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The Art and Science of Nature in Nature - Canadian Centre for

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study centre mellon lectures 13 April 2004


Processes and Structures: The Art and Science of Nature in Nature
Martin Kemp
The invitation to deliver a public lecture at the Canadian Centre for Architecture gives me a welcome opportunity to look back again over the regular column -- generally consisting of six-hundred-word pieces, each with one illustration -- that I have been writing in the science magazine Nature. The first two years of essays (at that point I was writing on a weekly basis) were brought together in the book Visualizations. Since then, there have been three years of monthly essays. It is good to be able to reflect on the years of writing, and to share with you some thoughts as to whether they are anything more than a series of separate, discrete essays. Each obviously had to stand on its own. However, are there motifs and undercurrents that can be drawn out of the diverse topics, which span a wide range of sciences, technologies, and visual arts from the Renaissance to today?
Nature, as we know, is a very distinguished periodical. Founded in 1869, it has undergone many reincarnations, signalled by the multiple redesigns of its cover -- a process that has occurred ever more frequently as design fashions and technologies have changed at an accelerating rate. As a visual historian, one of the questions I am interested in asking is why Nature looks like it does now, and how this look relates to its past appearances. I wrote an essay in Visualizations specifically on this topic. The question as to why human-made things look like they do is a fascinating and complex matter, extending beyond the field of the history of art or even of design. It is a question we can ask of anything that has been contrived by humans -- anything that is “designed” in some shape or form. And there is a special message carried by each of the resulting

design solutions -- embodying what we call the style of the thing -- that can tell us a huge amounts about the processes of visualization, the intended modes of visual communication to the supposed audience, and the whole aura of the enterprise in which the content or subject (science in the case of Nature) and the form or vehicle (the weekly journal in this case) are complicit. For instance, no science magazine could now present itself seriously without openly brandishing a high-tech air on its cover.
In the introduction to the book of the essays, I used the term structural intuitions as a way of trying to capture what I felt about the way in which visuals arts and sciences relate -- at least as I am primarily interested in that problem. I am not so much interested in influence (however defined). Obviously science can be said to exercise an influence upon art, artists, and architects, and in particular instances art production and architecture have an influence on science. But to chart influence seems to me to be a less interesting question than to tunnel underneath the surface to ask: Are there shared intuitions at work? Is there anything that creators of artefacts and scientists share in their impulses, in their curiosity, in their desire to make communicative and functional images of what they see and strive to understand? Before attempting to show where three answers to these questions might lie, I should make a necessary qualification. Such is the variety in the practices in the “art world” and in “the sciences” that it is parlous to make overarching generalizations about all “artists (including architects)” and all “scientists.” I will be talking about something that I believe to be widespread and fundamental, but not uniform or universal across all of those pursuits we call arts and sciences.
It should also be said, in the present context, that structural intuitions have particular applicability to engineering solutions in architecture. An instinctive and often somatic sense of what might be stable and strong is obviously central to the processes of architectural design, particularly at the conceptual stage of projects that push at the boundaries of existing solutions.
I felt that the term structural intuitions served in one phrase to capture what I was trying to say, namely that painters, sculptors, architects, engineers, designers, and scientists often share a deep involvement with the beguiling structures apparent in the configurations and processes of nature -- both complex and simple. Looking at nature, we rely heavily
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on an inbuilt sense that there is some kind of order or underlying structures “out there.” I think we gain a deep satisfaction from the perception of order within apparent chaos, a satisfaction that depends on the way that our brains have evolved mechanisms for the intuitive extraction of the underlying patterns, static and dynamic. There is a delicious interplay between the structures we have in here -- in our brains -- and the structures out there -- not just static structures but also temporal processes. I am interested in that interplay, and in how many creative makers of things and scientists are involved in essentially parallel businesses when they develop their intuitions into their final products. How designers and scientists explore the interplay, how they develop their understanding, and how they embody their “results” in their creations, are obviously very different, particularly in terms of the vehicles they use and the institutional contexts within which they operate. But I think that there is often a shared itch of looking at something in a spirit of wonder, and then saying: I really want to know what that is about -- whether it is a flame leaping in a fire, water moving in a river, a tree branching, the spiral of a shell, the grandest motion of the heavens or tiniest scatter of atomic particles. Many scientists start with a fundamental feeling that there is a pattern, that there is something wonderful, fascinating, awesome in what lies behind the observed phenomena. Many designers of things start at fundamentally the same point. I think they are both starting with intuitions about processes and structures, about order and disorder.
