Analytic philosophy - Wikipedia, the free encyclopedia

[Marcus G. Daniels]

>
>
>     That's funny, because I have always thought of programs as extremely
>     refined arguments.
>
>
> No.  They are algorithms.  And can be built upon.
> Can be built upon in theory, but in practice they are with high
> probability thrown away and rebuilt from scratch.
>
> Because they are complex linguistic objects which, like philosophers'
> arguments, are often harder to figure out than to do over from first
> principles.

Except when they are discarded just because the readers lack the skills
and patience to figure things out.   In my experience, that's more often
than not.    In particular, I think programs that endure and grow are
unlike algorithms and philosophers' arguments or mathematical
derivations.   A point is reached where programs become more complex
than any one (even exceptional) person can really understand
completely.  In the form of support code, bug fixes, and algorithmic
refinements, they embed requirements and novel use cases that were not
evident to designers.   Efforts should be made to study, simplify and
extend these programs.  Meanwhile, efforts should also be made to
identify and eliminate abstractions that just confuse people.

Whether algorithms or arguments it doesn't really matter.  It depends on
the programming language.    Logic programming languages are more like
Wittgenstein and less like recipes.

Marcus

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[Nick Thompson]

Marcus,

Could you say a bit more about this?  It really interested me.

MD =====>Whether algorithms or arguments it doesn't really matter.  It
depends on
> the programming language.    Logic programming languages are more like
> Wittgenstein and less like recipes.<=====MD

For reference, here is definition of algorithm pulled off the web:

DICT===>a set of rules for solving a problem in a finite number of steps,
as for finding the greatest common divisor.<===DICT

Is this the sense in which you guys are using the term.  How, then, could a
mathematical proof NOT be a form of algorithm?  I guess I should confess
that my model for a mathematical proof is Euclid.  

Thanks.  

Nicholas S. Thompson
Emeritus Professor of Psychology and Ethology,
Clark University ([hidden email])
http://home.earthlink.net/~nickthompson/naturaldesigns/

> [Original Message]
> From: Marcus G. Daniels <[hidden email]>
> To: The Friday Morning Applied Complexity Coffee Group <[hidden email]>
> Date: 7/13/2009 8:09:23 AM
> Subject: Re: [FRIAM] Philosophy, Mathematics, and Science
>
> >
> >
> >     That's funny, because I have always thought of programs as extremely
> >     refined arguments.
> >
> >
> > No.  They are algorithms.  And can be built upon.
> > Can be built upon in theory, but in practice they are with high
> > probability thrown away and rebuilt from scratch.
> >
> > Because they are complex linguistic objects which, like philosophers'
> > arguments, are often harder to figure out than to do over from first
> > principles.
> Except when they are discarded just because the readers lack the skills
> and patience to figure things out.   In my experience, that's more often
> than not.    In particular, I think programs that endure and grow are
> unlike algorithms and philosophers' arguments or mathematical
> derivations.   A point is reached where programs become more complex
> than any one (even exceptional) person can really understand
> completely.  In the form of support code, bug fixes, and algorithmic
> refinements, they embed requirements and novel use cases that were not
> evident to designers.   Efforts should be made to study, simplify and
> extend these programs.  Meanwhile, efforts should also be made to
> identify and eliminate abstractions that just confuse people.
>
> Whether algorithms or arguments it doesn't really matter.  It depends on
> the programming language.    Logic programming languages are more like
> Wittgenstein and less like recipes.
>
> Marcus
>
> ============================================================
> FRIAM Applied Complexity Group listserv
> Meets Fridays 9a-11:30 at cafe at St. John's College
> lectures, archives, unsubscribe, maps at http://www.friam.org

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

Can be built upon in theory, but in practice they are with high probability thrown away and rebuilt from scratch.

Because they are complex linguistic objects which, like philosophers' arguments, are often harder to figure out than to do over from first principles.

-- rec --

Well said Roger.   I think we have all had the experience of choosing to:

1. rederive an equation
   
2. redesign an algorithm
3. rewrite a piece of code
4. rehash a philosophical argument

when there was already a perfectly good (maybe) equation/algorithm/program/argument layed at our feet.

For me, this is a mixture of:

1. Pride
2. Trust
3. Understanding

This was a major challenge to code re-use at one time...  about the only published Algorithms many of us trusted were those published in Knuth!  And even then, we had to rewrite the actual code in whatever context we were operating in, and were generally proud to do it.  But we couldn't help  noodling on the algorithms, trying to think of a new, more elegant, more general, or more efficient way of solving the problem at hand.

Often, by the time one has worked through an algorithm forward to backward, backward to forward, one might as well have designed it.  The existing algorithm provides a few important things, however:

1. Existence proof.  We *know* there is at least one algorithm that achieves the desired result.
2. Hints.  Even if we don't understand an algorithm on first blush, we usually get a sense of it's arc.
3. Reference.  When we think we've got ours right, we can go back and test it against the original.  In fact, we probably now understand the original as well as our own and if we have any humility may throw *ours* away and use the one made available to us in the first place

For proceduralists, C's concise method of creating complex objects (data structures and pointers to them) made it possible to build good/interesting/understandable libraries from tried and true algorithms.  With the introduction of ObjC/C++/Java and a huge new influx of programmers (the Internet may not have *created* new programmers, but it connected them to the rest of us in a way that was unprecedented), the number of libraries went up dramatically.   With the Open Source movement, these accreted and evolved into some pretty interesting, trusted and useful libraries.   Today, only a hardcore group like this crowd here are likely to rederive/redesign/rewrite/rehash.

