Deep Beauty

Several years ago Nick Bostrom at Overcoming Bias suggested as an intellectual exercise to write a hypothetical apostasy: whether or not you actually believe it, could you write a plausible argument renouncing your most deeply held beliefs?

Later, reading through The Sensory Order, I knew that my own would have to hinge on this Lovecraftian thought (8.39):

The fact that the world which we know seems wholly an orderly world may thus be merely a result of the method by which we perceive it.

To talk about the beauty or order of the universe, of mathematics – of anything really – becomes a statement not about those things themselves, but about the structure of the perceiving mind. This statement may even be equally valid for all minds; a description of the necessary structure of human thought. The human brain, the book argues, is a classification apparatus, and as such is totally incapable of even perceiving a wholly disordered system, or an object which has no connection to previous experience. Things are perceived by their meaning to the mind, and deep disorder means – precisely – nothing. The mind, therefore, “imposes” order on a cold world.

What if it is all a conspiracy then? When a person forces too many events into a neat narrative, we call him paranoid. Is the sensus divinitatis – even the sensus pulchritudine – merely a convenient paranoia to sustain the rational faculty through the inhospitality of a cold world?

Here, perhaps unexpectedly, we find an evolutionary answer. Could the rational faculties have had such resounding success, not only in reproduction but in material advancement, if they did not indeed reflect something objectively true (and not merely intersubjectively valid) about the universe? The feedback loops which drive both natural selection and economic growth would be dead ends if the inception of the rational faculty on the one hand, and the continued use of it on the other, did not bring tangible and investible success. And what can such success mean except a real correspondence, imperfect as it may be, between the structure of thought and the structure of the universe?

What this means is that there is no need for the dualism that strictly separates the clean and abstract logical-mathematical world from the messy and concrete real world. For the real world, though messy, is indeed ordered “cleanly” in a manner which corresponds to the structure of our own minds. We don’t “impose” arithmetic and logic on the world, but we don’t exactly observe them there either. Jan Pavlik calls this the monistic (as opposed to dualistic) approach to evolutionary apriorism:

If the functioning of human mind includes some kinds of necessary a priori relationalisations (such as the teleological order of thought, the principle of constantly operating causes, formal logic, universal grammar, etc.), and if human mind is a part of nature and stems from it, then nature, too, must contain some sorts of necessary relations and interconnections . . . Thus, the necessary relations and interconnections (laws of nature) which enabled the rise and functioning of the necessary a priori relationalisations which take place in human minds, have to exist really (objectively).

In other words, though we cannot directly perceive those “clean” rules by which the universe operates, we find them mirrored in our own psyches, enabling us to make sense of what we perceive by our senses. These a priori rules form the basis of rational thought. They themselves do not constitute rational thought, for numerous are the animals without such a capacity. But as it became clear enough to support what we recognize as rational thought, this reflection enabled substantial and undeniable material success.

The theory of spontaneous order, compelling as it is so far as it goes, is thus insufficient to account for the facts. The earth is not merely order out of chaos, as if beneath all the order lay merely chaos. The material success of mankind – reproductively, economically, and scientifically – testifies to the universe’s fundamental order reflected in the structure of human thought. Again Pavlik:

The a priori causal relations as imposed by our reason into relationless sensory phenomena correspond to some relations as existing in the reality which is the external source of our sensations. Namely, the external (physical) reality appears via sensations only partly, in a reduced manner – as being devoid of relations at all; the a priori causal relationalisation, as performed by our reason, supplements, so to say, what is missing at the level of sensory phenomena, and helps us to have a full, non-reduced reflection of reality. Thus . . . the imposition of relations is at the same time their reflection.

Without these universal rules mirrored in our own minds, sense data would appear to us relationless – meaningless and chaotic. The rules which our mind “imposes” on sense data in order to derive significance from them, reflect these universal rules as they actually exist.

To lack the rational faculty completely would be, from an evolutionary perspective, preferable to a rational faculty which did not correspond to the logical structure of the universe. We know plenty of non-rational animals, but there are no irrational animals. This suggests that the rules of the innate rational faculty are by no means complete; they are simply not wrong so far as they go. What our mental apparatus does not possess innately, we extend via science and philosophy. As Hayek put it, again in The Sensory Order (8.24),

Science tends necessarily towards an ultimate state in which all knowledge is embodied in the definitions of the objects with which it is concerned; and in which all true statements about these objects therefore are analytical or tautological and could not be disproved by any experience. The observation that any object did not behave as it should could then only mean that it was not an object of the kind it was thought to be.

In other words, the goal of cognitive effort, both in science and philosophy, is not merely to accumulate sense data, but to extend the realm of the a priori categories beyond those that we possess innately. Pavlik’s paper discusses this process at length.¹ These rules and categories, both the innate and the extended, are the means by which we perceive beauty. Indeed, beauty is the organizing principle (whether tacit or explicit) of all the other categories – and in this sense it might be called a meta-category. However deeply we probe, however many turns of the spiral we take, beauty cannot be transcended in the same way that other a priori categories can, because its pursuit is what impels the transcendence of the other categories. Indeed, in the process of extending our knowledge, beauty is not found but assumed – and then delighted in once confirmed. Science cannot dispense with the assumption of fundamental beauty, nor can it falsify it. A cold, godless, and fundamentally chaotic universe would be one in which science could elucidate nothing.

The appreciation of beauty is at the core of the rational faculty; the core of what makes us human. This is what the old theologians meant in saying that the human will is oriented towards the good in a formal sense, however the will might understand that. The Good – the Beautiful – is not just a philosophical abstraction, but is built a priori into the structure of human thought at a deeper level even than the concepts of time and space. At this deepest level we must surmise that the fundamentality of beauty to human cognition is no paranoia, but like the extensible categories, reflects something objectively true about the universe.

C.S. Lewis describes at the end of Perelandra a divine vision of unfathomable complexity – and “even then, at the very zenith of complexity, complexity was eaten up and faded, as a thin white cloud fades into the hard blue burning of the sky, and a simplicity beyond all comprehension, ancient and young as spring, illimitable, pellucid, drew him with cords of infinite desire into its own stillness.” Is this not mankind’s experience of our world? From what simple principles do we build up such complex mathematics, and with what complex mathematics do we finally prove that the electromagnetic and weak forces were aspects of the same thing all along! The search for a unified theory of physics proceeds frantically. What faith have these scientists in a beautiful universe!

It is, of course, a faith like a whetted appetite. A glimpse of beauty and the fervent desire for more. But isn’t this what any faith worth having has always been?

Footnotes

1. His example is the transition from classical to quantum mechanics: the a priori rule of causal determinism was revealed to be merely a special case of more general quantum principles. Here, however, the hard limits of the extension of the mind’s a priori categories become plain. Those categories are indeed extensible, but not indefinitely; and are certainly no match for the extent of what could in principle be observed scientifically. Quantum physics is, by all accounts, unintuitive – not merely in the sense that it doesn’t conform to one’s immediate intuition, but that it is actually impossible to grasp intuitively in the way classical physics could be done. We can go where the math takes us, but the mind is ill-suited to grasp its meaning in physical terms.