Logical Consistency

quote-Albert-Einstein-there-is-no-logical-way-to-the-41100_2

Reference: Subject: Logic

The essay on Viewpoint & Objectivity states:

“The logical consistency is determined within a personal context at first. As the context broadens toward universality, the logical consistency improves to become increasingly objective.”

To contemplate on logical consistency let’s start from point (11) from the essay referenced above.

  1. “The mental sense develops as it interprets order among these ideas and images through an intuitive sense of logical consistency.”

  2. This intuitive sense of logical consistency involves a sense of approach toward equilibrium.

  3. The system of ideas and images of a certain context acts like a closed system.

  4. In a closed thermal system, equilibrium is suggested by a uniform “temperature” throughout the system per the Zeroth law of thermodynamics.

  5. Similarly, within a certain context, equilibrium is suggested by a uniform sense of logic throughout the context.

  6. During the process of attaining equilibrium the internal energy of a closed thermal system is conserved per the First law of thermodynamics.

  7. Similarly, the total logical sense within a certain context is conserved during the process of attaining equilibrium.

  8. This approach of a closed system toward thermal equilibrium involves spontaneous maximization of entropy per the Second Law of Thermodynamics. Entropy is the ratio of internal thermal energy to temperature.

  9. Similarly, the approach toward equilibrium within a certain context involves spontaneous maximization of total logical sense while making the sense of logic uniform throughout the context.

  10. This defines what we refer to as the intuitive sense of logical consistency.

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ADDITION (12/20/15)

This essay shows that the actual logic is limited by the context one uses and not because of lack of intuitive sense of logical consistency.

This means that the usual mental drawbacks in life arise from a context that is somehow narrow, binding and confusing.

The solution is to spot logical inconsistencies in the context one is using and look at them closely. This helps increase the context.

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NOTES (Oct 27, 2022):

  1. The degree of continuity, consistency and harmony determines the logic of a system.
  2. The maximization of logic is constrained by the bounds of the context.
  3. Perfect logic is possible only within an infinite context.
  4. Intuition arises from broadening one’s context and viewpoint.
  5. To be perfectly logical one must broaden one’s viewpoint as much as possible.

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December 19, 2015 – 8:52 AM Categories: Science | Comments (1)

Speed of Light

Animation from Wikipedia

Reference: Speed of Light Essays

Einstein’s book “Relativity – The Special and General Theory” starts out by looking at Euclidean geometry objectively.

Euclid sees that the concept of space is derived from material dimensions. Therefore, he assumes space to be perfectly rigid. This means that the distance and direction determined by two points in space are absolute. All  proofs in Euclidean geometry are built on this assumption.

Euclidean Geometry uses matter as its basis to understand space.

Einstein points out that nothing in reality is perfectly rigid. Therefore, space cannot be perfectly rigid, and distance and direction specified by two points in space cannot be absolute. Physics must modify geometrical concepts to make them logically consistent with physical reality. Therefore, Einstein’s theory of Relativity treats space as relative and not absolute.

Einstein uses matter more realistically as the basis to understand space. 

Einstein famously postulated that light does not need material medium to travel. This puts light in a very different class of its own called the wave-field. Einstein declared that “electromagnetic field” is a more basic form of substance than matter.

“Electromagnetic field” is very likely a more fundamental basis from which to understand space.

Let’s review the concept of electromagnetic field. Light is a form of electromagnetic wave. It propagates as a transverse wave, similar to the disturbance we see on the surface of a pond. It does not propagate like a longitudinal wave, an example of which is sound wave moving through air.  The difference is that a longitudinal wave moves through a medium, where a transverse wave travels at the interface of two media.

Since light is a transverse wave, it does not move through any medium; instead it forms at the interface of electrical and magnetic fields. These two fields continually transmute into each other like the peaks and valleys of the wave on the surface of pond. In doing so, the two fields drive the disturbance forward (see the animation from Wikipedia above). It so happens that the electrical and magnetic fields are part of light itself.

An electromagnetic wave is a disturbance propagating in space.

Light moves as a wave disturbance and not as a mass particle. The idea of light particle (photon) appears only in reference to energy interactions. The photon may not be discrete in space as assumed by many.

Light moves as a wave disturbance at the speed of 3 x 108 meters/second according to units assigned on the basis of matter. That disturbance is not in some material medium but in space itself. The Disturbance Theory postulates space to be a primeval field of zero frequency that turns into electromagnetic field of finite frequency when disturbed. Space may be compared to the undisturbed surface of a pond.

