Research into the formative forces of living organisms from mathematical , geometrical, and even musical perspectives has been published by Anthroposophical authors.
‘Natura e scritta lingua mathematica‘ Nature is written in the language of Mathematics: Galileo.
‘Becoming aware of the Idea in reality is the true communion of mankind.’ Steiner
The Section for Mathematics and Astronomy
This section supports and encourages original perspectives and imaginative approaches to Geometry, Mathematics and Astronomy. It is partly guided by indications for research in the works or Rudolf Steiner and in Anthroposophy as it has developed as a whole. It strives to build bridges between current thinking in these realms and the spiritual understanding arising in Anthroposophy .
A course of lectures on Astronomy was given by Rudolf Steiner in 1921 (GA323) which sets out research strategies for developing Astronomy and Cosmology. Here and in the other scientific lecture courses ( GA 320 321 322 324 326) Steiner indicates the kind of mathematics which will be needed in developing new forms of cosmology, and to grasp the concept of metamorphosis in biology.
For example, it is suggested to trace the real astronomical movements, rather than merely picture images of relative motion, through the observation of the forms of living organisms that have evolved on the Earth. We recognise the good work done in this field over the last century by Lily Kolisko , George Adams , Lawrence Edwards, Olive Whicher and Ernst Michael Kranich to name a few.
Growth measure and the polar vortices. Based on the work of Lawrence Edwards who pioneered a geometrical approach to the flexible forms of tree buds and other organic forms. ( source Wikipedia Article on Projective Geometry )
Projective Geometry, a modern and more comprehensive form of geometry, has been taken up by several Anthroposophists notably George Adams , Lawrence Edwards and Nick Thomas. The flexible imaginative way of looking at space, the picturing of infinity within the infinitesimal as well at the periphery of space , have been fruitful for pioneering attempts to overcome philosophical materialism in Physics Chemistry and Biology.
The value of mathematical and geometrical contemplation is not only for its application in scientific fields but can also support a path of spiritual development for example by enabling mobile and pictorial thinking . The Anthroposophical path begins with the observation of thinking, and pure mathematical thinking, without reference to any outer perceptible content is ideally suited for the self-observation of thinking which can begin the path to Anthroposophy.
Mathematics Education is also part of the Section research tasks. An approach to numbers through the division of unity rather than the summing of units, leads to a qualitative appreciation of mathematics to balance the merely quantitative. It is important for children to grow up with a grasp of the deeper significance of mathematics in the spiritual and cultural life of humanity. The state school geometry curriculum in England is an emaciated fragment of Euclidean Geometry and as such has not even begun to approach the new forms of thought that have arisen in the past few hundred years.
‘Anyone who trains himself to see numbers as divisions and parts of one and the same whole, develops in him a basic social feeling. The effect of number as it extends into the moral-ethical realm is of special concern to the teacher and educator. The way numbers are dealt with is not a matter of indifference to the child’s whole development.‘
Bindel: The Spiritual Nature of Numbers Reflected in The Cultural Ages of Humanity.
In the realm of pure mathematics, the stimulus for an Anthroposophical approach is neatly expressed by the Mathematician Felix Klein ( 1849-1925) :
‘With regard to the concept of number, the deepest root is extremely hard to uncover. …A very prevalent view maintains that the concept of number is closely bound up with the concept of time, of temporal sequence. Its representatives are Kant among the philosophers and Hamilton among the mathematicians. Others believe that number has more to do with spatial beholding; they explain number in terms of the simultaneous seeing of various objects in proximity to one another. Finally a third tendency sees in our ideas of number the expression of a special mental/spiritual capacity which stands independently, parallel to, or even above the beholding of space and time. I think that this view is well characterised if with Minkowski one applies to numbers the quote from Faust: Goddesses are enthroned in solitude sublime; around them is no Space and even less of Time. ‘
Felix Klein: Elementary Mathematics from a Higher Standpoint.
There are several groups active in Britain active in studying projective geometry. There is a sacred geometry group developing artistic work from geometry, and a group working for a revival of the Seven Liberal Arts . In a modern context these seven could be called Liberating Arts as their practice and cultivation was always understood to be necessary for the development of free human beings . The four liberating arts comprising what was known as the Quadrivium are Mathematics, Geometry, Astronomy and Music.
The Science Group of the Anthroposophical Society in Great Britain publishes articles and advertises research events also in Mathematics and Astronomy .
The Mathematical Astronomocal Section at the Goetheanum:
A web site created by Nick Thomas a prominent researcher into applications of projective geometry in science:
https://nct.goetheanum.org/volatile.htm
Representation of the apparent motion of the Sun, Mercury, and Venus from the earth by Cassini .Taken from the ‘Astronomy’ article in the Encyclopaedia Britannica (1st Edition, 1771; facsimile reprint 1971). This geocentric diagram shows, from the location of the earth, the sun’s apparent annual orbit, the orbit of Mercury for 7 years, and the orbit of Venus for 8 years, after which Venus returns to almost the same apparent position in relation to the earth and sun. Relative movement views of the planetary orbits have kindled some interest in diverse research fields in recent years. Relative Movement could also be called movement as a relationship.
For further details please contact the Section Coordinator :
Alexander Murrell: alexandermurrell@hotmail.com
