Re: [FRIAM] Isomorphism between computation and philosophy

[Douglas Roberts]

+2

On Wed, Apr 17, 2013 at 11:40 PM, Steve Smith sasm...@swcp.com wrote:

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

 *The Halting Problem**
 **Pretty Girl; Cocktail Party**
 **Knowing when to sto**p*


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

 N

 -Original Message-
 From: Friam [mailto:friam-boun...@redfish.com friam-boun...@redfish.com] 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, lrudo...@meganet.net 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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 at St. John's College to unsubscribe 
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-- 
*Doug Roberts
d...@parrot-farm.net*
*http://parrot-farm.net/Second-Cousins*http://parrot-farm.net/Second-Cousins
* http://parrot-farm.net/Second-Cousins
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Re: [FRIAM] Isomorphism between computation and philosophy

[Joseph Spinden]

Another result (the unsolvability of the halting problem) may be 
interpreted as implying the impossibility of constructing a program for 
determining whether or not an arbitrary given program is free of 'loops'.


Martin Davis, Computability and Unsolvability, 1958


--Joe




On 4/17/13 10:43 PM, Russ Abbott wrote:
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 http://ssrn.com/abstract=1977688/

/  Google voice: 747-/999-5105
  Google+: plus.google.com/114865618166480775623/ 
https://plus.google.com/114865618166480775623/
/  vita: /sites.google.com/site/russabbott/ 
http://sites.google.com/site/russabbott/

CS Wiki http://cs.calstatela.edu/wiki/ and the courses I teach
/_/


On Wed, Apr 17, 2013 at 9:30 PM, Joseph Spinden j...@qri.us 
mailto:j...@qri.us 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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--

Sunlight is the best disinfectant.

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


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Re: [FRIAM] Isomorphism between computation and philosophy

[Joseph Spinden]

I was suggesting the contributors to this chat could go read the 
Wikipedia article to give them something useful to say to the beautiful 
woman about the halting problem. (Not to be taken to imply that none of 
the readers if this are beautiful women, only some of the readers..)


Joe



On 4/17/13 11:04 PM, Nicholas Thompson wrote:

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

N

-Original Message-
From: Friam [mailto:friam-boun...@redfish.com] 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, lrudo...@meganet.net 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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--

Sunlight is the best disinfectant.

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



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Re: [FRIAM] Isomorphism between computation and philosophy

[Marcus G. Daniels]

On 4/18/13 7:57 AM, Joseph Spinden wrote:
Another result (the unsolvability of the halting problem) may be 
interpreted as implying the impossibility of constructing a program 
for determining whether or not an arbitrary given program is free of 
'loops'.


Well, compilers can't reason about all forms of loops, but note how the 
compiler realized that the accumulating
sum didn't require iteration.   (In the assembly it collapses to a 
movl $30,%eax.)  Flat maps and reductions with simple 
transformation/aggregation functions can be determined to exit.


$ cat collapse.c
int
main ()
{
   unsigned i;
   unsigned sum = 0;

   for (i = 0; i  10; i++) sum += 3;
   return sum;
}
$ gcc -S -O3 collapse.c
$ cat collapse.s
.filecollapse.c
.section.text.startup,ax,@progbits
.p2align 4,,15
.globlmain
.typemain, @function
main:
.LFB0:
.cfi_startproc
movl$30, %eax
ret
.cfi_endproc
.LFE0:
.sizemain, .-main
.identGCC: (GNU) 4.7.2 20121109 (Red Hat 4.7.2-8)
.section.note.GNU-stack,,@progbits

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Re: [FRIAM] Isomorphism between computation and philosophy

[glen]

Joseph Spinden wrote at 04/17/2013 07:21 PM:
 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.

Well, saying there are N! maps is different from saying there are N!
ways to map.  While there may only be N! potential maps, there are many
many more ways to demonstrate or realize those maps.

The difference lies in the methods, something that is often left out of
math presentations.  This is one area where I think computation helps
boost the intuitionist or constructivist sense of math, as well as the
incremental/iterative conception of sets.

-- 
== glen e. p. ropella
Or at least come to a show



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Re: [FRIAM] Isomorphism between computation and philosophy

[Nicholas Thompson]

And I am trying to get folks here to confront the problem of putting in
their own words things they think are obvious for other folks for whom these
things are not obvious. 

-Original Message-
From: Friam [mailto:friam-boun...@redfish.com] On Behalf Of Joseph Spinden
Sent: Thursday, April 18, 2013 8:06 AM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Isomorphism between computation and philosophy

I was suggesting the contributors to this chat could go read the Wikipedia
article to give them something useful to say to the beautiful woman about
the halting problem. (Not to be taken to imply that none of the readers if
this are beautiful women, only some of the readers..)

Joe



On 4/17/13 11:04 PM, Nicholas Thompson wrote:
 I don't think the beautiful woman would accept go read the Wikipedia 
 article as am answer.

 N

 -Original Message-
 From: Friam [mailto:friam-boun...@redfish.com] 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, lrudo...@meganet.net 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 
 http://redfish.com/mailman/listinfo/friam_redfish.com




-- 

Sunlight is the best disinfectant.

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



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Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe
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Re: [FRIAM] Isomorphism between computation and philosophy

[Nicholas Thompson]

Owen wrote -

 

At times your discourse tends to be as specialized as any techy's, I think.

 

Nick replies --  Well, then call me on it!  There is nothing that drives me
wilder - in myself or others  than pretentious bafflegab.  The problem
becomes more difficult when one is talking to a highly various audience like
FRIAM.  But any time you - owen -- don't understand something that I am
saying, demand clarification and  I will do my best to find a common
language by which to express myself.  Another fair question you might ask,
is, Ytf should I care?  This sort of intensive communication may involve
going off line, lest I drive the list nuts, because, as you all know, I am
relentless about this sort of thing.  And of course, there is always the
possibility of discovering that the thing one was trying to say was not
clear in the first place.  Those are ugly but educative moments. 

 

There is an important distinction between communicating and mouthing off and
I am determined to honor it.  

 

Nick 

 

From: Friam [mailto:friam-boun...@redfish.com] On Behalf Of Owen Densmore
Sent: Thursday, April 18, 2013 10:49 AM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Isomorphism between computation and philosophy

 

On Thu, Apr 18, 2013 at 10:08 AM, Nicholas Thompson
nickthomp...@earthlink.net wrote:

And I am trying to get folks here to confront the problem of putting in
their own words things they think are obvious for other folks for whom these
things are not obvious.

 

This reminds me of Einsteins famous quote: Everything should be made as
simple as possible, but not simpler.

 

And, forgive me Nick, you have the same problem too, right?  At times your
discourse tends to be as specialized as any techy's, I think.

