Seeking truth using different methods

Mathematics and physics are entirely different subjects, both in their methodology and results. The differences are illustrated with how they view randomness, enumeration, and truth. In physics, randomness can be an unknown, an observational error, an unpredictable event, or a quantum mystery. In math it is just part of probability theory. Mathematics has subtle properties of infinities that physics does not directly observe. Logical positivism is a philosophy that explains how mathematics and physics search for truth in different ways, but it has been rejected by modern philosophers, leaving them with deeply flawed views of what math and physics are all about. Submitted to the FQXi.org 2015 Essay Contest answering: “Trick or Truth: the Mysterious Connection Between Physics and Mathematics” Author Bio: Roger Schlafly has a BSE from Princeton U, and a PhD in Mathematics from U California Berkeley, under I. Singer. He blogs at DarkBuzz.com. Introduction 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. Mathematics and physics have many formal similarities. Both use numbers and formulas, and use them in ways that seem unintelligible to outsiders. The Newton-Leibniz discovery of differential and integral calculus was simultaneously a huge advance for both fields. This essay emphasizes the differences. To illustrate the differences, random and infinite numbers are examined to show that they are viewed very differently in each field. Finally, these are related to philosophical foundations for science. 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. They both use numbers. Different views of randomness The differences between math and science are well illustrated in their different views of randomness. In many sciences, especially the social and medical sciences, much of the quantitative part of research is devoted to distinguishing causal influences from random influences. For example, a drug company will do a randomized clinical trial to try to get approval for a new drug. Patients will be randomly divided into two groups, with one getting the new drug and the other getting placebo pills. Assuming that the drug group does better, a statistical analysis must be done to decide whether the result was caused by the new drug, or could be explained by just random sampling.