Isomorphism between computation and philosophy

[Owen Densmore]

On Wed, Apr 17, 2013 at 10:27 AM, Nicholas Thompson <[hidden email]> wrote:

 

<snip>

So, Owen, you meet a beautiful woman at a cocktail party.  She seems intelligent, not a person to be fobbed off, but has no experience with either Maths or Computer Science.  She looks deep into your eyes, and asks “And what, Mr. Densmore, is the halting problem?”  You find yourself torn between two impulses.  One is to use the language that would give you credibility in the world of your mentors and colleagues.  But you realize that that language is going to be of absolutely no use to her, however ever much it might make you feel authoritative to use it.  She expects an answer.  Yet you hesitate.  What language do you use? 

Your basic English.

You would start, would you not, with the idea of a “problem.”  A problem is some sort of difficulty that needs to be surmounted.  There is a goal and something that thwarts that goal.  What are these elements in the halting PROBLEM?    And why is HALTING a problem? 

Well, I do get asked a lot about computation and have found a "progressive disclosure" approach best.  I'd start by saying exactly what Michael Sipser, Intro to Theory of Computation, does: 

     "The general problem os software verification is not solvable by computer".  

Usually that is clear enough but if more is needed, we progressively discuss what software is and how it is modeled in computer theory.  Believe it or not, I've had this sort of thing lead to Finite State Automata, first as circles and arrows but then to the formal 5-tuple.  And this was not a mathematically sophisticated person.

   -- Owen

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[Nick Thompson]

“But Mr. Densmore:  what is the problem of software verification.”

 

I would bat my eyes, by my eyebrows would get in the way. 

 

Nick

 

From: Friam [mailto:[hidden email]] On Behalf Of Owen Densmore
Sent: Wednesday, April 17, 2013 3:03 PM
To: The Friday Morning Applied Complexity Coffee Group
Cc: Frank Wimberly
Subject: Re: [FRIAM] Isomorphism between computation and philosophy

 

On Wed, Apr 17, 2013 at 10:27 AM, Nicholas Thompson <[hidden email]> wrote:

 

<snip>

 

So, Owen, you meet a beautiful woman at a cocktail party.  She seems intelligent, not a person to be fobbed off, but has no experience with either Maths or Computer Science.  She looks deep into your eyes, and asks “And what, Mr. Densmore, is the halting problem?”  You find yourself torn between two impulses.  One is to use the language that would give you credibility in the world of your mentors and colleagues.  But you realize that that language is going to be of absolutely no use to her, however ever much it might make you feel authoritative to use it.  She expects an answer.  Yet you hesitate.  What language do you use? 

 

Your basic English.

You would start, would you not, with the idea of a “problem.”  A problem is some sort of difficulty that needs to be surmounted.  There is a goal and something that thwarts that goal.  What are these elements in the halting PROBLEM?    And why is HALTING a problem? 

 

Well, I do get asked a lot about computation and have found a "progressive disclosure" approach best.  I'd start by saying exactly what Michael Sipser, Intro to Theory of Computation, does: 

 

     "The general problem os software verification is not solvable by computer".  

 

Usually that is clear enough but if more is needed, we progressively discuss what software is and how it is modeled in computer theory.  Believe it or not, I've had this sort of thing lead to Finite State Automata, first as circles and arrows but then to the formal 5-tuple.  And this was not a mathematically sophisticated person.

 

   -- Owen

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[Steve Smith]

!Owen -

I can't wait for Marilyn Monroe (with a Groucho Marx moustache and cigar and Nick Thompson eyebrows) to break into "Happy Birthday Mr. Computer Guy!, Happy Birthday to you.... "

I have to say (Owen) that this doesn't even come close to any reality I live in: 

   "The general problem os software verification is not solvable by computer".  (sic)

This would never work at any cocktail party I've been to...   I admit it might be the simplest way of saying it that has a chance of being explained in *one more* unpacking, but is more likely to just end the conversation (young lady with Nick's eyebrows cocks her head and says "I think I hear my stock broker calling!" as she walks off).  So maybe your approach to progressive disclosure is more "recursive" than "iterative".   If her "Big Bold Naivete" comes with her "Nick Thompson eyebrows", she might stick around for another couple of rounds of unpacking.  Like "what in heaven's name does 'software verification' have to do with anything, and why would I *care* if you can do it with a computer or not?".  

In facte I would claim that *almost literally* anyone who understands your postulation:

   "The general problem os software verification is not solvable by computer". 

agrees with it, and anyone who doesn't probably has *virtually* no clue what you are talking about?

I admit that Nick (in Marilyn drag) has set you up a little by using words like HALTING, suggesting the (s)he has a more familiar vocabulary/lexicon than in fact (s)he probably does. I suppose anyone who knows the technical definition of "halting" probably already understands the phrase:

   "The general problem os software verification is not solvable by computer". 

Beyond this, I don't understand why someone (Owen?) would understand this phrase:

   "The general problem os software verification is not solvable by computer".  (sic)

yet would imagine that the rigorous methods of computer science would put Philosophical questions to bed.   I'd suggest that *most* of Philosophy has been hand-verifying programs written in logic, classifying them, and creating an (ever growing?) bin of "quite possibly undecidable"   (but non-trivial and interesting) statements.     I sense that you (Owen) don't agree/believe that this ever-growing bin is a *result* of the application of very formal methods (although driven by intuition and executed in psuedo-natural language) rather than *in spite of* the same?  


- Steve

“But Mr. Densmore:  what is the problem of software verification.”

 

I would bat my eyes, by my eyebrows would get in the way. 

 

Nick

 

From: Friam [[hidden email]] On Behalf Of Owen Densmore
Sent: Wednesday, April 17, 2013 3:03 PM
To: The Friday Morning Applied Complexity Coffee Group
Cc: Frank Wimberly
Subject: Re: [FRIAM] Isomorphism between computation and philosophy

 

On Wed, Apr 17, 2013 at 10:27 AM, Nicholas Thompson <[hidden email]> wrote:

 

<snip>

 

So, Owen, you meet a beautiful woman at a cocktail party.  She seems intelligent, not a person to be fobbed off, but has no experience with either Maths or Computer Science.  She looks deep into your eyes, and asks “And what, Mr. Densmore, is the halting problem?”  You find yourself torn between two impulses.  One is to use the language that would give you credibility in the world of your mentors and colleagues.  But you realize that that language is going to be of absolutely no use to her, however ever much it might make you feel authoritative to use it.  She expects an answer.  Yet you hesitate.  What language do you use? 

 

Your basic English.

You would start, would you not, with the idea of a “problem.”  A problem is some sort of difficulty that needs to be surmounted.  There is a goal and something that thwarts that goal.  What are these elements in the halting PROBLEM?    And why is HALTING a problem? 

 

Well, I do get asked a lot about computation and have found a "progressive disclosure" approach best.  I'd start by saying exactly what Michael Sipser, Intro to Theory of Computation, does: 

 

     "The general problem os software verification is not solvable by computer".  

 

Usually that is clear enough but if more is needed, we progressively discuss what software is and how it is modeled in computer theory.  Believe it or not, I've had this sort of thing lead to Finite State Automata, first as circles and arrows but then to the formal 5-tuple.  And this was not a mathematically sophisticated person.

