Patterns

A couple of weeks ago, I offhandedly added a small brachiopod specimen to my fossil collection, picking it up as a raffle prize at a fossil club meeting.  The tag associated with it gave its scientific name as well as the location where it was found – Eichwaldia reticulata; Silurian brachiopod; Waldron Formation; Flat Rock, Indiana.  (The Silurian Period was from 444 to 416 million years ago.)  Frankly, I often don’t accept at face value the labels that other collectors apply to such fossils and so I typically end up doing some research on them.  In this instance, as is frequently the case, the impulse was the right one; the tag was wrong as to genus name.  Since 1994, it’s been Eodictyonella, and wasn’t Eichwaldia after the late 1890s when Dictyonella was generally accepted.  (Anthony D. Wright, Eodictyonella, a New Name for Dictyonella Hall, 1868, Not Dictyonella Schmidt, 1868, Journal of Paleontology, July 1994)

Brachiopods in general have seen much better days.  The few extant species of these marine organisms are the remnants of a vast array of species that widely populated the oceans until the mass extinction at the end of the Permian (251 million years ago).  Though they look like mollusks with two valves, they are not, constituting their own phylum.  Brachiopods were once so abundant that it’s common to find slabs of shale imprinted with shells in such huge numbers that the distinctive symmetrical patterns of individual shells are superimposed one upon another in a riotous array.  The picture below shows such a spread of fossils from the Devonian (416 to 359 million years ago) in a chunk of shale found on a mountain roadcut in West Virginia.

After unpacking the mystery of the name of this little Silurian fossil (a cast, I believe, of the exterior of both valves), the next step was to put it into a drawer with a label and be done with it.  The picture below shows the fossil along side a penny for scale; the brachiopod is ½ inch in length.  Not much to look at.

But fossils almost invariably reward a closer look.  Prompted by descriptions in the literature on Eodictyonella, I took a jeweler’s loupe to the fossil and discovered the marvelous exterior ornamentation that species in this genus exhibit.  Macro photographs of both sides of the fossil show these patterns.

I found the fossil’s geometric array of intersecting arcs, clearly evident despite the wear and tear of over 400 million years, spellbinding.  The arcs appear to originate on either side of where the two valves come together in a point, the brachiopod’s beak or umbo.  The cells in the grid pattern appear to expand and contract depending upon the contour of the surface of the brachiopod, particularly as edges are reached.

The grid cells or pits in the network pattern on the Eodictyonella brachiopod contain one or more small openings or puncta which, according to Anthony Wright, connect to pores that open on the inner shell surface.  Wright cites research suggesting that the pits in the shells may have been part of a defensive network against predators seeking to drill through the shells.  Each of the openings in the shell may have contained organic caeca or sacks which held some form of organic material which, based on evidence from extant brachiopods, may “be beneficial in that punctate shells are less bored by predators, suggesting that caecal secretion inhibited penetration . . . .”  (Anthony D. Wright, The External Surface of Dictyonella and of Other Pitted Brachiopods, Paleontology, Volume 24, Part 3, 1981, p. 475)

The network pattern on the Eodictyonella is startlingly familiar, reminiscent of what one sees in the double spiral patterns of plant leaf or floret arrangements (phyllotaxis) such as in the picture below of the head of a sunflower (Helianthus).  The two systems of spiral arcs flow in opposite directions.

