Dear Sir,
Your essay not only points to your great intellectual acumen and capacity to think out of box, but also provides a cogent reason for the present maladies of science. 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. But over dependence on mathematical modeling and prior belief on the "established theories" to look for probabilities is making physicists more and more dependent on results of observation by Engineers to modify or tentatively extend the existing theories leading to development of many contradictory branches, while leaving many aspects unexplained or even unexplored. Because of your independent thinking, we provide you some inputs that can be extended further.
To substantiate our above statement, we give one example about the unexplained questions relating to the strings. Given the measurement problem of quantum mechanics, what happens when a string is measured? Does the uncertainty principle apply to the whole string? Or does it apply only to some section of the string being measured? Does string theory modify the uncertainty principle? If we measure its position, do we get only the average position of the string? If the position of a string is measured with arbitrarily high accuracy, what happens to the momentum of the string? Does the momentum become undefined as opposed to simply unknown? What about the location of an end-point? If the measurement returns an end-point, then which end-point? Does the measurement return the position of some point along the string? (The string is said to be a Two dimensional object extended in space. Hence its position cannot be described by a finite set of numbers and thus, cannot be described by a finite set of measurements.) How do the Bell's inequalities apply to string theory? And so on.
You have correctly described the Bayes' rule of statistical inference with the notion of prior belief, but left out other interpretations after hinting about them; probably you did not consider them as important. But if we interpret inference as the processing of the fresh input in the memory of an agent or by the collective, we have to admit that it is not restricted only to probability, but is a certainty - a notion of being able to repeat an experiment with arbitrary precision - though the degree of its accuracy or the proximity of the outcome to the universal or true distribution depends upon the memory content. An arbitrary command to a computer will prove this. Only conscious actions can change it or give the distribution a 'jolt' as you describe it. Because in cognition, it may be a specific choice of prior beliefs (data bank); but it will be with the sheen of more objectivity due to the notion of causality. From the input, we may be able to predict the outcome or from one input, we may derive other connected outputs. Many aspects of perception have been discussed in our essay "Information Hides in the Glare of Reality" published on May 31.
Your description of collective inference is akin to reductionism. There is a story of six blind men, who went to "see" an elephant. Each one touched a specific part in such a way that they covered the whole body of the elephant. When their descriptions are compiled, it did not make any sense, though their individual descriptions were authentic. The reason is each was describing his perception as that of the elephant - which was their prior belief - without referring to the sequence of his body like in a jigsaw puzzle. It is like your description of the visit to Hawaii. Regarding your agents model, sample this limerick:
There was this young lady from the West.
Who thought her husband an unfaithful pest,
For, he and her li'l son Tyke,
Look so apart and hardly alike,
And the divorce court is trying out a Hypothesis test! (joking only).
Your description of perturbation includes both 'change of mind' as well as the uncertainty induced by the interaction with the field. While the first is a conscious action, the last is mechanical action. Thus, there is no wonder that "the number of fitting parameters is no longer an unconstrained number" - as you put it.
In our essay, we have raised some very important and interesting issues related to physics. You are welcome to comment on those.
Regards,
basudeba