Friday, June 29, 2012

The Mind Projection Fallacy

There is an argument that I have noted a couple of times when scientific colleagues with religious beliefs have tried to explain to me how they reconcile these seemingly contradictory things. Reality, they say, is divided into two classes of phenomena: the natural and the supernatural. Natural phenomena, they say, are the things that fall into the scope of science, while the supernatural lies outside of science’s grasp, and can not be addressed by rational investigation. This is completely muddle-headed, and seems to me to be based on an example of something called the mind projection fallacy.

A similar argument also crops up occasionally when advocates of alternative medicine try to rationalize the complete failure of their favorite pseudoscientific therapy to provide any evidence of efficacy in rigorous trials.

The very word ‘supernatural,’ at its heart, though, is one of those utterly self-defeating terms, like ‘free will’ and ‘alternative medicine,’ completely devoid of meaning and philosophically bankrupt. What is this free will that people keep going on about? Is it the freedom to break the laws of physics? No, and since every particle in your brain obeys the laws of physics, you are not free to make non-mechanistic decisions, so can we please shut up about free will? (Granted, I am using a restricted meaning of the term ‘free will.’)

And what is alternative medicine? Medicine is the use of interventions that are known to work in order to lessen the effects of disease. If it doesn’t work, or is not known to work, then its not medicine, full stop. There is no alternative. Lets please shut about alternative medicine.

What is the supernatural? Nature is by definition everything that exists and happens. What is outside nature is therefore necessarily an empty set.

The etymology of the word ‘supernatural’ is the result of an error of thinking. This error is the mind projection fallacy: falsely assuming that the properties of one’s model of reality necessarily exhibit correspondence with the actual properties of reality. The following dictionary definition of ‘supernatural’ was quoted to me in a recent discussion of the term (reportedly from Webster’s):

Supernatural. [adjective:] 1. of, pertaining to, or being ‘above or beyond what is natural or explainable by natural law’. 2. of, pertaining to, or attributed to God or a deity. 3. of a superlative degree; preternatural. 4. pertaining to or attributed to ghosts, goblins, or other unearthly beings; eerie; occult.

Number 1, is where we have to focus. Numbers 2 and 4 are, in origin at least, based on erroneous application of number 1, while number 3 is just weird. ‘Of a superlative degree’? That’s not supernatural, by any reasonable standard. ‘Preturnatural’? This word has two meanings (according to one is ‘supernatural’ (wow, that’s helpful) and the other is ‘exceptional or abnormal.’ Finding a hundred euros on the pavement would be both exceptional and abnormal, but again, not supernatural unless we are willing to debase the meanings of words to the level of uselessness.

So what about the primary meaning of supernatural, ‘above or beyond what is natural or explainable by natural law.’ The first part poses a problem, since there is no supplied procedure for determining what is natural, other than the obvious definition: ‘whatever is not supernatural.’ Now I’m aware that all word definitions are ultimately circular, but this is a case where the radius of curvature is clearly far to small to represent any useful addition to the language. The second part stipulates ‘explainable by natural law,’ which succumbs to exactly the same objection, but I strongly suspect that many people have failed to see this exactly because they have committed the mind projection fallacy – in this case, conflation of natural law with our description of it. Natural law is the set of principles, whatever they may be, that determine how real phenomena evolve. If a phenomenon is real, then it would be explainable by natural law. If a phenomenon is not real, then what is the point in debating whether or not it is supernatural? I feel, however, that too many people think that natural law is some set of equations, like E = mc2, written down in text books – but this is merely our model of natural law. I see no other convincing way to account for the appearance of this phrase in the quoted dictionary definition, than to assume that natural law is being commonly confused with known science in this way, since there seems to be no other good reason to postulate that a phenomenon is not governed by natural law (I know, the exact word was ‘explainable,’ but I think it is hard to rescue the situation by invoking this subtle difference).

By this common understanding of ‘supernatural,’ the photoelectric effect would have been supernatural in and prior to 1904, but natural before the end of 1905. A strange state of affairs, you might think.

