A Short Course on Projective Geometric Algebra
held in English by Russell Arnold & Charlie Gunn
This course develops geometric algebra as it originated in Clifford’s time, within projective geometry, hence the name “projective geometric algebra (PGA)”. The key ingredient is the Cayley-Klein construction (1859), creating metric spaces within projective space by specialising the cross ratio with respect to a chosen polarity, called the Absolute.
Recent developments in the 21st century extending PGA to Euclidean space involved building space out of planes rather than points. These were made possible by PGA’s natural “double algebra” approach. PGA provides a unified structure integrating space and counterspace. In this context, the course will study George Adams’ interest in geometric algebra as expressed in “Letter to Olive Whicher”.
The course will present PGA in 1, 2, and 3 dimensions, with exercise sessions, and text study centered on the relation of geometry and algebra. Students should have some experience with university-level mathematics, and be on good terms with projective geometry.
The detailed program can be found HERE. Please register by 01 October 2024 via https://goetheanum.ch/en/events/PGA.
Paper on Bud Research
In the framework of the research project Rhythmical Change of Shape in Mistletoe Berries According to Moon and Zodiac Constellations by Renatus Derbidge at the Natural Science Section of the Goetheanum a first paper was published in the open access journal PLOS ONE. It presents methods and software to capture and measure the shape changes of mistletoe berries and leaf buds over time. The paper describes the software used to automatize a number of tasks including contour recognition, optimization of fitting the contour via hill-climbing, derivation of the path curves, computation of Lambda and blinding the pictures for the operator. The validity of the program is demonstrated by results from three independent measurements showing circadian rhythm in mistletoe berries. The program is available as open source and will be applied in a project to analyze the chronobiology of shape in mistletoe berries and the buds of their host trees.
Coauthors of the paper are Linus Feiten (Faculty of Engineering, Chair of Computer Architecture, University of Freiburg, Freiburg, Germany), Oliver Conradt (Section for Mathematics and Astronomy, Goetheanum, Dornach, Switzerland), Peter Heusser (Centre for Integrative Medicine, University of Witten/Herdecke, Witten, Germany) und Stephan Baumgartner (Hiscia Institute, Society for Cancer Research, Arlesheim, Switzerland).