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 a 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.

Determinism, Quantum Physics, and Free Will

I''ll begin this essay with a story. In 2011, having completed a Personal Growth course through Youthline, the free New Zealand youth phone counselling service, I graduated to a course intended to teach us wannabe counsellors phone counselling skills. At the first session a number of cards were given out to the group members, all of us sitting around on beanbags, each with an abstract multicoloured pattern or image on it, and we were each asked to choose the one we most identified with. I was drawn to two cards: the first was angular, sort of mathematical, and the second more free-wheeling, free-spirited. As the reader may guess, this game was New Agey pseudo-pyschological bullshit. I knew that the first card signified a personality with a kind of rational analytical way of looking at the world while the second indicated a personality more intuitive and emotional; I simply sensed this. Of course the students were not supposed to consciously realise which personality type each various card represented. At the time, I was torn between these two different ways of viewing myself but I was strongly drawn towards the first card. At the last moment, almost as though some force was propelling me, I selected the second card. It might be that I intuited that this was the card the others in the group would want me to select; perhaps the spell I was under somehow led me to the second card After I chose it, the two group facilitators beamed approvingly at me and told me that this was the card that they themselves would pick. It was almost as though some kind of supernatural force had influenced my choice. I will return to the significance of this moment later in the essay.

The purpose of this essay is, first, to critique the recent work of philosophy and science, Determined: Life Without Free Will by Robert Sapolsky, secondly to discuss quantum physics again, and thirdly to approach the idea of free will from a different perspective than that taken by Sapolsky. My aim in discussing quantum physics is to correct and clarify some ideas I presented in a recent post "Quantum Physics for Dummies and a New Idea". I will try to state my view of probability more clearly. Although it seems that in this essay I am attempting to cover quite different topics, there is significant overlap because some of Sapolsky's key arguments concern quantum physics.

A general comment first. I saw part of an interview with Robert Sapolsky by Lawrence Krauss and Sapolsky himself comes across as very nice man, although he has an evident tendency towards depression and a strong leaning towards biological fatalism. Sapolsky's intention in Determined is to disprove the existence of free will. Before I discuss Sapolksy's argument, I should remind reader that there is in fact a fairly simple well established argument against free will that runs as follows: A particular action by a person is the result of a deterministic chain of effects and causes that extends back to a time and place outside the person's 'control' or is initiated by a chance event or both. In no case can the person be said to be exercising free will because it seems intuitively obvious that a person cannot be held responsible for events that occurred in her environment, before she was born, or that occurred at random. If the reader wants to learn more about this argument, I recommend an old Youtube video "Compatibilism Debunked" by Alex O'Conner or his quite recent debate with Ben Shapiro. Alex's argument is informed by an essay, "The Powers of Rational Beings" by Peter van Inwagen but I suspect that those of us who have always been skeptical of the idea of free will have often arrived at this argument independently although few of us have articulated it in a philosophical essay or Youtube clip.

Although the argument above seems to me to inform Sapolsky's approach, his stated method is somewhat different. Sapolsky is attempting to show that science has disproved the idea of free will. Sapolsky is a professor of neuroscience but he is not attempting to show that neuroscience alone has disproved free will; rather he is saying that all the scientific disciplines taken together collectively show that free will does not exist. "Crucially, all these disciplines collectively negate free will because they are all interlinked, constituting the same ultimate body of knowledge." (p.9) Thus genetics, neurobiology, endocrinology, psychological theories concerning child development and later behaviours, sociology, and cultural anthropology, together with all the sciences I haven't listed, collectively leave no room for free will. "There's not a single crack of daylight to shoehorn in free will."(p.9) Implicit in his argument is the idea that this body of knowledge contains no holes, no puzzles, something that Rupert Sheldrake has, I believe, called "scientific triumphalism". Sapolsky sometimes, particularly in the section concerning genetics, seems to be trying to overwhelm the reader with jargon as if to say, "Don't try to say the science is wrong or incomplete because that will just signal to the world you are stupid; we scientists understand everything." 

Although I have argued consistently in this blog that free will does not exist, I am a contrarian and so intend in this essay to show that Sapolsky's arguments are flawed. I shall argue that the science is indeed incomplete. There is a particular aspect of Sapolsky's argument in particular that I think can be criticised: although the explicit aim of his book is to disprove the idea of free will, implicitly he is also seeking to show that any religious or mystical view is also incorrect, that the supernatural does not exist. In the world we live in, religious faith and a belief in free will go hand in hand; at the same time, it is common for atheists to deny that free will exists. However it is possible to believe in the supernatural and deny that free will exists (just as it is possible to be a materialist atheist and embrace the notion of free will as Daniel Dennett for instance does). It is possible to believe this without subscribing to Calvinism. One aim of this essay is to show that it may be possible to "shoehorn" in the supernatural. It may even be possible to somehow salvage the notion of "free will", something I will attempt at the end of the essay.

Even though I intend to criticise Sapolsky, I still think people should read his book. He is engaging and often funny and (usually) has his heart in the right place. The absolute best thing about the book is that he kills Evolutionary Psychology, the idea that our behaviour is genetically determined. (I don't intend to discuss this part of the book in this essay but refer the reader to Determined itself.) However I believe he makes mistakes. If you do read it, just remember that he is engaging in motivated reasoning and may be cherry picking studies that support his position.

To begin, I want to say something about the term 'consciousness'. Sapolsky, at the beginning of a section concerning whether or not free will needs to be conscious, says "I don't understand what consciousness is, can't define it" (p. 31). Sapolsky's bete noire, Daniel Dennett, has argued that free will exists but consciousness doesn't. People who either can't define the term 'consciousness' or argue that it doesn't exist at all have not really considered the meaning of the word. Presumably you, dear reader, are reading this on your computer or smart device – you are conscious of this essay, conscious of your computer or smart device, you are conscious of the furniture in the room. You are not conscious of the people in the next apartment over unless they start banging on the wall. More esoterically, you are presently conscious of some part of your mind and unconscious of other parts – you are not currently bringing into conscious awareness memories from your childhood for instance. Such memories can be described as subconscious because sometimes you bring them into the conscious part of your mind but at other times they sink back into the unconscious part. There may be constituents of your mind that you never bring into conscious awareness at all, such as the part of your mind or brain that regulates digestion – such constituents can proper be described as being part of the unconscious. The term 'consciousness' simply describes the activity of being conscious of things in either the outer or inner world. This seems self-evident to me. Those who struggle to understand it or deny that it exists must presumably be working with some loose definition of 'consciousness' that is wrong or which I cannot understand.