Of course, word meanings don’t have to stick exactly to their original literal meanings, and anybody is free to apply the word ‘supernatural’ to any putative phenomenon they wish: gods, ghosts, whatever (as long as they are clear in what they are doing), but I argue firstly, that this is a misnomer, as nothing can be literally beyond nature (supernatural) and secondly, that use of this misguided word leads to horrendous confusions, such as those allowing highly educated and otherwise rational people to claim that religious phenomena (or homeopathy or chi) are by definition supernatural, and therefore by definition beyond the scrutiny of science.

The mind projection fallacy also raises its head in science, all too often, such as in quantum physics, and, in my opinion, in thermodynamics. It has also had very substantial consequences in the development and application of probability theory. Since scientific method generally strives to avoid fallacious reasoning, I feel that it is important to get well acquainted with this particular mental glitch, and to recognize some of the fields in which it still extends a corrupting influence.

Looking at thermodynamics, the famous second law, stating that the entropy of a closed system tends to increase, is often explained by the experts as resulting from our inability to distinguish between individual molecules (or other particles). My conviction, however, is that the mechanical evolution of an ensemble of such particles is unchanged if we are granted a means to identify them after they have evolved. The real reason for the second law seems to be that the proportion of possible initial microstates that result in non-increased entropy is very tiny (and such states appear, therefore with vanishing probability), but polluted with the standard language of the discipline, one can find it hard to grasp this. Why is this standard language an example of the mind projection fallacy? Because there is something unknown to us (the identities of the particles), and the fact of it being unknown is attributed as the cause of the physical evolution of the system, and therefore a physical property of the system. It is not, though, it is a property of our knowledge of the system.

With regard to quantum mechanics, I am open minded on the matter of whether or not nature evolves deterministically or non-deterministically. As I try to be a good scientist, I wait for the evidence to favour one hypothesis strongly over the other before casting my judgement. As much as we know about quantum mechanics already, that evidence is not yet in. I am, however, highly uncomfortable and skeptical about the possibility of something operating without a causal mechanism, yet exhibiting clear tendencies. It seems I am not alone in this, as several other well regarded thinkers have apparently shared this view, notably among them, the exceptional theoretical physicists Albert Einstein, Louis de Broglie, David Bohm, John Bell, and Edwin Jaynes. Imagine my delight, therefore, when I discovered the following passage by Jaynes in a book of conference proceedings1, articulating magnificently (and far better than I ever could) many of my own long-felt misgivings about the language of quantum mechanics:

The current literature on quantum theory is saturated with the Mind Projection Fallacy. Many of us were first told, as undergraduates, about Bose and Fermi statistics by an argument like this: “You and I cannot distinguish between the particles; therefore the particles behave differently than if we could.” Or the mysteries of the uncertainty principle were explained to us thus: “The momentum of the particle is unknown; therefore it has a high kinetic energy.” A standard of logic that would be considered a psychiatric disorder in other fields, is the accepted norm in quantum theory. But this is really a form of arrogance, as if one were claiming to control Nature by psychokinesis.

Whether or not the position and momentum of a particle (as related in the most familiar version of the Heisenberg principle) are truly ‘undetermined’ or merely unknowable to us, I am unsure, but there is a commonly encountered assumption that these two possibilities must be the same, and this results from the mind projection fallacy. It is indeed a mighty challenge to reconcile quantum phenomena with a fully deterministic mechanics. Some have succeeded, but it remains a challenge to pin down whether or not this is nature’s way. Many, however, follow Bohr and assert that there can be no underlying mechanism behind quantum phenomena. Let me quote Jaynes again (this time from ‘Probability theory: the logic of science’):

the ‘central dogma’ [of quantum theory]… draws the conclusion that belief in causes, and searching for them, is philosophically naïve, If everybody accepted this and abided by it, no further advances in understanding of physical law would ever be made… it seems to us that this attitude places a premium on stupidity.

The field in which the mind projection fallacy has had its most significant practical consequences is perhaps probability theory, which is a colossal shame, as probability is the king of theories: the meta-theory that decides how all other theories are obtained.

