Nagel - Shadows and Ephemera

Shadows and EphemeraAuthor(s): Sidney R. NagelSource: Critical Inquiry, Vol. 28, No. 1, Things (Autumn, 2001), pp. 23-39Published by: The University of Chicago PressStable URL: http://www.jstor.org/stable/1344259 .Accessed: 25/03/2014 01:16

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Shadows and Ephemera

Sidney R. Nagel

The serenity of the picture of the drop falling obscures the violence taking place beneath the surface as the fluid fissions and becomes two sepa- rate drops. The sinuous contours of the drop, apparently hanging quietly in space, give no suggestion that at a more microscopic scale molecules are moving rapidly, tearing apart from one another. We see a departure from smoothness only at the apex of the conical neck connecting the round liquid sphere at the bottom to the brass nozzle at the top. If we had taken the picture a moment later, the liquid would be in two discon- nected pieces separated at the tip of that cone; a moment earlier it would have hung together in one large and rather boring blob. An extraordi- nary transition is taking place (figs. la-b).

Am I captivated by this image because of its sensuous gracefulness? by its freezing in time of rapid dynamics? or am I engaged by it because the photograph is itself a shadow suggesting and contributing to a more complete view of the drop-an image giving us a handle on what pro- cesses are at work as the drop breaks apart? I am attracted for all these reasons.

I have used the word shadow deliberately since it suggests two important aspects of the research that produced this image. The word is of course the symbolic metaphor at the heart of Plato's myth of the cave in which we, in the real world, can only glimpse shadows cast by the eternal forms. Our knowledge and understanding of the world is incomplete until we perceive the forms themselves. The word has also been used by William Henry Fox Talbot, one of the inventors of photography, who

Critical Inquiry 28 (Autumn 2001) ? 2001 by The University of Chicago. 0093-1896/01/2801-0008$02.00. All rights reserved.

23


24 Sidney R. Nagel Shadows and Ephemera

characterized his invention as "the art of fixing a shadow."'' The marvel of photography is, of course, that it allows one to record, permanently and precisely, the patterns of light and shadow on a sheet of paper. Pho- tography plays many roles: for a photographer like Minor White it is the art of catching a dream, while for a street photographer like Robert Frank it is the art of capturing the iconography of a time and place.2 However, for a scientist such as Harold Edgerton, the task can be more straightfor- ward: photography provides a means of catching the shadows cast by the ephemeral objects of our world, which we can then analyze later at our leisure.

My guess is that most physicists are Platonists at heart. We are taught from the very first that there are laws governing the way nature behaves. Although these laws are, we like to think, universal and immutable, they are not obvious. The laws of mechanics, of electricity and magnetism, of relativity and quantum mechanics are all remarkable, subtle, and of exceptional generality. Something that is not as often emphasized is that the idea of universality can extend to the objects themselves and is not merely relegated to the laws that govern their interactions.

Let me give one example of a common object that displays this universality of form to a remarkable extent. Everyone is by now aware of the electron. Electrons run through our household wires, they surround all atoms and participate in the chemical bonding that keeps our world together and gives it form. The electron is as real to us (and in some cases more real) than most other objects in our world. Yet none of us has ever actually beheld an electron. It is far too small to be seen by our eyes, touched by our hands, smelled, tasted, or heard. It is not an obvious concept, and a few hundred years ago it probably had not even been con- jectured. Yet today we know electrons exist. Moreover, today the electron exists in a manner that is absolutely surprising and would have, I believe,

1. William Henry Fox Talbot, Some Account of the Art of Photogenic Drawing, or the Process by Which Natural Objects May Be Made to Delineate Themselves without the Aid of the Artist's Pencil (London, 1839).

It is also the title of a book on the history of photography: Sarah Greenough et al., On the Art of Fixing a Shadow : One Hundred and Fifty Years of Photography (exhibition catalog, Na- tional Gallery of Art, 7 May-30 July 1989).

