Crystal Edges Blog

Fig. 1. Window of the ‘Creation’ at the Church of the Holy Spirit, Lake Forest, Illinois, USA.

Little did I know that after my essay on the meaning of symmetry on the cathedral rose windows, I will be writing another brief posting soon thereafter on a related theme.  However, it just so happened that on Friday, April 11, 2014 there was a lecture in one of the churches of my hometown, Lake Forest, IL, entitled ‘The Brilliance of Stained Glass Windows in Lake Forest’. After my introduction to the theme by the work of Painton Cowen and my own interest, as related in the previous essay, I just couldn’t resist attending.

The lecture was offered by the Lake Forest Preservation Foundation (LFPF), an organization devoted to maintain and preserve the historical and visual character of Lake Forest, a small community on the Northern shores of Lake Michigan, about thirty miles north of Chicago. The lecture was presented within the temple of the First Presbyterian Church of Lake Forest by Paul Bergmann and Jan Gibson. Just by coincidence, Ms. Gibson is a person that I had known for a few years now as a fellow commuter to the city.

The church itself has a good collection of windows from the modern artists of the stained glass craft including works by Louis C. Tiffany (1848-1933), Charles J. Connick (1875-1945) and others, and the lecture was illustrated with examples illuminated in the Sanctuary of the church on that beautiful Spring morning. During the course of the lecture, I learned that other churches in Lake Forest, for example Church of The Holy Spirit, St. Mary, St. Patrick and St. James Lutheran Church, among others also had noteworthy examples of stained glass windows.

The speakers reviewed some of the technical details of the new windows and the different styles of the modern glaziers from Tiffany to Connick and the Gothic revivalist Henry Wynd Young.  They allowed the attendees to see, touch and appreciate for themselves the different windows to fully recognize the masterpieces that were in front of them. From the images and content of these windows it was clear that I was not looking at abstract, geometric, symbols of reality (although some of the modern windows are abstract in nature). They represented religious scenes, allegories and metaphors well documented in the Gospels or the New Testament.  As I strolled around the various windows, I could not leave aside the concluding paragraph of my previous essay (italics my emphasis for this note):

‘These reflections illustrate how various symmetrical figures and entities that are part of our world, and which can be described by the rigorous framework of group theory in mathematics, have been used throughout history to convey different thoughts, insights and perceptions of the artist (or the scientist) as a draughtsman and executor of the cosmological view of the times. Both artists and scientists will continue to create and unveil novel symbols of their times to illuminate and enrich the world in which we all live. Further research efforts and artistic ingenuity will carry the torch of our predecessors. ‘

Among the examples included in the booklet provided by the lecturers there was one window from the church of The Holy Spirit representing the Creation that immediately caught my attention (Fig. 1). The window represents the Creation as related by the Song of Creation and it was completed by the Willet Stained Glass Studios of Philadelphia and installed in 1996 within the secluded space of the columbarium within the Sanctuary itself. The precise detail of the representation of the different events of creation caught my attention: the Sun and the planets, the animals of the land, the birds, the creatures of the sea; and then, the surprise. I was amazed and pleased to see a pristine and accurate representation of ice and snow crystals within the circle corresponding to the creation of water. I said to myself: I am delighted that what we now know about water, ice and crystals is represented in this new ‘updated’ version of the ‘Creation’.  The content is all well presented within a balanced mirror symmetric framework including a swirling leave or branch that reminded me of ‘single stranded DNA’, although I doubt that it was the intention of the artist to include such a reference in the window. The lecture was an excellent introduction to the marvels of modern glass windows in modern churches in America and in other parts of the world, something that Mr. Painton Cowen (my colleague from the previous essay) had already emphasized and that I had failed to fully appreciate in our previous conversations: the art form of stained glass has been and still is quite alive all over the world.

But the ‘single stranded DNA’ from the previous window set into motion a recollection of another representation of that theme in another window that I had seen a few years earlier in the chapel of King’s College in London. To connect the two, it is necessary now to remember that in the early 1950’s Maurice H.F. Wilkins and colleagues had started to examine and study with X-rays a biological material of the outmost importance: deoxyribonucleic acid (DNA), the atomic carrier of biological inheritance. It was not crystalline per se but the material aggregated readyly in sheaves of fibers that were amenable to be analyzed using long X-rays exposures. And that it was at this laboratory where Rosalind E. Franklin came to work soon thereafter to continue the research. Rosalind Franklin, the diminished and derided ‘Rosy’ in J.D. Watson’s book The Double Helix soon produced very significant and insightful experimental results that provided most of the building parameters for the DNA model proposed by Watson and Crick in the 1953 publication in Nature, which opened the door to structural and molecular biology; a scientific breakthrough of enormous consequences.

