Dear Sir,
Your essay is a beautiful analysis on information and its relation to the physical world from the true perspective ending with an explanation of the poser presented in the beginning. It appeared to us as the twin of our essay "Information hides in the glare of Reality" published on May 31, though we approached the subject from a different perspective. Our essay complements your essay in many ways.
Many of the points raised by you have been discussed in the first chapter of an ancient treatise on Sanskrit grammar called Mahabhashya written more than 2000 years ago. All observables are called 'padaarth' in Sanskrit, which means a word (language) signifying a concept (pada) about some object (arth) or as you say "there is an information encoded and stored in natural elementary structures at the root of all". Another ancient work Vakyapadiya, which gave rise to the study of linguistics, elaborates this concept further. You have also quoted Ferdinand de Saussure to convey the same meaning: what is natural to mankind is not the faculty of speech, but the ability of constructing a language, i.e. a system of distinct signs corresponding to distinct ideas. The binary or yes-no format is about isomorphism that asserts whether the object matches the concept or not, which is the information received by the conscious observer.
But mathematics cannot always express the isomorphism in its totality. It 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.
The importance of initial conditions cannot be denied. But it does not evolve as an isolated system. The chains of other influences that lead the "the flap of a butterfly's wings in Brazil" to "set off a tornado in Texas" are as important. These influences introduce the element of uncertainty in the projection of initial conditions. The object evolves in time independent of observation, but it makes meaning only when it is so cognized. The detailed mechanism of perception including invariance has been discussed in our essay.
As you have pointed out, the findings of Rawlinson that if the first and last letters are in the right position, the internal order of the letters does not matter (for example, "to raed is good for hatelh"), applies to a Latin-based tongues, while for other languages with different symbols and grammar, it is necessary to look for other methods. However, "the material support is of little importance" has to be treated carefully. When we perceive something for the first time, our memory only registers it. Next if we perceive something similar, we cognize it as the object we had perceived earlier. If we had heard a word (name) describing the concept generated out of such perception, we use that word. Alternatively, we may conjoin some other word like children do very often to describe something. It is true that the word does not signify the object, but signifies the concept attached to the object. However, the memory will not function without any external impulse directly or indirectly linked to the concept.
Animals also have their language, though it is not as developed as human language. As long as they communicate and understand these signs linking the concept to the objects, it must be treated as a language - however primitive. These are parts of Natural language. An ancient work by Bharata divides language into four categories: 1) purely scientific language that builds on the matching process of physical evolution and acoustic evolution, 2) human language based on strict principles of grammar, 3) human language based in general, but loose principles of grammar, and 4) Language of other animals. It is the third category that is used as a signifier.
But you should not confuse between the abstractions of language with the abstraction in mathematical physics. Abstractions of language refers to abstract ideas depicting a mental state that cannot be physically symbolized (like the feelings of love, romance, etc as different from hugging and kissing), expressed in human language in a skillful manner (such as lyrical rhythm) to keep the mind focused on the subject or feeling. The abstraction of mathematical physics comes from the dimensional differences of mathematical structures and physical structures.
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. The numbers are assigned to points on the piece of paper or in the Cartesian graph, and not to points in space. If one assigns a number to a point in space, what one really means is that it is at a certain distance from an arbitrarily chosen origin. Thus, by assigning a number to a point in space, what one really does is assign an origin, which is another point in space leading to a contradiction. The point in space can exist by itself as the equilibrium position of various forces. But a point on a paper exists only with reference to the arbitrarily assigned origin. If additional force is applied, the locus of the point in space resolves into two equal but oppositely directed field lines. But the locus of a point on a graph is always unidirectional and depicts distance - linear or non-linear, but not force. Thus, a physical structure is different from its mathematical representation.
Regards,
basudeba
