Author Archives: vinaire

I am originally from India. I am settled in United States since 1969. I love mathematics, philosophy and clarity in thinking.

Middle School Math Review

Middle School

 

MIXED OPERATIONS REVIEW

Reference: MILESTONE 6: Mixed Operations

Review 50: Order of Operations

Review 51: Addition and Subtraction

Review 52: Multiplication and Division

Review 53: Expression and Terms

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INTEGERS REVIEW

Reference: MILESTONE 7: Integers

Review 60: Integers, What They Are

Review 61: Sign and Absolute Value

Review 62: Counting with Integers

Review 63: Multiplying & Dividing Integers

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FACTORS REVIEW

Reference: MILESTONE 8: Factors

Review 70: Factors, What They are

Review 71: Single-Digit Prime Numbers

Review 72: Double-Digit Prime Numbers

Review 73: Prime Factors of a Number

Review 74: Prime Factors Divisibility

Review 75: Division by Factoring

Review 76: Greatest Common Factor

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FRACTIONS REVIEW

References: MILESTONE 9: Fractions (Part I) / MILESTONE 10: Fractions (Part II)

Review 80: Fractions, What They Are

Review 81: Unit Fractions and Multiples

Review 82: Proper and Improper Fractions

Review 83: Mixed Numbers

Review 84: Equivalent Fractions

Review 85: Comparing Fractions

Review 86: Least Common Multiple

Review 87: Addition &Subtraction

Review 88: Multiplication & Division

Review 89: Mixed Operations

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DECIMAL NUMBERS REVIEW

Reference: MILESTONE 11: Decimal Numbers

Review 90: The Decimal System

Review 91: Decimal Numbers

Review 92: Decimal Fractions

Review 93: Decimal and Common Fractions

Review 94: Decimal Addition & Subtraction

Review 95: Decimal Multiplication & Division

Review 96: Periodic or Repeating Decimals

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Elementary School Math Review

elementary-school1

COUNTING REVIEW

Reference: MILESTONE 1: Numbers & Place Values

Review 01: Counting on Fingers

Review 02: Counting on Abacus

Review 03: Counting with Regrouping

Review 04: Writing the Count

Review 05: Counting to One Hundred

Review 06: Units and Numbers

Review 07: Numbers and Digits

Review 08: Place Values

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ADDITION REVIEW

Reference: MILESTONE 2: Addition

Review 10: Addition is Counting Together

Review 11: Adding by Counting More

Review 12: Adding by Regrouping

Review 13: Adding Double-Digit Numbers

Review 14: Practice Mental Addition

Review 15: Adding by Columns

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SUBTRACTION REVIEW

Reference: MILESTONE 3: Subtraction

Review 20: Subtraction is Finding the Difference

Review 21: Subtracting by “Reverse Addition”

Review 22: Subtracting by Columns (Traditional)

Review 23: Subtracting by Columns (Reverse Addition)

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MULTIPLICATION REVIEW

Reference: MILESTONE 4: Multiplication

Review 30: Multiplication is Repeated Addition

Review 31: Multiplication Shortcuts

Review 32: Multiplication Properties

Review 33: Multiplying by Column

Review 34: Multiplying Large Numbers

Review 35: Math Trick Multiply Using Lines

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DIVISION REVIEW

Reference: MILESTONE 5: Division

Review 40: Division is Repeated Taking Out

Review 41: Exact and Inexact Division

Review 42: Some Division Facts

Review 43: Dividing by Column

Review 44: Dividing by Large Numbers

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Awareness and Light

Aura

“Awareness is the state or ability to perceive, to feel, or to be conscious of events, objects, or sensory patterns. In this level of consciousness, sense data can be confirmed by an observer without necessarily implying understanding.”  ~ Wikipedia

At the most fundamental level, awareness seems to have the nature of disturbance. The wave-length of this disturbance is nearly infinite, and the frequency nearly zero. The period and velocity are infinite for all practical purposes.

Self-awareness at this level appears to be a light-like aura. This is a very raw level of awareness. There is no other self, soul, energy, God, etc.

Awareness and light seem to be two different aspect of some primordial phenomenon of consciousness – awareness being the spiritual, while light being the physical aspect. The spiritual and physical aspects seem to go hand in hand.

Awareness and light seem to weave together to make various phenomena, entities, objects and the universe. They cannot be separated from each other.

There is no spiritual universe separate from the physical universe. There is only a single universe. It is the superset of all that exists with their spiritual and physical aspects.

There are no spiritual entities separate from physical objects. The spirituality of objects is expressed as their properties. This is well expressed in the periodic table of elements at the atomic and molecular levels.

