  Pr(H/B)

                      Pr(E/B)  

       Now this formula looks daunting, but it actually says something fairly simple. A new hypothesis that I am thinking about, and trying to understand, seems more and more likely to be correct the more that I keep encountering new evidence that the hypothesis can explain and that I can’t explain using any of the models of reality that I already have in my background stock of ideas. When I set the values of these terms, I will assume, at least for the time being, that the evidence that I saw (E) was as I saw it, not some mistake or trick or delusion, and that the rest of my background ideas/beliefs about reality (B) are valid.

               

        I tend more and more, then, to believe that a hypothesis is a true one the bigger Pr(E/H&B) gets and the smaller Pr(E/B) gets. 

        In other words, I more and more tend to believe that a new way of explaining the world is true, the more it can be used to explain the evidence that I keep encountering in this world, and the less I can explain that evidence if I don’t accept this new hypothesis into my total set of ways of explaining and understanding the world.

               

         Now all of this is beginning to seem intuitive, but once we have a formula set down it also is open to criticism and attack, and the critics of Bayesianism see a flaw in it that they think is fatal. The flaw that they point to is usually called “the problem of old evidence”. 

Chapter 6   Part C 

The mechanism of cultural evolution being described here is profoundly disturbing; it deserves some digression. What is being said here is that humans often do behave in ways that seem irrational by purely Bayesian standards. Even in our time, some adults still spank kids. Some men still bully women. Some states still execute their worst criminals. Research, as well as careful observation and analysis of these and many other patterns of behavior, suggests strongly that they don’t work; these behaviors do not achieve the results at which they aim. In fact, they reduce the chances that we will achieve those results. These behaviors and the beliefs underlying them are exactly what is meant by the term “counterproductive”. Therefore, we must ask an acute question: “Why do we do them?” Which is to say: “Why do we, as rational humans who usually operate under a Bayesian belief-building system, hold on so obstinately, in a few areas of our lives, to beliefs that cause us to act in utterly irrational ways?”

 Electric chair (used to execute criminals) 

The reply is that we do so because our culture's most profound programming institutions –  the family, the schools, the media, etc. – continue to indoctrinate us with these values so deeply that once we are adults, we refuse to examine them. Instead, our programming directs us to bristle, and then defend our "good old ways", violently if need be. When deep moral beliefs, and the morés that they foster, begin, by one mechanism or another, to die out, some folk are even willing to die out with them. If the ensuing lessons are harsh enough, and if there is a reasonable amount of available time, sometimes the larger society learns, expels the reactionaries, and then adapts. But the process of deep social change is always difficult and fraught with hazards. "The major advances in civilization are processes which all but wreck the societies in which they occur." (A.N. Whitehead) (4.)

Alfred N. Whitehead 

It is also worthwhile to say the obvious here, however politically incorrect it may be. All of our obsolete but obstinate beliefs, moral values, morés, and behavior patterns did serve useful ends and purposes at one time. For example, in some, not all, early societies, women were programmed to be submissive, first to their fathers and brothers, then to their husbands. The majority of the men in such societies were far more likely, in purely probabilistic terms, to help to nurture the children of their socially-sanctioned marriages because they were confident that the children they had with these submissive women, and that they were being asked to help to nurture, were theirs. Biologically theirs.

Raising kids is hard work. In early societies, if both parents were committed to the task, the odds were simply better that those kids would grow up, marry, have kids of their own, and go on to program into those kids the same values and roles that the parents themselves had been raised to believe in. Other, non-patriarchal societies taught other roles for men and women and other designs for the family, but they simply weren’t as prolific over the long haul. Patriarchy isn’t fair. But it makes populations.

Magazine image of the American family (1950's) 

“Traditional” beliefs about male and female roles didn’t work to make people happy. But they did give some tribes numbers and, thus, power. They are obsolete today partly because child nurturing has been taken over to a fair degree by the state (schools), partly because no society in a post-industrial, knowledge-driven economy can afford to put half of its human resources into homes for the stagnant, bored, and dejected, and partly because there are too many humans on this planet now. Population growth is no longer a keenly sought goal because it no longer brings a tribe/nation power. But more on this matter later. It is enough here to say that all of our traditional values, mores, roles, etc. once did serve useful purposes. Many of them clearly don’t anymore, even though it is like pulling back molars without anesthetic to get the reactionaries among us to admit that many of their cherished “good, old ways” are usually just in the way in today’s world.   

       

Thus, in all areas of their lives, even those that they think of as “sacred”, “traditional”, and “timeless”, humans do change their beliefs, values, and patterns of behavior in the manner suggested by Bayesianism. We do always adopt a new view of reality and the human place in it if that new view is more coherent with the facts that we are observing and experiencing, and it gets us better lives. We’ve come a long way in the West in our treatment of women and minorities. Our justice systems aren't race or gender neutral yet, but they're much better than they were even one hundred years ago.

The larger point, however, can be reiterated. For deep social change, we do undergo the Bayesian decision process, but in the most final of senses. Sometimes what has to learn to adopt new beliefs, values, and mores isn’t the individual; sometimes it is a whole community or even nation.

The evidence proving that a given, deeply imprinted, old value and the behaviors that it fosters have become counter-productive and outmoded is often not even recognized by the ones who hold and live by that value. Rather, the evidence is recognized by the nation, or even by the whole human race, when those people, their values, and their way of life don't survive as well as their competitors do. Then, they slowly adjust, by modifying some of their ways, if that is possible in the available time, or they, their values, and their ways die out altogether. The El Molo are almost gone. The Canninites, Bo, Anastazi, and Beothuk are gone. Troy and Carthage are gone. None of this is fair. It’s just over.

