Introduction to Subject Clearing

Reference: Course on Subject Clearing

Subject Clearing is a methodology to bring clarity to the mind on a subject. It not only clarifies one’s confusion on the subject but it also helps detect unnecessary assumptions and distortions present in the subject and clears them up.


Fundamental Postulates

Normally, there are always some basic postulates on which the subject is built. But the rest of subject must proceed from these postulates in a continuous, consistent and harmonious manner. If there are any gaps then some knowledge is missing. Those gaps needs to be filled by discovering the missing knowledge. Sometimes, such an effort may require questioning the very postulates on which the subject rests.

Fundamental progress has occurred whenever the basic postulates have been improved upon. An obvious example is Einstein’s improvement of Newton’s postulates that revolutionized the subject of Physics.



Many gaps in knowledge have existed when means of observations have not been available. Such gaps are then covered up by assumptions. Rapid progress has taken place when better means of observation has been available. The invention of Telescope has helped us understand the solar system we live in. The invention of Microscope has helped us understand the source of diseases that have afflicted mankind. 

But the tool which made such inventions possible has been the mind of man. Behind these inventions are mathematics and scientific theories, which are fantastic inventions of the mind on their own right. 


The Mind

The mind has amazing abilities that have yet to be explored fully. On average, the mind is operating far below its potential. The reason for this has been explored to some degree but we still need better theories that can be applied to improve the mind’s potential in all cases. Hopefully, Subject Clearing may allow us to approach “the subject of the mind” in productive ways to come up with viable solutions.

Subject Clearing is essentially a project of the mind to handle itself.


Anomalies: Assumptions & Distortions

Reference: Course on Subject Clearing

When studying a subject one should be able to detect the hidden assumptions and distortions present in it. This is especially necessary when one is studying the fundamentals of a subject. Such distortions can be very pervasive. They may even enter the definitions of words provided in dictionaries. One should be able to detect such assumptions and distortions and clear them up.

In Subject Clearing, we refer to these as ANOMALIES. The anomalies stand out because of their inconsistency with reality. Since one’s perception of reality itself may be corrupted by anomalies, it is important to define what reality is.



The integrity of reality underlies the very concept of universe. The word UNIVERSE is derived from a Latin root, which means “entire, all, literally, turned into one.” Therefore, the reality of the universe is the continuous, consistent and harmonious aspect that can be seen as ONE. When applying the scientific method, it is the consistency of observations that one is seeking. Any inconsistency alerts one to something amiss. 

We define reality as that continuous, consistent and harmonious aspect of the universe which is perceived as ONE.



The dictionary defines “anomaly” as something irregular, odd, peculiar, or strange condition, situation, quality, etc. It is an incongruity or inconsistency. A violation of the integrity of reality would be an anomaly.

Since reality has the quality of continuity, consistency and harmony, we may provide a formal definition for ANOMALY as follows.

We define anomaly as any violation of the integrity of reality, such as, discontinuity (missing data), inconsistency (contradictory data), or disharmony (arbitrary data).

An anomaly flags the presence of a hidden impression on the mind, which is generally expressed in the form of an assumption. A fixed assumption or idea then leads to a distortion of what one views. When the hidden impression on the mind is discovered, it collapses the assumption and its resultant fixed ideas. As the consequence, there are realizations, which resolve the anomaly.


Other Definitions

In his Data Series, Hubbard defines anomalies in the form of the following outpoints. Outpoint is generated when one,

  1. Omits a fact.
  2. Changes sequence of events.
  3. Drops out time.
  4. Adds a falsehood.
  5. Alters importance. 

In other words, for Hubbard reality has the following properties.

  1. All relevant facts are known.
  2. Events are in actual sequence.
  3. Time is properly noted.
  4. The data is true or valid.
  5. Relative importances amongst the data are recognized.

Hubbard doesn’t go as far as recognizing the ONENESS of reality, but his Data Series is a brilliant piece of work.


