Reflections: Philosophy of 3-D Form

Thoughts on Organic Form from Nature

Prior to retirement, I occasionally carved wooden logs. I followed the lead of the log and of my tools, producing flowing curves that brought out the beauty and sensuality of the wood, as it had grown within a tree. I felt a kinship to the sculptures of Henry Moore and learned about the abstraction of 3-D form from his masterpieces. As I became more involved in sculpture—including ceramics and plaster casts—I wondered increasingly about the role and nature of sculpture in today’s world, given the developments in the field during my lifetime. This chapter presents some of my reflections on that question.

Historically, organic sculptural form was often associated with representation of the bodies of humans and animals. The invention of mechanical reproducibility with photography and video not only changed the aura of those works (according to Benjamin), but also questioned the role of realistic likeness in sculpture. Modern European sculpture transitioned from realistic representation to more abstract study of 3-D forms in the oeuvres of Rodin, Brancusi, Degas, Giacometti, Moore, etc. That transition period in the history of sculpture by the generation or two before me has appealed to me more than subsequent developments, like metal constructions of geometric or industrial forms, experiments with high-tech materials, environmental happenings or pop-art plays on everyday artifacts.

As this book documents, I have explored a delimited range of possibilities of 20th and 21st century sculpture. This included studies and reproductions of ancient sculptures, including the earliest known human examples: Paleolithic, Cycladic, pre-Columbian and modern masterpieces. I took courses on realistic sculpture of the human body and used live models for portraits and torsos, to develop and understand the techniques involved and to study the forms. The idea of “opening up” a log or lump of clay to create negative as well as positive forms and spaces is one specific direction that I have pursued.

The Working of a Work of Art

Art—in contrast to objects of daily utility—functions to make our world visible, tangible and sensuous. It opens up the working of the works of art. One wants to explore, touch, move around and contemplate pieces of sculpture in ways one rarely interacts with other objects. Everyday objects are simply present for use in actions that are focused on action goals; we tacitly exploit these objects as mere subservient means, paying little heed to their inherent qualities.

Space is the Place

Works of art draw attention to themselves, rather than to some other realm. They stand out in the everyday world by creating their own space. Space is an unobserved structure that is normally taken for granted or abstracted as a simple mathematical configuration or empty volume. We move through space and glance through space without explicitly perceiving the space itself. Every physical object takes up a space, which it defines by the volume within and around its surface. By displaying itself as a visual object, a sculpture can make visible the space it fills and the space it opens up around itself. It is even possible for a sculpture to be designed to open up spaces within the positive forms of the sculpture’s material, creating negative spaces, which can themselves become centers of focus.

Making Reality Visible

Objects from different realms have different forms. Sculptures can make these obtrusive and perceptible. Architecture (which was originally inseparable from sculpture) can both construct and reveal the spaces within which humans reside. Pop art makes the character of everyday, taken-for-granted commodities noticeable. Forms of the sea and sea life differ from those of the land; sculpture can contrast these forms. Scale—which sculpture can play with—also makes a difference, bringing out details, relationships and spaces that are hidden on accustomed scales.

Mass Production

Manufactured objects today are commercial commodities, explicitly designed for easy mass production by automated machinery, and mass produced with standardization for universal assembly. They have flat, 2-D surfaces, following simplistic mathematical shapes. They are efficient to fabricate by machine and are interchangeable for economical exchange on the global commodity market. They are derived forms of abstract value, not specific to any characteristics of origin, setting or intended application.

Natural Evolution

Organic forms, by contrast, evolve in response to their immediate environment. Their form follows from their uniquely situated function: a tree’s limbs bend to allow their leaves to capture sunlight in their particular setting, and a bird’s bones are shaped to provide strength and mobility with minimal weight and mass. Such conditions of growth result in flowing, but unique and complex formations, with parts that support distinct functions connected by transitional forms, which flow into each other, rather than simply butting up against each other and requiring connectors. An organism consists of an integrated formation, with specialized forms merging into each other. Organic sculpture can aim to capture such structure in ways that display it to an observer’s senses.

The Manufactured Environment

In a philosophic passage, I once wrote that my sculptures are responses to the artificial character of the contemporary synthetic environment. The urban setting consists of plastic and concrete structures manufactured with homogenous materials and uniform geometric shapes, rather than with the organic forms of nature. Technologies of manufacture have imposed these rigid, flat, symmetric shapes that are totally controlled by their makers and machines. These shapes are simple and instantly understood by observers, so they fade into the background of assumed second nature, rather than provoking attention.

In the twentieth century, several sculptors explored biomorphic abstraction, which features the subtle, flowing forms of nature in contrast to manufactured designs. These sculptures have always appealed to me and inspired my own efforts. Perhaps the biomorphic approach complemented the mathematical paradigm, which dominated my professional life in computer science.

Organic Form

My sculptures are not ahistorical; not the result of some primordial experience of self-consciousness interacting with unmediated nature. They are late-twentieth-century and early-twenty-first-century explorations of form and material. In them, organic three-dimensional forms are showcased to contrast with socially prevalent two-dimensional representations and with the geometric shapes produced by automated machinery. The inherent characteristics of the materials of nature are brought forth, in contrast to the artificial plastic substances that retreat from our consciousness in commodities. Furthermore, the usual pragmatic representational function of semiotic objects is overcome in the study of their abstracted physical forms and materiality. In negating and surpassing (Hegel: “Aufhebung”) the commonplace characteristics of signs—which point away from themselves—the non-representational sculptures obtrusively confront their creator and viewers with the nature of the artifact itself as intentionally formed material object. Not representing some external subject, they point to themselves.

