Category Archives: Education

Mindful Subject Clearing

Reference: Course on Subject Clearing

Mindful Subject Clearing is the most powerful tool currently available to bring clarity to the mind on any subject. It not only brings about a much better understanding of a subject but also helps detect the basic postulates, assumptions and erroneous ideas present in that subject.

The basic postulates help one understand the grounds on which a subject stands. Ideas based on these postulates must be demonstrable. There must not be inconsistencies among these postulates, ideas and reality.

If assumptions and erroneous ideas are not detected and isolated, it can cause serious problems with the application of the subject. Such erroneous ideas can be very pervasive, and may even enter the definitions of words provided in dictionaries. It is, therefore, very important not to miss them in your study. 

The true purpose of study is to resolve inconsistencies (things that do not make sense) as you come across them in a subject or in life. This develops clarity of mind and the ability to think fast on your feet.

Since additional information on a subject may easily be accessed through Internet these days, the purpose of study is to not memorize but to improve critical thinking.


The Steps

Here are the steps to Mindful Subject Clearing:

1.    Make a list of key words in the subject.

Every subject has its own vocabulary. It may even use certain common words in a special meaning. Start making a list of key words used in that subject. If you are familiar with the subject you may already know some of those words. Otherwise, skim through the chapter that you are going to study, and obtain some key words from it. Put that list on an Excel worksheet. This list may grow as your studies get deeper into the subject.

2.    Enter the broad concept on the worksheet next to the word.

Look up the word in good dictionary. Read the ‘history’, ‘origin’, and/or ‘derivation’ for that word. Simply work out the broad concept underlying that word and write it down on the worksheet next to the word. Do so for each word on the list. Here are some broad concepts associated with some words.

STUDY = “eagerness, intense application”.
MATHEMATICS = “something learned”.
ARITHMETIC = ARITHMOS number + TECHNE skill = “number skill”.

3.    Read the subject material one paragraph at a time.

Procure the study materials in the form of an editable file on the computer. Study the materials of the subject one paragraph at a time. If the paragraph is too big, break it down into chunks of reasonable size.  If the paragraph is too small, and the thought continues to the next paragraph then read the two paragraphs together. Go over the paragraph as many times as necessary to understand the main thought.

4.    If the paragraph is fully understood, write down your understanding of its main thought along with your comments.

Make sure you fully understand the paragraph. If not then go to step 5. Once you have fully understood the paragraph, then summarize its main thought in your mind and look at your reactions to it. Write down below that paragraph your understanding of its main thought along with any comments. Treat this action as having a conversation with the author. Then go to step 7 below.

5.    If the paragraph is difficult to understand then look for the first word not fully understood.

If you find your mind going blank as you read the paragraph, something in that paragraph is not fully understood. Trace that sense of misunderstanding to the earliest sentence in that paragraph,  and to the earliest word in that sentence. Here you have to be very careful because the misunderstanding can come from having assumed the wrong definition for a simple word like “on”, “of”, “in”, et cetera. Usually there is an obvious word, whose meaning you may have guessed in the past, but never actually looked up in a standard dictionary. At least there is some uncertainty in your mind about how that word is being used in the given context. We shall call it MU (misunderstood) for short. Write that MU word down on a sheet of paper. 

NOTE: If it is a key word in that subject, then see if its is defined in that paragraph or in the glossary of that book. Then write its definition down on the Excel worksheet of Step 1 above.

Do not look for anything else in that paragraph until you have cleared up this MU. You must be very honest with yourself in keeping this discipline.

6.    Clear up the MUs in that paragraph until that paragraph is fully understood.

(6a) Look up the MU word in a standard reference — This reference could be a standard dictionary or an Internet resource, such as, Wikipedia and Google Images.

(6b) Understand the concept underlying the word — Per step 2 above.

(6c) Look up the definitions of the word — Look up the definitions of the word. Visualize the definition in the context in which that word is used. If it doesn’t fit go to the next definition. You may visualize a definition better if you make a few of your own sentences, or examples from your experience, with that word. Some words may require the use of “Google Image.” Always keep the basic concept in your mind that underlies the word . It is best to check out all definitions this way until you find the definition that clarifies the MU. 