The Key words and their Definitions

Arranging key words in logical sequence may reveal anomalies. Incomplete definitions of the key words may also reveal anomalies. They may at first appear as something puzzling. But closer examination may reveal the exact anomaly.

A claim made in a subject without further explanation is a postulate. A postulate, at best, is an educated assumption. Every subject starts with a postulate. That is normal. But when there is a postulate in the middle of a subject, it is more likely an assumption that is hiding some gap in knowledge. When the gaps in knowledge becomes clear, then real progress also becomes possible.



There are likely to be many contributors to a subject. For example, many different cultures have contributed to the broad subject of religious knowledge. Religions were the earliest attempts at understanding this universe. We find many gaps in knowledge among otherwise deep and astute observations.

When we look at religion as one subject we may find many similar concepts referred to by different words in different cultures. When we seek consistency among these concepts we may develop a deeper understanding of the universe.

It is the resolution of anomalies that leads to deeper knowledge.


Purpose of Study

The true purpose of study is to resolve anomalies as you come across them. The anomalies that you come across are either in the materials you study, or in your own thinking. The resolution of anomalies develops a clarity of mind and the ability to think fast on your feet.


Selecting the Subject to Clear

Reference: Course on Subject Clearing

Subject clearing starts with selecting a subject to clear. In school we study many subjects. Some of them are really important for our career path. Similarly, there are life skills important for our success. This gives us a list of subjects to clear.

One should clear these subjects in the order that they are taking up one’s attention.

You probably know the subject you would like to study. But you may find that your attention is stuck back in subjects that you had trouble with in the past. It is advisable to recover all that attention first before you devoting your time to studying the subject of your interest. You want to clear up those subjects only to the point that your attention is no longer stuck on them. 


Make a Complete List

Your first step is to make a list of all the subjects that you struggled with. Broadly, the basic subjects are language, grammar and mathematics, but these may be broken down into specific subjects that you remember.

Keep listing the subject until you feel that the list is complete. You will feel much better at this point because you know that all your earlier confusion is confined to this list of subjects.


Arrange the List in Order

Arrange this list in the order you would like to clear up these subjects.

Now look up the derivation of the subject titles one by one in the order listed. Make sure you settle with the root meaning of each subject title. For example, the root meaning of the title ARITHMETIC is “skill with numbers.” You do this until you understand the basic purpose of having each subject.

Now rearrange this list in the order these subjects are important to you.


Clear up the Basic Postulate

Take up each subject one by one in the order listed, and determine the most basic idea that subject is based on. For example, the subject of arithmetic is based on the idea of counting and measuring. You do this until you understand the basic postulate underlying each subject.

Now rearrange this list in the order you attention goes to these subjects.


Clear up the Basic Key Words

Take up each subject one by one in the order listed, and do the following.

  1. Make a list of key words for the subject that you remember. Do this until the list is complete.
  2. Arrange the key words in a logical order that makes sense to you.
  3. Clear up the meaning of each word starting from its derivation.

Repeat these steps for a subject until your attention is fully handled on that subject before you move on to the next subject.

Complete the whole list of subjects this way.


Handle Stuck Attention

Start all over once again with the list of subjects you struggled with. Strike out the subjects you no longer have attention on. Add new subjects that you now have attention on. You may now broaden you list of subjects to subjects other than school subjects.

Repeat the procedure above.



By following the procedure above, you may, ultimately, end up with subject(s) that you are really interested in learning in detail. Here you may even get into researching these subjects. We shall get into that aspect later. 

You may find that as the mind starts to clear up its persisting confusions and questions, the mental and physical health also starts to improve—sometimes miraculously.


The Core of Subject Clearing

Reference: Course on Subject Clearing

The Core

The core of Subject Clearing is the following idea:

The fastest and guaranteed method to discover and resolve the earliest holes in the understanding of a subject is to follow the logic of that subject.

The first logical step is an understanding of why a subject is there. This may be grasped from the title of that subject. For example, ARITHMETIC is the title of a subject. The root meaning of the word “arithmetic” is: “skill with numbers.” So, the subject of arithmetic is there to help one develop skill with numbers.

