I can't help myself. I have never ever been on for blowing my own trumpet.
Einstein had a deep interest in philosophy. ‘Science without epistemology,’ he wrote, ‘is – in so far as it is thinkable at all – primitive and muddled.’ In explaining his own philosophy of science, he used the phrase ‘free creations of the human mind’ on several occasions. The first seems to have been in ‘Geometry and Experience’, a public lecture he delivered in 1921 at the Prussian Academy of Sciences. In it, he addresses the question of whether mathematics, whose truths are absolutely certain and indisputable, can furnish us with knowledge about the world. His answer, in brief, is that ‘in so far as the laws of mathematics refer to reality, they are not certain, and in so far as they are certain, they do not refer to reality.’ In this spirit, he distinguishes ‘axiomatic geometry’, such as the system outlined in Euclid’s Elements, from ‘practical geometry’, which supplements such systems with ‘real objects of experience’. The axioms are free creations of the human mind, and in axiomatic geometry the words ‘point’, ‘straight line’ and so on stand only for empty conceptual schemata; what gives them substance lies outside mathematics. When these conceptual schemata are supplemented by objects of experience, the geometry that results, ‘practical geometry’, is ‘evidently a natural science; we may, in fact, regard it as the most ancient branch of physics.’ That the theorems of Euclidean geometry follow from its axioms is certain and indisputable, but the question of whether the practical geometry of the universe is Euclidean or not can only be answered by experience. Without this view of geometry, Einstein told his audience in Berlin, ‘I would have been unable to formulate the theory of relativity.’ If we are to understand the world of experience, he added, ‘we must abandon Euclidean geometry,’ and being able to do so depends on its axioms’ being ‘free creations of the human mind’.
IN THERE LIES OUR FUTURE. IN THERE LIES OUR DESTINY
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