Mathematics and Music

[Nick Thompson]

All,

One of the running arguments I have with one of my favorite colleagues here in Santa Fe is about whether Mathematics is (or isn't) different from all other intellectual enterprises, such as psychology or philosophy. in that, unlike them,  mathematics "adds up," in the long run. Contrary to psychologists and philosophers like me, who are besotted with ephemeral traditions and ideologies, and keep changing the rules of the game, mathematicians have built a structure that is not subject to vicissitudes and whims of intellectual history. (I hope I have represented this argument fairly.) Although I have tried to give him as little comfort as possible, I confess that I have been impressed more and more by this argument as I continue to read accessible works on the history of mathematics.

For this reason, I was startled to find a contrary argument in a powerful book written by the Music Critic of the New York Times, Edward Rothstein on the relation between music and mathematics, EMBLEMS OF THE MIND [Times books, NY: 1995]. I am curious to know what anybody thinks of it. I will key in a brief passage (from page 43-4) below for comment:

Begin quote from Rothstein =====>

"Because context is so important, aspects of mathematical truth may alter over time. ...

.... Paradoxically, this is one reason why so few mathematicians ever study the history of their own discipline. The apparent uniformity of truth through time might seem to suggest that a geometer might as profitably study Descartes as Lobachevsky, or a number theoretician might as usefully read Euler as Hardy. In fact, the language of mathematics today bears so little resemblance in style and form to the languages of the past that it would take a great deal of effort to "translate" the mathematics of the past into contemporary terms. ...

One example of shifting context and the transformation of mathematical styles was discussed by the mathematicians Philip J. Davis and Reuben Hersh in THE MATHEMATICAL EXPERIENCE, [Boston: Birkhauser, 1981]. They present a simple theorem of arithmetic that has been generally known as the Chinese remainder theorem."

<===== End quote from Rothstein.

Davis and Hersh (according to Rothstein) then summarize the presentations of this same theorem in mathematicians from Fibonacci to E. Weiss.

Rothstein now concludes.

Begin quote from Rothstein =====>

"Mathematical style is far more important than it usually seems. It is intimately connected to the essence of mathematical work. It defines conditions and expectations. It presents a set of rules, of course, but it also does something more: it reflects what is considered important at a particular historical moment and shapes the evolution of future inquiries. It resembles, in this way, musical style."

<===== End quote from Rothstein.

So I am wondering: Is this a bridge too far????

Nick

 

This discussion is posted  in the Noodlers' Corner, at http://www.sfcomplex.org/wiki/MathematicsAndMusic

 

Nicholas S. Thompson

Emeritus Professor of Psychology and Ethology,

Clark University ([hidden email])

 

 

 

============================================================
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

[Orlando Leibovitz]

Nick,

Concerning the following quote from your email one could easily replace musical style with painting style or writing style or  clothing style or............ style. 

Orlando

"Mathematical style is far more important than it usually seems. It is intimately connected to the essence of mathematical work. It defines conditions and expectations. It presents a set of rules, of course, but it also does something more: it reflects what is considered important at a particular historical moment and shapes the evolution of future inquiries. It resembles, in this way, musical style."

Nicholas Thompson wrote:

All,

One of the running arguments I have with one of my favorite colleagues here in Santa Fe is about whether Mathematics is (or isn't) different from all other intellectual enterprises, such as psychology or philosophy. in that, unlike them,  mathematics "adds up," in the long run. Contrary to psychologists and philosophers like me, who are besotted with ephemeral traditions and ideologies, and keep changing the rules of the game, mathematicians have built a structure that is not subject to vicissitudes and whims of intellectual history. (I hope I have represented this argument fairly.) Although I have tried to give him as little comfort as possible, I confess that I have been impressed more and more by this argument as I continue to read accessible works on the history of mathematics.

For this reason, I was startled to find a contrary argument in a powerful book written by the Music Critic of the New York Times, Edward Rothstein on the relation between music and mathematics, EMBLEMS OF THE MIND [Times books, NY: 1995]. I am curious to know what anybody thinks of it. I will key in a brief passage (from page 43-4) below for comment:

Begin quote from Rothstein =====>

"Because context is so important, aspects of mathematical truth may alter over time. ...

