Category Archives: Uncategorized

Remedial Math Level 2


Middle School Review 2


Lesson 1: Number to Integer

Exercise: Integer Problems from Dubb


Lesson 2: Terms & Expression

Exercise: Arithmetic Expression Problems from Dubbs


Lesson 3: Factoring

Exercise: Factoring Problems from Dubb

Prime Factors

Common Prime Factors

Greatest Common Divisor

Least Common Multiple

Word Problems


Lesson 4: Fractions

Exercise: Fraction Problems from Dubb

Integer to Fraction

Mixed Number to Improper Fraction

Improper Fraction to Mixed number

Reducing Fraction to a Denominator

Reducing Fraction to Lowest Terms

Reducing Fraction to LCM & GCD

Addition of Fractions

Subtraction of Fractions

Multiplication of Fractions

Multiplication Word Problems

Division of Fractions

Finding Part of a Number

Reducing Complex Fractions

Complex Fraction Word Problems

Word Problems for Fractions


Lesson 5: Decimals

Exercise: Decimal Problems from Dubb

Writing Decimals

Reading Decimals

Decimals to Common Fractions

Common Fractions to Decimals

Addition of Decimals

Subtraction of Decimals

Multiplication of Decimals

Division of Decimals


Lesson 6: Review of Basics

Make yourself familiar with these basics

Real Numbers

The Basics of Math

Additional Math Concepts

Equations & Transposition




To be used for students needing more details.

MS B1 Mixed Operations

MS B2 Integers

MS B3 Factors

MS B4 Frac Props

MS B5 Frac Ops

MS B6 Decimals


The Emotional Curve


Reference: Mindfulness Approach


The weighted center of the mental matrix is perceived as the “I” of the person. It directs attention at parts of the matrix to activate them. The activation of the matrix forms thoughts. The cumulative effect of thoughts appears as emotional charge. This charge acts on the endocrine system of the body, which makes the body exert effort.

Thus, emotion is the direct index of the state of the mental matrix or “I” that is also reflected in the state of the body. The effort manifested in the body is then perceived back by the mental matrix. Accomplishment of intended effort discharges the emotional charge.

When there is a sudden drop in the emotional state of a person, we have an emotional curve. It comes about with the realization of failure or inadequacy. A person has at least one emotional curve in their past. Contemplation on the emotional curve leads straight to the incident, which gave the person his computation.

In this exercise the student focuses on a time when he was happy and suddenly was made sad. He contemplates on it until the actual emotional charge comes up . He fully experiences the emotions and contemplates on the incident over and over until the emotional charge is fully gone. One should be extremely thorough about discharging the emotional curve.


EXERCISE: The Emotional Curve

PURPOSE: To discharge the sudden emotional downturns in one’s life.

PREREQUISITE:  In case of extreme discomfort, return to the exercise Accessibility of Memory.

GUIDING PRINCIPLE: The Discipline of Mindfulness


  1. Focus your attention on a time when you were happy and suddenly were made sad. Let the data come up and freely associate. Continue with this contemplation until a memory of sudden emotional downturn comes up with full force.

  2. Experience those emotions fully without holding anything back. You may get into grief discharges, fear discharges or anger discharges. Experience them over and over until the charge is fully gone. Be extremely thorough about discharging the emotional curve.

  3. Make sure you let the mind carry out its associations naturally without being directed. In case there is increasing mental stress, return to the exercise Accessibility of Memory

  4. Repeat the above steps to discharge other emotional curves from your life. The exercise is completed when no more emotional curves are coming up.

  5. Continue with this exercise in, at least, 20 minutes long sessions until it is completed.


Obsolete: Disturbance Spectrum

See: Inertial Frame of the Universe


Reference: Disturbance Theory


A disturbance level is defined as logarithm of frequency on base 2, so that a wide range of disturbances can be conveniently displayed on a manageable scale,

The frequency of yellow light is 5.8 x 1014 Hz = 249 Hz. Therefore, the disturbance level of yellow light is referred to as DL49.

The Disturbance Level is calculated as, DL = log (frequency) / log 2

The Disturbance spectrum displays the frequencies of electromagnetic radiation and the de Broglie frequencies of mass particles in one place in the form of disturbance levels. Here are some of these disturbance levels.

Radio Waves (3 Hz – 3 GHz) ……………. DL 1.6 – 31

Microwaves (3 GHz – 300 GHz) ………… DL 31 – 38

Infrared (300 GHz – 300 THz) …………… DL 38 – 48.5

Visible (400 THz – 800 THz) …………….. DL 48.5 – 49.5

Ultraviolet (800 THz – 30 PHz) ………….. DL 49.5 – 54.7

X-Rays (30 PHz – 30 EHz) ……………….. DL 54.7 – 64.7

Gammy Rays (> 30 EHz) …………………. DL 64.7 and greater

Electron ……………………………………… DL 66.7

Proton ………………………………………… DL 77.6

Neutron ………………………………………. DL 77.6

Earth ………………………………………….. DL 235.6

This graph plots the levels of any disturbance as a function of frequency. The disturbance levels are defined in terms of the doubling of frequency. The basic disturbance DL0 has a frequency of 1 (20). The subsequent disturbance levels (DL 1, DL 2, DL 3 … DL n.) have frequencies of 21 (2), 22 (4), 23 (8) … 2n. It can be seen from this graph that negative disturbance levels may be postulated to exist with the halving of frequency. The frequency never reaches the zero of ground state. As long as some frequency is present, awareness is also present in some form.


