The Gravity (old)

Please see PM Chapter 9: Inertia & Gravity.

Reference: Essays on Substance

The Gravity

Newton interpreted gravity as an innate force that acted at a distance. However, he was at a loss to explain how force acted so. Faraday theorized that such a action occurred through lines of force, which later developed into the idea of fields.

Einstein interpreted gravity as the curvature of spacetime caused by mass and energy. To him, spacetime was a mathematical abstraction. Massive objects warped the fabric of spacetime, creating paths along which matter moved. This curvature was gravity.

The Theory of Substance defines substance having inherent properties of consistency (thickness) and motion. Consistency and motion have inverse relationship. They balance each other such that a body has a constant speed. The velocity of light is finite and constant because its motion is balanced by its consistency.

Thus, a system of two or more bodies always forms a dynamic configuration such that their consistencies and motion are in equilibrium at all times. For example, the Sun, all its planets and their moons are dynamically aligned in such a way that their consistencies and motions are in equilibrium.

The theory of substance does not see gravity as a force. Instead, it sees gravity as the natural tendency of a system to dynamically arrange itself such that there is an equilibrium among all the consistencies and motions involved.

We see the manifestation of gravity in the dynamic configurations of the galaxies, the planetary systems, and the atoms, including their internal structure.

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The Inertia

Reference: Postulate Mechanics

The Inertia

INERTIA is the resistance that is felt when something is pushed. If something offers no resistance then there can be no push either. Therefore, for force to be manifested there must be inertia opposing it. Both force and inertia are the manifestation of the consistency of substance.

When the force upon an object and its inertia are in exact balance, there exists a uniform state of motion, or rest, in which there is no acceleration. The fact that the speed of light is constant means that it has inertia that is balancing any electromagnetic force acting upon it. If there is no inertia, the speed shall be infinite.

A body with infinite consistency shall have infinite inertia and it would not be displaceable from its location. We may assign it zero absolute motion. As the consistency reduces, the inertia also reduces and some displacement would become possible. This shall bring about a configuration similar to that of a rotating galaxy. We can thus show an inverse relationship between consistency and absolute motion.

When an object is accelerated to a higher speed with the application of an external force, and the external force is removed; then the inertia of the object will start acting to bring the object back to its original balanced speed. If the inertia is also reduced in the process, then the higher speed shall be maintained.

Both Force and Inertia are manifestations of consistency.

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The Mass

Reference: The Book of Physics

Mass is the key property of matter, that is directly linked to its weight. Mass reflects the consistency of matter.

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Definition of MASS

The substantialness of matter is called mass. The mass of matter allows it to be divided into very small particles. A material object, regardless of its size, can be treated mathematically as if all its mass is concentrated at a point. We call this point the “center-of-mass.”

The “center-of-mass” allows a material object to be treated as a point particle in most mathematical visualizations. This property is peculiar to matter, and it does not exist for other forms of substance, such as, energy and thought. 

In case of matter, mass represents its consistency. According to The Motion, the intrinsic motion of substance is related to its consistency. Therefore, an object has a natural motion in free space that depends on its mass. Even the slightest change in the mass changes this motion. Therefore, we observe relative motion among objects, such as the planets, due to differences in their mass.

The rest mass of an object is measured, when it is moving naturally in free space, or when it is at rest relative to the observer.

The term ‘relativistic mass’ was invented to convey the idea that it is harder to push a moving object, as you have to be moving faster than the object to push it. It is a misconception that a particle’s mass gets bigger as it speeds up.

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Notes

The mass of an object is the total of the masses of its molecules. The mass of a molecule is the total of the masses of its atoms. The mass of an atom is the total of the masses of neutrons, protons and electrons that constitute it. Therefore, when we talk about the total mass of an object, it is the sum of the mass of all the particles that constitute that object. The mass of individual particles differ as follows:

Mass of neutron = 1.675 × 10−27 kg
Mass of proton = 1.673 × 10−27 kg 
Mass of electron = 9.109×10−31 kg

Very small differences in the mass of an object are capable of producing significant relative motion in free space. This property of mass may provide some clue to the nature of gravity.

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Key Misconception

The key misconception in Newtonian mechanics is that an object is not seen as having a natural motion in free space as a function of its mass.

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More Misconceptions

You may discover more misconceptions on your own, if you contemplate on each sentence of the above definition with mindfulness. Please see:

The 12 Aspects of Mindfulness

Or, you may end up improving upon this definition.

Good luck!

