Proportion: Science, Philosophy, Architecture
Of the many arguments for proportion systems in architecture the most ancient and compelling is that the natural world is an intelligible, mathematically ordered whole, and the artifacts we place in it, as extensions of nature, should obey the same laws. Although this was still the argument of Le Corbusier - as earlier of Alberti - it was profoundly shaken by post-Renaissance science and the empiricist philosophy which flowed from it.
In Proportion, Richard Padovan looks at the problem from a new angle, taking empiricism as a starting-point. In order to know anything about the world, we have to discover regularities in it. These regularities can be explained, not by assuming that they are inherrent in nature and that nature impresses them on the mind but they are inherent in the mind and the mind impresses them on nature. Our perception of the world, our scientific hypotheses, are therefore artifacts, no less than our buildings and other works of art. Both science and art are ways of making the world intelligible; that is to say, of making in intelligible world. And in art as in science the key to intelligibility is mathematical order.
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Chapter one THE HARMONY OF THE WORLD MADE MANIFEST IN FORM AND NUMBER
Chapter two ABSTRACTION AND EMPATHY
Chapter three UNIT AND MULTIPLIER
Chapter four THE HOUSE AS MODEL FOR THE UNIVERSE
Chapter five THE PROPORTIONS OF THE PARTHENON
ORDER OUT OF CHAOS
CHANGE CONTINUITY AND THE UNIT
THE GOLDEN SECTION AND THE FIVE REGULAR SOLIDS
Chapter eleven HUMANISM AND ARCHITECTURE
Chapter twelve RENAISSANCE COSMOLOGY
Chapter thirteen THE WORLD AS A MACHINE
Chapter fourteen FROM THE OUTER TO THE INNER WORLD
Chapter fifteen THE GOLDEN SECTION AND THE GOLDEN MODULE
Chapter sixteen THE HOUSE AS A FRAME FOR LIVING AND A DISCIPLINE FOR THOUGHT
Chapter nine VITRUVIUS
Chapter ten GOTHIC PROPORTIONS
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abstract aesthetic Alberti ancient architect Architectonic Space architectural proportion Aristotle Aristotle’s arithmetic artist beauty Cathedral centre century Chapter Chartres circle Classical column concept construction Corbusier Corbusier’s corresponding cube decagon derived diagonal diameter dimensions dodecahedron double square elements empathy equal equilateral Euclid example facade Figure foot measure geometry golden rectangle golden section Gothic Greek H.van der Laan Hambidge harmony height Heraclitus Hume Hume’s Ibid icosahedron ideas infinite inscribed irrational numbers Jay Hambidge knowledge Laan’s laws Le Corbusier Le Modulor length mathematical measures mind modern modulor nature nature’s Newton objects octahedron Palladio Parthenon pentagon philosophy physical plastic number Plato polyhedra Proportion in Architecture proportion systems Pythagoras Pythagorean R.Wittkower ratio reason regular relation Renaissance right angle S.Sebastiano semicircle shape side square root stylobate system of proportions Table Theory of Proportion things Timaeus triangle unit University Press Vitruvius whole whole-number width Wittkower writes