There is no soul that separates from the body at death. The aliveness comes from the connectedness of awareness among the atoms, molecules, and organs of the body. There is a smooth flow of awareness throughout the body that creates the live organism. When this flow ceases death occurs. The body disintegrates into parts containing their own separate awareness.

The assumption that ‘physical’ and ‘spiritual’ are two separate phenomena is in error.  Like “space-time”, we have “spiritual-physical”  as a single or relative phenomenon. Neither spirituality nor physicality is absolute in itself.

The universe is the superset of all existence.  Spiritual and physical are two different aspects that weave together into every particle and crevice of the universe. The fundamental nature of “spirtual-physical” is “awareness-light”.

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Theism, Atheism and Non-theism

Prayer

[NOTE: The earlier version of this essay titled “Theism versus Atheismhas been obsoleted]

(Wikipedia) The term theism derives from the Greek theos meaning “god”. … they are “strictly and properly called Theists, who affirm, that a perfectly conscious understanding being, or mind, existing of itself from eternity, was the cause of all other things”.

(Wikipedia) Atheism is rejection of theism in the broadest sense of theism; i.e. the rejection of belief that there is even one deity.

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Theism views God, in its special role, to be separate from all existence.  A culture that believes in theism assigns a similar role to self as being spiritual and separate from the physical existence around it.

The concepts of theism and atheism are coming strictly from a SELF-CENTRIC viewpoint. They are for or against “self” being the ultimate reality. The concepts of theism and atheism are created out of a focus on self.

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The concepts of theism or atheism are foreign to the East and do not apply to the Vedic religions. Therefore, we may call Vedic religions non-theistic in nature. Some people consider Vedic religions to be atheistic or polytheistic because they are looking through a filter of theism-atheism.

Abrahamic religions, such as, Judaism, Christianity and Islam, are theistic. The Vedic religions, such as, Hinduism, Buddhism and Sikhism, are non-theistic.

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Non-theism is based on the reality of existence. A non-theistic culture does not separate self from other things, but sees everything as part of the same reality of existence. The concept of non-theism, therefore, comes from a REALITY-CENTRIC viewpoint.

Theism, therefore, is self-centric. Non-theism is reality-centric.

Theism is based on subjectivity. Non-theism is based on objectivity.

Theism takes the affinities of people and molds it into a reality that is built around the idea of God. Non-theism takes the existing reality and transforms it into a sense of all-inclusive affinity.

The focus of Theism is on the uniqueness of self (individuality). This gives rise to the ideas of us and them. The focus of Non-theism is on oneness of all existence. Thus, differences may arise but they are secondary.

Theism holds a special idea of God. The idea of being one with God is unacceptable to it. Non-theism holds no special idea of God. The idea of being one with ultimate reality is part of it.

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The Ultimate Reality (old-1)

Reference: A Model of Reality

The essay above defined reality as what we perceive at any moment. This reality is made up of filters (thoughts, ideas, assumptions, speculations, visualizations, etc.). The filters include what is observed, the modulation of what is observed, as well as the observer.

What is beyond the filters may be called the ultimate reality.

The Ultimate Reality is basically a starting postulate one uses to make sense out of all existence. If the reality of existence is not consistent with the starting postulate then that starting postulate is not the right one.

Abrahamic religions use a “super self” or God as the starting postulate, or ultimate reality.

Vedic religions use “neti, neti” (not this, not that) or the shedding away of all that is relative, conditioned and impermanent to define their concept of ultimate reality as “Brahma.”

Scientology uses a “Static” or “an abstract ability to postulate and to perceive” as its ultimate reality. This ability is postulated to have no mass, no motion, no wavelength, and no location in space or in time.

The postulate of Ultimate Reality is true only to the degree that it brings consistency and coherency to the understanding of all existence.

All existence seems to boil down to the fact of awareness. It is anything that one can be aware of. The belief in “God,” “Static” or “Brahma,” simply means the awareness of a starting postulate that brings consistency and coherence among all the beliefs and logic that a person uses.”

The rarest of all awareness has to be the awareness of pure disturbance. Prior to that there would be no awareness. Only a theoretical ground state may be postulated in terms of undisturbed primordial field that contains no frequency, wavelength or period.

But this ground state shall forever be unknowable and shall remain only theoretical because there is no awareness to go with it. Awareness arises only when this ground state is disturbed. The awareness then accompanies a disturbance that looks like light and which seems to be traveling through an invisible field that looks like space.

Therefore, the starting postulate of ultimate reality arrived at in KHTK is as follows:

The Ultimate Reality is an undisturbed primordial field of no frequency, wavelength or period. This primordial field produces awareness only when disturbed, and therefore it is inherently unknowable.

This is a theoretical postulate, and not something actual.

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