Is programming a mathematical formalism

[Nick Thompson]

Ever since I first came to Santa Fe, and joined the extensive  computation
culture here, I felt I have detected in the software people here something
equivalent to the physics- envy that we psychologists are prone to: let's
call it math-envy.  Math-Envy seems to be that while programming is subject
to the vicissitudes of any linguistic enterprise, mathematics displays true
formalism.... "you always know where you stand" in mathematics.  

The more I have read ... most recently Rosen, Reuben Hersh, George Laykof,
Monk's biolography of Wittgenstein --- the more it seems that the best one
can say of mathematics is that "If you know where you are standing in
mathematics, you know where you stand" in mathematics.  Take Zero for
instance, and minus numbers, and roots of minus numbers, etc., etc.  All of
these things are metaphoric extensions and, as Laykof points out,  in fact
zero is different depending on which of several metaphors one has in mind
when one is using it.  Thus, the sense of safety one gets in mathematics
comes from the tendancy of mathematicians to hide out in deep silos, rather
than from a greater power or universality of their inter-silo discourse.
It is the same sense of safety that one gets in any monastery.  Or, I
imagine, that one gets from deep involvement in any programming language.  

Now, the proposition having been stated so baldly -- and no doubt ineptly
-- by an outsider, I suspect that ALL mathematicians on the list will now
agree that the case has been OVER stated and that, whatever the differences
in degree of formalism within the various forms of mathematics, all
mathematics is clearer than other forms of argument, such as plain old
vanilla philosophy,  or, say,  experiment and proof in psychology.  Getting
you all to agree in this way will have been my highest achievement of the
day.  

Nick  

Nicholas S. Thompson
Emeritus Professor of Psychology and Ethology,
Clark University ([hidden email])







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[glen ep ropella]

Thus spake Nicholas Thompson circa 10/01/2008 10:01 AM:
> Ever since I first came to Santa Fe, and joined the extensive  computation
> culture here, I felt I have detected in the software people here something
> equivalent to the physics- envy that we psychologists are prone to: let's
> call it math-envy.  Math-Envy seems to be that while programming is subject
> to the vicissitudes of any linguistic enterprise, mathematics displays true
> formalism.... "you always know where you stand" in mathematics.  

Which character does this sense of math-envy seem to you?

1) mathematical _skills_ envy -- i.e. computationalists wish they were
better mathematicians, or

2) mathematical _progress_ envy -- i.e. computationalists wish the
discrete math of computation had as much theorem-proof infrastructure as
continuum (and linear) math?

The distinction is clear to me.  I _definitely_ envy traditional
mathematics as a body of knowledge because it has had so many years and
so many brilliant minds working on that infrastructure.  If I want to,
e.g., learn about fluid dynamics, I have a plethora of _textbooks_,
hammered out over decades, to which I can turn.  But if I want to learn
about, say, impredicative definitions, I have to bounce between
philosophy, ill-written stuff like Rosen's work, category theory, etc.

In contrast, I don't experience (1) type envy any more than I, e.g.,
wish I could build a house or fix my car.  The envy is there; but, it's
intellectually mitigated by knowing that I chose not to learn those
skills as thoroughly as I chose to learn other skills.

When I think of (2) type envy, I wish I were born, like, 100 years from
now so I wouldn't have to work so !@$@#$%# hard to V&V a computer model.

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


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[Phil Henshaw-2]

Or to paraphrase, if I may Nick, "Simple clear math has no environment.
Math with an environment is no longer simple and clear".

