Oh, no! Not math again!
Among those who try to imagine alien first contact, many believe that mathematics will be the basis of initial communication. This is based on the perceived universality and inevitability of mathematics. They see math as so fundamental any intelligence must not only discover it, but must discover the same things we’ve discovered.
There is even a belief that math is more real than the physical universe, that it may be the actual basis of reality. The other end of that spectrum is a belief that mathematics is an invented game of symbol manipulation with no deep meaning.
So today: the idea that math is universal and inevitable.
In this post I’ll show how Set Theory allows us to define the natural numbers using sets. It’s admittedly a very abstract topic, but it’s about something very common in our experience: counting things. Seeing how numbers are defined also demonstrates (contrary to some false notions) that there is a huge difference between a number and how that number is “spelled” or represented.
Note: I am not a mathematician! This topic is right on the edge of my mathematical frontier. I wanted this addendum to the previous post, but be aware I may misstep. I welcome any feedback from Real Mathematicians!
But go on anyway… keep reading… I dare ya!
The ship sailed when I was moved to rant about cable news, but I originally had some idea that Sideband #32 should be another rumination on bits and binary (like Sidebands #25 and #28). After all, 32-bit systems are the common currency these days, and 32 bits jumps you from the toy computer world to the real computer world. Unicode, for example, although it is not technically a “32-bit standard,” fits most naturally in a 32-bit architecture.
When you go from 16-bit systems to 32-bit systems, your counting ability leaps from 64 K (65,536 to be precise) to 4 gig (full precision version: 4,294,967,296). This is what makes 16-bit systems “toys” (although some are plenty sophisticated). Numbers no bigger than 65 thousand (half that if you want plus and minus numbers) just don’t cut very far.