 

   -- Owen

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Meets Fridays 9a-11:30 at cafe at St. John's College
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[Owen Densmore]

Its starting to get lonely here!

On Wed, Apr 17, 2013 at 4:44 PM, Steve Smith <[hidden email]> wrote:

!Owen -

I can't wait for Marilyn Monroe (with a Groucho Marx moustache and cigar and Nick Thompson eyebrows) to break into "Happy Birthday Mr. Computer Guy!, Happy Birthday to you.... "

I have to say (Owen) that this doesn't even come close to any reality I live in: 

   "The general problem os software verification is not solvable by computer".  (sic)

This would never work at any cocktail party I've been to...   I admit it might be the simplest way of saying it that has a chance of being explained in *one more* unpacking, but is more likely to just end the conversation (young lady with Nick's eyebrows cocks her head and says "I think I hear my stock broker calling!" as she walks off).  So maybe your approach to progressive disclosure is more "recursive" than "iterative".   If her "Big Bold Naivete" comes with her "Nick Thompson eyebrows", she might stick around for another couple of rounds of unpacking.  Like "what in heaven's name does 'software verification' have to do with anything, and why would I *care* if you can do it with a computer or not?".  

In facte I would claim that *almost literally* anyone who understands your postulation:

   "The general problem os software verification is not solvable by computer". 

agrees with it, and anyone who doesn't probably has *virtually* no clue what you are talking about?

I admit that Nick (in Marilyn drag) has set you up a little by using words like HALTING, suggesting the (s)he has a more familiar vocabulary/lexicon than in fact (s)he probably does. I suppose anyone who knows the technical definition of "halting" probably already understands the phrase:

   "The general problem os software verification is not solvable by computer". 

Beyond this, I don't understand why someone (Owen?) would understand this phrase:

   "The general problem os software verification is not solvable by computer".  (sic)

yet would imagine that the rigorous methods of computer science would put Philosophical questions to bed.   I'd suggest that *most* of Philosophy has been hand-verifying programs written in logic, classifying them, and creating an (ever growing?) bin of "quite possibly undecidable"   (but non-trivial and interesting) statements.     I sense that you (Owen) don't agree/believe that this ever-growing bin is a *result* of the application of very formal methods (although driven by intuition and executed in psuedo-natural language) rather than *in spite of* the same?  


- Steve

“But Mr. Densmore:  what is the problem of software verification.”

 

I would bat my eyes, by my eyebrows would get in the way. 

 

Nick

 

From: Friam [[hidden email]] On Behalf Of Owen Densmore
Sent: Wednesday, April 17, 2013 3:03 PM
To: The Friday Morning Applied Complexity Coffee Group
Cc: Frank Wimberly
Subject: Re: [FRIAM] Isomorphism between computation and philosophy

 

On Wed, Apr 17, 2013 at 10:27 AM, Nicholas Thompson <[hidden email]> wrote:

 

<snip>

 

So, Owen, you meet a beautiful woman at a cocktail party.  She seems intelligent, not a person to be fobbed off, but has no experience with either Maths or Computer Science.  She looks deep into your eyes, and asks “And what, Mr. Densmore, is the halting problem?”  You find yourself torn between two impulses.  One is to use the language that would give you credibility in the world of your mentors and colleagues.  But you realize that that language is going to be of absolutely no use to her, however ever much it might make you feel authoritative to use it.  She expects an answer.  Yet you hesitate.  What language do you use? 

 

Your basic English.

You would start, would you not, with the idea of a “problem.”  A problem is some sort of difficulty that needs to be surmounted.  There is a goal and something that thwarts that goal.  What are these elements in the halting PROBLEM?    And why is HALTING a problem? 

 

Well, I do get asked a lot about computation and have found a "progressive disclosure" approach best.  I'd start by saying exactly what Michael Sipser, Intro to Theory of Computation, does: 

 

     "The general problem os software verification is not solvable by computer".  

 

Usually that is clear enough but if more is needed, we progressively discuss what software is and how it is modeled in computer theory.  Believe it or not, I've had this sort of thing lead to Finite State Automata, first as circles and arrows but then to the formal 5-tuple.  And this was not a mathematically sophisticated person.

 

   -- Owen

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Meets Fridays 9a-11:30 at cafe at St. John's College
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[Douglas Roberts-2]

Yes, there hasn't been an abstruse message in at least 10 whole minutes...

On Apr 17, 2013 6:37 PM, "Owen Densmore" <[hidden email]> wrote:

Its starting to get lonely here!

On Wed, Apr 17, 2013 at 4:44 PM, Steve Smith <[hidden email]> wrote:

!Owen -

I can't wait for Marilyn Monroe (with a Groucho Marx moustache and cigar and Nick Thompson eyebrows) to break into "Happy Birthday Mr. Computer Guy!, Happy Birthday to you.... "

I have to say (Owen) that this doesn't even come close to any reality I live in: 

   "The general problem os software verification is not solvable by computer".  (sic)

This would never work at any cocktail party I've been to...   I admit it might be the simplest way of saying it that has a chance of being explained in *one more* unpacking, but is more likely to just end the conversation (young lady with Nick's eyebrows cocks her head and says "I think I hear my stock broker calling!" as she walks off).  So maybe your approach to progressive disclosure is more "recursive" than "iterative".   If her "Big Bold Naivete" comes with her "Nick Thompson eyebrows", she might stick around for another couple of rounds of unpacking.  Like "what in heaven's name does 'software verification' have to do with anything, and why would I *care* if you can do it with a computer or not?".  

In facte I would claim that *almost literally* anyone who understands your postulation:

   "The general problem os software verification is not solvable by computer". 

agrees with it, and anyone who doesn't probably has *virtually* no clue what you are talking about?

I admit that Nick (in Marilyn drag) has set you up a little by using words like HALTING, suggesting the (s)he has a more familiar vocabulary/lexicon than in fact (s)he probably does. I suppose anyone who knows the technical definition of "halting" probably already understands the phrase:

   "The general problem os software verification is not solvable by computer". 

Beyond this, I don't understand why someone (Owen?) would understand this phrase:

   "The general problem os software verification is not solvable by computer".  (sic)

yet would imagine that the rigorous methods of computer science would put Philosophical questions to bed.   I'd suggest that *most* of Philosophy has been hand-verifying programs written in logic, classifying them, and creating an (ever growing?) bin of "quite possibly undecidable"   (but non-trivial and interesting) statements.     I sense that you (Owen) don't agree/believe that this ever-growing bin is a *result* of the application of very formal methods (although driven by intuition and executed in psuedo-natural language) rather than *in spite of* the same?  


- Steve

“But Mr. Densmore:  what is the problem of software verification.”

 

I would bat my eyes, by my eyebrows would get in the way. 

 

Nick

 

From: Friam [[hidden email]] On Behalf Of Owen Densmore
Sent: Wednesday, April 17, 2013 3:03 PM
To: The Friday Morning Applied Complexity Coffee Group
Cc: Frank Wimberly
Subject: Re: [FRIAM] Isomorphism between computation and philosophy

 

On Wed, Apr 17, 2013 at 10:27 AM, Nicholas Thompson <[hidden email]> wrote:

 

<snip>

 

So, Owen, you meet a beautiful woman at a cocktail party.  She seems intelligent, not a person to be fobbed off, but has no experience with either Maths or Computer Science.  She looks deep into your eyes, and asks “And what, Mr. Densmore, is the halting problem?”  You find yourself torn between two impulses.  One is to use the language that would give you credibility in the world of your mentors and colleagues.  But you realize that that language is going to be of absolutely no use to her, however ever much it might make you feel authoritative to use it.  She expects an answer.  Yet you hesitate.  What language do you use? 

