Friday, 18 April 2014
Faith in large primes
I saw Adam Spencer give basically this same talk at Tech Ed 2011 in Queensland. He talks about prime numbers, the ongoing search for larger primes, the discovery of Mersenne primes and one particular number, known as M48, that is simply too large to show on a slide, let alone to comprehend its massiveness.
Because it has been proven prime, and it being the largest known prime so far discovered, Adam says that he knows, with the same deep-down certainty as he knows anything else, that this number is prime - it has no factors but 1 and itself.
The thing is, what he's talking about isn't knowledge as such. Rather, he has faith that this number is prime. He has faith in the computers and software that performed the proof. He has faith in the people who created that hardware and that software - that they did not make mistakes in creating them, nor in running them. That no unforseen errors occurred and were accidentally buried. That no deliberate fraud was committed in order to claim the title of the discoverer of M48 (though I'm also pretty sure that's not the case). Because unless he performed these calculations himself, Adam cannot really know that M48 is prime. He is trusting that judgment to others. Trust and faith in maths too big to do for himself. That's what Adam has. It might not seem like a significant distinction, but it makes a significant difference when discussing science.
I don't, personally, know any forensic science, archaeology, anthropology or molecular biology. I trust my understanding of those topics to trained people or, more accurately, to popular journalism of those topics, filtered through all the news channels and brains that stand between me and the scientists doing that work. There are a lot of layers to trust there - a lot of translation and assumptions of honesty or even just accuracy. The point is, a lot of what you "know" about science is based on faith in a lot of people doing their jobs honestly and accurately. That is trust or faith, but it is not knowledge.
Mokalus of Borg
PS - Faith that computer hardware works as designed is pretty well-founded these days.
PPS - There are plenty of places where the story could go wrong, though.