Understanding you-folks
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Dear Friammers, When I came to Santa Fe a decade ago, a recently retired psychology professor and writer, it was with a great interest in complexity and a faith that, with enough patience, and diligence I could come to understand what you were all about. This has proved much more difficult than I had imagined. So it was, with renewed optimism, that I picked up Chris Bernard’s TURING’S VISION: THE BIRTH OF COMPUTER SCIENCE. It looked like the kind of book that I ought to be able to understand. (Note the use of modal language.) But, as so often happens with such deceptively simple, books-for-the-ordinary-citizen-like-me, its first few pages contained a few assumptions that seemed so bone-headedly counter-intuitive that everything I read thereafter was poisoned. So, I have four questions: 1. Has anybody read this book? 2. Do you understand it? 3. WTF is an Accept State? 4. And why is it called an “Accept State?” Hope the members of the Friam Mother Church are having good summer. You should know that you have had more rain in Santa Fe than we have had here in Massachusetts since I got back. My neighbors have started tearing up their lawns and laying down pebbles. Take care, Nick Nicholas S. Thompson Emeritus Professor of Psychology and Biology Clark University http://home.earthlink.net/~nickthompson/naturaldesigns/ ============================================================ 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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Fortunately this really is a simple idea. In one sentence: Assuming you already understand the basic idea of a Turing machine (a device that moves from state to state as it reads/writes symbols on its tape), an accept state is a state that is designated in advance to mean that if the machine ever gets to it the computation has finished successfully. On Jul 2, 2016 8:31 AM, "Nick Thompson" <[hidden email]> wrote:
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In reply to this post by Nick Thompson
An accept state is merely a final or end state. A Turing machine is a generalization (has greater capabilities) than a standard state machine. A state machine has states and transitions from one state to another, with the "accept state" as the end of the chain.
name derives from "acceptable" / "accepting"
Petzold's book, The Annotated Turing, does a better (more accessible to lay audiences) job of explaining Turing's 36 page paper than Bernard's.
davew
On Sat, Jul 2, 2016, at 09:30 AM, Nick Thompson wrote:
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Thanks, David; thanks, everybody. I smell a tautology, here. An accept state is a state that is acceptable. NIck Nicholas S. Thompson Emeritus Professor of Psychology and Biology Clark University From: Friam [mailto:[hidden email]] On Behalf Of Prof David West An accept state is merely a final or end state. A Turing machine is a generalization (has greater capabilities) than a standard state machine. A state machine has states and transitions from one state to another, with the "accept state" as the end of the chain. name derives from "acceptable" / "accepting" Petzold's book, The Annotated Turing, does a better (more accessible to lay audiences) job of explaining Turing's 36 page paper than Bernard's. davew On Sat, Jul 2, 2016, at 09:30 AM, Nick Thompson wrote:
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Re: FW: Understanding you-folks
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It's much easier to understand this via Finite State Machines. Here's the idea: 1 - There are several nodes in a graph. 2 - One is the "start" node, another is the "end" node. 3 - An input string (set of symbols) is given the start node. 4 - Each node has a set of rules as to how it transitions to other nodes on a given symbol. 5 - If at the end of the string, if the FSM is at the end node, then the string is accepted by the FSM. The most usual example is a 2 state FSM used for opening/closing doors at super markets. -- Owen On Sat, Jul 2, 2016 at 1:06 PM, Nick Thompson <[hidden email]> wrote:
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In reply to this post by Nick Thompson
That is, it’s a definition, not a theorem.
