Nick, It's fantastic how you punch right through the rhetoric to the deeper philosophical points. Thanks.
It all depends on how you define "compute". I think the best definition offered here (by Lee) is Soare's: "A computation is a process whereby we proceed from initially given objects, called inputs, according to a fixed set of rules, called a program, procedure, or algorithm, through a series of steps and arrive at the end of these steps with a final result, called the output. The algorithm, as a set of rules proceeding from inputs to output, must be precise and definite, with each successive step clearly determined. (Soare, 1996, p. 286; definitional emphases in the original)" The tricky part, in my opinion, is the "definite" requirement. Definiteness seems like a relatively simple concept. But it's not. cf eg: https://aphilosopherstake.com/2016/06/11/is-the-universe-part-of-the-world/ "We often speak as if we can quantify over absolutely everything, or at least absolutely every-actual-thing, but then continue to reason as if all of those (actual) things form a set. In many cases this looks perfectly harmless. If we’re talking about medium-sized dry goods, for example, we can think of our quantifiers as being implicitly restricted to e.g. physical objects (our second-order quantifiers to sets of those, etc). As on even the most liberal views of what counts as a physical object, there aren’t more than continuum-many (the cardinality of the real numbers) of them, we shouldn’t run into an immediate problems." On 07/05/2016 09:43 PM, Nick Thompson wrote: > Thanks, Frank. > Now all is clear. > > On 07/05/2016 07:31 PM, Frank Wimberly wrote: >> You can decide what it means to compute the square root of 2. For example, >> you can program the Turing machine to enter an accept state if it finds a >> number (it can) whose square is within 10^-9 of 2. >> >> On 07/05/2016 06:25 PM, Nick Thompson wrote:> Thanks, Eric, >>> >>> Can one “compute” the square root of two? -- glen ep ropella ⊥ 971-280-5699 ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com
