Featured: Euclid’s ELEMENTS by Oliver Byrne [Vol. 3, #34]

September 20, 2010 — 1 Comment


“Distinctively Particular Ways of Thinking
About the Spaces We Inhabit

A Review of
The First Six Books of The Elements of Euclid

By Oliver Byrne.

Reviewed by Chris Smith.

The First Six Books of The Elements of Euclid
By Oliver Byrne.

Two Volume Set in Clamshell Case: Taschen, 2010.
Buy now: [ Amazon ]

Oliver Byrne - EUCLID'S ELEMENTSA dozen years ago this Fall, I was just starting my graduate studies in philosophy of science, working toward a PhD.  I was particularly interested in the ways that humankind has historically understood and talked about the spaces that we inhabit.  But as I got further and further into my research, I grew increasingly frustrated with the depth of layer upon layer of abstraction inherent in contemporary systems of geometry and physics.  Eventually, I got to the point at which I could no longer continue to be so heavily invested in these abstract worlds and I had to take a break from my graduate studies for my own sanity.

One hundred and fifty years before my graduate school experience, a little known Irish mathematician and surveyor by the name of Oliver Byrne had a similar experience.  Byrne’s frustrations – aimed particularly at the way geometry was taught – led him to craft one of the most elegant geometry books ever printed.  And now thanks to Taschen Books, Byrne’s book The First Six Books of The Elements of Euclid, is back in print. As its title implies, Byrne’s work is an adaptation of Euclid’s Elements, but its novelty lies in its use of color to identify specific figures.  Consider, for instance, the following proof which Byrne offers in the book’s along with its parallel in the traditional rendering of Euclid to demonstrate the contrast between the two methods:

This example posited by Byrne emphasizes that his use of color was not employed “for the purpose of entertainment, or to amuse by certain combinations of tint and form,” but rather a didactic mechanism used specifically to simplify the learning of geometry by the naming of particular figures that are named by shape and color, instead of the abstract figures (e.g., triangle ABC) that are relied upon in traditional renderings of Euclid.  The Taschen reprint volume of Byrne’s work is accompanied in a sturdy clamshell case by a second, slimmer volume containing two essays on Byrne’s work (presented in three languages, English, German and French) by Werner Oechslin.   This supplemental volume’s second essay, entitled “To facilitate their acquirement,” is particularly helpful in setting Byrne’s work in an historical context.   Byrne’s treatment of Euclid was dismissed as a mere “curiousity” by his contemporary, the noted logician Augustus De Morgan.  Although, as Oechslin details, Byrne and De Morgan may have had a personal rivalry that reached back prior to the release of this work on geometry, it is not difficult to imagine why one of the first prominent modern logicians, who had a vested interest in the abstract processes at work in geometry, was so reviled by a work like that of Byrne, which intentionally sought to eliminate much of the abstraction in geometrical thought.   DeMorgan, indeed, would later articulate his advocacy for the abstract nature of logic: “[L]ogic is the only science which is admitted to have made no improvements in century after century, is the only one which has grown no symbols” (Oechslin 19).  Byrne’s work, in contrast, is refreshing precisely because it develops a geometry rooted in the particularity of specific symbols on the printed page, defined by color and shape.

Oechslin makes a strong case, however, for the importance of Byrne’s work, not within the history of mathematics, but rather within the history of art, as a predecessor to the work of Mondrian and the other artists of the De Stijl school of modern art.   And indeed Oechslin is correct that the work of both Byrne and Mondrian is not only strikingly similar in its visual appearance (relying upon basic geometrical shapes and primary colors), but also are rooted in similar philosophical soil, namely reflection upon the nature of abstraction and “how it forces itself into the visible world” (34).  However, it seems that despite these key visual and philosophic similarities, Byrne and Mondrian actually arrived in these similar realms of thought while moving in opposite directions: Byrne sought to reduce abstraction and forge a method of teaching geometry (and thereby describing space) that was rooted in specific empirical figures; Mondrian’s neo-plastic approach to art on the other hand intentionally reduced empirical forms to simple, abstract shapes and colors.

Although in our postmodern age, one might be skeptical of Byrne’s claims that his method of geometry would “assist the mind in its researches after truth,” it seems that Byrne’s work does offer, in its resistance to abstraction, a new way of thinking and talking about space that is rooted not in abstract ideal figures, but rather in particular empirical ones.  His work is not only a delightful masterpiece of printed work and a striking way to teach and learn geometry, but it gives us a glimmer of hope that we may one day recover distinctively local and particular ways of thinking of the spaces we inhabit.  Many thoughtful artists and poets have undoubtedly developed their own particular, localized languages, but Byrne’s work is significant in that it suggests that our hope of recovering localized ways of thinking and talking about space is not confined merely to the realm of the artistic.

Oliver Byrne’s The First Six Books of Euclid’s Elements is a lovely work, which not only teaches us geometry in a way that is pleasing to the eyes, but also in so doing plants a firm foot in resistance to abstraction and thereby gives us a glimmer of hope that we might recover distinctively local and particular ways of describing the spaces we inhabit.