Some Thoughts About “Reality Is Scalar”

[Galilée] déclare que dans tous ces phénomènes il faut mesurer tout ce qui est mesurable, et tâcher de rendre mesurable tout ce qui ne l’est pas directement.
[“[Galileo] declares that in all these phenomena we must measure all that is measurable, and try to make measurable all that is not directly so.”]
—Thomas-Henri Martin, Galilée: Les Droits de la Science et la Méthode des Sciences Physiques (1868)

When we describe the world, we often use categories to do so. We say that there are red objects and blue objects, poor people and rich people, lions and tigers, etc ad inf. These categories are useful to us, because they provide useful rules of thumb for understanding the world and predicting what the effects of our and others' actions will be. We can predict that a lion will behave differently to a tiger, or a red object will match some othe object better than a blue one.

Where we go wrong is to think that those categories that we apply to the world for our convenience are absolute. Taking the colour example, in truth these are just ranges on a scale, and fuzzy ranges at that, which we group into convenient bands. English is developed enough that we have basic colour names to a fairly high degree of specificity, but there are many languages with far fewer basic colour names, and even in English the cross-over points between different colours are fuzzy, ill-defined.

Our categories are useful only insofar as they correspond to real differences within scalar ranges. In particular, there are often threshold effects: tipping points at which a major change in some property of the object occurs, even when there is little change in that property outside of those ranges. Temperature and states of matter are a good example of this. For many basic substances there are two temperature thresholds where the substance undergoes a rapid and significant—and real—change in its properties: the melting / freezing point; and the boiling / condensing point. Water at 90°C behaves differently to water at 10°C, but in some important ways they are still more similar to each other than either is to water at 110°C. The temperature is scalar in a linear way; the state of matter depending (largely) on the temperature is scalar in a stepped way. Around the thresholds, the stepped scale moves faster, and is observable as a scale: for example, within the narrow range around the melting / freezing point, melting is a process rather than a binary switch. These differences in properties between ranges are real, but that does not make the categories absolute in themselves; we could usually choose different boundaries if it were useful to us to do so. Reality itself must be seen as scalar.

Where do categories tend to arise, especially in nature? At some point we do need to make decisions, and because those decisions are categorical, we must crystallise the spectrum into categories corresponding to the decisions we need to take. The feedback effect from those decisions in turn forces scalar reality to diverge and categorise. An excellent example is the binary division between the sexes: a thousand million years of sexual reproduction, with millions of millions of sex acts every day, have reïfied those mating decisirons into (by the scalar standards of the natural world) an unusually rigid and uniform system of sex differences. Speciation results from the same effect: aeons of mating decisions resulting in visibly categorical outcomes.

The problematic effects of treating scalar reality as categorical (sometimes called “binary thinking”, the most extreme version of the error) appear in many places. Most of all, due to the forcing effect of decision-making, they stem from our treating our decisions as iron laws rather than pragmatic guidelines. Because reality is scalar, even when there are extreme threshold effects, there will always be edge cases that cannot be appropriately covered by iron laws. It may sometimes even be more appropriate to treat the edge cases as a category in themselves, but either this is precluded by categorical thinking rigidly insisting on its categories, or the edge cases are treated so rigidly as their own category that their similarities to their adjacent categories on the continuous scale are themselves ignored.

This is especially true in the social sciences and moral philosophy¹, because they themselves exist in the central portions of the reality scale between hard material reality, where it is usually obvious to think in a scalar fashion, and pure concept, where it is unproblematic or even appropriate to think in categorical terms. The social and moral domains are precisely about how our concepts map to underlying behaviours that are impossible to measure precisely, and where our decisions are of profound personal importance. But just because it is difficult for us to measure socio-moral properties does not mean that those properties are purely conceptual, and therefore categorical rather than scalar. While there are cases where our decisions have been reïfied into categories, in practice the more common error is treating our descriptive categories as defining reality itself.

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