The next logical step is to understand the postulate on which that subject is based. The subject of ARITHMETIC is based on the postulate is that all things can be counted or measured. Therefore, arithmetic starts with COUNTING and NUMBERS.

Counting naturally develops into the skill of ADDITION. The opposite of addition is SUBTRACTION. These are the first two skills to master.

Repeated addition develops into the skill of MULTIPLICATION. The opposite of multiplication is DIVISION. These are the next two skills to master.

Repeated multiplication develops into POWER displayed through the use of exponents. The opposite of power is LOGARITHM with a certain base. Use of these are additional skills.

This sequence of skills provides us with a dimension in which the subject of arithmetic has logically developed.


Development of a Subject and Key words

The logical development of a subject is encased in the key concepts of that subject. These concepts are expressed through words that form the terminology of that subject. We may call them KEY WORDS. Such key words may be arranged according to the logical development of the subject.

Some of the key words of the subject of Arithmetic are capitalized above. These key words may be arranged in a logical order as follows:


The key words above provide only one dimension of the subject of Arithmetic. Another dimension could be presented as follows:


The understanding of later concepts depends on the understanding of earlier concepts. The earlier is a key word in the logical development of a subject that is not understood or misunderstood, the deeper is the hole it creates. It has the most disastrous consequences when misapplied.

If the key words of a subject available in a logical order with correct definitions, then one can rapidly recognize the holes one has in the understanding of that subject, and make rapid progress in understanding it fully. 

Subject clearing is the clearing of one’s holes in the understanding of a subject by studying its key words in a logical order.

One should always clear up the basics of a subject first before trying to understand the later details.


Missing Key words and Definitions

We, at first, encounter subjects that are formally introduced to us in schools. It may be easy to figure out the logical order of their key words. But there are many other subjects that we encounter later, such as those associated with job skills, like doctor, engineer, lawyer, etc. There are also many life skills, like communicating, problem solving, mindfulness, etc., which are very important subjects to understand.

The above approach of subject clearing applies to any subject you can think of. Many subjects, however, are riddled with assumptions and false data. They have either missing key words, or missing correct definitions for those key words. To understand these subject, one would also have to figure out the missing key words and correct definitions. 

Subject Clearing also detects and handles holes in the subject itself, but more on that later.

For now we shall focus on schooling.


Physics II: Chapter 2

Reference: Beginning Physics II

Chapter 2: SOUND



Sound Velocity, Rms Velocity, Wave-Front, Wave Power (Two Dimensional), Wave Power (Three Dimensional), Intensity, Plane Wave, Reflection, Refraction, Interference, Decibel Scale, Reverberation, Reverberation Time, Absorption Coefficient, Absorbing Power, Quality, Pitch, Beats, Doppler Shift, Shock Waves



For details on the following concepts, please consult Chapter 2.

The velocity of sound in air is,

The root-mean-square velocity of the gas molecules themselves is,

Waves in two and three dimensions have a wave-front. It is circular or spherical as shown below.

The wave-front isan imaginary line or surface drawn through the crest (or trough) of one of the ripples at a given instant of time. We are looking at the same phase of the disturbance at all different locations in the fluid. The circular or spherical shape of the wave-front means that the wave propagation of the disturbance is characteristic of the material through which the wave moves. The direction of propagation of the wave at any location is perpendicular to the wave front at that location.

For water ripples, the power transmitted through a unit length parallel to the wave-front is being diluted as the circular wave-front expands to larger circumference. Since the circumference of a ripple increases in proportion to its growing radius R, the power per unit wave-front length must decrease as 1/R.

Similarly, the energy and power of the wave, per unit area perpendicular to the direction of propagation of the wave fall off as 1/R2.

The power per unit area perpendicular to the direction of propagation is called the intensity, I. The intensity for a three-dimensional wave is given by,

I = P/A

A wave moving through space in which the wave-front is planar is called a plane wave, and is characterized by the fact that every point on the planar wave-front is in phase at the same time. A small window on the spherical wave front is almost planar if the dimensions are small compared to the distance from the source of the wave. The wave equation for such a wave is exactly the same as for the longitudinal waves in a long tube.