To give a concrete example of what I mean by structural intuitions, let me take what was one of the most surprising and delightful episodes in the whole of my writing in Nature.
I wrote about a youngish British artist who -- amongst other things -- has made dust landscapes. These landscapes are made by taking a large steel plate, into which holes are drilled at irregular intervals. A layer of cement dust is sieved evenly onto the plate. Obviously, some powder drops through the holes. The result is a wondrous landscape of mountains and cellular valleys, linked by hyperbolic ridges. Some of his dustscapes have filled whole rooms, and are infinitely varied and complex, yet somehow unified and harmonious.
When I first saw a small-scale model of the landscapes, I said to him: “This reminds me of the theory of self-organized criticality [a relatively
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new idea at that time], which is exemplified in the model of a sand pile.” If sand grains are dropped continuously from a fixed point, they will accumulate as a conical pile, but, as we are likely to know from childhood games on sandy beaches, the sides of the pile tend to collapse as their angle becomes steeper. Avalanches suddenly occur. We know from complexity theory that the occurrence of the avalanches is unpredictable but not random. There are probabilities at work, and limiting parameters on the steepness of the slope, but the point in time when the pile collapses and turns into a different cone is not precisely predictable, nor is the precise post-avalanche shape.
Jonathan Callan did not know about self-organized criticality, and there is no reason why he should have done. I was not trying to prove whether he studied science or not, but I wanted to suggest that he had exploited his own kind of artist’s sense of something fascinating in the shapes and patterns that emerged from his process. I suggested to him that the configuration should be photographed directly from above as well as from a lateral view, because I was very interested in the cellular structure that had emerged. If you look his dustscapes from a “bird’s eye” view, they present a pattern of cells, separated by cell walls. When the article was published in Nature, Adrian Webster, from the Royal Observatory in Edinburgh, wrote to the journal explaining that the configuration was that of Voronoi cells, named after Georgii Voronoi, a Russian mathematician working at the turn of the nineteenth to the twentieth century. Voronoi cells can be created as follows. A series of point vacuums are distributed irregularly across a plane. Each mobile particle on the plane will cascade towards the vacuum closest to it. If we draw the boundaries that decree in which direction a given particle will move, we find that they form irregular polyhedra around the “nuclei” of the vacuums. The whole array is called a Voronoi tessellation. Webster also pointed out that one of the possible models for the organization of galaxies is a “Voronoi sponge,” a three-dimensional version of this flat system, and that the galaxies might be arranged along the cell walls. The appearance of this model is a kind of cosmic foam. But this was not the end of the story. Ian Stewart subsequently picked up the theme of Callan and Voronoi cells in his column on “Mathematical Recreations” in Scientific American. From their artistic beginnings, Jonathan Callan’s little bits of dust underwent a remarkable galactic voyage.

The way that the whole discussion developed was unexpected and thrilling for me. The process of creating a work of art through a physical process had tapped into basic patterns of organization, ranging from tiny cellular structures to the largest configurations that we can envisage. Something that emerged, very delightfully, is that the artistic and mathematical intuitions are not dependent on scale; that is to say, they potentially apply not only to the smallest systems we can discern but also to the very largest we can conceive, embracing all the intermediate steps.