Space is an undisturbed theoretical field of zero frequency.

The speed of electromagnetic disturbance (light) is constant and depends on the electromagnetic properties of space, as shown by Maxwell’s equations.

In the model proposed by the Disturbance Theory, space and time are experienced as disturbance of a theoretical field. There is no other way to measure space and time, except through the phenomenon of the disturbance. The cycles of electrical and magnetic fields determine Time. The spread of disturbance determines Distance.

Space and time appear in the units of “wavelength” and “period” of the disturbance respectively. The constant “c” describes the ratio of wavelength to period. Thus, space and time combine through “c” and the relative measure of disturbance is expressed through frequency.

The disturbance levels (DL) within the electromagnetic field are described as log base 2 of frequency.

Here are some notable disturbance levels (DL).

Space (Theoretical)                         DL 0 

Visible Light                                  ~ DL 49

Gamma Ray                                   > DL 64

Electron                                            DL 67

Neutron/Proton                                DL 78

DL > 78 is the region of matter. For matter, wavelength and period are infinitesimal and we can use the Euclidean concept of “dimensionless point” as a good approximation for location. This approximation for locations in field, however, does not hold that well. A “point location” in field has dimensions of finite wavelength-period. Thus mathematics takes a strange and complex form in Quantum Mechanics.

Locations in field cannot be approximated by Euclidean points.

Around DL of 67 the disturbance converges upon itself and electrons start to form within the electromagnetic field. The electron is a more complex electronic field within the basic electromagnetic field. The ratio “c” likely contributes to the properties of “spin” and electrical charge within the electronic field.

It is logical to postulate that as one moves from the periphery to the center of electronic field the disturbance levels increase and the disturbance condenses.

Around DL of 78 the disturbance condenses and a still more complex field starts to form at the center of the electronic field . This field may be identified as the nucleus of atom.

An atom is made up of nuclear and electronic fields within the electromagnetic field.

In a nuclear field the disturbance levels collapse and the disturbance appear as mass. The ratio “c” likely contributes to formation of gravity. Maybe mathematics will help us gain new insights into these relationships.

The speed of light is contained within the material objects. The material objects move relative to each other.

The speed of light “c” evidently has a nature very different from the speed of material objects.

The conjectures made above are logically consistent. They are worthy of further investigation.

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December 17, 2015 – 12:40 PM Categories: Science | Comments (11)

Viewpoint & Objectivity

Objectivity-in-question

Reference: Subject: Logic

  1. Time is the ordering principle.

  2. We view time when we view order.

  3. We view order among parts through the view of whole.

  4. The order becomes more balanced as the context broadens.

  5. The viewpoint develops from personal to universal.

  6. A personal viewpoint is narrow when it is looking through personal bias, prejudice, fixed idea, assumption and blind faith. We may call it a “self-centric” viewpoint.

  7. A universal viewpoint is broad when it is inclusive of all things from which to view. We may call it a “scientific” viewpoint.

  8. Formation of viewpoint begins with physical sense experience.

  9. The physical sense experience consists of electrical impulses arriving at the brain through physical sense channels.

  10. The physical sense experience is interpreted into ideas and images by genetically programmed associations in DNA.

  11. The mental sense develops as it interprets order among these ideas and images through an intuitive sense of logical consistency.

  12. The overall context broadens as the physical and mental experience broadens.

  13. Logical inconsistencies present themselves as the overall context broadens.

  14. Objectivity develops as logical inconsistencies are resolved.

  15. And viewpoint develops from “self-centric” toward “scientific”.

The logical consistency is determined within a personal context at first. As the context broadens toward universality, the logical consistency improves to become increasingly objective.

Viewpoint is objective when it is logically consistent within a broad universal context.

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NOTES (Oct 7, 2022):

  1. Only in the universal context can we see continuity, consistency and harmony of reality properly.
  2. Only through the context of spectrum of substance can we view space, time and energy properly.
  3. Space is the extent of substance that is shrinking per the spectrum.
  4. Time is the duration of substance that is increasing per the spectrum.
  5. Energy is the consistency of substance that is thickening per the spectrum.
  6. At a point on the spectrum, space provides ordering of spatial locations.
  7. At a point on the spectrum, time provides ordering of temporal events.
  8. At a point on the spectrum, energy provides constancy to space and time.
  9. A narrow viewpoint sees reality in a narrow context only.
  10. A narrow viewpoint does not provide a clear picture of reality

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December 15, 2015 – 6:39 AM Categories: Science | Post a comment