When sound wave-fronts hit a barrier, such as, the side of a mountain, part of the wave reflects and part is transmitted into the barrier. The part of the wave that is reflected has diminished amplitude but the same frequency and velocity as the original wave, and hence the same wavelength.

When a wave travels through a medium of varying densities (for example, layers of air at different temperatures) the velocity of different parts of the wave-front are different, and the direction of propagation of the wave changes as a consequence. This is called refraction.

Interference is the effect of having more than one wave passing a given point, and the possibility that the two waves will reinforce or weaken each other as a consequence of the phase difference between the waves.

To describe the range of sound intensities it is useful to create a logarithmic scale called the decibel scale (db), which gives a quantitative measure to “loudness”, which we label n, and define as:

n = 10 log (I/Io)

The persistence of a sound after its source has stopped, caused by multiple reflection of the sound within a closed space.

The reverberation time is defined as the time it takes for the intensity of a given steady sound to drop 60 db (or six orders of magnitude in intensity) from the time the sound source is shut off. Reverberation times depend on the total acoustic energy pervading the room, the surface areas of the absorbing materials and their absorption coefficients. A formula that gives good estimates of the reverberation time is given by:

tr = 0.16V / A

where tr is the reverberation time (s), V is the volume of the room (m3) and A is called the absorbing power of the room.

The absorption coefficient of a surface is defined as the fraction of sound energy that is absorbed at each reflection. Thus, an open window has an absorption coefficient of 1 since all the energy passes out of it and none reflects back in. Heavy curtains have a coefficient of about 0.5, and acoustic ceiling tiles have a coefficient of about 0.6.

The absorbing power A is just the sum of the products of the areas of all the absorbing surfaces (m2) and their respective absorption coefficients.

When a note on a musical instrument is played, the fundamental is typically accompanied by various overtones (harmonics, i.e., integer multiples of the fundamental) with differing intensity relative to that of the fundamental. The sound of harmonics is pleasing to the ear, and while the note is identified by the listener with the fundamental frequency, the same note from different instruments will sound differently as a consequence of the different harmonic content. These different sound recognitions by the human ear are called the quality of the note.

The pitch of a note is the human perception of the note as “high” or “low” and is closely related to the frequency but is not identical to it. The pitch involves human subjective sense of the sound. While a higher frequency will be perceived as a higher pitch, the same frequency will be perceived as having slightly different pitches when the intensity is changed. When the human ear hears a fundamental and harmonics it perceives the pitch as that of the fundamental.

If we have two frequencies that differ only by a few Hz we can indeed detect “interference” effects that oscillate in time slowly enough to be easily detectable. This variable amplitude corresponds to a maximal loudness in the sound, called a beat. The number of beats per second is just the difference of the two frequencies.

The Doppler shift is a change in pitch caused by motion of the source of a sound wave through the air (as in the example of the siren of an ambulance) or by the motion of the listener through the air. If the source is moving toward the listener, the sound waves are bunched up, and the listener would detect shorter wavelengths or higher frequencies. If the source is moving away from the listener, the sound waves are more separated, and the listener would detect longer wavelengths or lower frequencies.

For more general case, when the velocity of the listener is included,

When supersonic (faster than the speed of sound) motion occurs a compressional wave, due to the object cutting through the air, is emitted by the traveling body and forms what is called a shock wave. The shock wave moves at a specific angle relative to the direction of motion of the object through the air, and can sometimes be of sufficient intensity to cause a loud booming sound.

R/x is the ratio of the opposite side to the hypotenuse of a right triangle with angle  as shown. Then:

The direction of propagation of the shock wave is perpendicular to the wave-front and makes an angle (90° – ) to the direction of motion of the object. Shock waves accompany speeding bullets, and an example in a medium other than air is the bow wave of a speed boat in water.