Biomorphic Form and Cubism

Biological organisms have evolved over eons to integrate multiple organs. Each organ has its distinctive function. The structure of the organism unites its constituent organs together into a smooth functioning, creating a higher-level formation. Analogously, a complex sculpture can integrate multiple 3-D forms, which complement or contrast with each other. Different faces of a particular mass can assume forms at tension with each other. A successful sculpture unifies its many sub-forms into a coherent structure. My wood sculptures tend to be biomorphic, adopting 3-D forms similar to biological organisms.

Cubism tried to capture multiple perspectives on an object simultaneously. As works of 3-D form, sculptures embody multiple perspectives when viewed from shifting angles. Cubism freed the arrangement of parts of a given object—such as organs within an organism or body—and sculpture can adopt that freedom by displaying parts of a body selectively according to a unity of the sculpture that differs from that of its model. The structure of the sculpture represents selective aspects and arrangements of its model, while presenting its own structural form, its re-integration of formal elements.

A sculpture may integrate subparts at multiple levels. A complex form like Return of the Osprey may have numerous parts, each of which forms an organism of 3-D forms flowing into each other. It may take a viewer some time and effort to explore the sculpture at different scales and viewing angles.

Rodin’s dynamic human poses and Degas’ dancers make visual and haptic the structural potentials of the human body, with its joints and musculature. They often exceed or exaggerate the possible poses, combining specific perspectives and consecutive views slightly out of time. There is a tension between the model and the sculpture, in which post-photographic realism extends what is possible in the literally represented original.

Rodin Working on Works

In his book on Rodin, Rilke emphasized the creation of “works” as a driving force for Rodin. The ephemeral work on sculptures was often more important than the persistent sculptures that resulted. The resultant sculptures were always somehow inadequate; the problems that had been pursued in them were not completely or satisfactorily solved; it was hard to say when a given piece was finished—except by noting if it had been signed in preparation for sale. Rodin lived above all to engage in his sculptural work.

Degas never exhibited or sold his sculptures, except for “The Little Dancer.” He did not cast them, but simply worked on them in his studio for their own sake, as explorations of the possibilities of sculpture and the potentials of human bodily movement through space. Similarly, Giacometti was driven to work and re-work his pieces endlessly, searching to capture his vision, rather than to produce finished pieces. The important thing is the working that goes into the work, rather than the resultant object, which captures and preserves the working. Rodin, Giacometti and Degas all liked to come back to old pieces and re-work them—undercutting the sense that works were ever final, that they were no longer subject to working.

In my recent involvement in sculpture, my days often revolve around an agenda of working on some current piece. The point is not so much to produce yet more objects, since I am not selling or using the resultant products. The point is to engage in the work, explore a sculptural or technical problem, re-discover what some other sculptor found in creating something that inspired me. The working is more important than the work, which drives and results from the working.

Degas’s Dancers

Sculpture can display the structure of objects, rather than just their surface appearances and attributes. Degas’ dancers, balanced instantaneously on one leg, capture the ephemeral structure of a ballerina’s motion through space around a center of gravity. The placement of the ballerina’s feet and the twist of her torso reflect slightly different moments in time and thereby imply and capture motion, like the subtly superimposed feet of Degas’ galloping horses, caught impossibly in mid-air.

Although Degas’ sculptures, like “Grand Arabesque,” represent the human form realistically, they are freed from traditional conventions to centrally incorporate space, void and motion by allusion. His fleshed-out female forms begin to act as structural indications of space, with limbs reaching out in every direction. Dance suggests the flux of time, in which Degas’ figures unfold from one study to the next in growing configurations of space and figure integrated. Degas thereby defined the transition from representation to structure in the history of sculpture according to Charles Millard, Curator of the Hirshhorn, in his study of Degas.

Giacometti’s Plaster Sculptures

Giacometti’s emaciated plaster busts and human figures capture the core spatial existence of a man or woman. The irreducible residue of one of his female sculptures reduces her entire reality to being seen, according to John Berger, who feels that Giacometti created his plaster figures during his lifetime, for himself, as observer or anticipator of his future absence, his death, his becoming unknowable after occupying an un-shareable reality. We now take the place of Giacometti in looking at the tall woman, in her structure as a solitary presence.

Despite all the talk of Giacometti’s figures as representing existential alienation, his figures inevitably take up social and spatial positions in the shared world—with the many other plaster figures in his studio, with selected companions in exhibition collections and within spaces explicitly defined by their platforms, glass enclosures and metal cage outlines. Individual human forms are elements in composite structures.

The structures of Giacometti’s constructions prominently include spatial relationships, with the distances between plaster figures indicating social distances and their glances passing by and ignoring each other to accentuate the reduction to solitary individuals in communal settings. The spaces defined between figures, cages or platform edges create distance from the viewer, much as a painting’s chosen perspective does. Giacometti’s sculpture creates vacuum, starting from mass or plenum, according to Sartre—locating his friend’s work within the dialectical conceptualizations of Being and Nothingness. The radically reduced positive space of the sculpture projects negative space all about it, stretching out to the viewer and distancing the figure as alone and un-reachable.

I have been intrigued by the creation of space through configurations of matter and nothingness. Lived, meaningful space is not a mathematical manifold or Newtonian coordinate system, extending uniformly everywhere, absolute and independent of content arbitrarily located within it. Rather, it is a felt openness to being, projected around specific materials in concrete formations. Space contains objects, flows around them, opens opportunities for other shapes; it penetrates into gaps through and between the objects. The sculptural form opens up the space in which it appears and also in which it pointedly does not appear.

