Euclid lived around 300 bC and published his Elementa (Gr. Stoicheia) as an overview of a specific kind of mathematical knowledge dating back to the Babylonian, Egyptian and earlier Greek thinkers as Thales and Pythagoras. Although it could be called a ‘state of the art’ at the time it was published, it remained intellectually the dominant approach until the later part of the 19th century – and in everyday didactics it is still dominant. The way his work was and is kept is a good example of a codification of a certain approach, almost a cultural monopoly.

The relation with bodily movement can be seen throughout history in the geometrical design of disciplinary organizations of human bodies and their movements, beginning in the earliest monasteries, later in armies and social institutions such as homes for the poor, orphanages and schools. This aimed primarily at becoming disciplined into a well functioning member/ part of a group-body.

The Euclidian approach has been develop into mechanics by Archimedes from Syracuse (280-212 bC) who studied with followers of Euclid in Alexandria but developed into a more original worker. Not only did he invent the integral calculus, but he also experimented constantly and is widely remembered because of his many discoveries and practically oriented physical ‘laws’. He ran out of his bathtub, naked through the streets of Syracuse, shouting ‘Eureka’ (‘I have found it’) after he had discovered what has been called ‘The law of Archimedes’, while taking a bath. He also began to discover the specific weight of distinct metals and was an inventor of many practical devices (such as the screw of Archimedes), the compound pulley and war-machines that helped to ward of the Roman attack on Syracuse for three years, until they captured Syracuse and killed him.

There are some interesting examples of how movement is forcefully generated by arrangement of points and lines: the screw of Archimedes (which is still used for irrigation) turns in a straight line around one point.

Archimedes also formulated his version of “The law of the Lever’, trying to explain how the lever worked, something which had been debated already for centuries. To underline the power of the lever he exclaimed (there are some versions of this) “Give me one firm spot and I will move the earth!” This nice picture can be seen as a paradox which actually confronts us with our incapacity to move the world, as we can only live from within it. Understood in that sense we can laugh about it; it becomes a metaphysical cartoon.

 

But this idea of a ‘one point’ or ‘Archimedical point’ has been quite important in the search for a way to try to rise above the world and dominate it. It was the conviction of Decartes to have found such a solid foundation {"Archimède, pour tirer le globe terrestre de sa place et le transporter en un autre lieu, ne demandait rien qu'un point qui fût fixe et assuré. Ainsi j'aurai droit de concevoir de hautes espérances si je suis assez heureux pour trouver seulement une chose qui soit certaine et indubitable”. (From his Second Meditation in the Méditations métaphysiques - 1641)}

There is a wall painting (from around 1600) in the Mathematics room of the Uffizi Gallery in Florence, where this metaphysical–technical idea is portrayed in an angelical sentimental way, which has often been the way to convey ‘absolute truths’ to the people. This image of control over the world fits well in the Jewish tradition of a God creating the universe, the earth or nature; a traditon which was continued in (an indequate self-understanding of) the natural sciences in their program of control over nature, as rational (more perfect) re-creation. This features presently especially in the public’s expectations of genetical technologies. The Greeks with their polytheism – the many gods representing forces of nature and thus presupposing nature, acting from within the world, represent at this point a more interesting tradition than the Jewish root of European civilization which harmonized well with pragmatic power orientation of the Roman Empire, extended into the Roman Catholic church.

Together, Euclid and Archimede, or how their work has been received through the centuries, are representative of some dominant traits of our culture. The first represents a philosophical stagnation (especially regarding the meaning of geometry for understanding life & world) of some thousands of years, the second an instrumental creativity within that horizon of stagnation. Together they are symbols of an activist culture which reflects too little about its goals, turns around its own axis, produces more – and now too much - of the same.

Jan Baars