While we still have time to eat food that we haven’t grown or caught ourselves, it is still possible to go out to small gatherings (eat, drink, and be merry), and sometimes, even be entertained and enlightened at the same time.
This past weekend, some folks in my sphere held a salon, with the topic being Truth. There were a few presentations, but the most notable and mind blowing was one by a young university mathematician, who clued us in to the workings of mathematics, and of how some proofs are, in some sense, “more equal than others.”
The idea of this was a bit shocking. There are some mathematical proofs, as Paul Erdős, has said, that are “in the Book;” some that are so elegant that, “if you don’t believe in God, you can at least believe in the Book.” We’ve all seen beautiful proofs, say, of the infinity of primes, or the Pythagorean theorem, but when math starts to get in nosebleed territory, things can go awry, and awry fast.
In one set of papers shown (on “Tarksi’s Decidability Problem”), one paper, in response to another, even refers to the classic line, “people in glass houses shouldn’t throw stones.” Not exactly the stuff you find in high-end academic mathematics papers. You may not be able to follow the math, but you can certainly follow the vitriol. That there are controversies in science isn’t new; the theory of continental drift that Wegener put forth wasn’t accepted widely until the middle of the 20th century, and there are other examples as well. Perhaps what made my eyes go wide (like that of the lecturer at this salon) was that in some fashion (even in spite of things like Gödel’s Incompleteness Theorem, which was known to me) mathematics still had a sense of ‘pureness’ about it. So long as that some axioms were assumed together, the rest would follow, and some sort of common knowledge could be arrived at. Mathematicians, of course, are human, and subject to the same forces as the rest of us, and even the logic of mathematics cannot always survive Flatland, selfishness, and ego.
This all may seem trivial, given what we “know” to be true, regarding our common predicaments. It does point up, however, that even in something seemingly as abstract and ‘pure’ as mathematics, that there are controversies, and they can get pretty heated at times.
One trick answer, and a few questions:
- For the record, 1+1 = 2. Or 10, depending on your counting base!
- Is this sort of high-altitude mathematical quibbling about how many angels are dancing on the head of a pin any use to us? The one example that comes to mind is that yes, it may have an incredible impact on us. If someone could prove (or disprove) some mathematical conjectures regarding prime numbers, this might affect things such as encryption, the backbone of our modern computerized world.
- Is there any field that is honest about their own biases? The one that comes to mind is Buddhism; one great quote they’ve got is, “If Science proves us wrong, we will change.” Any others out there?