Help in teaching math

I have come across a number of books and websites that math teachers may find helpful - or, come to that, teachers of other subjects who want to build bridges for their students to the mathematical aspects of their own topics. There are the classics, such as Constance Reid's From Zero to Infinity: What Makes Numbers Interesting, and H.E. Huntley's The Divine Proportion: A Study in Mathematical Beauty. Several others are mentioned in my bibliography, including Michael S. Schneider's and Clifford A. Pickover's. These books are full of exercises, drawings, puzzles and anecdotes. One book that isn't in my Bibliography because I only just heard about it is Alex's Adventures in Numberland, by Alex Bellos, but it looks fun. Another is 50 Mathematical Ideas You Really Need to Know by Tony Crilly - highly recommended by several readers.

Everything connects

In practical terms, what can a university do to encourage the sense that "everything connects", that the individual disciplines concern aspects of a "whole", that the meaning of those disciplines depends on that which transcends them? In many cases it is not possible to redesign the curriculum. Nevertheless, it must be possible to do things within existing structures that will move things gradually in the right direction. We spoke, for example, of the importance of allowing opportunities for students to acquire first-hand experience of nature, whether through gardening or field trips, and also of other cultures

Transmodernism

Are we being modern, postmodern or premodern when we seek to recover and integrate the "lost wisdom" of the ancient world within the contemporary university? In discussing the point among the faculty of the University of St Thomas in Houston after the Earth Day lecture recently, we came up with the term "transmodern". It contains echoes of the "transcendent", and the prefix trans- suggests we are looking "across" the modern world, as well as beyond it, to find the elements of our synthesis. The goal is not to impose a Catholic or theological vision on all the disciplines, but to foster a deeper conversation within and between disciplines against a theological "horizon". That is, theology serves as a placeholder for the truth that lies beyond all of us.

We need in each case to seek within our own discipline for the direction in which truth lies, even if we never lay hold of it entirely. To give up the search or aspiration for truth would be to abdicate our reason. As McIntyre argues in God, Philosophy, Universities, there has to be the "conception of a whole to which each discipline contributes as a part" and towards which it is reaching by its own methods. It is in the search that we will find some convergence with other disciplines, or some opening towards them, some basis for conversation. And it is when we assume that we have attained all important truth within our own field, or alternatively when we have decided that truth is unobtainable, that we become closed off to one another. At that point the university (like the universe) fragments into a myriad shards.

Once again I want to recommend the Pope's lecture to La Sapienza University, before talking next time about some practicalities that came up during our discussion in Houston.

A veiled presence

While in Houston I took the opportunity to visit the Rothko Chapel right across the road from the Byzantine Fresco Chapel Museum, near the University of St Thomas and the Menil Gallery. Both chapels use modern materials to create an appropriate space to serve the art within. The Byzantine frescoes from the Church of Cyprus show Christ Pantokrator and the Blessed Virgin, with angels.They are displayed in a glass chapel at the heart of the structure and evoke a sense of the sacred in the traditional manner of sacred art. The Rothko Chapel is equally effective in a very

Creation and the University

I am currently in Houston to give the Earth Day Lecture at the University of St Thomas. I want to thank the staff, faculty and students, Sister Damien Savino FSE, the John Paul II Forum, and the Basilian fathers, for being so kind and gracious to me. Our discussions around the lecture focused largely on the question of how to implement the educational approach that my book tries to introduce and explore, and I hope to report more on these discussions in the weeks to come. One place where an approach like this is already being tried very successfully is Thomas More College in NH, where David Clayton has developed a "Way of Beauty" programme within the main curriculum of the College - this can be viewed here (make sure to follow the link from the main curriculum page to the Way of Beauty). David has also started an excellent Blog that you will enjoy.

My lecture was partly about the problems caused by specialization. Our knowledge has increased exponentially, yet as knowers we are increasingly fragmented. We seem to know more and more about less and less. But what is still possible for each of us to discover is how everything connects together. We might not know anything except our own field in great detail, but we can put a broken world back together, and that is the task of the new educators.  The role of philosophy is especially important in this, as John Paul II emphasized in Fides et Ratio, and Pope Benedict also explained in his wonderful lecture for La Sapienza University in 2008 about the university, the liberal arts, and the search for truth and wisdom.

The transcript of the Lecture plus ongoing discussion of the book and the visit from John Hittinger's JPII Forum blog can be found here, here, here and here.

Cosmology of the Sacraments

Sandro Magister's excellent website has reproduced one of the Pope's Easter homilies where he talks of the symbolism of the four sacramental elements (which correspond I suppose to the ancient "natural" elements of water, earth, fire and air). The Pope goes on to develop the link between oil and the priesthood. The whole thing is fascinating. Here is an extract:

There are four elements in creation on which the world of sacraments is built: water, bread, wine and olive oil. Water, as the basic element and fundamental condition of all life, is the essential sign of the act in which, through baptism, we become Christians and are born to new life. While water is the vital element everywhere, and thus represents the shared access of all people to rebirth as Christians, the other three elements belong to the culture of the Mediterranean region. In other words, they point towards the concrete historical environment in which Christianity emerged. God acted in a clearly defined place on the earth, he truly made history with men. On the one hand, these three elements are gifts of creation, and on the other, they also indicate the locality of the history of God with us. They are a synthesis between creation and history: gifts of God that always connect us to those parts of the world where God chose to act with us in historical time, where he chose to become one of us.

 Photo of Port Meadow by Rosie Caldecott

Beauty on the Cross

For Christians, the place to look for answers to all the important questions is the Cross of Christ.  In that Cross, read in the light of faith and tradition, we can find the keys to unlock the doors of the world.  And what we see there is not a distant world of Platonic archetypes, but the Archetype of archetypes wedded to the world, and allowing itself to be crushed by the world in order to transform it.

The figure on the Cross, covered in blood and spittle, has been made repulsive by torment. What we see, nevertheless, is the supreme work of art. We see a divine act that takes existing matter, the matter of history and prophecy, and weaves it into a new design, a fulfilment that could not have been expected or predicted but, seen by those who have the eyes and ears for it, is perfect, as though no stroke of the pen, no flick of paint, no note or chord, could be changed without diminishment. We see on the Cross an image that transforms the way we view the world. The Passion of Christ the Logos changes the world and remakes it, creating something new of it, bringing life out of death.

This is an extract from Beauty for Truth's Sake.  
The image is borrowed from Vultus Christi.