It is a dying art, which I am nostalgic about.  It is one of the entertainments I find on this list.   I liken what happens here (sometimes) to the WPA era when the very few remaining craftsmen in many building arts were found and encouraged/supported to building some last monuments to an old era of craftsmanship that no longer exists. 

Maybe huge systems built of handcut C (assembly?)  code, implementing custom algorithms are not as obviously beautiful or elegant as some of the grand WPA era National Park resorts (Mt Hood, Grand Canyon Lodge, Yosemite, ...)  but there is a similarity in the values and the processes.

I respect Nick and others here for wanting to apply the same principles to the context of our various constructions as well.  I don't always (even try to) follow the arguments but I appreciate the desire to (re)hash the hash, even if I don't always want to participate in it.

- Steve

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

What is the relationship between pseudo-code and code. 

 

Are actual codes  "realizations" of pseudocodes? 

 

Nick

 

Nicholas S. Thompson

Emeritus Professor of Psychology and Ethology,

Clark University ([hidden email])

http://home.earthlink.net/~nickthompson/naturaldesigns/

 

 

 

 

----- Original Message -----

From: [hidden email]

To: [hidden email]

Sent: 7/13/2009 9:16:11 AM

Subject: Re: [FRIAM] Philosophy, Mathematics, and Science

Can be built upon in theory, but in practice they are with high probability thrown away and rebuilt from scratch.

Because they are complex linguistic objects which, like philosophers' arguments, are often harder to figure out than to do over from first principles.

-- rec --

Well said Roger.   I think we have all had the experience of choosing to:

1. rederive an equation
   
2. redesign an algorithm
3. rewrite a piece of code
4. rehash a philosophical argument

when there was already a perfectly good (maybe) equation/algorithm/program/argument layed at our feet.

For me, this is a mixture of:

1. Pride
2. Trust
3. Understanding

This was a major challenge to code re-use at one time...  about the only published Algorithms many of us trusted were those published in Knuth!  And even then, we had to rewrite the actual code in whatever context we were operating in, and were generally proud to do it.  But we couldn't help  noodling on the algorithms, trying to think of a new, more elegant, more general, or more efficient way of solving the problem at hand.

Often, by the time one has worked through an algorithm forward to backward, backward to forward, one might as well have designed it.  The existing algorithm provides a few important things, however:

1. Existence proof.  We *know* there is at least one algorithm that achieves the desired result.
2. Hints.  Even if we don't understand an algorithm on first blush, we usually get a sense of it's arc.
3. Reference.  When we think we've got ours right, we can go back and test it against the original.  In fact, we probably now understand the original as well as our own and if we have any humility may throw *ours* away and use the one made available to us in the first place

For proceduralists, C's concise method of creating complex objects (data structures and pointers to them) made it possible to build good/interesting/understandable libraries from tried and true algorithms.  With the introduction of ObjC/C++/Java and a huge new influx of programmers (the Internet may not have *created* new programmers, but it connected them to the rest of us in a way that was unprecedented), the number of libraries went up dramatically.   With the Open Source movement, these accreted and evolved into some pretty interesting, trusted and useful libraries.   Today, only a hardcore group like this crowd here are likely to rederive/redesign/rewrite/rehash.

It is a dying art, which I am nostalgic about.  It is one of the entertainments I find on this list.   I liken what happens here (sometimes) to the WPA era when the very few remaining craftsmen in many building arts were found and encouraged/supported to building some last monuments to an old era of craftsmanship that no longer exists. 

Maybe huge systems built of handcut C (assembly?)  code, implementing custom algorithms are not as obviously beautiful or elegant as some of the grand WPA era National Park resorts (Mt Hood, Grand Canyon Lodge, Yosemite, ...)  but there is a similarity in the values and the processes.

I respect Nick and others here for wanting to apply the same principles to the context of our various constructions as well.  I don't always (even try to) follow the arguments but I appreciate the desire to (re)hash the hash, even if I don't always want to participate in it.

- Steve

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

[Douglas Roberts-2]

Nick,

I like you.  I really do.  But you sometimes make me just want to scream.

If you want to know what pseudocode is, go to the web and find out!  Here's a starting point for you:

http://en.wikipedia.org/wiki/Pseudocode

Then, if you still *really* want to know what psuedocode is, write some.  And then pick a language and turn it into actual code.  Then you will know what psuedocode is.

--Doug

On Mon, Jul 13, 2009 at 9:28 AM, Nicholas Thompson <[hidden email]> wrote:

What is the relationship between pseudo-code and code. 

 

Are actual codes  "realizations" of pseudocodes? 

 

Nick

 

Nicholas S. Thompson

Emeritus Professor of Psychology and Ethology,

Clark University ([hidden email])

http://home.earthlink.net/~nickthompson/naturaldesigns/

 

 

 

 

----- Original Message -----

From: [hidden email]

To: [hidden email]

Sent: 7/13/2009 9:16:11 AM

Subject: Re: [FRIAM] Philosophy, Mathematics, and Science

Can be built upon in theory, but in practice they are with high probability thrown away and rebuilt from scratch.

Because they are complex linguistic objects which, like philosophers' arguments, are often harder to figure out than to do over from first principles.

-- rec --

Well said Roger.   I think we have all had the experience of choosing to:

1. rederive an equation
   
2. redesign an algorithm
3. rewrite a piece of code
4. rehash a philosophical argument

when there was already a perfectly good (maybe) equation/algorithm/program/argument layed at our feet.

For me, this is a mixture of:

1. Pride
2. Trust
3. Understanding

This was a major challenge to code re-use at one time...  about the only published Algorithms many of us trusted were those published in Knuth!  And even then, we had to rewrite the actual code in whatever context we were operating in, and were generally proud to do it.  But we couldn't help  noodling on the algorithms, trying to think of a new, more elegant, more general, or more efficient way of solving the problem at hand.

