further reply to Edwin Klingman
Edwin Klingman
I have read most or your book ``The Automatic Theory of Physics'' that you referenced in your FQXi paper. Your book is very much on topic of this contest. Therefore, I think it appropriate to discuss it. It also forms one of the approaches to this topic. Overall I'm a bit disappointed.
You like eigenvalue functions. But these require nature to be made of linear relationships. How do we know the universe is everywhere linear? A later chapter addresses nonlinear possibilities, but these are also limited. Further the development of the validity of commutative and distributive may provide too strict a limitation. You briefly introduce noncommutitive operators such as in Quantum Mechanics. Concatenation and objects such a rubrics cube show noncommutative operators exist. Physics has examples where the measured values are way too large - Why? I suggest the feedback mechanism should be part of the discussion.
The robot can use only the math we now have. Consider the fractal math development. Fractal math was unknown and not considered by your book. Yet it is seen everywhere in nature - I mention trees. Suppose there is another type of math operation not yet known. I suggest a ``free will'' operation may exist. Like fractals, its development will probably be obvious after it is developed.
The ``basic goal'' is defined as to arrive at the simplest structure has already been achieved - by religions. Human know what they can predict, God fills in the remaining parts. It is complete and self--consistent. But it does little to advance man's survival or man's need to predict as part of survival.
Entropy math is used. Physics has many issues with the concept of entropy. Human knowledge advances with the input of energy from the Sun. So entropy increase rate is increased by increased knowledge.
I see the #5 robot property in Ch. 54 is of producing ``new'' action. Does this include using new mechanisms (machines) that are currently unknown? How are they designed? I suggest it cannot be linear or be treated wit forms of nonlinear action. It requires creativity, which is a random introduction of step functions - creativity and free will, which is unknown.
This brings up the subject of determinism and free will which you and I introduce but so far no other.
Your goal assumes the ability to digitize the universe. That is reducing the universe to numbers including the continuous. It seems you have no place for the continuous as one of the major components of the universe. Fair enough, but then you have no conversation of the standard measures needed for such a conversion. There are many problems with standard measures as I point out. These problems restrict the ability of your robot to work.
Gibbs and others have pointed the nature of today's science to be a social structure trying to maintain the status quo. But big advances happen anyway and are made by a radical redefinition of terms. The robot approach seems to be maintenance of the social structure that may not make the big (step function) leaps (yes I understand the introduction of Fourier analysis may be an attempt - but until you have the result Fourier analysis doesn't function). Perhaps your `` intelligent machines'' are scientists obeying the status quo rules of getting papers published.
You statements on P.406 echoes mine on the continuous. The ``embarrassing theory of everything'' is why I took the tack I did.