This is the clearest and best-written intro article on math, computability and big numbers I have read, period (and it’s from 1999, by the way).
More importantly, once the author (Scott Aaronson, a prof at MIT/CSAIL, and someone, hehe, semi-famously at odds with my client Stephen Wolfram) makes his way through the Ackerman sequence, Turing machines and Busy Beavers, he makes several very worthwhile arguments about our cultural understanding of big numbers. This is a topic that I’m keenly interested in, as I’m in the business, ultimately, of bringing advanced, and often algorithmically and computationally significant, technologies to market.
Specifically:
Indeed, one could define science as reason’s attempt to compensate for our inability to perceive big numbers. If we could run at 280,000,000 meters per second, there’d be no need for a special theory of relativity: it’d be obvious to everyone that the faster we go, the heavier and squatter we get, and the faster time elapses in the rest of the world. If we could live for 70,000,000 years, there’d be no theory of evolution, and certainly no creationism: we could watch speciation and adaptation with our eyes, instead of painstakingly reconstructing events from fossils and DNA. If we could bake bread at 20,000,000 degrees Kelvin, nuclear fusion would be not the esoteric domain of physicists but ordinary household knowledge. But we can’t do any of these things, and so we have science, to deduce about the gargantuan what we, with our infinitesimal faculties, will never sense. If people fear big numbers, is it any wonder that they fear science as well and turn for solace to the comforting smallness of mysticism?
Definitely required reading, and thanks to @mrflip for pointing me to this piece.
