A Catalog of Difference

A Catalog of Difference Andrew Lucia

A Catalog of Difference

A Catalog of Difference Andrew Lucia

UMinn Papers on Architecture University of Minnesota School of Architecture

Contents

Foreword—Samuel C. Fletcher 7 Acknowledgments 11 A Catalog of Difference Planar 19 Curvature 54 Spherical 76

A Catalog of Difference

Appendix

Lux Sphaerae 101 Projections 112

Notes on the Structure of Ambient 116 Light in Organic Environments

On the Reception of Multiple Ambient Images 120

Foreword—Samuel C. Fletcher A Catalog of Difference

Integral to architectural practice and theory are techniques for the representation of form: not just the forms of building structures, but also the networks of utilities that make them habitable, the natural, biological, and social processes they engender or inhibit, and the interaction of all of these with their exterior environment and interior space. The techniques used have their own subtle histories and conventions, based and constrained both in the abstract prevailing ideas about what is and is not important to represent, and in the material technologies available to do so.

For example, as rich and successful as perspective drawing has been, it carries with it its own assumptions about the nature of perspective—that it can be adequately captured in a planar frame—and the Euclidean geometrical space the viewer inhabits.

In A Catalog of Difference, Andrew Lucia seeks to challenge and unseat, or at least unsettle, the comfort with which practitioners of design make these assumptions. Its three series of studies of increasing complexity progressively apply new techniques for the representation of ambient light and geometrical surfaces. These new methods fairly sample points from an image or surface, assigning to those points vectors representing a kind of average rate and direction of change of brightness or curvature, respectively. These vectors are then transported from their particular and distinct locations on the image or surface to a common space in which the transformed images and objects of the exhibition are rendered. Thus, the products of these representations are literal catalogs of one sort of local change.

The first set of studies, Analysis on the Order and Structure of Ambient Light Embedded within Planar Imagery, applies this method of brightness-gradient calculation and aggregation to square digital frames of images whose subjects span nature, architecture, and classical, modern, and contemporary art. The resulting radial diagrams, reminiscent of the images of x-ray crystallography, reveal hidden similarities between the forms of the images in terms of the starkness and orientation of the edges (or lack thereof) contained within.

The second set of studies, Analysis on the Order and Structure of Surface Curvature, shifts attention from ambient light to geometric form, representing local changes in curvature across a two-dimensional surface in an allied way. The curvature of a point of a surface measures the tendency for initially parallel nearby lines to diverge or converge, as on the surface of a saddle

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or a sphere, respectively. In this series, the two-dimensional surfaces are already embedded in a three-dimensional space, so that the curvature at points sampled from the surfaces are represented by vectors pointing perpendicularly outward from the surface. Unlike the planar radial depictions of the previous series, these catalogs of curvature span three dimensions, with their implied surfaces resembling diatoms.

The third set of studies, Analysis on the Order and Structure of Ambient Light Embedded within Spherical Imagery (Lux Sphaerae), returns to the representation of ambient light but through original spherical photographs of natural and architectural subjects. These photographs capture the light incident from all angles on a point, not just those from some limited angular range as with a traditional camera. Like with the first series, a brightness gradient is calculated, but like the second, the resulting vectors lie on the surface of the image sphere so that, when aggregated in a single space, they span three dimensions.

The resulting clouds of points, rendered variously in motion, in static perspective, or in printed objects, evoke vast star fields, delicate filamentary steel, and blocks of coral reef.

In juxtaposing more familiar images and forms with their respective visual catalogs constructed using his proprietary algorithms, Lucia invites viewers’ attention to at least three conceptual aspects of the representation of form in general: how the conventions of a representational practice highlight certain aspects of a subject while obscuring others; with what extrinsic properties those practices supplement the intrinsic features of the depicted subject; and whether single localized, situated, and particular perspectives should give way to a multiplicity.

An instance of the first aspect is the use of the perspective drawing. As a powerful tool, its rectangular window on the world has at the same time tended to focus attention on the exteriority of structures, precisely because that is what the tool is effective at conveying. In general, the adoption of new construction and drafting technologies changes which aspects of the design process receive considered attention: automation expands what is practically feasible in part by trading the labor-intensive judgment of the artist for a tool whose delimited features can be mastered. Unlike the tactile strokes of a painting, the processing of the automated tool is usually seen only through its final product. Lucia’s proprietary techniques, in revealing patterns

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Foreword—Samuel C. Fletcher A Catalog of Difference

unapparent in the typical images used, are not being suggested as somehow privileged above the latter—these techniques, too, can be made to seem so natural as to obscure their own presuppositions. Rather, they urge the viewers to consider what is visible and what is hidden in their own practices of representation.

In addition to problems of omission, a form can also be distorted through the addition of properties or relations arising from the representational process and not inherent in the form depicted. Besides the familiar distortions with which cartographers must grapple in their representations of portions of the Earth’s surface, the perspective drawing is again pertinent here, for it represents its subject accurately only from a single vantage point. One compensatory strategy is to devise representations which consciously minimize features extrinsic to the form under consideration, as is increasingly possible with three-dimensional models. Another, complementary strategy is to take a multiplicity of perspectives over a single, linear one. In this way, Lucia’s project shares affinities with Cubist aspirations to depict a subject abstractly and simultaneously from multiple viewpoints, but whereas the Cubists executed their studies in traditional artistic media, Lucia here pushes towards technological novelty.

That said, these issues are extraordinarily difficult to avoid and remain present in the exhibition. The brightness and curvature gradients of an image or surface omit much other information, such as variation in hue or relative size to other objects. It is often not the case, in other words, that the image or surface can be uniquely reconstructed from its catalog of internal variation.

Furthermore, the aggregation into a single space of the vectors representing varying curvature on a two-dimensional surface and brightness on an image sphere requires an external perspective, an embedding into a three-dimensional space. And the different renderings of the spherical images as metallic filamentary clouds or chunks of coral depends as much on the details of the visualization software and three-dimensional printing process as on the image itself. A Catalog of Difference is therefore not a proposed solution to these perennial issues about the representation of form, but an evocative reminder that renewed attention to them offers both challenges and opportunities for innovation in design.

