Archives For Mathematics


“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:

Continue Reading…


Our favorite music critic Andy Whitman
reviews U2’s new album NO LINE ON THE HORIZON

“Time is irrelevant, it’s not linear,” Bono proclaims near the beginning of No Line on the Horizon (4 stars), U2’s 12th studio album, which releases March 3 but is already posted on the band’s MySpace page. When you’ve spent 30 years in the circus, are well into middle age, and are still working the territory most commonly associated with preening 20-year-olds, it’s a reasonable stance to take. Fittingly, it’s a preoccupation Bono circles back to again and again, and it results in the band’s most thematically rich album in a storied career.

Read the full review:


Release Date: 3 March 2009
Buy now:  [ Amazon ]

THE OTHER JOURNAL reviews Katie Ford’s
new book of poems COLOSSEUM.

When the lights go down in Colosseum, Katie Ford’s second collection of poetry, we find ourselves in the poet’s cranial theater, an old-fashioned movie palace of flickering reels and irregular splicing. It is here that the book’s preoccupation unfolds: a remembering of New Orleans during and after Hurricane Katrina. And it’s here that the memory landscape shifts from history book to watercolor dream cycle, nightmarish in its images and vagaries. Showing a deft sense of humor, or perhaps just irony, Ford includes a poem about the late great New Orleans movie theater lost to fire months after the hurricane, the “Coliseum Theatre”—it is, of course, an elegy.

To say the poems in Colosseum record anxiety, trauma, and a stunned sense of coping might belittle Ford’s surprising chemistry in mixing the loss of New Orleans with the destruction and devastation of the classical world. At first it might seem that the thematic thread is a project, and arbitrary—why Rome? Why not Rhodes? Only after reading and re-reading Colosseum did I see Ford’s book as an attempt to honor New Orleans by placing its destruction into the tradition of the great dead: Athens, Rome, Carthage, Alexandria. Is Ford’s point that every vanquished city is worthy of such high simile, or is it just New Orleans? Feeling runs so high in this collection that I must admit that reading it put me in mind of testimonies from Vietnam War veterans

Read the full review:

Katie Ford.

Paperback: Graywolf Press, 2008.
Buy now: [ Doulos Christou Books $12 ] [ Amazon ]


If you’ve ever read Leopold’s A Sand County Almanac, finding it hard to put down, then Nature’s Second Chance is your chance to witness the ecological wonder as Steven Apfelbaum transforms his tired farmstead once used to grow corn crops into a Midwestern paradise: a biologically diverse and healthy prairie, with wetland, forest and spring brook. Leopold’s writings culminated in the land ethic philosophy. Nature’s Second Chance puts it into practice, not only at Apfelbaum’s eighty acre Stone Prairie Farm over a period of thirty years, but at the Prairie Crossing “conservation development” north of Chicago and, perhaps, in a community near you though projects spearheaded by the now internationally-acclaimed, multimillion dollar ecological restoration business, Applied Ecological Services.

Writes Apfelbaum: “I envisioned a network of restored lands that would reconnect dispersed and isolated habitats. This may be viewed as an ecological systems approach to rethinking the landscape or a community land ethic where the health of the land — not just of individually owned parcels — is a measure of land community vitality.”

This highly readable treatise on a more ecologically mindful approach to living on the land provides both enlightening anecdotes and descriptive policy changes needed that will allow us to restore the health of diverse ecological systems on which our own very survival is based. Through his work both at Prairie Stone Farm and with Applied Ecological Services, Apfelbaum rekindles the spirit of service to all of creation, with humans, themselves, playing the central role in nurturing the renewal work so crucial in this Century and in the emerging restoration economy.

Read the full review:

Steven Apfelbaum.

Hardcover: Beacon, 2009.
Buy now: [ Doulos Christou Books $21 ] [ Amazon ]


As explained by Livio, the history of mathematics is partly a struggle between these points of view: that math is how God (or nature) organizes the world, or it is simply a human tool to understand that world.

Livio comes down in the middle, contending that math may well be both invented and discovered. He points, for instance, to the eternal truth contained in the geometry formulated by Euclid 2,400 years ago. By the 19th century, however, iconoclasts had posited and established a whole new world of non-Euclidian geometry. Livio writes about the symmetries of the universe: the immutable, if incompletely understood, laws of math and physics that make a hydrogen atom, for instance, behave in the same way on Earth as it acts 10 billion light years away. Another sign of universal structure, as teased apart with the help of math? No, Livio writes, it is more likely a sign that “to some extent, scientists have selected what problems to work on based on those problems being amenable to a mathematical treatment.”

The author acknowledges that some readers will find his inconclusive conclusion to be unsatisfying. I didn’t. Sometimes the adventure, the intellectual ride, is more important than the final destination.
Read the full review:

Mario Livio.

Hardcover: Simon and Schuster, 2009.
Buy now:  [ Doulos Christou Books $21 ] [ Amazon ]