 

   -- Owen


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Re: [FRIAM] Isomorphism between computation and philosophy

[Owen Densmore]

On Tue, Apr 16, 2013 at 11:10 AM, Nicholas Thompson 
nickthomp...@earthlink.net wrote:

 snip


 Translatability has been a crucial issue in modern analytical philosophy.
 Translation implies that you and I have the same piano and that, while we
 may call the keys by different names, there is a key on your piano that
 corresponds to every key on mine.  But philosophers have more or less given
 up on translateablity, I think.


That seems like a useful concept.  Why did they give up on it?


 Still, I am tempted to start with the assumption that there is a word, or
 small group of words, in my vocabulary that corresponds to your word,
 undecideable.   Can you guess at what those words might be?


Interestingly enough, the stanford encyclopedia of philosophy has
decidability all over the place, so maybe (un)decidable is a reasonably
good philosophical concept already.  They use it in basically the same way
computing folk do.  But then Frank tells me that the philosophy departments
are using highly specialized mathematics.

Unfortunately, if an area of philosophy is undecidable, it has a halting
problem .. i.e. no sense discussing it any further!  :)


 Nick


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Re: [FRIAM] Isomorphism between computation and philosophy

[Nicholas Thompson]

Owen, 

 

I wish we could drag Frank into this conversation, because he is the only
person we know who stands firmly in both worlds.  

 

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 

 

From: Friam [mailto:friam-boun...@redfish.com] On Behalf Of Owen Densmore
Sent: Wednesday, April 17, 2013 9:09 AM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Isomorphism between computation and philosophy

 

On Tue, Apr 16, 2013 at 11:10 AM, Nicholas Thompson
nickthomp...@earthlink.net wrote:

snip

 

Translatability has been a crucial issue in modern analytical philosophy.
Translation implies that you and I have the same piano and that, while we
may call the keys by different names, there is a key on your piano that
corresponds to every key on mine.  But philosophers have more or less given
up on translateablity, I think. 

 

That seems like a useful concept.  Why did they give up on it?

Still, I am tempted to start with the assumption that there is a word, or
small group of words, in my vocabulary that corresponds to your word,
undecideable.   Can you guess at what those words might be? 

 

Interestingly enough, the stanford encyclopedia of philosophy has
decidability all over the place, so maybe (un)decidable is a reasonably good
philosophical concept already.  They use it in basically the same way
computing folk do.  But then Frank tells me that the philosophy departments
are using highly specialized mathematics.

 

Unfortunately, if an area of philosophy is undecidable, it has a halting
problem .. i.e. no sense discussing it any further!  :)

Nick


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Re: [FRIAM] Isomorphism between computation and philosophy

[Barry MacKichan]

On a tangential note, I was told in 1961 of a project to prove (on a computer) 
the theorems in Principia Mathematica. It went well through the first section, 
and then they hit the brick wall when they encountered statements like there 
exists and for every. When dealing with infinite sets, these can be hard. 


On Apr 16, 2013, at 9:12 PM, Owen Densmore o...@backspaces.net wrote:

 On Tue, Apr 16, 2013 at 6:10 PM, Nicholas Thompson 
 nickthomp...@earthlink.net wrote:
 I don’t think I said that math couldn’t be mapped onto things.  I only said 
 that such mappings are not essential to math and, further, that when such 
 mappings occur, the door is opened for confusion that is opened in any 
 semantic relation. 
 
 
 Could you show me such a thing?  I demonstrated that computers for example do 
 not suffer from this confusion.  Computing is a branch of mathematics that 
 looked inward and found it could provide real world mappings from 5-tuples 
 defining a computing engine (the FSA) to real computers.  Every time you step 
 on the in/out mat for a door at a store, you are implementing a FSA.  (Note I 
 bow to your door above :)
 
 Call it Applied Mathematics if you'd prefer.  But it certainly has a very 
 high reality coefficient.  There is no ambiguity and there is semantic 
 binding.
 
 (Note: I realize that ABM does deal with this, and we've dealt with it with 
 your MOTH model, but it is not necessarily general.)
 
 Let me simplify.  Is there a realm in which philosophy can exhibit a bug? And 
 more specifically  by simply running the philosophy engine?
 
 I believe this may be possible, but I'm not sure.  Maybe we'd have to create 
 a new field.  Certainly Turing, Church, von Neumann, Shannon, and many other 
 in the computational world did.  They stood on a brink, vital for going 
 forward.  Von Neumann had to argue for a computer to be admitted to the 
 Institute for Advanced Study in Princeton .. it was considered just a 
 machine.  Church and Turing showed that to be nonsense.  Can we do the same 
 for philosophy?
 
 NB: I'm not referring to computational complexity in which we deal with the 
 running time issues of an algorithm, but to the semantics of computation 
 itself.  We really do have a strong grasp on what computation is and we do 
 not quibble about meaning .. at least without heading immediately to 
 axiomatic solutions.
 
-- Owen
 
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Re: [FRIAM] Isomorphism between computation and philosophy

[glen]

Well said, Steve!  Mostly, what's kept me from commenting on the
isomorphism thread is ... well, the word isomorphism. [grin]

I spend _all_ my time... seriously ... arguing against the Grand
Unified Model (GUM).  For some reason, everyone seems so certain,
convicted, that there exists the One True Truth (and they usually think
Cthulu whispers in their ear about it).  Even those of us who admit that
it may not exist, claim it's a Worthy Goal and we should all tow the line.

I do not believe there exists a single isomorphism between computing and
philosophy.  If _any_ exist at all, there are many. [*] And if I believe
that, then I have to consider the efficacy of my spending time figuring
out a single isomorphism.  Yes, to show that one exists would be
interesting.  But all it would achieve is continual and annoying
[mis]citation of that one demonstration, giving ammo to the GUM crowd.

Not only is that not in my ideological best interests, it's not even in
my practical best interests.  It would be a result analogous to Goedel's
Incompleteness Theorems, where everyone from postmodern Eddington
typewriters to serious people would jump in and muddy the waters.
Practically, all I want to do is find ways to get my work done and
finding/demonstrating a single isomorphism won't help me do that ...

UNLESS we could demonstrate there are _multiple_ isomorphisms.  Or
better yet, draw up a rough characterization of the distribution of all
morphisms, including multiple iso-s.

In the interests of problem solving, perhaps we could break down the
task and, rather than searching for an isomorphism, we could just lay
out one example morphism in some practical detail?  I think we could
mine the IACAP crowd for examples: http://www.iacap.org/  I had a lot of
fun at the one meeting of theirs I managed to attend.

[*] I'll leave the parentheticals alone and avoid trying to explain how
there can be multiple isomorphisms between any 2 particular things. ;-)

Steve Smith wrote at 04/17/2013 12:18 PM:
 The stew is getting nicely rich here.   While I wanted to ignore Owen's
 original question regarding isomorphisms between computing
 (language/concepts/models?) and philosophy as being naive, I know it
 isn't totally and the somewhat parallel conversation that has been
 continuing that started with circular reasoning has brought this out
 nicely (IMO).