--Barry On 2 Jul 2016, at 13:06, Nick Thompson wrote: > I smell a tautology, here. ============================================================ 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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Nick, It is not a tautology, because (at the least) it is a program written by people, so the definition of an accept state is determined outside the system in question. At its most basic level, the Turing machine isn't calculating the answer to a problem, it is accepting or rejecting a hypothesis by following a quirky set of rules. Those rules might have you see what is written on a really long piece of paper, might have you modify the writing that is in front of you, and might have you move to various different spot in the really long paper (for subsequent reading and writing). But in the end, either you reach a state where you accept the inputs, or you reject them.... or you go on forever without an answer. (It is interesting to figure out what problems can be solved, and how long it can take to solve them, but the possibility of running forever is, IMHO, what makes the whole thing so damned interesting). For example, we could write a Turing program that tells you whether one number can be divided cleanly by another. In this case, the "accept state" is that a sub-part of the division event occurs without remainder. That is, if I ask (yes/no) whether you can divide 8 by 4, you will reach an accept state and stop rather quickly. In contrast, if I ask (yes/no) whether you can divide 8 by 9, you will go on dividing forever, never reaching an accept state. We can get around this by adding additional rules. For example, I might have the program give a "reject" if you get the same numeral 5 times in a row. (Obviously, that rule won't work for all circumstances, but it will work here.) Input -> Can you divide 8, 4? 2 Accept (i.e., the program says that you should accept that 8 is cleanly divided by 4) ------ Input -> Can you divide 8, 9? 0 0.8 0.88 0.888 0.8888 0.88888 Reject (i.e., the program says that you should reject that 8 is cleanly divided by 9) ------ If we were less interested in answering the yes/no question, and more interested in reading the output to find out what happens during the division, then you could add an additional accept state. For example, I might be a high school teacher who allows a rule that you can turn in an answered rounded to the nearest hundredth. Under such a condition, there would be two accept states: 1) You complete a division step with no remainder. 2) You get a non-zero number in the thousandth place and round. Input -> Divide 8, 9 0 0.8 0.88 0.888 0.89 Accept (i.e., the program says that when you divide 8 by 9 and round to the nearest hundredth, you get to an acceptable stopping point) ----- Note that, from a theory-of-computation perspective, the latter program is utterly uninteresting. Such a program has no risk of running forever, and it won't ever find itself in a rejection state (assuming its inputs are two numbers); it will always reach an "accept" state. Nevertheless, it is a useful program to have because after the program ends up in the "accept" state, you can read the paper and see where it was when it stopped. But always remember that the main point of cogitating about Turing-machines isn't to imagine reading what's on the paper; the main point is to determine what types of problems can lead to accept or reject states, given a set of rules and some inputs (and whether they will do so in a finite amount of time). That is, the point is to determine what types of thing are, in principle, computable; i.e., what types of problems can be solved using only methods of computation, without any leaps of creativity, i.e., Kohler-style "insight." Best, Eric On Mon, Jul 4, 2016 at 5:13 PM, Barry MacKichan <[hidden email]> wrote: That is, it’s a definition, not a theorem. ============================================================ 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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Thanks, Eric, That all made a lot of sense to me. Now, it may have made sense because you are NOT, as I am not, a computer person, and therefore I understood you. Are we about to be told we are both wrong? We’ll see. One definitional point. If one has to use an “artificial” stop rule such as “quit when you get to the tenth decimal point”, is such a problem deemed “computable” or “non-computable”? Can one “compute” the square root of two? Nick Nicholas S. Thompson Emeritus Professor of Psychology and Biology Clark University http://home.earthlink.net/~nickthompson/naturaldesigns/ From: Friam [mailto:[hidden email]] On Behalf Of Eric Charles Nick, It is not a tautology, because (at the least) it is a program written by people, so the definition of an accept state is determined outside the system in question. At its most basic level, the Turing machine isn't calculating the answer to a problem, it is accepting or rejecting a hypothesis by following a quirky set of rules. Those rules might have you see what is written on a really long piece of paper, might have you modify the writing that is in front of you, and might have you move to various different spot in the really long paper (for subsequent reading and writing). But in the end, either you reach a state where you accept the inputs, or you reject them.... or you go on forever without an answer. (It is interesting to figure out what problems can be solved, and how long it can take to solve them, but the possibility of running forever is, IMHO, what makes the whole thing so damned interesting). For example, we could write a Turing program that tells you whether one number can be divided cleanly by another. In this case, the "accept state" is that a sub-part of the division event occurs without remainder. That is, if I ask (yes/no) whether you can divide 8 by 4, you will reach an accept state and stop rather quickly. In contrast, if I ask (yes/no) whether you can divide 8 by 9, you will go on dividing forever, never reaching an accept state. We can get around this by adding additional rules. For example, I might have the program give a "reject" if you get the same numeral 5 times in a row. (Obviously, that rule won't work for all circumstances, but it will work here.) Input -> Can you divide 8, 4? 