Tuesday, 16 January 2024

Religiosity and Scientism

For several weeks recently, often when I walked at night past the Edinburgh Castle, a tavern on Symonds Street, I encountered a woman engaged in vigorous conversation with invisible companions. I could only catch snippets of what she was saying but on one occasion she mentioned something about "five hundred civilian casualties." Not long after I first met her, I asked her, "Who are you talking to?" She replied, "I'm just talking to the archangel Gabriel". I asked her, "Can you see him?" She said, "Sometimes." A little while later, when I encountered her again, I asked her, "Are you talking with the archangel Gabriel again?" She replied,"No, I'm talking to one of his friends." My feeling is that this woman, for reasons of course unknown to me, was suffering a rather benign kind of psychotic episode. I suspect that she believed she was helping to coordinate with the archangel Gabriel and his friends some sort of massive humanitarian operation. The fact that this was occurring during the ongoing war in Gaza suggests to me that this may have influenced her delusions. Of course this is just speculation. I decided that this woman, who told me she lived at the pub and wasn't badly dressed or in any other way manifesting any of the signs we associate with homelessness, might benefit from talking to a corporeal being, that I could be of some help. I thought because I understand psychosis it might be therapeutic for her to have someone like me to share her inner world with. I certainly didn't want her to end up in hospital or on drugs. So far she has been reluctant. When I suggested to her that we have a drink and a chat, I suspect she might have taken it the wrong way. But, at the time, she said something like, "Maybe later. I"m just helping load stuff on an airplane." 

I find it interesting that when I tell friends and family that I regularly bump into a woman who believes that she is conversation with and presumably assisting the archangel Gabriel, often they say, "She must have had a religious upbringing." When I told a friend about my suspicion that this woman believes she is assisting in some kind of enormous humanitarian operation, my friend conjectured that this woman might have at one time worked in the army. The problem here, of course, is that ordinary people simply don't understand psychosis. 

This little anecdote is a doorway to the topics I wish to discuss in tonight's post. One purpose of this essay is to discuss religion and specifically the relation between religion and morality – I promised to do this in the previous post. Often psychosis is associated with religiosity and in a country like New Zealand, where most people are secular, there is a widespread aversion towards the religious and religiosity generally, sometimes even a kind of contempt and sometimes even fear. This seems to me a kind of bigotry, a bigotry born of an inability to understand that other people are others. A second purpose of this essay is to show how religious ideas can take hold during psychosis and how they can be interpreted in relation to psychosis. In the last part of the essay I shall turn to a quite different topic and shall discuss physics again – I shall present an argument which I think shows that the Many Worlds interpretation of quantum physics is incoherent, a different argument to the one I made in "Quantum Physics for Dummies". I shall also discuss a central plank of the scientific method: statistical independence.

Now, in holding forth about religion, I am not pretending to be an expert like Bart Ehrman or a lecturer in Philosophy of Religion who taught me early last year, Timothy Mulgan. But I am not a total slouch either. Back around 2016, as a result of ongoing emotional distress, I considered various religious systems with some thought towards adopting one. I thought I could find some hope, "the thing with feathers" in Emily Dickinson's evocative words, in some religious framework, some kind of escape hatch. I seriously considered Gnosticism and would today be quite happy if people called me a Gnostic. The difficulty I faced was that I didn't believe in free will; this led me to also toy with Calvinist ideas. According to Calvin, some people are born predestined for heaven and others for hell; those who are destined for heaven are subject to "irresistible grace" and the process that leads a person to spiritual rebirth and eventual salvation involves a kind of "regeneration" which, according to some writers, can be spiritual torment, the dismantling and reassembling of a person's self somewhat analogous to the more modern notion of ego-death. Today, in 2024, I would reject the bleakness of the Calvinist vision in which everyone is wicked and sinful, in a state of 'total depravity', except for an elect few picked for salvation by God before they were born. A God who enjoys the suffering of sinners and consigns almost all of humanity to the sinner category is not a God I can believe in. This brings me to my first topic – the possibility of religion without morality, without a heaven or hell.

This is not really so hard to imagine. Let's start by considering the ancient Greeks. It may be that people today don't consider Greek mythology a religion but of course it should be thought of as such. The Greeks, as most people know, were polytheists. The chief god was Zeus but there were a whole raft of other gods like Athena, the goddess of wisdom, Mars, the god of war, Artemis, the goddess of the moon and hunting, Apollo, the god of the sun and the arts, Poseidon, the god of the sea, and so on. There were semi-divine beings like the Muses and the Fates, sometimes called the Furies. Greek mythology consists of an enormous number of stories concerning gods and the mortals who were the children of the gods. The elder gods were the children of the Titans and it may be that the Titans constituted an older mythology of an earlier civilisation that was superseded, rendered obsolete, by Zeus and his family. The gods of Greek mythology are very much like people and are conspicuously amoral – they squabble, become jealous, play practical jokes, and sometimes rape and kill. Leda, for instance, was raped by Zeus, a story which far more recently was the subject of a famous poem by Yeats. In The Iliad, composed in the eighth century BC, which concerns the war between the Greeks and the Trojans, Apollo, Artemis, Ares, and Aphrodite side with the Trojans, while Hera, Athena, Poseidon, Hermes, and Hephaestus side with the Greeks. Zeus pretty much stayed out of it. Even though Poseidon supported the Greeks, Odysseus manages to offend Poseidon by killing his Cyclops son and Poseidon's machinations, his attempts to kill Odysseus, prevent Odysseus from returning home to Ithaca for ten years, as recounted in the Odyssey. 

When I think about Greek mythology, I often wonder, "Did the ancient Greeks literally believe these stories?" It may be impossible to know – it may be that modern notions like 'truth' and 'fiction' didn't apply as neatly back then as they seem to today. Certainly I believe the Greeks worshipped their Gods and engaged in rituals such as propitiatory sacrifices. In a recent Sam Harris podcast, Brian Muraresku discusses the Eleusinian Mysteries that began close to two thousand years before Christ and probably persisted into the early Christian Era.  According to Muraresku, these rituals, which a person would participate in only once in his life, probably involved psychotropic compounds. This is interesting but the relevant point here is that these rituals also involved the myth of Persephone, the myth in which she was abducted and taken to the underworld by Hades to be his queen. According to one version of the myth, Zeus commands Hades to release her but, because she has eaten some pomegranate seeds while underground, she is only allowed to return to Olympus for part of the year and must remain in the underworld for another part of the year. The myth of Persephone was the ancient Greek way of explaining the changing of the seasons.

I tend to hope that my readers are literate enough to know a little mythology, whether it be Greek, Norse, Maori, or some other. We could try to explain the mythologies of ancient peoples by saying that 'primitive' societies used them to explain natural phenomena. But this would not be wholly satisfactory. Many Greek myths don't do this – we might think of the myths involving Theseus or Heracles, myths about the children of gods that seem even more removed from what we today tend to think of as religion. However the primary reason that many might be reluctant to identify Greek mythology as being a form of religion is that it didn't involve morality, at least 'morality' in the modern sense, although the Greeks certainly praised virtues like valour. The ancient Greeks might sacrifice oxen to a god in the hope that the god would respond with a bountiful harvest; however I don't believe the ancient Greeks thought that if an individual performed virtuous deeds and refrained from vice, the gods would reward him or her in this life or the next. This is not to say that the Greeks were amoral. Wikipedia credits the invention of Ethics to Socrates, who was born around 470BC, but philosophical thought concerning morality must have existed in Greece before him. Ancient Greek philosophy and mythology seem to be somewhat distinct, something that lends credibility to the idea that the ancient Greeks simply gave lip service to all these stories. Socrates thought we should try to be good simply for the sake of being good, not because the gods want people to be good and reward good people. Interestingly, Aristotle came to the conclusion that the world required a First Mover, an argument we find today in Christian Apologetics and which has become popular again recently. But, even though Aristotle seems to be anticipating the monotheism of Abrahamic religions with this argument (an argument that, of course, predated Christianity although it didn't quite predate Judaism), what Aristotle didn't do is identify this first mover as Zeus (or Cronus or Uranus or Gaia or Chaos, the family lineage that begat the Olympians). 

Modern Christianity not only fundamentally concerns itself with morality, it makes the promise that after a person dies, if she has been good, she will go to some kind of paradise, which we term 'heaven'. This notion is almost absent from Greek mythology. According to the ancient Greeks, everyone when she dies descends underground, crosses the Styx, and ends up stuck forever in the underworld. The whole premise of my favourite Greek myth, the myth of Orpheus, is that the underworld is unpleasant and one should want to be rescued from it if this can be at all achieved. Sometimes the underworld is not dissimilar to hell. Sisyphus is punished by the gods to endlessly attempt to roll a boulder up a hill, and Tantalus found himself in a fairly analogous predicament. Not everyone who dies is punished eternally but the underworld is nevertheless pretty dire. There are some hints of something like a heaven – the Elysian Fields (or Isles of the Blessed) occur sometimes in Greek fable and seem like a precursor idea to the Christian heaven. Initially, when first conceived, this paradise was reserved for children of the gods and great heroes but, as it developed in some strands of Greek thought, entry was permitted to people of great virtue. But Elysium seems to be a minor movement within Greek mythology. In the Odyssey, Odysseus arrives at the outskirts of the underworld and talks to a number of ghosts; he talked to Achilles who tells him that he would rather be a poor peasant on Earth than a ruler among the dead. I found a rather tendentious blogpost about this scene by New Zealand classicist Peter Gainsford (who writes a blog called "Kiwi Hellenist") in which he argues against the common interpretation of this scene that it is intended to show the superiority of the living world to the world of the dead. Having with some effort found a free translation of the scene on the Interweb, I discovered that the the realm of Hades is indeed however described fairly grimly as a "joyless place" and in terms of a "gloomy darkness" and so we seem quite entitled to believe that Homer and presumably many ancient Greeks didn't view the afterlife particularly positively.