Often, by the time one has worked through an algorithm forward to backward, backward to forward, one might as well have designed it.  The existing algorithm provides a few important things, however:

1. Existence proof.  We *know* there is at least one algorithm that achieves the desired result.
2. Hints.  Even if we don't understand an algorithm on first blush, we usually get a sense of it's arc.
3. Reference.  When we think we've got ours right, we can go back and test it against the original.  In fact, we probably now understand the original as well as our own and if we have any humility may throw *ours* away and use the one made available to us in the first place

For proceduralists, C's concise method of creating complex objects (data structures and pointers to them) made it possible to build good/interesting/understandable libraries from tried and true algorithms.  With the introduction of ObjC/C++/Java and a huge new influx of programmers (the Internet may not have *created* new programmers, but it connected them to the rest of us in a way that was unprecedented), the number of libraries went up dramatically.   With the Open Source movement, these accreted and evolved into some pretty interesting, trusted and useful libraries.   Today, only a hardcore group like this crowd here are likely to rederive/redesign/rewrite/rehash.

It is a dying art, which I am nostalgic about.  It is one of the entertainments I find on this list.   I liken what happens here (sometimes) to the WPA era when the very few remaining craftsmen in many building arts were found and encouraged/supported to building some last monuments to an old era of craftsmanship that no longer exists. 

Maybe huge systems built of handcut C (assembly?)  code, implementing custom algorithms are not as obviously beautiful or elegant as some of the grand WPA era National Park resorts (Mt Hood, Grand Canyon Lodge, Yosemite, ...)  but there is a similarity in the values and the processes.

I respect Nick and others here for wanting to apply the same principles to the context of our various constructions as well.  I don't always (even try to) follow the arguments but I appreciate the desire to (re)hash the hash, even if I don't always want to participate in it.

- Steve

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

[Marcus G. Daniels]

Nicholas Thompson wrote:
> How, then, could a mathematical proof NOT be a form of algorithm?  
To me, the word algorithm suggests an emphasis on clarity and economy of
effort, whereas a proof emphasizes the fact a conclusion in correct, and
why.   But a problem can be cast either way.

In logic programming (Prolog):

factorial(1,1).
factorial(N,F):-
  N > 1,
  NN is N - 1,
  factorial(NN,FF),
  F is N * FF.

The point here is that given an expression like factorial(5,F) the
Prolog interpreter _solves_ for F, or, given a query like
factorial(5,100) will answer "no" (it's actually 120).  The execution
trace of such a program is the proof.. (Although it would often being
intolerably long.)

In a typical imperative programming (Java), the code just moves forward
step by step until n <= 1.
The execution path is defined, instead of being deduced (or more
generally in constraint logic programming systems.. found).

    public static long factorial( int n )
    {
        if( n <= 1 )  
            return 1;
        else
            return n * factorial( n - 1 );
    }




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

Nick and I had an off-list discussion that may speak to some of the  
recent posts.

Begin forwarded message:

> From: Owen Densmore <[hidden email]>
> Date: July 13, 2009 10:38:08 AM MDT
> To: [hidden email]
> Cc: John Kennison <[hidden email]>, Owen Densmore <[hidden email]
> >
> Subject: Re: Cauchy sequence - Wikipedia, the free encyclopedia
>
> On Jul 12, 2009, at 10:30 PM, Nicholas Thompson wrote:
>> http://en.wikipedia.org/wiki/Cauchy_sequence
>>
>> Sorry.  I dont know why this came up.  I see that it's some nice  
>> mathematics,but I dont see its relevance.
>
> The sub-theme was "Bridging the Gap" .. in this case between  
> philosophy and mathematics.  In the above case, the CS is a  
> delightful example of bridging the gap between the CONtinuous and  
> disCRETE in Don Knuth's Concrete Mathematics .. a topic we've  
> discussed in the past.
>
> Or possibly more formally, applying the epsilon/delta idea to both  
> the continuous and discrete as discussed in the book we read last  
> summer, Journey Through Genius.
>
>> While I have your attention, is a mathematical proof a kind of  
>> algorithm?
>
> Although they share a step-wise approach, I think not.
>
>> Do you agree, that mathematical proofs are very rigorous arguments?
>
> Not arguments as in a way to resolve disagreements.  But arguments  
> as a line of thought.  Certainly rigorous.
>
>> Is a symbolic logical proof an example of mathematics?
>
> I'd say yes, but others might be more comfortable separating math  
> and logic.
>
>> Or of Philosophy?
>
> See the word comfortable above.
>
>> Was Bertrand Russel a mathematician or a philosopher?
>
> Both.  Wittgenstein studied under him, so the Both applies to him  
> too, as it does for Kant and others.
>
>> Since I think of mathematics as a kind of tremendously rigorous  
>> extension of the art of argument from philosophy, I would expect  
>> that most of these questions are bad questions.
>
> No, but you do feel argument is a sort of sport, not unlike  
> wrestling!  This is really more key that you might imagine.  
> Mathematicians and scientists, even though they do have  
> disagreements, generally argue/discuss means to an end (solving a  
> problem, creating a proof) rather than argue right and wrong.
>
>> You can take this on the list, if you like.  I think your answers  
>> would be interesting to list members, but I am leery of being  
>> called on the carpet for starting another philosophical discussion.
>>
>> I have cc'ed my mathematician friend John Kennison to see what he  
>> might say.
>>
>> Nicholas S. Thompson
>> Emeritus Professor of Psychology and Ethology,
>> Clark University ([hidden email])
>> http://home.earthlink.net/~nickthompson/naturaldesigns/
>
>

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FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

[Victoria Hughes]

Anybody interested in pseudo-code for creating? 