In my attempts to open up masses, such as in my recent ceramic constructions (see below my “Thoughts on opening up spaces”), I create structures that define intricate positive and negative spaces without covering up the surface or filling in the interior. One way to open up a space most effectively is to reduce the mass of the positive focal form to a minimum, as Giacometti did in his mature sculptures. For Giacometti, this approach corresponded to the character of human vision. He said he struggled to capture what his eye actually perceived, as opposed to what the mind constructs as a figure. Of course, his eye was uniquely trained by a lifetime of looking carefully at models. Moreover, what he referred to as the mind was its preconceptions and stereotypical images.

Realistic Sculpture

I have recently been working on realistic sculptures of live models and from photos of people, especially human faces, including my own. Working from a live model is invaluable training for seeing the structures of heads and bodies. Standard techniques for creating masses and planes are also helpful in roughing in the 3-D forms. However, the rote representation of a subject using established techniques for reproducing some supposedly objective view of the subject is not considered an artistic process. For instance, using pointing machines in the baroque era to produce copies of living bodies was useful for some processes, like making copies of a sculpture, but less for creating the original work of art.

When we see somebody—not by staring at their facial image as at a photo—as part of interacting with them, we do not perceive a smooth manifold with standard features and manifold details. We see the person, the personality, perhaps as synthesized into a vague mental image of their general likeness.

Consequently, a sculptural representation of the person should not be a 3-D reproduction of their body, frozen at one instant. It should be something that projects their personality. That is the source of Rodin’s emotional movement, often distorting the surface in energized waves of vibration. Similarly, it is the person’s spatial presence, at its essential core in Giacometti’s structures, which resist being confined to precise and smooth appearances. These sculptures may not look “realistic” in the photographic sense, but the artists felt that they captured reality in a sculptural way.

The critic, Leo Steinberg, argued that realistic sculpture is important even after the invention of the camera, but not in a rote, technological sense. He claimed that “the eye is part of the mind,” that is, that

technical capacity in imitation implies what no one seriously believes: that nature confronts man with a fixed, invariant look. We know better than that. Appearances reach us through the eye, and the eye is part of the brain and therefore inextricably involved in mysterious cerebral operations. Thus, nature presents every generation (and every person who will use his eyes for more than nodding recognitions) with a unique and unrepeated facet of appearance…. And if appearances are thus unstable in the human eye, their representation in art is not a matter of mechanical reproduction, but of progressive revelation.”

Works connected with discoveries of representation, purvey not given facts, but “the thrill and wonder of cognition.”

According to Steinberg, about half the great art generated by mankind—starting with Paleolithic art—is dedicated to the accurate transcription of the sensible world. However, artists do so in particular ways, rendering their subjects according to available technologies, cultures, conceptualizations, predecessors and the gleanings of their own work. Standardized techniques for capturing likeness miss the to-be-interpreted character of the subject.

A modern photo can instantaneously reproduce the physical appearance of a subject at a specific moment. However, for instance in the case of a face speaking or a body moving, the muscles involved (with their accompanying prominences and shadows) are continuously shifting. The perceived appearance over a time segment posits the unity to these momentary stages. It is the interpreted unity that projects an underlying character or personality or motion or emotion to the subject. The challenge is to then represent in a 3-D form the subject’s character through this unity—rather than simply a photo-like snapshot picture. If “realistic” means aiming for the snapshot, then sculpture needs to incorporate the techniques of realism without setting them as the ultimate aim. The representational goal is, rather, to capture the personality that shines through the unity of the likeness.

Tutorials on realistic sculpture rightly emphasize procedures of building up from skeleton to musculature to flesh (fat and skin). These are the layers that conduct the body’s motion: the joints, the tendons and the masses. They are not static structures, but vibrant effectors of motion. As they shift and swirl, the body’s forms swell and ebb. Each individual’s figure is defined by its unique configuration of bones, muscles, fat deposits and skin wrinkles. As a person breathes, speaks and moves, this unique complex cycles through its characteristic topologies. The sculptor struggles to capture this through his eye, mind, body, materials, skills, techniques and style.

Eye and Mind

For the philosopher Merleau-Ponty, human existence is fundamentally embodied. Visual perception is the primary mode of perception of the human body. Vision is intimately integrated with our tactile sense, so that “the visible world and the world of my motor projects are each total parts of the same Being” (Eye and Mind).

Sculpture corresponds to this foundational unity of vision and touch. A sculpture leads the hand and eye across its surfaces, whether actually or in the perceiver’s imaginative projection. Unlike painting or even relief, the 3-D forms lure perception around the facing façade and into the sculpture’s depth. Although only certain shifting surfaces are visible at any given moment, the different perspectives possible from around the mass flow into each other, evoking and leading eye and hand and mind.

Sculpture explores the depth of objects in the world. While depth is merely implied in painting, through tricks of perspective and shading, for instance, it is explicit in the massing of 3-D forms. The sub-forms of a sculpture reference each other by overlapping and concealing—only to then reveal as one circumnavigates the sculpture. As Merleau-Ponty puts it, “The enigma consists in the fact that I see things, each one in its place, precisely because they eclipse one another, and that they are rivals before my sight precisely because each one is in its own place.” As one successively perceives each facet, the previously seen planes recede into hidden but remembered depths. Each angle on the sculpture reveals new, unanticipated forms and integrates them into a felt 3-D whole, with depth in space.