.... Paradoxically, this is one reason why so few mathematicians ever study the history of their own discipline. The apparent uniformity of truth through time might seem to suggest that a geometer might as profitably study Descartes as Lobachevsky, or a number theoretician might as usefully read Euler as Hardy. In fact, the language of mathematics today bears so little resemblance in style and form to the languages of the past that it would take a great deal of effort to "translate" the mathematics of the past into contemporary terms. ...

One example of shifting context and the transformation of mathematical styles was discussed by the mathematicians Philip J. Davis and Reuben Hersh in THE MATHEMATICAL EXPERIENCE, [Boston: Birkhauser, 1981]. They present a simple theorem of arithmetic that has been generally known as the Chinese remainder theorem."

<===== End quote from Rothstein.

Davis and Hersh (according to Rothstein) then summarize the presentations of this same theorem in mathematicians from Fibonacci to E. Weiss.

Rothstein now concludes.

Begin quote from Rothstein =====>

"Mathematical style is far more important than it usually seems. It is intimately connected to the essence of mathematical work. It defines conditions and expectations. It presents a set of rules, of course, but it also does something more: it reflects what is considered important at a particular historical moment and shapes the evolution of future inquiries. It resembles, in this way, musical style."

<===== End quote from Rothstein.

So I am wondering: Is this a bridge too far????

Nick

 

This discussion is posted  in the Noodlers' Corner, at http://www.sfcomplex.org/wiki/MathematicsAndMusic

 

Nicholas S. Thompson

Emeritus Professor of Psychology and Ethology,

Clark University ([hidden email])

 

 

 

============================================================
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

[Nick Thompson]

Orlando,

 

I will be interested in what the mathematicians say.  It seems to me that the statement is too broad, that Owen is right, that mathematics IS more cumulative than, say, psychology.   However, this cumulative consistency is perhaps bought at a cost....   Unlike psychology, mathematics isnt ABOUT anything.  

 

What is making this book exciting to read is the relationship between math and music.  First, there are so many people I know that are good at both and,  second, music is so RATIOnal, in the mathematical sense .  

 

Nick  

 

Nicholas S. Thompson

Emeritus Professor of Psychology and Ethology,

Clark University ([hidden email])

 

 

 

 

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

From: [hidden email]

To: [hidden email];[hidden email]

Sent: 7/10/2008 10:24:05 PM

Subject: Re: [FRIAM] Mathematics and Music

Nick,

Concerning the following quote from your email one could easily replace musical style with painting style or writing style or  clothing style or............ style. 

Orlando

"Mathematical style is far more important than it usually seems. It is intimately connected to the essence of mathematical work. It defines conditions and expectations. It presents a set of rules, of course, but it also does something more: it reflects what is considered important at a particular historical moment and shapes the evolution of future inquiries. It resembles, in this way, musical style."

Nicholas Thompson wrote:

All,

One of the running arguments I have with one of my favorite colleagues here in Santa Fe is about whether Mathematics is (or isn't) different from all other intellectual enterprises, such as psychology or philosophy. in that, unlike them,  mathematics "adds up," in the long run. Contrary to psychologists and philosophers like me, who are besotted with ephemeral traditions and ideologies, and keep changing the rules of the game, mathematicians have built a structure that is not subject to vicissitudes and whims of intellectual history. (I hope I have represented this argument fairly.) Although I have tried to give him as little comfort as possible, I confess that I have been impressed more and more by this argument as I continue to read accessible works on the history of mathematics.

For this reason, I was startled to find a contrary argument in a powerful book written by the Music Critic of the New York Times, Edward Rothstein on the relation between music and mathematics, EMBLEMS OF THE MIND [Times books, NY: 1995]. I am curious to know what anybody thinks of it. I will key in a brief passage (from page 43-4) below for comment:

Begin quote from Rothstein =====>

"Because context is so important, aspects of mathematical truth may alter over time. ...

.... Paradoxically, this is one reason why so few mathematicians ever study the history of their own discipline. The apparent uniformity of truth through time might seem to suggest that a geometer might as profitably study Descartes as Lobachevsky, or a number theoretician might as usefully read Euler as Hardy. In fact, the language of mathematics today bears so little resemblance in style and form to the languages of the past that it would take a great deal of effort to "translate" the mathematics of the past into contemporary terms. ...