To commemorate this achievement, there is a stained glass window in the chapel of King’s College in London representing Jesus communicating the ‘wonders of creation’ to the people and among the listeners there is representation of Maurice H. F. Wilkins and Rosalind E. Franklin kind of  arguing about the structure of DNA. It is well known through the several accounts of that momentous discovery that Wilkins and Franklin did not get along very well, and soon Dr. Franklin left the laboratory to work with another luminary of structural biology John Desmond Bernal (i.e. ‘Sage’). But the window representing these events is amazing (Fig. 2a). It is a rectangular lancet-shaped window with Christ at the top speaking (possibly teaching or preaching), with a model of the atom behind him, to the people and at the very bottom we see Wilkins and Franklin consulting (or reading) a book containing the double-coiled

Fig.2a. Image of the ‘teaching’ window in the Chapel of King’s College, London, UK.

(double helical) structure of DNA (Fig.2b). There is no need to present an abstract representation: it is all there. The window also contains a poem where in addition to the work of Wilkins and Franklin, homage is paid

Fig.2b. Detail of the window at the Chapel of King’s College, London, portraying M.H.F. Wilkins and Rosalind E. Franklin, possibly discussing the structure of the DNA molecule that was unveiled thanks for the superb experimental data obtained by Dr. Franklin while at King’s College in the early 1950s.

to one of the premier theoretical physicists of all times, James C. Maxwell who also worked in that laboratory.

I do hope that this brief and informal account of my intellectual wanderings after the earlier essay about the symmetry of rose windows has reinforced the comment made in the last paragraph reproduced earlier. The stained glass windows continue to be used to convey, revise, actualize and refresh, our views (personal and societal) of the world and the significant events that reshape it.   I will only add a final wish: possibly in the future, I would like to see the image of Charles R. Darwin included in some of the new renditions of the Creation events.  This certainly will be a sign of the change of values and attitudes in society. I do hope that it is not too far into the future.

I need to apologize to the reader for not having written anything during the last few months. They have been months of frantic traveling and activity in the professional front, related to the celebration of the IYCr2014 at the UNESCO headquarters in Paris, January, 20-22, 2014. It was a rare opportunity to re-encounter old friends, colleagues young and old as well as practitioners of crystallography from all over the world. You can find more details of these events at www.iycr2014.org. However, this has been only part of the reason for not being able to write more on the blog.

There has also  been the effort to pursue a project related to the relationship between the magnificent rose windows in the Gothic Cathedrals of Europe and the symmetry and as follow up, the possible meaning of symmetry. This connection was mentioned in a brief sentence in the masterful book Symmetry by H. Weyl (1885-1955) where he wrote: ‘ Magnificent examples of such central plane symmetry are provided by the rose windows of Gothic cathedrals with their brilliant-colored glasswork’ (pg. 58).  The balanced composition, radial symmetry and rich content of the stained glass within the rose windows of the Gothic Cathedrals is apparent to anyone visiting the iconic cathedrals of Notre Dame, Chartres, Reims, Amiens and so many others in France, Germany, England, Italy and Spain.

Gothic ‘Rose Window’ in the temple of Santa Maria del Pi (Cita Vella, Barcelona, Spain). The planar point group symmetry of the composition is 12 mm.

The history, construction and meaning of these masterpieces of Gothic art have also been the object of extensive studies. During my visit to Paris last January, I was fortunate to meet Mr. Painton Cowen, an authority in the field of rose windows and stained glass with several books to his credit. I was prompted to meet him, talk to him and initiate a possible collaboration with him after I read and studied several of his books. My main point of interest was to attempt to classify rigorously the symmetry of the rose windows and his books and his website www.therosewindow.com, were amazing compendia of information.

A preliminary analysis and study of the data illustrated and discussed by Mr. Cowen has been recently published in Acta Crystallographica D (2014). You can access the article at Acta Crystallographica Section D: Biological Crystallography (2014), D70, 907-911(doi:10.1107/S1399004713032859).

This brief essay provides a window into the mathematical description of the symmetric arrangements present in rose windows in cathedrals and other monuments of the Middle Ages, and points towards the possible meaning of those iconic masterpieces that represent the legacy of builders, masons,  glaziers as well as the societies in which they lived in. After our first meeting in Paris, Mr. Painton Cowen and I are currently pursuing a collaboration to include  the rigorous description of symmetry in his website, and to use its analysis to provide further insights into the meaning of symmetry in those iconic pieces of architectural and artistic ingenuity as well as the world-view of their times that they represent. I encourage you to read the entire essay in Acta Cryst D. I will be delighted to hear your comments.

