Monthly Archives: April 2011

KG MATH 1: Orientation & Spatial Sense

April 23, 2011 – 5:54 PM

Spatial sense is having the sense of direction, distance and location with respect to one’s environment. Orientation is getting adjusted to that environment.

To get oriented one needs to spot the relative locations of various things in one’s environment. To spot a location one only needs to know the direction it is in and its distance from one.

A direction is the line along which attention may be directed. There is infinity of directions radiating out from one’s location. The main directions are FRONT, BACK, ABOVE, BELOW, LEFT and RIGHT. The directions of LEFT and RIGHT are difficult for a child to recognize until he or she reaches Kindergarten.

A distance is the separation between two locations. There is infinity of different distances in any one direction. The distances may be identified roughly as NEAR or FAR.

A position of an object tells us how it is located in relation to other objects, such as, IN, OUT, ON, UNDER, MIDDLE, and NEXT TO. A child may learn these positions as part of learning the language, but may also be taught as part of mathematics.

Spatial locations combine into shape. A very common shape is rectangle that most doors and windows have. Other shapes are triangles, circles, etc. These shapes may be drawn on a plane surface. They are two dimensional because they have length and breadth, or width and height.

Most objects are three dimensional because they have a third dimension of thickness or depth. Examples of simple objects are cubes, spheres, cylinders, cones, etc.

Shapes and objects are symmetrical when one half is the mirror image of the other half. Most bodies are symmetrical. Objects may slide, flip or spin in space.

Our body is an object that exists in space. Therefore, orientation and spatial sense is an important subject for a child to become familiar with. Here are some exercises in this subject for the kindergarten level.

LEVEL K1: ORIENTATION & SPATIAL SENSE

“Orientation & Spatial Sense” forms the foundation of the subject of GEOMETRY. It introduces the elements of space and how these elements may relate to the student.

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By vinaire | Posted in Mathematics | Comments (2)

Is there Divinity?

April 23, 2011 – 7:17 AM
Ganesha

Reference: Religion

Socrates almost had his finger on it when he posed the question, “Can man be made self-determined and responsible for his own actions?”

Plato lost it when he recommended the use of religion (supernatural authority and fear) to control the wild beast nature latent in every person.

Aristotle came close to defining it, but the logic that brought him so close to an understanding of divinity, also prevented him from defining it precisely. Let us take a look at that one final step that he could not take.

Aristotle follows Socrates’ lead to examine such common terms as, justice, morality, virtue, etc., to uncover the unknowing assumptions made by people. He applies Plato’s Doctrine of Ideas to voluminous observations to define the concepts, laws, and principles that underlie all that we sense. He coins many new terms, such as, faculty, motive, energy, actuality, maxim, principle, etc., to communicate those concepts precisely. He formulates a scientific method so others may continue with this process.

Aristotle digs deep into observations, especially in the field of biology and natural sciences, and comes up with general frame of references (universals) from which to evaluate further observations. Thus he simplifies the management of voluminous observations by uncovering categories with logical connections.

He, then, digs deep into these categories to come up with a more fundamental frame of reference. He reduces all observations to (a) FORM (the shaping force), and (b) MATTER (the raw material being shaped).

To Aristotle, FORM is the inner necessity or impulse which exists in MATTER. MATTER is continually being formed into new, complex shapes by FORM that is inherent to it.

Aristotle considers MATTER to be without beginning. MATTER is worked into more complex and varied shapes by FORM. To him, God is “Prime Mover Unmoved.” God is the source of all motion. But, God has no motion within itself.

Aristotle never answers the question how MATTER arose in the first place. To him, this is like asking the question, “How God came to be in the first place?” And, that is as far as Aristotle goes. The inherent consideration here seems to be that ability, or potential, needs a “vessel” through which to express itself.

We find most viewpoints in the “Western thought” to be based on this frame of reference. It leads to the viewpoint that God must have a beingness in which to exist.

Can there be God without beingness? Can there be FORM without MATTER? Can there be Motion with no motion at its core? Can there be a Cause that is not itself caused?

 

DIVINITY

When we observe this universe, we cannot separate GOD from BEINGNESS, FORM from MATTER, MOTION from NO MOTION, and CAUSE from EFFECT.

These pairs, or dichotomies, appear simultaneously when a manifestation is perceived. Even the most fundamental ideas of MANIFESTATION and PERCEPTION seem to form a dichotomy. We all have struggled with the questions, “How does a manifestation appear?” “How is it perceived?” “Who or what creates?” “Who or what perceives?” The ultimate focus has been on “how,” “who” or “what.” It all boils down to the speculation that somebody or something must exist beyond all existence.

Essentially, the mind and its logic has hit a ceiling. Any attempt to pierce this ceiling runs into a fundamental  inconsistency, such as, “unmoved Mover” or ”uncaused Cause.”  This inconsistency seems to point to something that cannot even be conceived.

It would be beyond any mental conception. It would be beyond logic. It would be beyond any description. It would not be a form or cause. It would not even exist or be.

It would seem that

  1. A manifestation may occur without any prior consideration.
  2. A perception may occur without any prior consideration.

And in there, somewhere, may be Divinity, or may be not…

The Creation Hymn of Rig Veda

“Neti, neti,”

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By vinaire | Posted in KHTK | Comments (10)

An interview with Dalai Lama

April 21, 2011 – 5:59 AM

This is a brief presentation of an interview where the Dalai Lama discusses how he would change his beliefs because of scientific data.

http://abcnews.go.com/GMA/video/dalai-lama-angry-13400561

In my view, Buddhism is very scientific to start with.