Susan Derges, about whom I have also written in the Nature series, is looking at comparable phenomena in her art. She regularly uses the technique of photograms, photographic prints made directly from nature without a camera. She works in Devon and has made a series of works on the flow of water in the River Taw over the seasons. At nighttime, underneath the surface of the flowing water -- or in the winter under the skin of ice -- she placed large slides containing photographic paper. They were about two meters high and one and a half meters across, dimensions comparable to the human body. She then fired a flashlight above the water, recording the “fingerprint” of the wave patterns in the water currents at that particular moment. Her photograms also recorded the shadows from overhanging branches. The results are uncannily like Japanese screens and it is no surprise to find that Derges has resided in Japan and is very involved with Japanese art.
The patterns that she picked up are of considerable interest to specialists in fluid dynamics, including “standing waves,” which are more or less stationary with respect to the banks. If you look into the detail, you can see dynamic patterns emerging from the apparent chaos of flowing water. We can sense an internal structure that is cellular in nature, like a magnified photograph of the human skin or other living tissue. Not only do we have a sense that the structures inherent in processes are valid across different scales, but that they also operate across different materials, solid and fluid. Susan Derges is very concerned with insights drawn from science and is well read in the sciences of complexity -chaos theory, fractals, and so on -- but she is not literally making works on scientific themes in an illustrative manner. She is not “influenced” by chaos theory, in a literal sense, but rather draws it into her everexpanding field of intuition and understanding.

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Fig. 1 Arthur Worthington: photographs showing the phases of a milk splash, 1908, as reproduced in D’Arcy Wentworth Thompson, On Growth and Form, Cambridge, 1917, 235, Blacker-Wood Library of Biology, McGill University, Montreal, photo © Megan Spriggs 2005
Fig. 2 Diagrams of the forms of cells, from D’Arcy Wentworth Thompson, On Growth and Form, 2nd ed., Cambridge and New York, 1942, 394, Blacker-Wood Library of Biology, McGill University, Montreal, image © Megan Spriggs 2005

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Many of the ways in which we have learnt to “see” natural phenomena since the nineteenth century have involved instruments to extend the capacities of our visual faculty. Photography is integral to these new modes of vision. Instantaneous or split-second photography is an important case in point. A notable early example is the series of remarkable photographs of splashes taken by Arthur Worthington and published in 1908 (Fig. 1). The beautiful corona thrown up by a ball dropping into a bowl of milk has become an iconic image, not least through the later entrepreneurial efforts of Harold Edgerton at MIT’s “Strobe Alley.” The image has developed a life of its own. For example, milk delivery tankers in the southeast of England are adorned with a rather literal version of the “Edgerton splash.” It has become the Mona Lisa of fluid dynamics, just as DNA has become the Mona Lisa of the biological sciences.
Worthington’s photographs were seized on by D’Arcy Thompson, the great Scottish biologist and classical scholar, who wrote an extraordinary book on natural morphologies, which has served as an enduring source of inspiration for artists, architects, and particularly engineers, since it was published in 1917. The book, On Growth and Form, is one of the greatest works of scientific literature (Fig. 2). In a very beautiful passage, Thompson writes of a thrown pot as a stilled splash.
To one who has watched the potter at his wheel, it is plain that the potter’s thumb, like the glass-blower’s blast of air, depends for its efficacy upon the physical properties of the medium in which it operates, which for the time being is essential a fluid. The cup and the saucer, like the tube and the bulb display (in their simple and primitive forms) beautiful surfaces of equilibrium as manifested under certain limiting conditions. They are neither more nor less than glorified “splashes,” formed slowly under conditions of restraint which enhance or reveal their mathematical symmetry.
