On Dec 30, 2008, at 12:51 AM, Steve Richfield wrote:
On a side note, there is the "clean" math that people learn on their way to a math PhD, and then there is the "dirty" math that governs physical systems. Dirty math is fraught with all sorts of multi- valued functions, fundamental uncertainties, etc. To work in the world of "dirty" math, you must escape the notation and figure out what the equation is all about, and find some way of representing THAT, which may well not involve simple numbers on the real-number line, or even on the complex number plane.
What does "dirty math" really mean? There are engineering disciplines essentially *built* on solving equations with gross internal inconsistencies and unsolvable systems of differential equations. The modern world gets along pretty admirably suffering the very profitable and ubiquitous consequences of their quasi-solutions to those problems. But it is still a lot of hairy notational math and equations, just applied in a different context that has function uncertainty as an assumption. The unsolvability does not lead them to pull numbers out of a hat, they have sound methods for brute-forcing fine approximations across a surprisingly wide range of situations. When the "clean" mathematical methods do not apply, there are other different (not "dirty") mathematical methods that you can use.
Indeed, I have sometimes said the only real education I ever got in AI was spending years studying an engineering discipline that is nothing but reducing very complex systems of pervasively polluted data and nonsense equations to precise predictive models where squeezing out an extra 1% accuracy meant huge profit. None of it is directly applicable, the value was internalizing that kind of systems perspective and thinking about every complex systems problem in those terms, with a lot of experience algorithmically producing predictive models from them. It was different but it was still ordinary math, just math appropriate for the particular problem. The only thing you could really say about it was that it produced a lot of great computer scientists and no mathematicians to speak of (an odd bias, that).
With this as background, as I see it, hypercomputation is just another attempt to evade dealing with some hard mathematical problems.
The definition of "hypercomputation" captures some very specific mathematical concepts that are not captured in other conceptual terms. I do not see what is being evaded, since it is more like pointing out the obvious with respect to certain limits implied by the conventional Turing model.
Cheers, J. Andrew Rogers ------------------------------------------- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244&id_secret=123753653-47f84b Powered by Listbox: http://www.listbox.com
