Constructing the Universe Classroom

Geometer and educationalist Michael Schneider has started a range of classes for young and old at his place in San Anselmo, CA. He writes: "I prefer to facilitate learning by beginning with a youngster's own natural interests. Some interests are fluid, and others lead to ongoing projects in some depth. These classes are not 'tutoring' sessions for the usual school topics although they often involve the same skills used in the context of an investigation. Young people can learn to see and appreciate the excellence of nature and its patterns which teaches many valuable lessons. I approach each subject to promote wonder at the ordinary, the interconnectedness of knowledge and a love of learning in general." Go HERE for details.

Constructing the Universe Classroom

Geometer and educationalist Michael Schneider has started a range of classes for young and old at his place in San Anselmo, CA. He writes: "I prefer to facilitate learning by beginning with a youngster's own natural interests. Some interests are fluid, and others lead to ongoing projects in some depth. These classes are not 'tutoring' sessions for the usual school topics although they often involve the same skills used in the context of an investigation. Young people can learn to see and appreciate the excellence of nature and its patterns which teaches many valuable lessons. I approach each subject to promote wonder at the ordinary, the interconnectedness of knowledge and a love of learning in general." Go HERE for details.

The Pope on the Pavement

When Pope Benedict XVI visited the United Kingdom in September, one of the most striking images was of him sitting side by side with the Archbishop of Canterbury, trading polite speeches, on the Cosmati Pavement of Westminster Abbey. That pavement is worthy of some attention, especially if, like me, you are interested in the symbolic meaning of geometrial forms and their role in the great cathedrals of Christendom. (The following notes are abridged from the official website description. But PLEASE WATCH this excellent documentary about the pavement. Bear in mind that the image I have chosen is just a detail.)

The pavement was laid down in 1268 by order of King Henry III who had started re-building St Edward the Confessor’s Abbey in the new Gothic style in 1245. The workmen came from Rome, with a man called Odoricus at their head. It is 24 feet 10 inches (7 metres 58 centimetres) square, with dimensions calculated in Roman feet, and consists of geometrical patterns built up from pieces of stone of different colours and sizes cut into a variety of shapes: triangles, squares, circles, rectangles and many others. The basic layout is a four-fold symmetry, but in detail the variations are endless. No two roundels are the same. Of the four "orbiting" roundels one is circular, one hexagonal, one heptagonal and one octagonal. The infill patterns are all different.

The inscriptions that accompanied the design, now damaged, read in part: "If the reader wisely considers all that is laid down, he will find here the end of the primum mobile" and "The spherical globe here shows the archetypal macrocosm."

The round stone at the centre contains colours representing the four elements. It is on this stone that every king or queen of England was crowned.

The Pope on the Pavement

When Pope Benedict XVI visited the United Kingdom in September, one of the most striking images was of him sitting side by side with the Archbishop of Canterbury, trading polite speeches, on the Cosmati Pavement of Westminster Abbey. That pavement is worthy of some attention, especially if, like me, you are interested in the symbolic meaning of geometrial forms and their role in the great cathedrals of Christendom. (The following notes are abridged from the official website description. But PLEASE WATCH this excellent documentary about the pavement. Bear in mind that the image I have chosen is just a detail.)

The pavement was laid down in 1268 by order of King Henry III who had started re-building St Edward the Confessor’s Abbey in the new Gothic style in 1245. The workmen came from Rome, with a man called Odoricus at their head. It is 24 feet 10 inches (7 metres 58 centimetres) square, with dimensions calculated in Roman feet, and consists of geometrical patterns built up from pieces of stone of different colours and sizes cut into a variety of shapes: triangles, squares, circles, rectangles and many others. The basic layout is a four-fold symmetry, but in detail the variations are endless. No two roundels are the same. Of the four "orbiting" roundels one is circular, one hexagonal, one heptagonal and one octagonal. The infill patterns are all different.

The inscriptions that accompanied the design, now damaged, read in part: "If the reader wisely considers all that is laid down, he will find here the end of the primum mobile" and "The spherical globe here shows the archetypal macrocosm."

The round stone at the centre contains colours representing the four elements. It is on this stone that every king or queen of England was crowned.

How the World Is Made?

One of the topics in my book is so-called "sacred geometry". I didn't do it justice, of course. It need a lot more, and better, illustrations, but that wasn't an option at the time. So instead, as readers will know, I recommend the work of educator Michael Schneider. He seems to strike the right balance of enthusiasm and sanity, and his book is full of nice pictures and geometical constructions. Unfortunately, sacred geometry and number along with numerology and astrology have become a playground of the New Age. But while this should certainly engender caution, it should not put orthodox Christians off completely. These symbolic systems are part of the great Classical and Medieval civilization and were employed in the writing of Scripture and the building of the great cathedrals. We need to understand them better. The two great modern masters of the subject are Keith Critchlow (who teaches at the Prince's School of Traditional Arts) and John Michell. Shortly before he died, Michell completed How the World is Made, which is recommended by Michael Schneider. The book is illustrated by Michell with full colour images like these, and is published by Inner Traditions in the US and Thames and Hudson in the UK. I hope to review it in Second Spring, where I will try to say why I think the subject is important, even though I have to attach a strong warning, because it is mixed together (as you will see in Michell's book) with a lot of eccentricity and downright anti-Catholic prejudice.

How the World Is Made?

One of the topics in my book is so-called "sacred geometry". I didn't do it justice, of course. It need a lot more, and better, illustrations, but that wasn't an option at the time. So instead, as readers will know, I recommend the work of educator Michael Schneider. He seems to strike the right balance of enthusiasm and sanity, and his book is full of nice pictures and geometical constructions. Unfortunately, sacred geometry and number along with numerology and astrology have become a playground of the New Age. But while this should certainly engender caution, it should not put orthodox Christians off completely. These symbolic systems are part of the great Classical and Medieval civilization and were employed in the writing of Scripture and the building of the great cathedrals. We need to understand them better. The two great modern masters of the subject are Keith Critchlow (who teaches at the Prince's School of Traditional Arts) and John Michell. Shortly before he died, Michell completed How the World is Made, which is recommended by Michael Schneider. The book is illustrated by Michell with full colour images like these, and is published by Inner Traditions in the US and Thames and Hudson in the UK. I hope to review it in Second Spring, where I will try to say why I think the subject is important, even though I have to attach a strong warning, because it is mixed together (as you will see in Michell's book) with a lot of eccentricity and downright anti-Catholic prejudice.

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.

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.