One example of shifting context and the transformation of mathematical styles was discussed by the mathematicians Philip J. Davis and Reuben Hersh in THE MATHEMATICAL EXPERIENCE, [Boston: Birkhauser, 1981]. They present a simple theorem of arithmetic that has been generally known as the Chinese remainder theorem."

<===== End quote from Rothstein.

Davis and Hersh (according to Rothstein) then summarize the presentations of this same theorem in mathematicians from Fibonacci to E. Weiss.

Rothstein now concludes.

Begin quote from Rothstein =====>

"Mathematical style is far more important than it usually seems. It is intimately connected to the essence of mathematical work. It defines conditions and expectations. It presents a set of rules, of course, but it also does something more: it reflects what is considered important at a particular historical moment and shapes the evolution of future inquiries. It resembles, in this way, musical style."

<===== End quote from Rothstein.

So I am wondering: Is this a bridge too far????

Nick

 

This discussion is posted  in the Noodlers' Corner, at http://www.sfcomplex.org/wiki/MathematicsAndMusic

 

Nicholas S. Thompson

Emeritus Professor of Psychology and Ethology,

Clark University ([hidden email])

 

 

 

============================================================
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

[Carl Tollander]

A tract on how the history might work, again, *sigh*:

http://www.dcorfield.pwp.blueyonder.co.uk/HowMathematicians.pdf

The point being, that mathematics, like Cluetrain products, are
conversations, and that those that coalesce and progress don't get made
without some awareness of the continuity and structure of effort, i.e.
histories.   ALL mathematicians, worth their salt, study the histories
of their own discipline.

What are the assumptions here about the "purity" of mathematics (yah, we
saw the XKCD cartoon)? From Sterling, "A small, beautiful, hand-crafted
society, living in harmony with its eco-region, relentlessly
parsimonious in its use of energy and resources, can't learn enough
about itself to survive".
The operative phrase here being "learn enough about itself".  
Mathematics flourishes, so it because of ignorance of its own history,
or because it has some idea, maybe, about how its own histories and
traditions work?

Music critics, bah.

C.

Nicholas Thompson wrote:

>
> All,
>
> One of the running arguments I have with one of my favorite colleagues
> here in Santa Fe is about whether Mathematics is (or isn't) different
> from all other intellectual enterprises, such as psychology or
> philosophy. in that, unlike them,  mathematics "adds up," in the long
> run. Contrary to psychologists and philosophers like me, who are
> besotted with ephemeral traditions and ideologies, and keep changing
> the rules of the game, mathematicians have built a structure that is
> not subject to vicissitudes and whims of intellectual history. (I hope
> I have represented this argument fairly.) Although I have tried to
> give him as little comfort as possible, I confess that I have been
> impressed more and more by this argument as I continue to read
> accessible works on the history of mathematics.
>
> For this reason, I was startled to find a contrary argument in a
> powerful book written by the Music Critic of the New York Times,
> Edward Rothstein on the relation between music and mathematics,
> EMBLEMS OF THE MIND [Times books, NY: 1995]. I am curious to know what
> anybody thinks of it. I will key in a brief passage (from page 43-4)
> below for comment:
>
> Begin quote from Rothstein =====>
>
> *"Because context is so important, aspects of mathematical truth may
> alter over time. ...*
>
> *.... Paradoxically, this is one reason why so few mathematicians ever
> study the history of their own discipline. The apparent uniformity of
> truth through time might seem to suggest that a geometer might as
> profitably study Descartes as Lobachevsky, or a number theoretician
> might as usefully read Euler as Hardy. In fact, the language of
> mathematics today bears so little resemblance in style and form to the
> languages of the past that it would take a great deal of effort to
> "translate" the mathematics of the past into contemporary terms. ... *
>
> *One example of shifting context and the transformation of
> mathematical styles was discussed by the mathematicians Philip J.
> Davis and Reuben Hersh in THE MATHEMATICAL EXPERIENCE, [Boston:
> Birkhauser, 1981]. They present a simple theorem of arithmetic that
> has been generally known as the Chinese remainder theorem."*
>
> <===== End quote from Rothstein.
>
> Davis and Hersh (according to Rothstein) then summarize the
> presentations of this same theorem in mathematicians from Fibonacci to
> E. Weiss.
>
> Rothstein now concludes.
>
> Begin quote from Rothstein =====>
>
> *"Mathematical style is far more important than it usually seems. It
> is intimately connected to the essence of mathematical work. It
> defines conditions and expectations. It presents a set of rules, of
> course, but it also does something more: it reflects what is
> considered important at a particular historical moment and shapes the
> evolution of future inquiries. It resembles, in this way, musical
> style." *
>
> <===== End quote from Rothstein.
>
> So I am wondering: Is this a bridge too far????
>
> Nick
>
>  
> This discussion is posted  in the Noodlers' Corner, at
> http://www.sfcomplex.org/wiki/MathematicsAndMusic
>  
> Nicholas S. Thompson
> Emeritus Professor of Psychology and Ethology,
> Clark University ([hidden email] <mailto:[hidden email]>)
>  
>  
>  
> ------------------------------------------------------------------------
>
> ============================================================
> 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