I’ve always felt that these double spiral patterns in plants offer a glimpse into a profound, underlying natural order.  When the leaves or florets in phyllotaxis patterns are numbered from youngest to oldest and displayed on a two-dimensional surface, adjacent leaves or florets along each of the systems of arcs have the same numerical relationship to one another (e.g., along one arc, leaf or floret numbers may differ by five, and by eight along an arc flowing in the opposite direction).  For each plant species, its pair of phyllotaxis numbers (for the two systems of swirls) has been found to be adjacent pairs in the Fibonacci sequence, that sequence of numbers in which the last entry is the sum of the two previous entries (0, 1, 1, 2, 3, 5, 8, 13, 21, . . . .).  The sequence was first laid out in the 13th century by Italian mathematician Leonardo of Pisa.  The connection to the Fibonacci sequence isn’t some mathematical magic, some mystery.  Rather, as science writer Philip Ball explains, the connection flows naturally because this arrangement provides for the most efficient packing together of leaves or florets.  (Ball, The Self-Made Tapestry:  Pattern Formation in Nature, 1999, p. 106 – 107)  Do I understand why this is so?  To be honest, not yet.  So, maybe it does remain a bit mysterious to me.

Although something similar may not be playing out in all of the external ornamentation of Eodictyonella, partly because the surface over which the pattern appears differs markedly from those involving plant leaves or florets, in certain areas the impulse may be the same.  Wright describes the pattern as an “apparently complex network of variably rhombohedral to hexagonal pits” arising from “simple radial growth modified by the inevitable geometrical results of closer packing of the pits,” as well as changes in the pace at which shell material is deposited along the growing edge of the shell and waves in the growing edge.  (p. 475, emphasis added)

In The Self-Made Tapestry, Ball argues that evolution cannot contravene certain fundamental forces, physical or chemical, as it shapes life.  As a consequence, he posits, similar forms and patterns may repeatedly appear in living organisms, as well as elsewhere in nature.  I wonder if the similarity between the phyllotaxis patterns and those appearing on the Eodictyonella may reflect such a constraint.  Ball writes,

 There are . . . forces guiding appearances that run deeper than those that govern life.  (p. 4)

Source of Photographs

All of these photographs are mine except for the one of the sunflower.  That photograph is by L. Shyamal and is reproduced here under the Creative Commons Attribution-Share Alike 2.5 Generic License.  It is found at Wikimedia Commons.

Contagion of Interests ~ A Case of Trilobite Arches

Interests can be insidiously contagious.  Though you may contract only a mild version of the enthusiasm that grips the person who initially exposed you, the damage has been done.  This posting is a cautionary tale.

Recently, my sister and her husband returned from a vacation in Venice with tales of architectural marvels, including trilobite arches.  They were certain this term would excite my paleontological persona, prompting an immediate mental connection with trilobites, those extinct arthropods of the class Trilobita.  With references on these arches from one of their guides to the city, Venice from the Ground Up (2008) written by James H.S. McGregor, chair of the Department of Comparative Literature at the University of Georgia, they launched me on several days of research, the drafting of this posting, and descent into . . . .

A bit of context may be in order.  Though these folks are not paleontology fanatics, some time ago I infected them with just enough of my passion for the science that they now go out of their way for something fossil related.  A case in point – during an Adirondacks sojourn, they stopped by Leeds, New York, so they could walk the town’s bridge, constructed of Becraft Limestone, a wonderfully fossiliferous Devonian stone replete with such treasures as crinoid stems, gastropods, and trilobites.

To the arches.  McGregor uses the term trilobite arch in describing aspects of the Basilica di San Marco (St. Mark’s Basilica) and the Ca’ d’Oro (House of Gold) on the Canal Grande, with particular attention to the latter.  He writes that the Ca’ d’Oro features trilobite arches in the loggias on the western façade’s first and second floors.  (The numbering of the floors is tricky, a ground floor sits at the canal’s edge.  A loggia is a covered gallery, open on one or more sides.)

To establish what I’m focused on here, below is my rendition of a trilobite arch drawn from those on the second floor of the western façade.  (I drafted it using Inkscape, an open-source vector graphic editor.)

Among the defining elements of this Gothic arch is not the outer edge (the extrado), which in this case is simply pointed, but rather the inner one (the intrado) which is divided into three spaces by two distinct protrusions on either side.