-- 
== glen e. p. ropella
And I know I ain't digging on your lies



FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
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Re: [FRIAM] Isomorphism between computation and philosophy

[Owen Densmore]

Er,, of course there are many, right?  With two finite sets of size N there
are N! 1-1, onto unique mappings, I believe.

But relax.  I went off the deep end with examples of things like
decidability.

All I'm curious about is whether or not it is possible to somehow make
philosophy, or simply intellectual conversation a bit more concrete.
 Wouldn't you think computation and algorithms could express at least an
interesting subset of intellectual discourse?

I remember being driven to watching Michael Sandel's great What Is The
Right Thing To Do Harvard Justice lectures by Nick's vocabulary and style.
 I found it a thrilling series and am glad its now part of a MOOC.  I'll
probably watch more of similar a nature.  Exciting!

Unfortunately, some of the philosophic conversations I hear are poorly
motivated and lack MS's great skill at driving people towards wanting
understanding.

   -- Owen


On Wed, Apr 17, 2013 at 2:09 PM, glen g...@ropella.name wrote:


 Well said, Steve!  Mostly, what's kept me from commenting on the
 isomorphism thread is ... well, the word isomorphism. [grin]

 I spend _all_ my time... seriously ... arguing against the Grand
 Unified Model (GUM).  For some reason, everyone seems so certain,
 convicted, that there exists the One True Truth (and they usually think
 Cthulu whispers in their ear about it).  Even those of us who admit that
 it may not exist, claim it's a Worthy Goal and we should all tow the line.

 I do not believe there exists a single isomorphism between computing and
 philosophy.  If _any_ exist at all, there are many. [*] And if I believe
 that, then I have to consider the efficacy of my spending time figuring
 out a single isomorphism.  Yes, to show that one exists would be
 interesting.  But all it would achieve is continual and annoying
 [mis]citation of that one demonstration, giving ammo to the GUM crowd.

 Not only is that not in my ideological best interests, it's not even in
 my practical best interests.  It would be a result analogous to Goedel's
 Incompleteness Theorems, where everyone from postmodern Eddington
 typewriters to serious people would jump in and muddy the waters.
 Practically, all I want to do is find ways to get my work done and
 finding/demonstrating a single isomorphism won't help me do that ...

 UNLESS we could demonstrate there are _multiple_ isomorphisms.  Or
 better yet, draw up a rough characterization of the distribution of all
 morphisms, including multiple iso-s.

 In the interests of problem solving, perhaps we could break down the
 task and, rather than searching for an isomorphism, we could just lay
 out one example morphism in some practical detail?  I think we could
 mine the IACAP crowd for examples: http://www.iacap.org/  I had a lot of
 fun at the one meeting of theirs I managed to attend.

 [*] I'll leave the parentheticals alone and avoid trying to explain how
 there can be multiple isomorphisms between any 2 particular things. ;-)

 Steve Smith wrote at 04/17/2013 12:18 PM:
  The stew is getting nicely rich here.   While I wanted to ignore Owen's
  original question regarding isomorphisms between computing
  (language/concepts/models?) and philosophy as being naive, I know it
  isn't totally and the somewhat parallel conversation that has been
  continuing that started with circular reasoning has brought this out
  nicely (IMO).



 --
 == glen e. p. ropella
 And I know I ain't digging on your lies


 
 FRIAM Applied Complexity Group listserv
 Meets Fridays 9a-11:30 at cafe at St. John's College
 to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com


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Re: [FRIAM] Isomorphism between computation and philosophy

[Owen Densmore]

On Wed, Apr 17, 2013 at 10:27 AM, Nicholas Thompson 
nickthomp...@earthlink.net 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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Re: [FRIAM] Isomorphism between computation and philosophy

[glen]

Owen Densmore wrote at 04/17/2013 01:53 PM:
 Er,, of course there are many, right?  With two finite sets of size N there
 are N! 1-1, onto unique mappings, I believe.

Heh, there are way more than that!  What I meant was that there exist
more than 1 morphism that results in the same snapshot of the mapping.  E.g.

{0, 1, 2} - {ooga, booga, slooga} via

   0 - ooga
   1 - booga
   2 - slooga

But there can be any number of meanings inside the -.  All that's
being represented by the morphism is that one goes to the other.  The
going is opaque, c.f. the other part of our conversation.  (I think
it's funny that we use this word morphism so often without remembering
the to morph part of it.)

 All I'm curious about is whether or not it is possible to somehow make
 philosophy, or simply intellectual conversation a bit more concrete.

Hm. I'm actually on Nick's side of that discussion.  Philosophy is
_more_ concrete than computing.  Even when it's abstract, it relies on
the thoughts and actions of people (or animals or inanimate objects).
Computing is, like mathematics, more symbolic.

Perhaps the word you're looking for is _definite_?

  Wouldn't you think computation and algorithms could express at least an
 interesting subset of intellectual discourse?

Not really.  Like I was trying to address in the other thread on
iteration vs. recursion, discourse (including intellectual) is messy,
which is whence it derives its usefulness.  The same can be said of
things like jury trials.  The interestingness doesn't lie in the
abstract law as defined for the average (or median or whatever) human.
 The interestingness lies in the special cases.  Although much
philosophy pretends that it's trying to find some normative basis for
thought, what I see, mostly, is humans trying to be human ... aka messy.

 Unfortunately, some of the philosophic conversations I hear are poorly
 motivated and lack MS's great skill at driving people towards wanting
 understanding.

Sturgeon's quote comes to mind: Ninety percent of science fiction is
crud, but that's because ninety percent of everything is crud.

-- 
== glen e. p. ropella
In this world where I am king



FRIAM Applied Complexity Group listserv
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Re: [FRIAM] Isomorphism between computation and philosophy

[Nicholas 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:friam-boun...@redfish.com] 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
nickthomp...@earthlink.net 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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Re: [FRIAM] Isomorphism between computation and philosophy

[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 [mailto:friam-boun...@redfish.com] *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 
nickthomp...@earthlink.net mailto:nickthomp...@earthlink.net 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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Re: [FRIAM] Isomorphism between computation and philosophy

[Owen Densmore]

Its starting to get lonely here!


On Wed, Apr 17, 2013 at 4:44 PM, Steve Smith sasm...@swcp.com 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 [mailto:friam-boun...@redfish.comfriam-boun...@redfish.com]
 *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 
 nickthomp...@earthlink.net 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


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

Re: [FRIAM] Isomorphism between computation and philosophy

[Douglas Roberts]

Yes, there hasn't been an abstruse message in at least 10 whole minutes...
On Apr 17, 2013 6:37 PM, Owen Densmore o...@backspaces.net wrote:

 Its starting to get lonely here!


