tag:blogger.com,1999:blog-6555947.post109763778120359228..comments2014-01-12T10:46:48.153-07:00Comments on The Geomblog: Computing with reals...Suresh Venkatasubramaniannoreply@blogger.comBlogger1125tag:blogger.com,1999:blog-6555947.post-1097639101447307582004-10-12T21:45:00.000-06:002004-10-12T21:45:00.000-06:00Nice thought-provoking article, thanks!
I don't k...Nice thought-provoking article, thanks!<br /><br />I don't know all that much about computing with reals at this point, but it seems unavoidable that representation schemes, as they become more inclusive, must tend toward 'algorithmic' representations rather than 'just data' representations (further blurring the von Neumann border :-). For example, pi can be represented as a short program that could, given arbitrary large resources, compute an arbitrarily precise rational representation of the 'real thing'. Then operations over the reals become meta-algorithms that transform these algorithms (to multiply pi by 2, just insert the 2 in appropriate places in the pi algorithm, for example).<br /><br />That idea, in turn, leads to the sort of speculations about the Church-Turing thesis that you mention.<br /><br />OK, so, now that I've guessed at a few things, I'll go read the papers you mention and hear what smarter-people-than-I have to say about these matters. :-)<br /><br /> Thanks,<br /> StevenAnonymousnoreply@blogger.com