Samuel C. Fletcher is an Assistant Professor in the Department of Philosophy at the University of Minnesota, Twin Cities and a Resident Fellow of the Minnesota Center for Philosophy of Science.

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Acknowledgments A Catalog of Difference

The contents of this book largely reflect the materials contained within A Catalog of Difference exhibited from February through April of 2017 in the HGA Gallery, Goldstein Museum of Design at the University of Minnesota. This exhibition was a culmination of a two year fellowship undertaken as part of the Cass Gilbert Visiting Professorship and was supported through the School of Architecture in the College of Design. The origins of this work, however, stem nearly a decade and have taken inspiration and insight from several sources outside of the realm of architecture. What follows is a very brief and oversimplified introduction to the work.

Many of the early kernels of thought evidenced here can be traced back to my graduate studies in the School of Design at the University of Pennsylvania under the chairship of Detlef Mertins. Those years culminated in my graduate thesis, Form between Matter (Annette Fierro, adviser, 2008), the echoes of which can be seen throughout this exhibition. This thesis project, which continues to this day, took insight from particular 20th century music composers and their novel approaches towards composition. These composers included, amongst others, Morton Feldman, Steve Reich, Alvin Lucier, John Cage, Karlheinz Stockhausen, Gyorgy Ligeti, and Iannis Xenakis. Specifically I found inspiration in these individuals’ fascination with the production of new compositional methods (effectively their tools), which required invention towards the pursuit of novel aural material. Furthermore, these methods were developed as a means of questioning inherited formal legacies.

It was more than merely their pursuit of aural affects that resonated with me, however. These composers found deficit in their own contemporary discourse, and the formal constraints they had inherited by way of language. To this dialogue direct parallels could be drawn to the architectural conversations in which I was surrounded, namely those involving discussions of the production of affect amidst the newly unleashed geometric playgrounds made possible by radical advancements in computation. While on the one hand these new computational capabilities provided the ability to generate new tools, they were

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simultaneously mired in the centuries-old languages of architectural legacy—namely those of geometry.

To some extent, my questions began as a thought experiment: If these composers can approach music (and more broadly material) in affectual terms as a priority, what would an architectural equivalent then be? How might one work in a manner that gives primacy to affect while working towards that affect’s form?

Mentioned among my key sources of inspiration is the Greek architect, engineer and composer Iannis Xenakis, who for several years worked in the office of Le Corbusier. Yet it wasn’t Xenakis’s architectural contributions that struck me, though no doubt significant. Rather, his writings and approach to composition (and more broadly sound as a material) rooted in statistics and information theory was, for me, revolutionary.

The approaches to a complex material world outlined in Xenakis’s Formalized Music1 opened a window that was undeniably prescient, one which could not be ignored. If, for Xenakis, sound was material, my parallel material world of architecture was light.2 In 2008 upon graduating, I was fortunate to find like minds in LabStudio, a hybrid research and design collaboration started by Dr. Peter Lloyd Jones and Jenny Sabin at the Institute for Medicine and Engineering and School of Design within the University of Pennsylvania. Through collaborations with biologists, mathematicians, material scientists, and systems engineers, I was generously afforded the support and mentorship to begin applying the insights gained in my thesis to other disciplinary realms, specifically those of medicine and biology. It was during this period that the impetus for many of the digital tools required to produce A Catalog of Difference found their origins in LabStudio and were applied therein.3 For this opportunity, mentorship and support, I am forever thankful and grateful.

I would like to include a last brief note of major influence among many not mentioned here, one which is significant enough to warrant mention. The work of the visual psychologist James Gibson has been of great inspiration, namely for the

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Acknowledgments A Catalog of Difference

novel treatment of light and its organization elucidated within his work, The Ecological Approach to Visual Perception.4 Those familiar with the works of Gibson will find echoes of his ambient optic arrays underpinning many of the gradient studies presented herein.

The aforementioned basis for my initial thesis investigations and subsequent endeavors have served as a guide in the development of ongoing research and course preparation, firstly at the University of Pennsylvania and subsequently Cornell. In the fall of 2015, I received the distinguished honor to be the Cass Gilbert Visiting Professor in the School of Architecture at the University of Minnesota. I am grateful for this opportunity, and to have been given the space and support to carry out a body of work that has been years in the making. I am extremely thankful to my many colleagues who have offered their support throughout, including Marc Swackhamer and Gayla Lindt who have been my steadies. To this, a huge thanks to the Cass Gilbert Foundation Fund for their generous financial support, without which none of this would have happened. To all the students (past and present) who keep me energized and constantly engaged through conversation and question—thank you. To Anthony Kling at the xyz Lab, whose help, generosity and patience allowed for the production of so many beautiful models. To Lin Nelson-Mayson, Eunice Haugen, Breana Jones, and all at the Goldstein Museum of Design for supporting and exhibiting this work—thank you.

Deserving of a separate paragraph, I cannot provide enough thanks to my two incredibly talented, patient and brilliant research assistants Zhetao “Don” Dong and Samantha Kowalke. The work presented herein has been elevated to what it is through your insights, breakthroughs and dedication. There is no question as to your importance to this output and what has been made possible. Thank you, my heart goes out to you!

To Annette Fierro whose patience, guidance, mentorship and friendship have kept me grounded all these many years— I thank you. To all my many mentors, teachers, friends, collaborators, protagonists, and provocateurs along the way who are

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too numerous to list: a massive thank you! A part of you is in everything I carry forward.

I dedicate this work to my parents, Peter and Kathy, first and foremost—thank you so incredibly much for your support and patience all these years; I love you. To Iroha—my love, partner, and steady guide in life; even away your support and patience gives me the strength to continue. To my friend, Taylan Cihan, whose collaboration and conversations I will never forget; you have forever elevated my work and life.

— Andrew Lucia Notes 1. Xenakis, Iannis. Formalized Music. Hillsdale, NY: Pendragon Press, 1992.

2. Lucia and Sabin. “Rethinking Xenakis and the Role of Information in the Immediate Production of Architectural Affects” proceedings of the MIA-AIM (Music in Architecture-Architecture in Music) Symposium, in CENTER 18, University of Austin, Texas, 2014.

