Thursday, 9 March 2023

Probability, Time, and Bad Science Part 2

In this week's post, I shall briefly discuss essay writing in general and then move on to slightly amending various ideas I presented in the previous essay. This essay is a companion piece to the previous essay and will make a lot more sense if you have read the other one. 

When most people think of an essay, they imagine the kind of essays people write in high school or university. You present a thesis in the introductory paragraph, usually in response to a question set by the teacher or lecturer, and provide an overview of the shape of the essay. Each successive paragraph consists of a thesis statement and various supporting sentences, perhaps for instance an example and then a sentence interpreting the example and relating it back to the thesis statement. The concluding paragraph summarises the argument and, although it should not give any new information, may suggest directions for future study. Students often have trouble finding ways to make the conclusion different from the introduction – it is tempting to write the same thing again in the same words.  Of course, fiction does not follow these stylistic and structural rules – and neither does serious non-fictional writing such as high quality popular science books, histories, biographies, and works of philosophy. TS Eliot advised budding poets to learn the traditional rules of poetry, such as rhyme and metre, even if they intended to throw them away later and write free verse instead. In the same way, capable writers may have learned the bog standard way of writing an essay but have, in a sense, outgrown it. Importantly, the original essay writer, Montaigne, did not follow such rules. The word essay comes from the French 'essai' which means the result of an attempt. Montaigne wrote 107 essays between 1570 and 1592. Sometimes Montaigne was didactic but often his essays exhibited a kind of flow of ideas, a 'stream of consciousness', were explorations rather than polemics. He wasn't simply trying to defend a position; his essays were enjoyable because they were aesthetically pleasing. Similarly, the essays I write in this blog seek to be part of this tradition, are often explorations. The post "Identity Politics", which I wrote a long time ago, perhaps best embodies this way of writing an essay. I look back on this post very fondly. It is this type of essay that I aspire to write.

However even a Montaigne-inspired essay requires a kind of underlying structure, a structure of ideas. The previous post was not always completely clear. It dealt with a number of different topics: probability (with a discussion of the Sleeping Beauty problem), determinism and quantum physics, governmental responses to crises, and the bad science surrounding schizophrenia focussing specifically on the supposed empirical finding that people diagnosed schizophrenic are cognitively impaired. These topics were all linked tenuously with each other but these links may have not been apparent to the reader – it may have seemed that I was exhibiting thought disorder or that the essay was a kind of 'word-salad', an impression no doubt  exacerbated by my use of words like 'Foucauldian', a word that makes sense if you are familiar with the work of Michel Foucault but otherwise may strike a reader as meaningless gibberish. (I shall discuss Foucault a little later.) For instance, I described the idea of intelligence lying on bell curves for both normal people and people diagnosed schizophrenic before I discussed how intelligence might be measured when it would have been clearer if I had presented these two ideas in the reverse order. I often digressed, in the last half of the essay, by telling stories about my own experiences and, although these anecdotes were generally at least tenuously connected with the points I was making, it may have been difficult for readers to see the connections. How can we tell the difference between the ramblings and ravings of a madman and a passage from Finnegan's Wake? This, of course, relates to the question of how we can diagnose thought disorder at all. In this essay, I intend to discuss some of the ideas I presented in the previous essay and make some of them clearer but I shall not attempt to make them all fit neatly under one thesis or into one structure. It will be a kind of miscellany. If this means that this essay will also be disjointed, so be it.

I shall begin by returning to The Sleeping Beauty Problem that I discussed in the previous post. The muddy thinking that informed my last essay led me to make a mistake – I said that if the coin lands heads Sleeping Beauty will be awoken and interviewed on Tuesday only. In the original essay by Adam Elga and the Wikipedia entry, if heads comes up, she will be interviewed on Monday only. However, the mistake I made makes no difference to my argument. It doesn't matter whether the Heads awakening occurs on the Monday or the Tuesday; the only relevant piece of information is that a tails result means two awakenings and a heads result only one. The difference is important to Elga's argument but not important to mine. In the previous post I said that Elga's argument seemed to involve some kind of sophistry or sleight-of-hand but said that discussing this would take me too far afield. In order to properly defend my halver position, I need to spell out what is wrong with Elga's argument.