2. See Mirrors And Windows: American Photography Since 1960, ed. John Szarkowski (exhibition catalog, Museum of Modern Art, New York, 28 July-2 Oct. 1978).

Sidney R. Nagel, the Stein-Freiler Distinguished Service Professor of Physics at the University of Chicago, has worked on problems dealing with nonlinear and disordered phenomena appearing in macroscopic systems far from equilibrium. He has recently coedited with Andrea J. Liu Jamming and Rheology: Constrained Dynamics on Microscopic and Macro- scopic Scales (London, 2001).


Critical Inquiry Autumn 2001 25

astounded even Plato. It is a pure embodiment of a Platonic form. All electrons are identical to one another-they have the same electric charge, the same mass, the same spin. There is no way, even in principle, of telling them apart. The statistics that we must use to describe these quantum objects takes this indistinguishability into account explicitly. We know of their existence only by secondhand observations, by detecting their sometimes small and sometimes large effects discernible in the macroscopic world-that is, in the metaphor of the cave, by detecting their shadows. If ever there was a case to be made for the material existence of a Platonic form, the electron surely must be that manifestation.

Electrons, of course, are not the only indistinguishable objects. All of the elementary particles have this same property. Thus all protons are the same and all neutrons are identical. Nor, as I alluded to above, does the concept of universality apply only to the microscopic scale. We see it on all levels. We are, I dare say, familiar with the nearly parabolic arc traversed by an object tossed in the air-a baseball knocked out of a sta- dium, for example. The marvelous photographs of a bouncing ball by Bernice Abbott capture an approximation to this ideal arc.3 Although one might quibble that this shape-of-the-trajectory is not a material object, it does nonetheless show how dynamics can produce both elegant and universal forms.

All of this brings me back to the picture of the drop that I mentioned at the outset. At its essence, this photograph displays another Platonic form-the drop at the moment of breakup. It shares with the example of the arc of the thrown ball that it is formed by the dynamics of the situation. However, it also shares with the example of the electron that it is a material object, however much the specificity of the object depends on the precise moment of its existence. What I want to argue is that this object is itself universal and that whenever we think of the thing a-drop- breaking-apart we necessarily allude to the scene depicted in the first photograph.

The explanation for why this is true is so elementary (although it can look complicated when the mathematical formulae are included to make the argument rigorous) that I cannot resist mentioning it here.4 It depends on the realization that in the vicinity of the neck, where the drop

3. See Bernice Abbott, Photographs (Washington, D.C., 1970), pp. 156-57. 4. The ideas of scale invariance in fluid dynamics go back a long way and appear in

many manifestations. The work on drop breakup is only one example of where these ideas arise. The work described in this article is from Xiangdong Shi, Michael P. Brenner, and Sidney R. Nagel, "A Cascade of Structure in a Drop Falling from a Faucet," Science, 8 July 1994, pp. 219-22; Brenner et al., "Breakdown of Scaling in Droplet Fission at High Reyn- olds Number," Physics of Fluids 9 (June 1997): 1573-90; and Itai Cohen et al., "Two Fluid Drop Snap-Off Problem: Experiments and Theory," Physical Review Letters, 9 Aug. 1999, pp. 1147-50. Much of the work on the breakup of drops is reviewed in Jens Eggers, "Nonlinear Dynamics and Breakup of Free-Surface Flows," Reviews of Modern Physics 69 (July 1997): 865-929.



eventually breaks apart, the thickness of the fluid must become arbitrarily small. After all, the neck decreases in diameter until its thickness goes to zero. Thus, at some point, it has become so much smaller than any other macroscopic length in the problem that those larger lengths can no longer matter for a description of the neck itself. It is smaller than the nozzle holding it. It is smaller than the size of the separating round drop at the bottom (whose size is determined by a competition of the downward pull of gravity against the force of surface tension holding the liquid together). If we ask what determines the dynamics in the vicinity of this thinnest point in the neck, we have to admit that it only makes sense that the dynamics should depend only on the thickness of the neck itself and cannot depend on the size of the nozzle or the size of the drop. So, the dynamics in the neck only depends on its thickness and we have arrived at a chicken-and-egg situation: The thickness of the neck depends only on the dynamics (since the dynamics is what pulls the neck into a thin thread in the first place), which in turn depends only on the thickness, and this repetition continues ad infinitum. As time goes on toward the point of pinchoff, the neck conforms to a very special shape-one that must be similar to its own shape at both an earlier and a later time. The only thing that happens as the drop gets closer to the point of snapoff is that the neck gets thinner and more stretched out, but the overall shape must remain the same-only scaled by different amounts in the radial and axial directions at different times. It is thus a universal shape.5