3. Lucia, Jones, and Sabin. “Memory, Difference, and Information: Generative Architectures Latent to Material and Perceptual Plasticity” in Knowledge Visualization Currents: from Text to Art to Culture, Frank T. Marchese and Ebad Banissi eds., Springer-Verlag, London, 2013.

4. Gibson, James .J. The Ecological Approach to Visual Perception. Hillsdale, NJ: Lawrence Erlbaum Associates, 1986.

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A Catalog of Difference

A Catalog of Difference is a study of change across material and perceptual environments, calling attention to those differences which make a difference.1 Through a series of visualizations and models this body of work explores formal diagrams that have been meticulously extracted from the gradients of surface curvature and ambient light within their respective environments.

Collectively, A Catalog of Difference speculates on the role of light as a dynamic force and formal generator of material phenomena and morphology.

The book is divided into three distinct yet related subsets examining: 1. ) Planar ambient light, 2. ) Surface curvatures, and 3. ) Spherical ambient light. Each of these groups questions a priority given to form versus its appearance. In this regard, A Catalog of Difference engages directly in a historic artistic debate between Disegno and Colore (drawing versus color).

Architecture, through its representational tools and design workflows, has predominantly favored the former of these distinctions, giving primacy to line and geometry at the expense of immanent capacities of material phenomena. The work presented here challenges this bias while deliberately paying favor to formal potentials inherent within the energetic realm, specifically those relating to ambient light.

Each visualization in the exhibition can be thought of as a derivative—a study of the rate of change across a given environment. This body of work operates through an informational2 framework, as a non-geometric approach to space and material within.

Notes 1. This phrase is adapted from the original, “…what we mean by information—the elementary unit of information—is a difference which makes a difference, …” from Gregory Bateson, Steps to an Ecology of Mind, University of Chicago Press, Ltd., London, 2000 (1972), p 459.

2. Information herein is of an information theoretic nature rooted in systems theory and cybernetics.

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Planar A Catalog of Difference

Analysis on the Order and Structure of Ambient Light embedded within Planar Imagery The studies presented are an interrogation into the order and organization of material environments, their appearances, and the correlating structure of ambient reflection within those environments.

This investigation begins with an examination of light projected to a picture plane—as the historically dominant modality by which images have been constructed and transmitted. From this framework and in the context of the exhibition, a critique is opened into the inherent biases of these representational constraints and their ramifications upon formal outcomes. This planar phase of the research is met with an open recognition that the light captured on a picture plane is but a small subset of all the ambient light projected to any point within an environment. As such, this phase of research is primarily focused on that planar subset of otherwise omnidirectional phenomena explored later in this exhibition through Lux Sphaerae.

The precedent works selected for this portion of the exhibition were chosen for their authors’ regard and treatment of light.

A Note on Ambient Light In contrast to luminous light, ambient light is regarded as that which has been reflected off of material. Arguably, almost all of the light in our environments is of an ambient nature. Even sunlight, for example, can be regarded as ambient from the moment in which it reaches earth’s atmosphere and begins a cascade of reflections upon particulates of matter. Ambient light and its arrangement thus carries with it unique structural light-based information regarding the environment from which it was generated. In this regard, the light reaching a picture plane is taken to be ambient, structured and containing unique visual information about a scene at a particular location in space, or potential point of observation.

Method and Analysis Through a custom written algorithm the gradient within each image is extracted and remapped to a polar coordinate system

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Planar Image Gradient Method

forming a scatter plot. The plot of each image gradient is a cumulative aggregation of data depicting the changing intensity and direction of light within the image. Each of these data points is measured locally within the image. Alternately stated, every point in an image asks itself, “to what degree and in which dominant direction am I different from my neighbors?”

The result is a visualization of the order and organization (structure) of difference within the image. Removed from its respective appearance, this structural light-based signature is thus a qualitative and quantitative description of the order within a scene’s image. Additionally, the number noted for each study is a measure of the amount of redundancy within each gradient. These values are plotted logarithmically with higher values indicating less redundancy, more disorder, and thus more information. Importantly this measure is not merely a histogram of each image, which would be a measure of the redundancy of all pixel values present. Rather, it is an account of the redundancy within the spatial difference of light values across the entire image. This type of difference ultimately underlies the spatial structure of ambient light-based information within a given scene.

Lastly, it should be noted that the order of physical material within the original scene is not an indicator of the amount of order in the light-based information that is contained within that scene’s image. For instance, the information in the appearances of many urban scenes’ images exceeds that of the natural environments’ images. Clouds, in particular, have a highly ordered ambient reflection and thus lower information content.

Planar

Planar Image Gradient Method Analysis and Visualization of the Rate of Change Across a Given Planar Image

Given planar image

Gradient visualized as vectors

pixel neighborhood

pixel (i,j)

A Catalog of Difference

pixel neighborhood

For each pixel (i,j) in a given image, the intensity as compared to all neighboring pixels is averaged from which a resultant vector (i,j) is produced.

Each vector (i,j) is remapped to the origin of a polar coordinate system.

A given image (top left) is evaluated for the relative change of intensity across itself. Here, for demonstration purposes, a grayscale image is tested (varying from black to white). At a given sample density across this image, the degree of changing intensity is then visualized first as a vector field atop the given image (above right) whereby the vectors point in the direction of greater average intensity, and where magnitude is determined by the degree of that intensity. Lastly, each resultant vector is mapped to a polar coordinate system (below right). Vectors plotted closer to the center correlate to moments of lower contrast, while those towards the peripheries correlate to moments of higher contrast.

