Or so Google tells me as of 1:25PM February 5th, 2018, at least. And this itself, if you think about it, is, well, scandalous. We know how to replicate the sun over thousands of targets scattered across the globe. We know how to destroy an entire world. Just don’t ask us how that knowledge works. We can’t even define our terms, let alone explain their function. All we know is that they work: the rest is all guesswork… mere philosophy.
By the last count provided by Google (in November, 2016), it had indexed some 130,000,000,000,000—that is, one hundred and thirty trillion—unique pages. The idea that no one, in all those documents, would be so struck by our self-ignorance as to call it a scandal is rather amazing, and perhaps telling. We intellectuals are fond of lampooning fundamentalists for believing in ancient mythological narratives, but the fact is we have yet to find any definitive self-understanding to replace those narratives—only countless, endlessly disputed philosophies. We stipulate things, absolutely crucial things, and we like to confuse their pragmatic indispensability for their truth (or worse, necessity), but the fact is, every attempt to explain them ends in more philosophy.
Cognition, whatever it is, possesses a curious feature: we can use it effortlessly enough, successfully solve this or that in countless different circumstances. When it comes to our environments, we can deepen our knowledge as easily as we can take a stroll. And yet when it comes to ourselves, our experiences, our abilities and actions, we quickly run aground. “It is remarkable concerning the operations of the mind,” David Hume writes, “that, though most intimately present to us, yet, whenever they become the object of reflection, they seem involved in obscurity; nor can the eye readily find those lines and boundaries, which discriminate and distinguish them” (Enquiry Concerning Human Understanding, 7).
This cognitive asymmetry is perhaps nowhere more evident than in the ‘language of the universe,’ mathematics. One often encounters extraordinary claims advanced on the nature of mathematics. For instance, the physicist Max Tegmark believes that “our physical world not only is described by mathematics, but that it is mathematical (a mathematical structure), making us self-aware parts of a giant mathematical object.” The thing to remember about all such claims, particularly when encountered in isolation, is that they simply add to the sum of ancient disputation.
In a famous paper presented to the Société de Psychologie in Paris, “Mathematical Creation,” Henri Poincaré describes how the relation between Fuchsian functions and non-Euclidean geometries occurred to him only after fleeing to the seaside, disgusted with his lack of progress. As with prior insights, the answer came to him while focusing on something entirely different—in this case, strolling along the bluffs near Caen. “Most striking at first is this appearance of sudden illumination, a manifest sign of long, unconscious prior work,” he explains. “The rôle of this unconscious work in mathematical invention appears to me incontestable, and traces of it would be found in other cases where it is less evident.” The descriptive model he ventures–a prescient forerunner of contemporary dual-cognition theories–characterizes conscious mathematical problem-solving as inseminating a ‘subliminal automatism’ which subsequently delivers the kernel of conscious solution. Mathematical consciousness feeds problems into some kind of nonconscious manifold which subsequently feeds possibilities of solution back to mathematical consciousness.
As far as the experience of mathematical problem-solving is concerned, even the most brilliant mathematician of his age finds himself stranded at the limits of discrimination, glimpsing flickers in his periphery, merely. For Tegmark, of course, it matters not at all whether mathematical structures are discovered consciously or nonconsciously—only that they are discovered, as opposed to invented. But Poincaré isn’t simply describing the phenomenology of mathematics, he’s also describing the superficiality of our cognitive ecology when it comes to questions of mathematical experience and ability. He’s not so much contradicting Tegmark’s claims as explaining why they can do little more than add to the sum of disputation: mathematics is, experientially speaking, a black-box. What Poincaré’s story shows is that Tegmark is advancing a claim regarding the deepest environment—the fundamental nature of the universe—via resources belonging to an appallingly shallow cognitive ecology.
Tegmark, like physicists and mathematicians more generally, can only access an indeterminate fraction of mathematical thinking. With so few ‘cognitive degrees of freedom,’ our inability to explain mathematics should come as no surprise. Arguably no cognitive tool has allowed us to reach deeper, to fathom facts beyond our ancestral capacities, than mathematics, and yet, we still find ourselves (endlessly) arguing with Platonists, even Pythagoreans, when it comes to the question of its nature. Trapped in millennial shallows.
So, what is it with second-order interrogations of experience or ability or activity, such that it allows a brilliant, 21st century physicist to affirm a version of an ancient mathematical religion? Why are we so easily delivered to the fickle caprice of philosophy? And perhaps more importantly, why doesn’t this trouble us more? Why should our civilization systematically overlook the scandal of self-knowledge?