 On Wed, Apr 17, 2013 at 4:44 PM, Steve Smith sasm...@swcp.com 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 [mailto:friam-boun...@redfish.comfriam-boun...@redfish.com]
 *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 
 nickthomp...@earthlink.net 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

Re: [FRIAM] Isomorphism between computation and philosophy

[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

   /ab?stro?os/
   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

/?b?t(y)o?os/
Adjective

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


Synonyms
dull - blunt - dense - slow-witted


   ^1 ab·stract

/adjective/ \ab-?strakt, ?ab-?\
1
/a/ *:* disassociated 
http://www.merriam-webster.com/dictionary/disassociate from any 
specific instance an /abstract/ entity
/b/ *:* difficult to understand *:* abstruse 
http://www.merriam-webster.com/dictionary/abstruse /abstract/ problems
/c/ *:* insufficiently factual *:* formal 
http://www.merriam-webster.com/dictionary/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 
http://www.merriam-webster.com/dictionary/theoretical /abstract/ 
science
/b/ *:* impersonal 
http://www.merriam-webster.com/dictionary/impersonal, detached 
http://www.merriam-webster.com/dictionary/detached the /abstract/ 
compassion of a surgeon --- /Time/

4
*:* having only intrinsic 
http://www.merriam-webster.com/dictionary/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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Re: [FRIAM] Isomorphism between computation and philosophy

[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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Re: [FRIAM] Isomorphism between computation and philosophy

[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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Meets Fridays 9a-11:30 at cafe at St. John's College
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Re: [FRIAM] Isomorphism between computation and philosophy

[Nicholas 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:friam-boun...@redfish.com] 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 http://www.merriam-webster.com/dictionary/disassociate  
from any specific instance an abstract entity 

b : difficult to understand : abstruse 
http://www.merriam-webster.com/dictionary/abstruse  abstract problems 

c : insufficiently factual : formal 
http://www.merriam-webster.com/dictionary/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 
http://www.merriam-webster.com/dictionary/theoretical  abstract science 

b : impersonal http://www.merriam-webster.com/dictionary/impersonal , 
detached http://www.merriam-webster.com/dictionary/detached  the abstract 
compassion of a surgeon — Time 

4

Re: [FRIAM] Isomorphism between computation and philosophy

[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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Re: [FRIAM] Isomorphism between computation and philosophy

[Joseph 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



FRIAM Applied Complexity Group listserv
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--

Sunlight is the best disinfectant.

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


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Re: [FRIAM] Isomorphism between computation and philosophy

[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 http://cs.calstatela.edu/wiki/ and the courses I teach
*_*


On Wed, Apr 17, 2013 at 9:30 PM, Joseph Spinden j...@qri.us 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


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

 Sunlight is the best disinfectant.

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


 
 FRIAM Applied Complexity Group listserv
 Meets Fridays 9a-11:30 at cafe at St. John's College
 to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com


FRIAM Applied Complexity Group listserv
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Re: [FRIAM] Isomorphism between computation and philosophy

[Nicholas Thompson]

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

N

-Original Message-
From: Friam [mailto:friam-boun...@redfish.com] 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, lrudo...@meganet.net 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 
 http://redfish.com/mailman/listinfo/friam_redfish.com



-- 

Sunlight is the best disinfectant.

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



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Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe
http://redfish.com/mailman/listinfo/friam_redfish.com



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Re: [FRIAM] Isomorphism between computation and philosophy

[Nicholas Thompson]

Doug, 

 

Gracious. 

 

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

 

Nick 

 

From: Friam [mailto:friam-boun...@redfish.com] 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 nickthomp...@earthlink.net 
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:friam-boun...@redfish.com] 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

Re: [FRIAM] Isomorphism between computation and philosophy

[Nicholas Thompson]

Owen, 

 

Ask Dede to provide a translation, would you? 

 

Nick 

 

From: Friam [mailto:friam-boun...@redfish.com] 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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Re: [FRIAM] Isomorphism between computation and philosophy

[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 sto//p/



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

N

-Original Message-
From: Friam [mailto:friam-boun...@redfish.com] 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, lrudo...@meganet.net 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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Re: [FRIAM] Isomorphism between computation and philosophy

[Douglass Carmichael]

Philosophy is very broad and includes many things like ethics and anesthetics. 
A good test case would be not logic, but poetry.

Blessings, 
Doug
http://dougcarmichael.com
http://gardenworldpolitics.com

On Apr 16, 2013, at 9:25 AM, Owen Densmore o...@backspaces.net wrote:

 On Sat, Apr 13, 2013 at 2:05 PM, Nicholas Thompson 
 nickthomp...@earthlink.net wrote:
 Can anybody translate this for a non programmer person?
 
 Nick's question brings up a project I'd love to see: an attempt at an 
 isomorphism between computation and philosophy. (An isomorphism is a 1 to 1, 
 onto mapping from one to another, or a bijection.)
 
 For example, in computer science, decidability is a very concrete idea.  
 Yet when I hear philosophical terms, and dutifully look them up in the 
 stanford dictionary of philosophy, I find myself suspicious of circularity.
 
 Decidability is interesting because it proves not all computations can 
 successfully expressed as programs.  It does this by using two infinities 
 of different cardinality (countable vs continuum).
 
 Does philosophy deal in constructs that nicely map onto computing, possibly 
 programming languages?  
 
 I'm not specifically concerned with decidability, only use that as an example 
 because it shows the struggle in computer science for modeling computation 
 itself, from Finite Automata, Context Free Languages, and to Turing Machines 
 (or equivalently lambda calculus).
 
 I don't dislike philosophy, mainly thanks to conversations with Nick.  And I 
 do know that axiomatic approaches to philosophy have been popular.  
 
 So is there a possible isomorphism?
 
-- Owen
 
 FRIAM Applied Complexity Group listserv
 Meets Fridays 9a-11:30 at cafe at St. John's College
 to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com

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Re: [FRIAM] Isomorphism between computation and philosophy

[lrudolph]

Nick:

 It's probably a good thing that I retired before I got wise. 

I think I hear the sound of the Arrow of Causality twanging in the bullseye.


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Re: [FRIAM] Isomorphism between computation and philosophy

[Barry MacKichan]

 Curious. Isn't the proof of Godel's theorem a special case of this?

As I understand it, the proof is this:

Consider the statement: This theorem is not provable. If it is false, the 
theorem is provable. Since 'provable' implies true, this is a contradiction. 
Therefore the theorem is true, which means it is true and not provable.

The genius in Godel's method is that he created an isomorphism between the 
domain of the previous paragraph, and arithmetic, and the isomorphism preserves 
truth and provability. Thus the above theorem corresponds to a statement in 
arithmetic that is true and not provable. What is this statement, you might 
ask. Well, evidently it is far to complex to compute or write down (although it 
would be interesting to see if more powerful computers or quantum computers 
would change this.)