The sculpture’s flow of curves and obtrusive features forms a surface, creating a boundary between the surrounding transparent space and the opaque internal mass. Depending upon the material of the sculpture, one may wonder about the nature of the interior. For instance, the hidden grain within a wood sculpture, its transition from outer to core wood, residues of its sticky amber sap, origins of its former branches and other organic vestiges of its growth may suggest mysterious structures of potential interest. The hardness of stone may challenge one to desire a glimpse inside and the homogeneity of clay might motivate an urge to break its impenetrability.

The dynamic of the observer’s perception of a work has its correspondence in the production of the work by the sculptor. The sculptor undergoes similar perceptual processes, possibly more focused, even conscious or reflective. The forms emerge in the work as the sculptor may attempt to bring out, structure and mold the perceptual effects. The material offers unexpected features and the sculptor’s work responds by enhancing or removing selected features to create interesting forms and an over-all work, with its effects of perceptual stimulation, motion, depth and space.

The successive stages of sculpting define forms at different scales, which may be compatible with each other. The selection of a particular log or a bag of clay; the roughing in of the log of the massing of clay; the construction of major forms or primary structural elements; the defining of flowing or rough surfaces; the refining of forms and surfaces; the finishing of surfaces with oil, glaze, paint, embedded elements; the mounting of the finished piece; lighting; photography; display.

As a sculptor explores and learns about specific material forms, he or she may try to render those discoveries visible and even dramatic in the work as a thing in the world.

A Heideggerian View of Sculpture

In his essay on “The Thing,” the philosopher of Being, Heidegger, considers the example of a jug, as created by a potter on a wheel. He suggests that the thingness of the jug is centered on its interior void, which can be filled with water or wine and can offer it for pouring and imbibing. But he does not describe how the jug comes to be what it is.

Learning to make pottery involves acquiring skills and knowledge to be able to produce jugs and other ceramic works that more or less fulfill that ability of a successful jug. This has many aspects; creating a jug involves a series of phases: acquiring and preparing the clay, gathering the tools and equipment, centering the lump of clay on the rotating wheel, opening a void in the lump, pulling the sides up in several pulls without the sides collapsing, shaping the form (with the interior curve matching the exterior curve), partially drying the piece to give it strength, trimming the thrown piece and cutting a foot on it, gently shaping a spout that will pour without dripping, attaching a pulled length of clay for a handle that will fit a human grip and provide balanced lifting, slowly drying the clay without cracking, optionally adding design to the surface, firing the jug, glazing it and firing it again.

Each stage of producing the jug is an experiment and the final product is always somewhat of a surprise. One learns through years of practice how to control each phase and what one prefers as results of each stage. However, at most phases there is usually some interplay between one’s aims and the results. Generally, when one sees the piece as it is uncovered during the drying or when it comes out of the kiln, one is confronted by an object with its own character, and one must take up what one finds as the starting point for the next phase. As Hegel said, the worker is alienated from his product as it becomes an independent object existing in the world. There are so many variables in the clay, the wheel speed, the drying conditions, the pressure of the hands, the chemical reactions of the glaze and the work of the potter that one can only approach an ideal of control where one can produce something like what one set out to make. Such control takes considerable experimentation and practice.

Ceramic jugs are one of the oldest and most universal of human artifacts. Once humans around the world harnessed fire, they learned to make and “fire” (bake) useful and beautiful jugs. My study of pottery is part of my philosophic investigation of the nature of artifacts.

In The Origin of the Work of Art, Heidegger writes:

“Although it becomes actual only as the creative act is performed, and thus depends for its reality upon this act, the nature of creation is determined by the nature of the work…. To create is to cause something to emerge as a thing that has been brought forth. The work’s becoming a work is a way in which truth becomes and happens.”

The craft of the artist involves creating an object that opens up a world and reveals something (as discussed in my philosophy dissertation). This craft requires a dialectical back and forth between the artist’s inquiring over time and the successive revelations of the objects produced. The artist—akin to a philosopher or scientist—proceeds along a journey of inquiry, gradually revealing new truths through sequences of more-or-less insightful works. This is a historical process, in which the artist pushes his or her own previous inquiries further in specific directions, confronting issues that arose in past works and employing techniques that have been developed in previous inquiries, including by earlier artists. This involves mastering crafts, materials and technologies of the past or of previous works. It involves posing specific problems to solve, and new directions to explore.

In his discussion of van Gogh’s painting, Heidegger generally misses its art-historical importance. He views the painting as purely representational of a peasant woman’s shoes. He misses the relationship to the impressionist revelations about light (and shadow) or van Gogh’s own exploration of brushstroke as an element of the materiality of paint.

The work involves a dynamic between revealing and concealing. As a work, a sculpture opens a special space around itself, structured by its 3-D form, which extends out of that space. The surfaces of the form are revealed, but they simultaneously conceal what lies below or beyond the surface: the interior of the wood, stone or other material. This dynamic that takes place at the surface of a sculpture is Heidegger’s notion of the “Riss,” which I always found to be the most obscure concept in his essay on art. I did not fully realize how Riss entails both the tearing conflict between un-concealing and re-concealing and also the design, outline or figure of the work, e.g., the surface form of a sculpture, which defines its shape while enclosing its interior.

Certain sculptures may attempt to open up the concealed interior—for instance by poking a hole into or through the surface forms, or by chipping away the smooth outer surface to expose internal material—and simultaneously to reveal the effort of carving the material by leaving traces of that human effort and procedure. Through such elements of the work’s design, the interior is opened up, but then simultaneously closed up along the new surfaces of the holes.

