Dear Sir,
You are absolutely right about the central role of the Observer, because, without observation, nothing exists for the system. By this, we imply the triplet of the Observer, the Observed and the Mechanism of Observation. The last two make sense only if the Observer observes. For this reason, "his own ability and rightness of actions" cannot be questioned or even discussed, as it is the be all and end all of all perceptions. We cannot even imagine anything beyond or contrary to what is observed, though we can compare between what is observed. Since there is no equation for observer, it is beyond mathematics also.
You are also right about the indignity piled upon us by the superstitious lot, who blindly believed LHC to such an extent that when in July 2012 it declared the discovery of the so-called God particle, they were euphoric, but ignored it when LHC declared in December the same year that they have not yet discovered the Higg's boson, but what they found was Higg-like. They also did not protest when it was reported that it gave mass to all particles, though in reality, if the theory is ultimately proved correct, it provided mass only via weak interaction, which is less than 1% of the total mass. We pity them because they do not even know what they are talking about. Look at the large number of different approaches or formulations to the foundations of QM - many contradicting each other. Then there are various interpretations. Can we call it a coherent theory?
The physics community blindly accepts rigid, linear ideas about the nature of space, time, dimension, etc. These theories provide conceptual convenience and attractive simplicity for pattern analysis, but at the cost of ignoring equally-plausible alternative interpretations of observed phenomena that could possibly have explained the universe better. Modern theories do not give a precise definition of the technical terms used, but give an operational definition that can be manipulated according to convenience. Wigner defined mathematics as the science of skillful operations with concepts and rules invented just for this purpose. This is too open-ended. What is skillful operation? What are the concepts and Rules? Who invented them? What is the purpose? Do all concepts and rules have to be mathematical? Wigner says: The great mathematician fully, almost ruthlessly, exploits the domain of permissible reasoning and skirts the impermissible, but leaves out what is permissible and what is not; leaving scope for manipulation.
Wigner admits not only the incompleteness of mathematics but also its manipulation according to the aesthetic sense of the operator. He gives the example of complex numbers and burrowing from Hilbert, admits: Certainly, nothing in our experience suggests the introduction of these quantities. Indeed, if a mathematician is asked to justify his interest in complex numbers, he will point, with some indignation, to the many beautiful theorems in the theory of equations, of power series, and of analytic functions in general, which owe their origin to the introduction of complex numbers. The mathematician is not willing to give up his interest in these most beautiful accomplishments of his genius. A reverse self-fulfilling effect!
Mathematics is the ordered accumulation and reduction in numbers of the same class (linear or vector) or partially similar class (non-linear or set) of objects. Coding or information is related to some physical objects. We cannot detach the physical objects from codes and say that the code or information has an independent existence - pi is in the sky! We believe in understanding the physical world through mathematics, but not creating the physical world through mathematics.
We thoroughly enjoyed your essay.
Regards,
basudeba