(6d) Look up MUs in the definition — If a definition contains an MU then look it up per this procedure. Write that MU down below the earlier MU. This may sometime get you in a long chain of MU words. Keep an account of these words on the list as you add them or cross them out after clearing them. It is okay to look up the same word again several times. Each time you look up the same word you get a deeper understanding of its meaning.

(6e) Review the original sentence — Review the sentence in which the original MU was found. Make sure that it now makes sense. If not then there may be another MU word in the sentence. Repeat the above procedure until that sentence is understood.

(6f) Review the paragraph — Once the sentence is cleared up, go back to step 4.

7.    Check the paragraph for key words/definitions.

Check the paragraph for key words and/or key word definitions that do not already appear on the Excel worksheet. If a key word definition is expanded upon then add it to the Excel worksheet.

8.    Continue with subsequent paragraphs per steps 4 to 7 until the end of chapter.

Continue as above with rest of the chapter building up the key word list on the Excel worksheet.

9.    Gradually build up the key word list for that subject.

Build up the key word list, with broad concepts and meanings of the key words, as you study the subject chapter after chapter, and book after book. Note down any additional concepts and meanings next to the appropriate word on the Excel worksheet. Also note down the questions that may arise in your mind about the words.

The broadest case would be the subject of religion. You may first make a key word lists for Judaism by studying the scriptures and commentaries. Then you may make key word lists for Christianity and Islam respectively. Then you may combine these lists to generate a key word lists for Western religions. Similarly, you may combine the key word lists for the Vedas, Hinduism, and Buddhism, etc., to generate a key word list for Eastern religions. Finally, you may combine all these word lists to generate the key word list for religion.

Here you may find many different definitions for the same key word, such as, God, all written down in one place. You may also find different words used in different religions for the same fundamental concept.

As you work on this step for a subject you will have many realizations along the way. This is a continuing step. So, you continue with the subsequent steps as well.

10.    Arrange the key words in sequences appropriate for understanding.

The concepts in a subject always evolve in some sequence. This sequence may be linear at first but then it branches out in different directions like a network or a matrix of concepts. This can easily be seen in Mathematics and Science.

In Excel, you may separate the key words on two different worksheets categorized as “fundamental concepts” and “derived concepts”. Then arrange the concepts in each worksheet in the order they evolved.

Since the sequence of the evolution of these concepts is multi-dimensional, you may set up the Excel worksheet to sort out these key words in different sequences. To do this you may create different “priority columns” in the worksheet. In each “priority column” assign a unique number to the key word so it sorts out in the order you want. The whole idea is to arrange these words in different ways to examine the connections among them.

11.    Note any inconsistencies among the concepts and clarify them.

As the study of the subject progresses, you’ll be collecting more data to describe each key word. Resolve any inconsistencies among that collection of concepts and meanings for each word through careful examination and contemplation. Once resolved, express the broad concept for each word in your own words. There may be one broad concept but several distinct meanings for a word. If so, then express the multiple meanings by numbering them. You are creating your own glossary.

Next, examine the evolution of the key words by arranging and rearranging them in different sequences. You are looking for inconsistencies that do not make sense. Here it is very important that you do not inject justifications in your examination. Be wary of arbitrary notions, assumptions and beliefs that may be covering actual holes among these concepts that need to be filled. Trace existing ideas in that area of inconsistency one by one for arbitrariness. 

Deeper research may be required to clearly identify holes among the concepts and fill them. First review your study materials to clarify such inconsistencies. If it does not clarify easily then note it down on the worksheet and research through other materials in the library, or on Internet, until the inconsistency is resolved.

12.    Clarify the fundamentals of the subject as a priority.

The consistency of the fundamentals determines the consistency of the whole subject. Any inconsistency at the fundamental level must be handled as a priority. For example, a unified theory is desperately being looked for in the subject of Physics, which could bring the fundamentals of Newtonian Physics, the Theory of Relativity, and Quantum Mechanics in line. This means that inconsistencies exist in our understanding of the fundamental level of physics

There are likely to be many contributors to a subject who may use different words for the same concept. This is the case with religious knowledge from different cultures. Group such words together to discover inconsistencies among concepts.

Study of inconsistencies may lead to discovery of arbitrary beliefs that were advanced in the absence of knowledge, or you may find erroneous observation, or simply some notions that are taken for granted. This may reveal gaps in the subject itself. Develop your own understanding by seeking consistency among the fundamental concepts in a subject.