Anyway, that true but non-provable theorem shows that number theory (aka 
arithmetic) is incomplete -- that's the definition of incomplete in this 
context.

--Barry


On Apr 16, 2013, at 10:25 AM, Owen Densmore o...@backspaces.net wrote:

 On Sat, Apr 13, 2013 at 2:05 PM, Nicholas Thompson 
 nickthomp...@earthlink.net wrote:
 Can anybody translate this for a non programmer person?
 
 Nick's question brings up a project I'd love to see: an attempt at an 
 isomorphism between computation and philosophy. (An isomorphism is a 1 to 1, 
 onto mapping from one to another, or a bijection.)
 
 For example, in computer science, decidability is a very concrete idea.  
 Yet when I hear philosophical terms, and dutifully look them up in the 
 stanford dictionary of philosophy, I find myself suspicious of circularity.
 
 Decidability is interesting because it proves not all computations can 
 successfully expressed as programs.  It does this by using two infinities 
 of different cardinality (countable vs continuum).
 
 Does philosophy deal in constructs that nicely map onto computing, possibly 
 programming languages?  
 
 I'm not specifically concerned with decidability, only use that as an example 
 because it shows the struggle in computer science for modeling computation 
 itself, from Finite Automata, Context Free Languages, and to Turing Machines 
 (or equivalently lambda calculus).
 
 I don't dislike philosophy, mainly thanks to conversations with Nick.  And I 
 do know that axiomatic approaches to philosophy have been popular.  
 
 So is there a possible isomorphism?
 
-- Owen
 
 FRIAM Applied Complexity Group listserv
 Meets Fridays 9a-11:30 at cafe at St. John's College
 to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com


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Re: [FRIAM] Isomorphism between computation and philosophy

[Nicholas Thompson]

Owen, 

 

One of the reasons that mathematical language can be so precise is that it
isn't ABOUT anything, right?   The minute one adds semantics .. the minute
one applies mathematics to anything . all the problems of ordinary language
begin to manifest themselves, don't they?  

 

Nick 

 

From: Friam [mailto:friam-boun...@redfish.com] On Behalf Of Owen Densmore
Sent: Tuesday, April 16, 2013 3:50 PM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Isomorphism between computation and philosophy

 

One has to be careful with nearly all the impossibility theorems: Arrow's
voting, the speed of light, Godel, Heisenberg, decidability, NoFreeLunch,
... and so on.

 

To tell the truth, Godel .. it seems to me .. says to the practicing
mathematician that the axioms have to be very carefully chosen.  Its sorta
like linear algebra: a system can be over constrained .. thus contain
impossibilities, or under constrained thus have multiple solutions.

 

But all I'm hoping for is any attempt to make the words Nick and others have
be as precise as a computer language.  If this is the case, then we can use
the lovely computation hierarchy from FSA, to CFL to Turing/Church.  But
then, most mathematicians know none of this structure either.  Sigh. 

 

I wish philosophy had the same constraints where bugs could be found.  On
the other hand, ambiguity can be a huge plus, as any spoken language shows.

 

   -- Owen

 

On Tue, Apr 16, 2013 at 3:39 PM, Barry MacKichan
barry.mackic...@mackichan.com wrote:

 Curious. Isn't the proof of Godel's theorem a special case of this?

 

As I understand it, the proof is this:

 

Consider the statement: This theorem is not provable. If it is false, the
theorem is provable. Since 'provable' implies true, this is a contradiction.
Therefore the theorem is true, which means it is true and not provable.

 

The genius in Godel's method is that he created an isomorphism between the
domain of the previous paragraph, and arithmetic, and the isomorphism
preserves truth and provability. Thus the above theorem corresponds to a
statement in arithmetic that is true and not provable. What is this
statement, you might ask. Well, evidently it is far to complex to compute or
write down (although it would be interesting to see if more powerful
computers or quantum computers would change this.)

 

Anyway, that true but non-provable theorem shows that number theory (aka
arithmetic) is incomplete -- that's the definition of incomplete in this
context.

 

--Barry

 

 

On Apr 16, 2013, at 10:25 AM, Owen Densmore o...@backspaces.net wrote:

 

On Sat, Apr 13, 2013 at 2:05 PM, Nicholas Thompson
nickthomp...@earthlink.net wrote:

Can anybody translate this for a non programmer person?

 

 

Nick's question brings up a project I'd love to see: an attempt at an
isomorphism between computation and philosophy. (An isomorphism is a 1 to 1,
onto mapping from one to another, or a bijection.)

 

For example, in computer science, decidability is a very concrete idea.
Yet when I hear philosophical terms, and dutifully look them up in the
stanford dictionary of philosophy, I find myself suspicious of circularity.

 

Decidability is interesting because it proves not all computations can
successfully expressed as programs.  It does this by using two infinities
of different cardinality (countable vs continuum).

 

Does philosophy deal in constructs that nicely map onto computing, possibly
programming languages?  

 

I'm not specifically concerned with decidability, only use that as an
example because it shows the struggle in computer science for modeling
computation itself, from Finite Automata, Context Free Languages, and to
Turing Machines (or equivalently lambda calculus).

 

I don't dislike philosophy, mainly thanks to conversations with Nick.  And I
do know that axiomatic approaches to philosophy have been popular.  

 

So is there a possible isomorphism?

 

   -- Owen


FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com

 



FRIAM Applied Complexity Group listserv
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Re: [FRIAM] Isomorphism between computation and philosophy

[Barry MacKichan]

I should correct myself. The mapping is not necessarily an isomorphism.

--Barry

On Apr 16, 2013, at 3:39 PM, Barry MacKichan barry.mackic...@mackichan.com 
wrote:

  Curious. Isn't the proof of Godel's theorem a special case of this?
 
 As I understand it, the proof is this:
 
 Consider the statement: This theorem is not provable. If it is false, the 
 theorem is provable. Since 'provable' implies true, this is a contradiction. 
 Therefore the theorem is true, which means it is true and not provable.
 
 The genius in Godel's method is that he created an isomorphism between the 
 domain of the previous paragraph, and arithmetic, and the isomorphism 
 preserves truth and provability. Thus the above theorem corresponds to a 
 statement in arithmetic that is true and not provable. What is this 
 statement, you might ask. Well, evidently it is far to complex to compute or 
 write down (although it would be interesting to see if more powerful 
 computers or quantum computers would change this.)
 
 Anyway, that true but non-provable theorem shows that number theory (aka 
 arithmetic) is incomplete -- that's the definition of incomplete in this 
 context.
 
 --Barry
 
 
 On Apr 16, 2013, at 10:25 AM, Owen Densmore o...@backspaces.net wrote:
 
 On Sat, Apr 13, 2013 at 2:05 PM, Nicholas Thompson 
 nickthomp...@earthlink.net wrote:
 Can anybody translate this for a non programmer person?
 