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Right: 8.620262

Right, above: Image gradient of Allegory of the Catholic Faith, 1670–72, Johannes Vermeer

Left: 8.9768305

Left, above: Image gradient of A Maid Asleep, 1656–57, Johannes Vermeer

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A Catalog of Difference

Planar

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Right:8.414118

Right, above: Image gradient of Young Woman with a Water Pitcher, 1662, Johannes Vermeer

Left:8.543451

Left, above: Image gradient of Woman with a Lute, 1662–63, Johannes Vermeer

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A Catalog of Difference

Planar

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Right:8.567827

Right, above: Image gradient of North Sea in Moonlight, 1824, Caspar David Friedrich

Left:8.230216

Left, above: Image gradient of Landscape in the Riesengebirge, 1810-11, Caspar David Friedrich

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A Catalog of Difference

Planar

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Right:7.818362

Right, above: Image gradient of Das groĂ&#x;e Gehege, 1832, Caspar David Friedrich

Left:8.546873

Left, above: Image gradient of The Sea of Ice, 1823-24, Caspar David Friedrich

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A Catalog of Difference

Planar

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Right:8.845473

Right, above: Image gradient of Shade and Darkness –The Evening of the Deluge, 1843, J.M.W. Turner

Left:8.976593

Left, above: Image gradient of Light and Colour (Goethe’s Theory)–the Morning after the Deluge–Moses Writing the Book of Genesis, 1843, J.M.W. Turner

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A Catalog of Difference

Planar

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Right:8.99053

Right, above: Image gradient of The Burning of the Houses of Lords and Commons, October 16, 1884, 1885, J.M.W. Turner

Left:8.360949

Left, above:Image gradient of The Fifth Plague of Egypt, 1800, J.M.W. Turner

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A Catalog of Difference

Planar

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Right:8.871692

Right, above: Image gradient of Morning on the Seine near Giverny, 1897, Claude Monet

Left:8.720234

Left, above: Image gradient of Haystacks (Effect of Snow and Sun), 1891, Claude Monet

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A Catalog of Difference

Planar

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Right: 9.370273

Right, above: Image gradient of The Manneporte (Étretat), 1883, Claude Monet

Left: 9.606461

Left, above: Image gradient of Rouen Cathedral: The Portal (Sunlight), 1894, Claude Monet

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A Catalog of Difference

Planar

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Right:8.837358

Right, above: Image gradient of i don’t recall [amarcord.2]_film still 7, 2012, Andrew Lucia

Left:10.306847

Left, above: Image gradient of i don’t recall [amarcord.2]_film still 2, 2012, Andrew Luciar

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A Catalog of Difference

Planar

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Right:10.140058

Right, above: Image gradient of i don’t recall [amarcord.2]_film still 9, 2012, Andrew Lucia

Left: 9.869547

Left, above: Image gradient of i don’t recall [amarcord.2]_film still 8, 2012, Andrew Lucia

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A Catalog of Difference

Planar

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Right:7.2408643

Right, above: Image gradient of Clouds at Sunset over Ithaca, July 15, 2014_4, Andrew Lucia

Left:8.000341

Left, above: Image gradient of Clouds at Sunset over Ithaca, July 15, 2014_1, Andrew Lucia

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A Catalog of Difference

Planar

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Right:8.032779

Right, above: Image gradient of Clouds at Sunset over Ithaca, July 15, 2014_8, Andrew Lucia

Left:7.9868464

Left, above: Image gradient of Clouds at Sunset over Ithaca, July 15, 2014_6, Andrew Lucia

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A Catalog of Difference

Planar

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Right:10.528879

Right, above: Image gradient of Cornell Botanical-Flora_4, 2014, Andrew Lucia

Left:10.655428

Left, above: Image gradient of Cornell Botanical-Flora_3, 2014, Andrew Lucia

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A Catalog of Difference

Planar

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Right:9.962804

Right, above: Image gradient of Cornell Botanical-Flora_6, 2014, Andrew Lucia

Left:8.806305

Left, above: Image gradient of Cornell Botanical-Flora_5, 2014, Andrew Lucia

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A Catalog of Difference

Planar

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Right:9.870872

Right, above: Image gradient of Embarcadero Afternoon_3, San Francisco, 2014, Andrew Lucia

Left: 9.197226

Left, above: Image gradient of Embarcadero Afternoon_2, San Francisco, 2014, Andrew Lucia

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A Catalog of Difference

Planar

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Right:8.942846

Right, above: Image gradient of Bradfield Hall at Sunset, Ithaca, 2014, Andrew Lucia

Left:9.795158

Left, above: Image gradient of Federal Plaza, Chicago, 2014, Andrew Lucia

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A Catalog of Difference

Planar

Analysis on the Order and Structure of Surface Curvature These studies of surface curvature interrogate the order and organization of given surface morphologies. Similar to the studies in ambient light, these surficial inquiries challenge the notion of an object’s underlying formal structure versus that of its appearance. Here, through a measure of intrinsic curvature, an object is re-presented as a description of the change across itself. In this regard, an object’s appearance does not distract from a visual evaluation of its underlying order and organization; we are no longer concerned with the object as a thing, rather how that thing is changing with respect to itself. In doing so, what would typically be a discussion of an object’s shape and surface is now framed akin to the approach undertaken through the light-based portions of this exhibition—those asking how a system is changing across itself. These types of systems do not rely on external observation and depend entirely on local understandings of difference.

A Note on Surface Curvature The curvatures expressed here are derived intrinsically, meaning that they are not reliant on external means of observation and measurement. Considered alternatively, we can imagine that there is a fictional being running blindfolded around a given surface who is reporting on the degree to which the ground beneath their feet is sloped; this is a matter of sensation.1 Technically, for these studies a Gaussian method of measure is employed whereby the product of the principle curvature in two directions is evaluated at every point across a surface. This common method of curvature extraction admittedly relies on geometric principles and thus a related description of surface.

This potential critique should be regarded as an indicator of the inherent bias imposed upon us by our tools. Alternatively, we could conceive of an energetically driven method of curvature extraction in the world of our imaginary blindfolded friend from above. In that being’s world, a non-geometric description of curvature could be derived through an account of the energy expended while traversing and reporting on the surface of an object.

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Curvature

Regardless of the particular measurement technique, an important translation has occurred whereby the characteristics of the surface in question have been removed from a discussion of shape and geometry to one of order, organization, and ultimately difference.