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By vinaire | Posted in Buddhism | Comments (8)

Pre-Kindergarten Math

April 19, 2011 – 10:40 PM

Math, or maths, is short for mathematics. Etymologically, mathematics means ‘something learned.’ Actually, mathematics is a tool that teaches one to learn systematically.

For a child, mathematics really starts with the observation of space. A child looks around to get oriented to the space. This aspect of mathematics is called Geometry. Etymologically, geometry means ‘measuring earth.’ Here are some exercises in geometry for the pre-kindergarten level. (Note: It is a pdf file.)

The observation of things in space introduces one to the idea of ‘how many.’ A child may see single objects that are unique, or several objects of the same type. This aspect of mathematics is called Arithmetic. Etymologically, arithmetic means ‘number skill.’ Here are some exercises in arithmetic for the pre-kindergarten level.

The observation of things in space also introduces one to patterns and relationships among objects. For example, a child may see alternating objects or objects increasing in size. This aspect of mathematics is called Algebra. Etymologically, algebra means ‘reunion and equation.’ Here are some exercises in algebra for the pre-kindergarten level.

These exercises provide a basic familiarity to a young child on which subsequent mathematical concepts may be built.

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By vinaire | Posted in Mathematics | Comments (0)

The Nature of Knowledge

April 17, 2011 – 9:15 AM

Is there an ultimate knowledge? Are there ultimate answers to all the questions we have?

One may use any word, or words, to describe the ultimate understanding; but it doesn’t really matter what words are used because a word is not the “thing.”

The problem here is that there is nothing to describe. As far as our knowledge is concerned we can only know what we consider. We can never know what lies beyond these considerations. We may certainly consider what lies beyond; but then, we would only know the consideration we make.

Thus, what lies beyond considerations is unknowable. As we dig deeper to know more we shall simply find more considerations. Actually, we may simply uncover more of our own hidden assumptions, speculations, etc.

This unknowable would then be nothing more than a carrot to help uncover the considerations, which may be hidden deep in our consciousness. That is more than wonderful.

What then is this consciousness? What is at the core of consciousness? Who or what is THAT, which considers, and which is conscious of these considerations?

THAT, which considers, and which is conscious, is beyond time because time itself is a consideration. Whether THAT exists for ever or for just a blink of an eye, is the same thing. All that we find existing is the consideration of TIME.

THAT is also beyond space because space itself is a consideration. Whether THAT occupies all space or no space at all, is the same thing. All that we find existing is the consideration of SPACE.

Similarly, THAT is beyond the considerations of energy and matter. Whether THAT is all powerful, or with no power at all, is the same thing. Whether THAT is complete substance, or with no substance at all, is again the same thing. Power and substance are considerations too.

Is consciousness just a consideration? Is THAT, which considers, and which is conscious of these considerations, itself a consideration? Would we ever know who we truly are?

The ultimate identification of “who”, “what”, “where” and “when” seems to be unknowable, as these questions lead to speculations and more considerations. I do not know what others’ experience has been in this regard; but for me the ultimate identification has been unknowable. I have to accept that.

Any answers to “who”, “what”, “where” and “when” then must be self-generated and self-contained. The seed must appear spontaneously and randomly somehow… from where… that is impossible to know. This seed may then balloon into a “sphere of considerations” in a background of unknown.

All considerations in this “sphere” must be interconnected. All these considerations must support each other somehow. We try to look for linearity, and a beginning and an end; but, on the ultimate scale, I do not find such linearity to be there.

No wonder, others find me to be going around in circles. There is definitely a truth to this accusation. I do not have the ultimate answer. Nor do I think that anybody else has the ultimate answer.

A seeming answer may lie in this self-contained and self-generated “sphere of consideration.” But that may only take one around in circles. Sorry! This is my conclusion.

But there seem to be freedom beyond a mere consideration of freedom. One can only be constrained by one’s own considerations. Freedom may mean not constrained by one’s own considerations. Only those considerations may constrain one that are being generated unconsciously. One may enjoy life fully; participate in any and all adventures, while also being aware of all considerations one is generating even at the deepest level.

That would be Nirvana of Buddhism… that would be Mukti of Hinduism… that may be the “salvation” of Christianity; for this doesn’t mean forsaking life and adventure.

Nirvana would simply mean absence of hidden considerations even at the deepest level. It would mean total command over oneself. The Vedic concept of Brahma, as built into the process “neti, neti,” helps one move in that direction. With the process of “neti, neti,” one is simply saying, “This may not be the ultimate answer because this could just be a consideration of mine.”

This process then helps one question what one has been taking for granted, and look at it more closely to see if it is not just what one is considering. It is boring into the unknown and finding more and more of one’s own hidden considerations. When one knows that there are no more hidden considerations then only one knows oneself fully. That, to me, is Nirvana. From that point on one knows when one is generating, sustaining or dissolving considerations. It is the state of perfect equilibrium. This is just my take. It may or may not be true for another person.

Thus, Nirvana would simply mean the ability to generate a consideration, hold on to that consideration, and then dissolve that consideration. Nirvana would not mean forsaking this universe. Nirvana would simply mean total control over one’s considerations. One may then attain Nirvana while being in this universe. In fact one’s enjoyment of this universe would be infinitely greater after attaining nirvana. Buddha lived to a grand age of 80, quite rare for his time, after attaining nirvana.

In that Nirvana… in that Mukti… in that Salvation… seems to lie the ultimate knowledge.

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Glossary

KNOWLEDGE
As far as our knowledge is concerned we can only know what we consider. We can never know what lies apart from these considerations.

NIRVANA
Nirvana would simply mean absence of hidden considerations even at the deepest level. It would mean total command over oneself.

NETI NETI
“Neti neti” is a Vedic process to locate THAT which is not an outcome of your consideration.

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By vinaire | Posted in KHTK | Comments (17)