 

Your basic English.

You would start, would you not, with the idea of a “problem.”  A problem is some sort of difficulty that needs to be surmounted.  There is a goal and something that thwarts that goal.  What are these elements in the halting PROBLEM?    And why is HALTING a problem? 

 

Well, I do get asked a lot about computation and have found a "progressive disclosure" approach best.  I'd start by saying exactly what Michael Sipser, Intro to Theory of Computation, does: 

 

     "The general problem os software verification is not solvable by computer".  

 

Usually that is clear enough but if more is needed, we progressively discuss what software is and how it is modeled in computer theory.  Believe it or not, I've had this sort of thing lead to Finite State Automata, first as circles and arrows but then to the formal 5-tuple.  And this was not a mathematically sophisticated person.

 

   -- Owen

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Meets Fridays 9a-11:30 at cafe at St. John's College
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[Steve Smith]

Owen -

Its starting to get lonely here!

It is kind of a "dogpile" here...   with Doug now perched on top! <grin>

I am *sympathetic* with your desire to have the (mostly formal) language you are most familiar/comfortable with to apply more *directly* to one you may merely have romantic ideas about.   But romance does not an isomorphism make?

Maybe we can reframe the discussion in a way that lets you out from under the crush...  Is it possible that you are asking something more like?

Why isn't the language of philosophical logic (ala Bertrand Russell)  sufficient for all philosophical discourse?  And if it is, can it not therefore be mapped completely (and obviously) into a specification suitable for automated processing by a computer program?   And who wouldn't want that kind of automated verifiability?

Nick cornered you (with his breathy Marilyn Monroe voice and Groucho eyebrows) in the cocktail conversation.  I *think* his point was at least partly that even *IF* you could reduce all philosophical discourse to being equivalent to computer science, it wouldn't help make the conversation accessible to anyone without significant experience/training/exposure to the specialized language involved?

Maybe the rest of us are just jealous if we imagine that you could "glibly" get away with such cocktail conversations (and by get away with, I mean successfully make the point to someone with limited domain-specific knowledge, not just get them to pretend to understand as they sidle off toward the exit or the group playing Twister in the corner)?  But that image (embellished by me of course) was Nick's, not yours so it isn't really fair to beat you with that one.

In a nod to Doug (perched smugly on top of the pile), I have to acknowledge the precision of his choice of the term "abstruse"... I had to look it up (not because I didn't have a working knowledge, but because I wanted to see if he and I likely use it the same way):

ab·struse  

/abˈstro͞os/

Adjective

Difficult to understand; obscure.

Synonyms

obscure - recondite - deep - profound

I have to admit to having always treated it as a portmanteau word formed roughly from "abstract" and "obtuse".   Not *quite* as generous as the definition given above:  "Annoyingly Insensitive" compounded with "dissociated from any specific instance".    Wait... maybe that *is* his use?

ob·tuse  

/əbˈt(y)o͞os/

Adjective

1. Annoyingly insensitive or slow to understand.
2. Difficult to understand.

Synonyms

dull - blunt - dense - slow-witted

¹ab·stract

adjective \ab-ˈstrakt, ˈab-ˌ\

1

a : <a href="http://www.merriam-webster.com/dictionary/disassociate" class="d_link" onclick="_gaq.push(['_trackEvent', 'Enhancement - link', 'Clicked', 'disassociate']);">disassociated from any specific instance <an abstract entity>

b : difficult to understand : abstruse <abstract problems>

c : insufficiently factual : formal <possessed only an abstract right>

2

: expressing a quality apart from an object <the word poem is concrete, poetry is abstract>

3

a : dealing with a subject in its abstract aspects : theoretical <abstract science>

b : impersonal, detached <the abstract compassion of a surgeon — Time>

4

: having only <a href="http://www.merriam-webster.com/dictionary/intrinsic" class="d_link" onclick="_gaq.push(['_trackEvent', 'Enhancement - link', 'Clicked', 'intrinsic']);">intrinsic form with little or no attempt at pictorial representation or narrative content <abstract painting>

— ab·stract·ly adverb

— ab·stract·ness noun

- Steve




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[lrudolph]

Nick asks Owen:
 

> So, Owen, you meet a beautiful woman at a cocktail party.  She seems
> intelligent, not a person to be fobbed off, but has no experience with
> either Maths or Computer Science.  She looks deep into your eyes, and asks
> "And what, Mr. Densmore, is the halting problem?"  You find yourself torn
> between two impulses.  One is to use the language that would give you
> credibility in the world of your mentors and colleagues.  But you realize
> that that language is going to be of absolutely no use to her, however ever
> much it might make you feel authoritative to use it.  She expects an answer.
> Yet you hesitate.  What language do you use?  
>
> You would start, would you not, with the idea of a "problem."  A problem is
> some sort of difficulty that needs to be surmounted.  There is a goal and
> something that thwarts that goal.  What are these elements in the halting
> PROBLEM?    And why is HALTING a problem?  

Nick, Owen may well disagree, but from my point of view you've already staked a dubious claim,
by assuming (defensably) that "problem" in the MathEng phrase "Halting Problem" can and should
be understood to be the same word as "problem" in your dialect of English.  But this is, I
think, a false assumption.  Now, at least, whatever the case was when the "Halting Problem"
got its original name (in MathGerman, I think), the meaning that "Halting Problem" conveys in
MathEng is the same (or nearly the same) as that conveyed by "Halting Question".  "Problem" is
there for historical reasons, just as, in geometric topology, a certain question of
considerable interest and importance (which has been answered for fewer decades than has the
"Halting Problem") is still called--even in MathEng!--"the Hauptvermutung".  The framing in
terms of "a goal" and "something that thwarts" is delusive.  There is, rather, "a question"
and--if you must be florid--a "quest for an answer".  Note, "*an* answer".  Of course, at an
extreme level (I can't decide whether it's the highest or the lowest: I *hate* "level" talk
precisely for this kind of reason) there is *the* answer ("no").  But that isn't, in itself,
very interesting (any more: of course it was before it was known to be "the" answer).  *How*
you get to "no" is interesting, and there are (by now) many different "hows" (for the "Halting
Question", the Hauptvermutung, Poincare's Conjecture, and so forth and so on), each of which
is *an* answer (as are many of the "not hows").  

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[Steve Smith]

Lee -

I feel a bit like Beavis (or is it Butthead?) in the light of Doug's "abstruse" comment and my introspections on "abstract" v "obtuse".

"Heh Heh Heh... he said 'Hauptvermutung' !"

I appreciate your use of "MathGerman" and "MathEng" which I think reinforces my point (for anyone who had to learn German or Latin as part of their university science education can appreciate) that while language is translatable, it *definitely* is not so on a word-by-word basis and being able to read the "original" and/or at least appreciate the culture from which a given idea or phrase sprung is worthwhile.   I *did not* have to learn such a language (it was decided by my era that a computer language (or two?) was an acceptable alternative).  I claim "NO!" but did not appreciate it at the time.    