Sapolsky's discussion of consciousness comes in the context of an early chapter about experiments first carried out by Benjamin Libet in 1983. Subjects were asked to press a button when they felt like it and then report on when they decided to press it. During the experiment, subjects were hooked up to an EEG machine. What the experimenters found is that the brains of subjects decided to press the button about three hundred milliseconds before the subjects were consciously aware of having made the decision. This finding is of course supposed to be profound. However I would like to point out that the notion that our decisions are at least influenced and perhaps fully determined by unconscious mechanisms goes back at least as far as Sigmund Freud. Yes, some of Freud's ideas, such as the Oedipal complex, seem ridiculous now – but he should be given credit for pretty much inventing the concepts of the conscious and unconscious mind. Freud was of course completely ignorant of neuroscience but the neuroscientists who thought they'd made a major breakthrough in 1983 should at least have been a little aware of Freud. Moreover we cannot be certain that this highly artificial experiment proves that all our decisions are made unconsciously first. (In mentioning all this, I am not critiquing Sapolsky because Sapolsky himself says, when discussing scientific and philosophical debates arising from these experiments, "these Libetian debates [...] are irrelevant to thinking about free will." Sapolsky's purpose is to show that the chain of cause and effect that leads to an action, regardless of when that chain becomes conscious, never includes a juncture which we can describe as 'freely willed'.)

My first criticism of Determined concerns Sapolsky's uncritical acceptance of psychiatric labelling. Sapolsky argues very consistently through the second half of the book that psychiatric labels let people off the hook with respect to responsibility. We now, he argues, recognise that 'schizophrenia' is a 'brain disease' and so when, as very occasionally happens, someone diagnosed schizophrenic does something antisocial, we can say that the person is 'not guilty by reason of insanity'. Similarly if we recognise that Autism Spectrum Disorder is simply indicative of neurodiversity in the population, that bipolar disorder, ADHD, dyslexia, and other psychiatric conditions are neurological diseases and so nothing the people afflicted with them can do anything about, we can forgive people their eccentricities. Furthermore people with such conditions can forgive themselves, tell themselves "it's not my fault, it's my brain's fault." Sapolsky goes so far as to suggest that many people who are obese are not responsible for their obesity because they carry genes that affect their metabolism or how food tastes to them. The problem here is that Sapolsky simply assumes, without ever expressing it directly or explicitly defending this view, that such conditions are congenital, incurable, and lifelong. For instance, he cites research that has supposedly found that people destined for a diagnosis of 'schizophrenia' were often bedwetters as children. (Someone should tell Sarah Silverman this.) This could lead us to look for clusters of symptoms in children and diagnose them as 'pre-schizophrenic' – something that I think could constitute a self-fulfilling prophecy. Sapolsky's attitude to labels evinces his biological fatalism.

There are two ways to argue against Sapolsky here, the first to invoke a kind of Rupert-Sheldrake-inspired-magic and the second more materialist, more neurosciency. I'll describe the first way briefly. I suspect that labelling a person with a psychiatric disorder actually somehow supernaturally affects the person, is effectively equivalent to laying a curse on that person, and that if we really want to help the 'mentally ill', we need to totally change society's and psychiatry's whole way of viewing and understanding 'mental illness'. We need to recognise that it can be temporary, that it can arise in a person's life as a result of proximal circumstances and later pass away. A major reason why people usually don't recover from 'psychiatric disorders' is simply that everyone, including the afflicted sufferers, assume that they cannot.

I may have readers who find this idea a bit woo-woo and so I will sketch out another more rational seeming rejoinder. One idea in neuroscience that Sapolsky touches on but does not explore thoroughly is neuroplasticity. Consider first that if a person regularly works out at a gym and has the right type of endocrine system, he or she will gain muscle mass. The bones in the racket-holding arm of a tennis player will actually become stronger through continued use. Similarly, although a few decades ago people thought brain damage was irreparable, we now know the human brain can change and even fix itself. A person can have a stroke that impairs her ability to use language and through workaround solutions the brain of the person can reacquire this linguistic faculty. A famous example of a New Zealander who had a stroke, lost his ability to verbally communicate, but seems to have fully recovered is poet and academic CK Stead. Presuming you remember some ideas in this essay and that materialism is true, I have literally caused a physical change in your brain. I'll give one more fascinating example of neuroplasticity. Before GPS, London cabbies had to memorise London's whole topography – this was called "The Knowledge." It was found that a part of these cabbies' brains had become larger than those who had a more quotidian feel for London's layout.

Towards the end of Determined, Sapolsky briefly discusses homosexuality and because this used to be an obsession of mine and because it is related to the present discussion, it may be useful to say something about it. In 1991, Simon Le Vay discovered that a region in the brains of gay men was smaller than the corresponding region in the brains of straight men, in fact comparable in size to the corresponding region in straight women. Sapolsky does not say this but I have learnt from other sources that this region is in the visual cortex and I would wager is involved when heterosexual men surveil the world for attractive females and/or is involved in sexual fantasy. Sapolsky, in a gratuitous display of virtue signalling, quotes Lady Gaga: "God makes no mistakes, I'm on the right track, baby, I was born this way." However, when we consider neuroplasticity, an alternative explanation to the idea that gay men are born gay can be considered. It might be that Le Vay and other gay men make a 'decision' to be gay in early adolescence and, as a result of being gay for many years, this part of their brains atrophies or never grows at all.

If this idea of neuroplasticity is at all true, it suggests that people diagnosed with psychiatric disorders can recover. Certainly I have recovered from the psychoses I experienced years ago and hopefully this essay is halfway coherent and so demonstrates this. Readers may say that this apparent cogency is evidence that the drugs I am legally compelled to take are working and so I need to say something briefly about the dosage I am currently on. At the beginning of last year I was taking 300mgs of Olanzapine a fortnight; I am now only taking 210mgs a month. It has gradually been reduced over the last two years and I have had two injections at the new dosage level. I have not experienced any recurrence of psychotic symptoms, feel more clear headed, can concentrate better, am reading more, and am generally feeling happier. My aim when I see my psychiatrist next is to persuade him to reduce my dosage to 150mgs with the goal of getting off medication entirely within six months. This though is still a very difficult ask. The point here is that if a person diagnosed (or perhaps misdiagnosed) with schizophrenia can fully recover and go off drugs, the same may be true for all other psychiatric disorders. (Of course, schizophrenia is presumed to be a neurotransmitter imbalance rather than a result of brain damage, but the argument I have made can be generalised to cover this.) It may seem that Sapolsky's prescription is more compassionate, more humane, than mine because it seems that I am suggesting that people with psychiatric disorders are in a sense responsible for them – but this is not the case. I think that people diagnosed with psychiatric disorders can take steps towards recovery but that they require help. Friends, family, and society generally are collectively responsible for helping people recover from 'mental illness'.