Give me two-three weeks (other projects midstream) I'll write some; this could be fun.

Thanks for the link.

Tory

ps re note below- give it time. 

I note my challenge on the two VSI books (Math, Wittgenstein) was ignored.    -Owen

On Jul 13, 2009, at 9:49 AM, Douglas Roberts wrote:

Nick,

I like you.  I really do.  But you sometimes make me just want to scream.

If you want to know what pseudocode is, go to the web and find out!  Here's a starting point for you:

http://en.wikipedia.org/wiki/Pseudocode

Then, if you still *really* want to know what psuedocode is, write some.  And then pick a language and turn it into actual code.  Then you will know what psuedocode is.

--Doug

On Mon, Jul 13, 2009 at 9:28 AM, Nicholas Thompson <[hidden email]> wrote:

What is the relationship between pseudo-code and code. 

 

Are actual codes  "realizations" of pseudocodes? 

 

Nick

 

Nicholas S. Thompson

Emeritus Professor of Psychology and Ethology,

Clark University ([hidden email])

http://home.earthlink.net/~nickthompson/naturaldesigns/

 

 

 

 

----- Original Message -----

From: [hidden email]

To: [hidden email]

Sent: 7/13/2009 9:16:11 AM

Subject: Re: [FRIAM] Philosophy, Mathematics, and Science

Can be built upon in theory, but in practice they are with high probability thrown away and rebuilt from scratch.

Because they are complex linguistic objects which, like philosophers' arguments, are often harder to figure out than to do over from first principles.

-- rec --

Well said Roger.   I think we have all had the experience of choosing to:

1. rederive an equation
   
2. redesign an algorithm
3. rewrite a piece of code
4. rehash a philosophical argument

when there was already a perfectly good (maybe) equation/algorithm/program/argument layed at our feet.

For me, this is a mixture of:

1. Pride
2. Trust
3. Understanding

This was a major challenge to code re-use at one time...  about the only published Algorithms many of us trusted were those published in Knuth!  And even then, we had to rewrite the actual code in whatever context we were operating in, and were generally proud to do it.  But we couldn't help  noodling on the algorithms, trying to think of a new, more elegant, more general, or more efficient way of solving the problem at hand.

Often, by the time one has worked through an algorithm forward to backward, backward to forward, one might as well have designed it.  The existing algorithm provides a few important things, however:

1. Existence proof.  We *know* there is at least one algorithm that achieves the desired result.
2. Hints.  Even if we don't understand an algorithm on first blush, we usually get a sense of it's arc.
3. Reference.  When we think we've got ours right, we can go back and test it against the original.  In fact, we probably now understand the original as well as our own and if we have any humility may throw *ours* away and use the one made available to us in the first place

For proceduralists, C's concise method of creating complex objects (data structures and pointers to them) made it possible to build good/interesting/understandable libraries from tried and true algorithms.  With the introduction of ObjC/C++/Java and a huge new influx of programmers (the Internet may not have *created* new programmers, but it connected them to the rest of us in a way that was unprecedented), the number of libraries went up dramatically.   With the Open Source movement, these accreted and evolved into some pretty interesting, trusted and useful libraries.   Today, only a hardcore group like this crowd here are likely to rederive/redesign/rewrite/rehash.

It is a dying art, which I am nostalgic about.  It is one of the entertainments I find on this list.   I liken what happens here (sometimes) to the WPA era when the very few remaining craftsmen in many building arts were found and encouraged/supported to building some last monuments to an old era of craftsmanship that no longer exists. 

Maybe huge systems built of handcut C (assembly?)  code, implementing custom algorithms are not as obviously beautiful or elegant as some of the grand WPA era National Park resorts (Mt Hood, Grand Canyon Lodge, Yosemite, ...)  but there is a similarity in the values and the processes.

I respect Nick and others here for wanting to apply the same principles to the context of our various constructions as well.  I don't always (even try to) follow the arguments but I appreciate the desire to (re)hash the hash, even if I don't always want to participate in it.

- Steve

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

[Steve Smith]

Nicholas Thompson wrote:

How, then, could a mathematical proof NOT be a form of algorithm?

Marcus G. Daniels wrote:

To me, the word algorithm suggests an emphasis on clarity and economy of effort, whereas a proof emphasizes the fact a conclusion in correct, and why.   But a problem can be cast either way.

In some abstract sense, I think you can say a mathematical proof is always an algorithm. (reading the Nick/Owen offline, I see I might be in perfect opposition to Owen on this?)

Some are pretty simple (degenerate unto ridiculous?) algorithms... like a proof by example.  Inductive proofs are more obviously what we think of as "algorithms".  Exhaustive proofs are the most common proofs to be implemented as an algorithm (executed by human or computer).

As a practical matter, plenty of algorithms have been written to *generate and test* complex logic statements, supporting the pursuit of a proof.  The Four Color problem is the most well known example of a computer-assisted-proof and its correctness remains a question among many Mathematicians, but I think most Algorithmaticians (???) and Computer Geeks would believe that they can infer the accuracy of the results of the algorithms by inspecting the algorithms that generate and test the very large number of examples this particular proof requires.

I believe that one of our own (Jack Horner) has written his own formal logic program to test the writings of Thomas Aquinas and has, in fact, found many of Aquinas' threads of logic to be lacking.  At the risk of getting Jack in to the food fights here, I think some of the folks here would find his work in this area entertaining.

http://en.wikipedia.org/wiki/Automated_theorem_prover

http://en.wikipedia.org/wiki/Computer-assisted_proof

http://en.wikibooks.org/wiki/Amateur%27s_guide_to_proving_the_four_color_theorem

Alas, none of this is Applied Complexity...  (or is it?)