I also liked how you brought out:

*How* you get to "no" is interesting, and there are (by now) many different "hows"

Which I think is responsive to Glen's point about the "many morphisms of interest"  earlier in the discussion.  But also relates to Glen's "It depends!" answer.   My sense is that "it depends" is a given, but "what and how does it depend upon" is what makes it interesting.

- Steve

   

Nick asks Owen:
 

So, Owen, you meet a beautiful woman at a cocktail party.  She seems
intelligent, not a person to be fobbed off, but has no experience with
either Maths or Computer Science.  She looks deep into your eyes, and asks
"And what, Mr. Densmore, is the halting problem?"  You find yourself torn
between two impulses.  One is to use the language that would give you
credibility in the world of your mentors and colleagues.  But you realize
that that language is going to be of absolutely no use to her, however ever
much it might make you feel authoritative to use it.  She expects an answer.
Yet you hesitate.  What language do you use?  

You would start, would you not, with the idea of a "problem."  A problem is
some sort of difficulty that needs to be surmounted.  There is a goal and
something that thwarts that goal.  What are these elements in the halting
PROBLEM?    And why is HALTING a problem?  

Nick, Owen may well disagree, but from my point of view you've already staked a dubious claim, 
by assuming (defensably) that "problem" in the MathEng phrase "Halting Problem" can and should 
be understood to be the same word as "problem" in your dialect of English.  But this is, I 
think, a false assumption.  Now, at least, whatever the case was when the "Halting Problem" 
got its original name (in MathGerman, I think), the meaning that "Halting Problem" conveys in 
MathEng is the same (or nearly the same) as that conveyed by "Halting Question".  "Problem" is 
there for historical reasons, just as, in geometric topology, a certain question of 
considerable interest and importance (which has been answered for fewer decades than has the 
"Halting Problem") is still called--even in MathEng!--"the Hauptvermutung".  The framing in 
terms of "a goal" and "something that thwarts" is delusive.  There is, rather, "a question" 
and--if you must be florid--a "quest for an answer".  Note, "*an* answer".  Of course, at an 
extreme level (I can't decide whether it's the highest or the lowest: I *hate* "level" talk 
precisely for this kind of reason) there is *the* answer ("no").  But that isn't, in itself, 
very interesting (any more: of course it was before it was known to be "the" answer).  *How* 
you get to "no" is interesting, and there are (by now) many different "hows" (for the "Halting 
Question", the Hauptvermutung, Poincare's Conjecture, and so forth and so on), each of which 
is *an* answer (as are many of the "not hows").  

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[Douglas Roberts-2]

I believe we might actually, for a change, be cutting a bit closer to the bone here.

-Doug

On Wed, Apr 17, 2013 at 7:24 PM, Steve Smith <[hidden email]> wrote:

:  "Annoyingly Insensitive" compounded with "dissociated from any specific instance".    Wait... maybe that *is* his use?

ob·tuse  

/əbˈt(y)o͞os/

Adjective

1. Annoyingly insensitive or slow to understand.
2. Difficult to understand.

Synonyms

dull - blunt - dense - slow-witted

¹ab·stract

adjective \ab-ˈstrakt, ˈab-ˌ\

1

a : disassociated from any specific instance <an abstract entity>

b : difficult to understand : abstruse <abstract problems>

c : insufficiently factual : formal <possessed only an abstract right>

2

: expressing a quality apart from an object <the word poem is concrete, poetry is abstract>

3

a : dealing with a subject in its abstract aspects : theoretical <abstract science>

b : impersonal, detached <the abstract compassion of a surgeon — Time>

4

: having only intrinsic form with little or no attempt at pictorial representation or narrative content <abstract painting>

— ab·stract·ly adverb

— ab·stract·ness noun

- Steve

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Doug Roberts
[hidden email]

http://parrot-farm.net/Second-Cousins

505-455-7333 - Office
505-672-8213 - Mobile

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[Joe Spinden]

Owen is right that there are N! ways to map a set of N objects 1-1, onto
another set of N objects. The first object can go to 1 of N objects, the
next to 1 of N-1, etc. That's pretty standard.

As to the Halting Problem, Why not start with the first few lines of the
Wikipedia article ? That is simple and easy to understand.

Joe




On 4/17/13 7:32 PM, [hidden email] wrote:

> Nick asks Owen:
>  
>> So, Owen, you meet a beautiful woman at a cocktail party.  She seems
>> intelligent, not a person to be fobbed off, but has no experience with
>> either Maths or Computer Science.  She looks deep into your eyes, and asks
>> "And what, Mr. Densmore, is the halting problem?"  You find yourself torn
>> between two impulses.  One is to use the language that would give you
>> credibility in the world of your mentors and colleagues.  But you realize
>> that that language is going to be of absolutely no use to her, however ever
>> much it might make you feel authoritative to use it.  She expects an answer.
>> Yet you hesitate.  What language do you use?
>>
>> You would start, would you not, with the idea of a "problem."  A problem is
>> some sort of difficulty that needs to be surmounted.  There is a goal and
>> something that thwarts that goal.  What are these elements in the halting
>> PROBLEM?    And why is HALTING a problem?
> Nick, Owen may well disagree, but from my point of view you've already staked a dubious claim,
> by assuming (defensably) that "problem" in the MathEng phrase "Halting Problem" can and should
> be understood to be the same word as "problem" in your dialect of English.  But this is, I
> think, a false assumption.  Now, at least, whatever the case was when the "Halting Problem"
> got its original name (in MathGerman, I think), the meaning that "Halting Problem" conveys in
> MathEng is the same (or nearly the same) as that conveyed by "Halting Question".  "Problem" is
> there for historical reasons, just as, in geometric topology, a certain question of
> considerable interest and importance (which has been answered for fewer decades than has the
> "Halting Problem") is still called--even in MathEng!--"the Hauptvermutung".  The framing in
> terms of "a goal" and "something that thwarts" is delusive.  There is, rather, "a question"
> and--if you must be florid--a "quest for an answer".  Note, "*an* answer".  Of course, at an
> extreme level (I can't decide whether it's the highest or the lowest: I *hate* "level" talk
> precisely for this kind of reason) there is *the* answer ("no").  But that isn't, in itself,
> very interesting (any more: of course it was before it was known to be "the" answer).  *How*
> you get to "no" is interesting, and there are (by now) many different "hows" (for the "Halting
> Question", the Hauptvermutung, Poincare's Conjecture, and so forth and so on), each of which
> is *an* answer (as are many of the "not hows").
>
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[Nick Thompson]

Steve,

 

I am, I confess, rankled to be called abstrooos, because I try hard to be clear.  Bad as I am at it, it is a central passion of my life.  The temptation is always just to mouth the words that make one feel like an expert, rather than try out words that might actually communicate one’s understanding to a person who does not yet share it.  In this conversation, I see that a lot of people, yourself included, have been working very hard to be clear to one another, although it is very hard work.   Doug has little standing to criticize others for being abstrooos, because he has usually ducked any request that he explain something difficult to somebody who does not share his training.  He may hold the view …. And has, in fact, in at least one conversation defended the view … that talking to non-experts about matters in a field in which he holds expertise is simply not a useful exercise.  But that, I think, quickly leads to the idea that we should be governed by scientist-kings in all important matters to which scientific expertise is relevant.   That prospect is pretty scary to me.   Unless one favors such a government, one really has no choice but to jump in the sty with the rest of us pigs and wallow around with us. 

