Man is equally incapable of seeing the Nothing from which he was made, and the infinite in which he is swallowed up.” So wrote Blaise Pascal, the 17th-century French mathematician, physicist, inventor, theologian, and philosopher. Like many thinkers before and since, Pascal was intrigued by the concept of infinity, and how humans occupy the middle ground somewhere between the infinitely large and the infinitely small.
But while Pascal—along with countless other thinkers of the past—grappled with the puzzle of infinity using reason alone, we now have the tools of modern physics to help us understand more precisely the vast scales of space and time that surround us.
What modern physics can tell us about nothingness and infinity—and its implications for the universe, life, and the mind—is the ambitious topic explored by physicist Alan Lightman in his latest book, Probable Impossibilities.
Let’s start with some numbers that neither Pascal nor any pre-modern thinker would have known. Taking three objects—an atom, a human, and the sun—we can ask two related questions posed by Lightman: First, how many times would the size of a human have to be halved to reach the size of an atom? Answer: 33.
Second, how many times would the size of a human have to be doubled to reach the size of our sun? Answer: 30. Roughly speaking, then, the size of a human lies halfway between an atom and a star. Just as Pascal imagined, we are truly positioned between two immensely large and infinitesimally small worlds.
But we know that these are not the smallest or largest structures in the universe, and we know that, mathematically speaking, we can always add one to a number or divide a number by two. This raises two further questions: (1) Can we always just move a little farther out in the universe, without end, going on forever in infinite space? (2) Can we keep dividing an atom in half, finding ever-smaller constituent parts ad infinitum?
While Pascal may have thought the answer was yes to both questions, modern physics, according to Lightman, says the answer is no. While theoretical or potential infinities exist (in mathematical terms), actually physical infinities likely do not, as modern physics places limits on just how small or large something can get.
Let’s start with the small. Since the discovery of the atom, we have since identified several subatomic particle types and have further discovered that protons and neutrons (which make up the atomic nucleus) are themselves composed of smaller units known as quarks. In an article titled How big is a quark?, physics professor Jon Butterworth describes the size of a quark:
“It is, as one might expect, very small indeed. The data tell us that the radius of the quark is smaller than 43 billion-billionths of a centimetre (0.43 x 10−16 cm). That’s 2,000 times smaller than a proton radius, which is about 60,000 times smaller than the radius of a hydrogen atom, which is about forty times smaller than the radius of a DNA double-helix, which is about a million times smaller than a grain of sand. So there. Quarks (along with electrons) remain the smallest things we know, and as far as we can tell, they could still be infinitely small.”
Quarks may be the smallest things we know, but this may simply be a limitation of our ability to measure anything smaller. It could be that quarks are themselves composed of smaller parts, and those, in turn, composed of smaller parts still. Can this go on infinitely, as the mathematics suggests it could?
It turns out that there is in fact a physical limit to perpetual division. If you were to continue to divide a quark, you would eventually reach a size called the Planck length: the smallest conceivable size where gravitational physics and quantum physics merge. Although we don’t yet have a fully worked out theory of “quantum gravity,” we know that the very concepts of space and time no longer exist in a way that has any meaning to us below this size. (“The Planck length,” as Lightman wrote, “is smaller than the nucleus of an atom by about the same ratio as the nucleus is smaller than the state of Rhode Island.”)
This has led some physicists to propose that the smallest elements are not particles at all, but rather one-dimensional strings of energy the size of the Planck length. The problem is that these “string theories” (there are more than one) are impossible to test, requiring particle accelerators the size of the earth.
Either way, it appears that we’ve reached the limit of the infinitely small within the haziness of quantum physics. What this means in terms of quantum gravity, string theory, or the multiverse theory remain open questions, and as Lightman suggests, may remain open forever. Our mathematics is suggesting scales and dimensions too small or inaccessible for our technology to measure. (Here’s another way to think about the scales involved: if a quark were the size of the sun, the Planck length would be a grain of sand.)
One interesting implication of all this, Lightman tells us, is that our everyday concepts of space and time and cause-and-effect simply do not hold at the quantum level, suggesting, among other things, that the universe need not have been “caused” at all, as is maintained by theologians of various stripes. We, of course, do not know whether or not the universe required a cause, but the danger has never been in claiming ignorance where we have no knowledge, but rather in proclaiming knowledge where we have only ignorance (religion). The ultimate origin of the universe—regardless of what is claimed by the religions of the world (and even some of the more dogmatic scientists)—remains a mystery, and it is this sense of mystery that compels us to seek answers and continually update our knowledge.
Let’s move on to the larger scales of space. Since it is well established that the universe is expanding, with galaxies moving away from each other like points on an expanding balloon, if we run the calculations backwards, we can predict the point in time when all matter was condensed into a region of enormously high density and temperature—the Big Bang. This occurred about 14 billion years ago, and the universe has been expanding ever since.