Phil

> -----Original Message-----
> From: [hidden email] [mailto:[hidden email]] On
> Behalf Of Nicholas Thompson
> Sent: Wednesday, October 01, 2008 1:01 PM
> To: [hidden email]
> Subject: [FRIAM] Is programming a mathematical formalism
>
> Ever since I first came to Santa Fe, and joined the extensive
> computation
> culture here, I felt I have detected in the software people here
> something
> equivalent to the physics- envy that we psychologists are prone to:
> let's
> call it math-envy.  Math-Envy seems to be that while programming is
> subject
> to the vicissitudes of any linguistic enterprise, mathematics displays
> true
> formalism.... "you always know where you stand" in mathematics.
>
> The more I have read ... most recently Rosen, Reuben Hersh, George
> Laykof,
> Monk's biolography of Wittgenstein --- the more it seems that the best
> one
> can say of mathematics is that "If you know where you are standing in
> mathematics, you know where you stand" in mathematics.  Take Zero for
> instance, and minus numbers, and roots of minus numbers, etc., etc.
> All of
> these things are metaphoric extensions and, as Laykof points out,  in
> fact
> zero is different depending on which of several metaphors one has in
> mind
> when one is using it.  Thus, the sense of safety one gets in
> mathematics
> comes from the tendancy of mathematicians to hide out in deep silos,
> rather
> than from a greater power or universality of their inter-silo
> discourse.
> It is the same sense of safety that one gets in any monastery.  Or, I
> imagine, that one gets from deep involvement in any programming
> language.
>
> Now, the proposition having been stated so baldly -- and no doubt
> ineptly
> -- by an outsider, I suspect that ALL mathematicians on the list will
> now
> agree that the case has been OVER stated and that, whatever the
> differences
> in degree of formalism within the various forms of mathematics, all
> mathematics is clearer than other forms of argument, such as plain old
> vanilla philosophy,  or, say,  experiment and proof in psychology.
> Getting
> you all to agree in this way will have been my highest achievement of
> the
> day.
>
> Nick
>
> 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

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[Russ Abbott]

Excellent points -- although they sidestep Nick's issue -- which I take to be that some software people (although not you or I) wish that software were as apparently definitive as mathematics.  Mathematics has an aura of certainly -- even the certainty about uncertainty seems certain. Software is just code that changes from moment to moment depending on the whim of the developer or customer. Wouldn't it nice (Nick is saying that some software people seem to think) if software were as certain as mathematics.

Of course software can't be as certain as mathematics since it's a constructive discipline. We create new worlds, and the new worlds are in some real sense arbitrary. Mathematics proves things about existing worlds.  Of course mathematics also creates new worlds to prove things about, e.g., Euclidean and non-Euclidean geometry, but in some ways that's similar to software libraries.

Is it possible to V&V mathematics models of reality more easily/effectively/definitively than software models of reality? I doubt it. The only advantage mathematics has is that (perhaps) one has somewhat more confidence in the internal structure of the model, i.e., how the model behaves.  But if the model is complex enough, even that advantage disappears.

-- Russ

On Wed, Oct 1, 2008 at 11:05 AM, glen e. p. ropella <[hidden email]> wrote:

Thus spake Nicholas Thompson circa 10/01/2008 10:01 AM:
> Ever since I first came to Santa Fe, and joined the extensive  computation
> culture here, I felt I have detected in the software people here something
> equivalent to the physics- envy that we psychologists are prone to: let's
> call it math-envy.  Math-Envy seems to be that while programming is subject
> to the vicissitudes of any linguistic enterprise, mathematics displays true
> formalism.... "you always know where you stand" in mathematics.

Which character does this sense of math-envy seem to you?

1) mathematical _skills_ envy -- i.e. computationalists wish they were
better mathematicians, or

2) mathematical _progress_ envy -- i.e. computationalists wish the
discrete math of computation had as much theorem-proof infrastructure as
continuum (and linear) math?

The distinction is clear to me.  I _definitely_ envy traditional
mathematics as a body of knowledge because it has had so many years and
so many brilliant minds working on that infrastructure.  If I want to,
e.g., learn about fluid dynamics, I have a plethora of _textbooks_,
hammered out over decades, to which I can turn.  But if I want to learn
about, say, impredicative definitions, I have to bounce between
philosophy, ill-written stuff like Rosen's work, category theory, etc.

In contrast, I don't experience (1) type envy any more than I, e.g.,
wish I could build a house or fix my car.  The envy is there; but, it's
intellectually mitigated by knowing that I chose not to learn those
skills as thoroughly as I chose to learn other skills.

When I think of (2) type envy, I wish I were born, like, 100 years from
now so I wouldn't have to work so !@$@#$%# hard to V&V a computer model.