The point I want to emphasize is that the object shown in the photograph of the drop breaking apart is, like the electron, a Platonic form. The photograph has fixed on paper a shadow that is precisely the shadow of the Platonic metaphor. Every drop of water falling will look exactly like this in the vicinity of snapoff. It does not matter that this drop was held by a nozzle and was pulled down by gravity. As we can see in figure lb, the drop actually breaks up in at least two points, one near the bottom as shown in the first picture and again when the satellite drop breaks off

5. Making this argument rigorous requires finding a scaling description for the interfacial shape near the point of snapoff. If h(z,t) is the radius of the drop at a vertical position, z, and time, t (where z and t are each measured with respect to the position and time of the snapoff singularity), a scaling solution asserts that h(z,t) is related to H(C), a function of a single variable, = z t-:

h(z,t) = tr H(5) where a and p are exponents that need to be determined. The idea of universality classes is that over a wide range of physical parameters, these exponents a and P will not vary and that all systems in the same class will have the same shape at snapoff. Such a solution is verified by inserting it into the Navier-Stokes equations describing the motion of the fluid interface. The scaling equation for the shape near the singularity, using the single variable C, provides a much simplified description of the shape and the dynamics of the drop. The understanding of the process that I detailed in the text is obtained from an analysis of the implications of such scaling phenomena.



near the nozzle. The second image shows that the cone-into-sphere shape of the snapoff is the same pointing upward near the nozzle as it was pointing downward near the initial drop. The point of breakup would have looked the same even if it had been formed from a wave tossed into the air at the shores of Lake Michigan.

The shape of the drop at snapoff is robust-indeed, universal. The reason for this remarkable fact is that there are so many constraints on the shape (it must look both as if it is almost separated into two drops and also as if it is almost one single mass of fluid) that the normal variety of parameters that we can vary for a liquid does not play an important role in the physics at the point of snapoff. However, we can tune the parameters so that different regimes appear in the viewfinder of our camera. Thus the picture on the front of this journal is a drop of one liquid breaking apart while falling through a second fluid rather than through air, as was the case in figures la and lb. In this image the region around the point of fission looks different. However, over a wide range of parameters this shape, too, would be robust and universal. It is another Platonic form. These photographs have helped us isolate the one particular region of universal behavior in an otherwise profoundly mundane object. It has, at the same time, managed to make visible the elegant and serene. Pho- tography as a tool has managed to let us isolate a truly ephemeral object, the drop-at-the-point-of-snapoff. Without this tool, it would have been impossible to see the shape of the drop both because the snapoff process occurs too rapidly and because the features of the neck are too difficult to resolve with the naked eye alone.6 Photography has made objective the

6. This discovery by photographic means recalls a passage from Walter Benjamin on the optical unconscious:

The enlargement of a snapshot does not simply render more precise what in any case was visible, though unclear: it reveals entirely new structural formations of the subject. So, too, slow motion not only presents familiar qualities of movement but reveals in them entirely unknown ones.... Evidently a different nature opens itself to the camera than opens to the naked eye-if only because an unconsciously penetrated space is substituted for a space consciously explored by man.

