Dear Sir,
We thoroughly enjoyed your excellent essay. Here are certain elaborations of your concepts.
The halting problem (what can/cannot be computed) arises due to a wrong question: "How long are you willing to wait"? We are familiar with irrational numbers, which are mostly non-computable. Yet, we know that they hover around a limited range. We choose as precise a value we want and proceed with it. Thus, the right question should have been: "How precise we want to be"?
The other problem is equating language to a set of strings over an alphabet. In our essay in this forum, we have defined language as the "transposition of information to another system's CPU or mind by signals or sounds using energy (self communication is perception). The transposition may relate to a fixed object/information. It can be used in different domains and different contexts or require modifications in prescribed manner depending upon the context". In our 2013 essay, we had said: "In perception, these tasks are done by the brain. Data are the response of our sense organs to individual external stimuli. Text is the excitation of the neural network in specific regions of the brain. Spreadsheets are the memories of earlier perception. Pictures are the inertia of motion generated in memory (thought) after a fresh impulse, linking related past experiences. Voice is the disturbance created due to the disharmony between the present thought (impulse) and the stored image (this or that, yes or no). Video is the net thought that emerges out of such interaction. Software is the memory. Hardware includes the neural network. Bytes and bits are the changing interactions of the sense organs (including sound that produces words - strings) with their respective fields generated by the objects evolving in time." The problem arises when we treat the language as a set of strings. The elements of a set have fixed value. But the words in a sentence can have various meanings depending upon the context.
The unpredictability of behaviors arises from our method of measurement, where we can measure only limited aspects over limited time, even though everything perpetually evolves in time due to interconnectedness and interdependence of everything with every other thing. Because of these limitations, a physical universe has to be described by a probabilistic law. You are correct also regarding past and future. Please note that future is strictly ordered in a sequence based on present. But past can be related to present in various random ways. This signifies the arrow of time. Your reference to the bigger set is interesting. We have also used the same concept along with Russell's paradox in our essay in this forum.
You have correctly described that mathematics is only the quantitative description of Nature, whereas physics describes its qualitative aspects. You are also absolutely correct that "Consciousness can explore mathematics, but mathematics cannot describe consciousness".
However, there are many problems with relativity and there is no standard interpretation of quantum physics. Many of its interpretations are contrary to observation elsewhere. Thus, there is a need for introspection and review of the present theories based on the presently available information. Unfortunately, most papers are building on "established theories" even though the latest observations prove it to be not true.
The points you raise at page 7 are interesting and important. We can explain it all. But this is not the forum for that. Just to give one hint: pain may be in the legs or hands, but it is experience in our brains just like a tiger may be confronted in the jungle, but fear in our mind induces reactions in our body. Thus, the cognizer is different from the physical cause. The content of cognition as "I know ..." remains invariant in all cognitions. That it is universal is proved from the fact that language conveys the same information to the other. By this we are not talking about religion or God, though we are hinting at a universal meeting point which you may call Scientific God.
Regards,
basudeba