Let's now consider the religion/mythology of a people who lived fairly near the ancient Greeks: the Jews. The writings that formed the basis for the first part of the Hebrew Bible were collected in the fifth century BC. Of course I am not an expert on what Christians call the Old Testament but my sense is that it is a mix of mythology, history, and moral instruction. The stories of Adam and Eve, Cain and Abel, Noah, and so forth seem quite a lot like mythology. There also may be something historical about the Hebrew Bible. It is full of genealogical information – so-and-so begat so-and-so who begat so-and-so and so on. It recount wars between the Jews and the other peoples who lived in the near East and famously of course the period when the Jews were captive in Egypt. It may not be possible to clearly distinguish between mythology and history in the Hebrew bible. (This is true of Greek mythology as well. The Trojan war may actually have happened.) Judaism, unlike Greek mythology, was monotheistic. In talking about ancient Judaism I shall say something that, even though it is obviously true, may offend some people. The God of the Hebrew Bible was God of the Jews and of no-one else – His role was to help the Jewish people. This is why we commonly refer to the Jews as the "chosen people". The other peoples in the region had their own gods although the Jews didn't recognise these other gods as being worthy of worship. The God of the Jews would often aid them in their wars and, when the Jews lost, as occasionally happened, it was because the Jews had failed in some way in their devotion to their single God. In The Marriage of Heaven and Hell, written around 1790, William Blake poetically accentuates the absurdity that people tend to ignore. In this poem, he presents the almost Postmodern notion that "a firm persuasion" can change the world, and has Ezekiel say "from these opinions [those of King David] the vulgar came to think that all nations would at last be subject to the Jews. This said he, like all firm perswasions, is come to pass, for all nations believe the Jews' code and worship the Jews' god, and what greater subjection can be."

Unlike Greek mythology, Judaism does explicitly involve a kind of morality. We might consider the Ten Commandments that Moses brings down from Mount Sinai, or all the rules in Ezekiel and elsewhere, such as the rule that two or more different types of seed shouldn't be sown in the same field or that a man shouldn't have a pointed beard. The morality of the Hebrew Bible was a blind obedience to God's laws as laid out in their holy texts. Again, of course, this is obvious. A foundational myth within Judaism is the story of how God instructs Abraham to sacrifice his son to prove his piety only to spare the son at the last moment. However, unlike modern Christianity, the Jews didn't believe that they would be rewarded for their obedience to the laws laid out in scripture with a blissful afterlife. In Judaism there was and still is no real notion of a heaven. The word the Jews used for the abode of the dead was 'Sheol', and Sheol is even less clearly described in Jewish writings than the Greek underworld is in Greek writings (although some later Jewish mystics have made the attempt). Like the realm of Hades, Sheol is subterranean and both the virtuous and the wicked end up there. Apparently, some Jewish thinkers compartmentalised Sheol in the same way that some Greeks invoked the idea of Elysium but there was no consistency to this. On a whole Sheol is also imagined as a joyless, gloomy place. The Jewish God was not really concerned with the fates of individuals after death; rather He was concerned with the living Jewish people. We can see this today in modern Israel among Orthodox Jews who see the Jewish state as something promised to them by their God, view God as fundamentally concerned with the living Jewish community.

And now we arrive at a religion/mythology more closely connected with me and perhaps many of my readers than the others: Christianity. It may seem provocative to argue this but one could well regard many or most of the stories associated with Jesus as myths. The tale of the Three Kings arriving at the manger, and the resurrection of Lazarus, for instance, probably simply didn't happen. It is also fairly evident that Christianity has from the beginning involved morality; the significance of Jesus, as we understand him today, is as a moral teacher. Where the Old Testament says, "An eye for an eye and a tooth for a tooth", Jesus said that if you are struck, you should "Turn the other cheek." Jesus said that one should love one's neighbour, that it is easier for a camel to pass through the eye of a needle than for a rich man to enter the Kingdom of Heaven, that blessed are the peacemakers. It is in Christianity that we first start to get the idea of heaven, at least in Europe and the Near East. But we still don't get the simple doctrine that if you do good deeds, you go directly to heaven when you die and if you sin you plummet immediately into hellfire. The sacrifice of Jesus, his expiation of human sin, opened up the possibility of going to heaven, a possibility that had not been available to the heathens of previous millennia. But the way to get to heaven was through belief in Christ and through the Eucharist, the consumption of Christ's flesh and blood, not through virtuous action. 

And for the early Christians it was not immediate. Today most Christians and non-Christians alike imagine that people have souls and that, if heaven exists, the person's soul soars to it straightaway after death. But the early Christians thought something quite different. They thought that when you die, you get buried and then, on the Day of Judgment sometime in the future, you get bodily resurrected and, if you've been good, subsequently get to enjoy an eternity of happiness here on Earth. Many Christians today have no problem with the idea of cremation but for most of the Christian Era, the idea of cremation would have profoundly disturbed most Christians. If you had no physical remains, they thought God couldn't resurrect you. Even today very clever Christians can be found who literally believe in the Day of Judgment and the General Resurrection and deny that people have souls distinct from their bodies. Of course, there has always been disagreement among Christians concerning eschatology but the notion that people have souls distinct from their bodies I think didn't really become widely popular until Rene Descartes in the seventeenth century proposed his philosophy of Cartesian Dualism. I am not sure how our modern conception of heaven emerged but it is worth noting that even people who today do believe in heaven can tell us very little about what they believe it to be actually like.

There are a couple of points related to the previous discussion that it might be interesting to draw attention to. According to traditional Christian doctrine, no one living before Christ could possibly wind up in heaven. This seems a little cruel of God. In the early fourteenth century, Dante Alighieri, in The Divine Comedy, went to some effort to try to describe hell, purgatory, and heaven, an epic poem indicating, incidentally, that by this time the notion of the General Resurrection was not the only way people made sense of the afterlife. In the first part of the Divine Comedy, Dante descends into the inferno. The first circle of hell, the least hellish, is Limbo. This is where the unbaptised and the virtuous pagans dwell. We learn that the great Jewish patriarchs originally found themselves in Limbo but were rescued by Christ shortly after his crucifixion. In Limbo there is a palace in which the major Roman and Greek poets and philosophers who had lived before Christ reside. Even though they are not permitted to go to heaven, their afterlives are, thankfully, quite pleasant. In this way, Dante sought to reconcile religious doctrine with a more humanist view of the people he admired but were unlucky enough to be born before Christ. (There is admittedly very little more humanism in the Inferno.)

Another point which I think might be important to note concerns Gnosticism. In the Christianity we have today, there is continuity between the Old and New Testaments. Both are regarded as holy books. In the Hebrew Scripture there many prophecies associated with the Messiah and in the New Testament the apostles continuously speak of Jesus as having fulfilled these prophecies. (Religious Jews today of course don't accept that Jesus was the Messiah; they are still waiting for the genuine Messiah to arrive.) However in the early centuries of the Christian Era, a kind of religious system arose known as Gnosticism that took a rather different view. It is a matter of debate as to whether or not Gnosticism was a kind of Christianity; it was denounced as a heresy and stamped out by the early Church Fathers. According to the Gnostics, the material wold was not created by the true God but by a lesser deity known as the Demiurge who they considered evil; the world consequently is evil. Christ is a divine figure who came to Earth from a separate and purer realm to draw people towards the true good God who dwells apart from the wicked material world. The Gnostics even developed their own convoluted mythology. The Gnostics did not believe that people attained salvation through virtuous action; rather they thought that one achieved salvation through a kind of mystical esoteric insight. Interestingly, and this is the point, many Gnostic sects believed that Yahweh, the Jewish God of the Old Testament, was not the true God but rather the Demiurge. There was thus for many Gnostics a sharp divide between the Old and New Testaments; Christ was the emissary of an entirely new religion. When we look at this period in the development of religion around and north of the Mediterranean, we can wonder what might have happened if Gnosticism had survived and flourished. The tensions found within and between the three major monotheistic religions, Judaism, Christianity, and Islam, religions we collectively refer to as Abrahamic, may never have arisen.

The theme that has emerged from the discussion so far is that I am eliding the terms 'mythology' and 'religion'. My reason for doing so is to stress the commonalities between the two concepts. Of course many theologians and other religious people may think it very important to clearly demarcate the two. They may say, for instance, that religion necessarily involves morality in a way that mythology does not, or that religions make genuine truth claims that mythologies do not. However, I have my reasons for the elision that will become clearer later. I note furthermore that my selection of mythologies is very Eurocentric. The reason I am not talking about Islam, Hinduism, Buddhism, Shinto, and Confucianism, or discussing South American or Maori mythology is that if I did this essay would just wind up too long.

Religious and mythological thought is complex and interesting. It is possible to approach it from a literary perspective, as constituting a collective treasure house of marvellous stories, rather than in terms of clearly isolable systems making different truth claims. We can suspend our disbelief. We might think of it the way Neil Gaiman does in the Sandman comic books and his novel American Gods. We might think of another comic book series from the 'nineties, The Invisibles, which consciously plays around with Gnostic ideas. Religious and mythological stories fascinate those of us with inquisitive minds. However fundamentalists of all stripes tend to cling to their own preferred systems and react sometimes with fear to anything they don't understand. Consider how Evangelical Christians in the US tried to ban the Harry Potter books in I think the early 2000s because they thought JK Rowling was promoting witchcraft. But there is another kind of fundamentalism – atheist materialist fundamentalism. Many people, especially here in New Zealand, genuinely dislike religious people because they don't understand them. There is a stereotype of the Born Again Christian who is homophobic, intolerant, anti-science, and right-wing; furthermore sometimes I think atheists are afraid of being judged by sanctimonious Christians and found morally wanting. Unfortunately some people can be found who fit the stereotype. We might think of the Republican Party in the US, current House Speaker Mike Johnson, or former Vice-President Mike Pence. However there is a different sort of religiosity – the sort displayed by people experiencing psychosis.

