In the 1960s, physicist Eugene Wigner famously asked about the
"unreasonable effectiveness of mathematics for the natural sciences."
Physicist Ed Klingman answers this in "The Automatic Theory of Physics".
The answer obviously begins with measurements: Klingman shows how these numbers are
produced and how they are used to create feature space. With this minimal description
of physical objects or events, the question switches to optimization: how to create the
best feature set, and eventually the best physical theory.
Because human consciousness of math seems so mysterious, Klingman removes the mystery
by using a robot physicist, who makes no claim to "understand" math, but has been programmed
(from the logic gates up) to generate numbers and use them to formulate theories.
The robot is formally treated as automata, hence "The Automatic Theory of Physics".
Targeting professionals, most of the book is Klingman's 1979 PhD dissertation.
But in 2009, "Science" published several papers that address the same problems in the same manner,
and Klingman has analyzed these and other recent topics such as self-organizing maps.
For those struck with wonder at the seamless joining of math and the physical world,
this book is an eye opener and a joy.