Negative form can be viewed as an effort to reverse what is concealed and what is revealed. In some sculptures, I have tried to reveal the space itself by simply outlining it or otherwise indicating it. In others, I have tried to open up the normally concealed interior space by providing just a structure to define it as a space, while leaving the interior—or at least the interior space—visible. One could consider Giacometti’s thin plaster sculptures to be presenting just the interior of a figure, absent the usual concealing layer of fat and skin. (See my Study of Giacometti Tall Figure in contrast to my Chatham Sunbather or Tony’s Torso.)

The work of art is also a communication between the creator and the observer of the work, an attempt to guide the viewer/preserver to see what the creator has made visible in the work. As Heidegger notes about viewing art, “Preserving the work does not reduce people to their private experiences, but … grounds being for and with one another as the historical standing-out of human existence in reference to un-concealed-ness.” Thus, the work functions to build historically situated inter-subjectivity, grounded in the work.

 A work of sculpture brings some thing into the world, opening up a space for it to do its work in its historical social setting.

Pre-historic Sculpture

Like every cultural tradition, sculpture is an on-going conversation across generations of practitioners. Art is considered a characteristically human mode of expression. Sculpture as 3-D form takes its place along with 2-D drawing or painting, music, dance, and other art forms. Particularly since communication was established globally, artists in one part of the world have been influenced by exemplars of art from other places and times. For instance, it is now possible to see paradigmatic samples of art from the primary stylistic epochs and principal world regions collected next to each other at major museums.

I have been interested in prehistoric and non-European sculpture, particularly during my travels to the countries where these were created. Sculptures from non-technological cultures are often quite abstract, in the sense that they abstract away from details and capture larger forms in a stylized way. This abstraction may be attributed to the limitations of the sculptural materials (bone, stone, clay) and tools (hand, sharpened rock) or to cultural traditions or to some innate human mode of observation, thought and expression. One can learn much from these works. I was astonished at the extent to which the oldest known sculpture of the human figure teaches you when you try to duplicate it and was delighted by how the earliest Latin American carvings do so as well.

In my own sculptural attempts, I have often tried to follow the lead of historic (or pre-historic) examples. By mimicking their forms in my own way and in my own materials, I have been inspired and gained insight into 3-D forms.

The Tübingen Venus

The Venus of Hohle Fels is an Upper Paleolithic figurine dated to between 40,000 and 35,000 years ago. It is one of the oldest undisputed examples of figurative prehistoric art.

This figurine of a voluptuous woman carved from mammoth ivory and excavated from a cave in southwestern Germany is the oldest known example of 3-D or figurative representation of humans, and sheds new light on the origins of art.

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Four views of the Venus of Hohle Fels. The figure is about 2 ½ inches tall (slightly larger than the picture here).

The intricately carved headless figure is at least 5,000 years older than previous figurines and dates from shortly after the arrival of genetically modern humans in Europe. It exhibits many of the characteristics of fertility, or Venus, figurines carved millennia later.

It was found in southern Germany in the Danube valley, the migration corridor for modern Homo Sapiens into Europe. The figurine’s site was successively and repeatedly home to both Neanderthals and Homo Sapiens. This raises the possibility that such figurative art arose through the confrontation or intermixing of these two humanoid species. There is no evidence of art in the culture of the Neanderthals, but also no art like this in the culture of Homo Sapiens until they left Africa and met the Neanderthals. It is now known that the two species met and even mated, although the nature of their relationship in general is controversial. The theory that Homo Sapiens violently eradicated the Neanderthals is currently doubted. The Neanderthals existed for much longer than Homo Sapiens has, survived the ice age and exhibited many skills. Art always thrives in cultural mixing pots.

The Venus of Hohle Fels shows a range of entirely unique features as well as several characteristics present in later female figures. The Venus lacks a head. Instead, an off-centered, but carefully carved ring is located above the broad shoulders of the figurine. This ring, despite being weathered, preserves polish suggesting that the figurine was worn as a pendant. Beneath the shoulders, which are roughly as thick as they are wide, large breasts project forward. The figurine has two short arms with two carefully carved hands with visible fingers resting on the upper part of the stomach below the breasts.

The Venus has a short and squat form with a waist that is slightly narrower than the broad shoulders and wide hips. Multiple deeply incised horizontal lines cover the abdomen from the area below the breast to the pubic triangle. Several of these horizontal lines extend to the back of the figurine and are suggestive of clothing or a wrap of some sort. Microscopic images show that these incisions were created by repeatedly cutting along the same lines with sharp stone tools. The legs of the Venus are short and pointy. The buttocks and genitals are depicted in more detail. The split between the two halves of the buttocks is deep and continues without interruption to the front of the figurine where the vulva is visible between the open legs. There can be no doubt that the depiction of oversized breasts, extenuated buttocks and genitalia result from the deliberate exaggeration of the sexual features of the figurine. In addition to the many carefully depicted anatomical features, the surface of the Venus preserves numerous lines and deliberate markings.

Many of the features, including the emphasis on sexual attributes and lack of emphasis on the head, face and arms and legs, call to mind aspects of the numerous Venus figurines well known from the European Gravettien, which typically date between 22,000 and 27,000 years ago. The careful depiction of the hands is reminiscent of those of Venuses including that of the archetypal Venus of Willendorf, which was discovered in 1908. Despite the far greater age of the Venus of Hohle Fels, many of its attributes occur in various forms throughout the rich tradition of Paleolithic female representations.

The figure, about 2.4 inches tall, was carved from a mammoth tusk. The intricate detailing achieved with primitive stone tools indicates the amount of energy invested in these little objects—tens if not hundreds of hours.

