Reconnect with nature

The word “ecology” was coined only as recently as 1873, by the German zoologist Ernst Haeckel. He based it on the Greek word oikos meaning “house, dwelling place, habitation” (plus, of course, logos). But though the scientific study of ecology, referring to the complex inter-relationships of biological entities with each other and with their environment, is a modern development, the traditional worldview has a great deal to say on the matter. The medievals did not possess posters showing the fragile earth floating in a dark sea of space, but they were deeply aware of the inter-relatedness of the natural world, and of man as the focus or nexus of that world, which they expressed in the doctrine of correspondences. It was, of course, more poetic than scientific in its formulation, but it expressed a profound insight that remains valid, and the present ecological crisis could only have developed in a world that has forgotten it, or forgotten to live by it. The cosmological principles underlying the quadrivium, even today, can help us learn to dwell more wisely in our common home.

James S. Taylor’s Poetic Knowledge: The Recovery of Education encapsulates the wisdom of the Integrated Humanities Program taught at the University of Kansas in the 1970s and 80s. Taylor writes, for example:

“The implications for education, especially for learning in the poetic mode, as a result of the Cartesian revolution should not be difficult to trace since modern education is dominated, in one way or another, by its influence. Any school of philosophy that claims that one particular science (mathematics and scientific method in the case of Descartes and his followers) must be applied to all other subjects of knowledge, will impose a formal rigor upon the entire curriculum, eliminating even the contemplative nature of mathematics and science. Sooner or later, it is all reduced to ‘facts.’ This approach bypasses the contemplative nature of knowledge, leaving the student disconnected from his nature and the nature out there.”

It is not Taylor’s conviction – and it is certainly not that of Beauty for Truth's Sake – that we can or should do without “rigor” in science or in education; just that we must keep things in right proportion. Contemplative, or poetic, or intuitive ways of knowing can give profound insights into reality. Any education that fails to integrate such knowledge is liable (as most of our schools demonstrate) to produce men and women alienated from their own full humanity and from nature itself.

Sacred geometry

The vesica piscis is one of the most important figures in sacred geometry, and symbolically speaking an image of the source of life. It may best be described as a lens shape formed by intersection of two circles with the same radius, intersecting in such a way that the center of each circle lies on the circumference of the other. The name in Latin means the bladder of the fish. The shape is also called, somewhat more poetically, mandorla ("almond" in Italian).

The Mandorla halo, often seen in religious art enclosing Christ or his Mother, is also often taken to represent the womb, and to have been associated with the power of giving birth, since it was used to generate many other numbers and forms, beginning with three and four, the triangle and the square. In Christian art, the area where the two circles overlap may be taken to represent the Incarnation, the beginning of the union of divine and human natures.

The figure was the subject of intense mystical speculation among the Pythagoreans and their successors. The mathematical ratio of its width to its height is the square root of 3, the ratio 265:153 being the best possible approximation to this square root using small whole numbers. As a result the number 153 was sometimes called “the number of the fish”. It is probably no coincidence that the number 153 also appears in the Gospel of John (21:11) as the number of fish Jesus caused to be caught miraculously after his resurrection. The writer of the Gospel would hardly have recorded the number if it had not been believed to be highly significant, and its occurrence is suggestive of a Pythagorean or Platonist influence.

But why as a Catholic do I speak of “sacred geometry”, a term so associated with the New Age movement? I believe that, as the Pope says in The Spirit of the Liturgy, the “mathematics of the universe… comes from the Logos, in whom, so to speak, the archetypes of the world’s order are contained.” And I agree with Michael S. Schneider that children miss out if they are exposed to numbers merely as quantities instead of qualities, each with a distinct character, connected with all others in endlessly fascinating patterns. Such patterns can awaken us to a world of wonder and beauty, and point to the underlying harmony between science, art, and religion.

As you might see from the Comments, Charlotte Ostermann and others are adapting some of these ideas for Catholic homseschoolers. If you are interested to find out more, add a comment of your own, or get in touch directly. In the sidebar you'll find a section where I plan to collect useful ideas for what to do with younger kids to get them interested in all this - not just in geometry, but in the whole process of learning and the development of a vision of how everything connects together.