Hi Robert Cordingley, I thought your follow-up question--about analog computing--to Nick's is an intriguing one, especially in the context of the definition for computing that Steven brought. Solving a set of differential equations certainly leads to an answer, though not necessarily to a discrete answer. This *is *a process that involves a specific trajectory through a continuous phase space ... so, perhaps, that trajectory can be thought of as your "accept state" of sorts.
To be sure, is analog computing still computing? What are the states in the continuous-phase space of analog computing and how does this paradigm compare with the discrete states of a finite state machine? Perhaps as a key idea, if we can liken state space <https://en.wikipedia.org/wiki/State_space> with phase space <https://en.wikipedia.org/wiki/Phase_space> then analog computing seems to fit rather well into the general genre of computing. State space is conceptually similar to phase space > <https://en.wikipedia.org/wiki/Phase_space>, but for discrete rather than > continuous dynamical systems. Thus, I see *analog computing* just as a *different *species of computing that has some advantages over digital computing: speed and theoretical precision depending on the application and the precision of measurement. Biological systems are continuous dynamical analog systems and, in fact, parallel processing systems of multiple simultaneous inputs. As it turns out MIT (and DARPA) are rediscovering the advantages of analog computing for simulating biological systems <http://news.mit.edu/2016/analog-computing-organs-organisms-0620>. BUT, I don't want to go so far as to say that living systems are computers; and so, this caveat would seem to conflict with categorizing analog computing as the *same *species as digital computing. In terms of this argument then, I see digital computing as a possible virtualization of analog computing. We can solve differential equations on digital computers as well. Yes? Going a bit further, some liken the universe to an infinite-state-machine (ISM) which may or may not be more powerful than a Turing Machine, but this gets a bit philosophical. Still, could analog computing be thought of as a localized ISM? Not sure. Maybe let's not go there. Interesting to reflect on this in the context of Nick's original question or thought experiment. Such reflection does seem to be able to take the conversation along different trajectories, but hopefully not straying too far from the original question. It's easy to get lost in the weeds ... and maybe I have here. š Cheers, -R On Wed, Jul 6, 2016 at 3:31 PM, Robert J. Cordingley <rob...@cirrillian.com> wrote: > My question is then what do Analog Computers > <https://en.wikipedia.org/wiki/Analog_computer> do and how do they fit > into Nick's exploration? As I recall they have no procedures but do produce > 'answers' without computation as we commonly know it these days. They > probably have an 'accept state' to tell the user when the 'answer' is > available. The same Wikipedia article (linked) speaks to ongoing research > into their use. > Robert C > > On 7/6/16 1:05 PM, Nick Thompson wrote: > > I didn't ask it because I wasn't smart enough to think of it. > > I guess what I was fishing for is some sort of exploration of the idea that > not all procedures for arriving at answers are computations. > > Not so smart, after all, eh? > > Nick > Nicholas S. Thompson > Emeritus Professor of Psychology and Biology > Clark University > http://home.earthlink.net/~nickthompson/naturaldesigns/ > > > -----Original Message----- > From: Friam [mailto:friam-boun...@redfish.com <friam-boun...@redfish.com>] On > Behalf Of Marcus Daniels > Sent: Wednesday, July 06, 2016 2:47 PM > To: The Friday Morning Applied Complexity Coffee Group <friam@redfish.com> > <friam@redfish.com> > Subject: Re: [FRIAM] Understanding you-folks > > "Ask" could be a higher order function that takes as an argument a "says" > function. > Provided those are made precise enough to be operational, then you would have > a "consult the Oracle" program/algorithm. Details such as "how to acquire > the Dad" (and what to do in his absence) would need to be spelled-out. > With such a program one might build another program which would be "predict > what the Oracle will say given different values". > That program would demonstrate insight on the part of the author. I'm not > sure what you are driving at here. Why don't you just say? > I thought it was probably "computing is not insight" or something like that? > > -----Original Message----- > From: Friam [mailto:friam-boun...@redfish.com <friam-boun...@redfish.com>] On > Behalf Of Nick Thompson > Sent: Wednesday, July 06, 2016 12:33 PM > To: 'The Friday Morning Applied Complexity Coffee Group' <friam@redfish.com> > <friam@redfish.com> > Subject: Re: [FRIAM] Understanding you-folks > > Thanks, Glen, > > I assume that the following is NOT a program in your sense. > > ;;Compute the sum of 2 and 2;;. > > Begin > > Ask Dad, "Dad, what is the sum of 2 and 2? > > Dad says, "Four" > > Four > > End. > > It is, however, an algorithm, right? > > > Nicholas S. Thompson > Emeritus Professor of Psychology and Biology Clark University > http://home.earthlink.net/~nickthompson/naturaldesigns/ > > > -----Original Message----- > From: Friam [mailto:friam-boun...@redfish.com <friam-boun...@redfish.com>] On > Behalf Of glen ep ropella > Sent: Wednesday, July 06, 2016 11:56 AM > To: The Friday Morning Applied Complexity Coffee Group <friam@redfish.com> > <friam@redfish.com> > Subject: Re: [FRIAM] Understanding you-folks > > 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 > weāre 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 arenāt more than > continuum-many (the cardinality of the real numbers) of them, we shouldnāt > 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 ācomputeā the square root of two? > > > > -- > glen ep ropella ā„ 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 > > > ============================================================ > 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 > ============================================================ > 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 > > > ============================================================ > 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 > > > -- > Cirrillian > Web Design & Development > Santa Fe, NMhttp://cirrillian.com281-989-6272 (cell) > Member Design Corps of Santa Fe > > > ============================================================ > 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 >
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