A Catalog of Difference

Method Using a custom written algorithm the rate of change across a given surface is evaluated, visualized as a vector, and remapped to a common origin producing a spatial scatter plot (here, a point cloud). The corresponding spatial point cloud is a visual measure of the organization, order, and distribution of curvature inherent within a given surface. Having been removed from any single image of the surface, the resultant figure of each curvature gradient becomes a cumulative aggregation of visual data depicting the changing morphology across an entire surface. As with the image gradients, each point of evaluation upon the surface is taken and measured locally. Alternately stated, every point on the surface asks itself, “to what degree and in which direction am I different from my neighbors?”

Notes 1. A correction to this metaphor was brought to the author’s attention on the occasion of the exhibition opening by Samuel Fletcher, Department of Philosophy, UMN. This metaphor would not, in fact, qualify as an intrinsic description of the rate of change on a surface. Insofar as gravity is allowed to play a role in the fictional being’s energy expenditure and description of resistance as they traverse a given surface, it cannot be said to be intrinsically measured. Said another way, the system is reliant on an external influence (that of gravity) and hence extrinsic. Because the energy expended depends on the magnitude of the force pushing the being into the surface, the metaphor relies on an embedding of the surface into a threedimensional space, only by which the force of gravity can act so as to be resolved into components tangent and perpendicular to the surface.”

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Curvature Gradient Method Analysis and Visualization of the Rate of Change Across a Given Surface

Given Surface

Curvature Measurement

Visualize Curvature as Normal Vectors

m

de

tu

ni

ag

Vectors Mapped to Origin

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Curvature A Catalog of Difference

Resultant Spatial Point (vector) Cloud

A given surface (above left) is evaluated for its intrinsic curvature, or rate of change across itself (above right, showing color intensity map of curvature). At a given sample density across this surface its curvature is measured and translated to vectors whose direction is normal (perpendicular) to the surface, and whose magnitude is a governed by the degree of curvature (middle) at each respective sample point. Each curvature vector derived from the surface above is translated to a common origin point. Each vector retains its normal direction from the surface and magnitude correlating to the degree of curvature at its loci. Once remapped these vectors form a dense cloud of points (below). At a sufficiently dense sample density approaching infinity an approximate surface is implied.

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58 Right: Intrinsic Curvature Study of a Deformed Plane 2

Left: Intrinsic Curvature Study of a Deformed Plane 1

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A Catalog of Difference

Curvature

60 Right: Intrinsic Curvature Study of a Deformed Plane 4

Left: Intrinsic Curvature Study of a Deformed Plane 3

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A Catalog of Difference

Curvature

62 Right: Intrinsic Curvature Study of a Deformed Plane 6

Left: Intrinsic Curvature Study of a Deformed Plane 5

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A Catalog of Difference

Curvature

64 Right: Intrinsic Curvature Study of a Deformed Torus 1

Left: Intrinsic Curvature Study of a Deformed Plane 7

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A Catalog of Difference

Curvature

66 Right: Intrinsic Curvature Study of a Deformed Torus 3

Left: Intrinsic Curvature Study of a Deformed Torus 2

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A Catalog of Difference

Curvature

68 Right: Intrinsic Curvature Study of an Annulus (4 twists), printed model

Left: Intrinsic Curvature Study of an Annulus (2 twists), printed model

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A Catalog of Difference

Curvature

70 Right: Intrinsic Curvature Study of an Annulus (8 twists), printed model

Left: Intrinsic Curvature Study of an Annulus (6 twists), printed model

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A Catalog of Difference

Curvature

72 Right, above: Intrinsic Curvature Study of Plücker’s Conoid (variant 2), printed model

Right, below: Intrinsic Curvature Study of Plücker’s Conoid (variant 1), printed model

Left: Intrinsic Curvature Study of an Annulus (10 twists), printed model

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A Catalog of Difference

Curvature

74 Right: Intrinsic Curvature Study of Plücker’s Conoid (variant 5), printed model

Left, below: Intrinsic Curvature Study of Plücker’s Conoid (variant 4), printed model

Left, above: Intrinsic Curvature Study of Plücker’s Conoid (variant 3), printed model

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A Catalog of Difference

Curvature

Analysis on the Order and Structure of Omni-directional Ambient Light The culmination of research presented here reflects a major twofold shift occurring in modalities of visual representation.

1.) A transition from planar to spherical modes of projection, and with this 2.) An extrinsic to intrinsic reframing of an observer relative to their perceptual environments. This latter spherical type of projection has always physically existed but has largely been conceptually neglected at the expense of neatly framed and geometrically managed windows to the world—those mediating devices that separate us from our environments.

Already noted in the planar examples earlier in the exhibition, the light captured on a picture plane is but a subset of all the omnidirectional ambient light reaching an observation point within an environment. That limited subset, typically manifest as a framed planar image, is ultimately only a fragment of a much larger spherical domain of light.

e

d

f

a

c

b

Diagram of Perspective Construction after Leon Battista Alberti: De Pictura (conceived 1435-36): (ab) ground plane; (c) vanishing point (centric); (d) viewer’s eye; (abe) picture plane; (df) viewing distance; (dfc) horizon line.

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Spherical

Spherical modalities are already usurping the planar, infiltrating common mediating technologies and quickly becoming ubiquitous within all of our personal devices. Google Street View, for instance, relies on spherical projections as we navigate its interiors. While the typical user still experiences the image of spaces through the picture plane of their device screen, this too will soon be antiquated. The final convergence of a truly spherical representational shift is already occurring through the apparatuses of virtual and augmented reality, whereby our observational vantage point is centered within a world of spherical imagery. These apparatuses will soon be seamlessly incorporated into the body. Ultimately, this affects the manner in which we frame our presence and experience relative to an external reality; we will no longer be looking at images of the outside world projected to a picture plane. Rather, we become entirely embedded at the interior of an image, at a unique point of observation containing all light-based information about an environment—within a Sphere of Observation.

A Catalog of Difference

Analysis on the Order and Structure of Omni-directional Ambient Light and its Figuration (Lux Sphaerae) Lux Sphaerae are theoretical bodies that have been figured by the structure of omnidirectional ambient light at their unique point of observation within the environments from which they were extracted.

Method Through a custom written algorithm the image gradient of each environment is extracted and remapped to a common origin forming a spatial scatter plot from the resultant vectors. The method used here is similar in nature to that of the planar image gradient extraction described in this exhibition. Here, however, the gradient is taken across an omnidirectional spherical image.