This is a beautiful insight. Looking at Worthington’s corona, he could see that it rhymed with many other forms and phenomena, including the semi-liquid clay rising under the shaping caress of the potter’s hand. He also looked, as we will see, to analogous forms in polyps and medusoids. What Thompson is doing here corresponds precisely to what I am calling structural intuitions. What I am trying to capture with this phrase is the age-old way that scientists, like artists, want to see inside the structure
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Fig. 3 Leonardo da Vinci: drawing of a seated figure and studies of water in movement (Royal Library, Windsor) from The Notebooks of Leonardo da Vinci, ed. and trans. Edward MacCurdy, London, 1938, vol. II, opposite p. 105, Call. no. CAGE W7606, Collection Centre Canadien d’Architecture / Canadian Centre for Architecture, Montréal
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Fig. 4 Leonardo da Vinci: studies of a woman’s head and coiffure, ca 1504–06, for Leda (Royal Library, Windsor) from The Notebooks of Leonardo da Vinci, ed. and trans. Edward MacCurdy, London, 1938, vol. II, opposite p. 284, Call no. CAGE W7606, Collection Centre Canadien d’Architecture/Canadian Centre for Architecture, Montréal
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of seen phenomena, extracting orders of varying complexity from the apparent chaos of appearance. No one was more consistent in this respect than Leonardo da Vinci.
Leonardo was continually asking about the structures, static and dynamic. All his remarkable depictions of forms and phenomena represent acts of structured demonstration rather than “simple” or direct recording. His water drawings, for example, are replete with ideas about how water should work according to the laws of dynamics as conceived in the Aristotelian tradition (Fig. 3). They are very much constructed images, in which it is impossible to separate observation and representation from analysis and synthesis. Leonardo, like Dürer, never looked at anything without asking questions about the nature of the seen phenomenon. The art of drawing for Leonardo as for Dürer -- albeit in distinctively individual ways -- is an art of understanding. They are neither artists nor scientists, in that our pedestrian terminology simply fails to capture what they did in blending the deepest intellectual insight into the operations of nature with the highest imaginative acts of remaking.
One of the most characteristic motifs in Leonardo’s thought involves visual analogy. Looking at water flowing turbulently, he writes:
Observe the motion of the surface of water, which resembles the behaviour of hair, which has two motions, of which one depends on the weight of the strands, the other on the line of its revolving; thus water makes revolving eddies, one part of which depends on the impetus of the principle current, and the other depends on the incident and reflected motions.
He is thus breaking down phenomena in statics and dynamics into two vectors to satisfy intellectually his intuitive sense that one thing reminds him of another. Accordingly, when he designs a wig for Leda in his painting of Leda and the Swan, his artificial structure exploits these insights. His artificial elaboration of the natural motif is set in telling counterpoint to Leda’s natural hair as it spouts impetuously from apertures at the centre of the lateral whorls in her wig (Fig. 4).
Leonardo’s indelible sense that processes and structures were locked together in patterns definable according to mathematical rule is nicely
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manifested in his vision of fluid flow through tubes or channels. Whether the system of flow involved water in rivers, sap in a tree, or the bronchi of lungs, he argued that the same ragione applied. The volume of fluid passing within a tube is understood by Leonardo as proportional to the cross-sectional area of the tube. Thus at each level in a branching array the total cross-sectional area should remain constant for efficient flow. The designer of canals who wished to achieve non-turbulent flow in a branching system should learn the necessary lesson from nature’s branching systems.
Thompson proceeded very much along the same lines. He looked, for instance, at the way in which viscous substances dropped into thinner media produce wonderful branching shapes, which resemble the forms of gelatinous marine organisms such as medusoids. In a nice instance from modern ceramics, the artist Joan Lederman has been using mud millions of years old, excavated deep in the sea bed by oceanographic surveyors, to glaze thrown pots (Thompson’s splashes). She discovered that the muds, rich in foraminifera skeletons from ancient eras, spontaneously adopt dendritic formations during the course of firing -- a set of splashes within a splash, as it were.
In a related structural realm, Thompson also delighted in the elegant experiments on soap films performed by Plateau, the Belgian physicist, in which wire frames were used to set up “membranes” in a variety of geometrical configurations. Thompson was drawn to the evident parallels with some marine micro-organisms, most notably the skeletons of the radiolaria illustrated in Ernst Haeckel’s beautifully illustrated book Radiolarien in 1862 (Fig. 5). Studying the comparable configurations disclosed by Plateau and Haeckel, Thompson was, like Leonardo, stimulated to ask some basic questions. Does the inorganic engineering of soap films in relation to the frames in which they are suspended tell us something fundamental about the way in which certain living things organize their structures in nature? Or, more broadly, is there such a thing as “natural engineering” that explains analogous configurations in animate and non-animate worlds in the context of physico-chemical laws? Or, in modern terms, are there common principles of spontaneous selforganization at work across the inorganic and organic worlds?
