Euclid and Whitehead: Found Poem

February 5, 2016

Thanks to Alissa Simon, HMU Tutor, for today's post.

A colleague suggested that I re-read Euclid as if his definitions were a poem. Considering I study poetry often, this sounded like a fun exercise. I was unprepared, however, for the depth of insight that followed. I already discussed how important it was for Euclid to be both precise and abstract, but I did not realize how truly applicable this revelation was. Euclid's Elements contain nearly every characteristic of poetry: precise, concise, abstract, yet specific, and most of all, endlessly interconnected. From that exercise, I decided to arrange a few of the passages into a found poem. (A found poem basically takes words and phrases of others and connects them in a poetic format.) The following poem combines words from both Euclid (in italics) and Alfred North Whitehead. Enjoy!

Our Inaccurate Laws


[T]he first noticeable fact

about arithmetic

is that it applies

to everything

to tastes and to sounds

to apples and to angels

to the ideas of the mind and

to the bones of the body


A point is that which has


but not dimension


The nature of things is perfectly



A line is length

without breadth


In a mountainous country distances are often reckoned

in hours


A line which lies evenly between its

extreme points

is called

a straight line


To see what is general in

what is particular

and what is permanent in

what is transitory is

the aim of scientific thought


Any combination of points, of lines, or of points and lines

in a plane

is called a plane figure.


any number x which is greater than 1

gives x + 2 > 3

there are an infinite number of numbers

which answer to the some number

in this case



The vital point

in the application of mathematical formulae is

to have clear ideas and

a correct estimate of their relevance to

the phenomena under observation.


our inaccurate laws may be                   good enough


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Euclidean Utopia

December 25, 2015

Today, the day that celebrates the birth of Jesus, presents the perfect opportunity to continue our discussion of utopia. To catch up on past conversations, visit the last blog posts about Utopia here: (Universal Spirit and Utopia  or Imperfect Ideal ).

Looking for Paradise”, a song by Alejandro Sanz and Alicia Keys, grounds today's discussion. Feel free to listen while reading: Sanz sings: “Estoy buscando ese momento....Todo el mundo va buscando ese lugar...Looking for Paradise”. (“I'm looking for that moment...The whole world is looking for that place...Looking for Paradise”). A single soul looking for paradise in both a single moment and single location.

Any discussion of utopia must begin from a focal point: an individual, for example. Some form of context allows us to navigate both time and space, which otherwise appears fluid. Reason creates an association to both time and space in chronological terms: in terms of past and present and future. Therefore, our sense of space is also chronological. Is there an alternative way to structure our society? Alfred Kroeber suggests that “[s]ince the day of the Roman empire and the Christian church, we hardly think of a social activity except as it is coherently organized into a definite unit definitely subdivided.”

Image ID: 60608956 Copyright: Mikhail Pogosov.

Image ID: 60608956 Copyright: Mikhail Pogosov.

Time is unavoidable. It allows for communication, structure and plan. It also allows us to think. There are certain, marginalized (and not well-understood) societies that speak in a language of perpetual present tense. Much like their lives, they do not discuss the future, and only abstractly narrate the past. Their past often involves deities, but not familial or ancestral members. These societies have structured their lives in a way different than mainstream societies. Language offers evidence of this structure, which reinforces the premise that we function in a pre-existing worldview, though we may not be aware of it. So, our solidly structured lexicon of past-present-future might actually hinder our engagement with an idea like utopia. We say utopia and simultaneously imply future utopia without even realizing it.

The I Ching states that “[a]ny journey is ruled by the twin houses of mystery and discovery.” But nowhere in there does it mention structure. Mystery, discovery, freedom: these are ideas opposed to structure. They function and regenerate in a world if not separate from, certainly opposed to, structure. We build a certain skill level, a certain art, when attempting to navigate either the completely new and foreign as well as a known and quantified social structure. Yet, we do create meaning from new environments by linking a new idea to an old, by assimilating characteristics and grouping like things together. In the Introduction to Euclid's Elements, he states, “Thus it is the province of Geometry to investigate the properties of solids, of surfaces, and of the figures described on surfaces.” So, if the figure we desire to define is utopia, then the path towards creation runs not through figures, but through events, through the most horrible and the most brilliant times of human history. These events have historically been the barometer of utopia.

Image: 46829242 Copyright: Onur ERSIN.

Image: 46829242 Copyright: Onur ERSIN.

In the article, “A Non-Euclidean View of California as a Cold Place to Be”, Ursula Le Guin, however, suggests that our current situation is our utopia. She says that we might not recognize it, but in searching for some linear, contract-bound society, we aim incorrectly. Instead, she suggests something like “perservering in one's existence as a completely worthy social goal”. It is interesting to note the proposition that the pursuit of self leads to a utopian society. The interplay of individual and society is important, and this quote asks us to look back at Kroeber's quote from the beginning...the map of social subdivisions as they emanate from ancient times. Instead of mapping new terrain, Le Guin asserts our right to celebrate the existence that we have, the pre-existing pathways inside each one of us that leads to something great.

In this theory, there are a frightening number of unknowns and perhaps a sad realization that utopia is not filled with chocolate and luxury. But as we discussed in previous blogs about utopia, the impossibility of creating hard and fast categories for every scenario, of defining happiness for a multitude of individuals, is everpresent. Perhaps utopia is singular, but enjoyed collectively. Perhaps it is this single moment (by which I mean any moment, not necessarily a holiday) spent in celebration of something we cannot quite comprehend. Through participation, we can and do enjoy. “Estoy buscando ese momento ... Todo el mundo va buscando ese lugar..."

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