If you scan through the articles I have posted here on probability, you’ll observe that most if not all make use of Bayes’ theorem. It is an incredibly important and useful part of statistical reasoning, and represents the core of how human knowledge advances. It is also derived simply, as a trivial rearrangement of two of the most basic principles of probability theory: the product and sum rules. Yet, for a significant portion of the 20th century, when statistical theory was undergoing explosive development, Bayes’ theorem was rejected by the majority of authorities and practitioners in the field. How on Earth could this have come about? The mind projection fallacy, of course.

Because the theory models real phenomena in terms of probabilities, it was assumed that these probabilities must be real properties of the phenomena. Yet Bayes’ theorem converts a prior probability into a posterior probability by the addition of mere information. And since merely changing the amount of information cannot affect the physical properties of a system, then Bayes’ theorem must simply be wrong. QED.

The property that probability was thought to correspond to was frequency. For example, a coin has a 50% probability to land heads up because the relative frequency with which it does so is one half. For this reason, the orthodox school of statistical thought has become known as frequentist statistics.

One of the most extraordinary scientists of the 20th century, Ronald Fisher, for example, was one of the people who dominated the development of statistical theory during his lifetime. In his highly influential book, ‘The design of experiments,’2 he gave three reasons for rejecting Bayes’ theorem, foremost of which is:

… advocates of inverse probability [Bayes’ theorem] seem forced to regard probability not as an objective quantity measured by observable frequencies….

Clearly, he meant that the impossibility to reconcile Bayes’ theorem with the view of probability as a physical property of real objects (the frequencies with which different events occur) made it impossible to accept the theorem. (His other two reasons are just as bad.) It was Fisher’s deeply held objection to the logical foundations of probability theory that led him to do some of the most important work developing and popularizing the frequentist significance tests, which, as I have argued in detail here and here, are a poor method for assessing data. 

Another influential textbook, by Harald Cramér3, asserts that ‘any random variable has a unique probability distribution.’ Again, assuming that the probability is something objective and immutable, a physical property. The randomness is assumed to be necessarily a property of the system under study, rather than a statement of our lack of information – our inability to predict it before hand. To instantly recognize the ridiculousness of both Fisher’s and Cramér’s views, consider that I have just tossed a coin, which has landed, and I am asking you to assess the probability that the face of the coin pointing up is the one depicting the head: your only rational answer is 0.5, and it is the correct answer, for you. For me though, the correct answer is 1, because I am looking at the coin, and I can see the head facing up. Same physical system, different probabilities, dependent on the available information.

On the subject of probabilities as physical properties of the systems we study, I can again quote Jaynes, who has summarized the situation beautifully:

It is therefore illogical to speak of verifying [the Bernoulli urn rule, a law for determining probabilities] by performing experiments with the urn; that would be like trying to verify a boy’s love for his dog by performing experiments on the dog.

We can easily identify other instances of the mind projection fallacy in probability reasoning, some of which I have already discussed in earlier posts. For example, the error of thinking discussed in Logical v’s Causal Dependence, consisting of the belief that the expression P(A|B) can only be different from P(A) if B exerts a causal effect on A (an error that has made it into a number of influential textbooks on statistical mechanics) seems to arise from the conviction that a probability is an objective property of the system under study. If B changes the probability for A, then according to this belief, B changes the physical properties of A, and must therefore be, at least partially, the cause of A.

Another instance is to be found in The Raven Paradox, and consists of the belief that whether or not a particular piece of evidence supports a hypothesis is an objective property of the hypothesis, or the real system to which the hypothesis relates. In that post, we examined the supposition that observation of a sequence of exclusively black ravens supports the hypothesis that all ravens are black. We discovered an instance where such observations actually support the opposite hypothesis, illustrating that the relationship between the hypothesis and the data is entirely dependent on the model we chose. To think otherwise was shown to lead to disturbing and indefensible conclusions about ravens. 

[1] 'Maximum Entropy and Bayesian Methods,' edited by J. Skilling, Kluwer Publishing, 1989

[2] 'The Design of Experiements,' R.A. Fisher, Oliver and Boyd, 1935

[3] 'Mathematical Methods of Statistics,' H. Cramér, Princeton University Press, 1946