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God and Geometry


That view is from the chapter house of York Minster [2] in York, England. It’s part of photographer David Stephenson’s book [3] on European cathedral vaults.

See more at Stephenson’s website [4]. Stunning stuff. This homeschooling adventure in Paris is going to be so much fun. Driving to tutorial this morning, Matthew told me he was looking forward the most to Chartres. Not sure how big he is on religion just now, but geometry, he can definitely relate to. We’re about to read together “Universe of Stone,” [5] science journalist Philip Ball’s engrossing book about the Chartres Cathedral, and the philosophical and theological ideas that gave birth to Gothic architecture. I blogged on it here [6], and posted this excerpt from Ball’s book:

The building was a sacred symbol, and every part had the primary function of expressing piety and encoding a belief in divine order. We no longer know how to read this code. It unites the physical with the metaphysical: according to Abbot Suger, building a church involved the transposition of the material into the spiritual. Artists of later ages, even until the present, have tried to achieve something analogous, but they have had no rules to guide them. Their attempts to forge materials into an expression of the ineffable therefore become highly personal visions, reflections of one individual’s spiritual world.

The theoretical principles governing the construction of the Gothic cathedrals were geometry and clarity. The structure of these buildings is dictated by proportion, by simple numerical relationships between the key dimensions. These mathematical relations were deemed to be expressions of perfection, a belief that stemmed from ancient Greek thought and for which some found endorsement in the Bible. So when we experience unity and order in Chartres Cathedral, it is the result of careful and rational planning, motivated not by aesthetics but by morality. The building expresses a conviction that the glory of God’s universe is expressed as a system of eternal order.

We no longer know how to read the code. Alas for us. Still, might we be able to feel the presence of divine order, even if we don’t really know what we’re looking at? That was absolutely my experience of the Chartres cathedral when I was 17 years old. I walked out of there knowing that, in Walker Percy’s phrase, that I was onto something.

(H/T: Fr. S.)

20 Comments (Open | Close)

20 Comments To "God and Geometry"

#1 Comment By Ed Steegmann On August 20, 2012 @ 3:49 pm

I highly recommend Henry Adams’ “Mont St. Michel and Chartes” if you haven’t read it already. He seems to me to have cracked the code. One need not agree with all of his conclusions to find it a moving and deeply learned book.

#2 Comment By M_Young On August 20, 2012 @ 3:58 pm

“We no longer know how to read the code.”

But Dan Brown does!

#3 Comment By MH – Secular Misanthropist On August 20, 2012 @ 4:36 pm

I didn’t see any logarithmic spirals ( [7]) in those pictures.

While God may have an inordinate fondness for beetles, God has an even greater one for Fibonacci numbers!

#4 Comment By Charles Cosimano On August 20, 2012 @ 4:41 pm

What is that phrase from Masonry? “The Grand Geometer.”

#5 Comment By MikeCLT On August 20, 2012 @ 4:42 pm

If you plan on taking a tour of Chartres, you should go with Malcolm Miller. Explain your circumstances and purpose. He adjusts the tour to the level of the audience. You might be able to arrange a private or semi private tour. Or perhaps tag along if he is giving a tour to a non tourist group.

I have been to Chartres twice. It is truly awe inspiring. The first sight of the cathedral as you walk up the hill is a thrill.

#6 Comment By EngineerScotty On August 20, 2012 @ 5:25 pm

“Und zees is how ve say good-bye in Germany, Dr. Jones!”


“I think I liked the Austrian way better…”

#7 Comment By Sam M On August 20, 2012 @ 5:58 pm

Couldn’t someone read the existence of geometric truths as the opposite of divinity? What that guy thought was the presence of the holy spirit was actually… Pi. I believe that the pyramids were also based on geometric principles. I am sure people who viewed them felt inspired in the same way you did. But these things can’t really be pointing at the same truth, since the pharoah’s god is not your god.

Just because mathematical truths are employed to good aesthetic effect doesn’t necessarily argue that houses of worship which they serve are “correct.”

#8 Comment By Patrick Moore On August 20, 2012 @ 5:58 pm

Chartres and the Birth of the Cathedral ( [8])

Burckhardt, an amazingly gifted intellectual with a particular genius for sacred symbolism and the traditional arts and sciences, is very well equipped to explain the rigorous science linking the physical glory of Chartres cathedral to spiritual principles.

This exceptionally clear text by Guenon states the principle governing the scientific rigor of traditional symbolism including the architectural; this is basic patristic doctrine, among others.

“All that exists, in whatever mode this may be, necessarily participates in universal principles, and nothing exists except by participation in these prinicples, which are the eternal and immutable essences contained in the permanent actuality of the Divine Intellect. Consequently, it can be said that all things, however contingent they may be of themselves, express or represent these principles in their own way and according to their order of existence, for otherwise they would be purely and simply nothingness. Thus, from one order to another, all things are linked together and correspond, to come together in total and universal harmony, for harmony is nothing other than the reflection of principal unity in the manifested world; and it is this correspondence which is the veritable basis of symbolism.”