I viewed the original carving on my last trip to Tübingen and was given a scale replica of it. I decided to create a larger version to see the sculptural forms of the carving more clearly, abstracting from the intentional scratching of the surface as well as the cracks from assembling the many pieces of the original find.

As I worked on the piece, I was impressed at the elegant abstraction of the human female form as well as its capture of the maternal stance of the pregnant woman. Early humans during the Ice Age clearly had much of the perception, empathy, concern and craftsmanship that would rival that of contemporary people.

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My clay sculpture, holding a scale model of the 40,000-year-old original.

The Valdivian Owl

In September and November 2017, I carved a set of two sculptures in cherry wood, based on an ancient stone sculpture from Ecuador.

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Friends had commissioned me to make a sculpture for them and I thought for some time about doing a sculpture of a bird, since they loved birds, particularly owls. One day, browsing through pictures I had taken of pre-Columbian sculptures in a museum in Ecuador in 2013, I came upon my favorite of the collection and started to research it on the Web.

Here is the photo I took—as well as a collection of other Valdivian stone sculptures:

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This carving is one of the earliest known sculptures in the Americas, a Valdivian stone carving from Ecuador. Valdivian stone figures are rectangular in shape with delineated eyes and features in characteristic minimalist style.

The Valdivia Culture is one of the oldest settled cultures recorded in the Americas. It emerged from the earlier Las Vegas culture and thrived on the Santa Elena peninsula near the modern-day town of Valdivia, Ecuador, between 3500 BC and 1800 BC.

First, I carved a sculpture based on the Valdivian owl for my friends. I liked it so much, I made another one for my own collection, perched on a branch.

The Cycladic Figure

In 2015, I carved a sculpture based on early ancient Greek Cycladic sculpture. The wood is English Plane (related to sycamore) from a large tree we had taken down in our back yard a couple of years earlier. It was one of several logs that I had the arborist cut from the tree before removing the rest by crane. I started carving the log, based on a small copy of a Cycladic sculpture that I had purchased in Greece. During two visits, Rusty assisted in the carving.

Because my sculpture is based on the Greek marble Cycladic sculptures from the birth of Western sculpture and because of their connection with fertility, I named my sculpture “Baby” and dedicated it to Rusty and Sarah's daughter, my second granddaughter, Ruby, upon her birth.

It was at first difficult to achieve the three-dimensional symmetrical form of the model. In addition, the quality of the wood seemed ragged, so I wondered if I would be able to get a nice surface or reveal an interesting grain. It was not until the piece was completed and oiled that the beauty of the wood was revealed.

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The original Cycladic sculptures date back to the Neolithic era of pre-history, between 5000 BCE and 2400 BCE. They were carved in the finest Greek marble, which is local to the Cycladic islands and was later exported to Athens and elsewhere in classical Greek times. Little is known about the Cycladic people and their world, although the group of islands was a crossroads of the Mediterranean even before sailing ships were invented.

The Cycladic sculptures were likely fertility objects. Most of them represented young women of childbearing age and accentuated their female features. Certainly, they involved the life cycle, and are often found in graves.

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The Cycladic sculptures all possess certain features: canonical (e.g., folded arms), proportional and simplistic. They appear in museums now as pure in their whiteness. However, these sculptures were frequently painted. Pigments were used to add detail. The only facial feature carved was the nose. The sculptures have all been excavated at Cycladic cemeteries.

The Neolithic and Bronze Age Cycladic figures present an intriguing link between prehistoric art and Western art; between the figurines of Galgenburg and Willendorf and the sculptures of Brancusi and Modigliani. As Lord Colin Renfrew states of these sculptures, “a handsome standing figure, with quiet, unassertive rhythms and balanced proportions, achieves one of the most compelling early statements of the human form.”

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Is it that there is something incredibly modern about these prehistoric figurine sculptures, or has humankind always portrayed the human form in a manner that utilizes elegance and simplicity, with figures mastered by style and yet full of life? The emotional pitch is achieved by the omissions, distortions and exaggerations, and in so doing the artist creates a tension between the abstract and the real.

The Museum of Cycladic Art in Athens—a favorite of mine—is dedicated to the study and promotion of ancient cultures of the Aegean and Cyprus, with special emphasis on Cycladic Art of the fifth millennium BC. It was founded in 1986. Its collection is one of the finest collections of Cycladic artifacts in the world.

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The Cycladic Islands of Greece are set in the Aegean Sea. The ancient Greeks called these islands the Kyklades, a scattered kyklos or circle, of islands around the holy island and sanctuary of Apollo: Delos. The Cyclades had rich mineral deposits and fine marble. They were close to each other, which made safe navigation between the islands in rowboats easy (sailing ships were only invented ca. 2000 BC). During the Early Bronze Age, when people started using bronze for their tools and weapons, a sophisticated culture flourished in the Cyclades that thrived for almost a millennium. This period—called Early Cycladic—ranges from 3200 to 2000 BC.

The Early Bronze Age inhabitants of the Cyclades used their local supplies of premier white marble to make both figurines and a variety of stone vases. The development of sculpture was one of the most impressive achievements of the Early Cycladic culture, no doubt made possible by bronze technology. Archaeologists organize the well-known stylized marble figurines in two basic types: schematic and naturalistic. The majority of Cycladic figurines represent nude females in standing position. Less frequent are models of male musicians, warriors and groups of figures in a range of postures.

I took these photos at the Museum during May 2010, when we went on a wonderful cruise of the Cycladic Islands to celebrate my 65th birthday:

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Pre-Columbian Sculpture

I have always loved pre-Columbian sculptures and figures—at least since my family trip to Mexico when I was 17. The Olmec, Maya, Inca and Aztec cultures all had wonderful pottery, masks and carvings.