(Walter Benjamin, "The Work of Art in the Age of Mechanical Reproduction," Illuminations: Essays and Reflections, trans. Harry Zohn, ed. Hannah Arendt [New York, 1969], p. 236)

In an explication of this notion, Joel Snyder asks: "If the photograph fails to show us 'the way things look,' does it achieve accuracy by showing us 'the way things are?' How shall we characterize the relation of photographs to the world? In Benjamin's view, the photograph destroys the traditional relationship of the picture to the world as perceived" (Joel Snyder, "Benjamin on Reproducibility and Aura: A Reading of 'The Work of Art in the Age of Its Technical Reproducibility,"' in Benjamin: Philosophy, Aesthetics, History, ed. Gary Smith [Chicago, 1983], p. 161).

These excerpts raise important issues related to how we learn, or decide upon, the "truth" in scientific thought. I do not want to digress into those issues here. I would simply maintain that a discovery about nature made through the use of photography is not so different in its implications for scientific knowledge than the myriad other discoveries made



robust features of the physics--features that I would argue are as universal as the inherent properties of an elementary particle.

The argument that I have used to suggest that the drop near the point of snapoff has universal properties, and thus qualifies as a Platonic form, rests on the idea that we can scale the shape at different times so that the set of pictures for each drop approaching snapoff can be super- imposed onto a common curve. This is a symmetry of nature no less than, for example, the mirror symmetry that takes right into left-handedness. If one magnifies an object and finds that upon increasing its size one again obtains the same pattern, then we call the object a fractal. Some objects have this symmetry and some do not, just as some objects are sym- metric between right and left and some, such as your hands, are not. The human eye is particularly sensitive to many types of patterns-to sym- metries in particular. Indeed, much of modern scientific work in pattern formation and pattern recognition is an attempt to put what the eye natu- rally sees and comprehends into mathematical form so that it can be made quantitative.

The scaling symmetry appears in a myriad of ways in nature. Its ap- pearance at the snapoff singularity in the drop is only one of its elegant manifestations. I would like to illustrate it in a more familiar case. I have taken pictures of barren trees in winter near dusk where the branches stand out clearly against the thickening sky. There is a certain quality to the light coming through branches such as these that is appealing and subtle. We can ask what is behind our attraction to this light just as we can ask about the quality of light in the canvases of Corot. What makes us perceive it as beautiful? One thing that I think is obvious is that there is a delicacy about the way the light is broken up as the branches bifurcate over and over again into smaller and finer structures. The tree is an approximation of a fractal: an enlargement of the finest branches congregat- ing to form larger limbs has the same form as the larger limbs coming together to form the trunk. This symmetry pattern, repeated over and over again at different parts of the canopy, gives more than just a delicacy to the light (which could have been achieved after all with a pattern made of just the smallest twigs with no large branches at all). The pattern, I submit, is interesting to the eye because it has an underlying symmetry- what we call the scaling or dilation symmetry of a fractal object. It is this same dilation symmetry that is at work, albeit in a less obvious manner, at the point of snapoff in the drop depicted earlier (figs. 2a-c).

I now conclude by looking at some photographs of very small objects that celebrate the variety of forms that nature can produce. I have taken a series of images of water and oil mixtures. At this small scale, there are

from precision measurements of phenomena that the unaided human body would otherwise have been unable to detect. The use of photography as a scientific tool may, however, have implications for the aesthetic quality of some of those discoveries.



again only few forces giving the liquids their shape. As we know from common experience, oil and water do not mix. When they are forced to be together, each liquid forms islands which touch the other fluid only at their perimeter. The islands do not easily coalesce because to do so would involve the complete removal of all intervening liquid from between them. This takes a long time to happen, so the islands remain in place for extended periods. I find the shapes that these mixtures display endlessly fascinating. Each interface is described by a precise and delicate arc. When looked at as pure elements of form, they have a sensuous quality. Indeed I am tempted to ascribe almost sentient characteristics to them- in some cases vulnerability, in some cases sheltering, in some cases joy. The objects in these images are created with a very limited set of forces. Yet the austerity of the situation does not prevent them from enjoying an enormous diversity. I find that it is essentially impossible for nature to make an unharmonious design at this level (figs. 3a-d).