 - Steve

PS.  I am writing these long-winded missives while watching our new Laser Scanner extract millions of surface points from various test objects .  Each scan takes 2-10 minutes.  Just enough time to get all philosophical about matters mathematical/computational/algorithmic.   I will be handing the scanner off to more practical people than I soon, and will therefore give the list a break from these ponderings.

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Meets Fridays 9a-11:30 at cafe at St. John's College
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[Roger Frye-3]

Gowers edited the magnificent Princeton Companion to Mathematics
http://press.princeton.edu/titles/8350.html
It's a bargain at $0.10/page.

On Jul 12, 2009, at 5:45 PM, Robert Holmes wrote:

> By the way, if anyone feels like exercising their gray matter, the  
> author of VSI Mathematics (Timothy Gowers) has a rather nice math-
> oriented blog at http://gowers.wordpress.com


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[Nick Thompson]

Thank you Marcus.  

I think I got it!

Nick

Nicholas S. Thompson
Emeritus Professor of Psychology and Ethology,
Clark University ([hidden email])
http://home.earthlink.net/~nickthompson/naturaldesigns/

> [Original Message]
> From: Marcus G. Daniels <[hidden email]>
> To: The Friday Morning Applied Complexity Coffee Group <[hidden email]>
> Date: 7/13/2009 10:13:41 AM
> Subject: Re: [FRIAM] Philosophy, Mathematics, and Science
>
> Nicholas Thompson wrote:
> > How, then, could a mathematical proof NOT be a form of algorithm?  
> To me, the word algorithm suggests an emphasis on clarity and economy of
> effort, whereas a proof emphasizes the fact a conclusion in correct, and
> why.   But a problem can be cast either way.
>
> In logic programming (Prolog):
>
> factorial(1,1).
> factorial(N,F):-
>   N > 1,
>   NN is N - 1,
>   factorial(NN,FF),
>   F is N * FF.
>
> The point here is that given an expression like factorial(5,F) the
> Prolog interpreter _solves_ for F, or, given a query like
> factorial(5,100) will answer "no" (it's actually 120).  The execution
> trace of such a program is the proof.. (Although it would often being
> intolerably long.)
>
> In a typical imperative programming (Java), the code just moves forward
> step by step until n <= 1.
> The execution path is defined, instead of being deduced (or more
> generally in constraint logic programming systems.. found).
>
>     public static long factorial( int n )
>     {
>         if( n <= 1 )  
>             return 1;
>         else
>             return n * factorial( n - 1 );
>     }
>
>
>
>
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[Owen Densmore]

Here's the errata page for PCM:
   http://gowers.wordpress.com/2009/03/17/pcm-errata-ii/
.. the new printing should be out soon.

I definitely plan to get it, especially after reading the VSI.  
Brilliantly clear.  I've been reading a digital copy (torrent) of the  
VLI/PCM (VLI=Very Long Introduction) and it is just as wonderful and  
thoughtful.

Maybe a group read/discussion group?

     -- Owen


On Jul 13, 2009, at 11:28 AM, Roger Frye wrote:

> Gowers edited the magnificent Princeton Companion to Mathematics
> http://press.princeton.edu/titles/8350.html
> It's a bargain at $0.10/page.
>
> On Jul 12, 2009, at 5:45 PM, Robert Holmes wrote:
>
>> By the way, if anyone feels like exercising their gray matter, the  
>> author of VSI Mathematics (Timothy Gowers) has a rather nice math-
>> oriented blog at http://gowers.wordpress.com
>
>
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[Steve Smith]

Owen to Nick said:
>>
>> No, but you do feel argument is a sort of sport, not unlike wrestling!
Well characterized.

Although, for my own part, I find it to be a bit more like being in a
group of boys trying to catch a greased pig!

There *is* a point to the exercise, it just looks kinda silly to anyone
not in the pen trying to do the catching.

- Steve



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[Nick Thompson]

Some of the confusion here may come from different uses of the word
argument. From Dic.com

ar·gu·ment  (ärgy-mnt)
n.
1.
a. A discussion in which disagreement is expressed; a debate.
b. A quarrel; a dispute.
c. Archaic A reason or matter for dispute or contention: "sheath'd their
swords for lack of argument" (Shakespeare).
2.
a. A course of reasoning aimed at demonstrating truth or falsehood:
presented a careful argument for extraterrestrial life.
b. A fact or statement put forth as proof or evidence; a reason: The
current low mortgage rates are an argument for buying a house now.
c. A set of statements in which one follows logically as a conclusion from
the others.

I hate and deplore arguments in sense 1.  

I have a lot of reverence for arguments in sense 2a.

