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Galileo and the Origins of the Modern World. David Banach Department of Philosophy. Galileo and the Origins of the Modern World David Banach. Discoverer of new worlds. Proponent of New Theories. Saint for Science. Galileo at Arcetri. Galileo and Milton at Arcetri.
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Galileo and the Origins of the Modern World David Banach Department of Philosophy
Galileo and Scientific Method • 1602-Pendulum experiments. • 1604- Inclined plane experiments of natural acceleration. • 1607-Systematic manipulation of shapes and weights of wax balls to study flotation. • Investigation of projectile motion. Discovery of parabolic character of projectile motion.
Science and the Modern World • Scientific Method as a model for Reason: The new method of knowledge introduced by Galileo and the Scientific Revolution increased the confidence in the power of human reason and its ability to transform civilization. The hundred or so years following the Scientific Revolution (the 1700’s, the Enlightenment) saw an unprecedented revision of the forms of human government and culture on the basis of the application of this new method. The Post-Modern world will ask whether Science can deliver on the promise of objectivity and whether a society can be ordered on the basis of reason. • The Mechanistic world view: The Scientific revolution introduced a radically new view of the world as a mechanism composed of inert parts, whose configuration and mechanical relations determine all of its properties. The Post-Modern world will ask whether human values and the human soul can find a place in this mechanistic world. This is the real conflict between science and religion.
The Scientific Method • Science does not trust the senses. It mistrusts and re-interprets them. • Science does not aim at understanding the particular, but at isolating how nature acts under ideal conditions • Scientific discovery involves more than merely looking in the right place. It requires uncovering the hidden order within appearances.
The Scientific Method • Purifying the Appearances • Separating the Relative from the Absolute
Separating Relative and Absolute:The Copernican Revolution • The senses tell us that the sun is moving. Using our minds we can see that the motion of the sun in the sky is really our motion, merely relative to us.
Copernicus’s Revolution: The Motion we see outside us in the Sun
Is not in the sun but in us; Is not real but merely relative
The Laws of Terrestrial Motion • 1. Free fall: Aristotle believed heavy objects fell faster than light objects, since they had more earth than air or fire or water in them. Galileo saw that all objects fall at the same rate. The senses supported Aristotle. Galileo’s experiments aimed at purifying the senses and isolating only the effects of weight from all the other causes involved such as air resistance, friction, and buoyancy. • 2. Inertia: Aristotle thought that an object in natural motion moved to its natural place and stopped and that to keep it moving in violent motion required energy. Galileo formulated the law of inertia: that an object in motion tends to stay in motion. The senses supported Aristotle. Only Galileo’s purification of the senses in experiments proved him to be correct.
Purifying the appearances Simple unified motions often arise from an impure conglomeration of forces such as friction and air resistance. The scientific method systematically manipulates properties to isolate the real source of phenomena.
The Law of Inertia • The senses tell us that objects require force to keep them moving and eventually slow down. • Only under ideal conditions does an object in motion tend to stay in motion
Three Experiments • 1. The Pendulum: Used to demonstrate the law of inertia and that heavy and light bodies fall at the same rate. Galileo also discovered the mathematical laws governing the length of the string, the period of the motion, and the amplitude of the swing.2. The Inclined Plane and the Rate of Acceleration: Galileo used the inclined plane to slow the motion of falling objects enough to accurately measure how their speed increased. • 3. Projectile Motion: Galileo also used the inclined plane to control the speeds and heights of projectiles in order to discover the mathematical properties of their paths.
Pendulum • "...repeat many times the fall through a small height in such away that I might accumulate all those intervals of time that elapse between the arrival of the heavy and light bodies respectively at their common terminus, so that this sum makes an interval of time which is not only observable, but easily observable." • "...two balls, one of lead and one of cork, the former more than a hundred times heavier than the latter, and suspended them by means of two equal fine threads, each four or five cubits long. "This free vibration repeated a hundred times showed clearly that the heavy body maintained so nearly the period of the light body that neither in a hundred swings nor even in a thousand will the former anticipate the latter by as much as a single moment, so perfectly do they keep step." Galileo
Pendulum • Momentum is conserved
Pendulum • 1. Robust Regular motion remains independent of impurities in environment. • 2. Demonstrates regular fall of bodies and law of inertia. • 3. Allows mathematical study of dependence of motion on string length and mass of pendulum.
Inclined Plane"...in such a plane, just as well as in a vertical plane, one may discover how bodies of different weight behave..." Galileo
Inclined Plane"...in such a plane, just as well as in a vertical plane, one may discover how bodies of different weight behave..." Galileo
Inclined Plane"...in such a plane, just as well as in a vertical plane, one may discover how bodies of different weight behave..." Galileo Total distance traveled is proportional to the square of time.
Inclined Plane Slows down motion to enable the measurement of mathematical relationships. Corrects for the effects of air resistance. Simplifying and purifying the appearancesallows discovery of first mathematical law of motion.
Projectile Motion • Purifying the appearances: Separating and Analyzing the Components of motion.
The apparent single motion is actually composed of two different motions