[Paul Paryski]

A larger question might be (perhaps indicating my own ignorance) : is mathematics inherent in the universe or a rational construct of the human mind? 
Paul


**************
Get the scoop on last night's hottest shows and the live music scene in your area - Check out TourTracker.com!
(http://www.tourtracker.com?NCID=aolmus00050000000112)
============================================================
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

[Nick Thompson]

Somebody called it "neutral", i.e., neither of the mind nor of the world by lying between. 

 

Was it William James? 

 

Love to know.

 

N

 

Nicholas S. Thompson

Emeritus Professor of Psychology and Ethology,

Clark University ([hidden email])

 

 

 

 

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

From: [hidden email]

To: [hidden email];[hidden email];[hidden email]

Sent: 7/11/2008 12:24:00 PM

Subject: Re: [FRIAM] Mathematics and Music

A larger question might be (perhaps indicating my own ignorance) : is mathematics inherent in the universe or a rational construct of the human mind? 
Paul


**************
Get the scoop on last night's hottest shows and the live music scene in your area - Check out TourTracker.com!
(http://www.tourtracker.com?NCID=aolmus00050000000112)

============================================================
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

[David Mirly]

Glenn, I personally agree with your analysis of what mathematics is  
either in large part or wholly.

But there are others who do not.  The field of mathematical philosophy  
has many branches of opposing belief.

None of which has been proven for the most part and the subject has  
mostly languished for the last 100 years
or so.  I suppose mainly due to Gödel and our interpretation and use  
of his work.

One of the more opposite views, however, is the Platonist view (I  
think I have that right) where mathematical concepts
are a set of universal truths and we just discover them as opposed to  
creating them.

We touched on this many months (maybe even a year) ago when someone (I  
think Paul?) suggested, perhaps impishly,
that pi was "magic" which of course raised my hackles.  But I have to  
admit it is strange how pi, e and other transcendental
numbers pop up in a number of places mathematically.  Others pointed  
that out when I protested, I don't remember their
names either - sorry.

We have also talked about the lack of rigorous mathematical  
representation of complexity and that being a barrier to progress
in the science.  So I think conversations like these are very relevant  
and necessary.


On Jul 11, 2008, at 11:58 AM, glen e. p. ropella wrote:

> Nicholas Thompson wrote:
>> Somebody called it "neutral", i.e., neither of the mind nor of the  
>> world by lying between.
>
> This is a weird discussion.  But, it seems like I ought to point out
> that math is a language just like any other.  Granted, it is less like
> English and more like first order logic; but, it's a language none  
> the less.
>
> So, the study of mathematics is exactly analogous to linguistics.  
> It's
> not that math isn't _about_ anything, any more than English isn't  
> about
> anything.  Languages are methods by which we communicate, describe,  
> and
> represent.  So, the study of language is the methodology of
> communication, description, and representation.
>
> Various constructs (stories, arguments, etc.) in the language (e.g.  
> the
> Calculus) do build up over time.  But we have to distinguish between a
> build up of the language, itself (methods in the toolbox), versus a
> build up of any given construct within the language.
>
> It's been shown (dead horse alert) that mathematics, itself, as the
> study of a set of formal languages, is ill-defined in the same sense
> (but more precisely) that English is ill-defined.  But there are
> particular constructs within mathematics that are well-defined.
>
> Mathematics, as a language, is a toolbox created, evolved, and used by
> humans to describe aspects of reality.  The constructs in math like  
> the
> Calculus represent some idealization/abstraction/aspect of reality  
> (e.g.
> the apparent smoothness of spatio-temporal extent, velocities,
> acceleration, etc.).  Other constructs described in math (e.g. graphs)
> describe other (again particular) aspects of reality.
>
> But it is a mistake to confuse the language with the constructs in the
> language.  That's like confusing a John Grisham novel  (a particular
> construct) with English (the language in which the construct is  
> written).
>
> --
> glen e. p. ropella, 971-219-3846, http://tempusdictum.com
>
>
> ============================================================
> 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