N

Nicholas S. Thompson
Emeritus Professor of Psychology and Ethology,
Clark University ([hidden email])
http://home.earthlink.net/~nickthompson/naturaldesigns/

> [Original Message]
> From: Owen Densmore <[hidden email]>
> To: The Friday Morning Applied Complexity Coffee Group <[hidden email]>
> Date: 7/13/2009 10:41:50 AM
> Subject: Re: [FRIAM] Philosophy, Mathematics, and Science
>
> Nick and I had an off-list discussion that may speak to some of the  
> recent posts.
>
> Begin forwarded message:
>
> > From: Owen Densmore <[hidden email]>
> > Date: July 13, 2009 10:38:08 AM MDT
> > To: [hidden email]
> > Cc: John Kennison <[hidden email]>, Owen Densmore

<[hidden email]

> > >
> > Subject: Re: Cauchy sequence - Wikipedia, the free encyclopedia
> >
> > On Jul 12, 2009, at 10:30 PM, Nicholas Thompson wrote:
> >> http://en.wikipedia.org/wiki/Cauchy_sequence
> >>
> >> Sorry.  I dont know why this came up.  I see that it's some nice  
> >> mathematics,but I dont see its relevance.
> >
> > The sub-theme was "Bridging the Gap" .. in this case between  
> > philosophy and mathematics.  In the above case, the CS is a  
> > delightful example of bridging the gap between the CONtinuous and  
> > disCRETE in Don Knuth's Concrete Mathematics .. a topic we've  
> > discussed in the past.
> >
> > Or possibly more formally, applying the epsilon/delta idea to both  
> > the continuous and discrete as discussed in the book we read last  
> > summer, Journey Through Genius.
> >
> >> While I have your attention, is a mathematical proof a kind of  
> >> algorithm?
> >
> > Although they share a step-wise approach, I think not.
> >
> >> Do you agree, that mathematical proofs are very rigorous arguments?
> >
> > Not arguments as in a way to resolve disagreements.  But arguments  
> > as a line of thought.  Certainly rigorous.
> >
> >> Is a symbolic logical proof an example of mathematics?
> >
> > I'd say yes, but others might be more comfortable separating math  
> > and logic.
> >
> >> Or of Philosophy?
> >
> > See the word comfortable above.
> >
> >> Was Bertrand Russel a mathematician or a philosopher?
> >
> > Both.  Wittgenstein studied under him, so the Both applies to him  
> > too, as it does for Kant and others.
> >
> >> Since I think of mathematics as a kind of tremendously rigorous  
> >> extension of the art of argument from philosophy, I would expect  
> >> that most of these questions are bad questions.
> >
> > No, but you do feel argument is a sort of sport, not unlike  
> > wrestling!  This is really more key that you might imagine.  
> > Mathematicians and scientists, even though they do have  
> > disagreements, generally argue/discuss means to an end (solving a  
> > problem, creating a proof) rather than argue right and wrong.
> >
> >> You can take this on the list, if you like.  I think your answers  
> >> would be interesting to list members, but I am leery of being  
> >> called on the carpet for starting another philosophical discussion.
> >>
> >> I have cc'ed my mathematician friend John Kennison to see what he  
> >> might say.
> >>
> >> Nicholas S. Thompson
> >> Emeritus Professor of Psychology and Ethology,
> >> Clark University ([hidden email])
> >> http://home.earthlink.net/~nickthompson/naturaldesigns/
> >
> >
>
>
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[Nick Thompson]

But Doug:  I don't want MY answer;  I want YOUR answer.

 

Nick

 

Nicholas S. Thompson

Emeritus Professor of Psychology and Ethology,

Clark University ([hidden email])

http://home.earthlink.net/~nickthompson/naturaldesigns/

 

 

 

 

----- Original Message -----

From: [hidden email]

To: [hidden email];[hidden email]

Sent: 7/13/2009 9:50:00 AM

Subject: Re: [FRIAM] Philosophy, Mathematics, and Science

Nick,

I like you.  I really do.  But you sometimes make me just want to scream.

If you want to know what pseudocode is, go to the web and find out!  Here's a starting point for you:

http://en.wikipedia.org/wiki/Pseudocode

Then, if you still *really* want to know what psuedocode is, write some.  And then pick a language and turn it into actual code.  Then you will know what psuedocode is.

--Doug

On Mon, Jul 13, 2009 at 9:28 AM, Nicholas Thompson <[hidden email]> wrote:

What is the relationship between pseudo-code and code. 

 

Are actual codes  "realizations" of pseudocodes? 

 

Nick

 

Nicholas S. Thompson

Emeritus Professor of Psychology and Ethology,

Clark University ([hidden email])

http://home.earthlink.net/~nickthompson/naturaldesigns/

 

 

 

 

----- Original Message -----

From: [hidden email]

To: [hidden email]

Sent: 7/13/2009 9:16:11 AM

Subject: Re: [FRIAM] Philosophy, Mathematics, and Science

Can be built upon in theory, but in practice they are with high probability thrown away and rebuilt from scratch.

Because they are complex linguistic objects which, like philosophers' arguments, are often harder to figure out than to do over from first principles.

-- rec --

Well said Roger.   I think we have all had the experience of choosing to:

1. rederive an equation
   
2. redesign an algorithm
3. rewrite a piece of code
4. rehash a philosophical argument

when there was already a perfectly good (maybe) equation/algorithm/program/argument layed at our feet.

For me, this is a mixture of:

1. Pride
2. Trust
3. Understanding

This was a major challenge to code re-use at one time...  about the only published Algorithms many of us trusted were those published in Knuth!  And even then, we had to rewrite the actual code in whatever context we were operating in, and were generally proud to do it.  But we couldn't help  noodling on the algorithms, trying to think of a new, more elegant, more general, or more efficient way of solving the problem at hand.

Often, by the time one has worked through an algorithm forward to backward, backward to forward, one might as well have designed it.  The existing algorithm provides a few important things, however:

1. Existence proof.  We *know* there is at least one algorithm that achieves the desired result.
2. Hints.  Even if we don't understand an algorithm on first blush, we usually get a sense of it's arc.
3. Reference.  When we think we've got ours right, we can go back and test it against the original.  In fact, we probably now understand the original as well as our own and if we have any humility may throw *ours* away and use the one made available to us in the first place

For proceduralists, C's concise method of creating complex objects (data structures and pointers to them) made it possible to build good/interesting/understandable libraries from tried and true algorithms.  With the introduction of ObjC/C++/Java and a huge new influx of programmers (the Internet may not have *created* new programmers, but it connected them to the rest of us in a way that was unprecedented), the number of libraries went up dramatically.   With the Open Source movement, these accreted and evolved into some pretty interesting, trusted and useful libraries.   Today, only a hardcore group like this crowd here are likely to rederive/redesign/rewrite/rehash.

