**Newtonianism** is a philosophical and scientific doctrine based on Isaac Newton's ideas and methods. Newton's work in physics and mathematics, which described the universe as governed by rational and understandable laws, greatly influenced Enlightenment thought. Newtonianism extended these principles to various fields, establishing modern science, as well as influencing philosophy, political thought, and theology.

## Beliefs[edit | edit source]

### Binomial Series[edit | edit source]

The binomial series in mathematics extends from the binomial formula, like (x + y)^{n} for a nonnegative integer n. It's the MacLaurin series for the function f(x) = (1 + x)^{α}, where α is any complex number with |x| < 1. In simpler terms, it's expressed as:

This series converges under certain conditions:

- If |x| < 1, it converges for any complex α.
- If |x| = 1, it converges if Re(α) > 0 or α = 0.
- If |x| = 1 and x ≠ -1, it converges if Re(α) > -1.
- If x = -1, it converges if Re(α) > 0 or α = 0.
- If |x| > 1, it diverges unless α is a non-negative integer, in which case it's a finite sum.

### Calculus[edit | edit source]

Calculus is the mathematical study of continuous change, similar to how geometry studies shapes and algebra studies arithmetic operations. It has two main branches: differential calculus and integral calculus. Differential calculus focuses on rates of change and slopes of curves, while integral calculus deals with accumulation of quantities and areas under curves. These branches are connected by the fundamental theorem of calculus, which relies on the concepts of infinite sequences and series converging to a limit.

### Newton's Law of Motion[edit | edit source]

Newton's laws of motion are three fundamental principles that describe how objects move and interact with forces. These laws, forming the foundation of Newtonian mechanics, can be summarized as follows:

- An object remains at rest or moves at a constant speed in a straight line unless acted upon by a force.
- The net force on an object equals its mass times its acceleration, or the rate of change of its momentum.
- When two objects exert forces on each other, the forces are equal in magnitude and opposite in direction.

Isaac Newton first presented these laws in his 1687 work, Philosophiæ Naturalis Principia Mathematica. These principles have been used to explain the motion of various physical objects and systems. Over time, additional concepts like energy further developed classical mechanics. However, Newton's laws have limitations, requiring new theories for objects moving at high speeds (special relativity), very massive objects (general relativity), or very small particles (quantum mechanics).

### Newtonian Mechanics[edit | edit source]

In physics, a force is anything that causes an object's speed to change, making it accelerate. Forces come from fields like electrostatic (from static electrical charges), electromagnetic (from moving charges), or gravitational (from mass).

Newton was the first to mathematically explain the relationship between force and momentum. His second law of motion states that the force acting on an object is equal to the rate of change of its momentum. This law can be expressed as

F = ma , where F is the force, m is the mass, and a is the acceleration.

It's like saying, "**Force equals mass times acceleration**". Consider an example where friction is the only force acting on an object. Friction opposes the object's motion and depends on its velocity. This creates an equation where force equals mass times the object's velocity's rate of change. Solving this equation shows how the object's velocity decreases over time due to friction.

Other important forces include gravity and the Lorentz force for electromagnetism. Newton's third law says that if one object exerts a force on another, the second object exerts an equal and opposite force back. This law helps understand forces in action, like when magnets attract or repel each other. Work and energy are also crucial concepts. Work is done when a force moves an object over a distance. If the force is constant, work equals the force times the distance. If the force changes, we use a line integral to calculate the work. The kinetic energy of an object, its energy due to motion, is given by half its mass times its velocity squared. The work-energy theorem states that the work done on an object equals the change in its kinetic energy.

Conservative forces, like gravity or spring forces, can be described using potential energy. This energy is stored and can be converted into kinetic energy when the object moves. Conservation of energy says that the total energy, the sum of kinetic and potential energy, remains constant over time.

### Optics[edit | edit source]

Newton's "Opticks" was one of his most important scientific works, akin to his Principia, yet his name was absent from the first edition's cover. Newton explores light's nature, color, and diffraction phenomena, overturning the belief that pure light is colorless. He reveals light's composition of spectral hues and demonstrates color's subjective nature. Newton's experiments on dispersion led to the invention of multiple-prism arrays, important for modern laser technology.

### Universal Gravitation[edit | edit source]

Newton's law of universal gravitation states that every particle in the universe attracts every other particle with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centers. This means objects attract each other as if all their mass were concentrated at their centers. The publication of this law unified the understanding of gravity on Earth with astronomical phenomena.

Newton combined his laws of motion with new mathematical analysis to explain Kepler's empirical results. His explanation was in the form of a law of universal gravitation: any two bodies are attracted by a force proportional to their mass and inversely proportional to their separation squared.

This general physical law was derived from empirical observations using inductive reasoning, and it was first presented in Isaac Newton's 1687 work, *Philosophiæ Naturalis Principia Mathematica*. The equation for universal gravitation is:

F = Gm_{1}m_{2} / r^{2} , where F is the gravitational force, m_{1} and m_{2} are the masses of the objects, r is the distance between their centers, G is the gravitational constant, G ≈ 6.67 × 10^{-11} m^{3}kg^{-1}s^{-2}.

### Theology[edit | edit source]

Newton's writings reveal his deep knowledge of early Church teachings. He sided with Arius in the Athanasius-Arius conflict over the Trinity, viewing Christ as a divine mediator subordinate to God. He considered the worship of Christ as God to be idolatry, the fundamental sin. While Newton is famous for his laws of motion and universal gravitation, he cautioned against viewing the universe purely as a machine, emphasizing the need for divine power to explain celestial motion. Newton's religious studies were extensive, producing works on biblical criticism and prophecy.

Newton rejected the pantheism of Leibniz and Spinoza, advocating for an ordered universe understood through reason. He believed in evidence of divine design in the universe, though he acknowledged that divine intervention was necessary to correct instabilities over time. This view was mocked by Leibniz, who argued for a self-sustaining universe.

## How to Draw[edit | edit source]

## Relationships[edit | edit source]

### Friends[edit | edit source]

- Christianity -
*This most beautiful system of the sun, planets, and comets, could only proceed from the counsel and dominion of an intelligent and powerful Being.*~~But trinitarianism is not real.~~ - Classical Liberalism - I was a Whig in the United Kingdom.

### Frenemies[edit | edit source]

- Einsteinianism - Improved on my work.
~~Wait a minute, you're an agnostic~~ - Aristotelianism - You were good, but objects don't have a desire to stay at rest!

### Enemies[edit | edit source]

- Atheism - You are all senseless. Look at the solar system. That cannot have formed by chance.
- Catholicism - The solar system is NOT geocentric!
- Cambrianism - The earth began in 3998 BC!

## Further Information[edit | edit source]

### Wikipedia[edit | edit source]