[Prof David West]

Mathematicians have asserted both positions - some believing that math
is a process of "discovery" of the intrinsic nature of the universe (or
the mind of God) while others believe it is a process of "invention" and
isomorphism between the invention and the universe is serendipitous.

davew

On Fri, 11 Jul 2008 14:23:50 EDT, [hidden email] said:

> A larger question might be (perhaps indicating my own ignorance) : is
> mathematics inherent in the universe or a rational construct of the human
> mind?  
> Paul
>
>
> **************
> Get the scoop on last night's hottest shows and the live
> music scene in your area - Check out TourTracker.com!
>      
> (http://www.tourtracker.com?NCID=aolmus00050000000112)

============================================================
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

[Prof David West]

>
> We have also talked about the lack of rigorous mathematical  
> representation of complexity and that being a barrier to progress
> in the science.  


the idea of magic raised your hackles - the above sentence raises mine.

implicit in the sentence is some variation of "mathematics is a better /
superior / privileged / real language compared to all other languages
used by humans to think and therefore we cannot really think properly or
rigorously unless we are thinking mathematically."

this annoying attitude is expressed / believed by a majority of
intellectuals and academicians - not just mathematicians.  We cannot be
"scientists" unless we 'mathematize' our field of enquiry.

Interestingly enough, all advances in science stem from the uses of
metaphor - not mathematics.  (see Quine)  The premature rush to abandon
the language of metaphor and publish using arcane squiggles is the real
- in my not very humble opinion - barrier to progress.

davew


============================================================
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

[Günther Greindl]

> Interestingly enough, all advances in science stem from the uses of
> metaphor - not mathematics.  (see Quine)  The premature rush to abandon
> the language of metaphor and publish using arcane squiggles is the real
> - in my not very humble opinion - barrier to progress.

Well, depends on what you want to do - developing _new_ theories is best
done via metaphor; to get a qualitative feel for the stuff; speculative
philosophy, if you like (that is indeed what I like to do :-))

But to make it into science, which means that you can make predictive
models certainly means mathematizing the theory.

Look at Einstein for instance: the ideas he had very hanging around
"intuitively" for quite some time; but he mathematized it, it went
experimental, and voila, scientifically confirmed and accepted.

Cheers,
Günther

--
Günther Greindl
Department of Philosophy of Science
University of Vienna
[hidden email]
http://www.univie.ac.at/Wissenschaftstheorie/

Blog: http://dao.complexitystudies.org/
Site: http://www.complexitystudies.org/

Research Proposal:
http://www.complexitystudies.org/ph.d.-thesis.html


============================================================
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

[Carl Tollander]

Perhaps the invention is intrinsic?   The either/or conundrum seems
artificial, unless one buys into a narrower definition of mathematician.

C.

Prof David West wrote:

>
> Mathematicians have asserted both positions - some believing that math
> is a process of "discovery" of the intrinsic nature of the universe (or
> the mind of God) while others believe it is a process of "invention" and
> isomorphism between the invention and the universe is serendipitous.
>
> davew
>
> On Fri, 11 Jul 2008 14:23:50 EDT, [hidden email] said:
>> A larger question might be (perhaps indicating my own ignorance) : is
>> mathematics inherent in the universe or a rational construct of the human
>> mind?  
>> Paul
>>
>>
>> **************
>> Get the scoop on last night's hottest shows and the live
>> music scene in your area - Check out TourTracker.com!
>>      
>> (http://www.tourtracker.com?NCID=aolmus00050000000112)
>
> ============================================================
> 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]

Michael Agar wrote:

> Is a computer program a mathematization?
>  
Proof is that Mathematica is in large part written in the functional
programming language Mathematica, and Macsyma/Maxima written in Lisp.

