Steve wrote:
"You act like the common and agreed knowledge of painting and theorems does not contribute to their objective natures when you examine a painting or a theorem."
It does not contribute to their objective nature. It contributes to their subjective nature. Objective means the "same for everyone" - even aliens that have no knowledge of the cultural significance that everyone on earth happens to attach to some symbol in a painting.
Objectivity demands universal agreement, not just "common" or majority agreement.
"Without common agreement among a lot of people on the meaning of measurement and quantification, there is no meaning for either paintings or theorems."
There does not need to be any such agreement a priori. That is what relativity theory is all about. You can measure things any subjective way you want. But you cannot compare your measurements, directly, to any other measurements, that used a different subjective system; all subjective measures have to be transformed (after the fact) to a "common" reference (not the same as an objective reference).
"The bottom line with FT's is all about both understanding the past and predicting the futures of objects." FT's are all about exploiting the mathematical (not quantum mechanical) principle of superposition, in order to solve differential equations. It is one thing to say FTs are useful for solving equations used by physicists. But it is quite another to say that reality is a FT (i.e. superposition).
"Where is the noise in the Shannon function coming from? Chaos or uncertainty?"
The uncertainty principle is simply a peculiar way of stating the limiting case of the Shannon Capacity theorem; The absolute limit on the minimum number of bits of information, that can ever be recovered from a measurement, is identically equal to one. (That is the uncertainty principle - it has nothing to do with "uncertainty".) Any fewer and you have not made a measurement containing information. Any more, and it is not the minimum.
This minimum corresponds to measuring a wave-function that is so short and so band-limited, that there is no possibility of ever obtaining more than one independent measurement - any additional measurements will be entirely correlated (dependent) with the one independent measurement. If this one independent measurement has only one significant bit (due to "noise" inherent in the wave-function itself (the noise is an unavoidable result of the process that created the wave-function, i.e., if there can be no wave-function, without the noise), then, as far as the wave-function's information content is concerned, the entire thing consists of a single, one-bit sample. That is the uncertainty principle.
Rob McEachern