Author Archives: vinaire

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

The Logic of God

Golden pendulum swinging

Golden pendulum swinging

Reference: The Logic of Non-Duality

According to the reference above, duality appears when we focus only on the extreme states of a varying characteristic. So, when we look at the idea of a spiritual entity called God having created a physical universe, we may ask, “Is that just looking at the extremes and not considering the gradients in between?”

Are God and Physical Universe the extreme states of some continuously varying characteristic?

We look at God as infinite cause, the effect of that is the physical universe. God and physical universe are essentially Cause and Effect. The continuously varying gradient from cause to effect shall consist of cause-effect elements, each contributing to the overall change in a consistent manner. We may compare this to the domino effect, but the time between successive “falling of dominoes” shall be infinitely small indeed. We can say that from cause to effect there is a continuously varying change.

The fundamental unit of cause and effect is CHANGE.

When we look at the two extreme ends of a scale of change as Cause and Effect with an infinite gap between them, we see them as infinite. So we call them an invisible God and a visible universe.

This change is occurring in a myriad of ways. It is visible in the changing of the seasons, in the blowing of wind, in temperature fluctuating, and birds chirping. It is visible throughout this wonderful universe. Everything in this universe seems to be participating in a cosmic dance of change.

The scale that lies between the Creator God and the created Universe is the scale of change, and that change is still going on in the infinite number of dimensions that make up this universe.

We see a continuously changing universe, but we do not see the source of that change. We do not know how the universe was in the beginning, or how it is going to end up. We don’t even know if the universe has a beginning or an end.

The universe appears to be a disturbance arising from some undisturbed state. It is now trying to return to that undisturbed state. But in that attempt at restoration, it tends to overshoot the undisturbed state and then tries to restore itself again. It seems to be a cosmic oscillation much like a swinging pendulum.  The harmonic motion of a pendulum occurs under the constant pull of gravity. This means that there is a constant all-pervading influence, which is driving the change in the universe.

We may refer to that fundamental attribute, which lies in the background of this universe, as God; but it is not so concrete that it is comparable to the image of man.

The concept of BRAHMA in Hinduism is this infinitely abstract cosmic influence that underlies the continuous change.

There is a kind of inevitability associated with the cosmic oscillations. This shows up in the laws of this universe, such as, “conservation of mass and energy”. But it is more like “conservation of cosmic oscillations”. The idea of INERTIA points to this inevitable oscillatory movement. And from this inevitability also comes the idea of KARMA.

Karma is essentially a very complex cycle of action that is moving forward towards its completion in slow motion. There is a sense of inevitability associated with it. Any hindrance to that cycle results in all kind of repercussions. But these repercussions once again force that complex cycle toward its completion.

So karma and inertia are closely related to each other. Karma is simply a more complex view of inertia.

The logic of God consists of complex ideas, such as, Change, Brahma, Karma and Inertia.

This essay describes these ideas in detail.

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The Logic of Duality

images

Reference: The Logic of Truth

In this essay we are going to look at the logical structure of the universe. A logical universe shall be a universe that is consistent throughout. It shall have a ring of truth to it simply because it is consistent.

In the process of looking at the universe logically we are bound to run into inconsistencies. We shall look at each inconsistency more closely and see where they would lead us to if we resolve them.

The very first inconsistency that comes up about the nature of the universe is. “Is this universe basically an expression of duality or non-duality?”

Everywhere we see opposing concepts—such as, ‘night and day’, ‘good and evil’, ‘man and woman’, etc. Actually, the question above itself is an expression of duality. Any concept seems to brings about an opposite concept. Can we then conclude that this universe is an expression of duality?

“Not so fast,” says the non-dualist, “Non-duality points to the idea that the universe and all its multiplicity are ultimately expressions or appearances of one essential reality.” It is asserted that there is a reality that transcends the opposites.

How can we grasp that reality conjured up by the non-dualist?

A logically consistent universe shall be made up of states that proceed from one state to the next in a consistent manner leaving no gaps.

On a number line, the value of a number changes from one point to the next in a consistent manner without any gaps.  The number line extends in a consistent manner from negative infinity to positive infinity.

Is the concept of number the “one essential reality,” which expresses itself in the duality of negative and positive infinities?

Let us consider the duality of ‘night and day’ of the real universe. We find that night is changing into day, and day is changing into night with the steady rotation of earth. We notice the continuously varying characteristic of illumination, which expresses itself in the extremes of night and day.

Is illumination that “one essential reality,” which expresses itself in the duality of night and day?

We shall see a duality when we focus on the extremes and do not take into account the continuously varying nature of some attribute of the universe. The bigger is the gap between two points on the scale of that attribute, the more is the likelihood that those points shall appear as opposites.

So, duality appears when we focus only on the extreme states of a varying characteristic. Duality disappears when we recognize the characteristic that is varying continuously.

Thus we settle the argument about the essential nature of the universe by taking a mindful approach to looking at the “opposites” more closely.

