Manifolds: RIchard Penn

Richard Penn, Manifold iv (2011)

Day Twelve of South Africa's The Lockdown Collection presents two works by Richard Penn, Manifold iv (2011) and Manifold xiii (2011), each painting encased in aluminum frames. The frames are irregularly shaped, with a missing upside down "L-shape" in their upper right quadrant, evoking the absent L-shaped camera field of vision in the NASA Hubble space telescope's famous images of the Pillars of Creation, a stellar nursery in the Eagle nebula, 6,500-7,000 light years from earth, where stars come into existence. The abstracted images are derived from optical and electron microscopy of bacteria and diatoms--a class of algae, including many plankton, which account for about 50 percent of the world's oxygen production, and which provide life-sustaining biomass to many of the planet's essential bio-systems, including the Amazon basin.

Richard Penn's Statement regarding Covid-19:

In 2011 I went through a period of quiet anxiety about viral and bacterial plagues. Covid-19 won't wipe us out but I don’t have much hope that it will change the minds of world leaders to do the right thing about climate change or the more numerous minds of the species about multiplying unchecked across the planet. The combination of overpopulation and the blind consumption of our natural resources will probably be the cause of our demise. This pandemic is a portent of our inevitable death by our own hands.

Richard Penn's statement about the drawings (Manifold series)

Manifold xiii (2011),

The ‘stealth bomber’ shape of these drawings is a reference to the famous photograph taken by the Hubble Space Telescope of the ‘Pillars of Creation’. The shape was due to one of Hubble’s four cameras having a different resolution to the other three. In these drawings I bring together the extremely large as seen by Hubble and the extremely small in the form of bacterium and diatoms.

I am interested in how science has taken us far beyond what we can experience with our natural senses. When exploring reality at the scale of the extremely small or the extremely large, our ability to grasp the nature of things becomes elusive. It is an example of how human intelligence has transcended our physical limitations, transported us into a universe of abstraction and at the same time, extended our scope to dream.



What is a Manifold?

Mark Auslander:  Appreciating Richard Penn's striking work requires a brief excursion into the history of mathematics and philosophy. The great German mathematician Bernhard Riemann (1826-1866)  introduced the concept of the manifold (Mannigfaltigkeit in German)  into the field of mathematics known as topology: a "manifold" is a shape that has a localized component (called by topologists a "neighborhood") that can be described in Euclidean terms, that is to say, in terms of an X axis and a Y axis, or (for three dimensional objects) in terms of X,Y, and Z axes. Thus, a flat plane is a manifold, because any locally restricted part of it can be described through the Euclidean framework of the familiar X and Y axes. A sphere or a torus (a doughnut-shaped form) are also manifolds, because any given small part of them (a neighborhood") can be described through X,Y and Z axes.  (I'm grateful to my dad, the mathematician Joe Auslander for trying to explain these concepts in elementary terms.)

I believe (though I am not entirely sure)  that the pioneering mathematicians Riemann and Henri Poincaré  (whose Poincaré Conjecture on the nature of three dimensional manifolds was until recently one of the great unsolved problems in topology) were inspired by the use of the term "manifold"  (mannigfaltigkeit) in the writings of philosopher Immanuel Kant. Kant characterizes the process of synthesis as "the act of putting different representations together, and grasping what is manifold in them in one cognition.”  Manifold in this sense denotes underlying similarity that may initially escape our focus on the seeming difference of apprehended forms: thus, Kant was a champion of the ultimate unity of the seemingly differentiated human species, along the way coining the term "Anthropology," as the unified science of all humankind. The Kantian terminology, of resolving difference into unity, or of rigorously differentiating apparent unity, has been adapted in fluid mechanics to  characterize a machine element that combines or separates a gas or a liquid, as in the inlet and exhaust manifolds of an internal combustion engine.

Hubble image of Pillars of Creation, showing absent L shape

Diversifying Manifolds: The Art Works

Consistent with this intellectual history, Richard Penn's "Manifold" series explores mysteries of difference and sameness, at vastly different scales. He presents framed-off images within a plane (itself a topological manifold), that has been truncated in an interesting way, emulating the world famous image from the Hubble Space Telescope, that lack an L-shape component, due to variation in camera resolution. The vast elephant trunk- shaped pillars of the stellar nursery are among the largest manifolds in the known universe,  inasmuch as their local components or neighborhoods can be described mathematically through X,Y, and Z axes.

In turn, the microscopic organisms represented in two dimensional form within the plane (a manifold) bounded off by each aluminum frame, are themselves manifolds in three dimensional space: they are shaped in many instances like elongated sausages, any "neighborhood" or local surface segment of which can be described according to X,Y, and Z axes.  It is a most fascinating feature of the universe that these enormously large and extremely tiny entities share the same fundamental mathematical form---they are all,  at the end of the day, manifolds--for all their endless, marvelous variations.

(As it happens. Richard Penn and I share a great fondness for Stephen Baxter's science fiction Manifold Trilogy[1993-2003] set across alternate, parallel universes that are collectively known as "The Manifold. " Like a topological manifold, each of Baxter's universes is a kind of transformation of all the others, allowing for surprising underlying similarities that enable, at least at the level of storytelling, an ultimate form of synthesis between seeming opposites, in a move that seems to echo Kant's seminal understanding of "manifold.")

Richard Penn, Manifold iv. 2011

Penn's art work Manifold iv represents a conglomeration of diatoms, microcosmic organisms that evolved on our planet around 200 million years ago and which continue to be the foundation of the vast global tree of life. They produce, as noted above, something like half the world's oxygen, and their staggering biomass sustains, ultimately, a vast range of plant and animal life, in oceans, freshwater, and on land. Many scientists believe that diatoms can sequester,  deep in the oceans, the greenhouse gas carbon dioxide released into the atmosphere, and that they are thus a potential bulwark against rapid global warming.

Diatoms have unusual silica coatings. which help give them the shimmering opal-like appearance which Penn highlight in Manifold iv.  This coating is vulnerable to ocean acidification, an increasing global danger from human industrial civilization,  Future human generations (if our species survives) will be astounded that in our era we have put at risk these precarious organisms, without which biodiversity would be impossible, through climate change, oil spills,  and other environmental hazards.

Manifold xiii, in turn, references bacteria, which are potentially both life-sustaining (for instance within the human gut in enabling digestion) and deadly, all the more so given the spiraling overuse of antibiotics, including in the food supply, which accelerates the micro-evolution of drug resistant 'super-bugs.'  In Penn's image, small green bacteria appear to be traveling through an organic passageway, perhaps within a human body. We are left to wonder if they are on a mission that is life-sustaining or life-destroying for their host.

All these biological micro-organisms are encased within the jagged shaped metal frame that Penn compares to a B-2 stealth bomber, a radar-evading nuclear weapons delivery system of almost unimaginable destructive power. This seems altogether appropriate, given that advanced industrial civilization seems increasingly prone, as the present Covid-19 crisis reminds us, to unleashing catastrophic biological dangers upon the world population, accelerated through passenger jet travel and population density.

Science and technology, anchored in mathematics, the "queen of the sciences," have given us unrivaled capacities to map the largest and tiniest structures of the universe, to grasp the music of the spheres, and the dazzling complexity of manifolds, at every imaginable scale. It remains to be seen if we will, ultimately, prove responsible stewards of all organic manifolds--of "all things bright and beautiful"--and of our most precious manifold of all, the spherical planet Earth itself--our shared, beautiful, imperiled home.