A corollary to Newton's ideas was the so called Clockwork Universe model. A concept that states that the total momentum of the Universe is conserved, interactions redistribute the momentum, but the total never changes. In this model, God only starts the clock (initial cause), then it runs by itself for the rest of time.

As stated earlier, as you demonstrated today, experimentally determination of the conservation of momentum during this time period is not really possible. Had Galileo been able to do this rigorously, he might have been available to develop much of Newtonian mechanics.

Conservation of momentum is difficult to see in every day life because of the role of friction in the real world.

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Newton invented a scientific method which was truly universal in its scope. Newton presented his methodology as a set of four rules for scientific reasoning. These rules, written in the Principia , are:

1. We are to admit no more causes of natural things such as are both true and sufficient to explain their appearances

2. The same natural effects must be assigned to the same causes

3. Qualities of bodies are to be esteemed as universal

4. Propositions deduced from observation of phenomena should be viewed as accurate until other phenomena contradict them.

Which of these "rules" is actually redundant? What is important about rule 1? What does rule 4 say about the nature of science?

Newton's laws of motion:

• 1st law: a body remains at rest or moves in a straight line of constant velocity as long as no external forces acts on it

• 2nd law: a body acted on by a force will accelerate such that force equals mass times acceleration (F=ma)> More accurately, a Force is the time rate of change of the momentum.

• 3rd law: for every action there is an equal and opposite reaction



But remember, Newton implicitly assumes instantaneous communication time between objects. The concept of finite communication time and relativity is not here.

Instantaneous communication time means that all events which occur reach any detector simultaneously. You can easily derive thought experiments to show this can't be correct, else you would violate causality .



Well fine, if gravity is an attractive force, then how come the moon doesn't come crashing into the earth, or the earth into the sun. What causes an orbit to be stable?

An orbit is the balance between inertial and gravitational forces. That is, the earth is continually falling toward the sun, but inertia also wants the earth to keep moving in a straight line. When these two forces are in balance a stable orbit results:





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Newton's development of the underlying cause of planetary motion, gravity, completed the solar system model begun by the Babylonians and early Greeks. The mathematical formulation of Newton's dynamic model of the solar system became the science of celestial mechanics, the greatest of the deterministic sciences.

Newton, the person:

Newton was extremely sensitive to criticism, and even ceased publishing until the death of his arch-rival Hooke. It was only through the prodding of Halley (e.g. Halley's comet) that Newton was persuaded at all to publish the Principia Mathematica.

In the latter portion of his life, he devoted much of his time to alchemical researches and trying to date events in the Bible. After Newton's death, his burial place was moved. During the exhumation, it was discovered that Newton had massive amounts of mercury in his body, probably resulting from his alchemical pursuits.

Newton singlehandedly contributed more to the development of science than any other individual in history. He surpassed all the gains brought about by the great scientific minds of antiquity, producing a scheme of the universe which was more consistent, elegant, and intuitive than any proposed before. Newton stated explicit principles of scientific methods which applied universally to all branches of science. This was in sharp contradistinction to the earlier methodologies of Aristotle and Aquinas, which had outlined separate methods for different disciplines.

Although his methodology was strictly logical, Newton still believed deeply in the necessity of a God. His theological views are characterized by his belief that the beauty and regularity of the natural world could only "proceed from the counsel and dominion of an intelligent and powerful Being." He felt that "the Supreme God exists necessarily, and by the same necessity he exists always and everywhere." Newton believed that God periodically intervened to keep the universe going on track.

Newton mathematized all of the physical sciences, reducing their study to a rigorous, universal, and rational procedure which marked the ushering in of the Age of Reason. Thus, the basic principles of investigation set down by Newton have persisted virtually without alteration until modern times.

It is therefore no exaggeration to identify Newton as the single most important contributor to the development of modern science. The Latin inscription on Newton's tomb, despite its bombastic language, is thus fully justified in proclaiming, "Mortals! rejoice at so great an ornament to the human race!" Alexander Pope's couplet is also apropos: "Nature and Nature's laws lay hid in night; God said, Let Newton be! and all was light."

Calculus as a Language

This is a methodology known as "limits". There are two principle manifestations of this.

1. Deriving the instantaneous rate of change of some quanity

2. Finding the total area "under" some function.

These two principles are graphically shown below:

Differentiation

Integration:

This procedure allows for a rigorous determination of physics using functions.

For example, how do I compute the area of a circle.

A circle is that which is enclosed by a surface which a line of radius r has been rotated through 360 degrees.

From the language of Calculus this means the following:



Language should evolve so that communication becomes more efficient; i.e. the above graphic shows how to derive the area of a circle in the least amount of steps


Meanwhile, back to humanities!

Newton died in 1727 What is the state of european government/culture by this time? How is it reflective of this Age of Reason?

Relevant Notes