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:[email protected]] On Behalf Of Marcus Daniels
Sent: Wednesday, July 06, 2016 2:47 PM
To: The Friday Morning Applied Complexity Coffee Group <[email protected]>
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:[email protected]] On Behalf Of Nick Thompson
Sent: Wednesday, July 06, 2016 12:33 PM
To: 'The Friday Morning Applied Complexity Coffee Group' <[email protected]>
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:[email protected]] On Behalf Of glen ep ropella
Sent: Wednesday, July 06, 2016 11:56 AM
To: The Friday Morning Applied Complexity Coffee Group <[email protected]>
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 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?
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