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The Logic of Truth

Logic of Universe

Truth, as perceived, is never absolute. Truth is perceived from one logical state to the next logical state in a relative manner only. The smooth transition of truth from one step to the next is the harmony that qualifies the truth.

The harmony of truth reflects in the consistency of observations from one moment to the next. When the consistency is missing in observation then there is probably some truth hidden somewhere.

One may have no idea of what the absolute truth is; but one can definitely spot inconsistency when it is present. There is a built-in sense within us that flags inconsistencies.

When we are searching for truth it does not really matter whether that truth is absolute or relative. We just want to discover the missing step, which is causing the inconsistency in one’s observation. When we find that missing piece of truth, the consistency in observation is restored.

Looking for absolute truth may be an impossible task. But looking for consistency in observation is feasible.

Maybe if we start seeking consistency in everything, we may ultimately reach the absolute truth. That is a hope and not certainty.

There may be many levels of consistency in what we observe. Once we have achieved a certain level of consistency, we may know intuitively that there must also be consistency at a deeper level of abstraction. We may now become aware of new inconsistencies at deeper levels. And so we look for deeper truth to attain deeper harmony within ourselves.

Thus, truth is not just one-dimensional affair. Truth is probably two-dimensional, or even multi-dimensional. This may point to the universe having a multi-dimensional logical structure as we see in the subjects of mathematics and philosophy.

The whole logical structure of the universe may be looked upon as one single truth. That truth may be absolute, or maybe not, but it can definitely provide a context in which the relativity and interconnection of all other truth could be seen.

Knowing this overall logical structure of the universe may lead us to the absolute truth.

The absolute truth may be a moving target, but the strategy outlined here, at least, gives us a workable approach toward it.

Also See: The Quest for Certainty

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Disturbance, Inertia, Matter and Gravity

 

Electron

 [NOTE: I am celebrating my 5th anniversary of blogging at WordPress.com with this article.]

To have the awareness of velocity there should be at least two objects. In a one dimensional space the two objects will either be approaching each other or moving away from each other. If the objects have mass then there will also be gravitational attraction between them, and therefore, there will be acceleration. There will be velocity but it will not be constant.

Let’s consider a 3D-space, which is made up of at least four non-planar objects with mass. The objects are moving in this space. There has to be gravitational attraction among them. They all will be accelerating one way or another, if not linearly then in terms of changing direction. There shall always be acceleration no matter how imperceptible it is. It seems that constant velocity will be a rare phenomenon in this universe.

We observe that as long as objects have mass they can never be free of acceleration. That means there is always some force acting on an object in this universe. If it is not direct push or pull it will be some sort of reaction due to gravitational force, friction, etc.

Mass is a form of inertia that generates gravitational force. And the force generates acceleration. There is no constant velocity.

Inertia, force and acceleration seem to be different stages of the same thing.

Constant velocity may exist only for inertia-less particle. A photon is massless and it may come closest to being inertia-less depending on its frequency.

“Inertia-less-ness” acquires inertia by acquiring frequency. This gives us a photon. As the photon increases in frequency, its inertia increases also. This is evidenced by light bending near heavy cosmic objects.

The frequency is basically a disturbance. When frequency of the photon reaches the region of gamma rays, the photon becomes unstable under the influence of its own inertia. The high frequency photon, instead of propagating linearly, seems to converge on itself when shocked in some way.

An electron has a “mass” that corresponds to the frequency of gamma rays per Einstein equations: E = mc^2 = hf. An electron may be described as the stable state resulting from the shocked convergence of gamma photons. The surface of the electron shall consist of something similar to a shock wave. The frequency within an electron is likely to increase along its radius. The maximum frequency shall appear at the center of the electron.

Mass may be a phenomenon resulting from shocked convergence of high frequency photons.

The next stable particle that we get after an electron is a hydrogen atom. Here a lot more has converged because of some cosmic reaction. The outer shell is still like an electron, but in addition, there is an inner solid core. The high frequency center seems to have undergone another shocked convergence. The surface of the nucleus shall also consist of something similar to a shock wave.

A hydrogen atom is very likely to be a single particle that breaks into an electron and a proton during atomic reactions. There is a succession of stable particles beyond the hydrogen atom that gives us the periodic table. They happen to have near integral multiples of the atomic mass of the hydrogen atom. They also break into electrons, protons, and other particles during atomic reactions.

We assume that these integer values of atomic mass mean that a number of electrons, protons and other particles exist within an atom, but that may not necessarily be the case. Each atom could just be a single particle, and the integral values may appear due to resonances observed due to wave mechanics.

Once we have “mass” in the nucleus, we have particles of large inertia. And so we have matter, material objects, gravity, force and acceleration, which we are most familiar with.

Inertia (frequency and mass), force (gravity) and acceleration are simply the different stages of cosmic disturbance.

This is a simple model of how the universe logically may be at its core.

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The Future of Education

Dropout

Reference: The Book of Subject Clearing

The Situation

A person drops out of High School because he is faced with confusion in his schooling that seems to be increasing exponentially. He feels hopeless about learning. He can’t see any benefit from continuing in school. So he drops out.

