“You have an irrational belief in rational thought.” ~Dr David Scholes, directed towards me.
“Humankind cannot bear very much reality.” ~T.S. Eliot
I just finished the book Mathematical Cranks by Underwood Dudley, part of a trifecta of skeptical mathematics books.
Doctor Dudley is a professor of mathematics at Depau University and a connoisseur of cranks with a mathematical bent.
What is a mathematical crank?
Mathematics is a peculiar field. Whether or not some aspects of mathematics exist independent of humans is an ongoing debate, but within its axioms and proofs is a consistent body of well defined, internally consistent knowledge.
Within that knowledge, ideas can, under the rules of mathematics and logic, can be proved or disproved, to be absolutely true or false or to be impossible.
No prior plausibility that pester the world of scientific medicine and the evaluation of woo. No borderline p values that hint at effects. No biologic variability. No placebo effect. No investigator or patient bias. No placebo effect. No N rays. No unproven water memory or meridians or subluxations.
Just clean, beautiful, mathematics. True or false. Possible or impossible. I simplify a bit, but mathematics, especially at the lower levels, is an internally consistent field of study. What happens in the math of 11 dimension string theory is beyond my puny intellect.
In mathematics there are things that are impossible. Absolutely impossible. No ifs, ands, or buts. Impossible. Can’t be done no how no way. In the world of mathematics, things are not only impossible, they are proven truly impossible within the boundaries of the mathematical discipline.
An example of mathematical impossibility is the quadrature of the circle, also called squaring the circle.
It is impossible, using only a straight edge ruler and a compass, to construct a square with the same area as a given circle. It was proved to be impossible in 1882 by Lindeman. Not improbable or unlikely or very, very, very difficult. With in mathematical reality, it is impossible.
Just because it is impossible does not prevent people from attempting to square the circle. They send these ‘proofs’ to mathematicians for comment.