#9 Comment By Patrick Moore On August 20, 2012 @ 6:04 pm

From a brief but well written review on goodreads ( [9]):

In Chartres, Burckhardt’s gift for opening the spiritual and artistic treasures of the traditional worlds for modern readers shines forth once again. The author’s description of the didactic themes of the cathedral’s great doorways and rose windows covers virtually the whole of the Christian story and amount to a comprehensive presentation of Christian theology and metaphysics. At the same time, his insights go far beyond the limits of Christianity as a confessional world. Basing himself on the permanent and universal principles of the religio perennis, Burckhardt enables the reader to understand and appreciate the intellectual vision which inspired the creative joy of the artistic productions of the Middle Ages.
Richly illustrated with 16 full color photos, 10 black & white photos plus over 100 line drawings.

#10 Comment By Luc de Lasalle On August 20, 2012 @ 6:43 pm

Christ est parmi nous ! (Christ is among us!- in French)

Bonsoir Rod.

As an Orthodox Christian like you I learned recently that there were some interesting differences between the Orthodox and the Catholic in terms of church architecture, notably on symbolism, on height, etc.

Here’s a sample of a PDF document written by an Orthodox expert from Great-Britain:

From the Gothic onwards, the dominant trend in British and Northern European church design has been for long and high naves, their verticality further emphasised by the pointed arch and thin columns. Many of the
Anglican churches available to the Orthodox in Britain are such churches, either victorian creations or neo-Gothic remodellings. The intuition of the
Orthodox Church seems to be that this has created a church type which, for all its particular beauty, has an atmosphere which tends to be too impersonal, and not incarnational enough for its adoption. This is not to denigrate the great accomplishments of cathedrals such as Chartres or York Minster, but simply says that many aspects of their design are not
appropriate to the Orthodox Church . When looking for ideas in western architecture we would therefore be inclined to look to the earlier Anglo-Saxon and Romanesque periods (little survives of Celtic churches).

If you want to read more, here’s the site:

-Love in Christ
Montréal, Canada

#11 Comment By James C. On August 20, 2012 @ 7:11 pm

Rod, I strongly recommend for you and your son a viewing of Lord Kenneth Clark’s landmark 1969 BBC series, “Civilisation” It’s an enthralling, erudite personal tour of Western art history.

The second episode, “The Great Thaw”, deals with the Gothic High Middle Ages, and Lord Clark focuses on Chartres.

BBC has a blu-ray version out now, but for convenience the YouTube version will do:

#12 Comment By James C. On August 20, 2012 @ 7:33 pm

I forgot to add that you can see Lord Clark’s visit to Chartres at 34:00.

#13 Comment By James C. On August 20, 2012 @ 7:36 pm

Yes, Rod, one must go back to Romanesque and Anglo-Saxon styles—the Gothic, being post-filioque, is graceless and corrupt. 😉

#14 Comment By Terry Ward On August 20, 2012 @ 8:06 pm

Check out “The Sun in the Church: Cathedrals as Solar Observatories” by Heilbron about the uses of Churches as solar observatories. From the Amazon description:

Between 1650 and 1750, four Catholic churches were the best solar observatories in the world. Built to fix an unquestionable date for Easter, they also housed instruments that threw light on the disputed geometry of the solar system, and so, within sight of the altar, subverted Church doctrine about the order of the universe.

A tale of politically canny astronomers and cardinals with a taste for mathematics, The Sun in the Church tells how these observatories came to be, how they worked, and what they accomplished. It describes Galileo’s political overreaching, his subsequent trial for heresy, and his slow and steady rehabilitation in the eyes of the Catholic Church. And it offers an enlightening perspective on astronomy, Church history, and religious architecture, as well as an analysis of measurements testing the limits of attainable accuracy, undertaken with rudimentary means and extraordinary zeal. Above all, the book illuminates the niches protected and financed by the Catholic Church in which science and mathematics thrived.

Superbly written, The Sun in the Church provides a magnificent corrective to long-standing oversimplified accounts of the hostility between science and religion.

#15 Comment By Gavin On August 20, 2012 @ 8:12 pm

You must have a look at Stratford Caldecott’s writing, especially Beauty for Truth’s Sake. And check out Second Spring (he is the editor) secondspring.co.uk

#16 Comment By MMH On August 20, 2012 @ 9:42 pm

Patrick Moore at 5:58 unintentionally gives the appropriate response to Sam M., also at 5:58.

#17 Comment By alcogito On August 21, 2012 @ 12:47 am

Show your kids this youtube video of the classic Disney short film before you go” Donald in Mathmagic Land.


Fascinating for all ages. See the golden section in Notre Dame and the Mona Lisa, and in all the classical buildings in Paris.

#18 Comment By Dave Dutcher On August 21, 2012 @ 1:43 am

Different tastes, I guess. Abstract appreciation of the principles of divine order doesn’t really engage me, but I can see its appeal for others.

#19 Comment By Liam On August 21, 2012 @ 4:49 am

Glad to see the author does not limit the scope of his study to France, England, Germany and Italy: points east are just as worth of study (and not just east) – some of the most breathtaking churches, abbeys and cathedrals are in eastern Germany, Poland, the Baltic, et cet., typically ignored in collegiate architectural history books.

Count me as a fan of Romanesque over Gothic, btw. Gothic can be great for small jewel-box chapels, but the acoustics in vaster spaces can just get too diaphanous for my taste.

And the acoustical element of design is as important as the visual. But it doesn’t lend itself to anywhere near the amount of written commentary.

#20 Comment By Sean On August 21, 2012 @ 12:00 pm

This topic reminded me of one of my favorite paintings (engraving?), William Blake’s “Newton”, where the great scientist is a sort of divine geometer.