As I have talked about before in this blog, the definition of 'schizophrenia' is always changing. Nevertheless a common 'symptom' that psychiatrists and others still often associate with 'schizophrenia' is 'religiosity'. The fact that psychiatrists consider religiosity a symptom of a neurological disease, a problem, demonstrates how committed psychiatrists mostly are to atheist materialism. It also indicates one way in which psychiatrists dehumanise their patients, by denying that the spiritual questions that often preoccupy them might be legitimate concerns. I believe that religiosity does indeed often feature in psychosis although it is not universal. About five months or six months ago, I read Finding Hope in the Lived Experience of Psychosis. In this book, the now retired psychiatric registrar Patte Randal tells the story of her life. I have met Patte a couple of times and have shared things in my life with her that I haven't talked about in this blog. Patte has made contributions to the treatment of the mentally ill, particularly in her advocacy for the use of a therapeutic tool she invented called The Gift Box, a tool that may be helpful to many people if deployed by the right therapists although it wouldn't have been any help to me. Patte has actually experienced seven brief but intense psychotic episodes herself over the course of her life. What is relevant here is that although Patte came from a secular Jewish family, she fell into Christianity later in life, from memory I believe after her second episode. It wasn't a sudden Road to Damascus conversion but rather a process that involved her closely reading the whole Bible. Patte's faith is very important to her and she has written journal articles about the relationship between faith and mental health. Her faith supports her. Patte is an important voice validating the religious concerns of people who have experienced mental illness but find themselves among the intolerant and close-minded.

I have seen other evidence of religiosity. I knew a woman, another patient, who told me that she sometimes spoke to God. A number of times when she came into the clinic she would bring a tattered old book, a book she presumably found in a second-hand bookshop, in which its author seeks to show that Christianity is compatible with reincarnation. This little anecdote hints at the difference between the religiosity we associate with close-minded bigots and the religiosity of people who have experienced psychosis – the religiosity associated with psychosis involves a kind of spiritual journey, a spiritual curiosity, a spiritual questing. It is not dogmatic. This woman obviously can't be considered someone who was indoctrinated in childhood by religious ideology, ideology she has never questioned, if she is researching whether or not Christianity can be reconciled with reincarnation. People who experience psychosis are looking for meaning and may experiment with multiple religious, philosophical, and mystical traditions and theories before finding the one that suits them best (if they ever do). The risk for people who have experienced psychosis is that they are thus vulnerable to being captured by cults although I have seen only a little evidence of this.

The best way to explain how religiosity enters into psychosis is to talk about my own life and experiences again. I am a little reluctant to do this because I feel that I've said pretty much all that I need to say about my own life in this blog. However it may be possible to extrapolate from a single life to the experiences of a whole group of people, and the only life I know really well is my own. My own experiences may illuminate religiosity more generally.

When I was little I briefly went to Sunday School. My parents are both atheists (although my mother says she subscribes to Christian values) and I don't know why they sent me to Sunday School for at least a short while but they definitely did. At Sunday School I read children's versions of famous Biblical stories such as the stories of David and Goliath, and of Samson. This early religious exposure didn't seem to affect me, at least consciously. As a child and into my early teenage years I read an enormous amount of fantasy and science fiction novels rather than religious works. Books that made a strong impression on me included the Thomas Covenant novels by Stephen Donaldson, the books of Ursula Le Guin, and the science fiction novels by Ian M. Banks. I loved Terry Pratchett and Douglas Adams. I still adore The Sandman series of comic books. Like everyone else my age I was a big fan of the first Star Wars trilogy. Relevant to what I shall discuss later, I also read science fiction books by Julian May and Joan D. Vinge, books full of characters with psychic abilities like telepathy and telekinesis. During my time at high school, I shifted from fantasy and science fiction to 'serious' literature but even then I preferred literature with a magical bent such as The Satanic Verses by Salman Rushdie, The Trial by Kafka and One Hundred Years of Solitude by Gabriel Garcia Marquez. My mind was full to the brim with fantastical fictions.

Despite my fascination with fabulous stories, I grew up into someone totally irreligious. I subscribed wholly to the atheist materialist paradigm and thought religious people were all deluded. At high school, morning assemblies always began with a prayer – all the the other boys, most of whom were probably atheists or adherents to non-Christian religions, would automatically bow their heads, but I made a point of never doing so. This was my small act of defiance. Unlike the New Atheists, however, I didn't think atheists should try to convert the religious to atheism. When I met religious people, I didn't try to dissuade them of their convictions. I thought that because religious faith was ridiculous it must also be fragile, and I worried that I might harm believers accidentally by proving to them that their beliefs were stupid. I put all my faith in science. Looking back, I think my rejection of everything paranormal had its roots in a childhood fear of the supernatural, of ghosts and ghouls and vampires. I recall that in Seventh Form I learnt about the Placebo Effect. The idea that a person's beliefs could influence that person's physical body profoundly perturbed me. This discovery had lasting effects on how I viewed the world and I never fully reconciled it with my faith in science.

So I have always been torn between my love of myths and wondrous stories, and my commitment to atheist materialism. I suspect that one reason for the importance of fiction to human life is that to know 'reality', we also have to know 'unreality'. This idea, that dreams and the real world mutually define each other, that both are necessary, is one Neil Gaiman hints at evocatively in the comic collection Brief Lives. It is actually quite a Derridean conception. But I shall not develop this idea here because I don't really have a theory about it yet. 

Then in 2007 at the age of twenty-seven I experienced my first psychotic episode. As a result of acute stress, my sense of reality shifted sideways. I have talked about this so much in this blog that there is no point revisiting it here in detail. What is significant is that during this episode and the subsequent episodes I suffered is that little bits of my life, memories, all the stories I'd read or viewed, history, and my incomplete understanding of biology, psychology, psychiatry, physics, all the sciences, inspired and constituted the delusions I entertained. I was no longer sure where to draw the line between reality and fantasy. I felt compelled to arrive at some new worldview based on these materials. People often use the term 'psychotic break' and I am not sure whether or not this term is too strong for what I experienced. In Jerusalem,William Blake said, "I must create a system, or be enslaved by another man's." I felt compelled to try to make sense of what had happened to me and was happening to me and this led me to conclusions that most people would consider crazy.

Many of these delusions were somewhat scientific. In 2007, for a number of months, I thought that there was a microphone in my glasses. Years later I told my psychiatrist this and he said, "They have the technology to do that, you know." I remember in 2007 reading an article in the New Zealand Herald about how the Y chromosome is shrinking. This is true – the Y chromosome in humans and many other animals has been gradually shortening over many millennia. At the time, I decided that this might explain why all of humanity seemed to have turned or be turning homosexual. I was constantly trying to come up with biological or psychological explanations for the cause of homosexuality. In July 2009, as I recounted in the post "The Nocebo Effect and the Cardinal Principle", I heard a voice that said, "The only difference between you and them is testosterone." I decided that the drug I was on might somehow turn me gay by messing with my hormone levels and shortly after managed to get my psychiatrist to permit me to discontinue it by threatening suicide. Of course (and I can't stress this enough), even today there is no accepted biological or psychological theory that credibly explains the cause of homosexuality although no shortage of cranks have proposed unlikely hypotheses.

Despite appearances, I am not anti-science. In early 2013, I read an article in Mother Jones that argued that the massive increase and decrease of crime that occurred in the twentieth century and peaked in the early 'nineties was the result of lead poisoning, particularly from car fumes. The argument is that lead damages the frontal cortex, the part of the brain that handles executive function. I wrote a letter about this to the New Zealand Herald which the Herald published. I was actually totally well when I wrote this letter but became 'ill' again shortly after partly as a result of what I sensed to be people's reaction to it. This theory is not unscientific. I strongly suspect that the neuroscientist Robert Sapolsky, for instance, would agree with me that the lead hypothesis is quite plausible. However when I was put under a Compulsory Treatment Order in early 2014, the fact that I had written this letter was adduced as evidence of my insanity. It demonstrates how stupid psychiatrists are that they don't even understand basic neuroscience, something you'd think they'd know at least a little about.

However, of course, not all my delusions were quasi-scientific like those I have described above. In January 2009, I was lying in the bath attempting to go through the derivation for the Special Theory of Relativity in my head again but couldn't get started. I heard a voice that said, in a Texan accent,  "Do you want George W. Bush to help you?" This was almost the first time I ever heard a voice. Deciding that he would be of little assistance, I changed the subject. I asked him, "Are you straight?" He said, "I think so." I asked him if he believed in God. He said, "No." I asked him how then we could be communicating. He said, "Midi-chlorians." After I got out of the bath I asked him what the real reason for the war in Iraq was and he replied with some bosh about the Clash of Civilisations. I said to him, "You do believe in God, don't you." He said, "So you do know a joke when you hear one."

The principal delusion I entertained in 2009, the delusion that began with this conversation and that was most vivid over the summer of 2009 and 2010, was that I could communicate telepathically with others. Jon Stewart and Barack Obama were two of those I spoke with. What I realise now is that this delusion probably derived from the science fiction books I'd read as a child and adolescent, and from Star Wars. Of course notions like this circulate in the collective unconscious and sometimes find expression through urban myths. This delusion, that everyone was telepathic, led me to think that one could only communicate with living people. I only spoke with a dead person once, briefly, and it happened to be Michel Foucault. Even at the time, it seemed strange to me that a dead person should speak with me. Years later, when reading about the experiences of others who'd experienced psychosis, it would puzzle me that they had sometimes spoken with dead people. Another feature of this episode is that my interlocutors would sometimes say to me, "Where are you now?" and I would sometimes say this to them. We all seemed to need to be reminded of where we actually were. Unlike the woman I described in the opening of this essay, I never lost sight of my actual physical location. It is interesting to note that although Bush was the first person I spoke with, I heard him only once more, in early 2010. When he spoke to me this time, he didn't at first sound like himself. He said something like, "Hold on, I need to remember what I sound like."