I turn now to my second criticism of Determined. Sapolsky cites research claiming that rain forest dwellers tend to invent polytheistic religions while desert dwellers tend to produce monotheistic religions, research that suggests that there is a causal link between type of religion and climate. I need to give a little admittedly amateurish history lesson to show the mistake here. From the little I know, the first monotheistic people were the Jews. But the people from whom the Jews descended were polytheists. Incredible fact alert: Yahweh was originally a thunder god, part of a pantheon, and had a wife. The ancient people who became the Jews came to practice something known as monolatry which means they tended to worship one god while acknowledging the existence of other gods; over time the cult of Yahweh took over and the rest of the pantheon, including the wife, slipped away into oblivion. We arrived at the Judaism gradually built up over centuries and documented in the Old Testament. What about the other monotheistic religions? Christianity, of course, sprang out of Judaism, and Islam, through some process about which I am not entirely clear because I haven't looked closely at the history of Islam, sprang out of the older two Abrahamic religions in the early seventh century. There are a few other monotheistic religions such as the Druze faith, which developed out of Islam in the eleventh century in modern day Lebanon, and the Baha'i faith which developed in the nineteenth century in Iran and took inspiration from all the other major world religions. Although I have not looked at all the monotheistic religions (there are about ten) it seems likely that the fact that monotheistic religions have all, I think, arisen in the Middle East is a historical coincidence rather than evidence that arid climates somehow deterministically cultivate a belief that there is only one God. Sapolsky is making the classic error undergraduates are warned against: he is mistaking correlation for causation. In order to know if desert climates somehow naturally engender monotheistic religions we would need to run an experiment in which we play out world history from somewhat different initial conditions on a hundred Earths and see if a correlation between deserts and monotheism arises that is statistically significant. Otherwise we are entitled to doubt Sapolsky's claim.

Sapolsky's assertion that there is a causal link between desert cultures and monotheism is not a key part of his overarching argument but the reason I have focussed on it is that it may by indicative of other errors in the book, other moments where he has presented speculation as fact, that I and others may not pick on.

Even if the monotheism claim is fairly trivial, there is another strand in his argument, a strand that resurfaces repeatedly throughout Sapolsky's book, that really does deserve to be challenged. This strand concerns experiments involving 'priming'. To define this term, I shall simply quote Wikipedia: "Priming is the idea that exposure to one stimulus may influence a response to a subsequent stimulus, without conscious guidance or intention." For instance, early on Sapolsky says, "Ask someone to name their favourite detergent, and if you have unconsciously cued them earlier with the word ocean, they become more likely to answer, 'Tide'" (p. 16). Sapolsky mentions a study that shows "that disgusting smells make subjects less accepting of gay marriage" (p. 47) If a religious person has to unscramble the letters "lehl" or "neehav" they will, apparently, become more prosocial. (p.258) Although these examples fall purely within psychology, sometimes the examples Sapolsky gives also involve endocrinology or EEG scans, neuroscience. Sapolsky's intention is clear: we tend to associate free will with "conscious guidance or intention" and if the behaviours of a group of people can by influenced (on average slightly more than would occur by chance alone) by prior stimuli, this weakens the belief that our decisions are rational, are the result of "free will".

The problem here is with the whole concept of 'priming'. In Freud's day, psychology was very different than it is today. Freud and his followers were therapists who would listen to their patients, attempt to interpret their dreams, and sought to devise elaborate and sometimes silly theories concerning individual pathologies and general features of the human conscious and unconscious mind. Today, though, psychology is trying very hard to be a proper science – and that involves experiments. 'Priming', a term coined by Segal and Cofer in 1960, is a useful concept for psychologists today because it enables researchers to take a number of generic individuals, expose them to a stimulus and measure the results, all in the lab. These days academic psychologists all over the world are performing 'priming' experiments hoping to get novel results, get published in reputable journals, get lots of citations, and bring in all the consequent funding. Of course, this creates perverse incentives. In the post "Threading the Needle", I briefly discussed 'the replication crisis' (sometimes referred to as the reproducibility crisis). Good science does not just involve publishing surprising findings, it also involves repeating experiments carried out by others to ensure that the original studies were sound, weren't artefacts or accidents. Unfortunately repeating others' experiments is not particularly sexy and so it was not until the last five or ten years that it was realised that a great deal of science, including apparent findings that had become canonical, were not replicable. This is especially true of psychology. In fact, in 2022 a giant within the field of psychology, Daniel Kahneman, said in a lecture that behavioural priming research was "effectively dead." In Determined, Sapolsky briefly mentions the replication crisis and says that he is only considering "findings whose brand conclusions have been independently replicated." (p. 47n.) I would like to suggest that the crisis is so bad that we should regard all research into priming as suspect.

The concept of priming seems to me reminiscent of an earlier fad within psychology, behaviourism, an approach which has not entirely gone away but which is much less fashionable today than it once was. Readers may have heard of Pavlov's dog who was conditioned to salivate at the sound of a bell. I believe animals like dogs and cats and octopuses have inner lives that we know little or nothing about because they can't tell us about them – I have often thought that when Pavlov's dog heard the bell, she probably thought to herself, "Goody, that means someone is going to feed me soon" and salivated accordingly. This way of thinking about living things, that they have minds as well as bodies, is precisely what behaviourists rejected because the inner life is unobservable from the outside. This brings me to another idea concerning priming. In a recent Youtube video, Rupert Sheldrake discusses the reproducibility crisis and then segues into a very intriguing idea, that scientists can psychically affect the results of their experiments. He argues that chemists, for example, may be able to telekinetically affect the rate at which chemical reactions occur. I suspect this may go a little too far but, if we grant for a moment that paranormal phenomena are real, then it raises the possibility that when priming experiments actually do produce statistically significant results, it may be because the experimenters and experiment itself psychically affect the behaviour of the subjects. What others think of a person may affect the person mentally and perhaps even behaviourally. This is the reason for the story I told at the beginning of this essay. I note by the way that Sheldrake himself believes in free will but I am not myself here defending free will but rather proposing a kind of supernatural causation.

I'll consider one last study that Salpolsky alludes to. Four social psychologists (Cohen, Nisbett, Bowdle, and Schwarz) carried out three experiments in 1996 which explicitly sought to prove that a "culture of honour" exists among White males from the Southern US that can affect their "cognitions, emotions, behaviours, and physiological reactions" in certain circumstances. Just before the experiment was supposed to take place, each subject was bumped into by a confederate in the corridor outside the lab and called an "asshole". Subsequently it was found that subjects from the South were "more likely to think their masculine reputation was threatened", had higher cortisol and testosterone levels, and were more likely to engage in aggressive and dominant behaviour. Subjects from the North were pretty much unaffected. The problem with these experiments is that although the researchers assert baldly that these reactions show the effects of this "culture of honour", there are a number of other possible explanations. Perhaps people in the South are just nicer than people in the North and so Northerners, having been exposed to such conduct growing up, found it easier to shrug off. Perhaps the Southerners were already finding it difficult living in Michigan (where the experiments took place) and so were more predisposed to take offence. Perhaps they sensed that they had been chosen to participate in the experiments simply because they were from the South and were consequently more vigilant, more paranoid. The issue here is what Philosophers of Science call "the underdetermination of theory by data" – we can't be sure that these reactions show the pervasive influence of a Southern "culture of honour". Sapolksy employs this example to argue that culture affects behaviour, is transmitted intergenerationally, and can persist over centuries. However it seems here that Sapolsky is again presenting speculation as fact.