Einstein, Space & Time

space-time

Reference: Subject: Logic

Einstein struggled with the concepts of Space and Time till the end of his life. He even dived into subjectivity, which is a dangerous thing for a scientist to do. In his 1952 essay “Relativity and the Problem of Space” Einstein says the following about Space:

The psychological origin of the idea of space, or of the necessity for it, is far from being so obvious as it may appear to be on the basis of our customary habit of thought. The old geometers deal with conceptual objects (straight line, point, surface), but not really with space as such, as was done later in analytical geometry. The idea of space, however, is suggested by certain primitive experiences. Suppose that a box has been constructed…

When a smaller box s is situated, relatively at rest, inside the hollow space of a larger box S, then the hollow space of s is a part of the hollow space of S, and the same “space”, which contains both of them, belongs to each of the boxes. When s is in motion with respect to S, however, the concept is less simple. One is then inclined to think that s encloses always the same space, but a variable part of the space S. It then becomes necessary to apportion to each box its particular space, not thought of as bounded, and to assume that these two spaces are in motion with respect to each other.

Before one has become aware of this complication, space appears as an unbounded medium or container in which material objects swim around. But it must now be remembered that there is an infinite number of spaces, which are in motion with respect to each other.

The concept of space as something existing objectively and independent of things belongs to pre-scientific thought, but not so the idea of the existence of an infinite number of spaces in motion relatively to each other.

By considering if space has bounds, Einstein is treating space as an object. Space is not an object. It is neither bounded nor unbounded. Space is abstraction of the bounds of matter.

Einstein is correct in saying that space does not exist independent of objects, but we can view space objectively despite Einstein’s opinion otherwise. Please see The Boundary of Space.

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Einstein says the following about Time:

What do we mean by rendering objective the concept of time? Let us consider an example. A person A (“I”) has the experience “it is lightning”. At the same time the person A also experiences such a behaviour of the person B as brings the behaviour of B into relation with his own experience “it is lightning”. Thus it comes about that A associates with B the experience “it is lightning”. For the person A the idea arises that other persons also participate in the experience “it is lightning”. “It is lightning” is now no longer interpreted as an exclusively personal experience, but as an experience of other persons (or eventually only as a “potential experience”). In this way arises the interpretation that “it is lightning”, which originally entered into the consciousness as an “experience”, is now also interpreted as an (objective) “event”. It is just the sum total of all events that we mean when we speak of the “real external world”…

Now what is the position in this respect with the “events” which we have associated with the experiences? At first sight it seems obvious to assume that a temporal arrangement of events exists which agrees with the temporal arrangement of the experiences. In general, and unconsciously this was done, until sceptical doubts made themselves felt.  In order to arrive at the idea of an objective world, an additional constructive concept still is necessary: the event is localised not only in time, but also in space.

When Einstein “apportions each box its particular space and assumes that these spaces are in motion with respect to each other,” he is subjectively apportioning separate consciousness (viewpoint) to each box. Later, when talking about time, Einstein is attributing objectivity to agreement among separate viewpoints (points of consciousness). Agreement among viewpoints would be like a mixture of oil and water if those viewpoints are to keep their separate individuality.

Objectivity does not come from agreement among viewpoints. Objectivity comes from the context a viewpoint is using to view. The broader is the context the greater is the objectivity. For example, before Galileo appeared on the scene, people believed that Earth was the center of the universe; and therefore Sun revolved around the Earth. Since then Physics has helped broaden the context in which we can see that Sun is at the center of a planetary system. Sun appears to revolve around Earth because Earth rotates on an axis.

Objectivity is the characteristic of a viewpoint. The broader is the context of a viewpoint the more objective it is.

Thus we may express objective view of Space as follows.

Space is neither bound nor unbound. Space exists only as the boundary of this universe.

It seems that when there is no universe there would be no space either. The universe consists of matter as well as electromagnetic field. We tend to confuse this electromagnetic field with space.  Dark energy and matter seem to be aspects of electromagnetic field. The current research into Disturbance Theory attempts to resolve this confusion. (Reference: The Boundary of Space)

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Time is the ordering principle of the universe. Objectivity of time comes from looking at the order of things in the broadest context possible.

We may provide an analogy in terms of looking through the window of a moving train. The narrower is the window the more chaotic seems to be the order of things viewed through it. When one climbs to the roof of the train’s cabin, one has a 360° view of the surroundings. The order of all things acquires a proper perspective. One now has a more objective view of time. It is only by referencing to the whole can one objectively evaluate the relationships among parts.