One of the vital elements of the Sleeping Beauty Problem, as presented by Veritasium and Wikipedia, is that when Sleeping Beauty is awoken and interviewed, she knows neither which day it is nor whether the coin came up heads or tails before the interview. (Obviously she can't know that it came up heads or tails because the whole point of the problem is that she is being asked to assess her credence that it came up heads.) Elga however does not spell this detail out when introducing the Sleeping Beauty Problem in his essay. Later in his argument he explicitly presents the situation in which on being first awakened on Tuesday, she is told that the coin came up tails. Elga uses this to argue that the probability that it came up tails and it is Monday is equal to the probability that it came up tails and it is Tuesday, something that is quite true. The mistake Elga is making here is that the whole point of his argument is that she is supposed to make her estimate having learned nothing new upon being awoken and, in this situation, she is being given new information. Prior to being told that the coin came up tails, she should, as I argued in the previous post, estimate the probability of the coin coming up heads at 1/2; having been told that it came up tails, she should change her estimate. Quite simply, she should estimate the probability of it having come up tails as 1 and the probability that it came up heads as being zero. Furthermore she should estimate the probability that it is Monday as being 1/2 and Tuesday as being 1/2. Elga then presents a different situation. Sleeping Beauty is awoken and told that it is Monday. Again she is being given new information, but this information is different than the information she received in the first situation. This new information does not affect her estimate of the probability that the coin came up heads or will come up heads – it was 1/2 before she was told that it is Monday and remains 1/2 after she is told. However, she has to revise her estimate of the probability that it is tails and Monday or tails and Tuesday. Prior to being told that it is Monday, she would estimate the probability that it is tails and Monday at 1/4 and tails and Tuesday at 1/4. When she is told that it is Monday, she should change her estimate. The probability that it is (or will be) tails and that it is Monday is now 1/2 and the probability that it is tails and Tuesday is zero. In the two situations Elga discusses, Sleeping Beauty is provided with new information that is different in each case and so assesses the probabilities differently – we can't equate the two situations, as Elga does, and then conclude, as Elga concludes, that the heads scenario, the Monday-tails scenario and the Tuesday-tails scenario all have equal probability. Elga has shown that the probability of it being Monday given a tails result is equal to the probability that it is Tuesday given a tails result. I agree. Both have a probability of 1/2. Elga then goes on to show that the probability of the coin coming up heads given that it is Monday is equal to the probability of it coming tails given that it is Monday. Again I agree. Both have a probability of 1/2. The problem is that Elga is trying to claim that the probability of Monday-tails is equal to the probability of Tuesday-tails which is equal to the probability of Tuesday-heads and because these three outcomes are mutually exclusive and exhaustive, the three possibilities add up to 1, meaning that the probability of a heads result is actually 1/3. In fact, what he has shown is that the probability of it being Monday given that the coin came up tails is equal to the probability that the coin has or will come up tails given that it is Monday which is equal to the probability that the coin has or will come up heads given that it is Monday. These three outcomes are not mutually exclusive and so do not have to add up to 1. According to my arithmetic, they add up to 1.5.

There is a second argument that we could use for the halver position against the prevailing thirder position. We could employ Bayes' theorem. Let us presume, as is generally believed, that Sleeping Beauty, when woken and interviewed, know neither the day nor the result of the coin toss. We wish to find the probability that it came up heads given the fact that it is either Monday or Tuesday. This probability can be found by multiplying the probability that it is either Monday or Tuesday given that the coin came up heads by the prior probability that any coin will come up heads, all divided by the probability that it is either Monday or Tuesday. This is 1 multiplied by 1/2 divided by 1. Or, to solve this complicated equation, 1/2.

This discussion of the Sleeping Beauty problem was quite dense but this essay will get easier from now on.