This purpose of this part of this essay is to discuss religiosity and the purpose of this section is to discuss how religiosity featured in my own experience of psychosis. Although the delusions I have already discussed did not involve religiosity, it did feature a lot in other delusions. Very shortly after I first became 'ill', after I had left bFM but before I was removed from the Big House and became a patient of the Mental Health System, I decided that Jesus was straight and that all the disciples were gay; I considered the possibility that I might be Jesus myself. This must sound monstrously blasphemous to my Christian readers if I have any. There were times when Biblical myths like that of Cain and Abel seemed particularly relevant to my situation. Later in the year I thought that we were all living in the End Times and that people in the world around me were being Raptured up to Heaven. There were times when I thought that like Jesus I had to divide the world into the Saved and the Damned, heterosexuals and closet homosexuals. A river of names flowed like a river through my mind at times and eventually I decided that everyone in the world should be saved. 

In 2009, the apocalyptic delusions didn't feature but I still had a sense of having been chosen to suffer for a salvific purpose. I recall visiting Waiheke (an island near Auckland) with my mother and one of her friends, a devout Catholic, in spring that year and hearing voices consulting with each other, saying things like, "Maybe he's the one". I remember asking them, "What is this - a committee?" Around that time I attended a Catholic service with these two and visited a nunnery – yes, there are indeed nunneries in New Zealand. Later in the year I had a very vivid experience that seems particularly significant. I went outside into our back garden and decided that the tree in the garden was one of the Suicide Trees from Dante's Seventh Circle of Hell. I had in my mind a terrible conception of all the young gay-seeming men in the world being driven to suicide by the misdiagnoses of sadistic psychiatrists. I thought I was in Gethsemane and, like Christ, wanted to say, "Take this cup away from me." I said to the voices, "Choose someone else!" They immediately said, 'Okay." I went back inside and lay on the couch. I asked the voices, "Am I Jesus or am I in hell?" They replied, "What's the difference?"

Despite this occasional religiosity, my most intense period of psychosis, over the summer of 2009 and 2010, didn't feature anything overtly religious at all. This was the period when I genuinely believed I was in constant communication with Jess, Jon, and Obama, among others. I felt my role was to help my friends by devising a religion for atheists. I can remember saying to Obama, "God is the goodness that speaks through men."

In discussing my own experience of religiosity, there is one further element of it that seems pertinent. Occasionally I would go to churches. Towards the end of 2007, I would often walk up the road to the Presbyterian church at night and sit by myself on one of the pews. I felt that my soul, my core sense of self, was in peril and thought religion could magically save me. In 2013, although I was not as seriously psychotic then as I had been in 2009, I would sometimes go to the Anglican Cathedral, light a candle, and make a wish sometimes for myself and sometimes for Jess. This was not a gesture of genuine Christian piety but rather a desperate appeal for some kind of magical or thaumaturgical intervention that I hoped could save me or her from the cruel machinations of God or Fate.

These anecdotes concerning my own life are ones I have told before in this blog but the reason for my returning to them is that they shed light on psychosis generally. We can interpret psychosis rationally or as involving something supernatural. As I hope I have shown in this essay and others, the content of my delusions were inspired and informed by all the diverse and often incompatible ideas I had come across in my life, from Dawkins' The Selfish Gene, Einstein's Theory of Relativity, works of fantasy and science fiction, to Greek myth, Judaism, and Christianity. I seemed to lose the ability to discern between those which were 'real' and those which were 'fictional'. However all these ideas seem to float around in the Collective Unconscious – people sometimes seem to inherit these ideas without knowing where the ideas have come from. It is interesting to note that twenty or thirty years ago a common delusion entertained by psychotics was that microchips had been inserted into brains; today, even though owing to research funded by Elon Musk among others such scenarios have become increasingly feasible, psychotics no longer tend to entertain this particular delusion. This is intriguing – one wonders why not. The idea of the Collective Unconscious, although it seemingly comes wrapped in the vestments of serious science, psychology, is really something mystical, paranormal. Some people seem to think that mythic archetypes are somehow coded into human DNA but we should regard this idea as absurd. An understanding of the Collective Unconscious requires a view somewhat mystical. Jung himself was inspired to arrive at the theory of the Collective Unconscious after a conversation with a schizophrenic; he probably experienced psychosis himself, experiences that led him to write the Red Book. Furthermore, he was probably a genuine theist. It may be that to really understand psychosis we also need to accept the idea of some kind of collective animating spirit that people come closer to during psychosis.

If we accept the idea of the Collective Unconscious, we can perhaps take a step that I think Jung didn't, the logical next step. We can postulate that this group mind or World Soul changes over time. The people who believed in Greek mythology became the people who accepted Jesus as their lord and saviour. The Protestant Reformation introduced a sea-change in the way many people interpreted Christianity. The Christians of the nineteenth century were replaced during the twentieth century by atheist materialists. Even today fundamental change is occurring – panpsychism has become not only popular but respectable, something that would have been unthinkable twenty years ago. Often these radical changes emerge from the words and actions of individuals – Buddha, Jesus, Mohammed, L. Ron Hubbard, the founders of religions. But we may also think of visionaries like Marx, Freud, Derrida, or Chomsky, founders of secular religions. Many of these 'prophets' are Jewish, interestingly. Psychotics are caught in the currents and vortexes of the Collective Unconscious. Sometimes they are influenced by old religions that have passed their use-by-dates – Islam was probably a good thing in the seventh century but is not so viable today, and the Old Testament of Judaism and Evangelical Christianity should similarly be regarded as obsolete. (I feel the same way about the US Constitution but to talk about this here would be to wander off-topic.) It seems that as the collective soul of a community or of humanity as a whole changes, new religions have to appear or old religions have to change. Psychotics are pulled simultaneous towards the past and the future, pulled back towards the mythologies we have inherited and forward towards the mythologies we are in the process of creating. The terms we use in political discourse, 'conservatives' and 'progressives', are truer than people realise.

There is a whole school of thought that Jesus was mentally ill. The people who propose this are of course usually atheists. C.S. Lewis, approaching this question from a theistic perspective, famously said that Jesus was either "mad, bad, or God". Another way of approaching this issue might be to suggest that the mentally ill are all a bit like Jesus. They see problems in the world and are trying, usually unsuccessfully, to solve them. In my case, it was the attitude of society towards homosexuality that was the problem. I suppose I should remind everyone that I am still straight – the issue I struggled with for years was not sexual confusion but rather my own homophobia. The position I eventually reached is that homosexuality is a choice that is not immoral. It is worth recalling that major changes in the world related to sexuality and gender have occurred in the last ten years. Gay marriage was legalised here in New Zealand in 2013 and in the US in 2015. People who opposed the law changes were usually Fundamentalist Christians who used scripture to justify their bigotry. In the Old Testament, God destroyed Sodom and Gomorrah because the men in Sodom had demanded that they 'know' a male angel carnally; in Leviticus, it says that if a man lieth with another man, both should be put to death. The god of the Old Testament was deplorably homophobic. In 2009, I would sometimes hear this Old Testament god in my head – He spoke precisely in the style of the King James Bible. This Old Testament god sometimes spoke to me during thunder storms. Back then I knew little about Gnosticism but even then I sensed this Old Testament god was not the 'real' god and my sense that this god was at the very least intolerant and conceivably evil that drew me to Gnosticism years later. I no longer worry about an evil god in the same way I once did. I am not proselytising on behalf of Gnosticism here. Rather I am trying to persuade atheists to view the religious more sympathetically and for the religious to realise that religions like Christianity can evolve and change over time as social attitudes change. We don't need to regard something written down two and half thousand years ago in Palestine as a timeless moral truth. 

At this point I wish to switch to talking about physics and science more generally. The transition may seem abrupt but in a way there is a common thread because some science today partakes in the esotericism of ancient mythology and religion. I think part of the reason I liked physics is because it held out the promise of explaining reality. However recently I have realised that really most physics today is concerned with either the very, very small or the very, very big – particles on the one hand and cosmology on the other. Yes, physics also deals with combustion engines and electronic devices but it is particle physics and cosmology that receive all the attention. I sometimes wonder if the meaning of life might be found in other sciences, sciences like psychology or sociology or ecology, or in the humanities, rather than in physics. The other thing I realised recently is how messy physics actually is. Physicists have a whole bunch of theories but they do not cohere neatly with each other.

This may seem like a strong claim but I can give an account that I hope will support it without making me sound like a crackpot. A couple of years ago I watched a Youtube video by Veritasium in which he discussed General Relativity. A central idea in General Relativity is that gravity is not really a force, it is a 'fictitious force' like the centrifugal force. You and the chair you're sitting in are not really being pulled down by a force; rather you are accelerating up and are being 'held down' by your own inertia. I think another way of expressing the same idea is to say that your frame of reference is actually accelerating down. In the video, Derek Muller says that because, according to electrodynamics as it was developed in the nineteenth century, accelerating charged objects radiate electromagnetic radiation, we could test General Relativity by seeing if apparently stationary charged objects produce radiation. I thought this must be wrong because if Muller's claim were correct, that an apparently stationary charged object continuously radiates energy, this would violate the law that energy is always conserved. I thought Muller must have misunderstood General Relativity and wrote a blogpost saying this. More recently however, not long before Christmas, Sabine Hossenfelder released a video saying the same thing as Muller, that gravity is not a force. I don't mean to be unfair to Derek but I have more respect for Sabine than him when it comes to physics; I wrote a comment asking if anyone could explain how General Relativity could be reconciled with electrodynamics. It didn't seem possible that Sabine could also be misunderstanding General Relativity. On Christmas Eve, while wandering around the city late at night, I realised that it wasn't Derek or Sabine who had made a mistake. It was Einstein. The Theory of General Relativity is wrong. Or at least incomplete.