2 Accept (i.e., the program says that you should accept that 8 is cleanly divided by 4) ------ Input -> Can you divide 8, 9? 0 0.8 0.88 0.888 0.8888 0.88888 Reject (i.e., the program says that you should reject that 8 is cleanly divided by 9) ------ If we were less interested in answering the yes/no question, and more interested in reading the output to find out what happens during the division, then you could add an additional accept state. For example, I might be a high school teacher who allows a rule that you can turn in an answered rounded to the nearest hundredth. Under such a condition, there would be two accept states: 1) You complete a division step with no remainder. 2) You get a non-zero number in the thousandth place and round. Input -> Divide 8, 9 0 0.8 0.88 0.888 0.89 Accept (i.e., the program says that when you divide 8 by 9 and round to the nearest hundredth, you get to an acceptable stopping point) ----- Note that, from a theory-of-computation perspective, the latter program is utterly uninteresting. Such a program has no risk of running forever, and it won't ever find itself in a rejection state (assuming its inputs are two numbers); it will always reach an "accept" state. Nevertheless, it is a useful program to have because after the program ends up in the "accept" state, you can read the paper and see where it was when it stopped. But always remember that the main point of cogitating about Turing-machines isn't to imagine reading what's on the paper; the main point is to determine what types of problems can lead to accept or reject states, given a set of rules and some inputs (and whether they will do so in a finite amount of time). That is, the point is to determine what types of thing are, in principle, computable; i.e., what types of problems can be solved using only methods of computation, without any leaps of creativity, i.e., Kohler-style "insight." Best, Eric
U.S. Marine Corps On Mon, Jul 4, 2016 at 5:13 PM, Barry MacKichan <[hidden email]> wrote:
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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. Frank Frank Wimberly On Jul 5, 2016 7:25 PM, "Nick Thompson" <[hidden email]> wrote:
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Thanks, Frank. Now all is clear. N Nicholas S. Thompson Emeritus Professor of Psychology and Biology Clark University http://home.earthlink.net/~nickthompson/naturaldesigns/ From: Friam [mailto:[hidden email]] On Behalf Of Frank Wimberly 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. Frank Frank Wimberly On Jul 5, 2016 7:25 PM, "Nick Thompson" <[hidden email]> wrote:
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Re: Understanding you-folks
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In reply to this post by Nick Thompson
Can one “compute” the square root of two? One can calculate using real or imaginary number types, but on can also calculate with expression types. Most modern programming languages have them these days.
So one can also “compute” on objects that relate concepts to one another. For example a two objects of equal length joined at a right angle will form a distance of sqrt(2) relative to their lengths. The machine-readable encoding of these definitions and
relationships form the basis of tools like wolframalpha.com. Marcus ============================================================ 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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In reply to this post by Nick Thompson
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 |
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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:[hidden email]] On Behalf Of glen ep ropella Sent: Wednesday, July 06, 2016 11:56 AM To: The Friday Morning Applied Complexity Coffee Group <[hidden email]> 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? -- 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 ============================================================ 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 |
Re: Understanding you-folks
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"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:[hidden email]] On Behalf Of Nick Thompson Sent: Wednesday, July 06, 2016 12:33 PM To: 'The Friday Morning Applied Complexity Coffee Group' <[hidden email]> 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:[hidden email]] On Behalf Of glen ep ropella Sent: Wednesday, July 06, 2016 11:56 AM To: The Friday Morning Applied Complexity Coffee Group <[hidden email]> 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? -- 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 ============================================================ 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 |
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In reply to this post by Nick Thompson
I tend to use the word "algorithm" to mean processes that are guaranteed to stop. Anything that's not guaranteed to stop is simply a "process". The process below may or may not have a guaranteed stop, depending on how it's implemented[*]. If you had not said "ask dad" and "dad says", then it would more directly imply its implementation. But the way you've described it sounds like it has parallel processes (me versus dad), in which case, I might wait for dad's response forever (because dad is in an infinite loop or perhaps there's a comm. failure... whatever). [*] Definiteness (definitude?) is not simple! 8^) On 07/06/2016 11:33 AM, Nick Thompson wrote: > 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? -- ☢ glen ============================================================ 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
uǝʃƃ ⊥ glen
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In reply to this post by Marcus G. Daniels
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:[hidden email]] On Behalf Of Marcus Daniels Sent: Wednesday, July 06, 2016 2:47 PM To: The Friday Morning Applied Complexity Coffee Group <[hidden email]> 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:[hidden email]] On Behalf Of Nick Thompson Sent: Wednesday, July 06, 2016 12:33 PM To: 'The Friday Morning Applied Complexity Coffee Group' <[hidden email]> 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:[hidden email]] On Behalf Of glen ep ropella Sent: Wednesday, July 06, 2016 11:56 AM To: The Friday Morning Applied Complexity Coffee Group <[hidden email]> 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? -- 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 ============================================================ 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 |
