Second Glance at Chalk in the Classroom

David Grandy
Department of Philosophy

As classrooms become increasingly technological, certain longstanding fixtures of the educational experience gradually disappear. One such fixture is the humble piece of chalk. It has enjoyed a long and storied career, and not just as a writing instrument. To hold a piece of chalk in one’s hand is to hold something that can be quickly transformed into an important teaching tool. I doubt, moreover, that colored markers and PowerPoint presentations will ever surpass chalk in its capacity to link the classroom back to nature. Chalk is primitive, earthy, gritty, and dusty, and it subtly reminds us that everyday earth experience is the ground of all intellectual abstraction.

When I teach Aristotle I always look for a piece of chalk to demonstratehis law of falling bodies. Why do thingsfall to the earth when  released in midair? Because, saidAristotle, they want to get back home. A piece of chalkis the perfect earthbound object because it obviously is earth. Colored markers don’t quite fit the bill, don’t have the right feel: too processed and synthetic, too far removed from their terrestrial origins. Someone might protest that since Aristotle had an incorrect theory of falling bodies, none of this really matters. But this response implies a lack of scientific and philosophical imagination. Newton’s law of gravity works for us—that is, inspires complete confidence—because we assume that the cosmos is mechanical and mostly lifeless. Rocks, pieces of chalk, and such consequently can’t “incline homeward” (to use the old language) because they are completely blank within; they have no “inner essence.” But this is an ideological commitment, not a scientific finding. Different assumptions about nature motivate different facts about the world, and a piece of chalk, seen in the light of Aristotle’s organic, teleological worldview, is a nice starting point from which to interrogate the modern thesis that nature is ruled by mechanical necessity.

One may, of course, dismiss chalk as cheap, unsophisticated, and commonplace, but these qualities, I propose, contribute to its adaptable, multifunctional virtue. Just as less is sometimes more, so simple and ordinary is sometimes precious, at least at second or third glance. In the hands of first-rate thinkers, chalk has been a window on the past, an emblem of creation, a philosophical object lesson, a means for illustrating the difference between ordinary reality and quantum reality, and a prop for the joyful sharing of ideas.

One hundred and fifty years ago, Thomas Huxley figuratively reached for “a piece of chalk” in order to demonstrate certain “startling conclusions of physical science.”¹ He insisted that “a great chapter of the history of the world is written in chalk”² and proceeded to illuminate the earth’s past by explaining chalk’s origin and nature. Chalk deposits are very gradually built up from the remains of marine microorganisms, most of which slowly drift to the bottom of the ocean upon death. Since these deposits now constitute large chunks of the dry land we live on, the  inescapable conclusion is that salt-water once covered much of our present habitat. As Huxley put it, “chalk is the mud of an ancient sea-bottom.”³ What is more, this mud is part of the geological record by which scientists reconstruct the earth’s biological past. Many species came and went before the buildup of chalk deposits, but other later species left their fossil remains therein.   The good thing about chalk deposits, said Huxley, is that they afford continuity between old and new, extinct and surviving species.

It is by the population of the chalk sea that the ancient and the modern inhabitants of the world are most completely connected. The groups which are dying out flourish, side by side, with the groups which are now the dominant forms of life. Thus the chalk contains remains of those strange flying and swimming reptiles, the pterodactyl, the ichthyosaurus and the plesiosaurus, which are found in no later deposits, but  abounded in preceding ages. . . . But, amongst these fading remainders of a previous state of things, are some very modern forms of life. . . . Crocodiles of modern type appear; bony fishes, many of them very similar to existing species, almost supplant the forms of fish which predominate in more ancient seas; and many kinds of living shellfish first become known to us in the chalk.⁴

Thus for Huxley chalk called forth an incredibly old earth and the vast evolutionary drama that has unfolded upon it. Another Englishman, G. K. Chesterton, also drew inspiration from chalk, calling a piece of chalk a “tremendous trifle.”⁵ He told of taking an excursion into the countryside, armed with multicolored chalk and brown paper, intent on making sketches of nature. The brown paper was essential background since it “represents the primal twilight of the first toil of creation,” and the chalk allowed him to “pick out points of fire” on the brown paper, “sparks of gold, and blood-red, and sea-green, like the first fierce stars that sprang out of divine darkness.”⁶ But as he sat on the hillside making his sketch it struck him that he had no white chalk, without which he could not add the climatic flourish. Whiteness, said Chesterton, is not the absence of color but the very epiphany of it, something “shining and affirmative,”⁷ particularly as it shows up against brown or darkish paper. But just as he was about to despair of finishing the sketch, he realized that his situation was like that of a man in the desert searching for sand to fill his hourglass. He was sitting, he tells us, “on an immense warehouse of white chalk.”⁸ As far as the eye could see, white chalk constituted the land about him, and so he reached down, broke off a piece, and finished his sketch.