Lots of us know a little about physics and take a recreational interest in it. We know, because people say this all the time, that quantum physics doesn't play nicely with General Relativity. On a whole we are not supposed to worry about this because when we are dealing with the very, very small, gravity is completely negligible and quantum physics works really well, and when we are dealing with the very, very big, General Relativity works really well and quantum effects are completely negligible. Supposedly the need for a quantum theory of gravity only arises if we want to understand Black Holes. However what I realised is that General Relativity doesn't even play nicely with the classical theory of electrodynamics. And Einstein knew this. He came up with General Relativity in 1915 and spent the rest of his life attempting to formulate a better theory. Einstein wasn't trying to reconcile General Relativity with quantum physics because, even though he helped invent quantum physics, he didn't particularly like it or the direction it had taken. He was trying to reconcile General Relativity with classical electrodynamics. And he didn't succeed.

There are other inconsistencies in physics. Physicists routinely say that nothing can travel faster than light, that causation itself travels at the speed of light. Then they kvetch about the implications of entanglement, that it involves spooky action at a distance. Einstein might have contributed to this interpretation of Relativity, that the speed of light sets an upper limit to the speed of causation. But in fact the Special Theory of Relativity only says that massive objects must travel slower than light and that electromagnetic waves and other kinds of waves travel at the speed of light in a vacuum. It does not say that information cannot travel faster than light. To infer this is to go further than the theory actually states. Of course, if we wanted to say that information can travel faster than light or, as we might speculate, that it can even travel backwards in time, we would need a good definition of 'information', something I have not been able to find on Wikipedia or anywhere else.

If you want more evidence of the messiness in physics, look no further than the endless debates concerning how best to interpret quantum mechanics. Something else I have been thinking about recently concerns the Many Worlds Interpretation of quantum physics; I believe that I have conceived of an almost watertight argument that shows this interpretation must be wrong. To present this argument I only need to go a little further than I did in the posts "Quantum Physics for Dummies and a New Idea" and "Determinism, Quantum Physics, and Free Will". If the reader recalls, in these essays I discussed diffraction and presented the view that experiments such as those concerning diffraction involve both primary and secondary measurements. In order to carry out a diffraction experiment, the experimenters need first to measure the width of the aperture through which a particle like an electron is to be fired, measure the distance to the screen on which it will arrive, and estimate its velocity in order to determine the particle's wavelength. These can be called primary measurements. Based on these primary measurements we can determine the particle's wave function. According to most interpretations of quantum physics (although not my own), this wave function is objective. Applying the Born rule to the wave function, we can determine the probabilities of where the particle will land on the screen. The determination of where it actually arrived constitutes the secondary measurement. The fact that we observe it arriving at a particular point rather than being distributed over an area is why we use the term 'wave function collapse'.

I first encountered the Many Worlds Interpretation when I was a teenager in a comedic science fiction novel The Schrodinger's Cat Trilogy by Robert Anton Wilson. At the time I thought it a fun fantastical idea but didn't give it much critical attention. These days I sense it must be ridiculous; I have the intuition that it must be wrong and I tend to trust my intuitions. I'll give again a brief description of the Many Worlds Interpretation. According to this Interpretation, the primary measurements are still used to determine an objective wave function – in this way it is no different than the traditional interpretation, the Copenhagen interpretation. However, unlike the Copenhagen interpretation, wave function collapse does not occur. Rather, every possible secondary measurement occurs, each in its own world which splits off from the world of the primary measurements. The observer and the subsystem being observed (the electron and its collision with the screen) are correlated or entangled; some number of universes diverge and in each one there is a different version of the observer and of the subsystem. There is some ambiguity in the way Many Worlds proponents present their theory. On the one hand, they present it as I have here, as involving the idea that every possible secondary measurement occurs each in its own world. On the other hand, Everett, who first proposed it in 1957, as well as many of his acolytes, stress the fact that the value of this theory is that in it wave function collapse never occurs at all and so the paradoxes associated with wave function collapse never arise. From this perspective, secondary measurements never actually happen, they just seem to us to happen.

The problem with the theory is this: why should we distinguish between primary measurements and secondary measurements? If secondary measurements never occur, it seems that for the sake of consistency we should also deny that primary measurements ever occur. No measurements are apparently ever made at all. If, however, we deny that primary measurements are ever made, we can never establish the wave function of a particle in the first place. We need empirical data to plug into the Schrodinger equation or Dirac equation. The word 'measurement' is difficult to define with respect to quantum physics but it seems to me that any observation of the world made by a sentient being can be considered a type of measurement. Every observation involves a wave function collapse, so if wave function collapse never occurs, this entails that observations never occur. It seems then that the Many Worlds Interpretation leads us to the conclusion that the empirical world does not really exist at all, that it only seems to exist. Or that our observations have no real relationship with underlying reality. This consequence is so deeply counterintuitive that it gives us strong reason to reject the Many Worlds Interpretation.

Proponents of the Many Worlds Interpretation might reply in the following way. They could draw an analogy between their theory and the idea of conditional probability, the idea that the probability of an event is predicated on prior circumstances. Given that the experimenter finds herself in a world in which the primary measurements take on the particular values that she observes, they might argue, all the possible secondary measurements and possible universes follow from the wave function she calculates. This reply involves a way of looking at time Everett and others assume without explicitly spelling out. The present world is constantly branching into multiple possible futures and then each possible future branches further into more possible futures; however the past is unitary, fixed, the same way that the branches of a tree lead back to the trunk. Although it seems intuitively correct to very many people, I find this asymmetry between the past and future implausible. Personally I think that the future is as unitary, as fixed, as the past, but that we tend to assume it is indeterminate because it is so difficult for humans to make accurate predictions about it. There is another alternative. We could rectify the asymmetry by proposing that if there are very many possible futures, there are also very many possible pasts. The second response however leads us to the same kind of extreme skepticism that the Many Worlds Interpretation seemed to imply and that we were trying to resist.

I have also been ruminating about science more generally. My impetus is the claim made by Robert Sapolsky that desert climates tend to produce monotheistic religions, that there is a causal connection, a claim that even though I think it mistaken is still fascinating. I have discussed this twice in recent posts. What is the difference between science and history? Historical works are narratives involving specific people, specific places, and specific events. Historians might study how specific monotheistic religions arose, when they did so, and where they did so. Often historians try to draw causal connections between events but we could also describe history as "just one damn thing after another". Science however involves abstractions or universals. Scientists study generic electrons, generic octopuses, generic persons. They hope to find rules governing generic causation. The mistake Sapolsky made is to try to treat history as though it were science, to think we have enough recorded instances of monotheistic religions independently arising in desert cultures to justify his claim that desert climates, considered generically, somehow naturally engender monotheistic religions considered generically. I have shown in the other posts why this claim is unsound.

Not only does science involve abstractions, the scientific method also depends fundamentally on another concept: statistical independence. One way to gesture towards a definition of this term is to say that events A and B are statistically independent if the probability of both occurring is the product of their individual probabilities of occurring. Science needs statistical independence. We want an experiment in Amsterdam on a generic electron, generic octopus, or generic person to be statistically independent of another experiment carried out a week later in the same place or a third experiment carried out in Sydney. We don't want to worry that one experiment might somehow magically affect another. However the concept of statistical independence is coming under fire from some surprisingly different directions.

Modern physicists are currently faced with the challenge posed by experiments that show that Bell's Inequality is often violated. This is another issue within quantum physics. These experiments seem to show that if two particles are 'entangled', a measurement on one will instantaneously affect the properties of the other even if the two are very far apart, a kind of spooky action at a distance. Many Worlders have tried to wriggle out of the implications of Bell's Inequality by arguing that this spooky correlation doesn't really exist because the measurements involved never happen. I think this is also ridiculous but it would take too long to give my reasons why here. Sabine Hossenfelder's response to the challenge is different. Sabine believes that a local hidden-variable theory interpretation of quantum physics must be right, as did her hero Einstein, and has argued that the loophole in Bell's Theorem is that it assumes statistical independence. Sabine believes in something known as Superdeterminism, a theory which, if true, might suggest that owing to a shared causal origin far in the past, we should expect bizarre and surprising correlations between spatially separate individuals in the present, something which would I think would look exactly like paranormal phenomena. One could describe this as being similar to "ubiquitous alien mind control". Even though Sabine is endeavouring to defend Einstein's intuitions, I suspect even Einstein might balk at the idea of giving up on statistical independence to save some kind of local hidden variable theory. 

Then we have Rupert Sheldrake, someone coming from a totally different perspective and background to Sabine but arriving at a similar conclusion. In 1981, Sheldrake proposed his theory of Morphic Resonance. This is the idea that owing to to morphological resemblances, organisms and sometimes apparently inanimate structures can magically influence each other over time and at a distance. An example Sheldrake gives is crystal formation: after a particular new kind of crystal is grown in one lab, it takes less time for it to form in other labs subsequently. More 'rational' scientists have proposed that this can be explained away by supposing that scientists have accidentally carried seed crystals between labs but Sheldrake sees this as clear evidence of Morphic Resonance. I don't know if Rupert has realised himself that his theories amount to an attack on the idea of statistical independence. He is very much an empiricist, someone who enjoys and is very good at devising experiments to test his paranormal theories; he might not realise himself that he is effectively employing the scientific method to undermine the scientific method itself.