First published diffraction pattern of a crystal of Zinc blend obtained by  W. Friedrich, P. Knipping and M. Laue ( 1912). The 3-fold symmetry of the pattern is a reflection of the symmetrical arrangement of the atoms inside the crystal. From the arrangement of the spots and their relative intensities the geometric disposition of the atoms in the crystal can be deduced: their Cartesian coordinates (x,y,z) in 3D.

As the year 2014 approaches, more and more institutions all over the world prepare to celebrate the International Year of Crystallography  (IYCr2014) with all kinds of activities and media to communicate to the lay public the importance of this obscure science.  Crystallography is an arcane science to the majority of the world population; yet, its theory and findings are the basics for the atomic knowledge of the world that surrounds us. The combination of crystals and X-rays in the physical phenomenon call ‘diffraction’ permit the unveiling of the atomic structure inside the crystals. This was the key insight of the Braggs (W. Henry and W. Lawrence, father and son) in 1913 when they discovered the arrangement of the atoms in the common salt (Sodium Chloride, NaCl).

May this brief note serve as the introduction to the excellent material (video, audio, photographs, interviews etc.) released by the Royal Institution in London to commemorate this event. I just encourage you to access this site and pick and choose whatever piques your curiosity and you will be amply rewarded.

http://www.richannel.org/celebrating-crystallography/

I could not write any better summary of the beauty of crystallography and of its impact in our world today and in the future. Previous and future postings on this site elaborate on the many different aspects of the science of crystallography. From its mathematical underpinnings on group theory to the physics of diffraction theory and Fourier Transforms, to the intricate atomic description of the structure of the molecules that are now being unveiled by modern crystallographers.

I wish you an insightful and enjoyable journey.

An op-ed article by Manil Suri (Professor of Mathematics, University of Maryland) in the New York Times on Monday, September 16
(http://www.nytimes.com/2013/09/16/opinion/how-to-fall-in-love-with-math.html) eloquently expresses the dismay of the author when he faces the shallow perception that the general public have for mathematics. The common expression “Do the math” typically implying the arithmetic of operating with numbers, as if balancing a checkbook or adding the family expenses would be the ultimate objective of mathematics.

He argues and illustrates that indeed ‘mathematics’ is infinitely more than just that. Through the ages, the realm of ‘mathematics’ has expanded the human mind and spirit from the Pythagorean’s perception of the world, to the use of calculus to accurately describe motion and change, and on to the non-Euclidian geometries to define and explain the space we live in. He argues that the richness of mathematics is comparable to the fullness of Art and Music with their similar unremitting searches although all in different domains.

The article immediately brought to my mind the thought: Isn’t that also true about other areas of science? What does Biochemistry suggest? Take your vitamins? In the worst possible scenario, an esoteric branch of science might just elicit silence or even an inconsequential response. How about ‘crystallography’, followed by ‘healing power of crystals’ or ‘crystals can predict the future’?

Unfortunately, many of the ill responses to mathematics discussed by the author of the article apply to many of the broader branches of science and quite often to the narrower specialties. And yet, in very different ways, all expand our knowledge of who we are and what surrounds us. Knowledge that later translates into conveniences or comforts that make our lives more enjoyable.

Going back to crystallography. Crystallography is an astonishing branch of science. Crystals have been studied from antiquity and fascinated human beings since they were discovered (see previous posting). Their external forms probably inspired the geometry of the Platonic solids and the mathematical description of its internal symmetry is related to ‘group theory’ and to artistic tessellations of two and three-dimensional spaces. Artists such as M.C. Escher (1898-1972) were inspired by their internal structure.

Fig.1. Diffraction pattern of a crystal of a blue-green algae protein named C-Phycocyanin.
A prismatic crystal of the protein is exposed to the X-rays oriented so that the hexagonal axis is along the direction of the X-rays. The symmetry of the diffraction pattern is a reflection of the symmetry of the crystal. A three dimensional data set of photographs like this permits the mapping of the atoms forming the protein in three-dimensions. Copyright C.A-Z.