The full western façade of the Ca’ d’Oro is pictured below.  (The image, taken by Didier Descouens, is reproduced under Creative Commons Attribution-Share Alike 3.0 Unported License, and appears at:  http://en.wikipedia.org/wiki/File:Ca%27_d%27Oro_facciata.jpg .)

McGregor describes this façade as follows:

Springing from two pilasters and supported on five columns, a complex tracery of stone distinguishes the first story.  The lowest area of the tracery is a series of trilobite arches, with frames that are steep and doubly curved and inner circumferences lightly marked with the outline of three partly overlapping circles.  In the open areas between each of these adjacent arches, the stone tracery outlines four-lobed openings.  The tracery comes to a point above each of these openings to form small trilobite spaces. . . .

The arcaded opening on the floor above is a more compact and delicate version of the one below.  Five shorter columns and two pilasters support six trilobite arches that terminate in a much simpler and more distinctly geometrical tracery above.  (p. 119-120, emphasis added)

I love that the “small trilobite spaces” he describes on the first floor (and, for that matter, those on the second floor) are upside down.

In fact, this kind of arch (right side up) appears widely in Venice.  For instance, Basilica di San Marco is replete with them.  The picture below of the southern doorway at San Marco shows a wonderful set of these arches framing the windows above the doors.  A separate photo focuses on the arches.

With these images in mind, I asserted that this term –  trilobite arch – applied to the delicately flowing structures on the Ca’ d’Oro façade made perfect paleontological sense.  Whoever named this arch, I believed, could only have been doing so with some knowledge of fossil trilobites.

I didn’t mean the connection was as simple as there are three divisions in each – the arch has three lobed spaces and the arthropod trilobite had three body lobes.  Rather, it was in the arrangement of those three lobes that the name made sense and here a bit of specific paleontological knowledge came into play.

Most people upon first encountering a fossil trilobite conclude that it is so-named because it has three stacked body parts dividing the animal from the head down to the tail – into cephalon, thorax, and pygidium.  The photo below of an Elrathia kingii (1 inch long) has been annotated to show those three divisions.

But that would be incorrect.  Further, that arrangement wouldn’t match the trilobite arch.  In point of fact, the names Trilobita and trilobite as applied to this extinct animal derive from the three lobes into which the body is divided longitudinally with these structures running the length of the body, two pleural lobes straddling a central axial lobe.  (Among other publications that discuss this source of the names is Trilobites by Riccardo Levi-Setti, 1993, p. 8.)

The longitudinal aspect of the lobes signaled to me a clear bond between trilobite arch and the trilobite arthropods.  With an open space typically extending down from the trilobite arch, one is presented with a structure whose name architecturally and paleontologically makes sense.

Only the connection is an illusion, it’s purely serendipity and the product of my paleontology delirium.  In my enthusiasm, I’d seen a connection between Venetian architecture and these fossil animals which is purely a coincidental, misguided product of a consuming interest.

Perhaps McGregor simply needed a different adjective with which to describe these three-lobed arches; he may well pronounce the word trilobite with an accent on the second syllable (tri-LO-bite).  Yes, the term trilobite arch is used elsewhere by others but very seldom.  A Google search came up mostly empty.  I realized that I’d seen intent where there wasn’t any, a point driven home when I found that, as far as I can tell, architect and renowned historian of Venetian architecture Richard J Goy in his book on the construction of the house (House of Gold:  Building a Palace in Medieval Venice (1992)) never once uses the term trilobite arch.

I’ve concluded that this kind of arch is perhaps most often labeled a trefoil arch.  (I should admit that Goy in the passage on page 145 of his book providing a succinct description of the western façade only uses the term trefoil arch a single time.)  From Oxford Art Online (available by subscription) comes this definition of a trefoil arch:

A triple arch composed of three sections of a circle, arranged scallop-fashion, the central being the highest.  It may be pointed or round.