13.    Make the subject as complete as possible.

There are many examples in the subject of religion where gaps in knowledge are hidden under fixed beliefs and dubious explanations. This may be the case with any subject where inconsistencies abound. Follow up on inconsistencies, which may then reveal gaps in the subject. Real progress then becomes possible.

Fill gaps in the subject with wider research. Make the subject as complete as possible through direct experience and experimentation.

14.    Keep your viewpoint as objective as possible when you research a subject.

This step is done after one has acquired a good bit of experience with subject clearing. This is an advanced step that consists of doing the following exercise: Know to Mystery Process



These are the steps of SUBJECT CLEARING. You do them again and again for the same or different subjects. This includes step 14. These steps lead you to wonderful realizations that keep coming. As you assimilate those realizations your viewpoint moves up toward KNOWING on the Know-to-Mystery scale.

You may find examples of NOTES & COMMENTS resulting from Subject Clearing below.

Comments on Books


‘College-For-Everybody’ Agenda

The following is a Forbes article by Tom Lindsay:

How the ‘College-For-Everybody’ Agenda Harms both Students and the Economy

Many in higher education worry continuously over the fact that only roughly half of students who enroll in college ever graduate, and that those who do graduate often take more than four years to do so. But few seek to go to the roots to attempt to discover the ultimate causes explaining these depressing statistics. One of the few who makes such an attempt is Charles Murray, whose contrarian explanation is, “Too many people are going to college.”

Regardless of whether one agrees with its conclusions, Murray’s Real Education, published in 2008, has received far less attention than the gravity of its arguments merits. Real Education defends what he deems are four simple truths about education, but truths that cannot be said publicly without engendering the wrath of a culture fallen prey to what he labels “educational romanticism.” They are “(1) ability varies; (2) half of the children are below average; (3) too many people are going to college; and (4) America’s future depends on how we educate the academically gifted.”

The American education system, says Murray, “is living a lie. The lie is that every child can be anything he or she wants to be.” The lie is bipartisan, he argues; it spans both Republican and Democratic Party platforms, its unrealistic assumptions driving and distorting both K-12 and higher-education policy.

In higher education, the vision “that everyone should go to college”—like all well-intentioned projects suffering only tenuous connections to reality—asks “too much from those at the bottom, . . . the wrong things from those in the middle, . . . and too little from those at the top.”

How many students, then, should go to college? In answering, Murray makes a key distinction—between “college-level instruction in the core disciplines of the arts and sciences” versus “the courses (and their level of difficulty) that are actually offered throughout much of the current American college system.” The difference between the two is large and widening. If getting a diploma proves the ability to “’cope with college-level material,’” then “almost anyone” can succeed who merely “shops for easy courses in an easy major at an easy college.” However, once we shift our focus to “college-level material traditionally defined, the requirements become stringent,” and toward satisfying this stricter demand, “no more than 20 percent of all students” qualify.

But if this is true, what of democracy’s rightful wish to see as many as possible benefit from a liberal education that fulfills John Stuart Mill’s vision of engendering “capable and cultivated human beings”? Murray agrees that more students should receive the “basics of a liberal education.” Nevertheless, the place for most students to do this is, he argues, in elementary and middle school, not college. K-8 education should seek to inculcate the core knowledge described in E.D. Hirsch’s Cultural Literacy—knowledge that “makes us Americans together rather than hyphenated Americans.”

Murray’s critique is not “the same as saying that the average student does not need to know about history, science, and great works of art, music, and literature.” Instead, he urges that we “not wait for college” to teach these subjects. In college, the study of these subjects should go much deeper; it should require close, careful reading of the foundational texts that constitute what Matthew Arnold called “the best that has been said and thought in the world.” For example, reading “the Odyssey in ninth grade is nothing like reading the Odyssey in a good college course.”

However, “most students at today’s colleges choose not to take the courses that go into a liberal education because the capabilities they want to develop lie elsewhere”—a fact that “colleges do their best to avoid admitting.” Instead, under universities’ “distribution requirements” (the sham version of a core curriculum), students can fulfill their humanities and literature requirements through taking courses such as Indiana University’s “History of Comic Book Art”; Dartmouth’s “Rock Music from 1970 to the Present,” and Duke’s “Campus Culture and Drinking,” to mention a few. Worse, the elite Brown and Vassar require no core courses, casting 18-year-olds into an endless abyss of “choice,” with neither compass nor yardstick.