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The Book of Mathematics

Reference: The Book of Subject Clearing

Pre-Kindergarten

Lesson 1: ORIENTATION & SPATIAL SENSE
Lesson 2: QUANTITY & NUMBER SENSE
Lesson 3: PATTERNS & RELATIONAL SENSE

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Kindergarten

Lesson 1: Orientation & Spatial Sense
Lesson 2: Numbers & Place Values
Lesson 3: Units & Fractions
Lesson 4: Counting & Measurements
Lesson 5: Numbers & Operations
Lesson 6: Patterns & Relational Sense
Lesson 7: Data Analysis & Probability

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Primary School

Lesson 1: Numbers
Exercise: Reading Numbers from Dubb
Exercise: Writing Numbers from Dubb

Lesson 2: Addition
Exercise: Addition Problems from Dubb

Lesson 3: Multiplication
Exercise: Multiplication Problems from Dubb

Lesson 4: Subtraction
Exercise: Subtraction Problems from Dubb
Exercise: Integer Problems from Dubb

Lesson 5: Division
Exercise: Short Division Problems from Dubb
Exercise: Long Division Problems from Dubb
Exercise: Arithmetic Expression Problems from Dubbs

Lesson 6: Units
Table: The Units of Measure
Exercise: Problems on Units from Dubb

  1. Long Measure
  2. Square Measure
  3. Rectangles
  4. Cubic Measure
  5. Time Measure
  6. Miscellaneous Tables
  7. Promiscous Examples
  8. Addition of Compound Numbers
  9. Subtraction of Compound Numbers
  10. Time between two Dates
  11. Time in Days between Two Dates
  12. Multiplication of Compound Numbers
  13. Division of Compound Numbers

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Middle School

Introduction

  1. What is Mathematics?
  2. Mathematics Overview
  3. Counting and Abacus 
  4. The Concept of Numbers
  5. Math Diagnostics

Lesson 1: Number to Integer
Exercise: Problems from Dubb (Word problems)

Lesson 2: Terms & Expression
Exercise: Problems from Dubbs (Word problems)

Lesson 3: Factoring
Exercise: Factoring Problems from Dubb

  1. Prime Factors
  2. Common Prime Factors
  3. Greatest Common Divisor
  4. Least Common Multiple
  5. Word Problems

Lesson 4: Fractions
Exercise: Fraction Problems from Dubb

  1. Integer to Fraction
  2. Mixed Number to Improper Fraction
  3. Improper Fraction to Mixed number
  4. Reducing Fraction to a Denominator
  5. Reducing Fraction to Lowest Terms
  6. Reducing Fraction to LCM & GCD
  7. Addition of Fractions
  8. Subtraction of Fractions
  9. Multiplication of Fractions
  10. Multiplication Word Problems
  11. Division of Fractions
  12. Finding Part of a Number
  13. Reducing Complex Fractions
  14. Complex Fraction Word Problems
  15. Word Problems for Fractions

Lesson 5: Decimals
Exercise: Decimal Problems from Dubb

  1. Writing Decimals
  2. Reading Decimals
  3. Decimals to Common Fractions
  4. Common Fractions to Decimals
  5. Addition of Decimals
  6. Subtraction of Decimals
  7. Multiplication of Decimals
  8. Division of Decimals

Lesson 6: Review of Basics
Make yourself familiar with these basics

  1. Real Numbers
  2. The Basics of Math
  3. Additional Math Concepts
  4. Equations & Transposition

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Further References

Course in Mathematics

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The Anomaly

Reference: Postulate Mechanics

The Anomaly

An anomaly is a violation of reality. It is characterized by

  1. Discontinuity (missing data)
  2. Inconsistency (contradictory data)
  3. Disharmony (arbitrary data).

The violation of reality appears in the form of disagreements. There are two different realities and the bridge between them is missing. There are contradictions and disharmonies. In this situation, the anomalies must be recognized, isolated and listed precisely, and then addressed one by one.

Such anomalies commonly exist in one’s observations and reasoning; but they may go as far back as being part of one’s viewpoint and even postulates. Those basic anomalies can distort one’s observation and train of logic. They come about when the postulates did not get updated to account for new sensations. In other words, the new experience did not get fully assimilated. 

Such anomalies generate aberrations in one’s perception, judgment and behavior. When a person is not responding appropriately to a situation, he is suffering from some anomaly in his thinking. This is handled by looking more closely at the inappropriateness of all his reactions according to the broad reality, and then narrowing them down to specific triggers. And then looking for possible experiences that were not fully assimilated.

When one spots the right anomaly, it resolves easily. The reality becomes clearer and one realizes what was happening.

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