In his American Architecture:  An Illustrated Encyclopedia (2002), the late Cyril M. Harris defines a trefoil arch as follows:

A pointed arch whose inner surface is struck from three centers; the shape of the arch is determined by the position of the centers and radii of curvature; has a projecting cusp on each side.  (p. 338)

(Harris was professor of architecture and professor of electrical engineering at Columbia University.)

Use of the term trefoil arch appears to have deep roots.  Among the older material I turned up is The Principles of Gothic Ecclesiastical Architecture:  With an Explanation of Technical Terms, and Centenary of Ancient Terms (1849) by Matthew Holbeche Bloxam (1805 – 1888).  Bloxam worked professionally as a lawyer in his hometown of Rugby, England, and was widely known for his archaeological research and writing, particularly on Gothic architecture.  (An obituary appeared in the Journal of the British Archaeological Association, Volume 44, 1888.)  In The Principles of Gothic Ecclesiastical Architecture, Bloxam illustrates several variations of the trefoil arch.  One of his illustrations appears below.

The second arch in the second row and two arches in the bottom row are identified as variations of trefoil arches.

(Bloxam also figures in the historical scrum over the origins of the sport of rugby, but going there would be too much of a digression.)

With that, I bring this cautionary tale to a close, though with one small coda.  I now find myself awash in arches, acutely aware of what had previously remained mostly hidden in the background.  I play with terms such as trefoil and ogee arches, blind and containing arches, intrados and extrados, Gothic and Romanesque.  Trefoil arches make appearances in unexpected places such as New York City's Central Park with its Trefoil Arch.  Perhaps a visit to a natural history museum would help with my recovery, as long as I ignore the architecture of the building.

Poetic Pursuit in the Museum: Seamus Heaney and Bogland

Twilight at the museum, though, to be honest, it’s always twilight in much of this building, never night when, as we well know, the specimens on display would come alive.  The visitors are departing, leaving in their wake faint pulses of voices and fading fragments of sentences.

On a quest, I peer into one hallway – early and middle Cenozoic mammals – too early.  The Ice Age and beyond is to my left – much more promising.  In the soft gloom, I pass a giant sloth, round a corner and stop.  As though from a mist, rises Megaloceros giganteus, the Irish Elk.

What an amazing creature, seemingly a victim of size gone wrong.  During a brief warm period, some 12,000 to 11,000 years ago, the Irish Elk bulked up and grew those monstrous antlers, spanning upwards of 12 feet and weighing 100 pounds.  But, as Stephen Jay Gould described, the animal, neither an elk (it was a deer) nor exclusively Irish (fossil remnants are found throughout Eurasia), was a battleground over which Darwinians and their naysayers long fought.  The latter at times contending that an attribute such as those grossly huge antlers showed the impotence of natural selection, once an animal started down an evolutionary path, there was no turning back even if it lead directly to the animal’s extinction.  Though the former have won this field, they remain somewhat at odds among themselves over the forces actually at work in driving up body and antler size.

Gould, in his essay The Misnamed, Mistreated, and Misunderstood Irish Elk (in the essay collection Ever Since Darwin (1977)) offered evidence for the allometric relationship between body size and antlers (as the one increased so did the other), and concluded that selection was working on the antlers.  As selection drove an increase in antler size, body size increased along with them.  He proffered that the oversized antlers were used in ritualized combat between Irish Elk males, a process that established dominance hierarchies without inflicting fatal injuries on the vanquished, and, most importantly, ensured the reproductive success of the more robustly antlered victors.  Others argued that the key was body size and it was the antlers that were along for the ride.  The plaque below the skeleton of M. giganteus here in the Smithsonian’s National Museum of Natural History posits just that.  Extinction, Gould argued, came when the climate cooled and the flora changed with it, no longer able to support these animals.  The plaque cites as the principal cause of the beast’s extinction the impossibility of moving with their racks through the forests that arose with the changing climate.  Some have offered up a more convincing hypothesis, arguing that the nutritional requirements for animals of this size with their array of antlers could not be met by the newly available flora, and that it changed too quickly for the animals to adapt, all the while sexual selection continued to promote larger antlers. (Ron A. Moen, et al., Antler Growth and Extinction of the Irish Elk, Evolutionary Ecology Research, 1999.)  Regardless of the precise cause of the extinction, Gould concluded that all this was fully in keeping with the theory:

Darwinian evolution decrees that no animals shall actively develop a harmful structure, but it offers no guarantee that useful structures will continue to be adaptive in changed circumstances.  (p. 90)

So why my quest for the Irish Elk?  It grew out of my reading Bogland, a poem by Seamus Heaney, 1995 Nobel Laureate in Literature (awarded "for works of lyrical beauty and ethical depth, which exalt everyday miracles and the living past").  (Bogland was published in a 1969 collection titled Door into the Dark.  I am reading it in Opened Ground:  Selected Poems 1966 – 1996.)

I come late to Heaney’s poetry and have been reading mostly his earliest pieces, those that most center on the ebb and flow of rural life in Ireland and the Irish landscape.  Here a spongy, porous boundary separates past and present.  In this bogland of Ireland, this watery earth, the past is just below the surface and seemingly unchanged.  In Bogland, Heaney writes of butter buried for a hundred years reemerging “salty and white.”  And ancient trees that turn not to coal, but to “waterlogged trunks/ . . . , soft as pulp.”  In the harvesting of peat, the past is present – “Our pioneers keep striking/ Inwards and downwards,/ Every layer they strip /Seems camped on before.”

And my quest?  “They’ve taken the skeleton/ Of the Great Irish Elk/ Out of the peat, set it up,/ An astounding crate full of air.”

A striking and true image of the ribcage?  I think so.

But I am puzzled why it’s the ribcage the poet remarks on, not the massive set of antlers.  Perhaps it’s just a striking image, though I think not with this poet.  A comment on the meaning of the past?  On an effort to recreate it?

Bog-mediated preservation of the past recurs often in Heaney’s early poems.  For example, in a series of poems, including The Tollund Man, he finds a resonance between the violent troubles in his home land (Northern Ireland) and the well preserved bodies found in bogs in Denmark, victims of sacrifice 2,000 years ago.  (William Doreski, Diggings, Harvard Review, Spring 1996.)

The first of Heaney’s poems I read was Death of a Naturalist from the 1966 collection of the same name.  (Heaney was featured in a recent installment of the PBS NewsHour’s Poetry Series; the text of the poem and a video of Heaney reading it appear on the NewsHour’s website.)  The poem offers an almost maddening array of stimulations for the senses.  It demands to be read aloud and savored.  Every spring, the narrator, Heaney as a boy, I assume, gathered frogs’ eggs (“frogspawn”) in jars and watched them develop on window sills at home and shelves at school.  And, as the poem reads, every spring his teacher, Miss Walls, told the children of daddy frogs and mammy frogs.  To mark the boy’s youthfulness, the first portion of the poem ends with a delightful non sequitur about how the color of the frogs changes depending upon the weather – the prototypical young child telling all he knows about a subject, whether relevant or not.

That innocence vanishes in the second portion of the poem when the boy comes upon a gathering of croaking bullfrog – “Poised like mud grenades, their blunt heads farting.”  The would be naturalist?  “I sickened, turned, and ran.  The great slime kings/ Were gathered there for vengeance and I knew/ That if I dipped my hand the spawn would clutch it.”  Death of a naturalist.  Actually, I think not.

I am still working on this poem, considering if it’s about the death of sexual innocence (though why at that particular moment when Miss Walls had told him often about mammy and daddy frogs), if it marks the moment of the boy’s realization of the potential dangers of the natural world, if there’s some Irish folktale about vengeful frog kings, or if . . . .  Regardless, I do not, for a moment, believe that it describes the death of the naturalist in Heaney.  His poetry says otherwise.