The aim of Determined is to convince readers that free will does not exist and so Sapolsky must consider counterarguments, something he does in the middle of the book. He groups these counter arguments under three general headings: chaos theory, complexity, and quantum physics. As promised at the beginning of the essay, it is the third that I shall now turn to.

In the first of the two chapters on quantum physics, Sapolsky sketches out a rough picture of what quantum physics is and of its implications. He isn't a physicist and admits this – but we don't need to be quantum physicists to see its relevance to a discussion of determinism. Put very simply, quantum physics postulates that at a subatomic level events occur randomly. Quantum physics necessarily involves indeterminacy. In order to discuss "randomness", we need some sense of the meaning of the term, and so Sapolsky illustrates the idea by talking about it would mean for a particle to move randomly. This passage is too long to quote here but involves the idea that a randomly moving particle will always most likely be found at the point where it was last observed and has a kind of fractal trajectory in that the more we zoom in the path it has taken the more zigzags we find. 

My criticism here is that Sapolsky is presenting one conception of randomness as though it is definitive. It is not the only conception. I myself tend to think of randomness as involving an event with a number of possible outcomes – for instance, when a die is rolled, we take the view that there are six possible results, each of which is equally probable. If a very large number of factors are involved, if there are many events all with the same probability distribution and all independently contributing to a value, we get a normal distribution – this is why people's heights fall on a bell curve. (The wave function associated with a simple quantum harmonic oscillator in its ground state, incidentally, is also described by a normal distribution.) Sapolsky's view of randomness is of absolute randomness. This is like saying that we can roll a die and get a banana. My view is that there can be weighted or constrained randomness. This will become relevant later.

The issue for those us who are fascinated with quantum physics is that it lends itself to what Sapolsky calls "mystical gibberish" (p. 215). Ordinary people usually don't understand much quantum physics but have picked up on the idea that it is seriously weird – this leads people to slap the word quantum on everything as though religious or New Age beliefs have scientific backing. Sapolsky heaps scorn on Deepak Chopra for instance for his 1989 book Quantum Healing and adduces a journal on "quantum psychotherapy" which contains an article called "Quantum Logic of the Unconscious and Schizophrenia" as more evidence of mystical gibberish. What Sapolsky misses is that these supernatural associations must have come from somewhere and presumably originated with people who actually did understand quantum physics. Two defenders of the free will hypothesis that Sapolsky discusses, two who seek to find it in the quantum realm, are Stuart Hameroff and Roger Penrose – Penrose won the Nobel Prize in Physics in 2020 and so should not be dismissed as a quack. It is such quantum defenders of free will that Sapolsky seeks to criticise in the second chapter on quantum physics.

Years ago, when wondering about quantum mechanics, I thought that perhaps consciousness caused wave function collapse. Hameroff and Penrose argue, surprisingly, that wave function collapses cause consciousness. The idea is that subatomic apparently random events occurring in microtubules (organelles found in eukaryote cells like neurones) collectively generate free will. In arguing against this proposal, Sapolsky enlists the support of a number of neuroscientists and philosophers who also deem it stupid. Sapolsky argues that a brain is so much vastly larger than an electron wandering about randomly in a single organelle in a single brain cell that there is no way a single quantum event involving the electron could result in a human action. He says, "This is the bubbling-up problem in going from quantum indeterminacy at the subatomic level up to brains producing behaviour – you'd need to have a staggeringly large number of such random events occurring at the same time, place, and direction. Instead, most experts conclude that the more likely scenario is that any quantum event gets lost in the noise of a staggering number of other quantum events occurring at different times and directions." (p. 220). Sapolsky quotes a philosopher called Hobbs: "The law of large numbers, combined with the sheer number of quantum events occurring in any macro-level object, assure us that the effects of random quantum-level fluctuations are entirely predictable at the macro level, much the way that the profits of casinos are predictable, even though based on millions of 'purely chance' events." (p. 221). To pummel his point home, Sapolsky gets into the nitty gritty of neurobiology, pointing out that for a single neurone to activate its neighbour there are enormous number of neurotransmitter molecules and other processes involved, and, even if it does, it's still only affecting one neurone out of 100 billion.

Here is the question though. Is the human brain like a casino or more like the weather? Or, to put it another way, does the law of large numbers apply to the human brain? Famously, if a butterfly flaps its wings in the Amazon it can lead to a tornado in Kansas. This is the lesson of chaos theory. I am not engaging in idle hair-splitting here – Sapolsky devotes two chapters to chaos theory earlier in the book. Chaotic systems are in essence unpredictable: a tiny difference in initial conditions between two systems, a difference so small that it is effectively immeasurable, can lead to enormous differences later on. A famous example in physics of chaos at work is the three-body problem. There is no general solution to this problem. Even if we could task the most powerful computer in the world with finding the solution it would in principle be unable to do so. Sapolksy's reason for bringing in chaos theory is that some free-will proponents have argued that the brain is a chaotic system, therefore fundamentally unpredictable, and that this unpredictability is equivalent to indeterminacy. Sapolsky replies that unpredictability is not the same thing as indeterminacy: just because we don't know the cause of a behaviour doesn't mean it was causeless, 'freely willed'. He gives the example of behavioural variant frontotemporal dementia. In 1922, no one knew the cause of it. But today we can predict with high accuracy that an individual will develop it in later life if he was born with a mutation in a gene called MAPT. The mistake Sapolsky makes here is that this example has nothing to do with chaos theory: a chaotic system, such as the system that causes the tornado in Kansa or the three body problem, in principle can only be very approximately solved if solved at all. More pertinently to my present argument is that in the chapters on chaos theory, Sapolsky seems to concede that the brain might be a chaotic system and then in the chapters on quantum physics conveniently forgets this, citing only experts who think the brain is a kind of stable or linear system. If however there is both subatomic randomness in the brain and chaotic amplification of these random factors by the brain, it seems quite reasonable to believe that indeterminate quantum events could lead to indeterminate behaviour. 

Then again perhaps Sapolsky and the other quantum skeptics are indeed right, that a single quantum fluctuation gets lost in the noise. Let us grant this for a moment. There is another argument I would like to make in favour of 'indeterminism'. In order to set it out, I need to digress and discuss Neo-Darwinism or what is sometimes called the Modern Synthesis.