The current questioning of statistical independence is an extremely interesting development. Sometimes, within the context of Bell's Theorem, the axiom of statistical independence is called the free will axiom because it is equivalent to saying that the two scientists involved in the entanglement experiment are free to measure whatever they want independently of each other. There are many intellectuals today, such as Sam Harris and Robert Sapolsky, who reject free will but wholeheartedly endorse science. Such intellectuals, despite rejecting free will, might still balk at the idea of giving up statistical independence. But this is the direction some in the world are currently heading.

It is possible to bring the disparate topics of this essay together. The first point is that multiple religious and mythological systems have been created to describe the world; modern scientism is just another such system. I have only discussed three or four mythologies but there are many more. Fundamentalists of all stripes say that their particular systems are true and that the others are false; we should reject this view. Good people can come from any religious or spiritual background and still improve the world. And it is the idea of improving the world that is key. The carrot-and-stick paradigm of many religions, the idea that we should be good because then we will merit an eternity in heaven and avoid an eternity in hell, not only should be rejected but can be rejected. I don't think even Putin or Netanyahu deserve an eternity in hell. I think Trump and his supporters are stupid but I don't think that they are evil. We should do good, as Socrates preached, for its own sake. This is the sense in which I mean that it is possible to have religion without morality, without the notion that good people go to heaven when they die and bad people go to hell. It is moral questions like these that psychotics grapple with.

The view that I am expressing, a view that I can only set out tentatively, is that some collective spirit animates people and drives them forward. This is a kind of religious view but it is a view that encompasses all religions and leaves no one out, not those who belong to other religions nor people who have performed actions I disagree with. It is possible to believe in a kind of World Soul. Oddly enough many scientists, in questioning the idea of statistical independence and endorsing what Einstein disparaged with the title "spooky action at a distance", are arriving at a similar mystical position even though they began their journeys from materialist presuppositions. This is a striking new development. And one that may lead us into a new world that even though it is scary because it is unknowable may still be better than the world we have inherited.

Tuesday, 2 January 2024

The Two Envelopes Paradox

One advantage of writing a blog like this is that I can talk about anything I want. If I have readers at all, it may be that they are interested in my life, the condition with which I was diagnosed and from which I recovered, and other anecdotes drawn from my own lived experience. They may be interested in religion or narrative theory or Meinongianism or any of the other various topics I have covered from time to time. I may have readers who know something about quantum physics and are interested in speculation concerning it; I may have readers who know little about quantum physics but read the essays I have written about it because I have endeavoured to describe this recondite theory in clear accessible language. My vain conceit is that readers may come back to this blog because I am a fairly interesting person. Because I have little sense of who my readers are and because I earn no money from this blog there is no possibility of 'audience capture' – I am not like Bret Weinstein and Heather Haying who have built up an audience of vaccine skeptics and have to pander to this audience for an income. I am not like Alex O'Conner who specialises in discussing arguments for and against the existence of God because that is part of his brand. I can talk about anything that has taken my interest. 

Often in the interval between writing posts I consider various subjects upon which to expatiate and try to talk about all of them in a single essay. When considering what to write about in this essay, I thought about talking about what left-wing politics means to me and also considered writing about the relationship between religion and morality. I have decided not to pack everything into the same post but instead concentrate on a single topic in this one, a topic that has surfaced several times during this blog: probability. I want to briefly talk about the Monty Hall problem and then go into more depth on the Two Envelope Paradox. I want to write about the second because I became obsessed with it for a couple of weeks and when I tried to investigate it on the internet I found that every proposed solution to it, on Youtube and elsewhere, was wrong. Although I have not come up with the definitive solution, as I hope you will see, I have made major inroads towards a solution. So, I warn the reader, this essay involves mathematics. The mathematics involved is just simple algebra but I know from experience that arguments involving mathematics are hard to read unless you have specialised in mathematics or math heavy subjects at a university level. If maths is not your thing you can skip this post and wait for the next essay which will concern the history of religion, how morality got involved, and whether it might be possible or not to have religion without morality.

For a warm up, let us consider the Monty Hall problem. I imagine my readers will be familiar with it because it is famous. The pitch is that we have a gameshow in which a contestant is faced with three doors. Behind one door is a new car, which the contestant wants, and behind the other two are goats which the contestant definitely doesn't want because, perhaps, she lives in a small apartment in Manhattan. The contestant doesn't know which door conceals the car. She chooses one of the doors and tells the game show host which one she has chosen. The gameshow host knows which door the car is behind. If she has guessed incorrectly, the gameshow host opens another door behind which is a goat leaving two doors, the one she picked and one other which he knows contains the car. If she has guessed correctly, the gameshow host opens one of the other two doors at random: that is, with a conditional probability of 1/2 for each door. (The probabilities are conditional because they depend on the contestant correctly picking the door.) The gameshow host then asks the contestant whether she would like to stick with her original guess or switch. After she has decided, the door will be opened and she will find out whether she has won a car or a goat. The problem is this. What should the contestant do?

The answer turns out to be simple. The contestant should always switch. The probability of winning the car by sticking is 1/3 and the probability of winning it by switching is 2/3. You can work out that this must be the case by simply repeating the 'experiment' many times. Everyone who discusses the Monty Hall problem nowadays accepts that you should always switch but this wasn't the case in 1975 when the problem was first posed or in 1990 when it became famous after appearing in a column in the magazine Parade. The columnist's solution provoked an enormous backlash sometimes involving eminent mathematicians who couldn't believe the solution Marilyn vos Savant had advanced must be right. Surely it should make no difference whether you switch or not? Surely the odds are 1/2 for both sticking and switching because there are only two doors left? One reason for this confusion is that the Monty Hall problem strikes right at the heart of what we mean by probability. Nowadays, yes, we all know the correct answer but the philosophical justification, the reason why the correct answer is correct, remains disputed.

It is not the purpose of this essay to discuss the Monty Hall problem in depth but I want to present a variant on the Monty Hall problem that makes salient a counterintuitive implication. Suppose we imagine a gameshow identical to the one discussed above in every way except that the gameshow host doesn't know which door the car is behind. After the contestant randomly chooses a door, he then randomly opens any one of the three doors. Hopefully my readers know enough mathematics to realise that there are nine possible outcomes; hopefully, too, my readers will realise that each outcome is equally probable. We are not interested in outcomes in which the gameshow host opens the door the contestant has picked or outcomes in which he opens the door concealing the car. So we throw these outcomes out. This leaves four possible outcomes, two in which she has correctly chosen the car and two in which she hasn't. These outcomes are still equally probable. So, in the variant Monty Hall problem, the probability of winning the car by sticking and the probability of winning it by switching are both the same, 1/2.

Suppose you have an alien who accidentally catches the gameshow on TV. He sees the initial choice, the one door being opened, the contestant making her decision whether to switch or not, and then the next door being opened. If the alien doesn't know whether or not the gameshow host himself knows which door the car is behind, he has no way or knowing if he is watching Monty Hall Classic or the variant I have just presented. What is the difference between the two? In the first it is rational for the contestant to switch if she knows that the host knows which door the car is behind and is deliberately opening another door. In the second there is no rational reason for her to prefer either sticking or switching because she knows that the host doesn't know which door conceals the car himself. Somehow her prior knowledge of the host's knowledge affects the probabilities she assigns to either sticking or switching. Furthermore these probabilities seem to be, in a sense, objective, empirically grounded because we can determine them either through rational analysis or through repeated experimentation. It is common to say that probability estimates depend on information but this discussion leads us to wonder how exactly information is being communicated to the contestant and what 'information' actually is. In probability, there are deep mysteries indeed.

The main topic of this essay is, however, not the Monty Hall problem but the Two Envelope Paradox. It can also be set out simply. Suppose someone presents you with two envelopes and tells you that one envelope contains twice as much money as the other but doesn't tell you which. You pick one. Before you open it, you are given a choice. You can either stick with the original envelope or you can switch. Intuitively, because the situation is symmetrical, it should make no difference whether you switch or not. I shall call this the Intuitive  Common Sense argument or ICS argument.  However it is possible to make the argument that you should always switch, that this is the best strategy. According to Decision Theory, we should multiply the utilities of outcomes by their probabilities thus forming something known as Expected Utilities. Because we don't know the amount of money in the envelope we picked, we call it x. The other envelope either contains x/2 or 2x. Because the probability of choosing the higher amount is 1/2, the Expected Utility of switching and thus getting the lower amount is (1/2)(x/2). Because the probability of picking the lower amount is 1/2, the Expected Utility of switching and getting the larger amount is (1/2)(2x). The Total Expected Utility of switching therefore is the sum of the two, (1/2)(x/2) +(1/2)(2x) or 5x/4. Because on average there is a higher Expected Utility associated with switching than with sticking, because the total Expected Utility gained by switching is 5x/4 and the total Expected Utility of sticking is x, we should always switch. But then suppose you are asked again if you want to switch or not. By the same reasoning, you should switch once more. And continue switching forever. Obviously there must be something wrong with this argument somewhere.