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

[glen ep ropella]

David Mirly wrote:
> One of the more opposite views, however, is the Platonist view (I  
> think I have that right) where mathematical concepts
> are a set of universal truths and we just discover them as opposed to  
> creating them.

Well, I don't want to object to the idea that Platonism opposes the
claim that mathematics is a language; but I have to. [grin]

Platonism doesn't strictly claim that _mathematics_ is truth.  What it
claims is that certain constructs, as described in mathematics, are
true.  Platonists will still agree that math is a language with which to
describe reality.  Non-platonists will claim that the stable constructs
(described in math) are not true but either an artifact of the structure
of the language or the social system that created the language and the
constructs expressed in the language.

But both Platonists and non-Platonists will agree that mathematics is a
language and false things can be described in it.

Platonism has a very strong case, though, because a soft form of it is
simply that mathematics is the _best_ language for describing reality.
And I'm a soft Platonist in that sense (albeit accepting the previously
discussed inadequacy of our mathematical constructs in capturing
paradox), which means I'll have to disagree with Dave in my next message.

--
glen e. p. ropella, 971-219-3846, http://tempusdictum.com


============================================================
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

[glen ep ropella]

Prof David West wrote:

>
>> We have also talked about the lack of rigorous mathematical  
>> representation of complexity and that being a barrier to progress
>> in the science.  
>
>
> the idea of magic raised your hackles - the above sentence raises mine.
>
> implicit in the sentence is some variation of "mathematics is a better /
> superior / privileged / real language compared to all other languages
> used by humans to think and therefore we cannot really think properly or
> rigorously unless we are thinking mathematically."

I don't think that inference is implied by that sentence.  I so believe
math is a better language with which to describe reality than, say,
English.  But, that's not what the sentence above says.  The sentence
above states that a _lack_ of math rigor is a barrier to one particular
domain: plectics.

Your inference goes quite a bit further than the David's sentence.

> this annoying attitude is expressed / believed by a majority of
> intellectuals and academicians - not just mathematicians.  We cannot be
> "scientists" unless we 'mathematize' our field of enquiry.

And although I believe that math is the best known language for
describing reality, I don't believe that one must mathematize every
scientific field or that one cannot be a scientist without mathematizing
their field.

Science is the search for truth.  And truth can be sought using any
language... any language at all.  Some domains, particularly the ones
resistant to rigor are best studied with languages that have a high
tolerance for ambiguity... e.g. English.

Some domains that are not so resistant to rigor are best studied with
math.  Often, it takes a great deal of work using ambiguity tolerant
languages like English before an ambiguity intolerant language like math
can be effectively used.

If and when less ambiguous languages can be used, _then_ those languages
become more effective than the more ambiguous languages.

 From 50,000 metaphorical feet, this can be seen as a simple case of
specialization.  A generalist uses coarse tools and a specialist uses
fine tools.  Math is a fine tool that can only be used after the
generalists have done their upstream work in the domain.  Neither is
really "better", of course, when taking a synoptic view of the whole
evolution of the domain.  But math is definitely more refined... more
special.

> Interestingly enough, all advances in science stem from the uses of
> metaphor - not mathematics.  (see Quine)  The premature rush to abandon
> the language of metaphor and publish using arcane squiggles is the real
> - in my not very humble opinion - barrier to progress.

I agree.  Likewise, the tendency to stick with a coarse language when a
more refined language is called for is also a real barrier to
progress... "progress" defined as: the evolution of a domain from
general to special, coarse to fine.

--
glen e. p. ropella, 971-219-3846, http://tempusdictum.com


============================================================
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

[glen ep ropella]

Günther Greindl wrote:
> Well, depends on what you want to do - developing _new_ theories is best
> done via metaphor; to get a qualitative feel for the stuff; speculative
> philosophy, if you like (that is indeed what I like to do :-))
>
> But to make it into science, which means that you can make predictive
> models certainly means mathematizing the theory.