Because universities are “no longer in the business of imparting a liberal education,” it follows that those students lacking the capacity for and/or interest in a genuine core curriculum should have “better options than going from high school to college.”

But what of the need for even these students to attend college to enhance their capacity to make a living? Murray responds that four-year brick-and-mortar residential colleges are “hardly ever” the best places to “learn how to make a living.” To begin, for most vocations, excluding fields such as medicine and law, four years of class work is not only “too long” but “ridiculous.” For many of such students, two-year community college degrees and online education provide “more flexible options for tailoring course work to the real needs of the job.”

Moreover, the brick-and-mortar campus is becoming “increasingly obsolete.” The “Internet is revolutionizing everything”— university libraries have lost their indispensable character, and both faculty research and faculty-student interaction no longer require the “physical proximity” that brick-and-mortar campuses make possible.

But what of the “wage premium” reaped by college graduates? For Murray, high-school graduates who pursue the B.A. primarily to boost their earning power are “only narrowly correct.” Doubtless, B.A.-holders earn more on average than those without degrees, but this due in part to a “brutal fact.” Given the increase in the number of college graduates over the past half-century (more than a third of 23-year-olds now hold B.A.s), “employers do not even interview applicants” without degrees. “Even more brutal,” the B.A.’s comparative advantage “often has nothing to do with the content of the education” received. The average employment gains of college graduates must be weighed against the fact that “wages within occupations form a distribution.” Therefore, a student with average academic skills but exceptional “small-motor skills and special abilities” is more likely both to earn more and to be happier as, say, an electrician than as a mediocre middle-manager.

In addition to being happier as an electrician, this student would benefit from the fact that “there has never been a time in history when people with skills not taught in college have been in so much demand at such high pay as today.” In fact, as in the case of the proficient electrician, the wages of top performers in a plethora of occupations not requiring a B.A. are “higher than the average income for many occupations that require a B.A.”

Murray presents a higher-education system in which too many students are forced to spend too much time chasing their tails. His thesis that too many are going to college today goes no small distance toward explaining why roughly half of those who enroll in college fail to graduate. It goes a long way toward explaining why, of those who do graduate, 36 percent show little-to-no increase in the critical-thinking and writing skills that a degree is supposed to signify. It goes a long way toward explaining why, in the ‘60s, college students studied on average 24 hours a week, whereas today they spend only 14. Finally, it goes a long way toward explaining the rampant grade inflation perpetrated by universities eager to “accommodate” the masses of new students in college who can’t cope there. In the ‘60s, 15 percent of college grades nationwide were A’s. Today, that percentage has nearly tripled: 43 percent of all grades today are A’s. In fact an A is now the most common grade given in college.

Higher-education reformers read the statistics above and pronounce higher education broken. If they hope to fix it, one indispensable step is to face Murray’s thesis without blinking.


Old Geometry Book

Reference: Remedial Math

For application by the student

These sections are taken from PLANE AND SOLID GEOMETRY by George Wentworth and David Eugene Smith, first published in 1888.

G00 – Contents

G01 – Introduction

G02 – BOOK I. Rectilinear Figures

G03 – BOOK II. The Circle

G04 – BOOK III. Proportion. Similar Polygon

G05 – BOOK IV. Area of Polygons

G06 – BOOK V. Regular Polygons and Circles

G07 – Appendix to Plane Geometry

G08 – BOOK VI. Lines and Planes in Space

G09 – BOOK VII. Polyhedrons, Cylinders and Cones

G10 – BOOK VIII. The Sphere

G11 – Appendix to Solid Geometry

G12 – Miscellaneous & Index


Troubleshooting Math

To troubleshoot any difficulty you first look at the broad area of that difficulty, and then you gradually narrow it down until you have defined the actual difficulty precisely.

So, to troubleshoot a difficulty in math you start with the broad area of Mathematics.

Mathema (Greek) = Learn
Mathematics = Tools for learning

Mathematics provides you with analytical tools for learning. When you are troubleshooting mathematics, you are troubleshooting the difficulties a person is having with learning analytically. You narrow down to the area of mathematics where the person cannot think analytically.

Mathematics is analytical learning and not just memorizing of materials.