In the previous post, I discussed medical studies that could be used to determine if someone will have a heart attack this year, and I wish to expand on this example and make it a little clearer. I suspect some of my readers may have found it confusing. In doing so, I will make a really interesting epistemological suggestion related to causation. In the previous post, I made an assumption that the reader of this blog is American and then made the extraordinary claim that he or she has a 0.24% probability of having a heart attack this year. I arrived at this probability simply by dividing the number of Americans who had a heart attack last year by the total number of Americans. This estimate is based solely on my assumption that you are American; it assumes that I have no other information about you. If I know whether you're obese or not, I can revise the estimate. If you're obese I can increase the estimate and if you're not, I can decrease it. I can change the estimate because I have more information. The presumption that obese people are more likely to have heart attacks that those who are not is based on I think fairly well established medical science. How do we know this? Using Bayes' theorem, we can make estimates based on cohorts – we can compare the incidence of myocardial infarctions among the obese population with the incidence among the non-obese. However being obese is not a necessary condition for having a heart attack (thin people can still have heart attacks), nor is it a sufficient condition (some obese people don't have heart attacks).  Rather obesity increases the likelihood of a heart attack by some significant percentage. 'Significance' here has a technical sense. A result is considered significant if the probablity of it occurring simply by pure chance is less than 5% (I am here referring to Wikipedia). However, chance always has an effect on the numbers: even if the p-value is less that 0.05, there is always uncertainty in the probability estimate. The bigger the sample the more certainty we have; conversely the uncertainty and the p-value get bigger as the number of people in the sample gets smaller. In the previous essay, I suggested that we could improve our probability estimates by taking more and more information into account, make ever better estimates by making smaller and smaller groups that resemble each other in more ways. But there seems to be a paradox here because the smaller the group the higher the uncertainty and p-value.

And now for the interesting epistemological suggestion. In talking about chance, statisticians and all the scientists that rely on statistics (most of them) seem to be importing the idea of objective uncertainty into their fields from quantum physics.The notion of 'random chance' is instrumental to such statistical studies. If the universe is deterministic, however, any event, such as for instance a heart attack, is completely dictated by its causes – there is no such thing as pure chance. What we should do is talk of factors and claim that the causes of an event are some set of factors.  I would like suggest that we can distinguish between three different types of factor: measured factors, unmeasured factors, and unmeasurable factors. Studies in medicine, sociology, psychology, and so on try to find correlations between different factors. For instance, we can measure a factor such as obesity and also measure the factor of heart attacks and look for a correlation. Consider, now, the scenario in which an obese man is taking an experimental drug, has a heart attack, and ends up in hospital where he dies. Suppose that researchers are investigating the causal link between obesity and heart attacks and they never find out that he was taking an experimental drug. His heart attack will contribute to the finding that obesity is a risk-factor for heart attacks even if this man's heart attack wasn't caused by his obesity at all. The fact that he was taking an experimental drug is an unmeasured factor. (Of course, even if the researchers knew that he was taking an experimental drug, they couldn't be sure that the drug caused the heart attack unless they possessed a really persuasive story linking the drug to the heart attack. Without such a story, they would need to put, say, a thousand people on the drug and find out how many had heart attacks.) We also have unmeasurable factors such as, for instance, the butterfly that flaps its wings over Brazil, contributing to a storm in Chicago, that contributes to a person getting a cold, that then contributes to him or her having a heart attack. The reason that I cannot predict whether a coin you are about to toss will land heads or tails is that to do so I would need to know in advance the precise angular and linear momentum of the coin and all the distances involved, and these are all practically unmeasurable. I would like to suggest that what we call chance is the cumulative effect of all these unmeasured and unmeasurable factors. The reason large studies tend to be more accurate than smaller studies is that in the larger studies the unmeasured factors and unmeasurable factors tend to cancel out; in smaller studies, unmeasured factors and unmeasurable factors play a greater role. (I am not sure if this is quite the right way to explain why larger studies are more accurate than smaller studies, but this idea, even if wrong, might pave the way for better explanations.) However, if we were really good at determining the relevant factors, if empirical science was ideal, I think we could indeed go on reducing the size of groups, picking out more and more factors, and ever improving our probability estimates. Of course we could never arrive at certainty about whether or not a specific person will have a heart attack this year because of the influence of unmeasurable factors. It might even be that unmeasurable factors play a large role in determining whether a person has a heart attack and so we might never arrive at a probability higher than, to pick a number at random, 50%.

