Number 96 : April 1999 |
I posted my brief article on Mathematics - Discovered or Invented (see C95/37 - response to Valerie Ransford) to the ISPE discussion list. Here’s a medley of responses, though I have to admit I didn’t find them very inspiring. What do the rest of you think ?
Anthony Norris : Why limit the question to mathematics? What about language, something I think is the greatest invention/discovery?
Craig M. Parsons-Kerins : I've been sitting in front of my computer, cogitating on the idea of mathematics and language, trying to figure out whether they were an invention or a discovery. I'm trying NOT to fall into the old philosophy major's problem of saying "Gee, we need to define our terms!" I think, however, that we do need to. The question is, I guess - is a discovery the understanding of a novel relationship that was previously lacking, while an invention is the application of a discovery? and can an invention come into being prior to a discovery ? Mathematics, a science of relationships, seems to me to be a discovery, with the applications to the various fields of research an invention. Language, on the other hand, seems to fall into the category of an invention (at least in my mind) once the initial discovery of language "potential" has been established (here we go with definitions - just how far back into any subject do you want to go when trying to determine whether it should count as a discovery or an invention) - the relationships between naming and named being arbitrary. Well, these are just a couple of ideas.
Bob Clark : Part of the rub seems to be the Siamese nature of doing and being (a la Aristotle and Plato). How many times have we asked for a definition of what something IS and been greeted with what it DOES. When we use mathematics to describe the real world as is done in Physics, we may be abusing the subject. [What it Does]. I abjure definitions in terms of activity. Because they are intrinsically false. When we Are something, this is independent of our activity, or the context of it. When we Do something, it isn't even Necessary to say what we are. But just because we don't say what we Are when we do something doesn't mean we are nothing. There can be being without activity. In most cases. Ralph Waldo Emerson, conversely had a quote: "What you are screams so loudly I cannot hear what you say."
Bob Clark : To me, invented or discovered is a false distinction. As I view it, first comes a concept (invention) and then comes a lot of empirical work playing with the idea and implementing it. Both are usually necessary. As an example of how one feeds the other, I read in Popular Mechanics the other day the construction of a physical firewall using tiny gears to control a resource. The problem solved by a firewall didn't even exist ten years ago, before the Internet came into its own. Once the Internet arose, then came hackers, generating a problem to be solved by firewalls. So the invention was spurred by empiricism. But once the firewall was needed, and conceived, it has taken people a lot of empirical work to apply a technology to solve the problem.