|A half-mile hike through the woods|
|Looking for fossils|
|That thin blue line on the horizon is Maryland|
|From the observation tower at the edge of the woods|
|Archangel Michael Trampling the Devil Underfoot|
Simon Ushakov (1676)
Fæder ure þu þe eart on heofonum
si þin nama gehalgod
tobecume þin rice
gewurþe þin willa
on eorðan swa swa on heofonum
urne gedæghwamlican hlaf syle us to dæg
and forgyf us ure gyltas
swa swa we forgyfað urum gyltendum
and ne gelæd þu us on costnunge
ac alys us of yfele.
|The Poetry shelf, which contains maybe 2/3 of my collection|
There's more in the school room, and in my bedroom,
and on the table by my rocking chair, and . . .
|The bees love it|
The assumption of this system of education was that by learning to understand the harmonies of the cosmos, our minds would be raised toward God, in whom we could find the unity from which all these harmonies derive: Dante’s “love that moves the sun and the other stars.” Thus the quadrivium would prepare the ground for the study of the highest contemplative sciences: philosophy and theology.
The idea that the cosmos is built on mathematical harmonies, and that numbers themselves can be a path to God, flowed from Pythagoras and Plato down to the Middle Ages, where it influenced the cathedral builders and later the artists of the Italian Renaissance. It was also one of the essential factors in the birth of science . . . .
“Numbers are a map of the beautiful order of the universe, the plan by which the divine Architect transformed undifferentiated Chaos into orderly Cosmos. Cultures didn’t necessarily learn this from each other but only had to look at numbers and their relationships to see how they revealed harmonious models which are the same everywhere and at all times [quoting Michael S. Schneider in Constructing the Cosmological Circle].”
Yet our present education trends to eliminate the contemplative or qualitative dimension of mathematics altogether, reducing everything to sheer quantity. Mathematics is regarded as a form of logical notation, a mental tool with no relation to truth except the fact that it assists us in manipulating the world. This elimination of the symbolic dimension of mathematics is largely responsible for the divorce of science from religion, and art from science.
|Rose Window, Chartres|
image via Wikipedia (cropped)
The Pythagorean-Platonic tradition at the core of the Liberal Arts developed the following symbolic associations with the natural numbers:
The Unity of being, transcending all that exists. It is often represented by a circle, or else by a point. One is the number that when “squared,” i.e., multiplied by itself, produces itself. Symbolically, One is not the first in a series of numbers, but the number-beyond-number that includes all others, equivalent in that sense to the modern conception of infinity . . . .
If one is the source and archetype of Unity, two is the beginning of Diversity. It represents polarity and division, and also feminine receptivity and fruitfulness. In a Christian context it often signifies the separation of matter and spirit. Duality can also symbolize the beginning of the process of creation, which in the book of Genesis is described as taking place through a series of separations or polarizations (heavens and earth, light and dark, etc.). The division of Adam’s unity into duality gave us male and female . . . .
In nature there is no zero. Some writers on number symbolism therefore regard it as an interloper, whose introduction as a placeholder led to the loss of awareness of the symbolic properties of number, and especially of Unity (displacing it from its position at the beginning of the number series), creating a framework for the development of atheism . . . .
Personally, I am not so sure. Zero could also be taken as the ground of being, and a symbol for the return to one. Perhaps the mistake lay not in introducing zero, but failing to read it symbolically.
|My high score just before leaving town in July, which I have not been able to top since. |
This is driving me crazy.
|So tiny and beautiful|