This approach has relevance to psychiatry. Psychiatrists are doctors and so, when trying to determine the causes of a condition like schizophrenia, which they consider a disease, they look for medical explanations, somatic explanations. Fifteen years ago they believed that schizophrenia was caused by a schizophrenia gene but today know that no such schizophrenia gene exists. They have posited that a risk-factor for schizophrenia is a difficult child-birth. Another proposed risk-factor is having parents who are older than normal although curiously having young parents is also a risk-factor. Cannabis use is proposed as a risk-factor. In my view, I had a vulnerability to psychosis caused by my parents' divorce when I was seven and the psychotic episode I suffered in 2007 was triggered by the stress of working at bFM. Other patients I have met also attribute their 'illness' to adverse experiences in childhood and later life. It seems likely that adverse experiences are major factors in bringing about mental illness, something that seems obvious. Psychiatrists don't want to believe, however, that 'schizophrenia' is the result of traumatic experiences because that would mean that their medical paradigm is wrong and those psychologists who resist this paradigm, like John Read, are right. I suspect that medical researchers have, until quite recently, simply never carried out any studies looking for a correlation between adverse childhood experiences and later psychosis because they didn't want to find out it was true. It would threaten the whole of psychiatry. Adverse experiences were, until recently, an unmeasured factor. When rereading the Wikipedia article on schizophrenia for the previous essay, I learned that adverse childhood experiences are indeed now considered a risk-factor and that this is a very recent development in the science or discourse surrounding schizophrenia. It should have been obvious many decades ago. A recognition that adverse experiences can cause psychosis requires a change in practice. What we need now is a change in the form of treatment. Rather than simply prescribing drugs, psychiatrists will need to ask patients about their experiences and help them understand and come to terms with their experiences: they will have to stop just being doctors and partly take on the role of psychologists. Of course, in saying that adverse childhood experiences are a major factor in later mental illness, I am not suggesting that it is a necessary cause (not everyone diagnosed schizophrenic has experienced adversity in childhood) nor a sufficient condition (not everyone who has adverse childhood experience later goes on to be diagnosed schizophrenic). Every person diagnosed schizophrenic is different from every other person diagnosed schizophrenic. But I would strongly suspect that adverse experiences are indeed a major contributing factor, a factor that has only recently gone from being unmeasured to being, if perhaps only in small studies, measured.

In the next part of the previous essay, I discussed quantum physics. For the sake of honesty, I should say that I am not an expert on physics. I understand Special Relativity but don't really understand General Relativity, although I understand some of the predicted effects of General Relativity such as light bending around stars and clocks slowing down when in the presence of strong gravitational fields. If you were to ask me what the stress-energy tensor is I would be unable to tell you. I do not understand the details behind Bell's Theorem although I have made the effort to. I do understand at least some of its implications. I can't get my head around the long and complicated equation that is the Standard Model. Given my lack of proficiency in this field, it may seem arrogant for me to argue in favour of a non-local hidden variable interpretation of quantum physics. My argument is not physics-based but philosophical. It runs as follows. 

1. The universe is deterministic.

2. What we call chance, randomness, is the effect of unmeasured and unmeasurable factors.

3. Quantum physics presumes that the momenta and positions of particles are to some extent necessarily uncertain, random.

4. Quantum physics provides the best possible picture of the behaviour of particles. (This idea I believe arose with the the Copenhagen interpretation.)

Therefore – the positions and momenta necessarily depend on unmeasurable factors, hidden variables. These factors or variables are in principle unknowable, at least to the scientific method.

Thus we have an argument in favour of hidden variable theories derived from a simple set of non-mathematical premises. I understand from what I have read that if some hidden variable theory is true, it must be non-local. In fact, non-locality is now generally accepted whether we accept or reject hidden-variable theories – it follows from quantum entanglement, something that has now been experimentally shown to be a real phenomena. The only way to reject non-locality is to accept something known as superdeterminism. I will leave it to the reader to find out about this theory from sources online. Suffice it to say, here, that it is a kind of Fatalism and, to my mind, also a hidden variable theory.