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


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

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[Robert Holmes]

Nick,

Is programming a mathematical formalism? No. I know that when I'm cranking out Python scripts I am not doing any math. Is computer science a mathematical formalism? Yes. When I'm trying to work out whether my algorithm scales as N**2 or N.log.N, I'm doing math.

For an enlightening (and more than a little provocative) discussion of this difference, check out Mooney's "Computing as an Experimental Science or Exaggerated Formalist Rhetoric Considered Harmful" at http://www.cs.utexas.edu/~mooney/talks/expCS.ppt

Robert

On Wed, Oct 1, 2008 at 7:01 PM, Nicholas Thompson <[hidden email]> wrote:

Ever since I first came to Santa Fe, and joined the extensive  computation
culture here, I felt I have detected in the software people here something
equivalent to the physics- envy that we psychologists are prone to: let's
call it math-envy.  Math-Envy seems to be that while programming is subject
to the vicissitudes of any linguistic enterprise, mathematics displays true
formalism.... "you always know where you stand" in mathematics.

The more I have read ... most recently Rosen, Reuben Hersh, George Laykof,
Monk's biolography of Wittgenstein --- the more it seems that the best one
can say of mathematics is that "If you know where you are standing in
mathematics, you know where you stand" in mathematics.  Take Zero for
instance, and minus numbers, and roots of minus numbers, etc., etc.  All of
these things are metaphoric extensions and, as Laykof points out,  in fact
zero is different depending on which of several metaphors one has in mind
when one is using it.  Thus, the sense of safety one gets in mathematics
comes from the tendancy of mathematicians to hide out in deep silos, rather
than from a greater power or universality of their inter-silo discourse.
It is the same sense of safety that one gets in any monastery.  Or, I
imagine, that one gets from deep involvement in any programming language.

Now, the proposition having been stated so baldly -- and no doubt ineptly
-- by an outsider, I suspect that ALL mathematicians on the list will now
agree that the case has been OVER stated and that, whatever the differences
in degree of formalism within the various forms of mathematics, all
mathematics is clearer than other forms of argument, such as plain old
vanilla philosophy,  or, say,  experiment and proof in psychology.  Getting
you all to agree in this way will have been my highest achievement of the
day.

Nick

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
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[glen ep ropella]

Thus spake Robert Holmes circa 10/01/2008 11:29 AM:
> Is programming a mathematical formalism? No. I know that when I'm cranking
> out Python scripts I am not doing any math.

Just to be clear, programming is the _act_ of constructing a program.
As an act, it is not a formalism.  However, the program produced is a
construct within a particular formalism.  To boot, that formalism is a
mathematical formalism.

So, when you are programming, you are doing mathematics, even if you
don't realize it.  The same is true of the child counting on her
fingers.  She's doing mathematics even though she may not realize it.
The same is true of the plumbing contractor when she _figures_ out how
to lay pipe in a house.  She's doing math, even though she may not
realize it.

Programming is (a form of) mathematics.

But I don't want to give the impression that _everything_ is math.  When
we construct an actual/physical object, the object is not (necessarily)
a construct within a particular formalism.  So, when we build something,
say, a chair, we may or may not be doing math.  If we did all the
figuring prior to the construction, then the construction phase isn't
mathematics.  If, however, we use the various pieces to measure the
other pieces and figure things out during the construction process, then
we're doing math.

So, actions (and sensing) are not math.  Of course, Guenther will
probably pop back in and say that _if_ the entire universe is a
mathematical formalism and all things in the universe are constructs in
that formalism, then all actions and sensing are math, as well.  But
aside from that pathological ontological conclusion [grin], there are
non-math things.

I would also posit that general thought (not calculation or "figuring")
may be non-mathematical.  But I can't defend that position very well.

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


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[Russ Abbott]

Is catching/throwing a ball math? A robot would do these things using math. But we don't, and we don't prove the result.  We just check out the result against reality. So why call it math? Or if you wouldn't call it math, how does it differ from writing a program, which also produces a result/product/effect. We may not treat that result as a mathematical object. As with catching/throwing a ball, we often just check it out against the reality of its use.