The resultant spatial scatter plot of each scene’s image gradient becomes a cumulative aggregation of visual data depicting the local change of intensity and direction of light across a spherical image. Lastly, after remapping of the vectors, moments of most density within the resultant point cloud are figured and solidified as a surface.

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Given Spherical Image with Gradient Visualized as Vectors

Vectors Remapped to a Common Origin

Resultant Point Cloud (vectors) Surfaced A given spherical image (above) is evaluated for the relative change of intensity across itself. Here, for demonstration purposes, a grayscale image is tested (varying from black to white). At a given sample density across this image, the degree of change intensity is then visualized first as a vector field atop the given image sphere whereby the resultant vectors point in the direction of greater average intensity, and where magnitude is determined by the degree of that intensity. Lastly, each resultant vector is mapped to a common origin (middle) while retaining its direction and magnitude. As with the planar image gradients, vectors plotted closer to the central origin correlate to moments of lower contrast, while those towards the peripheries correlate to moments of higher contrast.

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Left: Spherical Image Gradient Method Right: Lux Sphaera 071616WAM (Weisman Art Museum, UMN)

Spherical Image Gradient Method Analysis and Visualization of the Rate of Change Across a Given Spherical Image

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80 Right: Lux Sphaera 071816RCAW (Regis Center for the Arts West-Balcony, UMN)

Left: Lux Sphaera 071816-RCAE (Regis Center for the Arts EastFoyer, UMN)

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Spherical

82 Right: Lux Sphaera 071816-NA (Northrop Auditorium-Foyer, UMN)

Left: Lux Sphaera 071816-WL (Wilson Library-Stacks, UMN)

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84 Right: Lux Sphaera 072716-FSP (Flandrau State Park, New Ulm, MN)

Left: Lux Sphaera 071816-BH (Bruininks Hall-Lobby, UMN)

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86 Left: Lux Sphaera 072716-PP (Pioneer Park-Streambed, New Ulm, MN)

Left: Lux Sphaera 080616-FSP (Flandrau State Park-Buggy, New Ulm, MN)

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88 Right: Lux Sphaera 072916SJ (St. John’s-Stairwell, Minneapolis, MN)

Left: Lux Sphaera 072816-LS_ NFB (National Farmer’s Bank of Owatonna-Lobby, MN)

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90 Right: Lux Sphaera 072716SMNU (St. Mary-Altar, New Ulm, MN)

Left: Lux Sphaera 080616-SJ (St. John’s-Altar, New Ulm, MN)

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92 Right: Lux Sphaera 080916SMGO (St. Mary’s Greek Orthodox, Minneapolis, MN)

Left: Lux Sphaera 080816-STM (St. Thomas More-Baptismal, St, Paul, MN)

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94 Right: Lux Sphaera 080616-SJ (St. John’s-Altar, New Ulm, MN), printed model

Left: Lux Sphaera 080616-SPB (St. Paul’s-Balcony, New Ulm, MN)

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96 Right: Lux Sphaera 080816-STM (St. Thomas More-front, St. Paul, MN), printed model

Left: Lux Sphaera 072716SMNU (St. Mary_1, New Ulm, MN), printed model

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98 Right: Lux Sphaera 072716SMNU (St. Mary-Altar_2, New Ulm, MN), printed sectional model

Left: Lux Sphaera 072716SMNU (St. Mary-Altar_2, New Ulm, MN), printed model

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Appendix

Appendix: Lux Sphaerae (Secret Life of Objects Competition, Finalist Entry) with Iroha Ito (design) and Samuel Fletcher (consultation)

A Catalog of Difference

“The Sun’s light when he unfolds it, depends on the organ that beholds it.”

—William Blake, for the Sexes: The Gates of Paradise, 1793 and 1818.

Lux Sphaerae are theoretical differential structures posited to exist at every event, or point, in space-time, at a relative fidelity, which transfigure all ambient photonic reflections reaching that unique event.

Lux Sphaerae may be described as virtual projective spaces structured at their event and fidelity of observation, and are completely unique to their space-time point of observation. This uniqueness arises from the necessarily energetic nature of their observation, wherein any obstruction or absorption of photonic energy on a given trajectory subsequently terminates the ambient reflection from which it originated. Once instantiated, Lux Sphaerae are without any privileged orientation and are fully autonomous from each other, contributing in kind to an evolving sea of ambient reflection events.

Alternately referred to as Spheres of Observation (SOs for short), Lux Sphaerae, as projective spaces, inherently have no scale, but can collectively summate a focal domain. Focal domains should not be confused with a notion of precision of focus or fidelity, wherein higher fidelity is often sought for purposes of clarity. Rather, focal domains reconstruct relative structural information as criteria for the spatio-temporal bounds upon physical/material structures affected by SOs. As opposed to a technical image Lux Sphaerae can be understood as an abstract evolution of the technical image, in that both Lux Sphaerae and technical images share the absorption and permanent loss of ambient light at the very event of their instantiation. These entities differ in general, however, in that the visible preservation of metric

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Notes 1. Spaulding, S., and Potapova, M. (2012). Stephanodiscus yellowstonensis. In Diatoms of the United States. Retrieved May 19, 2016, from http://westerndiatoms. colorado.edu/taxa/species/stephanodiscus_yellowstonensis 2. Sir Arthur Eddington, 1919 (public domain).

3. Bohn, A et al. “What does a binary black hole merger look like?� Classical and Quantum Gravity, 32 (6). Art. No. 065002. ISSN 0264-9381.

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Secret Life of Objects, Competition Finalist Entry (with Iroha Ito)

space is a typical precondition of the legible technical image, whereas within Lux Sphaerae only the gradient of ambient light within a scene is imprinted into a projective space, and is thereafter without scale. With the latter, only the differential structure of ambient light is preserved at the expense of ordinal pixel coordinates usually associated with and imposed by legible technical images.