In the next part of the previous essay, I considered the discourse surrounding schizophrenia and the various symptoms that are supposedly associated with it. I used the term 'Foucauldian'. I thought I could get away with this because in the past I have talked about Michel Foucault quite a bit. Perhaps I should pay readers who are unfamiliar with Foucault the courtesy of sketching out the meaning of this term as I understand it. Michel Foucault was a kind of philosopher-historian who looked at the history of concepts in terms of the discourses in which they played a part. He looked for instance at the history of the terms 'madness' and 'homosexuality' as well as diving into discourses associated with medical clinics and penitentiaries. Sometimes people associate Foucault solely with the idea that all relations between people are power relations – this is the way Jordan Peterson for instance characterises his work. What interests me about Foucault however is not power, but the implication in his work that discourses in a sense create their subjects, that as the discourse surrounding 'madness' for instance changes, so does 'madness' itself. Foucault was a kind of Nominalist – he thought abstract ideas like 'schizophrenia' and 'homosexuality' did not exist independently of the systems of knowledge we create in order to describe them. Foucault was a Postmodernist and lent support to the Postmodern claim that there is no such thing as objective truth and the claim that reality is socially constructed. For instance at least one Postmodernist, although not Foucault, has claimed that tuberculosis did not exist before it was discovered. I wish briefly to discuss Postmodernism in relation to what is current fashionable in intellectual and philosophical disciplines. I believe that Postmodernism went out of fashion about twenty years ago and has been succeeded by a new intellectual era, a new vogue, which has not yet been named. We could call it the New Scientism. What are the features of the New Scientism? One strand is the psychological research carried out by Amos Tversky and Daniel Kahneman and others inspired by them. Tversky and Kahneman pretty much invented the idea of cognitive bias. The notion of cognitive bias presumes, contrary to Postmodernism, that there is an objective truth – an objective truth that people can systematically deviate from. Importantly Tversky and Kahneman were not armchair philosophers but based their theories on empirical experiments and studies of real people. (This does not mean their experiments have held up under replication.) A second strand is the popularity of evolutionary psychology. I associate the New Scientism in particular with Steven Pinker. What unites the New Scientism is an optimistic faith that science and the scientific method can explain human nature. At the same time as the New Scientism came into vogue we've seen the emergence of Identity Politics. Jordan Peterson likes to call the Woke Left "Postmodern neo-Marxists" but advocates of Identity Politics are not really Postmodernists. They are Essentialists. There are Black people and white people, gay people and straight people, men who are born into female bodies and women who are born into male bodies, and so on. Foucault and a later Postmodernist, Judith Butler, rejected such Essentialism; Essentialism such as this is antithetical to Postmodernism. Identity Politics, like the New Scientism, shows that the culture has moved on from Postmodernism to something else. It seems to me that the New Scientism will perish even before it has been officially named. I think the missing heritability problem and the replication crisis, developments I discussed in the post "Threading the Needle", in addition to perceived failings of institutions during the Covid 19 crisis (despite the apparent success of vaccines) will lead people to be more sceptical of supposed scientific findings. I have no idea what will succeed the New Scientism or what, if anything, will succeed Identity Politics.

In the previous essay I discussed the apparent finding that people diagnosed schizophrenic are more likely to be cognitively impaired than ordinary people. I have thought of another reason how this research might be flawed. Something that should have come through strongly when I talk about my life is that if schizophrenia is anything at all, it is an episodic condition. This was the most important point I was trying to make in the film I wrote way back in 2012, The Hounds of Heaven (which you can find on the Internet). The idea that 'schizophrenia' is an episodic condition seems so obvious to me that I seldom stress it. However psychiatrists tend to treat the symptoms associated with schizophrenia as continuous, persistent. Let us consider now the science around intelligence. A core assumption behind IQ tests is that IQ is stable: whether I give you an IQ test today or in a year's time, it is presumed you will get almost the same score. The common-sense problem with this is that context matters. If you had a sleepless night or suffered an emotional shock just before sitting the test you are likely to do worse than if you are, say, on Ritalin. Similarly, a person diagnosed schizophrenic will do worse if she is made to sit an IQ test when she is in the middle of a psychotic episode than when she is in remission or has recovered. I recall in October or November 2009 I was being assailed by 'voices' all the time – if I'd been tasked with an IQ test then I would have probably done badly because I wouldn't have been able to concentrate. In late 2007, I spent time at an upmarket Respite facility and decided, while I was there, that all the other patients present were secretly geniuses. I played chess against one and decided he was playing to lose. I won in the end but felt like I'd lost. If someone had tested my intelligence back then and asked me, "Is a banana a fruit?" I would probably have suspected a trick question and answered "No". It may be that the finding that schizophrenics are cognitively impaired partly results from surveying patients when they are ill rather than when they are well. 