There are two ways to conceptualise this paradox, the Intuitive Common Sense perspective, which I am calling the ICS argument, or the argument involving Expected Utility which depends on the equation written above. Let's call this equation the TEP (the Two Envelope Paradox equation) because I will come back to it repeatedly. According to the TEP equation, EU = (1/2)(x/2) + (1/2)(2x), where EU stands for the Expected Utility of switching and x stands for the value in the envelope chosen first. Everyone assumes that the ICS argument, which suggests that it makes no difference whether you switch or not, is correct (which it is) – the solutions to the paradox always involve trying to find some flaw in the reasoning in the TEP argument. As I've said, all the solutions that I've found are incorrect. One attempted solution I found relies on the exponential function – obviously an attempt to solve this problem by involving exponents must have gone wrong somewhere. According to Jade Tan-Homes, who has a Youtube channel called "Up and Atom", the problem is that the TEP is using two different values of x. The first time x appears in the TEP it is the higher of the two amounts and the second time the lower. If we rectify for this error, Jade argues, the equation simply becomes EP = x and the paradox apparently evaporates. The problem here is that Jade is wrong. There is a mistake in the TEP but this is not the mistake. x simply stands for the amount in the first envelope picked: it is the other envelope that either contains x/2 or 2x. This is clearer if we give x a value. Let's suppose the picked envelope contains $10 – in that case the second envelope contains either $5 or $20 and, assuming the TEP is correct, has an Expected Utility of $12.5. Therefore, if we get a $10 (or any other value), we supposedly should always switch. So this solution, a solution which I think Jade presumably got from supposed experts in probability, fails.

Another solution I found attempts to show that the TEP doesn't apply when the envelopes are unopened but does apply when one is. If you open an envelope and find $10, they say that you should assume that the other envelope contains on average $12.5 and always switch. This article says this strategy would be bourn out by multiple experiments. I won't name and shame this site, partly because I can't remember its name, but this is also wrong, especially the claim about multiple experiments, as I will now show.

Having thought so much about the Two Envelope Paradox recently, I found it very helpful to think in terms of what I shall call studies, experiments and scenarios. I shall define scenario in a moment. I believe that if we  think about the paradox in these terms, we can understand it better and at least approach a solution. A study consists of, say, a hundred experiments and each experiment consists of a person choosing between two envelopes, a person who has no knowledge of the other subjects. Let us suppose that each envelope contains either z dollars or 2z dollars where z here does not mean the money amount in the envelope first picked (which throughout this essay I denote with the letter x) but rather the lower of the two amounts. On average, half of the people will randomly select the z envelope and half will pick the 2z envelope. Let us suppose that they are all following the switch strategy. Consequently everyone who picked the z amount switches to the 2z and everyone who picked the 2z amount switches to z. The total amount of money they will accrue collectively is 150z and on average each person will win 3z/2. Suppose they all stick. Everyone who picked the z amount first keeps it and everyone who picked the 2z amount first keeps it. They will still all make the same amount of money collectively and on average. If they all switch, the number who get the higher amount by switching is exactly balanced by those who got the lower by switching. It seems that neither strategy, switching or sticking, is better than the other. This little thought experiment shows that the ICS conception, that it makes no difference whether you stick or switch, is the correct conception.

I shall now define a scenario. It will be helpful to introduce some genuine numbers and, as I shall show, it is possible to introduce genuine numbers without distorting the logic. A scenario is a description of the types of experiment involved in a study. In Scenario A, all hundred experiments involve a $10 and a $20. As I have shown in the previous paragraph, it makes no difference whether subjects all stick or all switch – either way each will make on average $15. Let us imagine Scenario B, in which all hundred experiments involve a $5 and a $10. Once again it makes no difference whether subjects all stick or all switch – either way each will make on average $7.5. Now consider Scenario C. Suppose we have a study in which fifty experiments involve a $5 and a $10 and fifty involve a $10 and a $20. On average 25 people will pick a $5, fifty people will pick a $10, and 25 will pick a $20. Let us suppose that they all have been persuaded by the TEP argument and so all switch. Everyone who picked a $5 first will get a $10 but 25 of the people who picked a $10 will get a $5. 25 of the people who picked a $10 will get a $20 but everyone who picked a $20 will get a $10. Again it makes no difference whether everyone follows a switch strategy or everyone follows a stick strategy; on average each subject will receive the same amount of money either way. The total amount of money they will collectively receive is $1,125 and on average they will receive $11.25. Importantly however, if Scenario C obtains, not only everyone who initially picks $5 but everyone who initially picks a $10 benefits from switching – the EV is $12.5 for those who initially pick a $10. The problem is that the losses for those who initially picked a $20 not knowing they'd picked the highest amount cancels out the profits made by the other subjects.

Furthermore, as should be clear by now, it makes no difference whether or not the envelope is opened before the stick or switch decision is made, contrary to what the site I mentioned above says. Suppose all the envelopes contained either $10 or $20. If an individual opens an envelope containing $10, not knowing whether this is high or low amount, then rationally she should assume that the other envelope contains either $5 or $20. If a person opens an envelope containing $20, then rationally she should assume that the other envelope either contains either $10 or $40. The ICS argument leads us to the same conclusion whether or not one of the envelopes is opened before the choice to stick or switch is made. Some of the mathematicians I read argue that we should bring in other considerations. We might say the university carrying out the study is cash strapped and so $10 is more likely than $40. I don't believe that bringing in such considerations is justified by the paradox as usually presented. Considerations such as these are irrelevant.

What I have argued so far is that the ICS argument must be correct because when studies involving a hundred experiments (or any large of number of experiments) are actually carried out, it is evident that neither the switching nor sticking strategy is better than the other. The TEP argument must be wrong and this requires some explanation. Let us now imagine the following. A subject in a study, who we will call Jane, is presented with a pair of envelopes and opens one, finding that it contains $10. The other envelope must either contain $5 or $20. As I have argued above, whether or not the picked envelope is opened makes no difference. Let us suppose that in every experiment in a study, one envelope contains $10 and the other $20. In other words Scenario A obtains. If the subject knows she is in Scenario A, she should switch. However it could be that she is in Scenario B in which every experiment contains either $10 or $5. If she knows she is in Scenario B, she should stick. But she doesn't know whether she is in Scenario A or Scenario B. It could be that she should assign probabilities to each Scenario – she could apply the Principle of Indifference to Scenarios, presume that the probability of Scenario A is 1/2 and the probability of Scenario B is 1/2. If she does this, the TEP equation actually holds: the Expected Value of switching is (1/2)$20 + 1/2($5) or $12.5.

Scenarios A and B are not however the only possible Scenarios. Consider Scenario C again. This scenario is equivalent to saying that Scenarios A and B are equally probable and mutually exhaustive and exclusive. In this scenario, fifty experiments involve a $5 and a $10, and fifty involve a $10 and a $20. As I have shown, it still makes no difference whether all hundred subject stick or switch from a bird's eye perspective– they will still win the same amount of money on average. But we are now considering a subject, Jane, who opens an envelope and finds a $10. In this case, as above, the TEP actually holds – the Expected Value for switching is $12.5.  So she should switch. But she should only switch if she knows that she is in Scenario A or Scenario C (rather than Scenario B) and knows therefore that her chosen envelope contains either the intermediate or smallest amount.

Although I have so far mentioned only three scenarios, if the study contains a hundred experiments and the subject knows the money amount in her envelope, which we are here assuming to be $10, then there are in fact a hundred possible scenarios (the ordering of experiments is irrelevant). It might be that all experiments involve a $5 and a $10, that they all involve a $10 and a $20, that it is split 50-50, that 16 experiments contain a $5 and a $10 while 84 contain a $10 and a $20 and so on. It is at this point that I introduce my clever idea. It seems we need to introduce.a new variable a. This new variable is the humber of experiments containing a $10 and a $20 in the study divided by the number of experiments containing a $10. Suppose a subject opens an envelope and finds a $10. The probability of getting a $20 by switching is a and the probability of getting a $5 is (1-a). The Expected Value of switching is 20a + 5(1-a), or 5 + 15a . If we are in Scenario A, then a = 1 and the Expected Utility of switching is $20 as we would expect. We should always switch in this case. If we are in Scenario B, then a = 0, and the Expected Value of switching is $5 as we would expect. We should always stick in this case. If we are in Scenario C, then a = 1/2 and the Expected Value is 12.5 as we would expect if the TEP actually holds. In this case we should always switch. More generally, if the amount in the picked envelope is x, then regardless of whether or not we open the envelope, the Expected Value of switching is a(2x) + (1 -a)(x/2) or, when simplified, x/2 + 3ax/2. If a=0, the EV=x/2 and we should always stick; if a=1 the EV= 2x and we should always switch. I shall call this new equation the New and Improved TEP equation because it involves this new variable, a. This variable is a ratio, the number of experiments that contain a $10 and a $20 divided by the total number of experiments containing a $10.

The reader may ask if the studies we are imagining cover all possible circumstances. We might have a study in which some experiments contain a $1 and a $2, some a $3 and a a $6, some a $5 and a $10, some a $10 and a $20 and so on. We might have a study in which every experiment is different (although one envelope in each always contains twice as much as the other.) It might seem that if the study consists of a hundred different experiments we need a different distribution variable for each experiment, not just the single variable a. However, recall that we are assuming that the subject picks $10 first. The only possible values in the other envelope are $5 and $20. To reiterate the point, because it is important, this variable should be defined as the number of experiments containing a $10 and a $20 divided by the number of experiments containing a $10 where we are assuming a very large number of experiments.

We are now in a position to make a first pass at what is wrong with the reasoning involving the TEP that leads to the conclusion that we should always switch. The TEP argument involves two assumptions. Firstly it assumes that a = 1/2, that we are in Scenario C . If we replace a in the New and Improved TEP equation with 1/2 we arrive back at the original TEP equation. Secondly it assumes that the amount in the first envelope picked is the intermediate amount. What do I mean by intermediate amount? In the studies we imagined above, some experiments contain a $5 and a $10 and others contain a $10 and a $20. The $10 appears in all experiments and, quite evidently, is an intermediate value between the $5 and the $20. The problem with the reasoning that leads to the paradox seems to be that neither assumption is justified by the information given to us. We have no idea what the value a is and cannot justify our assumption that we have initially picked the intermediate amount. It could be argued that because we cannot justify either assumption that the whole edifice that led to the conclusion that we should always switch has no foundation. We simply lack the necessary information.