 Nick's question brings up a project I'd love to see: an attempt at an 
 isomorphism between computation and philosophy. (An isomorphism is a 1 to 1, 
 onto mapping from one to another, or a bijection.)
 
 For example, in computer science, decidability is a very concrete idea.  
 Yet when I hear philosophical terms, and dutifully look them up in the 
 stanford dictionary of philosophy, I find myself suspicious of circularity.
 
 Decidability is interesting because it proves not all computations can 
 successfully expressed as programs.  It does this by using two infinities 
 of different cardinality (countable vs continuum).
 
 Does philosophy deal in constructs that nicely map onto computing, possibly 
 programming languages?  
 
 I'm not specifically concerned with decidability, only use that as an 
 example because it shows the struggle in computer science for modeling 
 computation itself, from Finite Automata, Context Free Languages, and to 
 Turing Machines (or equivalently lambda calculus).
 
 I don't dislike philosophy, mainly thanks to conversations with Nick.  And I 
 do know that axiomatic approaches to philosophy have been popular.  
 
 So is there a possible isomorphism?
 
-- Owen
 
 FRIAM Applied Complexity Group listserv
 Meets Fridays 9a-11:30 at cafe at St. John's College
 to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com
 
 
 FRIAM Applied Complexity Group listserv
 Meets Fridays 9a-11:30 at cafe at St. John's College
 to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com


FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
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Re: [FRIAM] Isomorphism between computation and philosophy

[Barry MacKichan]

Actually, Godel said that the axioms [have to]-[can't] be very carefully 
chosen. The theorem says that any mathematical system that contains the 
integers cannot be both complete and self-consistent. It is unique in the list 
of 'impossibility' theorems in that it has a mathematical proof. The others in 
your list are all contingent on some form of observation. 

It's sort of like saying all sets of equations have to be overdetermined or 
underdetermined or both. Except its really hits at the roots of the 
mathematical enterprise. They say its announcement hit Bertrand Russell really 
hard.

-Barry



On Apr 16, 2013, at 3:49 PM, Owen Densmore o...@backspaces.net wrote:

 One has to be careful with nearly all the impossibility theorems: Arrow's 
 voting, the speed of light, Godel, Heisenberg, decidability, NoFreeLunch, ... 
 and so on.
 
 To tell the truth, Godel .. it seems to me .. says to the practicing 
 mathematician that the axioms have to be very carefully chosen.


FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com

Re: [FRIAM] Isomorphism between computation and philosophy

[Owen Densmore]

No, I think we can make a mapping from mathematical concepts to things.
 Integers, for example, can be made to map onto any discrete semantic
concept.  At the simplest level, we can nicely define an atom.  We can make
a countable mapping onto them (note: countable can be finite).  There's
lots of atoms, but mathematics comfortably manages.

Similarly, computers are concrete things.  We have a fine mathematics for
computational devices, a hierarchy of devices: Finite State Automata,
Context Free Languages, and Turring Machines.  They all have equivalent,
somewhat more powerful, devices like the Non Deterministic Finite Automata
set which can all be reduced to FSAs.

This is pretty concrete: we can with extreme confidence discuss what these
machines can do and classify programs that can or cannot be implemented by
them.

More properly, we can discuss inputs to devices as alphabets over symbol
sets.  We can define the accepting states of the device,
thus equivalently the substrings of the alphabets that are accepted by the
device.  We can also define our devices quite clearly.

For example, the FSA is a 5-tuple (Q, S, d, q0, F) where Q are a finite set
of states, S is the finite set of symbols, the alphabet, d is a delta
function which given a symbol and a state yields a next state, q0 is the
start state, and F is a subset of Q which accept the input string.  The
set of strings that end up at F are called the language of the device.

These are both abstract and concrete.  But given an alphabet and a FSA
5-tuple, I can prove things about the inputs and outputs.  In particular,
given an alphabet of {0,1}  I can prove that there is no FSA that can
accept the language of n-0s followed by exactly n-1's where n can be
arbitrary but finite.  In other words, I can prove a FSA cannot count.

Briefly, we can also show that the higher device level, the Turing Machine,
has similar limits.  The proof is fairly simple, proving that the languages
of a TM is the continuum while the number of inputs is countable infinite.
 Thus there are members of the languages that a TM could accept that are
outside of the countable computations of a TM.

So there's stuff we can't compute.

The joy of the symbolic/axiomatic approach is not that it is free of
semantics, but that we can devise ways to map math to real things.

I doubt you would say this does not mean anything.

   -- Owen


On Tue, Apr 16, 2013 at 3:53 PM, Nicholas Thompson 
nickthomp...@earthlink.net wrote:

 Owen, 

 ** **

 One of the reasons that mathematical language can be so precise is that it
 isn’t ABOUT anything, right?   The minute one adds semantics …. the minute
 one applies mathematics to anything … all the problems of ordinary language
 begin to manifest themselves, don’t they?  

 ** **

 Nick 

 ** **

 *From:* Friam [mailto:friam-boun...@redfish.com] *On Behalf Of *Owen
 Densmore
 *Sent:* Tuesday, April 16, 2013 3:50 PM
 *To:* The Friday Morning Applied Complexity Coffee Group
 *Subject:* Re: [FRIAM] Isomorphism between computation and philosophy

 ** **

 One has to be careful with nearly all the impossibility theorems:
 Arrow's voting, the speed of light, Godel, Heisenberg, decidability,
 NoFreeLunch, ... and so on.

 ** **

 To tell the truth, Godel .. it seems to me .. says to the
 practicing mathematician that the axioms have to be very carefully chosen.
  Its sorta like linear algebra: a system can be over constrained .. thus
 contain impossibilities, or under constrained thus have multiple solutions.
 

 ** **

 But all I'm hoping for is any attempt to make the words Nick and others
 have be as precise as a computer language.  If this is the case, then we
 can use the lovely computation hierarchy from FSA, to CFL to Turing/Church.
  But then, most mathematicians know none of this structure either.  Sigh.
 

 ** **

 I wish philosophy had the same constraints where bugs could be found.  On
 the other hand, ambiguity can be a huge plus, as any spoken language shows.
 

 ** **

-- Owen

 ** **

 On Tue, Apr 16, 2013 at 3:39 PM, Barry MacKichan 
 barry.mackic...@mackichan.com wrote:

  Curious. Isn't the proof of Godel's theorem a special case of this?

 ** **

 As I understand it, the proof is this:

 ** **

 Consider the statement: This theorem is not provable. If it is false, the
 theorem is provable. Since 'provable' implies true, this is a
 contradiction. Therefore the theorem is true, which means it is true and
 not provable.