It is a dying art, which I am nostalgic about.  It is one of the entertainments I find on this list.   I liken what happens here (sometimes) to the WPA era when the very few remaining craftsmen in many building arts were found and encouraged/supported to building some last monuments to an old era of craftsmanship that no longer exists. 

Maybe huge systems built of handcut C (assembly?)  code, implementing custom algorithms are not as obviously beautiful or elegant as some of the grand WPA era National Park resorts (Mt Hood, Grand Canyon Lodge, Yosemite, ...)  but there is a similarity in the values and the processes.

I respect Nick and others here for wanting to apply the same principles to the context of our various constructions as well.  I don't always (even try to) follow the arguments but I appreciate the desire to (re)hash the hash, even if I don't always want to participate in it.

- Steve

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[Douglas Roberts-2]

<scream>

On Mon, Jul 13, 2009 at 2:54 PM, Nicholas Thompson <[hidden email]> wrote:

But Doug:  I don't want MY answer;  I want YOUR answer.

 

Nick

 

Nicholas S. Thompson

Emeritus Professor of Psychology and Ethology,

Clark University ([hidden email])

http://home.earthlink.net/~nickthompson/naturaldesigns/

 

 

 

 

----- Original Message -----

From: [hidden email]

To: [hidden email];[hidden email]

Sent: 7/13/2009 9:50:00 AM

Subject: Re: [FRIAM] Philosophy, Mathematics, and Science

Nick,

I like you.  I really do.  But you sometimes make me just want to scream.

If you want to know what pseudocode is, go to the web and find out!  Here's a starting point for you:

http://en.wikipedia.org/wiki/Pseudocode

Then, if you still *really* want to know what psuedocode is, write some.  And then pick a language and turn it into actual code.  Then you will know what psuedocode is.

--Doug

On Mon, Jul 13, 2009 at 9:28 AM, Nicholas Thompson <[hidden email]> wrote:

What is the relationship between pseudo-code and code. 

 

Are actual codes  "realizations" of pseudocodes? 

 

Nick

 

Nicholas S. Thompson

Emeritus Professor of Psychology and Ethology,

Clark University ([hidden email])

http://home.earthlink.net/~nickthompson/naturaldesigns/

 

 

 

 

----- Original Message -----

From: [hidden email]

To: [hidden email]

Sent: 7/13/2009 9:16:11 AM

Subject: Re: [FRIAM] Philosophy, Mathematics, and Science

Can be built upon in theory, but in practice they are with high probability thrown away and rebuilt from scratch.

Because they are complex linguistic objects which, like philosophers' arguments, are often harder to figure out than to do over from first principles.

-- rec --

Well said Roger.   I think we have all had the experience of choosing to:

1. rederive an equation
   
2. redesign an algorithm
3. rewrite a piece of code
4. rehash a philosophical argument

when there was already a perfectly good (maybe) equation/algorithm/program/argument layed at our feet.

For me, this is a mixture of:

1. Pride
2. Trust
3. Understanding

This was a major challenge to code re-use at one time...  about the only published Algorithms many of us trusted were those published in Knuth!  And even then, we had to rewrite the actual code in whatever context we were operating in, and were generally proud to do it.  But we couldn't help  noodling on the algorithms, trying to think of a new, more elegant, more general, or more efficient way of solving the problem at hand.

Often, by the time one has worked through an algorithm forward to backward, backward to forward, one might as well have designed it.  The existing algorithm provides a few important things, however:

1. Existence proof.  We *know* there is at least one algorithm that achieves the desired result.
2. Hints.  Even if we don't understand an algorithm on first blush, we usually get a sense of it's arc.
3. Reference.  When we think we've got ours right, we can go back and test it against the original.  In fact, we probably now understand the original as well as our own and if we have any humility may throw *ours* away and use the one made available to us in the first place

For proceduralists, C's concise method of creating complex objects (data structures and pointers to them) made it possible to build good/interesting/understandable libraries from tried and true algorithms.  With the introduction of ObjC/C++/Java and a huge new influx of programmers (the Internet may not have *created* new programmers, but it connected them to the rest of us in a way that was unprecedented), the number of libraries went up dramatically.   With the Open Source movement, these accreted and evolved into some pretty interesting, trusted and useful libraries.   Today, only a hardcore group like this crowd here are likely to rederive/redesign/rewrite/rehash.

It is a dying art, which I am nostalgic about.  It is one of the entertainments I find on this list.   I liken what happens here (sometimes) to the WPA era when the very few remaining craftsmen in many building arts were found and encouraged/supported to building some last monuments to an old era of craftsmanship that no longer exists. 

Maybe huge systems built of handcut C (assembly?)  code, implementing custom algorithms are not as obviously beautiful or elegant as some of the grand WPA era National Park resorts (Mt Hood, Grand Canyon Lodge, Yosemite, ...)  but there is a similarity in the values and the processes.

I respect Nick and others here for wanting to apply the same principles to the context of our various constructions as well.  I don't always (even try to) follow the arguments but I appreciate the desire to (re)hash the hash, even if I don't always want to participate in it.

