I’ve recently been enjoying a three-part series on BBC Four called Magic Numbers: Hannah Fry’s Mysterious World of Maths.
It reminded me of the Horizon programmes I used watch when younger – some of which I still have VHS copies of (shh!) – which covered the weird and wonderful world of mathematics, from Fermat and Bourbaki to Cantor and Hilbert. Probabilities, theorems… and sets which don’t include themselves.
Sadly, mathematics didn’t like me as much as I liked it, which goes some way to explaining how I failed my joint honours maths degree. Twice.1
In fact, the only bits of the course that I truly enjoyed were the sessions on logic and, later, computability. I seemed to do way better with predicate logic, truth tables, modus ponens and syllogisms that I ever did with fluid dynamics. Or mechanics. Or statistics.
Dr Fry’s series posed the question: is mathematics a human invention, or is it all there waiting to be discovered?
I think of mathematics in the same way I think of communication: it exists. But in order for humans to express ourselves and our ideas we invent languages: English, algebra, Russian, calculus, emoji.
Mathematics, like ‘normal’ communication, only works if we’re working to the same set of instructions: the syntax and grammar. We generally accept that 11+1=12, but 11+1=14 in base 8 (octal), or c in base 16 (hexadecimal, beloved of web designers everywhere) or 1100 in binary2. You have to set your parameters first. And you definitely don’t want to get your metric and imperial units mixed up.
So it is with communications. Choose your language, context and subject before you start or you won’t make any sense to your recipient. Although… if our politicians did this, they wouldn’t be very good politicians at all. Politicians are quantum communicators; the same words can be interpreted differently by two different people, yet make exactly the same amount of sense. What does “Brexit means Brexit” mean to you?
Our understanding of mathematics has evolved over time. We have the number ‘zero’ now, and negative numbers, and imaginary ones. Whenever we think we have a handle on it, something new comes up to disprove most of what we thought we knew already.
The first rule of mathematics then, and probably also of communications, is that there’s always an exception to the rule, which means we may never know everything. There’s a communications equivalent to Gödel’s incompleteness theorems waiting to be written… but the margin of this blog is too small to express it.