What underlies that confusion are the holes in his understanding. There may be just a few holes in Kindergarten that, if not resolved, become significant by the end of the elementary school. Then, if they are still not addressed, they multiply and become substantial by the end of the middle school. Still not handled, these holes increase exponentially during the high school years until the student starts to drown in the resulting confusion.

The student’s attention is so fixed on the debilitating confusion that the underlying holes become invisible to him. He finds that the teachers and the after-school help are unable to help him with his confusion. All those lessons in the class he attends, just seem to add more to his confusion. He finds himself fighting a losing battle.

The student, and others trying to help him, focus on such holes “horizontally” at his grade level (see the graph above). But the solution does not lie in that direction. It lies in the direction of earlier grades. As you move down toward earlier education, the holes seem to merge into fewer holes. Thus, it becomes possible to trace all that confusion at the top to just a few holes at the bottom.

The cause of the massive confusion of a high school dropout is traceable to just a few holes in his early exposure to the subject.

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The Difficulty

Will it be helpful if the student can make this logical connection between the confusion at the top to the holes at the bottom? Will he experience relief? That is the theory.

But, in general, the student is so overwhelmed by his present confusion that the holes from his early schooling are not visible to him. You cannot ask him to review the early parts of his schooling. This is unacceptable to him.

Yes, the cause of the confusion “at the top” can be traced to the holes “at the bottom,” but there is no way to trace it without the cooperation of the student. The path of confusion along which to trace the holes is locked inside the student. The student cannot access those holes on his own. One-on-one troubleshooting works but it takes time, and it is a hit and miss affair.

The student is so confused that he cannot trace the path from his confusions to the underlying holes in his earlier education.

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The Possibility

All subjects start from some fundamental premise. From that premise a subject develops along logical lines. A good example is the subject of mathematics. Mathematics starts with counting, adding is “counting together,” subtraction is “reverse addition,” multiplication is “repeated addition,” division is “reverse multiplication,” and so it continues. When one talks about holes in understanding, one is really talking about missing grasp of a step in the logical structure of a subject.

A high school dropout cannot even describe what he needs help with, because he is pretty much confused about everything. When he needs help he cannot even put together his questions properly. He needs some firm context within which to formulate his questions. Maybe he can spot what he is missing if we present the outline of the subject to him in a logical sequence from its earliest premise.

The logical structure of a subject allows us to develop a context using which the student can discover the holes in his earlier education.

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The Experiment

A series of lectures were designed to provide the student with a proper context so he could formulate his questions. The lectures, very simply, introduced the broad purpose and scope of mathematics. They described various parts of mathematics. Then within that context the common area of trouble was identified as fractions. The subject of fractions was then approached by defining the fractions broadly. Simple exercises were provided that focused on the logical structure of fractions. 

This had an interesting effect on the students. They started to formulate questions about what was not clear to them. This was the start of a wonderful dialog that provided direction for subsequent lectures. The lectures followed the logical structure of mathematics while answering questions. From fractions, the lectures continued on division, factors, prime numbers, etc., and the interest of the students kept increasing and the questions kept coming. 

As lectures continued on this journey of discovery the hopelessness of the students started to diminish. They were more interested. Actually, this increasing interest was the indicator that the lectures were tracing the confusion correctly. This led to the following solution.

The way to trace back the confusion is to generate a “Q &A” dialog that closely follows the logical structure of the subject.

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The Proposal

The proposed solution is simple. Restructure the study materials at primary and middle school level such that they follow the logical structure of the subject. This was done for the subject of mathematics. Please see The Book of Mathematics.

So far these materials have been used in a private tutoring environment to handle student’s confusions at primary and middle school levels. The results have been fascinating. Not only the confusions of the students gets handled rapidly, they also become more interested in the subject of mathematics.

The approach used to develop these materials also led to the philosophy of Subject Clearing. One student who continued to be tutored through all four years of High School was also made familiar with the structured approach of subject clearing. Mathematics was his least favorite subject. He not only aced in Mathematics but in all other subjects as well. He truly developed confidence in his ability to learn.

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The Solution

The solution, therefore, involves the following steps, which helps the student become a SELF-LEARNER.

(1) The development of study materials that are structured logically, and
(2) Training the student in the use of Subject Clearing.

A self-learner is one who, on his own, can establish connection between his confusion and the relevant hole in his understanding. He can then proceed to fill that hole by searching for, and finding, the right material.

A self-learner knows how to clean up any confusion in real time so the holes don’t accumulate and become harder to handle later. His curiosity to learn, therefore, never diminishes, and he does not have to be pushed.

The effort of producing self-learners out of failing students may be organized into units called Self-Learning Clinics or SLCs. An SLC would be tasked with turning the “hopelessness about education” into an “eagerness to learn” within weeks.

More specifically, the purpose of a Self-Learning Clinic (SLC) is to help school drop-outs become effective self-learners.

The next step is to draw up a blueprint for the SLC in such a way that it becomes a reality with very little effort.

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