Thus we may express objective view of Time as follows.

Time is the ordering principle of the universe physically as well as conceptually and logically. 

It seems that one can arrive at the idea of an objective world only when one is looking from a broad universal context and not from a narrow personal context characterized by bias, prejudice, fixed idea, assumption and blind faith.

NOTES (Oct 7, 2022):

  1. It is only by referencing to the whole can one objectively evaluate the relationships among parts.
  2. Space and matter may be evaluated by referencing them to the spectrum of substance.
  3. Space forms the background while matter forms the foreground.
  4. The consistency of substance for matter is extremely high compared to that for space.
  5. The ratio of relative condensation of matter to space is extremely high. 
  6. This is also the ratio of relative condensation at a “point” for matter and space.
  7. This is also the ratio of relative duration of matter to space at a “material point.”
  8. This ratio is also known as the “speed of light.”

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December 14, 2015 – 11:02 AM Categories: Science | Post a comment

The Boundary of Space

348986-voyager-1-heliosphere

Reference: Subject: Logic

Here is a summary of some thoughts from Einstein’s essay “Relativity and the Problem of Space“.

  1. Newtonian physics treats space, time and matter to be independent of each other. This brings into question the physical reality of space. Newtonian physics does not offer answer to this question.

  2. The basic concept of space comes from the dimensions suggested by objects. Space is not considered by philosophers to have a physical reality of its own.

  3. We ascribe physical reality to those things that we can experience directly, and extend that reality through consistency of logical association among observations. The scientific thought evolves this way.

  4. Descartes is logical in arguing that space and bodies should be continuous; but the details of logical associations need to be worked out.

  5. Geometrical concepts, such as, straight line, point, surface, do not directly deal with space. Primitive experience of space comes from placing material objects in “empty space”; but it is difficult to think of unbounded space devoid of matter.

  6. The axiomatic structure of three-dimensional Euclidean geometry derives from the way bodies can be packed into space. There is an underlying assumption of bounded space, though it may not be so obvious.

Einstein had combined space and time by assuming a constant wavelength to period ratio (c) of electromagnetic disturbance, but he was still struggling with the problem of matter being looked upon as absolute. He knew that matter could somehow be combined with space.

How does space relate to matter? What is happening at the boundary of space with matter? Is space extension of matter? Euclidean geometry assumes space to be bounded. How is space bounded? What is the relationship of space with its “bounds”? If space has bounds then what is bounding those bounds? This leads to an infinite regression. One may then ask, “Is space itself a bound?”

The Disturbance Theory defines space as the limiting condition of electromagnetic disturbance as its frequency goes to zero. This is an assumption of the same nature as Einstein’s assumption that speed of light is constant.

Thus space acts as the lower bound of electromagnetic disturbance.

At the upper bound of electromagnetic disturbance we have frequency increasing toward infinity. We calculate the disturbance level of gamma rays to be greater than 65. NOTE: The disturbance level is log2 of frequency associated with disturbance.

Calculations show that the disturbance level of electron is 66.7, and the disturbance level of proton and neutron is 77.6. It appears that the electromagnetic disturbance exists as a field in which high frequency regions (in gamma range) start to converge into electrons, which then further condense into protons and neutrons. This conjecture is logically consistent and it is worth investigating further.

Thus matter seems to act as the upper bound of electromagnetic disturbance.

The Disturbance Theory reverses how we view the problem of space. The problem is not what bounds space, but what is it that space bounds. What space is bounding is not matter but disturbance. And it is disturbance that converges and condenses as matter.

The interface between matter and space consists of electromagnetic disturbance.

So, space does not have existence independent of matter. Its existence depends on disturbance and its convergence and condensation into matter. This explains the continuity that Descartes was looking for.

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NOTES (Oct 7, 2022):

  1. The “disturbance” of Disturbance theory is now recognized as the most general reference to SUBSTANCE. Substance is anything substantial enough to be sensed.
  2. The “frequency” of disturbance is now recognized as the consistency (thickness, solidity) of substance.
  3. Space is the limiting condition of substance as consistency goes to zero.
  4. Matter is the limiting condition of substance as consistency goes to infinity.
  5. From space to matter we have a spectrum of condensing substance.
  6. As the substance condenses its extent (space) shrinks and duration (time) increases.
  7. Lesser condensed substance forms the background of greater condensed substance.

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December 12, 2015 – 2:13 PM Categories: Science | Comments (4)