The September 2019 Special Issue of Scientific American is a must read. Unfortunately it is behind a paywall, so you should purchase a copy at a store or digitally online. All the articles are fascinating and relevant, and address basic questions of epistemology—how do we know what we know? The first section, “Truth”, is the most pertinent to my thinking, as it covers three subjects I have been pondering for years.

Physical Reality. The first article in the section is “Virtually Reality: How close can physics bring us to a truly fundamental understanding of the world?” by George Musser. I have addressed this issue of physical reality in my article Angular Momentum, with an emphasis on the role of mathematics. Musser cites the difficulties of trying to understand quantum mechanics after almost one hundred years or the failure to marry quantum mechanics with Einstein’s theory of gravitation as possible indications that there might be limits to our human endeavor to comprehend physical reality. This frustration is not new:

Over the generations, physicists have oscillated between self-assurance and skepticism, periodically giving up on ever finding the deep structure of nature and downgrading physics to the search for scraps of useful knowledge. Pressed by his contemporaries to explain how gravity works, Isaac Newton responded: “I frame no hypotheses.”

Mathematical Reality. The second article, “Numbers Game: Philosophers cannot agree on whether mathematical objects exist or are pure fictions” by Kelsey Houston-Edwards, discusses in depth the issue of mathematical reality, namely whether math is discovered or invented, as I did in my article Meditation on “Is” in Mathematics II – Mathematical Reality. Kelsey Houston-Edwards’ article reprises her excellent Youtube 2016 Infinite Series video Are Prime Numbers [and Math] Made Up? Huston-Edwards suggests that both invention and discovery are involved in mathematics. And she adds a third component, proof.

Mathematicians judge foundational objects (such as negative numbers) and their properties (such as the result of multiplying them together) within the context of a larger, consistent mathematical landscape. Before proving a new theorem, therefore, a mathematician needs to watch the play unfold. Only then can the theorist know what to prove: the inevitable, unvarying conclusion. This gives the process of doing mathematics three stages: invention, discovery and proof.

Personal Reality. Finally, the third article in the section, “Our Inner Universes: Reality is constructed by the brain, and no two brains are exactly alike” by Anil K Seth, discusses what I would call our personal reality, that is, how we physically perceive and establish the everyday reality of ourselves and our surroundings. I have been meaning to examine this last topic, since there are a number of unsettling recent discoveries that cast a new perspective on this ancient subject. But Seth’s article is an excellent summary.

The idea that the world of our experience might not be real is an enduring trope of philosophy and science fiction … Although these chunky metaphysical topics are fun to chew on, they are probably impossible to resolve. Instead what we have been exploring throughout this article is the relation between appearance and reality in our conscious perceptions, where part of this appearance is the appearance of being real itself.

The central idea here is that perception is a process of active interpretation geared toward adaptive interaction with the world through the body rather than a recreation of the world within the mind. The contents of our perceptual worlds are controlled hallucinations, brain-based best guesses about the ultimately unknowable causes of sensory signals. And for most of us, most of the time, these controlled hallucinations are experienced as real. …

What this means to me is that the property of realness that attends most of our perceptions should not be taken for granted. …

[Furthermore,] when we experience things as being real, we are less able to appreciate that our perceptual worlds may differ from those of others.

Seth discusses a number of experiments that involve virtual reality (VR) systems. The idea of a VR system becomes more than a tool. Joshua Rothman, in his 2018 New Yorker article “As Real as It Gets: Are we already living in virtual reality?”, narrates numerous experiences with VR systems that challenge our basic notions.

[Virtual reality researcher Mel Slater says,] “On some level, the brain doesn’t know the difference between real reality and virtual reality.” Embodied simulations seem to slip beneath the cognitive threshold, affecting the associative, unconscious parts of the mind. “It’s directly experiential,” Slater said. “It’s not ‘I know.’ It’s ‘I am.’ ”

All these efforts to “know”, to “understand”, that are mediated by our human minds are challenged by the fear that it is impossible. Yet we can’t seem to stop trying. I am ultimately left with my absolute favorite quote from my favorite author, Jorge Luis Borges, from one of his best essays, “Avatars of the Tortoise” (from Other Inquisitions 1937-1952, in Labyrinths, Selected Stories & Other Writings, Donald A. Yates and James E. Irby, editors, New Directions, New York, 1964):

It is daring to think that a coordination of words (philosophies are nothing more than that) can resemble the universe very much. It is also daring to think that of all these illustrious coordinations, one of them—at least in an infinitesimal way—does not resemble the universe a bit more than the others. I have examined those which enjoy certain prestige; I venture to affirm that only in the one formulated by Schopenhauer have I recognized some trait of the universe. According to this doctrine, the world is a fabrication of the will. Art—always—requires visible unrealities. Let it suffice for me to mention one: the metaphorical or numerous or carefully casual diction of the actors in a drama . . . Let us admit what all idealists admit: the hallucinatory nature of the world. Let us do what no idealist has done: seek unrealities which confirm that nature. We shall find them, I believe, in the antinomies of Kant and in the dialectic of Zeno.

“The greatest magician (Novalis has memorably written) would be the one who would cast over himself a spell so complete that he would take his own phantasmagorias as autonomous appearances. Would not this be our case?” I conjecture that this is so. We (the undivided divinity operating within us) have dreamt the world. We have dreamt it as firm, mysterious, visible, ubiquitous in space and durable in time; but in its architecture we have allowed tenuous and eternal crevices of unreason which tell us it is false.

Translated by James E. Irby [with three minor tweaks by me]