 ** **

 The genius in Godel's method is that he created an isomorphism between the
 domain of the previous paragraph, and arithmetic, and the isomorphism
 preserves truth and provability. Thus the above theorem corresponds to a
 statement in arithmetic that is true and not provable. What is this
 statement, you might ask. Well, evidently it is far to complex to compute
 or write down (although it would be interesting to see if more powerful
 computers or quantum

Re: [FRIAM] Isomorphism between computation and philosophy

[Owen Densmore]

Arrow's impossibility theorem is provable, basically social choice is
impossible given several fairly sound requirements: 3 or more things to
choose between and transitivity of choice.

C isn't a proof, agreed.  Although its acceptance is well seen by
observation.  And physics hasn't theorems in the same sense as mathematics.
 Bad choice on my part.

Heisenberg is directly provable from Schrödinger's equation

Decidability is provable by showing the acceptance set of TMs is countably
infinite while the possible languages is continuously infinite (integers vs
reals)

NoFreeLunch simply shows that random methods (GAs etc) have inputs that are
no better managed than uniformly random guessing.  But fortunately, the
pessimal inputs are rare and NFL did us the favor of finding where to look
for tractable stochastic algorithms.  Whew!


On Tue, Apr 16, 2013 at 4:13 PM, Barry MacKichan 
barry.mackic...@mackichan.com wrote:

 Actually, Godel said that the axioms [have to]-[can't] be very
 carefully chosen. The theorem says that any mathematical system that
 contains the integers cannot be both complete and self-consistent. It is
 unique in the list of 'impossibility' theorems in that it has a
 mathematical proof. The others in your list are all contingent on some form
 of observation.

 It's sort of like saying all sets of equations have to be overdetermined
 or underdetermined or both. Except its really hits at the roots of the
 mathematical enterprise. They say its announcement hit Bertrand Russell
 really hard.

 -Barry



 On Apr 16, 2013, at 3:49 PM, Owen Densmore o...@backspaces.net wrote:

 One has to be careful with nearly all the impossibility theorems:
 Arrow's voting, the speed of light, Godel, Heisenberg, decidability,
 NoFreeLunch, ... and so on.

 To tell the truth, Godel .. it seems to me .. says to the
 practicing mathematician that the axioms have to be very carefully chosen.



 
 FRIAM Applied Complexity Group listserv
 Meets Fridays 9a-11:30 at cafe at St. John's College
 to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com


FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
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Re: [FRIAM] Isomorphism between computation and philosophy

[Nicholas Thompson]

I don't think I said that math couldn't be mapped onto things.  I only said
that such mappings are not essential to math and, further, that when such
mappings occur, the door is opened for confusion that is opened in any
semantic relation.  

 

Barry will have to handle the rest of what you said.  

 

N

 

From: Friam [mailto:friam-boun...@redfish.com] On Behalf Of Owen Densmore
Sent: Tuesday, April 16, 2013 5:12 PM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Isomorphism between computation and philosophy

 

No, I think we can make a mapping from mathematical concepts to things.
Integers, for example, can be made to map onto any discrete semantic
concept.  At the simplest level, we can nicely define an atom.  We can make
a countable mapping onto them (note: countable can be finite).  There's lots
of atoms, but mathematics comfortably manages.

 

Similarly, computers are concrete things.  We have a fine mathematics for
computational devices, a hierarchy of devices: Finite State Automata,
Context Free Languages, and Turring Machines.  They all have equivalent,
somewhat more powerful, devices like the Non Deterministic Finite Automata
set which can all be reduced to FSAs.

 

This is pretty concrete: we can with extreme confidence discuss what these
machines can do and classify programs that can or cannot be implemented by
them.  

 

More properly, we can discuss inputs to devices as alphabets over symbol
sets.  We can define the accepting states of the device, thus equivalently
the substrings of the alphabets that are accepted by the device.  We can
also define our devices quite clearly.  

 

For example, the FSA is a 5-tuple (Q, S, d, q0, F) where Q are a finite set
of states, S is the finite set of symbols, the alphabet, d is a delta
function which given a symbol and a state yields a next state, q0 is the
start state, and F is a subset of Q which accept the input string.  The
set of strings that end up at F are called the language of the device.

 

These are both abstract and concrete.  But given an alphabet and a FSA
5-tuple, I can prove things about the inputs and outputs.  In particular,
given an alphabet of {0,1}  I can prove that there is no FSA that can accept
the language of n-0s followed by exactly n-1's where n can be arbitrary but
finite.  In other words, I can prove a FSA cannot count.

 

Briefly, we can also show that the higher device level, the Turing Machine,
has similar limits.  The proof is fairly simple, proving that the languages
of a TM is the continuum while the number of inputs is countable infinite.
Thus there are members of the languages that a TM could accept that are
outside of the countable computations of a TM.

 

So there's stuff we can't compute.

 

The joy of the symbolic/axiomatic approach is not that it is free of
semantics, but that we can devise ways to map math to real things.

 

I doubt you would say this does not mean anything.

 

   -- Owen

 

On Tue, Apr 16, 2013 at 3:53 PM, Nicholas Thompson
nickthomp...@earthlink.net wrote:

Owen, 

 

One of the reasons that mathematical language can be so precise is that it
isn't ABOUT anything, right?   The minute one adds semantics .. the minute
one applies mathematics to anything . all the problems of ordinary language
begin to manifest themselves, don't they?  

 

Nick 

 

From: Friam [mailto:friam-boun...@redfish.com] On Behalf Of Owen Densmore
Sent: Tuesday, April 16, 2013 3:50 PM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Isomorphism between computation and philosophy

 

One has to be careful with nearly all the impossibility theorems: Arrow's
voting, the speed of light, Godel, Heisenberg, decidability, NoFreeLunch,
... and so on.

 

To tell the truth, Godel .. it seems to me .. says to the practicing
mathematician that the axioms have to be very carefully chosen.  Its sorta
like linear algebra: a system can be over constrained .. thus contain
impossibilities, or under constrained thus have multiple solutions.

 

But all I'm hoping for is any attempt to make the words Nick and others have
be as precise as a computer language.  If this is the case, then we can use
the lovely computation hierarchy from FSA, to CFL to Turing/Church.  But
then, most mathematicians know none of this structure either.  Sigh. 

 

I wish philosophy had the same constraints where bugs could be found.  On
the other hand, ambiguity can be a huge plus, as any spoken language shows.

 

   -- Owen

 

On Tue, Apr 16, 2013 at 3:39 PM, Barry MacKichan
barry.mackic...@mackichan.com wrote:

 Curious. Isn't the proof of Godel's theorem a special case of this?

 

As I understand it, the proof is this:

 

Consider the statement: This theorem is not provable. If it is false, the
theorem is provable. Since 'provable' implies true, this is a contradiction.
Therefore the theorem is true, which means it is true and not provable.