I agree with your gist but not your specific words. [grin]  All pursuit
of truth is science, regardless of the language.  So, developing new
theories with metaphor _is_ science (as long as the theories are testable).

And mathematization isn't necessary for prediction, unless you really
widen the definition of "mathematics" to mean even qualitative
distinctions like "dead" or "alive".  I don't think, for example, a
physician is really describing her patient mathematically when she
hypothesizes that placing leeches on them will cure them of consumption.
  Yet, an experiment can be devised to (for the most part) falsify that
hypothesis.  So, science can be done without mathematics.

But it is _coarse_ science.  To be refined (or complete), you definitely
need math.

--
glen e. p. ropella, 971-219-3846, http://tempusdictum.com


============================================================
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]

Carl wrote:
> A tract on how the history might work, again, *sigh*:
>
> http://www.dcorfield.pwp.blueyonder.co.uk/HowMathematicians.pdf
Given a master with power and an apprentice without, don't see why the
genealogical view is necessarily at odds with tradition-constituted
enquiry -- such that one could say science was proceeding in one way or
the other.   It's just a question of intent.

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

[Mikhail Gorelkin]

Perhaps, we will come to better understanding of math if we see ***what math is not***. Here is Gregory Chaitin's Alan Turing Lecture on Computing and Philosophy, Mälardalen University, 2005:

 

www.youtube.com/watch?v=Rr0fOGeS7DE
www.youtube.com/watch?v=3bacYDSy19Q
www.youtube.com/watch?v=xaAhPo5KKUI
www.youtube.com/watch?v=0sjHUuL22hQ
www.youtube.com/watch?v=tW4a01hS3FU
www.youtube.com/watch?v=JbwRwX1ILpc
www.youtube.com/watch?v=zDl9L-_d8wk

 

--Mikhail Gorelkin

 

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

From: [hidden email]

To: [hidden email]

Sent: Friday, July 11, 2008 6:10 PM

Subject: Re: [FRIAM] Mathematics and Music

Prof David West wrote:

>
>> We have also talked about the lack of rigorous mathematical 
>> representation of complexity and that being a barrier to progress
>> in the science. 
>
>
> the idea of magic raised your hackles - the above sentence raises mine.
>
> implicit in the sentence is some variation of "mathematics is a better /
> superior / privileged / real language compared to all other languages
> used by humans to think and therefore we cannot really think properly or
> rigorously unless we are thinking mathematically."

I don't think that inference is implied by that sentence.  I so believe
math is a better language with which to describe reality than, say,
English.  But, that's not what the sentence above says.  The sentence
above states that a _lack_ of math rigor is a barrier to one particular
domain: plectics.

Your inference goes quite a bit further than the David's sentence.

> this annoying attitude is expressed / believed by a majority of
> intellectuals and academicians - not just mathematicians.  We cannot be
> "scientists" unless we 'mathematize' our field of enquiry.

And although I believe that math is the best known language for
describing reality, I don't believe that one must mathematize every
scientific field or that one cannot be a scientist without mathematizing
their field.

Science is the search for truth.  And truth can be sought using any
language... any language at all.  Some domains, particularly the ones
resistant to rigor are best studied with languages that have a high
tolerance for ambiguity... e.g. English.

Some domains that are not so resistant to rigor are best studied with
math.  Often, it takes a great deal of work using ambiguity tolerant
languages like English before an ambiguity intolerant language like math
can be effectively used.

If and when less ambiguous languages can be used, _then_ those languages
become more effective than the more ambiguous languages.

 From 50,000 metaphorical feet, this can be seen as a simple case of
specialization.  A generalist uses coarse tools and a specialist uses
fine tools.  Math is a fine tool that can only be used after the
generalists have done their upstream work in the domain.  Neither is
really "better", of course, when taking a synoptic view of the whole
evolution of the domain.  But math is definitely more refined... more
special.

> Interestingly enough, all advances in science stem from the uses of
> metaphor - not mathematics.  (see Quine)  The premature rush to abandon
> the language of metaphor and publish using arcane squiggles is the real
> - in my not very humble opinion - barrier to progress.