 

Come on in, Doug.  The mud’s just fine!  What is the halting problem? 

 

Nick

 

From: Friam [mailto:[hidden email]] On Behalf Of Steve Smith
Sent: Wednesday, April 17, 2013 7:25 PM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Isomorphism between computation and philosophy

 

Owen -

Its starting to get lonely here!

It is kind of a "dogpile" here...   with Doug now perched on top! <grin>

I am *sympathetic* with your desire to have the (mostly formal) language you are most familiar/comfortable with to apply more *directly* to one you may merely have romantic ideas about.   But romance does not an isomorphism make?

Maybe we can reframe the discussion in a way that lets you out from under the crush...  Is it possible that you are asking something more like?

Why isn't the language of philosophical logic (ala Bertrand Russell)  sufficient for all philosophical discourse?  And if it is, can it not therefore be mapped completely (and obviously) into a specification suitable for automated processing by a computer program?   And who wouldn't want that kind of automated verifiability?

Nick cornered you (with his breathy Marilyn Monroe voice and Groucho eyebrows) in the cocktail conversation.  I *think* his point was at least partly that even *IF* you could reduce all philosophical discourse to being equivalent to computer science, it wouldn't help make the conversation accessible to anyone without significant experience/training/exposure to the specialized language involved?

Maybe the rest of us are just jealous if we imagine that you could "glibly" get away with such cocktail conversations (and by get away with, I mean successfully make the point to someone with limited domain-specific knowledge, not just get them to pretend to understand as they sidle off toward the exit or the group playing Twister in the corner)?  But that image (embellished by me of course) was Nick's, not yours so it isn't really fair to beat you with that one.

In a nod to Doug (perched smugly on top of the pile), I have to acknowledge the precision of his choice of the term "abstruse"... I had to look it up (not because I didn't have a working knowledge, but because I wanted to see if he and I likely use it the same way):

ab·struse  

/abˈstro͞os/

Adjective

Difficult to understand; obscure.

Synonyms

obscure - recondite - deep - profound

I have to admit to having always treated it as a portmanteau word formed roughly from "abstract" and "obtuse".   Not *quite* as generous as the definition given above:  "Annoyingly Insensitive" compounded with "dissociated from any specific instance".    Wait... maybe that *is* his use?

ob·tuse  

/əbˈt(y)o͞os/

Adjective

1. Annoyingly insensitive or slow to understand.
2. Difficult to understand.

Synonyms

dull - blunt - dense - slow-witted

¹ab·stract

adjective \ab-ˈstrakt, ˈab-ˌ\

1

a : disassociated from any specific instance <an abstract entity>

b : difficult to understand : abstruse <abstract problems>

c : insufficiently factual : formal <possessed only an abstract right>

2

: expressing a quality apart from an object <the word poem is concrete, poetry is abstract>

3

a : dealing with a subject in its abstract aspects : theoretical <abstract science>

b : impersonal, detached <the abstract compassion of a surgeon — Time>

4

: having only intrinsic form with little or no attempt at pictorial representation or narrative content <abstract painting>

— ab·stract·ly adverb

— ab·stract·ness noun

- Steve

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[Douglas Roberts-2]

In summary, Nick: the problem appears to be two-fold:

1. The real day job is taking up every spare minute of my time, and
2. you guys clearly love to discuss abstraction for the seemingly sole sake of discussion way, way more than I do.  I don't get that, in all truth, but you all seem to be enjoying it so much, the very last thing I'd ever want to do would be to dampen all that pleasure.

Seriously, please carry on.

--Doug

On Wed, Apr 17, 2013 at 9:36 PM, Nicholas Thompson <[hidden email]> wrote:

Steve,

 

I am, I confess, rankled to be called abstrooos, because I try hard to be clear.  Bad as I am at it, it is a central passion of my life.  The temptation is always just to mouth the words that make one feel like an expert, rather than try out words that might actually communicate one’s understanding to a person who does not yet share it.  In this conversation, I see that a lot of people, yourself included, have been working very hard to be clear to one another, although it is very hard work.   Doug has little standing to criticize others for being abstrooos, because he has usually ducked any request that he explain something difficult to somebody who does not share his training.  He may hold the view …. And has, in fact, in at least one conversation defended the view … that talking to non-experts about matters in a field in which he holds expertise is simply not a useful exercise.  But that, I think, quickly leads to the idea that we should be governed by scientist-kings in all important matters to which scientific expertise is relevant.   That prospect is pretty scary to me.   Unless one favors such a government, one really has no choice but to jump in the sty with the rest of us pigs and wallow around with us. 

 

Come on in, Doug.  The mud’s just fine!  What is the halting problem? 

 

Nick

 

From: Friam [mailto:[hidden email]] On Behalf Of Steve Smith
Sent: Wednesday, April 17, 2013 7:25 PM

To: The Friday Morning Applied Complexity Coffee Group

Subject: Re: [FRIAM] Isomorphism between computation and philosophy

 

Owen -

Its starting to get lonely here!

It is kind of a "dogpile" here...   with Doug now perched on top! <grin>

I am *sympathetic* with your desire to have the (mostly formal) language you are most familiar/comfortable with to apply more *directly* to one you may merely have romantic ideas about.   But romance does not an isomorphism make?

Maybe we can reframe the discussion in a way that lets you out from under the crush...  Is it possible that you are asking something more like?

Why isn't the language of philosophical logic (ala Bertrand Russell)  sufficient for all philosophical discourse?  And if it is, can it not therefore be mapped completely (and obviously) into a specification suitable for automated processing by a computer program?   And who wouldn't want that kind of automated verifiability?

Nick cornered you (with his breathy Marilyn Monroe voice and Groucho eyebrows) in the cocktail conversation.  I *think* his point was at least partly that even *IF* you could reduce all philosophical discourse to being equivalent to computer science, it wouldn't help make the conversation accessible to anyone without significant experience/training/exposure to the specialized language involved?

Maybe the rest of us are just jealous if we imagine that you could "glibly" get away with such cocktail conversations (and by get away with, I mean successfully make the point to someone with limited domain-specific knowledge, not just get them to pretend to understand as they sidle off toward the exit or the group playing Twister in the corner)?  But that image (embellished by me of course) was Nick's, not yours so it isn't really fair to beat you with that one.

In a nod to Doug (perched smugly on top of the pile), I have to acknowledge the precision of his choice of the term "abstruse"... I had to look it up (not because I didn't have a working knowledge, but because I wanted to see if he and I likely use it the same way):

ab·struse  

/abˈstro͞os/

Adjective

Difficult to understand; obscure.