Modern evolutionary biologists have a very simple story to explain the evolution of organisms. We begin with a population of a single species inhabiting a particular environment, occupying a particular environmental niche. Every now and again a random DNA mutation occurs: usually these mutations are detrimental to the organism but sometimes a mutation is very slightly beneficial to the individual born with it. This individual, if also blessed with a little good luck, will have more offspring than its compatriots. Over time the number of individuals who possess this beneficial mutation will increase until they become the majority. Eventually it will be possible to say that the whole population, the whole species, has changed. This is how a species evolves. Because this mass change has resulted originally from an interaction between a single DNA mutation in a single individual and the organism's environment, it seems reasonable to describe evolution as a chaotic process (although it may be helpful to bring in another notion from chaos theory, 'strange attractors').

I once wholeheartedly subscribed to this doctrine. But then in 2013 I realised that there was a significant problem with it and in the years since decided that this simple little story just didn't make any sense at all. It would take me too far afield to go into detail about why I came to this conclusion in this essay. Suffice it to say that my rejection of the Neo-Darwinist story did not lead me to reject evolution altogether but rather to realise that some other process must be involved. In early 2018, a solution came to me, in fact via a voice. When a mutation occurs, it must occur to a large number of individuals in a population at the same time. It is almost as if some kind of collective spirit or idea that embraces the whole population simultaneously affects the whole population . 

The relation of this insight to the brain should be obvious. As quoted above, Sapolksy says, "you'd need to have a staggeringly large number of such random events occurring at the same time, place, and direction." But perhaps something like this is exactly what happens. Perhaps our behaviours result at least partially from a large number of quantum fluctuations that are coordinated. To reiterate, I am not here defending free will. What I am suggesting is that our behaviours may not be wholly biologically determined but may also be supernaturally or spiritually influenced. Quantum physics provides a bridge between the materialist universe and its supernatural counterpart. This influence results either from the chaotic amplification of quantum events by the brain or from the coordination of a number of quantum events within the brain that ultimately can be traced back to causal factors in a sense outside the brain. At this point I want to bring in another key plank in Sapolsky's case against free will. Sapolsky argues that if our decisions are undetermined, the mind would throw up so many possible options, perhaps an infinite number, that it would take a lifetime to choose between them, to select an appropriate behaviour for a particular circumstance. The problem with this argument is, as mentioned above, that Sapolsky views apparent randomness as absolute randomness. However it could be that biology only picks out a discreet number of possible alternatives. It could also be, and this is my preferred postulate, that each variable associated with an action lies on a normal distribution. Yes, extreme values are possible but are very unlikely – 95 percent of the possible values for a variable lie within two standard deviations of the mean if the variable can be described as normally distributed. Thus Sapolsky's argument here can be countered if we suppose that randomness is constrained or weighted rather than absolute. Although, of course, as I've just said, I am not here defending free will but rather arguing that our actions are underdetermined by biology.

Sapolsky has another response to defenders of quantum free will. He says that if our behaviours are at root random, we cannot be held responsible for them. My perspective on this idea should be deducible from what I will have to say about free will towards the end of the essay.

Whew. This essay has swollen into a monster. It probably would have been more sensible for me to talk only about Determined in this post. However in a recent post, "Quantum Physics for Dummies and a New Idea" I made a couple of errors that I feel I should correct. I also want to develop and clarify some ideas I proposed in that post. So at this point I want to move away from Sapolsky and discuss quantum physics more directly.

In that recent post, I discussed wave-particle duality. Although I did not say this directly, I implied that electrons and photons can both be described by the Schrodinger equation or Dirac equation. If any physicists read this blog, they will have of course spotted the obvious error. In particle physics there are two types of particle: fermions and bosons. The Dirac equation applies to the former and the Klein-Gordon equation to the later. Electrons are fermions and photons are bosons. When writing that previous post, I actually did realise that the Schrodinger equation does not apply to photons but wasn't clear about this. However, with respect to the example I discussed, diffraction, it doesn't matter which equation is used because the width of the bands that we conceive of as 'appearing' on the screen depend only on the width of the aperture, the wavelength of the particle, and the distance to the screen. Because we presume that both photons and moving electrons have characteristic wavelengths, the fact that each are described by different equations is irrelevant to this example.

The purpose of the recent post was to describe as clearly as possible the Measurement Problem. I have thought of another way to approach this puzzle. Let us suppose that we can make two different types of measurement: primary measurements and secondary measurements. Some experimenters want to perform a diffraction experiment involving electrons. Before they begin, they measure the width of the aperture and the distance to the screen and make a hopefully quite accurate estimate of the velocity of the electrons they are going to fire through the aperture. These can be described as primary measurements and are used to arrive at an initial approximation of the wave function. The experimenters also measure the location on the screen each electron arrives at: each of these can be described as a secondary measurement. My claim is that the experimenters formulate a model of the wave function of a particular electron based on the primary measurements but then must amend this model by taking into account the secondary measurement. The wave function is probabilistic and probability estimates must be revised to take into account new information; furthermore it is not just the present and future wave function that must be revised but also the particle's past history. With each additional measurement, the wave function changes, although, because of the Heisenberg Uncertainty Principle, no number of measurements will enable us to arrive at an absolutely accurate description of the particle's past history, present, and future. (There is a snag involved with this picture that I shall come back to in a moment.) Although I proposed, provisionally, the idea that we have two different kinds of measurement, this distinction should in fact be discarded and we should actually treat all measurements similarly.

In the recent post I described the three most prominent interpretations of quantum mechanics: the Copenhagen interpretation, the Many Worlds interpretation, and De Broglie-Bohr Pilot Wave Theory. The essay was a bit muddled because I wasn't sure which if any of these interpretations was compatible with my own theory. I realise now that none of them are. This is because all three treat primary and secondary measurements as quite distinct. The Copenhagen interpretation supposes that primary measurements determine a wave function that is real and objective; secondary measurements have no effect on the wave function. All they do is confirm, in aggregate (that is, after many electrons are fired through), the probability distribution given by applying the Born rule to this objective function. Many Worlds also presumes that the wave function is objective and, once determined by primary measurements, unchangeable. As I said in the earlier essay, according to this interpretation 'wave function collapse' never occurs. Rather every possible secondary measurement occurs, each in its own universe. I have thought in the past that my own theory might be compatible with Pilot Wave Theory but now suspect it is not. This is because Pilot Wave theory also assumes that the wave function is objective and cannot be affected by secondary measurements. In supposing that every measurement changes the wave function it is possible that I am making an enormous error somewhere but I don't know what this error could be.

