I’m often frustrated by the poor quality of discussion of the problem of overpopulation (if indeed it is a problem). It seems to me that almost all participants to the discussion have missed one of the most important insights of evolutionary theory, an insight attributable to Malthus.

The population of any species in any closed habitat would rise geometrically, but it cannot, because it always hits a “ceiling”. This ceiling is mostly set by supply. I mean to construe “supply” in the most general terms – usually what matters is the availability of such necessities for living as food, water, and light. But it can include more, such as the availability of ornaments used by bower birds in sexual selection.

Where weeds can grow, weeds do grow. The weed population expands, and only stops expanding when overcrowding prevents further expansion. Where bower birds can build ornate bowers, bower birds do build ornate bowers. The bower bird population expands, and only stops expanding when the quality of the poorest-quality bowers is too low for their builders to have realistic hopes of getting chosen by female bower birds, and hence to reproduce. In both cases, the population bounces along the ceiling like a helium balloon that has slipped out of a child’s grasp. The ceiling is set by supply, although what needs to be supplied differs sharply from one species to the next.

Of course there is an attrition rate: some members of the population are picked off by predators. But that rate is set by the population of the predators, which in turn is set by their food supply – in other words, by the replacement rate of the population they prey upon, which is exactly where we started.

How much each individual consumes of the supply decides how many individuals there are. For example, a given field that can sustain a population of 100 rabbits might only be able to sustain 10 sheep, or 50 rabbits and one fox.

So two components determine the number of individuals: the supply and the rate of consumption. (Perhaps I mean “demand” here, but I know nothing about economics, and I don’t want to suggest that I am talking about anything other than biology.)

The human population rose dramatically in recent centuries, not because humans decided they wanted to have more children, or because they became more sexually promiscuous, or because many generations have passed since The Great Flood, or even much because advances in sanitation and medicine lowered the attrition rate. It was mostly because food became easier to procure, thanks to cheaper energy and advances in agricultural technology.

So although there may be a human overpopulation problem, an increase in the population is a sign of good things happening, or at least of good things having happened. Although there may be trouble ahead, the trouble will not be that the expanding population finally “hits a wall” of the Earth’s “carrying capacity”. That “wall” is better understood as a ceiling, and the population has always been already at that ceiling. It is hardly ever acknowledged that the normal condition of the Earth is to be at “carrying capacity”, and that at all times some places enjoy a surplus while others suffer a famine, with the same statistical inevitability as floods and droughts. The trouble is not that we hit a wall or a ceiling but that the ceiling might start to get lower. This could happen if energy to produce food became significantly more expensive. The reality of a lowering ceiling is famine.

There are two obvious ways to lower the population, if indeed that is a good thing to do. The first is to artificially lower the ceiling by limiting the supply. The second is to increase consumption of each individual so that the same habitat can sustain fewer individuals. Suppose we are again considering grazing animals in a given field of grass. In effect, the first solution is to lower the number of rabbits by having less grass. The second solution is to lower the number of grazers by turning the rabbits into sheep.

In the case of rabbits and sheep, the “supply” is of grass. In the case of humans, the “supply” is of more costly and abstract items, things more like the ornaments of bower birds. All humans need an education, for example, although giving a child a good education generally entails having fewer children. In increasingly affluent countries, humans get increasingly ambitious about their need for houses, and cars, and expensive clothes, and foreign holidays, and memberships to golf clubs. Although we may disapprove of the levels of consumption here, we should remind ourselves that such levels are a good way of keeping the population down. People who have high expectations for their children have fewer of them, and invest more in each. This explains why as societies become more affluent, life becomes less cheap, and the birth rate generally drops.

Physics has gone mental

Nowadays physicists routinely talk about probability, information, entropy, order and so on as if physics were the science of mental properties, quantities or entities – as if its subject matter were the mind-stuff or “immaterial substance” of Cartesian fantasy.

I think that is silly, disappointing and wrong. In taking this “turn for the mental”, physics has become conceptually pathological. There are two obvious reasons why it took that turn. The first reason is that physics and modern Western philosophy have drifted apart over the decades, so that physicists no longer recognise the virtues of clarity, realism and materialism. And they give little thought to genuinely mental entities such as beliefs and desires. The second reason is that no one understands quantum theory, and many quantum phenomena are frankly weird. Some physicists (such as Richard Feynman) honestly admit that they don’t understand it. Others pretend that that they do understand it, and use the weirdness as a pretext for all manner of conceptual immodesty and metaphysical extravagance.

We have to accept weirdness as a last resort when it is thrust upon us – but that’s quite different from going straight for it as a first resort. Some recent physics warmly embraces “spiritualism” of a sort usually associated with primitive religions.

At one time, there was no distinction between physicists and philosophers. But as science grew more technical, philosophy grew more envious. Communication between the two grew more difficult. We have now reached a stage where there is almost no communication or mutual criticism at all. Philosophers do not dare to question physics, and physicists do not care enough to question philosophy, because they couldn’t be bothered to learn any. This is a tragedy for both of them. Philosophers squirrel away at irrelevancies, engaged in the narcissistic exhibition of technical prowess. Meanwhile physicists try to answer the big questions – and often fall flat on their faces because they’ve learned nothing from the mistakes that philosophers have made before them.

However, I think there is light at the end of the tunnel: it seems to me that sooner or later, the “spiritualism” of much modern physics will become testable. My money is on its being disproved by careful observation. In the spirit of adventure rather than the spiritualism of disembodied mind-stuff, I hereby offer some criticism.