Demasduit (one of the last Beothuk) 

In the more gradual adjustments that some societies have managed to achieve, it sometimes also happens that sub-cultures within a society die out without the whole tribe dying out, and thus some values and beliefs in the culture die out while the larger culture itself, after sustaining major trauma and healing, adjusts and goes on.    

          

For example, Hitler and his Nazi cronies ranted until their last hour that their "race" should fight on till they all went down in a sea of blood and flames because they had shown in the most vital of arenas, namely war, that they were weaker than the Russians. He sincerely believed his Nazi philosophy. In the same era, the Japanese cabinet and High Command contained members who were willing, eager, and adamant in arguing that the Japanese people should fight on, even in the face of hopeless odds. To do anything other than to fight on was literally inconceivable to these men. (Yukio Mishima's case was a curious last gasp of Japanese imperialism.) (5.) Fortunately, people who could face reality, learn, adapt, and then thrive eventually prevailed, in both Germany and Japan.

Yukio Mishima 

For centuries, human "nature" has not enabled humans to assess value systems by our cognitive abilities, and then adopt or drop these systems in that vacillating cognitive way. In our tribalism, we are built to see the values that we grew up with as being “right” and “good”. Humans are thus designed by evolution to fight to the death to defend and promulgate what we in the West call our “way of life”. When the ways of life of two different cultures come into confrontation, for whatever set of reasons, the war that often follows then decides which is the more vigorous way of life. The stronger society/culture goes on and expands; the weaker one fades and is absorbed. Or dies out. By this mechanism of cultural evolution, the total human culture-meme pool, for eons, has grown strong. For eons, this was good for the culture-meme pool, but bad for those caught up in the confrontations.   

A culture is just the software of a nation. A culture evolves and survives or else falls behind and dies in ways that are analogous to the ways in which a genome survives or dies. If a culture-program gets good practical results over generations, its carriers multiply; if not, they don't, and then they and it fade out of our species’ total culture pool. What was sad but true for centuries was that a society's fitness to survive was sometimes tested by famine or epidemic disease or natural disaster, but more often it was tested by war with one of its neighbors. For centuries, when a tribe, guided by its culture, was no longer vigorous enough to hold its territory against invasions by neighboring tribes, it fought and lost. Its men were killed, its women and children were carried off by the enemy; its way of life dwindled and was absorbed, or in some cases, died out altogether. Thus Joshua smote Hazor, the ancient Greeks crushed Troy, and the Romans crushed Carthage. Out of existence. The examples could go on. 

ruins of Carthage in modern Tunisia 

  

   So was Hitler right? Is war inevitable or even desirable? It depends. The question that we are left with is whether we will ever rise above our present, mainly war-driven system of cultural evolution. By reason or suffering or both, we are going to have to arrive at a new process for evolving culturally, which means continually adopting, in a timely way, constantly updated, more efficient values and the behavior patterns that are fostered by, and, therefore attached to, these values.

Changes in our environment always come. Some of them we even cause. We can cushion our way of life against them for a while, but over time, reality demands that we either evolve or die out.

But for now, I will leave the war digression and the socio-cultural mechanism of human evolution to be more thoroughly discussed in later chapters.

For now then, let’s settle for saying that this point that Bayesianism’s critics make about the way in which some areas of human behavior do not seem to be based on Bayesian types of calculations only seems at first to be an apt criticism. If we study the matter more deeply, we see that there are reasons for our apparently un-Bayesian attachments to some of our most counter-productive values and morés. They are just crude, upsetting, warmongering reasons -- design flaws that we are going to have to deal with because they have long since fallen out of touch with the physical reality that surrounds us (a physical reality that, in large part, we have created) and with the dilemma in which we find ourselves. "Mankind must put an end to war or war will put an end to mankind." (John Kennedy) (6.)

John F. Kennedy, 35th president of the U.S. 

Most importantly, for the purposes of this essay, we can see that the Bayesian model of human thinking still holds. Deeply held beliefs, values, and morés do get changed – sometimes even in whole nations – by the Bayesian mechanism. We do get rid of old beliefs and adopt new ones when the old ones are no longer enabling us to handle the physical and social realities that we are seeing before us. If the father and mother can’t drop ineffectual old beliefs and adopt new ones, then the son and daughter must, or else the tribe dies out altogether. In other words, we humans do learn, change, and adapt, both as individuals and as whole nations. Individuals can learn and change on most ordinary, practical matters, but by and large they won’t willingly alter their deepest, most general, core beliefs - especially the ones called “moral values”. But these do get changed when a whole nation gets taught a very large, painful lesson and then re-configures. And once in a long while, a stubborn culture dies out altogether. 

   

But more of these matters in later chapters. The first big criticism of Bayesianism has been dealt with. The Bayesian model, when it is applied at the tribal level of human behavior, can fully account for the apparently un-Bayesian behaviors of individuals. We now must move on to the second big criticism of Bayesianism, the theoretical one.

And perhaps this is the point at which I should also say that the next chapter is fairly technical, and it isn’t essential to my case. If you want to skip a chapter, my next chapter is one that you can skip and still not lose the train of thought leading to the conclusion of the whole argument.

Notes 

4. http://en.wikiquote.org/wiki/Alfred_North_Whitehead

5. http://en.wikipedia.org/wiki/Yukio_Mishima

6. www.jfklibrary.org/Asset-Viewer/DOPIN64xJUGRKgdHJ9NfgQ.aspx