Dear Roger Schlafly,
In your essay you write, "Mathematics and physics have one big thing in common. They both search for objective truths. Beyond that, they have little in common. Math uses the methodology of logic and proof. Physics uses observation and experiment. ...
By mathematics, I mean rigorously proving theorems from axioms, as in typical math journals. By physics, I mean explaining the fundamental causes of nature, such as energy, motion, and force. ...
Sam Harris writes: If determinism is true, the future is set -- and this includes all our future states of mind and our subsequent behavior. And to the extent that the law of cause and effect is subject to indeterminism -- quantum or otherwise -- we can take no credit for what happens. There is no combination of these truths that seems compatible with the popular notion of free will. [Harris] ...
... consider the use of infinite numbers. Mathematics uses them all the time, with the infinity of primes being one of the oldest theorems. But it is debatable whether any true infinities occur in science. Measurements always give finite values. Some physical entities are often thought to be infinite, such as the density of the center of a black hole, the unrenormalized charge of an electron, or the size of the universe. But none of these examples is very convincing, and many physicists are content to regard infinity as just some mathematical fiction.
...The 2011 FQXi essay contest asked, "Is Reality Digital or Analog?" The answers accepted the premise that reality had to be one or the other, and no one admitted the possibility that it might be neither because both are mathematical. [Schlafly] I could be wrong, of course, but I seem to be the only one to have seriously considered the possibility that fundamental physics is not perfectly describable by mathematics. I was influenced by a logical positivist philosophy that embraces a logical view of mathematics, and an empirical view of science. To me, these views are so different that it would be bizarre if one were completely reducible to the other."
I object to your characterization of the essays by the 2011 FQXi essay contestants. In an interview Francis Crick admitted being a reductionist but denied being a "caricature of a reductionist." What do infinity and measurement really mean? According to Virginia Woolf, "Nowadays it is easy enough to invent new words -- they spring to the lips whenever we see a new sight or feel a new sensation -- but we cannot use them because the language is old. You cannot use a brand new word in an old language because of the very obvious yet mysterious fact that a word is not a single and separate entity, but part of other words. ... words do not live in dictionaries, they live in the mind." How can the human mind be accurately described? If it can be done, my guess is that accurate description of the human mind would require superhuman intelligence. Words and formal symbols cannot be satisfactorily described and therefore mathematics and physics cannot be satisfactorily described. Whatever an "empirical view of science" might be, I claim that Milgrom is the Kepler of contemporary cosmology based upon empirical evidence accumulated by Milgrom, McGaugh, Kroupa, and Pawlowski, -- D. Brown