Chapter 8.                     Part C 

All basic concepts are illusions in the sense that they morph constantly 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, and 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.  Scientists tell lies. 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 to be considered complete. Real life keeps cropping up with situations that leave us and our thinking systems stranded in bafflement and ambivalence. Therefore, we learn, we improvise, we evolve.

There is a reality, material, sustained, and independent of whether I am perceiving it or not. It will go on after I am gone. I am confident of that – at the 99.99 percent level. But it is too fluid and dynamic for our minds ever to get a 100% reliable handle on it, i.e. a perfect program for responding effectively to 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.

Chapter 8.                                      Part B 

At bottom, the shifting nature of reality defies all categories, even "here", "now", and "stuff". (Matter, as Einstein showed, is really only a form of energy.) A mind (consciousness/sanity) is built up on concepts, some of them acquired from our genetics (babies fear heights and snakes, but grasp basic language concepts), 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 from 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 noise. A mind is any program that 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 (i.e. a human mind) really is deconstructed, as sometimes happens when a person's perceptions are distorted by drugs or sensory deprivation or mental illness, so that her/his programming becomes incoherent, some of his interactions with reality get beyond his ability to sort, and respond to, real world events. Then he has a "nervous breakdown". Real deconstruction of a human’s mindset, i.e. the set of programs that a person uses to organize 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 the borders of 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. She would have to continue until she had deconstructed her own mind as part of the full text 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 as long as they are functional, be that for seconds or centuries.

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 makes, and contains, systems of symbols for labeling and organizing its thoughts: the symbol systems cannot, in principle, contain it.

            

                               Tianhe 2  (world's most powerful computer 2013) 

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. The Bayesian model of knowing contains some difficult parts, but it does not stumble 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. But it does require of us that we 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 fruit, some of these 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. We learn them from our parents. We use them because they're useful. Even our ways of stating what we think are the laws of the universe are constantly being updated.

Once apples did not exist on this planet. Nor did the organic chemicals that make sweetness. Even "round" is a constructed concept that exists only in the human mind, only on a provisional basis, 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 that he fed his kids, and they survived to teach the concepts used in counting to their kids.

Chapter 7.                                      Part F 

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 of many concepts.

  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 tinker with them or 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 faster and better decisions and perform 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. 

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

   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's be content to sum up our points in a new chapter devoted solely to that summing up. 

          Notes 

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

Chapter 7.                                   Part E

A human mind experiences much cognitive dissonnance when it keeps observing evidence that does not fit any of its mental models. The person who is attempting to explain a bit of observed evidence that is inconsistent with his worldview, i.e. the person trying to hang on to on his background beliefs and to shut out the new theory his colleagues are talking about, keeps trying to tell himself that the observations of this evidence can't be correct. Some systemic error must be leading those other researchers to keep thinking they have observed (E), but they must be wrong. (E) is not what they say it is. "That can't be right," he says.

In the meantime, his more subversive colleague down the hall is arguing, even it is only in her own head, "I know what I saw. I know how careful I've been. (E) is right, therefore, the probability of (H), at least in my mind, has just grown hugely. And it's such a relief to see a way out of all the cognitive dissonnance I have been experiencing for the last few months. I get it now. Wow, does this feel good!"   

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 that significant logically, 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.

 

                       Harry Houdini with his "vanishing" elephant, Jenni

    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 harmonize 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.

Chapter 7.                            Part D 

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, 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, i.e. 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.

                          Chapter 7.                      Part C          

         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”.

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 consider adding 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. 

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.