Its true internal symmetry, however, was veiled from the human eyes and could only be revealed by X-rays. Those ‘naughty Roentgen rays’ were discovered by Wilhelm Conrad Roentgen (1845-1923) in 1895 and unsealed new fields in the history of science. Its mysterious nature and character unfathomable to Roentgen’s experimental probing: were they waves or a stream of particles? Eventually, they only yielded their innermost secret to the crystals themselves and the crystals in turn, confessed that they were arrays of atoms. Now the two were inseparable: crystals and X-rays.

The pattern of spots (i.e., ‘diffraction pattern’, Fig.1) resulting from the interaction of the X-rays with the atomic structure of matter inside the crystals has permitted the unveiling of the atomic universes that surround us, ever since the Braggs (William Henry and William Lawrence, father and son) revealed the structure of the commons salt (Sodium Chloride) in 1914.

Since then, the mathematical expansions of functions proposed by J.B. Joseph Fourier (1768-1830) in his 1822 memoir entitled the ‘The analytic theory of Heat’, have been the cornerstone of the mathematical underpinning of crystallography, permitting the discovery of the ever more complex atomic structures within the world that we inhabit. From the most common minerals to the double-helical structure of DNA that relates us to the ladder of organisms living and extinct. Isn’t this mind-blowing? Crystallography, is a division of science that combines mathematics, physics, instrumentation and chemistry to provide us with an unparalleled view of who we are and they world that we inhabit.

Without having to master the mathematics behind crystallography, any curious human mind can understand and appreciate all these wonders. Not even the ‘The Math Gene’ is necessary. I am not certain that the assertion by Stanford mathematician Keith Devlin that human beings are wired for mathematics is correct. Certainly, not all human beings are ‘wired’ or at least some are much more than others. However, I am certain that all human beings share the ‘curiosity gene’ at the most fundamental and ancestral level; you only have to look at the human child. Otherwise, we would not have arrived to where we are now. As scientists, each one of us in our own arcane specialties, need to learn and practice the avocation of transmitting this sense of wonder to our fellow humans so that our specialties are, if not fully understood, at least appreciated in the context of other human activities. This will make all of us richer and even more human.

A small gallery of the shapes and forms present in the atomic structures of proteins. This represents a simplified rendering of a few of the thousands of ‘atomic sculptures’ available from the Protein Data Bank. Further details can be found on Crystals and Life Plates 12.3, 13.1,14.1,20.1,20.2. Helices are represented by helical coils and beta sheets by ribbons. Various software packages can go from the atomic coordinates from the PDB to this schematic and artistic representation of protein structures. Each coordinate set has a four character accession code that annotates uniquely each coordinate set. Browse the PDB website for further details.

On August 1999, crystallographers from all over the world met in Glasgow, Scotland for the XVIIIth International Congress of Crystallography sponsored by the International Union of Crystallography (IUCr). The IUCr is the international association of crystallographic societies that was formed in 1948 to disseminate and promote the study and practice of crystallography all over the world. Towering figures of the field such as John D. Bernal, P. P. Ewald, the Braggs (W.L.Bragg and W.H. Bragg) and many others were the moving forces behind this association when the nations of the world were swept by a wind of internationalism after the trauma of WWII [1].

I took a day off from the sessions of the Congress to visit Edinburgh. I walked along the historic mile with special interest in the cathedral. The castle did not interest me at all. On a side alley, I discovered something interesting: ‘Writers Museum’. I walked into the house, visited the different rooms and up the stairs there was a special exhibit of a poet totally unknown to me until them. The name was quite plain: George Mackay Brown (1921-1996). What immediately caught my attention were those two poignant lines in one of the posters illustrating the work of GMB:

See this tall finger of science
Scratch the stars out! [2]

As a scientist, I felt as if I was – personally – the one scratching with my own fingernails the stars out of the sky. I was hooked! Why was he saying that?

Who was this George M. Brown anyway? You can find more details about this sensitive poet of the land and the sea at http://www.georgemackaybrown.co.uk. I learned later that he was referring to the presence of oil refineries in the solitude of the Orkney Islands in Scotland, occluding the limpidness of the night sky.