Not so very long ago, my daughter went through an interrogation-for-interrogation’s-sake phase, one which I initially celebrated. “What’s air?” “What’s oxygen?” “What’s an element?” “Who’s Adam?” As annoying as it quickly became, I was invariably struck by the ruthless efficiency of the exercise, the way she need only ask a handful of questions to push me to the, “Well, you know, honey, that’s a little complicated…” brink. Eventually I decided she was pacing out the length and beam of her cognitive ecology, mapping her ‘interrogative topography.’
The parallel between her naïve questions and my own esoteric ones loomed large in my thoughts. I was very much in agreement with Gareth Matthews in Philosophy and the Young Child: not so much separates the wonder of children from the thaumazein belonging to philosophers. As Socrates famously tells Theaetetus, “wonder is the feeling of the philosopher, and philosophy begins in wonder.” Wonder is equally the feeling of the child.
Socrates, of course, was sentenced to death for his wonder-mongering. In my annoyance with my daughter’s questions, I saw the impulse to execute Socrates in embryo. Why did some of her questions provoke irritation, even alarm? Was it simply my mood, or was something deeper afoot? I found myself worrying whether there was any correlation between questions, like, “What’s a dream, Daddy?” that pressed me to the brink almost immediately, and questions like, “How do airplanes fly without flapping?” which afforded her more room for cross-examination. Was I aiming her curiosity somehow, training her to interrogate only what had already been interrogated? Was she learning her natural environment or her social one? I began to fret, worried that my philosophical training had irreparably compromised my ability to provide socially useful feedback.
Her spate of endless, inadvertently profound questioning began fading when she turned eight–the questions she asks now are far more practical, which is to say, answerable. Research shows that children become less ‘scientific’ as they age, relying more on prior causal beliefs and less on evidence. Perhaps not coincidentally, this pattern mirrors the exploration and exploitation phases one finds with reinforcement learning algorithms, where information gathering dwindles as the system converges on optimal applications. Alison Gopnik and others suggest the extraordinary length of human childhood (nearly twice as long as our nearest primate relatives, the chimpanzee) is due to the way cognitive flexibility enables ever more complex modes of problem-solving.
If the exploration/exploitation parallel with machine learning holds, our tendency to question wanes as we converge on optimal applications of the knowledge we have already gained. All mammals undergo synaptic pruning from birth to sexual maturation—childhood and adolescent learning, we now know, involves the mass elimination of synaptic connections in our brains. Neural connectivity is born dying: only those fed—selected—by happy environmental interactions survive. Cognitive function is gradually streamlined, ‘normalized.’ By and large, we forget our naïve curiosity, our sensitivity to the flickering depths yawning about us, and turn our eyes to this or that practical prize. And as our sensitivity dwindles, the world becomes more continuous, rendering us largely oblivious to deeper questions, let alone the cavernous universe answering them.
Largely oblivious, not entirely. A persistent flicker nags our periphery, dumbfoundings large and small, prompting—for some, at least—questions that render our ignorance visible. Perhaps we find ourselves in Socratic company, or perhaps a child poses a striking riddle, sooner or later some turn is taken and things that seem trivially obvious become stupendously mysterious. And we confront the scandal: Everything we know, we know without knowing how we know. Set aside all the guesswork, and this is what we find: human experience, ability, and activity constitute a profound cognitive limit, something either ignored outright, neglected, or endlessly disputed.
As I’ve been arguing for quite some time, the reasons for this are no big mystery. Much as we possess selective sensitivities to environmental light, we also possess selective sensitivities both to each other and to ourselves. But where visual cognition generally renders us sensitive to the physical sources of events, allowing us to pursue the causes of things into ever deeper environments, sociocognition and metacognition do not. In fact, they cannot, given the astronomical complexity of the physical systems—you and me and biology more generally—requiring solution. The scandal of self-knowledge, in other words, is an inescapable artifact of our biology, the fact that the origin of the universe is far less complicated than the machinery required to cognize it.
Any attempt to redress this scandal that ignores its biological basis is, pretty clearly I think, doomed to simply perpetuate it. All traditional attempts to secure self-knowledge, in other words, likely amount to little more than the naïve exploration of discursive crash space–a limit so profound as to seem no limit at all.