There is an ongoing PBS TV series (also several books and also a website) called “Closer to Truth”. It is hosted by neuroscientist Robert Lawrence Kuhn. He’s featured in one-on-one interviews and panel discussions with the cream of the cream of today’s cosmologists, physicists, philosophers, theologians, psychologists, etc. on all of the Big Questions surrounding a trilogy of broad topics – Cosmos; Consciousness; Meaning. The trilogy collectively dealt with reality, space and time, mind and consciousness, aliens, theology and on and on and on. Here are a few of my comments on one of the general topics covered, mathematics.
Is Mathematics Eternal?
Simple, complex, beautiful, elegant, ugly, explains all, success story, fundamental bedrock, etc. These are words and phrases often associated with mathematics, especially beauty and elegant. That in itself doesn’t make mathematics eternal.
I suspect that no matter what the laws, principles and relationships of physics were to turn out to be, there would be some sort of mathematics to cover it. However, much of our mathematics bears no relationship to our physics – inverse cube relationship for example.
Is Mathematics Eternal 2?
What is the status of mathematics? Is mathematics eternal?
Mathematics has no status outside of the human mind. So mathematics is only as eternal as the duration that human minds exist. Mathematics is an invention of the human mind (since I know of no other life form that makes use of mathematics in any abstract sort of way) to assist humans in dealing with the many (also invented) complexities of human society (like trade, commerce and economics). Mathematics provides practical applications like navigation and provides ordering and predictability in the natural world that rule the human roost. Mathematics is a not-thing since it has no physical properties and cannot be detected via any of your sensory apparatus. Of course if we’re in a Simulated (Virtual Reality) Universe then we totally exist as, and in, a mathematical construct.
Of course mathematics might also be the invention of extraterrestrial intelligences, so mathematics might persist eternally in the cosmos as long as there are intelligent life forms around to use and abuse their mathematical inventions.
Is Mathematics Invented or Discovered 1?
IMHO, mathematics is a not-thing, an abstract concept that’s the invention of the human mind. Mathematics has none of the properties that we associate with things. Things can be discovered; concepts are invented. One plus two equals three (1+2=3) is not a thing. Pi is not a thing. The quadratic equation is not a thing. Mathematical theorems are not things. Mathematics can not be detected with any of the five senses, or even with instrumentation that extends our sensory abilities beyond that which our sensory apparatus can come to terms with. Mathematics is a useful tool of course, though many possible mathematics that could be aren’t. We search around for and adopt the kind of mathematics that fits in with what we observe, with what is useful, and chuck what doesn’t fit in into the rubbish bin. So the gravitational force can be accounted for by an inverse square law, but not by an inverse cube law, so the inverse cube relationship is put into the rubbish bin. Then we wonder at the beauty and elegance of the inverse square law explaining the way the gravitational force operates over distance and forget about the non-beauty and non-elegance of the inverse cube law. As an aside, beauty and elegance are not legitimate scientific or even mathematical terms. You won’t find them in any scientific or mathematical dictionary no matter how often scientists and mathematicians use them as per many of the interviews here on “Closer to Truth”.