The variety of shapes in this situation is in stark contrast to the argument that I gave before, in which I asserted that the shapes may be so constrained by the physics of the situation (that is, being on the border between a single drop and two separated ones) as to be universal. Drops breaking are Platonic forms; these pictures are part of a vast gallery of possibilities-none of which is universal. Yet there is something that, even if not Platonic, nevertheless is robust about the shape of the interface. The shape in every instance is governed by a strict set of laws that nonetheless allows a variation in overall form. This is in some sense similar to the example I gave above of the arc of a thrown ball that is always close to a parabola. Depending on the speed of the ball, the arc can have different amounts of curvature. Here we see the interfacial forces writ in the curvature of the interfaces of the liquids.

I am struck by the observation of Victor Hugo: "Where the telescope ends, the microscope begins, and which has the wider vision? You may choose."' I am seduced by the shape of objects on small scale. The forces that govern their forms are the same as those that are responsible for structures at ever increasing sizes; yet on the smaller scale those forms have a simplicity and elegance that is not always apparent elsewhere. We go great distances to view the wonders of our natural landscape-moun- tains, canyons, deserts, and oceans. At a more modest level I find these smaller objects of an equal if a more delicate beauty. Moreover, they have over their counterparts in the macroscopic domain the advantage that they are in some sense timeless: although mountain ranges may erode over time, a drop in the process of snapping off will have that same shape no matter when we observe it (of course assuming that we catch it at the moment of breaking apart!).

Wallace Stegner wrote about the need for wilderness: "The reminder

7. Victor Hugo, Les Misirables, trans. Norman Denny (Harmondsworth, 1976), p. 764.



and the reassurance that it is still there is good for our spiritual health even if we never once in ten years set foot in it. . . . It is important to us when we are old simply because it is there-important, that is, simply as idea."s The same thought can be applied to the images of these small mundane objects. Their beauty, precision, and elegance are often ignored and taken for granted. But once their magnificence has been asserted they are difficult to forget. The distress of being kept awake at night by the steady, interminable drip of a leaking faucet is mitigated when one considers the stunning and remarkable process occurring during each and every breakup event. In the ephemeral drop we glimpse the shadow of a universal form-a form that is filled with sensuality and grace. The oil slicks on one's driveway, too, when looked at closely have an unantici- pated and elegant structure. These are some of the objects that make up our everyday world-that give texture to our lives. It is important to look into the core of their structure to see what contributes to their splendor. These things are also important "simply as idea."

8. Wallace Stegner, "Wilderness Letter," Marking the Sparrow's Fall: The Making of the American West, ed. Page Stegner (New York, 1998), p. 112.


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Article Contentsp. 23p. 24p. 25p. 26p. 27p. 28p. 29p. 30p. [31]p. [32]p. [33]p. [34]p. [35]p. [36]p. [37]p. [38]p. [39]

Issue Table of ContentsCritical Inquiry, Vol. 28, No. 1, Things (Autumn, 2001), pp. 1-363Front MatterThing Theory [pp. 1-22]Shadows and Ephemera [pp. 23-39]Descartes's Geometry as Spiritual Exercise [pp. 40-71]Lyric Substance: On Riddles, Materialism, and Poetic Obscurity [pp. 72-98]Words and the Murder of the Thing [pp. 99-113]Fetishizing the Glove in Renaissance Europe [pp. 114-132]Modern Metamorphoses and Disgraceful Tales [pp. 133-166]Romanticism and the Life of Things: Fossils, Totems, and Images [pp. 167-184]The Russian Constructivist Flapper Dress [pp. 185-243]The Romance of Caffeine and Aluminum [pp. 244-269]A Pebble, a Camera, a Man Who Turns into a Telegraph Pole [pp. 270-285]Fateful Attachments: On Collecting, Fidelity, and Lao She [pp. 286-304]Dying Is an Art, like Everything Else [pp. 305-316]Paths That Wind through the Thicket of Things [pp. 317-354]Books of Critical Interest [pp. 355-363]Back Matter

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Nagel - Shadows and Ephemera

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