Synonyms

obscure - recondite - deep - profound

I have to admit to having always treated it as a portmanteau word formed roughly from "abstract" and "obtuse".   Not *quite* as generous as the definition given above:  "Annoyingly Insensitive" compounded with "dissociated from any specific instance".    Wait... maybe that *is* his use?

ob·tuse  

/əbˈt(y)o͞os/

Adjective

1. Annoyingly insensitive or slow to understand.
2. Difficult to understand.

Synonyms

dull - blunt - dense - slow-witted

¹ab·stract

adjective \ab-ˈstrakt, ˈab-ˌ\

1

a : disassociated from any specific instance <an abstract entity>

b : difficult to understand : abstruse <abstract problems>

c : insufficiently factual : formal <possessed only an abstract right>

2

: expressing a quality apart from an object <the word poem is concrete, poetry is abstract>

3

a : dealing with a subject in its abstract aspects : theoretical <abstract science>

b : impersonal, detached <the abstract compassion of a surgeon — Time>

4

: having only intrinsic form with little or no attempt at pictorial representation or narrative content <abstract painting>

— ab·stract·ly adverb

— ab·stract·ness noun

- Steve

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--

Doug Roberts
[hidden email]

http://parrot-farm.net/Second-Cousins

505-455-7333 - Office
505-672-8213 - Mobile

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[Owen Densmore]

Nick: its simple.  I married her.  Just after explaining Godel to the philosophy department, and to her Ex who promptly left philosophy and became a cardio doctor.  True.

In terms of the Halting problem, is Wikipedia too formal?  The first two paragraphs:

In computability theory, the halting problem can be stated as follows: "Given a description of an arbitrary computer program, decide whether the program finishes running or continues to run forever". This is equivalent to the problem of deciding, given a program and an input, whether the program will eventually halt when run with that input, or will run forever.

Alan Turing proved in 1936 that a general algorithm to solve the halting problem for all possible program-input pairs cannot exist. A key part of the proof was a mathematical definition of a computer and program, what became known as a Turing machine; the halting problem is undecidable over Turing machines. It is one of the first examples of a decision problem.

Did you find that foreign?  Dede doesn't.

But then she lived in Silly Valley for 20+ years .. its in the air there.  She thinks math is sexy .. well, hmm, that I am and she puts up with the math.

Don't forget I invited you to viewing and discussing Michael Sendel's Justice and you never antied up.  I think its time you read up on computation theory or discrete math, your choice.  You'd love it.

We've all jumped into your seminars and read your stuff.  Your turn.

   -- Owen

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[Joe Spinden]

You can state it pretty simply:  There is no algorithm that can decide whether an arbitrary computer program will ever stop (Halt), or will loop endlessly.. 

Definitely a problem for software testing..

Joe

On 4/17/13 10:15 PM, Owen Densmore wrote:

Nick: its simple.  I married her.  Just after explaining Godel to the philosophy department, and to her Ex who promptly left philosophy and became a cardio doctor.  True.

In terms of the Halting problem, is Wikipedia too formal?  The first two paragraphs:

In computability theory, the halting problem can be stated as follows: "Given a description of an arbitrary computer program, decide whether the program finishes running or continues to run forever". This is equivalent to the problem of deciding, given a program and an input, whether the program will eventually halt when run with that input, or will run forever.

Alan Turing proved in 1936 that a general algorithm to solve the halting problem for all possible program-input pairs cannot exist. A key part of the proof was a mathematical definition of a computer and program, what became known as a Turing machine; the halting problem is undecidable over Turing machines. It is one of the first examples of a decision problem.

Did you find that foreign?  Dede doesn't.

But then she lived in Silly Valley for 20+ years .. its in the air there.  She thinks math is sexy .. well, hmm, that I am and she puts up with the math.

Don't forget I invited you to viewing and discussing Michael Sendel's Justice and you never antied up.  I think its time you read up on computation theory or discrete math, your choice.  You'd love it.

We've all jumped into your seminars and read your stuff.  Your turn.

   -- Owen

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[Russ Abbott]

The problem isn't really looping vs stopping; it's searching vs. finding. Searching might be expressed iteratively (as a loop) or recursively. But what the program is really doing is looking for an element that satisfies some criterion. In many cases, it's not known in advance whether one exists. The only way to find one is to search sequentially through the space of possibilities, which may be infinite.  If there is no element that satisfies the criterion, the search never ends, and the program never stops.

 

-- Russ Abbott
_____________________________________________

  Professor, Computer Science
  California State University, Los Angeles

  My paper on how the Fed can fix the economy: ssrn.com/abstract=1977688
  Google voice: 747-999-5105

  Google+: plus.google.com/114865618166480775623/

  vita:  sites.google.com/site/russabbott/

  CS Wiki and the courses I teach
_____________________________________________ 

On Wed, Apr 17, 2013 at 9:30 PM, Joseph Spinden <[hidden email]> wrote:

You can state it pretty simply:  There is no algorithm that can decide whether an arbitrary computer program will ever stop (Halt), or will loop endlessly.. 

Definitely a problem for software testing..

Joe

On 4/17/13 10:15 PM, Owen Densmore wrote:

Nick: its simple.  I married her.  Just after explaining Godel to the philosophy department, and to her Ex who promptly left philosophy and became a cardio doctor.  True.

In terms of the Halting problem, is Wikipedia too formal?  The first two paragraphs:

In computability theory, the halting problem can be stated as follows: "Given a description of an arbitrary computer program, decide whether the program finishes running or continues to run forever". This is equivalent to the problem of deciding, given a program and an input, whether the program will eventually halt when run with that input, or will run forever.

Alan Turing proved in 1936 that a general algorithm to solve the halting problem for all possible program-input pairs cannot exist. A key part of the proof was a mathematical definition of a computer and program, what became known as a Turing machine; the halting problem is undecidable over Turing machines. It is one of the first examples of a decision problem.

Did you find that foreign?  Dede doesn't.

But then she lived in Silly Valley for 20+ years .. its in the air there.  She thinks math is sexy .. well, hmm, that I am and she puts up with the math.

Don't forget I invited you to viewing and discussing Michael Sendel's Justice and you never antied up.  I think its time you read up on computation theory or discrete math, your choice.  You'd love it.

We've all jumped into your seminars and read your stuff.  Your turn.

   -- Owen

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-- 

"Sunlight is the best disinfectant."

  -- Supreme Court Justice Louis D. Brandeis, 1913.

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[Nick Thompson]

I don't think the beautiful woman would accept "go read the Wikipedia
article" as am answer.  

N

-----Original Message-----
From: Friam [mailto:[hidden email]] On Behalf Of Joseph Spinden
Sent: Wednesday, April 17, 2013 8:21 PM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Isomorphism between computation and philosophy

Owen is right that there are N! ways to map a set of N objects 1-1, onto
another set of N objects. The first object can go to 1 of N objects, the
next to 1 of N-1, etc. That's pretty standard.

As to the Halting Problem, Why not start with the first few lines of the
Wikipedia article ? That is simple and easy to understand.