Why is intelligence important to me? Perhaps it is important to everyone. I might though give some reasons from my life history that might account for it. I attended Auckland Grammar School. This terrible institution streamed its students. The brightest were in the A stream while the least well performing were in, I think, M. After every term, we would receive reports telling us not only our percentage grades but where we sat in the class, for every subject and in the class as a whole. After every term, especially in the first couple of years, the least well performing boys (it was an all boys' school) would get shuffled down a class or two and the top performing boys would go up. After the end of term exams, we would all go round asking each other, "What's your aggregate?" trying to establish a pecking order. (One's aggregate was one's score out of 600 for the six subjects combined.) This system instilled in many of us a sense that one should measure one's self esteem quantitatively compared to everyone else. It was a great system for the students who spent five years in A. They would come out the other side with enormous self-confidence and perhaps superiority complexes. I imagine the effects were less positive for the students in M. My elder brother went through in A except for his last year. In Third Form, when I first entered Grammar, I was put in B. The English assessment for the first term consisted of an exam worth eighty percent and a journal worth twenty. I topped the school in the exam but got zero for the journal because I didn't hand it in. I was relegated to C where I spent the remainder of my high school days. Somehow I think I formed the belief that I was very clever but that it wasn't being recognised. (Of course, I never did any homework ever which may have been part of the problem.) Concerns about my intelligence didn't really preoccupy me when I first went to university and I failed some papers because I often didn't go to lectures. After completing my BA, for which I received fairly average grades, I did an MA in English and, in my second year and next semester received, I think, straight As and A+s. In 2004, I sat the GRE exam as I described in the previous essay. After that, I often entertained the belief (or delusion) that I was very intelligent while fending off doubts that I just might not be as clever as the people around me. Worries about relative intelligence didn't really feature strongly during my episodes in 2007 and 2009 although in 2007 I did sometimes think that people around me, such as my psychiatrist Antony Fernando, might be geniuses because they presumably knew the cause of homosexuality and I didn't. I might have had delusions of grandeur later on (I used to have conversations with Barack Obama in my head in early 2010) but I didn't deludedly think I was a genius. Rather I thought I had some kind of messianic role. Later in 2010, after I had recovered, I started attending a weekly pub quiz, which I still go to, at which I made some good friends, a ritual that has become very important to me. Our team usually finished in the middle of the pack. I can remember sending a text to Jess in 2011 describing pub quiz as "my weekly lesson in humility".

Our pub quiz fortunes changed dramatically about two years ago. The husband of one of my teammates, a chap also called Andrew, started attending. I think I can talk about Andrew because nothing I say will be critical. Andrew has won Mastermind twice and Sale of the Century once. He won half a million dollars on the Australian version of Who Wants To Be A Millionaire. Andrew is a librarian and spends all his time inhaling books and blogposts and online news sites. When I first met him, many years ago, I thought he might be a kind of idiot savant with an eidetic memory; I now realise that, although very shy, he is a genuine genius. When a question comes up on screen at pub quiz, he often answers it before I've finished reading it. Since Andrew started coming, we almost always win. This is a good thing but there is a downside. Andrew does make me feel a little stupid. This is not his fault. Rather, because he is so smart and knows so much, he has trouble gauging how smart other people are. His intellect means that he is on an island almost entirely by himself. I am the scribe for the team and, because I often misspell words, he has taken to spelling everything out. A little while ago, the answer to a question was George Nepia – I had heard of George Nepia, a famous Maori All Black who played in the 1920s, but probably wouldn't have been able to answer the question without help. Andrew spelt out the name. I said, "I know how to spell Nepia because it's a Maori name and Maori is always spelt phonetically."

This all relates to this blog and to my life at the moment. In order to write posts about philosophy or physics or psychiatric discourse, I need to feel that what I am writing is interesting and important. And so I need to buttress my self-confidence by telling myself that I am clever enough to say interesting and important things about these subjects. When I wrote The Hounds of Heaven in 2012, I used to imagine Jess and I onstage receiving an Oscar for Best Original Screenplay. (I now know that while it may have been a good story, The Hounds of Heaven might not have made a particularly good film.) I am currently in my second year of a Masters in Philosophy – I went back to university because I thought I might have something interesting and important to say about the philosophical underpinnings of literary interpretation. But I am often plagued by doubts. It is hard when one is a mature student going back to university after doing nothing for ten years. And I have no idea who could supervise the doctoral thesis I want to write. The other way the question of whether I am smart or not relates back to this blog is that, because I don't know who my audience is, a little like Andrew I can't gauge what a typical reader knows and what he or she doesn't. Do I need to spell out the meaning of the word Foucauldian? Can I assume my readers have a passing familiarity with the Schrodinger equation? When I wrote The Hounds of Heaven, my aim was to provide a picture of a condition that I had realised the general public didn't have a clue about. I realise now that although the psychiatric description of schizophrenia is wrong, the general public doesn't even know the psychiatric description. 

At the beginning of this essay I referenced Montaigne. This essay is not of the same quality as one of his. It is a bit disjointed because it is a companion piece to the previous post. However I hope that some of the many ideas I have thrown out land. I shall try to write a more cohesive essay about something or another soon.

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