What is the snag? In the previous essay I imagined a scientist, call her Jane, who has a conception of the wave function in her own mind based on primary measurements and then 'updates' her conception based on an observation of where the electron actually lands on the screen. The problem here is that although it is fairly easy for Jane to work out a wave function for the electron involved in a diffraction experiment based on primary measurements, it may well be fiendishly difficult for her to calculate a wave function that incorporates her knowledge of where the electron has actually made contact with the screen. So the idea that she 'updates' her conception based on the secondary measurement only makes sense if Jane can instantly solve a fiendishly difficult and perhaps impossible mathematical problem in her mind very quickly, something I think unlikely.

This brings me to the fundamental mystery. What is probability? In the past I have said that any probability estimate is 'subjective' in the sense that it is made by a person based on incomplete information. I can illustrate this with a scenario I have deployed several times before in this blog. Three people, Brenda, Don, and Amy, are asked to estimate the probability that the top card of a shuffled deck is the Queen of Hearts. Brenda knows nothing about the deck and so, applying the Principle of Indifference and thus assuming that each combination of cards is equally probable, estimates the probability as being 1/52. Don has more information. He knows that the top thirteen cards are all hearts and so estimates the probability as being 1/13. Amy, however, knows for sure that the top card is the Queen of Hearts and so estimates the probability as 100 percent. I view the universe as deterministic although, as I said above, I suspect that there is both natural and supernatural causation. If the universe is deterministic then if a person somehow knew everything, possessed all the information, she would estimate all probabilities as either being certainties or impossibilities. It is only because people lack some relevant information that probability estimates come into play. Furthermore one person can possess different information than another. This is why I have said that all probability estimates are subjective. However I am not saying that such estimates are completely arbitrary, that a person can just make any estimate he or she wants. In pure mathematics, the study of probability is a big deal: there are empirically well established axioms like the Principle of Indifference, the Law of Large Numbers, and the Central Limit Theorem (although it is possible that people sometimes apply these rules in situations where they shouldn't). The problem is that the philosophical foundations of probability theory do not seem to be well established: this is why the Monty Hall problem confused so many people in the 1970's and why the Sleeping Beauty problem confuses so many people today. Somehow we need to regard a probability estimate as subjective and objective at the same time. This is something I can't speculate on any further on in this essay.

The questions about probability I have raised in the above paragraphs are, of course, not wholly original with me although I believe I came up with them at least somewhat independently. Bayesian probability is well established. However, even though I am acquainted with very little scholarly research concerning quantum physics, I sense strongly that even though quantum mechanics is necessarily probabilistic, quantum physicists themselves have rarely if ever attempted to interpret quantum mechanics from a Bayesian perspective. Quantum mechanics is strange enough as it is: if we all decided that the wave function squared actually describes our knowledge about where and when a particle is rather than objective reality, it could cause us all to descend into the abyss of German transcendental idealism. Physicists themselves exhibit a reflexive antipathy towards interpretations of quantum physics that involve consciousness. This explains the popularity of 'objective collapse theories' and of the idea of 'decoherence' which many physicists wrongly believe solves the measurement problem. (I considered talking about decoherence in this essay but it is long enough as it is.)

And now, finally, I shall try to salvage some notion of 'free will'.

An important idea in modern philosophy is 'emergence', something Sapolsky talks about in the chapters on complexity. A traffic jam is constituted by a bunch of cars but is in a sense something else, in a sense emerges from its constituent parts. I am not a big fan of this term 'emergence' but it approaches the idea I intend to discuss. What I want to do is employ a different but closely related idea: 'levels of description'. At one level we can describe the phenomenon as 'fifty cars stuck front to back' or we can take a bigger picture view and call it a 'traffic jam'. Another example: suppose we encounter a friend, Kate, and note that she seems happy. Let us also suppose for a moment that the serotonin theory of mood is true. It seems we can say, "Kate has more serotonin circulating in her brain than usual" or we can say "Kate seems happy". These two description are both true (assuming of course that the serotonin theory is true) and both describe the same thing: Kate's mood. They are describing the same phenomenon on different levels. What I would like to suggest is that even if a person's behaviour at a particular time is determined, as Sapolsky argues, by action potentials in a neuronal network that is reacting to environmental stimuli, action potentials that are themselves completely determined not only by the stimuli but by hormones, glucose levels, upbringing, acquired culture, and genes, it is still possible to describe that behaviour, at the ordinary human level, as being the result of 'free will'. It may seem I am deploying a fallacious form of reasoning – I am simply stipulating that the meaning of 'free will' should be defined pragmatically, as being an explanation for human behaviours at the level of normal human interactions, in situations where we cannot open a hole in someone's skull and observe what the neurones and hormones are actually doing. The reason I am making this stipulation is that I believe that at the level of ordinary human actions, human behaviour is unpredictable.

Sapolsky would hate this argument. Throughout Determined he adduces examples of behaviours or phenomena that have simple causes, examples I have discussed in this essay. We can predict that a person will be diagnosed schizophrenic later in life if in childhood he wets the bed. Desert societies reliably invent monotheistic religions. Priming experiments reliably influence the choices of subjects. The culture of honour in the Southern US reliably informs Southerners' reactions to rude behaviour. A single gene almost invariably leads to a form of dementia. And so on. However when one considers one's friends, even though one tends to think of them as possessing stable characters or personalities, in conversation we can almost never predict what they will say next. If the brain is chaotic, behaviour is unpredictable. If quantum effects have supernatural origins and can influence behaviour, it becomes even more unpredictable. And if we accept both chaos theory and this quantum hypothesis, it becomes possible to believe in something like 'emergence' – we can justifiably imagine that our behaviours result from top-down causation as well as bottom-up causation.

There is another reason to defend some form of free will. More than three hundred years before the birth of Christ, Aristotle invented the 'lazy man argument'. He argued against predetermination on the grounds that if the future is fixed, there would be no point in planning for it or deliberating about it. This argument can easily be countered if we suppose that the reason people plan and deliberate is that they possess the illusion of free will. However Aristotle's argument does raise an issue for determinists. Sapolsky didn't write Determined just to earn a buck or two – he is trying to change the world. Although I object to his representation of psychiatric conditions as being lifelong, I agree with his arguments in favour of greater compassion and leniency towards criminals. Sapolsky wants to make the world a better place and thinks if we all stop believing in free will this will happen. He has a chapter called "The Ancient Gears within Us: How Does Change Happen?" In it, he spends some time discussing the neuronal circuitry of the sea slug with the goal of showing how environmental factors can cause lasting changes in the neurology of these simple organisms and by analogy much more complex organisms like people. There is a tension in the book between his biological fatalism and his lefty compassion for the victims of circumstance, his desire to create positive change. Either, despite himself, he possesses the illusion of free will, or some supernatural force he doesn't believe in is propelling him forward. I can relate to this. A couple of weeks ago I became preoccupied with issues to do with free will and Fate. It occurred to me that in 2009 I decided at some subconscious level of my mind to embark on a fourteen year project to change the world, or that something else had charged me with this task. It's not that my mission has been to persuade the world of the truth of some New Age pseudo-psychological bullshit involving quantum physics. Rather I have been trying to change people's attitudes concerning 'schizophrenia' and 'sexuality'. It seemed to me that I had finally succeeded, leaving me with the existential question, "What now?"  Of course my hopeful feeling that I have changed the world depends wholly on whether people read this blog or not – but let us suppose that they do. Sapolsky is arguing that occurrences in the past push people forward; I am proposing that people can be pulled forward by the future. This pull cannot be explained away rationally if rationality involves an ordinary understanding of time and causation. This is another motivation for my pragmatic definition of 'free will'. If a person is on the right path it seems entirely permissible to describe his or her actions as arising from 'free will' even if at some deeper level they really can't.