- Steve

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--
Doug Roberts
[hidden email]
[hidden email]
505-455-7333 - Office
505-670-8195 - Cell

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[Robert Holmes]

This response is either very very clever or very very lazy

-- R

On Mon, Jul 13, 2009 at 2:54 PM, Nicholas Thompson <[hidden email]> wrote:

But Doug:  I don't want MY answer;  I want YOUR answer.

 

Nick

 

Nicholas S. Thompson

Emeritus Professor of Psychology and Ethology,

Clark University ([hidden email])

http://home.earthlink.net/~nickthompson/naturaldesigns/

 

 

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[Douglas Roberts-2]

I've been holding my tongue a bit lately (really), but now might be a good time to share my opinion that many of the kinds of questions we see on the FRIAM list result from lazy mental processes.  E.g., it's too hard to figure an answer out for one's self, but it's quite easy to ask the list a (pick your topic) question under the guise of posing deep, philosophical/thoughtful questions.

I'm not naming names, but I do want to reiterate something Pirsig observed in this vein:

So it is with John. I could preach the practical value and worth of motorcycle maintenance till I'm hoarse and it would make not a dent in him. After two sentences on the subject his eyes go completely glassy and he changes the conversation or just looks away. He doesn't want to hear about it.

Sylvia is completely with him on this one. In fact she is even more emphatic. "It's just a whole other thing," she says, when in a thoughtful mood. "Like garbage," she says, when not. They want not to understand it. Not to hear about it. And the more I try to fathom what makes me enjoy mechanical work and them hate it so, the more elusive it becomes. The ultimate cause of this originally minor difference of opinion appears to run way, way deep.

Inability on their part is ruled out immediately. They are both plenty bright enough. Either one of them could learn to tune a motorcycle in an hour and a half if they put their minds and energy to it, and the saving in money and worry and delay would repay them over and over again for their effort. And they know that. Or maybe they don't. I don't know. I never confront them with the question. It's better to just get along.

Obviously, I'm less concerned with the "just getting along" part than Pirsig is.

--Doug

On Mon, Jul 13, 2009 at 4:22 PM, Robert Holmes <[hidden email]> wrote:

This response is either very very clever or very very lazy

-- R

On Mon, Jul 13, 2009 at 2:54 PM, Nicholas Thompson <[hidden email]> wrote:

But Doug:  I don't want MY answer;  I want YOUR answer.

 

Nick

 

Nicholas S. Thompson

Emeritus Professor of Psychology and Ethology,

Clark University ([hidden email])

http://home.earthlink.net/~nickthompson/naturaldesigns/

 

 

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[Robert Holmes]

I think the argument (I paraphrase) "all math/science is traceable back to Aristotle/Parmenides/Zeno/pick-your-philosopher, therefore everything subsequent is mere derivations of their original thoughts" is not completely sound. It's probably reasonable up to the period of Newton, Descartes and Leibniz: these people were philosophers and scientists. As has been pointed out several times, there was no real distinction between the two practices: they were just the one entity - natural philosophy.

But then came the Scientific Revolution and during the 16th-18th centuries both disciplines professionalized and - for all but a few exceptional individuals - they split. Philosophers did philosophy, scientists did science. Philosophers might comment on what was happening in science but that does not mean that they were driving it or suggesting the questions that scientists should ask. Philosophy might comment on science but - for most practitioners of science - it did not inform science.

My own experience bears this out. I'm a physicist and have worked in research environments all my professional life. When my colleagues and I discuss research priorities, or potential areas for study, or appropriate methodologies we refer to the work of other scientists, not philosophers. I don't think this is unusual. I strongly suspect that it is the work of other scientists and the lessons we learn from our scientific mentors that drive our scientific endeavors.

-- Robert

On Mon, Jul 13, 2009 at 7:18 PM, glen e. p. ropella <[hidden email]> wrote:

Thus spake Robert Holmes circa 09-07-11 07:47 AM:

> Y'know if Glen's resolution was true I'd expect more of the scientific
> papers I read to be referencing Quine and Aristotle rather than Landau and
> Lifschitz. Explicitly acknowledging their debt, if you will.

That's just plain silly.  You _know_ that math has its origins in
philosophy.  Just look at Russell and Whitehead's attempt to provide a
foundation for math that would lead to Hilbert's program (of which the
Riemann hypothesis was a part, and was instigated by Frege).  Or look at
Tarski's and Goedel's independent discoveries of
incompleteness/inconsistency, which derailed the program.

Sheesh.  Are you unable to use Google?  Are you that lazy?

> So perhaps you could give me some concrete
> examples: which philosopher should mathematicians thank for suggesting that
> the properties of the Riemann zeta function were worth studying?

Oh, I don't know.  Let's start with Zeno, shall we?  Without him, we
wouldn't have a clear concept of the limit, the foundation of modern
analysis.  Or, perhaps we go a little farther downstream and talk about
Cantor, whose work was philosophical enough to garner criticism from all
manner of authority.

> Which
> philosopher should physicists thank for suggesting that it's worth hunting
> for the Higgs boson?

Well, you can start with Democritus.  I could trace the evolution of the
Standard Model for you... but I won't because your questions are either
just snotty and/or lazy.  If you want to know which philosophers helped
cause the hypothetical higgs boson, then you look it up yourself.

--
glen e. p. ropella, 971-222-9095, http://tempusdictum.com

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[Steve Smith]

Douglas Roberts wrote:

<scream>

<grin>
    can we upgrade that from a beer to some Irish Whiskey on the rocks?
</grin>

On Mon, Jul 13, 2009 at 2:54 PM, Nicholas Thompson <[hidden email]> wrote:

But Doug:  I don't want MY answer;  I want YOUR answer.

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