The problem for Thompson was that it was not clear what the observed analogies actually proved, suggestive though they might be. There was a
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Fig. 5 Diagrams of Callimatra skeletons, after Haeckel’s Die Radiolarien, from D’Arcy Wentworth Thompson, On Growth and Form, 2nd ed., Cambridge and New York, 1942, 712-713, Blacker-Wood Library of Biology, McGill University, Montreal, image © Megan Spriggs 2005
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Fig. 6 Ernst Haeckel: Lucernaria, from Kunstformen der Natur, Leipzig and Vienna, 1899–1904, pl. 48, Institut für allgemeine Botanik, Hamburg, photo © Kurt Stüber, Max Planck Society for the Advancement of Science, 1999
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sense that he was producing “so-what?” science, in which the observations could not be related to any kind of causal explanation. Now, with the advent of modern methods of computer modelling, it is possible to program in the physical parameters of the processes that shape a viscous drop and a medusoid to see what physical forces are at work in the selforganization of such analogous morphologies -- and similarly with the radiolarian frames and films, with phyllotaxis in plants, and with other self-organizing processes that Thompson looked at.
The immediate future of Thompson’s insights lay as much with artists and architects as with biologists. By the 1940s and 1950s, painters, sculptors, architects, designers, and engineers were consuming Thompson’s On Growth and Form more avidly than biologists. Mies van der Rohe was a great fan, as the 2001 Mies in America CCA exhibition catalogue, edited by Phyllis Lambert, makes clear. A very good example of how Thompson served artists is provided by the Russian émigré sculptor Naum Gabo, working in St. Ives, who was introduced to Thompson’s work by Hubert Read, the art critic, and by Wilhemina Barns-Graham, a Scottish artist in St. Ives who had encountered the redoubtable Thompson in St. Andrews. Gabo uses a repertoire of quasinatural forms under tension and compression, very comparable to those analyzed by Thompson. Gabo is not copying Haeckel. Nor is he copying Thompson. But the principles of the engineering of the object are understood via Thompson and the examples he illustrated in On Growth and Form, such as the Plateau soap bubbles. Gabo himself was trained as an engineer, and I think it shows.
I think it is generally true that people who can exercise a choice of career tend to enter particular professions precisely because they have an instinctive feeling for the forms and processes of the things at the heart of that profession. It is no coincidence that Gabo was an engineer before he became a constructivist sculptor. His own structural intuitions were naturally strong in those related fields, involving a kind of somatic engagement with the structural integrity of three-dimensional forms in geometrical configurations. It is notable that a number of the scientists we will later be encountering showed an early interest in design, in graphics, and in three-dimensional modelling.
Equally, we find that important engineer-architects exhibit a strong reaction to the engineering of biological forms in nature. The example
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I am choosing is Antonio Gaudí, architect of the Sagrada Familia, the extraordinary Catalan church on which he began work in 1883 and which is still under construction. Looking at the display in Barcelona devoted to his work on the great basilica, I was fascinated but not surprised to learn that he knew the works of Ernst Haeckel. He was immensely interested in Haeckel’s images of natural engineering in Kunstformen und Natur (1899--1904), which the German biologist had published specifically with artists and designers in mind, having found that they were already looking avidly at his illustrations (Fig. 6).