Appendix A Catalog of Difference

Plate 1: Physical Structures Whose Formal Attributes Suggest Tethering to their Respective Spheres of Observation. (left to right, top to bottom) ESM image of the diatom Stephanodiscus yellowstonensis1; bare tree in winter; negative of the 1919 solar eclipse taken from the report of Sir Arthur Eddington on the expedition to verify Einstein’s prediction of the bending of light around the sun2; a pair of black holes that are about to merge, with the Milky Way visible in the background.3

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Comparison of 2 or more data arrays giving rise to a Secret Life of Objects, Competition Finalist Entry (with Iroha Ito)

Sphere of Observation

Generation of Relative Information Data array 1

Data array 2

-relative -instantaneous or of memory

-relative -instantaneous or of memory

Sympathetic Information Model (multi-variate & subjective)

uncertainty of data through a channel Sender

Receiver

Standard Information Model (uni-directional)

Plate 2: From Standard to Sympathetic Models of Information through a Fusion of Relative Data.

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Appendix

e

d

f

a

c

b

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3

Plate 3: From Geometry to Information. Top, “Diagram of Perspective Construction” after Leon Battista Alberti: De Pictura (conceived 1435-36): (ab) ground plane; (c) vanishing point (centric); (d) viewer’s eye; (ae) picture plane; (df) viewing distance; (dfc) horizon line; bottom, cumulative summation values for information maps derived from a video as a camera is tracked down a corridor that demonstrate weighted “moderate” [log2(p)] (left) and “rare” [(1/p)log2(p)] (right) event information for an observer traversing a hallway.

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Secret Life of Objects, Competition Finalist Entry (with Iroha Ito) 4

Plate 4: From Plane to Sphere.Top, Draughtsman Drawing a Recumbent Woman, Albrecht DĂźrer, 1525; middle, Violation of the parallel postulate in positively curved sphericalspace; bottom, planar image mapping of the ambient environment associated with Lux Sphaera 042416_44-93-261.

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Appendix A Catalog of Difference

5

Plate 5: Spherical Image Mapping of the Ambient Environment Associated with Lux Sphaera 042416_44-93-261.

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Secret Life of Objects, Competition Finalist Entry (with Iroha Ito) 6

Plate 6: Schematic Diagram Depicting Ambient Photonic Reflections Projected to a Point within a given Sphere of Observation. Differential evaluation is obtained for each incoming photonic vector at random sample points at given fidelity around the SO. Formation of a lux sphaera shown ghosted within the interior.

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Appendix A Catalog of Difference

7

Plate 7: Artist’s Rendering of a Lux Sphaera under Electron Scanning Microscopy, origin unknown.

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Secret Life of Objects, Competition Finalist Entry (with Iroha Ito) 8

Plate 8: Artist’s Rendering of a Lux Sphaera under Electron Scanning Microscopy, origin unknown.

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Appendix A Catalog of Difference

9

Plate 9: Artist’s Rendering of Energy Fields Given Off by Lux Sphaera 042416_44-93-1a.

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This is telling of the form of energy.

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Formation and Symmetrical Structure of Primary Images

Appendix: Projections Is the structure of ambient light self-fulfilling? If flora, for instance, have evolved to efficiently harness not only luminous but ambient light conditions, it must then also be considered that the very structure of ambient light within photo responsive environments has co-evolved as both a product and reflection of the other—as a feedback of light-based processes.

Appendix

Ambient Image (instantaneous)

I

Iambient

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Reflexion

Iambient

Ambient Image (instantaneous)

Not Observed

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Formation and Symmetrical Structure of Primary Images

Ambient Image (instantaneous)

I

Observed

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I

Reflexion

Iambient

Reflexion

Iambient

Ambient Image (instantaneous)

Appendix

Ambient Image (instantaneous)

I

I

Imemory

Observed

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Reflexion

Iambient

Memory Image (of prior states)

Observed

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Infrared image of a forest canopy, photo credit Samantha Kowalke Flora

Appendix: Notes on the Structure of Ambient Light in Organic Environments Flora exist as a special class of organic matter, as nature’s avantgarde concerning light-based evolution. Flora have quite literally developed in response to light—through exposure and encounter. It can be assumed that it has done so efficiently and maximally, in doing so has arguably evolved as one of the most morphologically responsive entities in regards to both ambient and direct illumination, and furthermore does not solely respond to the latter.

It is generally accepted that this aforementioned evolution is primarily a function of energy absorption, of which little doubt exists. This standpoint does not, however, take into consideration an informational world formed through ambient structured arrays of energy, in particular light.

No doubt, vegetation has evolved as a product of several environmental factors—mechanical and chemical, for instance.

While there exist several influences, light undoubtedly holds a key position in vegetation’s morphological evolution. As surfaces embodying photosynthetic processes, it must be assumed that efficient reception of light within any folia’s respective environment has been of great importance to their survival and evolution. And while direct illumination is oftentimes advantageous therein, it is not always and most surely not the general case. One only need think of a forest canopy and its understory— the uppermost part receiving direct illumination, while the lower portions are almost entirely of an ambient type. The evolutionary advantage of efficient access/absorption (regardless of type) is exemplified here by lower canopy flora’s photosensitivity to almost entirely ambient conditions. More specifically, understory flora have adapted photosensitivity to varying spectra of ambient light within their environs using those wavelengths which have not been filtered by the canopy.

If such an adaptation exists, then it may also be speculated that foliage has evolved to specific structural conditions of ambient light, leading here to a speculation on the role of ambient light’s structure (order and arrangement) in the evolution of foliage and by extension all organic matter.

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Appendix

118 Infrared images of a forest understory, photo Samantha Kowalke

Infrared images of a forest canopy, photo Samantha Kowalke

Appendix A Catalog of Difference

Through time, this ambient light and the foliate surfaces from which it was generated would have developed reciprocally and continue to do so, existing within a sea of ambient light (ostensibly a sea of symmetrical ambient reflections). That is—the structure of the ambient light in any environment is generated by the material of that environment. Therein, both the ambient light and the material from which it was reflected would have coevolved and could be said to be of a durational sympathetic echo of each other.

Foliage is oftentimes not optimized to harness a single source of direct light, rather most often multiple ambient sources. A tree is not simply a bunch of leaves, rather it is a grouping or collection of stochastic receptors—a compound network of sensors.

