Dear Sir,
Information is specific data reporting the state of something based on observation (measurements), organized and summarized for a purpose within a context that gives it meaning and relevance and can lead to either an increase in understanding or decrease in uncertainty. Information is not tied to one's specific knowledge of how particles are created and their early interactions, just like the concepts signifying objects are not known to all. But it should be tied to universal and widely accessible properties.
Information could be of two types according to whether it is directly perceivable or inferred from some other perception. As long as the inference is logically consistent, it can be accepted as information. In the perception "this (object) is like that (the concept)", one can describe "that" only if one has perceived it earlier. Perception requires prior measurement of multiple aspects or fields and storing the result of measurement in a centralized system (memory) to be retrieved when needed. To understand a certain aspect, we just refer to the data bank and see whether it matches with any of the previous readings or not. We cannot even imagine something that we have either not perceived earlier or inferred from such perception. The problem arises when we try to imagine something not conforming to physical rules. We have seen rabbits and we have seen horns. But horns of rabbits is possible only in dreams and not in physics.
Reality must be invariant under similar conditions at all times. The validity of a physical statement is judged by its correspondence to reality. In a mirage, what one sees is a visual misrepresentation caused by the differential air density due to temperature gradient. All invariant information consistent with physical laws, i.e. effect of distance, angle, temperature, etc, is real. Since the perception of mirage is not invariant from different distances, it is not real. 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.
Your description of the circle and pi are very interesting. The abstraction comes for a different reason though. Mathematics is related to the measurement of time evolution of the state of something. These time evolutions depict rate of change. When such change is related to motion; like velocity, acceleration, etc, it implies total displacement from the position occupied by the body and moving to the adjacent position. This process is repeated due to inertia till it is modified by the introduction of other forces. Thus, these are discrete steps that can be related to three dimensional structures only. Mathematics measures only the numbers of these steps, the distances involved including amplitude, wave length, etc and the quanta of energy applied etc. 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. 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.
Number is a property of all substances 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. If something is not A, then it belongs to a different class that exists (out of many) or A is physically absent at "here-now". The physical absence at "here-now" is described by zero. Change in ownership is described by negative numbers. Infinity is like one - without similars. But whereas the dimensions (perception of differentiation between the internal structural space and external relational space of an object) of one are fully perceived, the dimensions of infinity are not perceptible. Since mathematics is accumulation and reduction of numbers, which are discrete units, no mathematics is possible using infinity.
You can visit our essay: "INFORMATION HIDES IN THE GLARE OF REALITY by basudeba mishra http://fqxi.org/community/forum/topic/1776" published on May 31 for further details.
How long will we continue with such fiction? When will we end the superstitious belief in the 'established theories' and start applying our mind? Why must we continue with a 'cut & paste' job? When will we start doing some original work? Is there no future for physics?
Regards,
basudeba
