There many fascinating threads in this contest. Alexey and Lev Burov have one of the most fascinating. Among other things they deal with "the unreasonable effectiveness" of math for physics; i.e., Wigner's quote.
I addressed Wigner's quote in my dissertation [my ref.5]. The key physical fact underlying our metaphysical reasoning is that the universe behaves logically. This can be exemplified by the creation of 'logic gates', AND and NOT, and subsequent sequential operation of these gates to construct all (finite) logical structures. In his 2009 FQXi essay Marcel-Marie LeBel noted that
"Maths are the metric extension of logic. Logic is therefore more primitive, more fundamental than mathematics."
It is not difficult to show that from logic gates one can easily construct counters to produce [finite] numbers, and comparators to test for relations (less than, equal, greater than]. From Kronecker we have reason to believe that, given the numbers, all else follows. Grossberg's mathematical model of neural nets allows us to construct similar logic and to sequence it, and to do so with 3-D structures. Given consciousness [!!] we become aware of these math relations, but without awareness of the material source of the logic, we may do as Robert Godwin says:
"One begins by abstracting from concrete existence, and ends by attributing concreteness to the abstraction."
As Alfredo Oliveira notes:
"Mathematics is a logic language, strictly logic; however, to where it leads depends on the hypothesis and assumptions on which it is applied. Because it is logical, it leads to 'understandable' models provided that the hypotheses and assumptions are "understandable"...
"Mathematics has also the possibility of fitting whatever set of data - it is just a matter of considering enough parameters." [... such] mathematical models are usually "not-understandable", they present logical inconsistency and parameters that obviously cannot represent a physical entity."
This is extremely well stated. He continues,
"However, many consider that these models of data are correct models of reality, and so they consider that the universe is "non-understandable". That seems to be the case of Wigner,..."
To which Alexy and Lev respond,
"Physics does not make the assumption that the laws are simple."
Regardless, they can be shown to be simple.
To further clarify "the unreasonable effectiveness" I [Klingman] note that my vehicle was to teach a robot how to derive a theory of physics from measurements, as briefly indicated in my endnotes. Thirty years later Schmidt and Lipson applied this theory via pattern recognition algorithms to
"automatically search motion tracking data captured from various physical systems..."
They found
"Without any prior knowledge about physics, kinematics, or geometry, the algorithms [the robot] discovered Hamiltonian's, Lagrangians, and other laws of geometric and momentum conservation."
This agreed with my theory. However what I found most fascinating was that the 'type' of law that the system found was determined by what variables were presented (to the robot observer). They discovered:
"... if we only provide position coordinates, the algorithm is forced to converge on a manifold equation of the system's state space. If we provide velocities, the algorithm is biased to find energy laws. If we additionally supply accelerations the algorithm is biased to find force identities and equations of motion."
I believe this is reasonable "proof" that the laws are simple.
This comment does not address life or consciousness. It addresses the question of the "unreasonable effectiveness" of mathematics, and falls on the side of "complete reasonableness" of mathematics, as it depends from logic, which can be demonstrated physically. To dispute this I believe requires that one demonstrate physically something that is not logical. And such a demonstration should not depend upon mathematical structures that have been projected onto physical reality, as described in my essay.
This in no way detracts from the beauty of mathematics, or the mystery of life and consciousness, but it does [I believe] remove the mystery of mathematics.
I thank FQXi for enabling such fascinating discussions.
Edwin Eugene Klingman