These narratives affirm the earlier point that a piece of classroom chalk subtly but powerfully links us back to nature, the ground of all our academic deliberations. Moreover, chalk, owing to its inexpensiveness and breakability, can function as a very good pedagogical aid.  Sometimes things need to be broken to make a point, and one can break chalk without difficulty or fear of penalty. I am thinking here of Martin Heidegger, who sought to point up a fact about physical objects by breaking a piece of chalk, not just once but twice.

During a 1935 lecture course at the University of Freiburg, Heidegger held a piece of chalk in his hand and noted its properties.⁹ It was “an extended, relatively hard, gray-white thing with a definite form.”¹⁰ As a thing, he further observed, it exists in space and time, at least that is our initial impression and way of talking. But this attitude incorrectly assumes that “space and time are in some sense ‘external’ to things,”¹¹ Heidegger added. Space does not end where the chalk begins; rather space informs the chalk and is filled by it. By this time his students were wondering about the inside of the piece of chalk, and to satisfy their curiosity, Heidegger broke the piece of chalk. He then asked, “Are we now at the inside?”¹² Most people would probably say yes—we are now looking at the inside of the chalk. But Heidegger insisted that we are again looking at an outer surface, somewhat smaller and rougher than before, but an outer surface nonetheless. We really didn’t get inside because the moment we broke it in half to discover its inside, the chalk “closed itself off ”¹³ by offering itself as an outer surface. We are still on the outside looking at an opaque piece of chalk, not experiencing chalk’s inner space.

Heidegger then stated: “[We] were unable to find the space we were looking for inside the chalk, the space which belongs to the chalk itself. But perhaps we weren’t quick enough. Let’s try breaking the piece of chalk once again!”¹⁴ After snapping the chalk in half again with the same disappointing result, Heidegger asked, “So where on earth does the inside of the chalk begin, and where does the outside stop?”¹⁵

By Heidegger’s lights, it would seem that the inside of the chalk never begins and the outside never ends. The chalk, which we first apprehend from without, always conceals or withholds itself as we try to open it up so as to know it from within. It re-veils itself even as it reveals itself, always offering yet another iteration of its outside self in lieu of what we really want: the chalk’s inside. This inside we can infer, of course, by examining the outer surfaces that keep reasserting themselves as we break the chalk into smaller bits, but we never find the chalk’s inner reality in a firsthand way.

I think Heidegger would say there is a double irony or covering-over here. Not only does the outer surface of the chalk keep showing up as we try to discover its inner reality, but the original anticipation behind breaking chalk gets forgotten or iterated out of sight in the process. After long familiarity with chalk we now know that breaking it yields another outer surface but, having forgotten our original intent, we generally feel no disappointment with the outer surface and count that as the chalk’s inside, even though, taken at face value, it is no such thing. Heidegger suggested, however, that we first broke chalk (and other things) with the expectation of finding something other than an outer surface. That is, we anticipated the immediacy of chalk’s inner reality, not another outer surface from which we can do nothing more than guess at the chalk’s inner reality from an outside perspective.

Some people might say this is much philosophical ado about nothing, but I believe it helps us get our bearings on certain difficult issues in science. Reductionism has long been part of the thrust of science, and it may be explained as the inclination to grasp the world as an assemblage of interacting parts. The first task of reductionistic science, then, is to pinpoint the fundamental part or building block of reality. In the West this has long been identified as the atom, or, more recently, as subatomic particles. We now know, however, that physical reality cannot be wholly reduced to the interaction of subatomic particles, at least as those particles were classically conceived. The world at bottom is much more complex and messy.

Part of the world’s complexity, I propose, can be traced back to what Heidegger had to say about a piece of chalk and what happens when we break it. We neverget inside it, even though that was the motivation for breaking it in the first place. This difficulty—this snag in the nature of things—is not far removed from that noted by Louis de Broglie, one of the architects of quantum physics. He pointed out that the concept of an atom—a standard fixture of the Western worldview—is inherently flawed.¹⁶ As it was anciently conceived, the atom is an indivisible bit of matter (in Greek, atomos means uncuttable) and therefore the point at which the reductionistic program of science comes to a halt: nature can’t be further subdivided. But since atoms are physical entities, they must take up space (however minutely), and all things with spatial magnitude have both an outside and an inside, or an outer surface bounding inner content. What, de Broglie asked, does an atom’s inside consist of? Given the way we have come to think about physical matter in the West, there are only two possibilities, neither of which makes sense. Either the indivisible atom contains divisible (non-atomistic) matter or it contains indivisible (atomistic) matter. If it contains divisible matter, then it seems that divisibility best describes the supposedly indivisible atom. But if it contains indivisible matter, then the atoms—the so-called ultimate constituents of nature—are upstaged by even smaller atoms within. And if we then call those smaller atoms the ultimate constituents, we slip into what de Broglie called a “vicious infinite”¹⁷ of ever smaller atoms, which is to say we slip into infinite divisibility.