Re: Understanding you-folks
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Nick writes.. "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. "
A program can guess randomly (or from probability distributions tabulated from past experiences) or simulate some physical process that realizes an observed procedure. Then the argument reduces a question of what constitutes sufficient fidelity of the process. -----Original Message----- From: Friam [mailto:[hidden email]] On Behalf Of Nick Thompson Sent: Wednesday, July 06, 2016 1:06 PM To: 'The Friday Morning Applied Complexity Coffee Group' <[hidden email]> Subject: Re: [FRIAM] Understanding you-folks 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:[hidden email]] On Behalf Of Marcus Daniels Sent: Wednesday, July 06, 2016 2:47 PM To: The Friday Morning Applied Complexity Coffee Group <[hidden email]> 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:[hidden email]] On Behalf Of Nick Thompson Sent: Wednesday, July 06, 2016 12:33 PM To: 'The Friday Morning Applied Complexity Coffee Group' <[hidden email]> 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:[hidden email]] On Behalf Of glen ep ropella Sent: Wednesday, July 06, 2016 11:56 AM To: The Friday Morning Applied Complexity Coffee Group <[hidden email]> 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? -- 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 ============================================================ 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 |
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In reply to this post by Nick Thompson
Nick writes:
> 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. Many would argue (eg Seth Llloyd http://www.nature.com/news/2002/020603/full/news020527-16.html) that *any* process that involves changes of state is computation. Can you name a "procedure for arriving at answers" that doesn't involve a series of processes that change state? -S _______________________________________________________________________ [hidden email] CEO, Simtable http://www.simtable.com 1600 Lena St #D1, Santa Fe, NM 87505 office: <a href="tel:%28505%29995-0206" value="+15059950206" target="_blank">(505)995-0206 mobile: <a href="tel:%28505%29577-5828" value="+15055775828" target="_blank">(505)577-5828 twitter: @simtable ============================================================ 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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In reply to this post by Marcus G. Daniels
Nick,
your fishing expedition will likely be thwarted in waters that are exceeding turbulent from the interaction of prevailing trends: nothing exists except information, (re)configurations of that information yield transformations of the Universe from one state to another, and all (re)configurations are "computational" in nature. davew On Wed, Jul 6, 2016, at 01:17 PM, Marcus Daniels wrote: > Nick writes.. "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. " > > A program can guess randomly (or from probability distributions tabulated > from past experiences) or simulate some physical process that realizes an > observed procedure. Then the argument reduces a question of what > constitutes sufficient fidelity of the process. > > -----Original Message----- > From: Friam [mailto:[hidden email]] On Behalf Of Nick Thompson > Sent: Wednesday, July 06, 2016 1:06 PM > To: 'The Friday Morning Applied Complexity Coffee Group' > <[hidden email]> > Subject: Re: [FRIAM] Understanding you-folks > > 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:[hidden email]] On Behalf Of Marcus > Daniels > Sent: Wednesday, July 06, 2016 2:47 PM > To: The Friday Morning Applied Complexity Coffee Group > <[hidden email]> > 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:[hidden email]] On Behalf Of Nick Thompson > Sent: Wednesday, July 06, 2016 12:33 PM > To: 'The Friday Morning Applied Complexity Coffee Group' > <[hidden email]> > 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:[hidden email]] On Behalf Of glen ep > ropella > Sent: Wednesday, July 06, 2016 11:56 AM > To: The Friday Morning Applied Complexity Coffee Group > <[hidden email]> > 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? > > > -- > 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 > > > ============================================================ > 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 ============================================================ 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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In reply to this post by Nick Thompson
Well, that's kindasorta where I was going by complaining about definiteness. [sigh] If we allow that computations can arrive at indefinite answers (which I think is possible with Marcus' comment about symbolic "computation"), then it's hopeless. Computation covers everything. But if we force ourselves to abide by Soare's definition and computation must be definite, then there's PLENTY of reasoning processes that are excluded. Of course, it's turtles all the way down, though. A pathological scenario is produced when you bind a variable with a schema so that you've effectively replaced one set of variables with another. You can keep doing that as long as you want ... even circularly. And that leads us to the higher order concept Rosen talks about, claiming that computers (or whatever your word for it is) are categorically different from living systems ... i.e. living systems can assign meaning to variables where machines cannot. Whether something fits the intuitive concept of "computation" usually ends up being about binding (or grounding). If it's all merely syntactic manipulation of symbols, then it's computation. If it's something more, if it _means_ something, then it's no longer computation. On 07/06/2016 12:05 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. -- ☣ glen ============================================================ 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
uǝʃƃ ⊥ glen
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