Finally I want to defend some notion of 'free will' for one more reason. Our values and feelings should be described as real. My dislike of Vladimir Putin, the leaders of Hamas, Benjamin Netanyahu, and the whole US Republican Party are genuine emotions. My empathy for the crazy and homeless people I meet in Auckland's CBD is genuine. Emotions like 'guilt' and 'shame' are real. Sapolsky's reductionism deprives such values and feelings of the importance they need to have to guide our actions. According to Sapolsky, biological determinism is good because it lets criminals off the hook morally; I think we should show compassion and leniency towards criminals because they could always regret their actions and repent. I admit that in presenting this argument I could be committing an informal logical fallacy philosophers refer to as 'wishful thinking'. But pragmatically it is compelling.

When one writes an essay one inevitably arrives at the problem of the conclusion. Perhaps I should just summarise what I have said. Although Sapolsky claims that science collectively has disproved the existence of free will, when he adduces findings from sciences other than neuroscience, these findings are dubious. His view that psychiatric disorders are permanent is wrong; his view that desert cultures reliably produce monotheistic religions is speculative; his reliance on priming experiments is misguided. If we presume that brains chaotically amplify quantum indeterminacy or that quantum events are somehow coordinated, we can imagine the possibility of supernatural causation. Quantum mechanics should in my view be rethought as involving a Bayesian conception of probability. And I think it necessary to at least pretend that something like 'free will' exists for pragmatic reasons. In this way we finally arrive at the end of the essay. Whether I am a rational analytical person or an intuitive emotional person is a question I leave to the reader.

An Open Letter to Robert Sapolsky

 Over the last week I have read almost all of Robert Sapolsky's book Determined. When I finish it, which should be today, I intend to start writing a reply to his argument and post it here. The reason I slowed down towards the end is because Sapolsky includes a section about 'schizophrenia' which I almost entirely disagreed with and it has been difficult for me to pick the book up again. I wrote an email to him concerning this section but received an automated response. The automated response does not say that he never reads emails but it seems likely that he will not read mine. So I have decided to publish the letter here.

Hi Dr Sapolsky,

I recently bought and have read most of Determined, Life Without Free Will. Although I have not yet quite finished it, I read with interest your discussion of schizophrenia. I am writing to you with some thoughts and criticisms concerning this part of the book.

You say that John Nash “struggled his entire adult life with schizophrenia”. I admit that this is the impression one gathers from watching the film A Beautiful Mind. However, although I have not read the biography the film is very loosely based on, I do know Nash said at some point in later life that he believed that medication "impeded the process of recovery". This strongly suggests that after he was permitted to go off medication, Nash indeed recovered. This though is not the message of the film, nor what you say in the book.

Interestingly I believe Virginia Woolf was schizophrenic. This may seem absurd – she was an accomplished writer who penned a number of literary masterpieces. However, if we recognise that if schizophrenia is anything at all it is an episodic condition, it seems less ridiculous. Just before she drowned herself, she wrote a letter to her husband saying, “The voices have come back and you and I can’t go through another one of those terrible times.” My feeling that Woof would have been diagnosed schizophrenic today is based not only on biographical information about her that I have picked up but on a reasonably close reading of the novel Mrs Dalloway.

You discuss research that suggests that the brains of schizophrenics shrink and quite rightly raise the question of whether it is the ‘condition’ or the medication that causes the brain shrinkage. You cite research that suggests the brains of schizophrenics have started shrinking even before the first psychotic episode, before the sufferer is put on ‘antipsychotics’. However I have read articles in psychiatric journals that suggest that it is indeed the drugs that cause the shrinkage. Olanzapine and Haloperidol were given to rats and monkeys (I think capuchin monkeys) and the experiments showed quite conclusively that it was indeed the drugs that caused the brain shrinkage. Research in areas like this is very heterogenous and is not conclusive. I wonder if you are cherry picking studies that support your argument.

I turn now to the most important issue. You describe ‘schizophrenia’ as “a disease of disordered thoughts”. You say that it is possible to pick that someone is schizophrenic from a thirty second encounter, from the “meandering incoherence” of their speech. I would like to suggest that you are quite wrong.

I first experienced a psychotic episode in 2007 at the age of twenty-seven. I believe that I had a vulnerability to psychosis caused by my parents’ divorce when I was seven and that the proximate cause of this first episode was acute stress occasioned by a stint working at a popular student radio station here in Auckland, New Zealand. I was removed from my flat and shortly after started seeing a psychiatrist who put me on the ‘antipsychotic’ Risperidone. At one of these early appointments, this psychiatrist leant towards me and said that his sister was schizophrenic, leading me to believe that I had been diagnosed schizophrenic myself. I experienced psychosis for the rest of the year, was reasonably well in 2008, and then became psychotic again in very early 2009. For the first time I began hearing voices. I was taking medication at the time. In August, after I threatened to kill myself, I was allowed to go off the Risperidone. Shortly after, I was put on Olanzapine. I was totally well from early 2010 until early 2013 at which time I became psychotic again and, having not been a patient of the Mental Health Service for a year, voluntarily reentered the Mental Health Service. My hope was to  receive competent psychological therapy rather than pharmacological treatment. In early 2014, I was put under a Compulsory Treatment Order which I am still under today. This has involved me coming into the clinic monthly, and for a period of several years fortnightly, to receive a long lasting injection of Olanzapine. 

In 2013, I asked my then psychiatrist what my diagnosis was. She said, “Schizophrenia”. Subsequently in medical reports I had to take to Social Welfare service centres, as they are called in New Zealand, my condition was described sometimes as “schizophrenia” and sometimes as “symptoms of schizophrenia”. I do not know if I am still supposedly diagnosed “schizophrenic” today but suspect that I still am.