Joe




On 4/17/13 7:32 PM, [hidden email] wrote:

> Nick asks Owen:
>  
>> So, Owen, you meet a beautiful woman at a cocktail party.  She seems
>> intelligent, not a person to be fobbed off, but has no experience
>> with either Maths or Computer Science.  She looks deep into your
>> eyes, and asks "And what, Mr. Densmore, is the halting problem?"  You
>> find yourself torn between two impulses.  One is to use the language
>> that would give you credibility in the world of your mentors and
>> colleagues.  But you realize that that language is going to be of
>> absolutely no use to her, however ever much it might make you feel

authoritative to use it.  She expects an answer.
>> Yet you hesitate.  What language do you use?
>>
>> You would start, would you not, with the idea of a "problem."  A
>> problem is some sort of difficulty that needs to be surmounted.  
>> There is a goal and something that thwarts that goal.  What are these
elements in the halting
>> PROBLEM?    And why is HALTING a problem?
> Nick, Owen may well disagree, but from my point of view you've already
> staked a dubious claim, by assuming (defensably) that "problem" in the
> MathEng phrase "Halting Problem" can and should be understood to be
> the same word as "problem" in your dialect of English.  But this is, I
think, a false assumption.  Now, at least, whatever the case was when the
"Halting Problem"
> got its original name (in MathGerman, I think), the meaning that
> "Halting Problem" conveys in MathEng is the same (or nearly the same)
> as that conveyed by "Halting Question".  "Problem" is there for
> historical reasons, just as, in geometric topology, a certain question
> of considerable interest and importance (which has been answered for
> fewer decades than has the "Halting Problem") is still called--even in
MathEng!--"the Hauptvermutung".  The framing in terms of "a goal" and
"something that thwarts" is delusive.  There is, rather, "a question"
> and--if you must be florid--a "quest for an answer".  Note, "*an*
> answer".  Of course, at an extreme level (I can't decide whether it's
> the highest or the lowest: I *hate* "level" talk precisely for this
> kind of reason) there is *the* answer ("no").  But that isn't, in
> itself, very interesting (any more: of course it was before it was
> known to be "the" answer).  *How* you get to "no" is interesting, and
> there are (by now) many different "hows" (for the "Halting Question", the
Hauptvermutung, Poincare's Conjecture, and so forth and so on), each of
which is *an* answer (as are many of the "not hows").
>
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   -- Supreme Court Justice Louis D. Brandeis, 1913.


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[Nick Thompson]

Doug,

 

Gracious.

 

But now I feel like rotter and a churl.  But thank you.  And, we probably will.

 

Nick

 

From: Friam [mailto:[hidden email]] On Behalf Of Douglas Roberts
Sent: Wednesday, April 17, 2013 9:48 PM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Isomorphism between computation and philosophy

 

In summary, Nick: the problem appears to be two-fold:

1. The real day job is taking up every spare minute of my time, and
2. you guys clearly love to discuss abstraction for the seemingly sole sake of discussion way, way more than I do.  I don't get that, in all truth, but you all seem to be enjoying it so much, the very last thing I'd ever want to do would be to dampen all that pleasure.

Seriously, please carry on.

 

--Doug

 

 

On Wed, Apr 17, 2013 at 9:36 PM, Nicholas Thompson <[hidden email]> wrote:

Steve,

 

I am, I confess, rankled to be called abstrooos, because I try hard to be clear.  Bad as I am at it, it is a central passion of my life.  The temptation is always just to mouth the words that make one feel like an expert, rather than try out words that might actually communicate one’s understanding to a person who does not yet share it.  In this conversation, I see that a lot of people, yourself included, have been working very hard to be clear to one another, although it is very hard work.   Doug has little standing to criticize others for being abstrooos, because he has usually ducked any request that he explain something difficult to somebody who does not share his training.  He may hold the view …. And has, in fact, in at least one conversation defended the view … that talking to non-experts about matters in a field in which he holds expertise is simply not a useful exercise.  But that, I think, quickly leads to the idea that we should be governed by scientist-kings in all important matters to which scientific expertise is relevant.   That prospect is pretty scary to me.   Unless one favors such a government, one really has no choice but to jump in the sty with the rest of us pigs and wallow around with us. 

 

Come on in, Doug.  The mud’s just fine!  What is the halting problem? 

 

Nick

 

From: Friam [mailto:[hidden email]] On Behalf Of Steve Smith
Sent: Wednesday, April 17, 2013 7:25 PM

To: The Friday Morning Applied Complexity Coffee Group

Subject: Re: [FRIAM] Isomorphism between computation and philosophy

 

Owen -

Its starting to get lonely here!

It is kind of a "dogpile" here...   with Doug now perched on top! <grin>

I am *sympathetic* with your desire to have the (mostly formal) language you are most familiar/comfortable with to apply more *directly* to one you may merely have romantic ideas about.   But romance does not an isomorphism make?

Maybe we can reframe the discussion in a way that lets you out from under the crush...  Is it possible that you are asking something more like?

Why isn't the language of philosophical logic (ala Bertrand Russell)  sufficient for all philosophical discourse?  And if it is, can it not therefore be mapped completely (and obviously) into a specification suitable for automated processing by a computer program?   And who wouldn't want that kind of automated verifiability?

Nick cornered you (with his breathy Marilyn Monroe voice and Groucho eyebrows) in the cocktail conversation.  I *think* his point was at least partly that even *IF* you could reduce all philosophical discourse to being equivalent to computer science, it wouldn't help make the conversation accessible to anyone without significant experience/training/exposure to the specialized language involved?

Maybe the rest of us are just jealous if we imagine that you could "glibly" get away with such cocktail conversations (and by get away with, I mean successfully make the point to someone with limited domain-specific knowledge, not just get them to pretend to understand as they sidle off toward the exit or the group playing Twister in the corner)?  But that image (embellished by me of course) was Nick's, not yours so it isn't really fair to beat you with that one.

In a nod to Doug (perched smugly on top of the pile), I have to acknowledge the precision of his choice of the term "abstruse"... I had to look it up (not because I didn't have a working knowledge, but because I wanted to see if he and I likely use it the same way):

ab·struse  

/abˈstro͞os/

Adjective

Difficult to understand; obscure.

Synonyms

obscure - recondite - deep - profound

I have to admit to having always treated it as a portmanteau word formed roughly from "abstract" and "obtuse".   Not *quite* as generous as the definition given above:  "Annoyingly Insensitive" compounded with "dissociated from any specific instance".    Wait... maybe that *is* his use?

ob·tuse  

/əbˈt(y)o͞os/

Adjective

1. Annoyingly insensitive or slow to understand.
2. Difficult to understand.

Synonyms

dull - blunt - dense - slow-witted

¹ab·stract

adjective \ab-ˈstrakt, ˈab-ˌ\

1

a : disassociated from any specific instance <an abstract entity>

b : difficult to understand : abstruse <abstract problems>

c : insufficiently factual : formal <possessed only an abstract right>

2

: expressing a quality apart from an object <the word poem is concrete, poetry is abstract>

3

a : dealing with a subject in its abstract aspects : theoretical <abstract science>

b : impersonal, detached <the abstract compassion of a surgeon — Time>

4

: having only intrinsic form with little or no attempt at pictorial representation or narrative content <abstract painting>

— ab·stract·ly adverb

— ab·stract·ness noun

- Steve

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[Nick Thompson]

Owen,

 

Ask Dede to provide a translation, would you?

 

Nick

 

From: Friam [mailto:[hidden email]] On Behalf Of Owen Densmore
Sent: Wednesday, April 17, 2013 10:16 PM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Isomorphism between computation and philosophy

 

Nick: its simple.  I married her.  Just after explaining Godel to the philosophy department, and to her Ex who promptly left philosophy and became a cardio doctor.  True.

 

In terms of the Halting problem, is Wikipedia too formal?  The first two paragraphs:

 

In computability theory, the halting problem can be stated as follows: "Given a description of an arbitrary computer program, decide whether the program finishes running or continues to run forever". This is equivalent to the problem of deciding, given a program and an input, whether the program will eventually halt when run with that input, or will run forever.