The ancient Olmec culture specialized in large stone carvings, which are relatively rare. I saw some near Vera Cruz on my honeymoon in 1989 and more during a trip to Guatemala in 2014. The Mayans, Incans and Aztecs had their pyramid temples with relief carvings, stone carvings and pottery incorporating striking images of gods and animals.

Over a dozen Mayan and Aztec sculptures named Chacmool have been found, dating from 800 AD on. The distinctive posture of the Chacmool is what allows the many sculptures to be united under one term: the figure reclines on his back, his knees bent and his body on a single axis from neck to toes. The elbows rest on the ground and support the torso, creating tension as the figure strains to sit upright. The hands meet at the chest, usually holding either a disk or a vessel, possibly for human sacrificial hearts. The head rotates ninety degrees from the axis of the body to present a frontal face. This recumbent position represents the antithesis of aggression: it is helpless and almost defenseless, humble and acquiescent.

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Chacmool excavated by Augustus Le Plongeon from Platform of the Eagles, Chichen Itza.

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Chacmool excavated in 1943 in Mexico City.

My mother brought me a small replica of Chacmool from a trip of hers to Mexico. I used this as a model for my larger clay sculpture.

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Chacmool. Red clay, painted base. Chatham. 2017.

I created several studies of pre-Columbian ceramics—see the section on Pre-Columbian Figure Series above.

Modern Sculpture

Brancusi Simplicity

Constantin Brancusi (1876-1957) is the modernist sculptor who reduced forms to their simplest essence. Born in Romania (where my paternal grandparents came from), Brancusi was active in Paris during the blossoming of abstract art, partially inspired by exotic sculpture of prehistoric and non-European cultures.

Throughout my life, I often visited the room in the Philadelphia Museum of Art dedicated to Brancusi’s sculptures. I also lingered in Brancusi’s studio, recreated in Paris. In particular, I loved the purity and sophistication of Brancusi’s “Bird in Flight” sculpture, which he produced in several media.

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Brancusi’s marble sculpture in his atelier, my oak sculpture in Rusty’s living room, my cherry sculpture outside my house.

To reawaken my sculpting after several years of non-use, I challenged myself to reproduce “Bird in Flight” in wood, using a curved white oak limb from a tree in my Philadelphia woodland. I later decided to do a larger version for outside my house in Chatham, from a wild cherry limb from my woodlands there.

Moore Forms

Henry Moore (1898-1986) has always been my primary inspiration in sculpture. His sculptures have allowed me to see and feel 3-D forms.

I have looked carefully at Moore’s sculptures whenever I came across them and have run my hands as well as my eyes over their surfaces, textures, curves and edges. I have read many books about his sculpture, which mainly involves looking at the pictures, which try to capture the 3-D sculptures in 2-D photos.

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Moore went beyond Brancusi by adding back some of the complexity of organic 3-D forms, while retaining the clarity of the simple underlying forms.

Moore was one of the pioneers of direct carving (as opposed to the academy’s use of pointing tools to mechanically copy models). He was also one of the first sculptors to explore holes or negative spaces in sculpture—whether leaving open space between forms or actually poking holes in solid masses.

I have always adopted direct carving and been interested in negative space. I am exploring how to go beyond Moore’s holes to open up masses even more, using intersecting negative spaces and defining negative spaces with partially surrounding positive forms.

Although Moore was primarily a stone carver, he did a number of wood sculptures. My approach to woodcarving is quite similar to Moore’s—although of course not at his level of artistry and professionalism. Once established, Moore was also able to work at a much larger scale than I can.

Studies of Giacometti

Sculptors generally make copies of works by their predecessors. Sometimes the goal is to reproduce the original faithfully, to some degree. Other times one adapts a pose or technique to a different subject. One can learn enormously by copying the masters. In previous times, students of sculpture learned through apprenticing an experienced artisan, working under their direction and being trained in their ways of seeing, planning, creating, reproducing and marketing sculpture. Copying interesting works is a way for students today to learn from a variety of experts, who are not personally available.

In Spring 2019 after returning from a stay in Florida away from my studio, I re-engaged in sculpting by studying the life and work of Giacometti. I read James Lord’s lengthy biography and looked at books of photos of his sculptures, which were mainly modeled in clay or wax and cast in plaster.

In quick succession, I copied several of Giacometti’s sculptures that appealed to me (see the section above on my “Giacometti Studies Series.” Most were from his early cubist period. I created each piece in clay and then made a rubber mold and cast it in plaster. I also fired the original clay version when possible.

On the way to Florida, I had seen all Degas’ sculptures in the National Gallery in DC. So, I did a clay study of his Little Dancer, the only sculpture he displayed during his lifetime.

Topology of 3-D Form

“Topology” is the logos of topoi, which is Greek for the logical structure or study of places, which are spaces defined by materials, such as the surfaces of 3-D objects. There is a field of mathematics devoted to formalizing topology. Euclid had already studied regular 3-D polyhedrons, such as the cone, pyramid, globe and the five Platonic solids.

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The five Platonic solids.

For modern topology, these are all topologically identical in that they have a continuous surface separating an inside from an outside. A donut shape, for instance, is different, because its surface could not be stretched to form one of the Platonic solids without somehow tearing the surface. I do not find the regular solids very interesting sculpturally, except perhaps as bases for stretching into twisted and asymmetric forms.