I do not believe I have ever exhibited thought disorder. Even when I heard voices these voices didn’t cause me to say anything incoherent. My experience of voice-hearing was that in 2009 and early 2010, I would enter into what I believed were telepathic conversations with people like Jon Stewart and later Barack Obama; even then though I do not think I ever displayed disordered speech when talking with real people in the real world. There is only one instance that I can think of that comes close to disordered speech. In 2007 and 2009 I thought all the apparent right-wingers in New Zealand were really left-wingers pretending to be right-wingers and vice versa. Sometimes during this period my lovely mother and I would visit my godmother who lives in the small city of Whanganui. At this time, the mayor of Whanganui was a horrible reactionary called Michael Laws. I thought my godmother and her friends were pretending to dislike Laws but secretly liked him. I made a comment to my godmother on one occasion ostensibly critical of Laws but, by means of vocal inflection, tried to communicate to her that I was being ironic; I was trying to play the ‘game’ that everyone else seemed to be playing. A look of confusion crossed her face. As a result of this I reevaluated my beliefs and recognised that Michael Laws is genuinely a shit.

You might say that I wasn’t in a position to know if I was exhibiting thought disorder during these periods of psychosis. But I can approach this question in another way. In 2010 and 2011 I attended a weekly Coffee Group, an opportunity to socialise with other patients, where I met and conversed with a rotating cast of young people who were supposedly ‘mentally ill'; I occasionally attended this coffee group in 2012 and 2013. During this time, at least until 2013,  I was completely well. I never noticed any thought disorder in any of the other patients, never had any trouble understanding them.

You talk about thought disorder in terms of people being “pulled by the sounds of words, their homonyms, vaguely discernible leaps of connnectiveness.” I never noticed this in others or myself. If your claim were true then, by this logic, poets should all be classed as schizophrenics. In very late 2009 I met a girl at a Hearing Voices group, another supposed schizophrenic, who I fell for immediately. I sensed straightaway that she was very clever indeed. This girl loved palindromes and shared a couple with me very soon after we met. She had also memorised pi to a thousand places and would sometimes recite it as a party trick. This girl has gone on to win a number of prizes in poetry and has twice come second in the Sunday Star Times short story contest, the most important short story contest in New Zealand. Her most recent volume of poetry contains mostly extraordinarily difficult poetry – but this is not indicative of thought disorder but rather the obscurity of modern poetry that began with Modernists like Ezra Pound and has flowed through into Postmodernism. Her poetry reminds me of a very famous American poet, John Ashbery. This problematises any idea that we can ascribe thought disorder to people like this girl.

I return to the idea in your book that it is possible to pick whether someone is schizophrenic or not based on a thirty second encounter. In 2012, when I was on a very low dosage and was in the care of my GP rather than a psychiatrist, I undertook a Masters in Creative Writing through an Auckland university. Partway through the year I decided to write a screenplay about schizophrenia based on the girl I just mentioned and partly inspired by my own experiences. Not a single person in the class realised that I was drawing from my own life. In the screenplay the girl, who I called Jess, decides that she is responsible for the February 2011 Christchurch earthquake, something the real girl did. When I told my lecturer about this, he said, “They do that, don’t they.” Incredibly, by chance, there was a retired psychiatrist in the class.  (She initially wanted to write a novel about a sane man who accidentally finds himself in a lunatic asylum, taking her inspiration presumably from One Flew Over the Cuckoo’s Nest.) She had no idea I was drawing from life experience. The class read a portion of the screenplay in which Jess starts overhearing the thoughts of others in a supermarket. The retired psychiatrist said to me that schizophrenics don’t hear voices in the way I described in the screenplay. I felt like saying, “I actually know more about this than you do.”

This raises the very serious issue of confirmation bias. If I had been a patient in this woman's consultation room when she was still practicing, she might well have deliberately looked for thought disorder and so found it, by which I mean falsely imputed it to me. Because I was a fellow student in a creative writing class, she was simply not looking for evidence of thought disorder in my speech and so never considered the possibility that I might have experienced psychosis myself  Not that I ever actually displayed any thought disorder at the time.

I’ll tell one last story. I see my psychiatrist for half an hour once every three or four months. I never have any idea what to talk about. The consequence is that I may sometimes seem to exhibit thought disorder in his eyes even if I don’t display any thought disorder when talking with friends and family. At my first appointment with him I had told him I wanted a job and a girlfriend. Relatively recently I had an appointment with him at which my mother, key worker, and a medical student were present. I can’t remember the conversation precisely but he started off by asking me how I was getting on getting a girlfriend and then in a weird awkward way opened up the question to include the possibility of me getting a boyfriend. I suspect he was modelling current ‘best practice’ to the medical student, modelling the idea that psychiatrists should keep an open mind and not be homophobic. He opened up this question despite the fact that I have been saying I am only sexually attracted to women since 2013. I told him that I was only attracted to young women, that my difficulty was that I was too shy with girls and said that I was “on the opposite end of the continuum from Donald Trump.” My mother told me later that she understood exactly what I meant but the psychiatrist somehow got it into his head that I was saying that I wanted to fuck Donald Trump. So I had to clarify again that I am only sexually attracted to women by recounting how in 2013 I had heard a voice that said, “You’ll get a girlfriend when you’r forty” and how my fortieth had rolled around and it didn't happen. After I said this the trainee doctor gave off a small of shit, something I have learned to associate with men who feel some feeling like shame or guilt, who feel implicated in proceedings that are mendacious or corrupt. The person who displayed signs of insanity during that consultation wasn’t me, it was the psychiatrist.

Having told these stories about my own life I want to spell out the problems with your discussion of schizophrenia in Determined. You seem to be part of a movement to define schizophrenia less in terms of hallucinations and delusions and more in terms of thought disorder. The problem is no one can be sure that someone is exhibiting thought disorder because such observations are so easily biased. There is a bigger problem. You seem to be suggesting that schizophrenia is caused by an interaction between genes and childhood development and that it is a permanent lifelong condition. Robert, this view is evil. You’re interested in biological determinism whereas I am interested in cultural determinism. The reason people don’t recover from ‘schizophrenia' is that no-one thinks they can. A person who has had a single psychotic episode is stamped with the lifelong label “schizophrenic” and told that he or she has to take antipsychotics for the rest of his or her life even though these drugs potentially cause brain damage and definitely cause cognitive impairment. To look back on a person’s childhood and try to find predictive factors is like finding meaning in a Rorschach test, finding patterns in random data; in reality the causes of psychosis are different for every single person. The term ‘schizophrenia’ should be retired and drugs, if used at all, should be used sparingly, only for the duration of the psychotic episode.

Despite these misgivings I found your book very interesting. But I regard it as a philosophical argument which can be challenged in a number of places. I do not take it as gospel. I hope this email makes you reconsider your understanding of ‘schizophrenia’ a little. 

The above is the letter I wrote to Robert Sapolsky. In the next post I intend to discuss other arguments in his book, particularly his arguments concerning quantum physics, and also correct and expatiate on the argument concerning quantum physics I presented in the previous post.