 

Alan Turing proved in 1936 that a general algorithm to solve the halting problem for all possible program-input pairs cannot exist. A key part of the proof was a mathematical definition of a computer and program, what became known as a Turing machine; the halting problem is undecidable over Turing machines. It is one of the first examples of a decision problem.

 

Did you find that foreign?  Dede doesn't.

 

But then she lived in Silly Valley for 20+ years .. its in the air there.  She thinks math is sexy .. well, hmm, that I am and she puts up with the math.

 

Don't forget I invited you to viewing and discussing Michael Sendel's Justice and you never antied up.  I think its time you read up on computation theory or discrete math, your choice.  You'd love it.

 

We've all jumped into your seminars and read your stuff.  Your turn.

 

   -- Owen

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[Steve Smith]

A spontaneous Haiku inspired by a pithy friend's analysis of our discussion:

The Halting Problem
Pretty Girl; Cocktail Party
Knowing when to stop

I don't think the beautiful woman would accept "go read the Wikipedia
article" as am answer.  

N

-----Original Message-----
From: Friam [[hidden email]] On Behalf Of Joseph Spinden
Sent: Wednesday, April 17, 2013 8:21 PM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Isomorphism between computation and philosophy

Owen is right that there are N! ways to map a set of N objects 1-1, onto
another set of N objects. The first object can go to 1 of N objects, the
next to 1 of N-1, etc. That's pretty standard.

As to the Halting Problem, Why not start with the first few lines of the
Wikipedia article ? That is simple and easy to understand.

Joe




On 4/17/13 7:32 PM, [hidden email] wrote:

Nick asks Owen:
  

So, Owen, you meet a beautiful woman at a cocktail party.  She seems 
intelligent, not a person to be fobbed off, but has no experience 
with either Maths or Computer Science.  She looks deep into your 
eyes, and asks "And what, Mr. Densmore, is the halting problem?"  You 
find yourself torn between two impulses.  One is to use the language 
that would give you credibility in the world of your mentors and 
colleagues.  But you realize that that language is going to be of 
absolutely no use to her, however ever much it might make you feel

authoritative to use it.  She expects an answer.

Yet you hesitate.  What language do you use?

You would start, would you not, with the idea of a "problem."  A 
problem is some sort of difficulty that needs to be surmounted.  
There is a goal and something that thwarts that goal.  What are these

elements in the halting

PROBLEM?    And why is HALTING a problem?

Nick, Owen may well disagree, but from my point of view you've already 
staked a dubious claim, by assuming (defensably) that "problem" in the 
MathEng phrase "Halting Problem" can and should be understood to be 
the same word as "problem" in your dialect of English.  But this is, I

think, a false assumption.  Now, at least, whatever the case was when the
"Halting Problem"

got its original name (in MathGerman, I think), the meaning that 
"Halting Problem" conveys in MathEng is the same (or nearly the same) 
as that conveyed by "Halting Question".  "Problem" is there for 
historical reasons, just as, in geometric topology, a certain question 
of considerable interest and importance (which has been answered for 
fewer decades than has the "Halting Problem") is still called--even in

MathEng!--"the Hauptvermutung".  The framing in terms of "a goal" and
"something that thwarts" is delusive.  There is, rather, "a question"

and--if you must be florid--a "quest for an answer".  Note, "*an* 
answer".  Of course, at an extreme level (I can't decide whether it's 
the highest or the lowest: I *hate* "level" talk precisely for this 
kind of reason) there is *the* answer ("no").  But that isn't, in 
itself, very interesting (any more: of course it was before it was 
known to be "the" answer).  *How* you get to "no" is interesting, and 
there are (by now) many different "hows" (for the "Halting Question", the

Hauptvermutung, Poincare's Conjecture, and so forth and so on), each of
which is *an* answer (as are many of the "not hows").

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[Douglas Roberts-2]

+2

On Wed, Apr 17, 2013 at 11:40 PM, Steve Smith <[hidden email]> wrote:

A spontaneous Haiku inspired by a pithy friend's analysis of our discussion:

The Halting Problem
Pretty Girl; Cocktail Party
Knowing when to stop

I don't think the beautiful woman would accept "go read the Wikipedia
article" as am answer.  

N

-----Original Message-----
From: Friam [[hidden email]] On Behalf Of Joseph Spinden
Sent: Wednesday, April 17, 2013 8:21 PM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Isomorphism between computation and philosophy

Owen is right that there are N! ways to map a set of N objects 1-1, onto
another set of N objects. The first object can go to 1 of N objects, the
next to 1 of N-1, etc. That's pretty standard.

As to the Halting Problem, Why not start with the first few lines of the
Wikipedia article ? That is simple and easy to understand.

Joe




On 4/17/13 7:32 PM, [hidden email] wrote:

Nick asks Owen:
  

So, Owen, you meet a beautiful woman at a cocktail party.  She seems 
intelligent, not a person to be fobbed off, but has no experience 
with either Maths or Computer Science.  She looks deep into your 
eyes, and asks "And what, Mr. Densmore, is the halting problem?"  You 
find yourself torn between two impulses.  One is to use the language 
that would give you credibility in the world of your mentors and 
colleagues.  But you realize that that language is going to be of 
absolutely no use to her, however ever much it might make you feel

authoritative to use it.  She expects an answer.

Yet you hesitate.  What language do you use?

You would start, would you not, with the idea of a "problem."  A 
problem is some sort of difficulty that needs to be surmounted.  
There is a goal and something that thwarts that goal.  What are these

elements in the halting

PROBLEM?    And why is HALTING a problem?

Nick, Owen may well disagree, but from my point of view you've already 
staked a dubious claim, by assuming (defensably) that "problem" in the 
MathEng phrase "Halting Problem" can and should be understood to be 
the same word as "problem" in your dialect of English.  But this is, I

think, a false assumption.  Now, at least, whatever the case was when the
"Halting Problem"

got its original name (in MathGerman, I think), the meaning that 
"Halting Problem" conveys in MathEng is the same (or nearly the same) 
as that conveyed by "Halting Question".  "Problem" is there for 
historical reasons, just as, in geometric topology, a certain question 
of considerable interest and importance (which has been answered for 
fewer decades than has the "Halting Problem") is still called--even in

MathEng!--"the Hauptvermutung".  The framing in terms of "a goal" and
"something that thwarts" is delusive.  There is, rather, "a question"

and--if you must be florid--a "quest for an answer".  Note, "*an* 
answer".  Of course, at an extreme level (I can't decide whether it's 
the highest or the lowest: I *hate* "level" talk precisely for this 
kind of reason) there is *the* answer ("no").  But that isn't, in 
itself, very interesting (any more: of course it was before it was 
known to be "the" answer).  *How* you get to "no" is interesting, and 
there are (by now) many different "hows" (for the "Halting Question", the

Hauptvermutung, Poincare's Conjecture, and so forth and so on), each of
which is *an* answer (as are many of the "not hows").

============================================================
FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe 
at St. John's College to unsubscribe 
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Meets Fridays 9a-11:30 at cafe at St. John's College
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--

Doug Roberts
[hidden email]

http://parrot-farm.net/Second-Cousins

505-455-7333 - Office
505-672-8213 - Mobile

============================================================
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Meets Fridays 9a-11:30 at cafe at St. John's College
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