When first thinking about the Two Envelopes Paradox it occurred to me that we could imagine another type of experiment that might be equivalent to it. Suppose the experimenter gives the subject $10 and then says, "If you want you can bet this ten dollars on a gamble. I'll throw a coin and if a head turns up, I'll give you your $10 back with another $10. If a tails comes up, I'll only give you $5 back." In the same way that if the TEP is correct it is would always be rational to switch, it seems you should always take this bet. What I subsequently realised is that this new experiment is not really equivalent to the two envelope paradox because, in this situation, a has a definite value, 1/2, and it is obviously evident that $10 is the intermediate amount. 

In our first pass we seem to have found that the TEP argument fails because we lack all the necessary information. Yet we have not fully come to grips with the paradox. The intuition implicit in the ICS argument, that it makes no difference whether we switch or stick, does seems reasonable, justifiable, and is bourn out by the thought experiments we have considered. I have just suggested that the reasoning that led to the switch strategy fails because we lack the required information needed to justify it. However we do seem to have enough information to justify the position that it makes no difference whether we switch or not. So we need to explore the paradox a little further.

We have imagined studies that each consist of a hundred experiments and I have argued that there could be a hundred different studies each involving a different scenario. I have suggested that because we don't know which scenario obtains, the value a is indeterminate. However it might be possible to reply to this argument in the following way. We could apply the Principle of Indifference to scenarios. We could say that, because we lack the information required to know which scenario obtains, we should assume that each scenario is equally probable. This is the fundamental idea behind the Principle of Indifference. Or we could say that a falls on a normal distribution with Scenario C as the mean scenario and Scenarios A and B as outliers. Either way the distribution is symmetric around Scenario C. Some philosophers might argue that, because of the Principle of Indifference, we are justified in supposing that a = 1/2. They might argue that this value a applies to all experiments in a study. In other words, when faced with a choice between two envelopes one of which contains twice as much as the other, we are justified in imagining that we are participating in a study in which Scenario C obtains and that we have chosen the intermediate amount, and should always switch.

However even if we do try to set a as being equal to 1/2, we still cannot reconcile the TEP argument with the ICS argument. Consider Scenario C. Everyone who got a $10 should always switch presuming she knows that $10 is the intermediate amount. But now consider a subject, call him Bob, who gets a $20. He doesn't know that he is part of the particular study described above, doesn't know that $20 is the highest amount, and so rationally should assume that the other envelope either contain $10 or $40. If he accepts the TEP equation he should switch. If he accepts the New and Improved TEP equation and assumes further that a is equal to 1/2, he should also switch. But he would be wrong to switch. Why? Earlier I defined a as the number of experiments containing a $10 and a $20 divided by the number of experiments containing a $10. I did this in the context of the study I was discussing. In Bob's case, the correct value of a is the number of experiments containing a $20 and a $40  divided by the number of experiments containing a $20. This number is of course equal to 0 because there are no experiments involving a $40 dollar prize. If we substitute 0 for a into the New and Improved TEP equation, we find that the Expected Value of switching is $10. If Bob knows that he has the highest amount, he should stick but the problem for him is that he doesn't know this.

We now arrive at a fundamental point. In introducing the variable a, I implied that this variable is the same for all experiments in a study – but this is not the case. The studies we have considered usually involve three different monetary prizes. When a subject picks an intermediate value, the value of a depends on the number of experiments involving the highest value divided by the number involving the intermediate value. However, in experiments in which the person picks the highest value, a should be 0. In experiments in which the subject picks the lowest value a should be 1. The idea that we simply set a as being equal to 1/2 because of the Principle of Indifference doesn't work because subjects cannot assume they have the intermediate prize: they do not know whether the money in the envelope they have picked is the highest, lowest, or intermediate amount. The value of a in a given experiment depends both on the scenario and which of the three values has been picked. So we have arrived back at the claim I made earlier, that the loophole in the TEP argument is that we don't know the value of a. Simply stipulating that it should be 1/2 fails.

I'll restate the argument I have made so far. Suppose Jane picks an envelope. She might not open it, or she might open it and find that it contains $5, $10, $20 or some other amount. The EV of switching is x/2 + 3ax/2 where x is the amount in her envelope. a can now be simply defined as the probability that Jane has picked the lowest amount of the two envelopes, a probability that she neither knows based on the information she possesses or can guess at as being, for instance, 1/2. Because she does not know a, she cannot work out the EV. 

This would suggest that it is impossible to work out whether you should stick or switch. Yet the ICS argument, which says that both strategies are equally good, seems not only Intuitive Common Sense but must be true based on the arguments I made above. Is there a way to reconcile the two approaches? Let us propose the following argument. 1.) The ICS argument is correct and so both the stick and switch strategies are equally good. 2.) If so, the EV of switching must be equal to the EV of sticking. 3.) The New and Improved TEP Equation says that EV= x/2 + 3ax/2. If these premises are true than we can set EV as being equal to x and formulate the following equation: x = x/2 + 3ax/2 . If we now solve this equation for a, we find a must equal 1/3. In other words, if both the New and Improved TEP argument and the ICS argument are sound, then the probability of Jane being in an experiment in which she has chosen the lower amount and should switch is 1/3, while the probability that she has picked the highest amount and should stick is 2/3.

This makes sense mathematically but does not make sense intuitively. There are at least three problems with it. First, if you or Jane or anyone else actually is given a choice between two envelopes one of which contains twice as much as the other, I don't believe anyone would assume that there is only a one third probability that he or she has initially picked the lowest. Everyone assumes that the odds are fifty-fifty. Secondly, the same type of logic can lead us to believe that it is the other envelope that has the one third probability of being the lowest. The third problem again involves a little algebra. Suppose we go right back to the beginning. Suppose someone presents you with two envelopes and tells you that one envelope contains ten times as much as the other envelope. Intuitively we would still believe that both sticking and switching are equally good strategies and we would be right. However the New and Improved TEP Equation is now EV = x/10 + 99ax/10. If we now set EV as being equal to x, we find that the probability that Jane has chosen the lower amount and should switch is 1/11. More generally, suppose that someone presents you with two envelopes and says that one envelope contains n times as much as the other. It seems, according to this line of reasoning, that the probability that one will initially pick the lower amount and should switch is 1/(n+1). In other words, it seems that the probability distribution is determined by the ratio between the amount of money in one envelope and the amount of money in the other. This seems deeply unintuitive.

I have spent a couple of weeks thinking about this problem. I think the New and Improved TEP Equation involving the variable is a very important step in the right direction but is only helpful in actual situations when one knows the value of a. For about a week I have been trying to find some way to reconcile the New and Improved TEP argument with the ICS argument in situations where we don't know the value a. It seemed to me that we could find an equation in which all occurrences of this value cancel each other out and in which the EV of switching is equal to the amount of money in the picked envelope (whether opened or not). I have not been successful. I could spend another couple of weeks thinking about it but feel it would be fruitless. I know that I have strung the reader along in that you may have hoped I would reveal the solution and am sorry that I have fallen at the last hurdle.

For what it's worth, I suspect that this paradox lies right at the heart of Decision Theory. This might be why it seems so insoluble, In a post a few months ago, "Rationality and Irrationality", I criticised Decision Theory on the grounds that I don't believe anyone makes decisions in the way Decisions Theorists prescribe, of if they do, only occasionally, when gambling. It may be the case that Decision Theory is itself incoherent. Either there is a serious problem at the heart of Decision Theory that this paradox reveals or, for some reason people have not so far as I know clearly articulated, Decision Theory does not apply with respect to the Two Envelope Paradox. Mathematical psychologists like Kahneman often bemoan the fact that the majority of people seem to him irrational in that they don't understand statistics but the most eminent and rational of mathematicians have failed to solve this particular paradox.

I shall leave my discussion of the Two Envelopes Paradox here.

Often in this blog I make corrections to previous posts. Usually I do this at the beginning of an essay but this time I am including them at the end. I actually thought the previous essay was quite good but there were a couple of points in it where I could have presented my argument better. In the essay I discussed Sapolsky's claim that desert cultures tend to produce monotheistic religions while rainforest cultures are much more likely to be polytheistic. I raised the objection that you could not be certain of a direct causal connection between the two, something he claimed. I said that the fact that most monotheistic religions can be traced back to the Middle East could be described as an "historical coincidence" but, of course, there are good historical reasons for the emergence of Judaism, Christianity, Islam, and the Baha'i faith, among others, in the Middle East. What I should have said was that any attempt to say that desert cultures somehow naturally engender monotheistic religions is far too simplistic to be true. I also said that the only way we could know if desert cultures somehow naturally engender monotheistic religions is to perform an experiment on human history in which we run through it on a number of different Earths. This was dumb – there is a simpler and more realistic alternative. The hypothesis that desert climates produce monotheistic religions could be strongly supported (if not fully proved) by showing that many monotheistic religions arose independently of each other in different desert environments. The problem with Sapolsky's claim, as I implied but did not express clearly, is that, so far as I know, all monotheistic religions are interrelated, usually sprang from each other. Furthermore there are counterexamples. Native Americans in North America often lived in arid conditions but did not devise a monotheistic religion. Similarly many Australian Aboriginals lived (and live) in desert environments but did not develop any kind of monotheism. Sapolksy's claim was stupid and I wish I had replied more clearly to it. There were some other things in the previous essay I wanted to clarify or correct but  I shall not get into them here. It was the detail concerning monotheism that had bothered me the most in recent weeks.

I shall discuss religion more fulsomely in the next essay, an essay which won't concern mathematics and should be easier to read.