I agree.  Likewise, the tendency to stick with a coarse language when a
more refined language is called for is also a real barrier to
progress... "progress" defined as: the evolution of a domain from
general to special, coarse to fine.

--
glen e. p. ropella, 971-219-3846, http://tempusdictum.com


============================================================
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

[Carl Tollander]

Well, the geneological enquiry (as described) seemed more adversarial
than the traditional - the G guy is trying to discredit the other guy by
showing that he is just on a power trip of some sort.  I tend to look at
them as subtractive (G) and additive (T) sculpture - complementary if
some common goal is in mind, but the G guy never gets there, as he has
no motivation or handy mechanism to do so.  Then again, one has to
recognize that this characterization leans dangerously towards using the
G approach to criticize the G approach (though I think Corfield realizes
that and deals with it).

C.

Marcus G. Daniels wrote:

> Carl wrote:
>  
>> A tract on how the history might work, again, *sigh*:
>>
>> http://www.dcorfield.pwp.blueyonder.co.uk/HowMathematicians.pdf
>>    
> Given a master with power and an apprentice without, don't see why the
> genealogical view is necessarily at odds with tradition-constituted
> enquiry -- such that one could say science was proceeding in one way or
> the other.   It's just a question of intent.
>
> 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
lectures, archives, unsubscribe, maps at http://www.friam.org

[Marcus G. Daniels]

Carl Tollander wrote:
> the G guy is trying to discredit the other guy by
> showing that he is just on a power trip of some sort.  I tend to look at
> them as subtractive (G) and additive (T) sculpture - complementary if
> some common goal is in mind, but the G guy never gets there, as he has
> no motivation or handy mechanism to do so.  
Yet the Will to Power is served by discovery and invention, as well as
by criticism.   A risk for the T guy is that the `intellectuals' in his
community are not acting in good faith and not trying to do more than
just refine a self-consistent story, which can then be passed on as the
canon.   So it could be the reverse, the T guys are the subtractive or
inhibitory player.  

Imagine optimizing a function of many variables using hillclimbing.  In
a bumpy landscape, the single trajectory (the community) will soon get
stuck at a local optimum, even though up to that point progress was
being made.   Better not to follow any search rules and just randomly
pick points for a while (multiple trajectories/communities/individuals).
Put another way, there are countless questions to ask, and certain
communities may serve just to create a comfortable consensus reality
which then fails to explore a problem thoroughly enough.

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

[Günther Greindl]

Glen,

> I agree with your gist but not your specific words. [grin]

:-)

> All pursuit
> of truth is science, regardless of the language.  So, developing new
> theories with metaphor _is_ science (as long as the theories are testable).

Ok, I agree. I like your distinction (below) between coarse science vs
refined/exact science.

> And mathematization isn't necessary for prediction, unless you really
> widen the definition of "mathematics" to mean even qualitative
> distinctions like "dead" or "alive".  I don't think, for example, a
> physician is really describing her patient mathematically when she
> hypothesizes that placing leeches on them will cure them of consumption.

Hmm - in the background he will have hypotheses; knowledge which is
implicit in the neural weigthing in his brain (representing the evidence
he has seen and categorized). So the physician has a mathematical
(probabilistic) model of the situation, albeit maybe not
verbalized/symbolized. He is probably not even aware of the mathamtics
his brain embodies.

> hypothesis.  So, science can be done without mathematics.
> But it is _coarse_ science.  To be refined (or complete), you definitely
> need math.

Truthseeking = science; we agree. Coarse science (metaphor etc) could be
subsymbolic science: knowledge that exists in individual brains about
the world and which can be incompletely conveyed via metaphor, the
metaphor being the result of (incomplete) introspection of the scientist
into his own thought processes.

When you go mathematical, you make it explicit. Knowledge can be
transferred exactly. You can even mechanize it, meaning that you do not
rely on neural weighting of the brain to which you communicate (drawing
on the other person's experience of living in the same world as you
actually).

Cheers,
Günther

--
Günther Greindl
Department of Philosophy of Science
University of Vienna
[hidden email]
http://www.univie.ac.at/Wissenschaftstheorie/

Blog: http://dao.complexitystudies.org/
Site: http://www.complexitystudies.org/

Research Proposal:
http://www.complexitystudies.org/ph.d.-thesis.html


============================================================
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