The structural principles on which Gaudí worked may be described as natural engineering, understood through an experimental method. This is exemplified in the method he adopted to design an arch-form in which all the lateral forces are resolved within the substance of the arch. A semicircular arch does not exhibit this property, and pointed gothic arches can be designed to achieve this end only to an incomplete degree. He saw that the solution is to adopt a catenary curve. This is the curve that results if we loosely suspend a chain (a catena) in a loop, hanging from its two ends. All the forces must necessarily be resolved within that curve. So Gaudí said in effect, why don’t I design the arches and vaulting patterns using upside-down, hanging models? In order to study the loading on the arches, why don’t I hang weights from the corresponding points on the upside-down arch? And if I then reinvert the whole thing, retaining the configuration of the catenary curves that have resulted from the resolution of the forces, I will have a structure that is wholly resolved and stable. This is an extraordinary act of intuitive brilliance on Gaudí’s part, literally a vaulting insight. The kind of structural intuition involved is simultaneously physical and visual. The results have that sense of harmonic rightness that we can all feel -- the kind of inevitable rightness that characterizes all great design.
More recently, the great Swiss engineer of thin shell structures, Heinz Isler, has adopted Gaudí’s inversion method to rework the principles of vault design. A frozen membrane, suspended from its corners, settles into a complex set of compound curves, serving as a template for a square vault springing upwards from four points. The breathtaking result of these kinds of structural explorations can be seen in the Brugg swimming pool by Gross and Meier, on which Isler served as the engineer. The way we often use the term “breathtaking” to describe such feats of engineering suggests that there is a bodily aspect to our response, as if
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Fig. 7 After Leonardo da Vinci: woodcut showing the dodecahedron as a solid form, from Luca Pacioli, Diuina Proportione, Venice, 1509, pl. XXVII, Call no. CAGE W10310, Collection Centre Canadien d’Architecture/Canadian Centre for Architecture, Montréal

Fig. 8 After Leonardo da Vinci: woodcut showing the dodecahedron as an open frame, from Luca Pacioli, Diuina Proportione, Venice, 1509, pl. XXVIII, Call no. CAGE W10310, Collection Centre Canadien d’Architecture/Canadian Centre for Architecture, Montréal

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Fig. 9 Johannes Kepler: model of the cosmos, from Mysterivm Cosmographicvm, Tübingen, 1596, pl. III, image © History of Science Collections, University of Oklahoma Libraries
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we are ourselves drawn into instinctive states of empathetic tension and compression, mirroring that of the structure itself.
One of the recurrent concerns of those drawn to these kinds of natural engineering has been the magic of the five regular polyhedra, the so-called Platonic solids. For Plato himself, the five regular bodies were identified with the four earthly elements and the cosmos, thus corresponding to a profound level of reality in the underlying organization of all things. Leonardo, while not accepting the Platonic doctrine in its literal form, was very much in tune with the idea that the perfect geometry of the solids spoke of deep truths in natural design. He was particularly fascinated by the way in which it is possible to work beguiling, semi-regular variations by truncating them (slicing off their corners) and by stellating them (building up pyramids on their faces). His most sustained engagement with the geometry of the solids came when he provided the illustrations for Luca Pacioli’s De Divina Proportione (Figs. 7 & 8). The mathematician arrived in Milan in 1496, under the patronage of the Duke Ludovico Sforza, and the manuscript was completed two years later. Leonardo invented a brilliant method of showing the bodies both in solid form, modelled like pieces of sculpture, and in skeletal form, so that their complete spatial configuration could be more readily seen. When the illustrations were printed in 1509, they became the only Leonardo images published in his own lifetime. His own independent sketches of variations on the solids testify that Leonardo was one of those remarkable people who possess such extraordinary powers of spatial visualization that they can undertake complex manipulations of geometrical sculpture in their minds.
It was exactly this ability that served Johannes Kepler so well in his conception of the cosmos, in which the orbits of the planets are envisaged in terms as a series of nested spheres within which are inscribed the Platonic solids. This scheme was expounded and brilliantly illustrated in his Mysterium Cosmographicum (Fig. 9)-- a wonderful title for a book. His later treatise on world harmony abandoned this system, but the later revision does not alter the brilliance of the three-dimensional insight into the possible organization of the cosmic system. Kepler was also concerned with the search for such “Platonic forms” in the new device of the microscope, and wrote a witty treatise on the six-cornered snowflake. Again, we are encountering shared insights at scales from the very tiny to the biggest then known, courtesy of the lens-based devices of microscopes
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