Dear Sir,
We fully agree with your views. The validity of a mathematical statement rests with its logical consistency. The validity of a physical statement rests with its correspondence to reality. 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 until they are 'given'. Whatever is 'given' (including inputs for emotion) 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.
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.
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.
You are absolutely correct that "A computer is programmed by intelligent beings to operate in certain manner. Computer definitely requires creator(s). It gives specific output for certain input. Computer is incapable to produce outputs that are not programmed into it." Nature appears to obey definite laws as computers because otherwise there would be chaos. Everything in Nature is the logical conclusion based on the simple laws of complimentarity: inertia and conservation. The inertia of motion brings in its conjugate inertia of restoration (elasticity). But who started the first inertia? It must be a conscious function, as mechanical functions are only logical reactions. The answer to this question answers everything.
You are also right in distinguishing between "real entities" like the physical world and "functional entities" like space and time, which, though experienced, cannot be physically shown to others. Space is the interval between objects and time is the interval between events. We describe these through alternative symbolism using objects and events. The intervals themselves are nothing and cannot be described. Consciousness is a functional entity.
Reality is not Observer dependent, as the observer only perceives or reports the state of objects, but does not interaction with it. Measurement being a comparison between similars, also does not interfere with time evolution of objects. We measure the state at time t and freeze the report for use at time t', t'' etc, when the object has evolved further. Thus, our description of the object is not the description of its exact state at the moment or the "ultimate objective state", as you put it, but state at a particular instant. We combine all other unknown states and call it superposition of states.
We shared these thoughts because our ideas are similar. You can read our essay: "INFORMATION HIDES IN THE GLARE OF REALITY by basudeba mishra http://fqxi.org/community/forum/topic/1776" published on May 31.
Regards,
mbasudeba@gmail.com