Aberration of light in SRF

Reference: Disturbance Theory


Problem: Celestial objects have apparent motion. (See )

What is true position of the celestial objects?


Mean Equator and Equinox of J2000.0: This coordinate system is oriented with its xy-plane parallel to the mean Earth equator at epoch J2000.0, and its z-axis pointing toward the mean north celestial pole of J2000.0. The x-axis points toward the mean equinox of J2000.0. This coordinate system is used for expressing the positions of stars in catalogs and planets in basic solar system ephemerides.

Right Ascension: Angular distance on the celestial sphere measured eastward along the celestial equator from the equinox to the hour circle passing through the celestial object.

Declination: Angular distance on the celestial sphere north or south of the celestial equator. It is measured along the hour circle passing through the celestial object.

Distance: The distance from the center of the Earth to the Solar System object, given in astronomical units (kilometers for the Moon). Distance is not calculated for stars.

Celestial Sphere: An imaginary sphere of arbitrarily large radius, concentric with Earth. All objects in the observer’s sky can be thought of as projected upon the inside surface of the celestial sphere, as if it were the underside of a dome or a hemispherical screen. The celestial sphere is a practical tool for spherical astronomy, allowing observers to plot positions of objects in the sky when their distances are unknown or unimportant.

Shouldn’t there be a motion?

The celestial sphere does not rotate with the earth. But it moves around the sun with earth. This may affect the observation of true position.

Annual aberration — a deflection caused by the velocity of the Earth’s motion around the Sun, relative to an inertial frame. This is independent of the distance of the star from the Earth.

Light-time correction is a displacement in the apparent position of a celestial object from its true position (or geometric position) caused by the object’s motion during the time it takes its light to reach an observer.

Is the aberration of light constant for all celestial objects?

It appears to be so for stars. For objects in the solar system their speeds become relevant.

Why is James Bradley’s (1729) explanation not adequate for the aberration of light?

Bradley conceived of an explanation in terms of a corpuscular theory of light in which light is made of particles that do not require a medium. His classical explanation appeals to the motion of the earth relative to a beam of light-particles moving at a finite velocity, and is developed in the Sun’s frame of reference. However, once the wave nature of light was better understood, a medium needed to be accounted for.

The aberration of light is an astronomical phenomenon which produces an apparent motion of celestial objects about their true positions, dependent on the velocity of the observer.

Let a star be at distance ‘d’ from earth. Light takes time = ‘d/c’ to reach earth from the star. If earth is moving at velocity ‘v’, then it has moved a distance ‘v.d/c’ during the time star light reaches earth. The ratio of these two distances is ‘v/c’. This is the angle of aberration.

In SRF, the only motion visible is acceleration. Uniform motion is indistinguishable from ‘rest’. Earth is always accelerating toward the sun, so this motion shall be visble in SRF. Earth’s velocity ‘v’ is the result of balanced acceleration.

Light’s velocity ‘c’ is also the result of balanced acceleration. It is a limiting velocity. Light has velocity ‘c’ because it cannot be accelerated anymore.

The motion visible in SRF is balanced acceleration. So, the explanation given above for angle of aberration based on ‘v’ and ‘c’ shall be valid in SRF.

In SRF, the motion of planets shall be perceived as if they are moving in a groove carved in space. Light is moving, similarly, in a groove carved in space.


James Bradley’s (1729) explanation for aberration of light became unacceptable in 1804 because light was established to be a wave. It was no longer looked upon as corpuscular as was assumed earlier by Newton. So, the medium of light (aether) became an issue.

In SRF (space reference frame), the aether is the space itself. From SRF point of view, the change in view of light from corpuscular to wave would not have created an issue in 1804 with the earlier 1729 explanation for aberration of light.




Remedial Physics


Physical Science 8th grade

The Physics Classroom

Schaum Beginning Physics I

Schaum beginning Physics II

Schaum Modern Physics

The Physics Hypertextbook

Asimov: Understanding Physics Volume 1

Asimov: Understanding Physics Volume 2

Asimov: Understanding Physics Volume 3

Maxwell: A Treatise on Electricity & Magnetism – Volume 1

Maxwell: A Treatise on Electricity & Magnetism – Volume 2

Faraday: Experimental Researches in Electricity – Volume 3