If the student is having trouble with higher mathematics, such as, Trignometry, Analytical Geometry, or Calculus, then start from there. You may explain the area the student does not understand. But if the student cannot understand the explanation analytically, then the troubleshooting may lead to one of the three areas below.

When you select one of these areas, explain it per Math Overview. You do not have to explain that whole document. Keep to the trail of trouble.

Ask, “What part of this area you have most difficulty with?”

Use the answer to narrow down further to the area of difficulty. Quiz the student on the key math vocabulary in that area. From student’s answers you may narrow down the area of difficulty further.

If the student cannot answer the question, simply start with the first lesson
related to that area at Mathematics. Follow student’s attention to fish around for the actual difficulty.

As you narrow down the area of difficulty, keep asking, “What part of this area you have most difficulty with?”

Check the key math vocabulary in the narrowed down area. Soon you’ll reach the actual difficulty. Handle it using the right materials selected from the appropriate level at Mathematics, or from student’s own materials.

Once that area is handled, the student may come up with another area that he or she has attention on. Narrow down to the actual difficulty in that area as above, and handle it.

Otherwise, start all over again from the diagram above. This time you may follow a different trail to a different area of difficulty.

Ultimately, teach the student how to troubleshhoot difficulties. This is the best thing you can ever do for the student.


Stress and Education


Reference: Critical Thinking in Education


The biggest challenge to education is the stressed child, or the stressed student. When a child is stressed his attention is introverted onto his personal issues and he cannot learn.

The education at SLS is successful because it is addressing the challenge of stress successfully through its special curriculum. Learning requires extroverted attention.  The SLS environment is very extroverting.

Rule: The school environment should be such that it extroverts attention.

The general stress in the current society is increasing. It is inevitable that a certain percentage of children coming to school have stressful situations that are holding their attention. Their introverted attention then does not allow them to learn.

It is absolutely necessary for school to provide a stress-free extroverting environment so that learning can take place. If the school’s environment is also stressful then the student becomes conditioned and robotic.

At SLS, the first half hour of the day is devoted to activities that extroverts attention. The following exercise may also be used to extrovert attention.

This exercise may be conducted with a group of students, or it could be applied to a student who has difficulty learning.



PURPOSE: To extrovert the attention by exploring the five physical senses.


(Touch – 5 minutes minimum)

  1. Go to an environment where you can explore the sense of touch.

(a)  Touch two different surfaces and compare how they feel.

(b)  Touch them alternately until you can discern the uniqueness of each surface.

(c)  Touch a third surface repeatedly to get a feel of it. Then touch it alternately with one of the earlier surfaces, until you can discern how this third surface is unique.

(d)  Similarly touch additional surfaces carefully until you can discern their uniqueness.

  1. Explore the sensation of touch until you can do so happily without feeling any resistance inside you.

  2. Exercise the sense of touch for at least 5 minutes. You may do it for as long as you want.


 (Sight – 5 minutes minimum)

  1. Go to an environment where you can explore the shapes and colors of things.

(a)  Look at two different objects and compare their shapes and colors.

(b)  Look at them alternately until you can discern the uniqueness of their shapes and colors.

(c)  Look at a third object repeatedly to get an idea of its shape and color. Then look at it alternately with one of the earlier objects, until you can discern how this third object is unique.

(d)  Similarly look at additional objects carefully until you can discern their unique shapes and colors.

  1. Explore the sight of objects until you can do so happily without feeling any resistance inside you.

  2. Exercise the sense of sight for at least 5 minutes. You may do it for as long as you want.


 (Hearing, Smell & Taste – total 10 minutes minimum)

  1. Sit around a table and unpack your lunches and drinks. Don’t hold yourself back from talking.

  2. Start smelling and tasting little bits of your lunch, while listening to each other talk. You may even listen to your own voice.

(a)  Explore the different sounds that you hear as to their timbre, pitch, loudness and other qualities.

(b)  Explore the different odors as to how pleasant or pungent they are, and as to their other qualities.

(c)  Explore the different tastes as to how sweet or salty they are, and as to their other qualities.

  1. Explore the sounds, smells and tastes until you can do so happily without feeling any resistance inside you.

  2. Do this exploration for at least 10 minutes. You may do it for as long as you want.

  3. Take some deep breaths, appreciate what is around you, and get ready for your next school activity.