Understanding you-folks

[Marcus G. Daniels]

"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."

I'm not claiming nature _is_ computational in nature.   But if it isn't we can't productively model nature at all.   There is nothing to talk about if phenomenology has no predictable regularities.  Pray to the Donald and hope for the best.
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[gepr]

On 07/06/2016 01:23 PM, Marcus Daniels wrote:
> I'm not claiming nature _is_ computational in nature.   But if it isn't we can't productively model nature at all.   There is nothing to talk about if phenomenology has no predictable regularities.  Pray to the Donald and hope for the best.

You're leaping too far.  Nature could be _near_ computational or structurally analogous to computation.  If that were the case, then we can productively model nature up to that nearness, within that ball of similarity.  Much like the Cheeto Jesus simulates a human.

--
☣ glen

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[Marcus G. Daniels]

``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.''

One way to divide things up is between computational science and computer science, where the computational scientists use computers as tools to integrate experiment & theory in the natural sciences.   Computer science considers the mathematics of computation itself.   I find that computational scientists tend to be less interested in topics like knowledge representation and the nature of intelligence than computer scientists.   What does it mean to _mean_ something?   Just grounding in some real world phenomenology?   Or does it require sensors and actuators -- robotics?
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[Robert Wall]

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? 

That pretty much covers it, Steven.  Very concise. It does more fundamentally ask the question, "Can all procedures be modeled as just state machines?"  

So, back to an early thought of a Turing Machine, which is a very simple--almost trivial--model of a computation, but this trivial device is capable of any computation that can be performed by any other computing device.  

[Sidebar: Is a medical procedure [protocol] as computation?  The objective is to get to an outcome that may not occur.  There are steps.  If we were to automate this "operation" with a machine, then we could easily think of this as a computational procedure.  Yes?]

In the context of a mathematical model of computation, the other missing piece here seems to be the allowable triggers or conditions established for transitioning out of any particular state. That's the key part of any algorithm especially for determining its complexity.  Also, an algorithm doesn't have to be guaranteed to finish (reach an accept state) at an answer in order to be considered a procedure or algorithm, IMHO.  For example, nothing may guarantee that a proper condition will arise for the procedure to transition to the next logical state.  And, there are algorithms that cannot theoretically be determined to finish or stop. But that is likely not in scope of addressing the original question: 

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.

Okay--at the risk of just throwing a bit more confusion into the mix--let's ask, "Is computation the same as information processing?"  This may just be a semantic argument but it is a point of departure for cognitive scientists who make the distinction that the brain is not a computer. See, for example, <a href="chrome-extension://oemmndcbldboiebfnladdacbdfmadadm/http://www.umsl.edu/~piccininig/Computation_vs_Information_Processing.pdf">Computation vs. information processing: why their difference matters to cognitive science (2010).  It is an interesting discussion in terms of the cognitive science concept of "computationalism" that arises in discussions of strong generalized artificial intelligence.

Since the cognitive revolution, it has become commonplace that cognition involves both computation and information processing. Is this one claim or two? Is computation the same as information processing?
The two terms are often used interchangeably, but this usage masks important differences. In this paper, we distinguish information processing from computation and examine some of their mutual relations, shed-
ding light on the role each can play in a theory of cognition. We recommend that theorists of cognition be explicit and careful in choosing notions of computation and information and connecting them together.

Again, this may just be a semantic argument or outside the scope of Nick's original query, though it is still interesting. 

Cheers,

-R

On Wed, Jul 6, 2016 at 1:33 PM, Stephen Guerin <[hidden email]> 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.

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

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[Robert Wall]

Sorry. Let's try again.  The link did not seem to come through for the cognitive science paper "Computation vs. information processing: why their difference matters to cognitive science (2010)"

-R

On Wed, Jul 6, 2016 at 2:46 PM, Robert Wall <[hidden email]> wrote:

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? 

That pretty much covers it, Steven.  Very concise. It does more fundamentally ask the question, "Can all procedures be modeled as just state machines?"  

So, back to an early thought of a Turing Machine, which is a very simple--almost trivial--model of a computation, but this trivial device is capable of any computation that can be performed by any other computing device.  

[Sidebar: Is a medical procedure [protocol] as computation?  The objective is to get to an outcome that may not occur.  There are steps.  If we were to automate this "operation" with a machine, then we could easily think of this as a computational procedure.  Yes?]

In the context of a mathematical model of computation, the other missing piece here seems to be the allowable triggers or conditions established for transitioning out of any particular state. That's the key part of any algorithm especially for determining its complexity.  Also, an algorithm doesn't have to be guaranteed to finish (reach an accept state) at an answer in order to be considered a procedure or algorithm, IMHO.  For example, nothing may guarantee that a proper condition will arise for the procedure to transition to the next logical state.  And, there are algorithms that cannot theoretically be determined to finish or stop. But that is likely not in scope of addressing the original question: 

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.