The animosity and tension between science and the arts has had a long history, particularly in the modern era when the exponential expansion of our knowledge has demanded specialization in almost all activities of the human mind. The influential essay about the ‘two cultures’ by C.P. Snow is widely known. I had encountered ‘anti-science’ poems before and I will illustrate a few at the end of this essay. From the disappointment of J. Keats in the poem Lamia, where he laments that Mr. Newton destroyed the rainbow by ‘unweaving’ it (reference to ‘Unweaving the Rainbow’, lines 229-238), to the boring explanations that Walt Whitman had to endure from the ‘Learned Astronomer’ (poem When I Heard the Learn’d Astronomer included in Leaves of Grass).
This latter one was particularly interesting to me because one day, I was inspired to modify it in relation to the beautiful macromolecular structures that protein crystallographers unveil from their crystal structures. The DNA double helix is probably the best-known icon of intrinsic splendor but many other structures illustrate the cover of specialized journals of biochemistry, molecular biology, cellular biology and so many other fields. The best way to have sense of the beauty and variety of these atomic sculptures is to access the Protein Data Bank web site (http://www.rcsb.org/pdb/home/home.do ) and use their educational and outreach tools (see Figs. 1,2). I recommend the tab Molecule of the Month (http://www.rcsb.org/pdb/101/motm_archive.do ) by David S. Goodsell for an amazing collection of shapes and forms.

For the layperson, crystals mean something solid, rock-solid, as in the crystals of quartz, pyrite, calcite, gypsum and others that are so common in the mineral stores. However, the crystals containing the molecules that make possible the biological world are so different: fragile, vulnerable and susceptible to damage by their surroundings (i.e., moisture, concentration of alien ions, temperature). Their properties reflect the delicacy and elegance of the materials necessary to sustain life. In a way they relate to the subtlety of poetry, as described by the poem of George M. Brown also reproduced briefly in my book [3-4]:

The mingling’s of sea and earth
Creel and plough
Fish and cornstalk
Shore people and shepherds
Are the warp and weft that go
To make the very stuff of poetry.

The revised version of Walt Whitman’s poem is included in my modest book about crystallography (Crystals and Life: A Personal Journey, IUL, 2002) and is reproduced below. I must confess that I was often tempted to change the title of the book to ‘Leaves of Crystals’ (or ‘Crystals of Leaves’) to convey the beauty and fragility of crystals of macromolecules such as proteins, nucleic acids and their complexes. I thought that the dichotomy suggested by the ‘organic’ and ‘inorganic’, or ‘biological’ and ‘mineral’, was perfectly reflected and condensed in those two words, using them with a slight alteration of the title of the inimitable poetry book by Walt Withman, Leaves of Grass. The purpose of the poem is certainly not to make a poetic ‘anti-science’ pronouncement. Quite to the contrary. It is to emphasize that behind the hard science of crystallography required to unveil the structures of these molecules and to analyze their function, there is the beauty of their atomic structure that reveals itself as a unique ‘atomic sculpture’ of singular and subtle properties.

When I Heard The Learn’d Crystallographer

When I heard the learn’d crystallographer
When the bonds, the angles, were ranged in columns before me,
When I was shown the charts and diagrams, to add, divide, and measure them,
When I sitting hear the crystallographer where he lectured
with much applause in the lecture room,
How soon unaccountable I became tired and sick,
Til rising and gliding out wander’d off by myself
In the mystical dim-lighted room, and from time to time,
Look’d up in perfect silence at the protein fold.

Adapted from When I Heard the Learn’d Astronomer (W. Whitman) by C. Abad-Zapatero.
Extracted from his book Crystals and Life: A Personal Journey. Chapter 27. pg. 207.

(www.iul-press.us/Books/BSFE01-Magic/magic.html)

_____________________________________________________________

Excerpt from Lamia (J. Keats, 1795-1821)
lines 229–238
[…]

Do not all charms fly
At the mere touch of cold philosophy?
There was an awful rainbow once in heaven:
We know her woof, her texture; she is given
In the dull catalogue of common things.
Philosophy will clip an Angel’s wings,
Conquer all mysteries by rule and line,
Empty the haunted air, and gnomèd mine—
Unweave a rainbow, as it erewhile made
The tender-person’d Lamia melt into a shade
[…]

Notes
[1] Kamminga, K. Acta Cryst. (1989). The International Union of Crystallography: Its Formation and Early Development. A45, 581-601.
[2] from Flotta Flare ORKNEY: Pictures & Poems, 1996 and 1998,
published by Colin Baxter Photography Ltd. Grantown-on-Spey, Scotland.
[3] Quote from the introduction by GMB to
George Mackay Brown, Selected Poems 1954-1992
published enlarged edition 1996, reprinted 1998
by John Murray Publishers Ltd.
Used on one of the posters at the Edinburgh exhibition.
[4] Before my departure from Scotland, I purchased several books by George M. Brown and once at home in Lake Forest, Illinois (USA), I ordered – and subsequently treasured – ORKNEY, Pictures & Poems by GMB and Gunnie Moberg. The combination of images and poems is magnificent.