2-Filteredness and The Point of Every Galois Topos by Dubuc E.J.

By Dubuc E.J.

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17 Decline of feudalism GROWTH OF TRADE IN ITALIAN COASTAL CITIES Shift from land-based to money-based economy New trading patterns and routes Increasing urbanization Booming cities and towns INCREASING FOREIGN TRAVEL Expansion of trade with the East Mainstream interest in finer food, fashion, art, literature, and music SURGE OF INTEREST IN CLASSICAL ANTIQUITY The 4 Lenses of Innovation New painting, sculpture, and decorative arts New styles, techniques, and technologies in art Growing popularity of theater and opera Demand for gold, ivory, tobacco, chocolate, spices 18 New technological inspiration from other lands Patronage of the arts and sciences More disposable income and leisure time Increased literacy New foods, fashions, philosophies Rise of powerful banking families New urban jobs in banking, commerce, and trades EMERGING MIDDLE CLASS SOCIETY Influence from Islamic and Asian societies Increasing use of oil paint Use of linear perspective Archeology of ancient Rome New architecture Rebirth of classical art, literature, science, and philosophy Demand for silk and cotton clothes Spinning wheels and horizontal looms RISE OF MECHANIZED INDUSTRIES Growth of cotton industry Use of blast furnaces Rapid spread of clockwork Increased use of fossil fuels More mining Growing iron and steel industry Better metallurgy Use of rails for underground transport Improved mechanical engineering ADVANCES IN MATHEMATICS AND SCIENCE Improved shipbuilding IMPROVED TRANSPORTATION Use of telescopes, compasses, astrolabes, quadrants Increased naval exploration Rapid adoption of the printing press Education reforms PROLIFERATION OF BOOKS Wide availability of literature, poetry, technology texts, sheet music, newspapers Growth in papermaking industry Study of classical mathematics Better boats Better canal locks and dikes Start of tourism Better horse-drawn carriages Discovery and exploitation of new worlds Use of rail International book trade Spread of libraries Use of eyeglasses Study of art, literature, mathematics, science, and music Rise And Spread Of Humanism Declining Respect For Papal Authority And Church Dogma Emergence Of Protestantism Wide variety of new scientific instruments Introduction of double-entry bookkeeping New approaches to medicine and surgery Advances in astronomy More efficient agricultural techniques Advent of dentistry New theory of heliocentricity More varied uses of wind and water power Introduction of patenting New financial trading mechanisms Improving chemical technology More invention Spread of scientific and technical knowledge Adoption of the scientific method Increased canal and river transportation The Mind of the Innovator Improved cartography and navigation 19 Consider Johannes Gutenberg, whose mechanical, movable 3 type printing press is considered by many to be the most important invention of the modern period.

21 The top part of the egg was his vision for the shape of the dome—tall and pointed rather The Mind of the Innovator than hemispherical. 25 Brunelleschi had just returned from several years in Rome, Since nobody knew how to counter the immense outward where he had been studying the architectural forms in the thrust such a giant dome would create, Brunelleschi bor- city’s ancient ruins. In particular, he had dedicated himself rowed from the design of wooden barrels or casks, with their to understanding the construction of the Pantheon and its horizontal metal hoops around the vertical staves.

It is important to note that Gutenberg’s background was in metalworking (hence the metal mirrors). He came from a long line of goldsmiths. 16 So it was natural for Gutenberg to take on the same trade, and over the years he acquired extensive knowledge and technical skills, not just in metalworking but also in gem-polishing. 17 This method of printmaking had been invented in Germany just over a decade before Gutenberg developed his movable type technology. Even more interesting is the fact that movable type had already been invented hundreds of years previously in China,18 and was already in use there as well as in Korea.

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