De Broglie felt that this philosophical conundrum foreshadows wave-particle duality, the realization that nature, at least at the quantum level, registers sometimes as wave-like and other times as particle-like, even though, classically speaking, the two concepts are mutually exclusive. The salient point is that getting inside things—reducing them to their ultimate units—has proved trickier than expected. Paralleling Heidegger’s inability to get inside a piece of chalk without re-encountering its outside, de Broglie couldn’t get inside the concept of atomism or indivisibility without re-encountering divisibility. And even with the technology of modern science, we still do not capture a clear, unequivocal picture of nature’s inner essence—that is a central lesson of quantum physics, which has far outstripped science fiction in its capacity to evoke bizarre, mind-stretching possibilities.

While any classroom object may be used to illustrate some of these possibilities, none works quite as well as a piece of chalk. Paul Dirac, another of quantum physics’ founding fathers, used to break chalk in class while explaining the idea of superposition. Famously low-key, Dirac was “not given to gestures” in the classroom, recalls John Polkinghorne, one of his students.¹⁸ The exception was “near the beginning of the course” when he “took a piece of chalk, broke it in half,” and pointed out that while a piece of chalk can be either here or there but not both places simultaneously, not so an electron: thanks to superposition, it can exist in many different places simultaneously.¹⁹ With nothing easily or permissibly breakable in today’s modern classroom, Dirac would have to illustrate superposition by different means, as would Heidegger his notion that broken objects re-veil their interior by revealing a new exterior.

Unlike chalk, the electronic gadgetry that fills today’s classrooms must be handled with care. It also can, like special effects in a movie, overwhelm thestoryline, the simple human narrative of sharing an idea. What I have in mind is Richard Feynman (a Nobel laureate, as were de Broglie and Dirac) teaching physics.

“I remember,” one of his students recalls, “how it was when you walked into one of his lectures. He would be standing in front of the hall smiling at us all as we came in, his fingers tapping out a complicated rhythm on the black top of the demonstration bench that crossed the front of the lecture hall. As latecomers took their seats, he picked up the chalk and began spinning it rapidly through his fingers in a manner of a professional gambler playing with a poker chip, still smiling happily as if at some secret joke. And then—still smiling—he talked to us about physics, his diagrams and equations helping us to share his understanding. It was no secret joke that brought the smile and the sparkle in his eye, it was physics.”²⁰

No doubt Feynman used chalk to write out his equations and diagrams, but it was also for him a stimulus to freewheeling thought and spontaneous celebration of the subject matter. Like a basketball player mindlessly dribbling the ball between his legs, Feynman mindlessly twirled a piece of chalk in his fingers, the mindless physical action signifying a relaxed confidence in one’s ability to perform at a higher, more exciting level— whether by driving to the basket or by solving a problem on the blackboard. In an electronic classroom one can, of course, twirl a laser pointer, but most would think twice before doing so. And how, after all, can one spring into action with a laser pointer? But that is just what the humble piece of chalk has allowed teachers to do for generations.

1. Thomas H. Huxley, “On a Piece of Chalk,” Collected Essays, vol.viii (New York: Greenwood Press, 1968), p. 4.
2. Ibid.
3. Ibid., p. 24.
4. Ibid., pp. 31-32.
5. G. K. Chesterton, “A Piece of Chalk,” Tremendous Trifles (New York: Dodd, Mead, and Company, 1909), pp. 8–16.
6. Ibid., pp. 9–10.
7. Ibid., p. 13.
8. Ibid., p. 15.
9. This incident is recounted in Graham Parkes, “Thoughts on the Way: Being and Time via Lao-Chuang,” Heidegger and Asian Thought, ed. Graham Parkes (Honolulu, HI: University of Hawaii Press, 1987), pp. 105–44.
10. Ibid., p. 132.
11. Ibid., p. 133.
12. Ibid., p. 134.
13. Ibid.
14. Ibid.
15. Ibid.
16. Louis de Broglie, Matter and Light: The New Physics, trans. W. H. Johnston (New York: Dover, 1946).
17. Ibid., p. 219.
18. John Polkinghorne, Serious Talk: Science and Religion in Dialogue, 3rd ed. (New York: Trinity Press International, 1995), p. 18.
19. Ibid.
20. Albert R. Dibbs, Introduction to Richard Feynmann, “Surely You’re Joking, Mr. Feynmann”: Adventures of a Curious Character (New York: W. W. Norton & Company, 1985), pp. 9–10.