For an example of how physicists have become purveyors of mind-stuff, consider probability. The word ‘probability’ is ambiguous, often dangerously and misleadingly so. In statistics, it refers to relative frequency, or more precisely to a limiting value of relative frequency. For example, the probability of throwing doubles with a pair of dice is one sixth: what that means is that in repeated throws of a pair of dice, a proportion of about one sixth will end up as doubles. The more throws there are, the closer that proportion tends to get to one sixth. So we can fine-tune this statistical understanding by saying that one sixth is a limiting value – it is approached as the limit of the relative frequency of doubles as the number of throws increases.

That statistical sense of the word ‘probability’ is relatively new. For most of history, and in everyday usage, words like ‘probable’, ‘probably’, ‘likely’, etc. express something quite different. They express not relative frequency but credibility: not a numerical proportion, but the idea that another idea ought to be believed. If I say “It will probably rain tomorrow”, I mean the idea, claim or proposition that it is raining tomorrow deserves belief. The two senses are often confused, especially in contexts where relative frequency is taken as the basis for belief. For example, most hands in poker do not contain four of a kind. When playing poker, I might actively adopt the belief that my opponents do not have four of a kind, because it is statistically such a rare event. (However, as professional gamblers know, that would not be a wise long-term strategy: in a long enough series of hands, four of a kind becomes a statistical inevitability.)

Relative frequency is a wholly “objective” feature of the world. It has everything to do with what numerical proportion of members of a class of real things have a real property, and nothing to do with truth or falsity, nothing to do with beliefs, nothing to do with oughts, nothing to do with ideas about ideas, nothing to do with rationality. Physics just doesn’t measure epistemic probability – the “subjective” matter of how much a claim ought to be believed. So probability in quantum theory must be construed statistically – that is, in objective numerical terms of relative frequency. That’s because physics doesn’t “do” beliefs, or propositions, or anything that has “meaning” like that.

Only representations have “meaning” – representations as found in the mind, in art, and in language. Representations as not found inside atoms, or between the galaxies of the cosmos. Things inside brains have “meaning”, of course, as does communication between brains in the form of human language. And brains are physical. But physics is not the study of brains or languages.

Epistemic probability is “subjective” in the sense that it always depends on what is already believed. How much the claim that it will rain tomorrow deserves to be believed depends on whether you have heard the weather forecast, on how much you trust the weather forecast, and so on. It depends on you. Since different people believe different things, epistemic probability differs from one individual to the next. And since an individual’s beliefs change with the passing seasons, epistemic probability also fluctuates with time. Because it is subjective like that, this sort of probability cannot be measured using numbers. In fact it is hard to say what a number could possibly refer to or quantify in this context. A belief either can be attributed to an individual, or else it cannot be so attributed. It’s an all-or-nothing matter, not a matter of degree. We might speculate that a number might measure the “depth” to which a belief is “entrenched” in the believer’s belief-system – in effect, the agent’s relative reluctance to abandon it in the face of countervailing evidence – but this is an extremely complicated and abstract sort of metric.

It doesn’t matter. As long as we remember that truth and falsity are “objective”, it is salutary to be reminded that credibility is “subjective”. It is a matter of judgement, and often a matter of intuition, not numbers.

The confusion of relative frequency and credibility tends to really get going when we jump from thinking about a class of events, plural, to thinking about an individual event, singular. Suppose quantum theory tells us that 50% of electrons from a given source have a particular property. This is like saying that 50% of tossed coins will result in “heads” rather than “tails”. In both cases, it might be tempting to think that we have some useful knowledge about how individual coins or electrons will behave. But all the knowledge we have is already fully expressed by the statistical claim about the class. We don’t know anything about individual electrons, or individual coin tosses.

If we fail to acknowledge our own ignorance here, we are liable to think we can attach a credibility of 50% to the idea that an individual electron or coin has a particular property. Next,we might imagine that the individual electron or coin has a “diluted” version of the property, one diluted by having a weaker “potential” to command belief. Now remember, apart from the conceptual murkiness of the move here, the credibility of an idea depends on the mind contemplating it, whereas genuine properties are objective features of the world. So it’s a completely nutty idea that individual electrons or coins could have a property of more or less “diluted credibility”. Such a bizarre property would be almost literally “attached” to the electron or the coin itself, like a price tag. This imaginary “tag” supposedly quantifies its “worth” – not its monetary worth, but how much it is worth believing that it will yield this or that result when observed or tossed.

If we’re honest, I think many of us will admit to thinking about probability in that way. We “objectify” something subjective, rather as we might suppose that the worth of a desired object is given by its price tag rather than by how much we desire it (which also depends on the mind). “A picture holds us captive”, as Wittgenstein would say. And it holds us captive because our intelligence has been bewitched by language, specifically, by an ambiguity in the word ‘probability’.

We needn’t be held captive if we insist that claims about probability in coin tosses and in quantum theory should be understood statistically rather than as ghostly disembodied “ideas about ideas” attached like price tags to as-yet untossed coins or as-yet unobserved electrons. Perhaps that commits me to some sort of (non-local) “hidden variables” interpretation of quantum theory. So be it – the alternative is grossly immodest conceptual madness, and avoiding that is as essential to decent science as avoiding ouija boards.

The malaise in physics isn’t limited to quantum theory. The word ‘information’ is as ambiguous as the word ‘probability’, and once again many physicists embrace a wonky “spiritual” interpretation as a first resort. I’ll return to the topic of “information” in a few days’s time. (In physics, it should be understood as reliable co-variation rather than as any sort of weird disembodied mind-stuff.)