----------empyre- soft-skinned space---------------------- Such a rich and complex post, with many points of resonance to earlier posts!
I think Alexander’s reference to Chaitin’s “Omega” number really needs some underlining, since I suspect most of us aren’t too familiar with the concept. I was only informed of its existence a year back, and while I can’t pretend to do any justice to the complex idea, I must say that I think proper understanding of it would likely prompt serious soul searching for those involved in the ontological foundations of computing. To the best of my knowledge (I would love a better explanation), Chaitin’s Omega is a number made up of random digits that cannot be computed, or put another way, there is a *process* to create the number (a list of computer programs that “halt”), yet it cannot be *computed* (it cannot be computed because you can never know when any one program will “halt”). Chaitin aligns this interesting computational result with physics, suggesting (against Leibniz) that some things do indeed occur without sufficient reason. Similarly with mathematics, it too has an infinite number of facts that cannot be proven in any reducible way. Saying that something is “irreducible” (be it computational, physical, or mathematical) is, according to Chaitin, akin to saying that it is not rigidly, (reductionist) “scientifically" knowable. Still knowable, but only “quasi-empirically”. So, here’s the rub, and the link to our earlier discussions (especially during the week on MATERIAL): computation is “quasi-empirical”. We were calling it “sub-phenomenal” or “sub-medial", but is this a limitation of human perception, or a limitation of the subject matter itself? I’ve probably butchered this all. Apologies: it’s well above my pay grade, but for anyone with the stomach, Chaitin does a good job of describing the technical specifics in this Scientific American article from 2006: http://www.umcs.maine.edu/~chaitin/sciamer3.pdf ~Quinn — iqdupont.com On October 21, 2014 at 1:26:05 AM, Alexander Wilson (cont...@alexanderwilson.net) wrote: > > ... > It is true that mathematics is plagued by a fundamental randomness: > Chaitin's famous "Omega" exemplifies this; it distributes all possible > decidable and undecidable computations in an algorithmically random manner. > ... > best, > Alexander > _______________________________________________ empyre forum empyre@lists.cofa.unsw.edu.au http://empyre.library.cornell.edu