What does this tell us about the size and limits of the universe? As Lightman writes:
“The universe could be infinite in extent, but we cannot see beyond a certain distance because there hasn’t been enough time since the Big Bang for light to have traveled from there to here….Thus in our search for Pascal’s infinity of the large, we reach a limit brought about by the finite age of our universe and the finite speed of light.”
It appears that modern physics has placed limits on both the infinitely small and infinitely large while at the same time defining those limits as out of our experimental reach. We can’t measure anything at the Planck length and cannot see anything beyond the age of the universe, and if this is the case, then we’ve reached the limits of our understanding. At the very least, this should inspire a sense of humility in us all.
However, it is difficult to predict where future advances in science will take us, so we should not prematurely conclude that these answers are unknowable. While we are apparently stuck spinning our wheels, we should nonetheless pursue the answers. As Lightman suggests, it has always been at the junction between what is known and what is unknown that humanity has made its greatest discoveries, advances that earlier generations could have never imagined. Perhaps string theory or the multiverse theory is true and we will eventually find clever ways to test them.
After discussing physics and cosmology, Lightman proceeds to cover the origins of life, the mind, consciousness, death, and more, reflecting on the human condition as positioned between the extreme scales of physics. Lightman carries on the theme of exploring the junction between the known and the unknown, as he contemplates the possibility of creating life from non-life and one day solving the hard problem of consciousness.
Here again, modern biological science is pushing against our cognitive limitations and the limits of our technology, just as modern physics is approaching the limits of what we can measure in space and time. Except, in the case of consciousness, Lightman doesn’t seem to recognize this.
We know that it is fashionable among scientists to proclaim that “consciousness is an illusion,” and Lightman is no exception. As a strict materialist, Lightman believes that it is “physics all the way down,” and that the arrangement and pattern of atoms within the brain produces the “illusion” of consciousness. But we can ask: If consciousness is an illusion, who or what is being deceived, exactly?
Let’s unpack this a bit. A good general definition of an illusion is the “perception of something objectively existing in such a way as to cause misinterpretation of its actual nature.” There are a wide variety of visual or auditory illusions, such as when a stick appears bent when submerged halfway in the water, for example.
But what you will notice is that, in every case, an illusion requires a conscious observer to note the difference between two perceived states (the “curved” stick in the water versus the straight stick pulled out of the water). Consciousness, in other words, is required for the proper comparisons to be made to call any phenomenon an illusion in the first place.
Even if we admit that it is possible that everything we see and experience in the world is an illusion—as our senses might deceive us regarding the “actual” underlying nature of reality—in what sense can our ability to experience anything at all be called an illusion? Doesn’t the existence of an illusion already presuppose the existence of a conscious agent to perceive the difference?
From what I can tell, the statement “consciousness is an illusion” is completely meaningless. You can’t be deceived into thinking you experience something when you’re really experiencing nothing. We can even put this in Cartesian terms: I experience, therefore I am.
Lightman claims to be fascinated by the topic of consciousness, and yet does a rather terrible job of presenting the other side of the philosophical debate. He fails to mention the arguments of Thomal Nagel, who, in his article titled What Is It Like to Be a Bat?, presents compelling arguments against the reductionist approach to the understanding of consciousness. Even Daniel Dennett, who sharply disagrees with Nagel, acknowledged that this article is “the most widely cited and influential thought experiment about consciousness.”
Also absent is any discussion of the problem known as Mary’s Room, another widely influential thought experiment that further challenges the physicalist explanation of consciousness and perception. Mary is a color-blind scientist who knows everything there is to know about color, including the various wavelengths of light and the neurophysiological processes of vision. Despite all of this knowledge, she still does not, and cannot, “know” what it’s like to experience seeing the color red—just like we can never experience what it’s like to be a bat navigating the world using echolocation.
Clearly, there is a difference between the physical description of color and vision and the actual experience of perceiving objects in color. There is also the question of how exactly an arrangement of atoms is able to create this emergent awareness. This is all part of the hard problem of consciousness.
These are difficult problems that science has not been able to resolve, and it’s difficult to see how more of the same type of science could ever resolve them. That Lightman offers no insights into these problems—and doesn’t even mention that these philosophical debates exist in the first place—results in a very shallow presentation of the topic.
For the record, I am not religious, nor do I believe in any traditional supernatural explanations for the “soul,” but I do agree with the British philosopher Colin McGinn when he stated that we can never understand consciousness because we can never get outside of our minds to do the analysis. Just as we can’t measure anything the size of the Planck length, or see anything beyond the age of the universe within the constraints of the finite speed of light, we likewise can’t step outside of our own consciousness to study it.
Humanity—trapped as it is between the infinitely small and large, inhabiting a small sliver of reality—seeks to understand the world in the face of significant cognitive, perceptual, and technological constraints. The best we can hope to do, it seems, is to carry on the scientific endeavor with humility, curiosity, and an open mind. Lightman reminds us that we’re perpetually standing at the junction between the known and the unknown, and, if we hold on to this sense of mystery and curiosity, we can collectively push the boundaries of knowledge infinitely farther.
Probable Impossibilities: Musings on Beginnings and Endings is available on Amazon.com.