Kumpulan 6 :

NG VI VIEN DB100574SIM LEE YUN DB100576FONG MEI YIN DB100687ER YOK NEE DB100898NA SIOW TENG DB100899

ASAS BENTUK DAN RUANGBBR 23203

Galileo

Kepler and Galileo o Descrided geometry was the key to understanding nature.

Galileo o Strand of renaissance Achimedean pratical mathematicians epitemic ambition.

16 th century

o Guidobaldo del’mante’s Liber Mechanicorum (1577) had pretty much completed a

geometrical description of simple statics and the compounding of the 5 simple machines.

o Archimedean mechanical stydy was the problem of motion, of projectile motion. This is the sort of forced, artificial motion that Aristotle’s physics had left outside rigorous and certain science.

Last half of the 16 th century

o It seemed commonly agreed amongst a small sector of artillered, applied mathematicians and academics that there ought to be laws of projectile motion.

For Galileoo Geometry was a tool.

( special tool, tool that allowed true and certain calculations.)

o Geometry, geometric analysis and geometric models allowed for the separation and unpacking of this complicated compouding into its unfelted ‘prefect’ component parts.

Descartes

o The third key figure in the scientific revolution.o Showed something of an inheritance from that Archimedean

mechanics as well as the Aristotelian answer to it.

o He postulated that matter came in ultimate small corpuscles of various sizes that filled all space, and that all material phenomena were caused by nothing more than the compounded and complex motions of corpuscles.

o These corpuscles had no properties whatsoever except that they occupied space, and then when hit by something, moved off according to simple billiard-ball mechanics until it was hit by something else.

o With such an austere ontology, Descartes was able to derive linear inertia25 in about three lines of reasoning.

DUALIST ONTOLOGICAL POSITION

1. Non-material Phenomenao Like emotions or thoughts or other phenomena of the spirit.o Which have no material qualities or effects whatsoever.o An idea his no weight or volume, and cannot move a pencil.

2. Material Phenomenao Which are ultimately derived from nothing more than the

motions of ultimate, inert material particles.o They only obey the laws of a geometrical mechanics.

GEOMETRY AS SCIENCE

o Geometry play roles in the new physics of Kepler, Galileo and Descartes.o The paradigmatic method of understanding nature was not just quantitative, but was through the use of geometry.o Nature ultimately behaves in a geometrically describe way: * mechanics * projectile motion * laws of nature

o The laws of nature are in some sense geometrical and can be demonstrated by geometry.

o Mechanics was exhibited as the paradigm science, but it had his status because it was paradigmatically geometrical.

o This is illustrated by Newton * in final section of the Principia * to sum up his grand model that synthesises a mathematic mechanics based on a notion of force

* celestial mechanics, based on a completely obscure force called universal gravity.o So in effect- celestial dynamics can be derived from geometry

alone.

The Enlightenmento Geometrically demonstrated laws of mechinics to model the physical world.o The nominal beginnings of a kind of physical- mathematical thinking that was to become the paradigm of the new physics of the Eighteenth century, called at the time Rational Mechanics. (Newton’s laws of gravity).o The laws of physics could be demonstrated geometrically without ontological commitment.

A More Public Face

o Natural philosophy and its applications came out of the ivory towers and noblemen’s courts.o A new status for a mathematical natural philosopher.o Geometry was the finest way to train the mind, the most perfect training in reasoning and clear thinking.

o Geometry was:a) The symbol of ordered and reasoned knowledge.b) A training in geometry was the surest buttress against any

sliding backwards into superstition, ill founded beliefs about the world.

c) The anti-rationalist occult natural philosophical heresies of the late renaissance.

o The geometrical good governance of the universe.o The infinitesimal calculus (geometry-of-the-infinite) was seen as the greatest triumph of the importance of the study of geometry.o The teaching of this geometry of the infinite was the ultimate exercise of the limits of the mind’s capacity to reason and reason abstractly.o Geometry has occupied any number of different social, intellectual, philosophical, and scientific positions over the ages.

THE END…

o Geometry is a role in our understanding of the world.o The status of geometry is what we make it to be.o It seems that one of the most fundamental of human scientific

intuitions is that the physical world is ultimately geometrical.o Study geometry is in some sense to uncover some kind of

ultimate essence of the physical world.

o Geometry sits in:

(a) social(b) intellectual(c) Instituitional context