Dear Sir,
Your essay was a pleasure to read and echoes concepts close to our essay published on May 31 and our comments on various threads.
You are absolutely correct about the crisis of mathematics, which is a result of perpetuating one's greatness through incomprehensibility that hampers understanding each other. Secondly, engineers have taken over the designation of experimental scientists and theoretical scientists have become almost extinct. With their mathematical background, the engineers have given primacy to manipulative mathematics in physics. Because of the economic success of technology, mathematicians are also influenced by them leading to a lack of understanding of fundamental mathematical principles. Thus, we have landed in problems such as the singularities, which are really not an issue. An 8th century Indian mathematician named Mahavir has shown that division by zero leaves the number unchanged. In various threads here we have given proof for the same. Two 11th century mathematical works in India hold that even though the result of multiplication of any number by zero is zero, the result of first division by zero and then multiplication by it leaves the number unchanged.
Mathematics explains only "how much" one quantity accumulates or reduces in an interaction involving similar or partly similar quantities and not "what", "why", "when", "where", or "with whom" about the objects involved in such interactions. These are the subject matters of physics. Mathematics is an expression of Nature, not its sole language. Though observer has a central role in Quantum theories, its true nature and mechanism has eluded the scientists. There cannot be an equation to describe the observer, the glory of the rising sun, the grandeur of the towering mountain, the numbing expanse of the night sky, the enchanting fragrance of the wild flower or the endearing smile on the lips of the beloved. It is not the same as any physical or chemical reaction or curvature of lips.
Long before Pythagoras, the ancient Indians defined the number concept as follows: Number is a characteristic of all objects by which we differentiate between similars. If there are no similars, it is one. If there are similars, it is many. Many can be 2,3,....n depending the step-by-step perception. The nomenclature "eka" for one, "dwi" for two, "tri" for three, "chatwaara" for four, "pancha" for five, etc, define their characteristics. While "eka" signifies uniqueness of perception, "dwi" and "tri" signify quick realization of perception in different modes. Hence even children, birds and animals can learn up to three easily. From "chatwaara" onwards, which literally means mobile perception, it becomes difficult to perceive. The other numbers have been named accordingly.
Zero is the temporal absence at "here-now". We must have prior knowledge of the object labeled as zero to perceive its absence. Hence neither positive nor negative signs could be assigned to zero. Infinity is like 1 - without similars. But while the dimensions of one are fully perceptible, the dimensions of infinity are not perceptible. Hence it is not a number. There is nothing like from minus infinity through zero to plus infinity. If it passes through zero, then we can perceive at least one end of it. But zero is absence at "here-now". Thus, it produces a contradiction. Infinity cannot pass through zero. Space and time are examples of infinity that co-exist, but do not interact with anything. Complex numbers are not physical. They vanish with correct transformation back into the domain of reality, i.e., positive real values.
Mass and energy are fundamental properties of all substances their ratio defines volume, which is also a fundamental property. Volume depends on radius. Thus, the effect of internal change on a body; i.e., the ratio of mass and energy, can be noted easily by noting changes in the radius. Alternatively by scaling up and down the radius, we can anticipate the ratio of mass and energy of the body. Since energy moves in quanta - the minimum mass-energy that can be displaced for the minimum distance, this gave the concept of increment symbolized by delta. But it has been thoroughly manipulated in undesirable ways.
Mathematics is related also to the measurement of area or curves on a graph - the so-called mathematical structures, which are two dimensional structures. Thus, the basic assumptions of all topologies, including symplectic topology, linear and vector algebra and the tensor calculus, all representations of vector spaces, whether they are abstract or physical, real or complex, composed of whatever combination of scalars, vectors, quaternions, or tensors, and the current definition of the point, line, and derivative are necessarily at least one dimension less from physical space.
The graph may represent space, but it is not space itself. The drawings of a circle, a square, a vector or any other physical representation, are similar abstractions. The circle represents only a two dimensional cross section of a three dimensional sphere. The square represents a surface of a cube. Without the cube or similar structure (including the paper), it has no physical existence. An ellipse may represent an orbit, but it is not the dynamical orbit itself. The vector is a fixed representation of velocity; it is not the dynamical velocity itself, and so on. The so-called simplification or scaling up or down of the drawing does not make it abstract. The basic abstraction is due to the fact that the mathematics that is applied to solve physical problems actually applies to the two dimensional diagram, and not to the three dimensional space. Yet, there is an unreasonable over-dependence on mathematics by physicists - often wrongly.
For example, the equality sign in the mass energy equation only shows that both mass and energy are inseparable conjugates (if one becomes zero, the other becomes zero) and their proportion in the totality vary in a fixed proportion like the two sides of the scale - if more is added to one side, it goes down (becomes dense) and vice versa. Yet, this has been interpreted as both mass and energy are exchangeable.
Measurement is a process of comparison between similars, one of which is called the unit. The result of measurement is always related to a time t, and is frozen for use at later times t1, t2, etc, when the object has evolved further. All other unknown states are combined together and are called superposition of states. Thus, perception, a characteristic of the observer, is time invariant. This differentiates the observer from the observed, which is subject to time evolution. In this view, the human body is not the observer, but only an observable or instrument of observation.
If multiple runs of experiments on strictly identical systems or different measurements over space and time of the same system return the same result, the underlying commonality is real. This commonality has three characteristics: it is measurable, it exists over time and space to be repeatedly measurable and the result of its measurement communicable to other observers. The first and the last are different aspects of perception: the first restricted to the mechanism of observation and the last universal to all observers. Thus, this definition is free from any bias.
Regarding your other ideas, you are welcome to read our essay dated May 31 and comment on it.
Regards,
basudeba