Okay--at the risk of just throwing a bit more confusion into the mix--let's ask, "Is computation the same as information processing?"  This may just be a semantic argument but it is a point of departure for cognitive scientists who make the distinction that the brain is not a computer. See, for example, Computation vs. information processing: why their difference matters to cognitive science (2010).  It is an interesting discussion in terms of the cognitive science concept of "computationalism" that arises in discussions of strong generalized artificial intelligence.

Since the cognitive revolution, it has become commonplace that cognition involves both computation and information processing. Is this one claim or two? Is computation the same as information processing?
The two terms are often used interchangeably, but this usage masks important differences. In this paper, we distinguish information processing from computation and examine some of their mutual relations, shed-
ding light on the role each can play in a theory of cognition. We recommend that theorists of cognition be explicit and careful in choosing notions of computation and information and connecting them together.

Again, this may just be a semantic argument or outside the scope of Nick's original query, though it is still interesting. 

Cheers,

-R

On Wed, Jul 6, 2016 at 1:33 PM, Stephen Guerin <[hidden email]> 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.

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

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[Marcus G. Daniels]

"Not to change the subject, but make an observation: It has always been my opinion that, had software development as a profession and practice been derived from the computational science of Ramon Lull and Leibniz instead of the computer science of Turing and Simon (Sciences of the
Artificial) trillions of dollars would have been saved and computers might be human affirming instead of human subordinating."

The military industrial complex is much more affiliated with the former, it seems to me.  (That's not a for or an against.)  That problem you describe is one with humans, not with some particular approach to science.

Marcus

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[Robert J. Cordingley]

My question is then what do Analog Computers 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 [[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 [[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 [[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

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[Eric Charles-2]

In plain language discussions it is clear that "computation" is only one of many ways to arrive at an answer.  I would suggest that anything that strays too far from that will become hopelessly confused.  If my daughter has homework,  and is supposed to compute the answer herself,  then asking me is not what she is supposed to be doing,  and no amount of trying to explain to the teacher that "all the universe is computation" not references to the informational change-states involved will persuade the teacher otherwise.

Is "ask dad" an algorithm?  Maybe, depends on how exactly that works. Am I computing the answer?  Maybe,  depends on what I'm doing.  But it should be clear that "asking dad" is not a means by which she "computes" the answer.

On Jul 6, 2016 4:55 PM, "Marcus Daniels" <[hidden email]> wrote:

"Not to change the subject, but make an observation: It has always been my opinion that, had software development as a profession and practice been derived from the computational science of Ramon Lull and Leibniz instead of the computer science of Turing and Simon (Sciences of the
Artificial) trillions of dollars would have been saved and computers might be human affirming instead of human subordinating."

The military industrial complex is much more affiliated with the former, it seems to me.  (That's not a for or an against.)  That problem you describe is one with humans, not with some particular approach to science.

Marcus

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[Robert Wall]

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 with phase space then analog computing seems to fit rather well into the general genre of computing.

State space is conceptually similar to 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.

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.  😊

Cheers,

-R

On Wed, Jul 6, 2016 at 3:31 PM, Robert J. Cordingley <[hidden email]> wrote:

My question is then what do Analog Computers 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 [[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 [[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 [[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 ⊥ <a href="tel:[phone]" value="[phone]" target="_blank">971-280-5699

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-- 
Cirrillian 
Web Design & Development
Santa Fe, NM
http://cirrillian.com
<a href="tel:[phone]" value="[phone]" target="_blank">281-989-6272 (cell)
Member Design Corps of Santa Fe

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[Marcus G. Daniels]

http://www.edn.com/design/analog/4313284/MOSFET-based-analog-circuit-calculates-square-root

 

From: Friam [mailto:[hidden email]] On Behalf Of Robert Wall
Sent: Wednesday, July 06, 2016 6:12 PM
To: The Friday Morning Applied Complexity Coffee Group <[hidden email]>
Subject: Re: [FRIAM] Understanding you-folks

 

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 with phase space then analog computing seems to fit rather well into the general genre of computing.

 

State space is conceptually similar to 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.

 

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.  😊

 

Cheers,

 

-R

 

On Wed, Jul 6, 2016 at 3:31 PM, Robert J. Cordingley <[hidden email]> wrote:

My question is then what do Analog Computers 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 [[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 [[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 [[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? 

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glen ep ropella ⊥ <a href="tel:[phone]" target="_blank">971-280-5699

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[glen ep ropella]

All computers are analog at their base.  The only thing that distinguishes so-called analog computers from typical computers is their lack of universality.  The analogies/models these analog computers implement are simply more obvious than those of the more universal, general purpose, computers.  Universality is proportional to the extent to which the computation is purely syntactical (non-semantic).  The less universal, the more specific, the more "analog".

The false identification of continuity with "analog" and discreteness with "digital" is a red herring and has caused all sorts of nonsensical hot air.  What's important is how the machine models its referent.  Analog computers (like the MOSFET √ Marcus linked to) simply have a natural and tightly bound referent.  It's that tight _binding_ that gives the analog computers both their efficiency edge and their lack of universality.  The meaning has already been assigned (or at least constrained).  Analog computers are implementations of domain-specific languages.


On 07/06/2016 02:31 PM, Robert J. Cordingley 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.

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