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as a point of observation, rather a Sphere of Observation. We immediately recognize that that the domain of SO2 is capable of encountering partial inverted images associated with O0 and O1.

While depicted here as a sphere, this receptive entity is essentially no different in kind than a picture plane such as P1. In this instance, while potential information is encountered by SO2 that potential information’s presence has perhaps not been made aware (in most cased it would be considered “out of focus”). Still, this suggests that there exists at least the encounter of multiple (infinite) non-affiliated ambient images for any SOn. Moreover, point O2 does in fact summate I"0 + I"1 ... + I"n. However, the nature of any point On being infinitesimally small would also

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The Encounter of Multiple Ambient Images

Appendix: On the Reception of Multiple Ambient Images In the diagram, The Encounter of Multiple Ambient Images, Primary Image I"n is noted to be the inversion of the incoming Primary Image I'n. In lay terms an image associated with I"n is flipped or inverted. It is a common misconception, however, that a lens (biological or artificial at a point of observation) is necessary and responsible for this inversion, ultimately leading to a “flipped image” projected upon a picture plane. In accordance with classical optics, the above example illustrates the contrary; there is no lens required to invert an image at any given point of observation. Rather, any conic area in space beyond a point of observation On will contain an inverted image I"n associated with its reciprocal In. A practical example known since antiquity can be appreciated with the use of a camera obscura, in which there is no lens. The projected image in this case will be inverted upon a rear picture plane within the apparatus (upon hypothetical plane P1, for instance, in the diagram).

This nontrivial point is preceded by the questions posited in the illustration: What gives primacy to O2’s Primary Image (I2 ), rather than a summation or fusion of inverted images I"0 + I"1 ... + I"n ? More simply, at any given point of observation, why does a primary image not present itself as many individual inverted images?

The answer to this questions is straightforward, although perhaps not obvious. When we consider the diagram (The Reception of Multiple Ambient Images), O2 is no longer considered

Appendix

I'1

I1 O1

I"1 I'2

I2 O2

I"2

P1

I'0

I0 O0

I"0

I"n == symmetrical inversion of I'n

What gives primacy to O2’s Primary Image (I2) rather than a summation or fusion of I"0 + I"1 ... + I"n ?

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In this example a planar section through 3 points of observation and their respective ambient image fields are illustrated for the sake of visualization, ultimately demonstrating an otherwise wholly spatial condition. Furthermore, the arc of potential information comprising Primary Image In in this illustration is spherical in nature, yet is demonstrated here through a planar limit so as to clarify the diagram.

The shaded regions beyond all On indicate an ambient field of potential information existing as a symmetrical inversion of I'n. If a receptive body such as hypothecial picture plane P1 is attuned to these ambient fields, it may encounter this ambient image I"n either in whole or part.

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A note on the illustrations In the illustrated diagrams presented here, a planar section is cut through an otherwise omnidirectional spatial condition. With this simplified illustration, there is an assumption that any incoming image I'n has an associated arc of projection. No such limiting arc exists; the incoming image I'n is entirely spatial and surrounds every observation point On in what is ostensibly a spherical image. As such, all I'n are inverted spherical images of I"n.

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Left: Images formed by pinhole effect through leaves during a partial solar eclipse. Image credit: Crescent Shadows, Meryl Natchez, 2012.

Right: The Reception of Multiple Ambient Images

determine that any partial image associated with In would be infinitesimally small and likely not perceptible as an individual image. However, the Primary Image I2 associated with point O2 does indeed summate I"0 + I"1 ... + I"n and may be generalized as such.

Any encounter or observational event exists within a sea of inverted ambient images. This also suggests than an infinitum of these non-local images are simultaneously present to any observing body. Yet on a practical level, for our persons these images are not apparent. This is not to say this sea of ambient reflection is not readily accessible, but rather may be so at the relative scale and fidelity of the observing body in relation to its surrounding informational world.

We are reminded of the wisdom of William Blake: “The Sun’s light when he unfolds it, depends on the organ that beholds it.”

— William Blake, for the Sexes: The Gates of Paradise, 1793 and 1818.

Appendix

I'1

I1 O1

I"1 I'2

I2

I"2

SO2 P1

I'0

I0 O0

I"0

I"n == symmetrical inversion of I'n

What gives primacy to O2’s Primary Image (I2) rather than a summation or fusion of I"0 + I"1 ... + I"n?

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On

If On is constrained to a point, its range of focus shall be a point, a limiting factor of itself. If it were multiple in nature, or a allowed to bound a space larger than a point (a sphere, SO2 for instance), it would be capable of encountering potential information outside of its bounding point of origin On. Here potential information becomes available as partial regions of the original I"0 and I"1. In this example, while potential information is encountered by SO2, that potential information’s presence is perhaps not made aware. Still, this suggests that there exists the encounter of multiple (infinite) non-affiliated ambient images for any SOn.

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A Catalog of Difference UMinn Papers on Architecture 2 Andrew Lucia Cass Gilbert Visiting Assistant Professor Zhetao Dong and Samantha Kowalke Research Assistants (BDA class of 2018) The research conducted for this exhibition was undertaken as part of the Cass Gilbert Visiting Fellowship in the School of Architecture, University of Minnesota and was generously supported therein.

This publication has been produced on occasion of the exhibition A Catalog of Difference held from February 2– April 30, 2017 at the HGA Gallery of the Goldstein Museum of Design.

Goldstein Museum of Design Staff Lin Nelson-Mayson, Director Eunice Haugen, Registrar and Exhibitions Coordinator Breana Jones, Lilla Bath Communications Assistant Support for this exhibition and programs provided by the Goldstein Museum of Design, the College of Design, and generous individuals. In addition, GMD programming is made possible by the voters of Minnesota through a Minnesota State Arts Board Operating Support grant, thanks to the legislative appropriation from the Arts and Cultural Heritage Fund.

Design: Luke Bulman—Office Printing and binding: Blurb All images of paintings on pages 22–37 were obtained through the public domain. ©2017, Andrew Lucia No part of this book may be used or reproduced in any form or manner whatsoever without prior written permission except in the case of brief quotations embodied in critical articles and reviews.