A simple topological trick is represented by the Möbius Strip sculpture. A Möbius strip is a 2-D band that has its two ends attached following a half twist. A simple band—either lying flat or with ends attached without the twist—has two sides: a top and bottom or inside and outside. However, with the twist, it only has one side! If you run your finger along one side, you end up on what looks like the other side before returning to where you started.

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A Möbius strip and a Klein bottle

A more obscure trick is represented by the Klein Bottle sculpture. A Klein bottle is a bottle shape whose neck is elongated, enters the jar through some fourth dimension, passes through the bottle and then flares out to form the body of the bottle. If you start at some point on what appears to be the inside surface of the bottle and move along that surface and out the neck, you can come around to what appears to be the outside surface of the bottle. Of course, the 3-D representation of a 4-D Klein bottle requires some artistic liberty.

Sculpture in the real world is neither 2-D nor 4-D, but has an inside (the wood or clay) and an outside (the oiled or glazed surface). However, if the sculpture has been opened up with negative spaces or surrounded holes, it can have different topological structures. For instance, some of my sculptures have zero, one, two or more holes—making their topological structures mutually incommensurable. Furthermore, sculptures like Mrs. Mayo have holes that interconnect, forming relatively complex topologies.

Sculpture, as the working of physical materials in the world, is conditioned by structural needs for strength and balance in order to persist and be displayed. The act of opening up a piece with significant holes must take these needs into account.

It is interesting that the Angel of Progress sculpture, as it winds up from its base, maintains two vertical supports at each of three stages. The two vertical supports flow out of the horizontal stage below and into the horizontal stage above. At each level, the two verticals and two horizontals form a circle framing the hole that is opened up there. The three topologically distinct openings are located at angles above each other, together defining an imaginary vertical negative space where the core of the log had been. Maintaining a pair of supports at each stage provides for strength and balance of the overall sculpture, which is delicately balanced and which takes advantage of the strength of the log’s vertical fibers. If any one of these verticals were removed, the weight of the upper part of the sculpture would produce a destabilizing torque, threatening breakage or collapse.

The Pod sculpture, by comparison, has three verticals at each stage, providing a considerably more stable structure. The Pod features three faces working collaboratively. The support for these faces spirals down through various forms, consolidating in three columns from the upper half of the sculpture that sit atop three columns from the bottom half. The bottom rests again on three legs. Maintaining a trio of support at each vertical level provides for substantial stability, avoiding the careful maintenance of balance needed in the Angel of Progress.

In a contrasting approach, the Hickory Bivalve is balanced on a small central base. This sculptural trick makes the sculpture seem to float without support. This requires a strong hidden bolt anchoring the sculpture to a broad base. Similarly, Saddle Curve is balanced on a single narrow support. However, in this case the sculpture was designed with a strong sense of internal balance. The sculpture has no separate base, but stands on a broad, three-toed foot that is integral to the design. The support section is a sculptural curve, a twisting 3-D parabolic form. The surface of the top-heavy upper part is a saddle curve, a topologically significant 2-D form. The saddle point—near the center of the log’s grain pattern—is a high point in one direction and a low point in the perpendicular direction, like a horse-riding saddle that slopes up in the front and back of the rider and slopes down on the sides under the legs. In calculus terms, a saddle point is simultaneously a relative maximum and minimum. In the sculpture, this surface is used to display the visually interesting grain that evolved at the base of the cherry tree, just above ground level. To accomplish this, the log was flipped wide side up, requiring a supporting form that would provide adequate stability.

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 A saddle curve: z=x2y2. Detail of twisting support curve of Saddle Curve. The horizontal saddle curve of Saddle Curve.

Sculptures with more complex topological structures may include interconnected openings. An early attempt at this by me is Hermaphrodite. It has two vertical supports forming an elongated opening, which are then connected to an opening from above. Bite of the Apple adds another opening, so that holes from four of the six perpendicular axes meet in the thereby opened up center of the piece. Similarly, Return of the Osprey has four openings that join in the middle of the log. Sly Eye has two openings defining the spiraling middle area of the rear of the piece entering into a cavernous opening of the wood’s mass from the front. Mrs. Mayo features the most involved set of openings, including some largely hidden holes down the center, linking multiple openings. The inside/outside relations of Hinged Forms are rather ambiguous, depending on whether the hinge is open or not; they can be seen as reducing the wood almost to an outline structure defining connected negative spaces, most notably the center of the log, for which opening the hinge provides easy access for the carving and the observation.

The view of sculptural material as structures defining negative forms comes from my ceramic models and sculptures. See the section on my Negative Structures Series, featuring the following: Slab Sculpture 1, Slab Sculpture 2, Slab Sculpture 3, Sculpture with Grog and Negative Structure. Here, the interconnected openings are too involved to count or describe. The approach shifts from opening up a solid mass to creating an open space by defining its boundaries.

Working in clay involves different gravitational—and hence topological—considerations than carving wood. The clay must hold its own weight as it dries and is fired, as well as balance properly as a finished piece. Clay structures are built up, whereas wood is carved away. So extreme opening up of negative spaces by reducing positive forms to a minimum involves adding clay until it is strong enough versus removing wood without making it too fragile to withstand checking during drying or breaking under stress. Ceramic sculptures can be built up from spans of clay coils or elongated slabs, whereas wood sculptures are carved out from solid logs. Although the results are often quite different, I often create ceramic models that I can hold in my hand, easily view in 3-D and quickly refine their masses, openings or connections. Such maquettes then inspire and guide the creation of wood sculptures requiring a hundred times as much time and effort. In this way, topological insights from one medium influence work in the other material. This is an important aspect of the dialectic between material and manipulation in sculpture.