 

The genius in Godel's method is that he

Re: [FRIAM] Isomorphism between computation and philosophy

[Owen Densmore]

On Tue, Apr 16, 2013 at 6:10 PM, Nicholas Thompson 
nickthomp...@earthlink.net wrote:

 I don’t think I said that math couldn’t be mapped onto things.  I only
 said that such mappings are not essential to math and, further, that when
 such mappings occur, the door is opened for confusion that is opened in any
 semantic relation.


Could you show me such a thing?  I demonstrated that computers for example
do not suffer from this confusion.  Computing is a branch of mathematics
that looked inward and found it could provide real world mappings from
5-tuples defining a computing engine (the FSA) to real computers.  Every
time you step on the in/out mat for a door at a store, you are implementing
a FSA.  (Note I bow to your door above :)

Call it Applied Mathematics if you'd prefer.  But it certainly has a very
high reality coefficient.  There is no ambiguity and there is semantic
binding.

(Note: I realize that ABM does deal with this, and we've dealt with it with
your MOTH model, but it is not necessarily general.)

Let me simplify.  Is there a realm in which philosophy can exhibit a bug?
And more specifically  by simply running the philosophy engine?

I believe this may be possible, but I'm not sure.  Maybe we'd have to
create a new field.  Certainly Turing, Church, von Neumann, Shannon, and
many other in the computational world did.  They stood on a brink, vital
for going forward.  Von Neumann had to argue for a computer to be admitted
to the Institute for Advanced Study in Princeton .. it was considered just
a machine.  Church and Turing showed that to be nonsense.  Can we do the
same for philosophy?

NB: I'm not referring to computational complexity in which we deal with
the running time issues of an algorithm, but to the semantics of
computation itself.  We really do have a strong grasp on what computation
is and we do not quibble about meaning .. at least without heading
immediately to axiomatic solutions.

   -- Owen

FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
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Re: [FRIAM] Isomorphism between computation and philosophy

[Nicholas Thompson]

Oh, gosh, owen.  I am trying to think of somebody to forward this on to.
Dennett would be the obvious guy, but he only rarely answers my mail.  

 

Eric, can you think of somebody in your acquaintance who would be willing to
comment on reference always introduces ambiguity, or whether there is an in
principle distinction between applied math and philosophical argument.  

 

Nick 

 

 

From: Friam [mailto:friam-boun...@redfish.com] On Behalf Of Owen Densmore
Sent: Tuesday, April 16, 2013 9:12 PM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Isomorphism between computation and philosophy

 

On Tue, Apr 16, 2013 at 6:10 PM, Nicholas Thompson
nickthomp...@earthlink.net wrote:

I don't think I said that math couldn't be mapped onto things.  I only said
that such mappings are not essential to math and, further, that when such
mappings occur, the door is opened for confusion that is opened in any
semantic relation. 

 

Could you show me such a thing?  I demonstrated that computers for example
do not suffer from this confusion.  Computing is a branch of mathematics
that looked inward and found it could provide real world mappings from
5-tuples defining a computing engine (the FSA) to real computers.  Every
time you step on the in/out mat for a door at a store, you are implementing
a FSA.  (Note I bow to your door above :)

 

Call it Applied Mathematics if you'd prefer.  But it certainly has a very
high reality coefficient.  There is no ambiguity and there is semantic
binding.

 

(Note: I realize that ABM does deal with this, and we've dealt with it with
your MOTH model, but it is not necessarily general.)

 

Let me simplify.  Is there a realm in which philosophy can exhibit a bug?
And more specifically  by simply running the philosophy engine?

 

I believe this may be possible, but I'm not sure.  Maybe we'd have to create
a new field.  Certainly Turing, Church, von Neumann, Shannon, and many other
in the computational world did.  They stood on a brink, vital for going
forward.  Von Neumann had to argue for a computer to be admitted to the
Institute for Advanced Study in Princeton .. it was considered just a
machine.  Church and Turing showed that to be nonsense.  Can we do the same
for philosophy?

 

NB: I'm not referring to computational complexity in which we deal with
the running time issues of an algorithm, but to the semantics of computation
itself.  We really do have a strong grasp on what computation is and we do
not quibble about meaning .. at least without heading immediately to
axiomatic solutions.

 

   -- Owen


FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
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Re: [FRIAM] Isomorphism between computation and philosophy

[Steve Smith]

Doug -

Thanks for weighing in here... as an aside, I skimmed Garden World and 
found it compelling... I hope others here will take the time!


On the thread topic, it would be rather convenient in many ways if 
there were such an isomorphism as Owen seeks (postulates), but I find it 
to reflect a fundamental misunderstanding of what is knowledge?


Other parts of the thread, relating to the question of semantics begins 
to address this.  Intuitively, it is like thinking that one can make 
visual art without awareness of the negative space and the context it 
exists in, or of writing poetry (or really anything but the driest of 
prose as well?) without appreciating that it much of what is being said 
is between the lines.


I have a friend who wrote a program to parse and analyze the logic in 
Aquinas' /Summa Theologica/ and claimed to find numerous (but not 
outrageous) simple errors in his logic.   That isn't in any way close to 
imagining that one could translate such a text into symbolic logic and 
determine anything (else) more significant from it than internal 
consistency and/or consistency with some external axiomatic system.


- Steve
Philosophy is very broad and includes many things like ethics and 
anesthetics. A good test case would be not logic, but poetry.


Blessings,
Doug
http://dougcarmichael.com
http://gardenworldpolitics.com

On Apr 16, 2013, at 9:25 AM, Owen Densmore o...@backspaces.net 
mailto:o...@backspaces.net wrote:


On Sat, Apr 13, 2013 at 2:05 PM, Nicholas Thompson 
nickthomp...@earthlink.net mailto:nickthomp...@earthlink.net wrote:


Can anybody translate this for a non programmer person?


Nick's question brings up a project I'd love to see: an attempt at an 
isomorphism between computation and philosophy. (An isomorphism is a 
1 to 1, onto mapping from one to another, or a bijection.)


For example, in computer science, decidability is a very concrete 
idea.  Yet when I hear philosophical terms, and dutifully look them 
up in the stanford dictionary of philosophy, I find myself suspicious 
of circularity.


Decidability is interesting because it proves not all computations 
can successfully expressed as programs.  It does this by using two 
infinities of different cardinality (countable vs continuum).


Does philosophy deal in constructs that nicely map onto computing, 
possibly programming languages?


I'm not specifically concerned with decidability, only use that as an 
example because it shows the struggle in computer science for 
modeling computation itself, from Finite Automata, Context Free 
Languages, and to Turing Machines (or equivalently lambda calculus).


I don't dislike philosophy, mainly thanks to conversations with Nick. 
 And I do know that axiomatic approaches to philosophy have been 
popular.


So is there a possible isomorphism?

 -- Owen

FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com




FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com



FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com