-- Russ

On Wed, Oct 1, 2008 at 11:48 AM, glen e. p. ropella <[hidden email]> wrote:

Thus spake Robert Holmes circa 10/01/2008 11:29 AM:
> Is programming a mathematical formalism? No. I know that when I'm cranking
> out Python scripts I am not doing any math.

Just to be clear, programming is the _act_ of constructing a program.
As an act, it is not a formalism.  However, the program produced is a
construct within a particular formalism.  To boot, that formalism is a
mathematical formalism.

So, when you are programming, you are doing mathematics, even if you
don't realize it.  The same is true of the child counting on her
fingers.  She's doing mathematics even though she may not realize it.
The same is true of the plumbing contractor when she _figures_ out how
to lay pipe in a house.  She's doing math, even though she may not
realize it.

Programming is (a form of) mathematics.

But I don't want to give the impression that _everything_ is math.  When
we construct an actual/physical object, the object is not (necessarily)
a construct within a particular formalism.  So, when we build something,
say, a chair, we may or may not be doing math.  If we did all the
figuring prior to the construction, then the construction phase isn't
mathematics.  If, however, we use the various pieces to measure the
other pieces and figure things out during the construction process, then
we're doing math.

So, actions (and sensing) are not math.  Of course, Guenther will
probably pop back in and say that _if_ the entire universe is a
mathematical formalism and all things in the universe are constructs in
that formalism, then all actions and sensing are math, as well.  But
aside from that pathological ontological conclusion [grin], there are
non-math things.

I would also posit that general thought (not calculation or "figuring")
may be non-mathematical.  But I can't defend that position very well.

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


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[glen ep ropella]

Thus spake Russ Abbott circa 10/01/2008 11:56 AM:
> Is catching/throwing a ball math? A robot would do these things using math.
> But we don't, and we don't prove the result.  We just check out the result
> against reality. So why call it math?

I would not call that math.

> Or if you wouldn't call it math, how
> does it differ from writing a program, which also produces a
> result/product/effect. We may not treat that result as a mathematical
> object. As with catching/throwing a ball, we often just check it out against
> the reality of its use.

It differs from math because there is no way to achieve a compilation
failure (or a run-time failure in the case of dynamic languages) for
throwing a ball.

I.e. there is no correct (especially syntactically correct) way to throw
a ball.  Likewise, there is no incorrect way to throw a ball.  But there
are [in]correct programs.

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


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[Russ Abbott]

I would liken a syntax error to tripping while going after a ball. Neither is really what we are talking about.  It's the semantics of the intended action if actually carried out.  No?

-- Russ

On Wed, Oct 1, 2008 at 12:05 PM, glen e. p. ropella <[hidden email]> wrote:

Thus spake Russ Abbott circa 10/01/2008 11:56 AM:

> Is catching/throwing a ball math? A robot would do these things using math.
> But we don't, and we don't prove the result.  We just check out the result
> against reality. So why call it math?

I would not call that math.

> Or if you wouldn't call it math, how
> does it differ from writing a program, which also produces a
> result/product/effect. We may not treat that result as a mathematical
> object. As with catching/throwing a ball, we often just check it out against
> the reality of its use.

It differs from math because there is no way to achieve a compilation
failure (or a run-time failure in the case of dynamic languages) for
throwing a ball.

I.e. there is no correct (especially syntactically correct) way to throw
a ball.  Likewise, there is no incorrect way to throw a ball.  But there
are [in]correct programs.

--

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


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[Marcus G. Daniels]

Robert Holmes wrote:
> Is programming a mathematical formalism? No. I know that when I'm
> cranking out Python scripts I am not doing any math. Is computer
> science a mathematical formalism? Yes. When I'm trying to work out
> whether my algorithm scales as N**2 or N.log.N, I'm doing math.
A compiler is in the position to determine that.   Is it doing math?  
Examples of current work:

http://www.osl.iu.edu/~kyross/pub/wgp2006-paper.pdf
http://llvm.org/devmtg/2008-08/Kremenek_StaticAnalyzer.pdf
http://www.microsoft.com/windows/cse/pa_projects.mspx

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[Robert Holmes]

Thus spake Glen...

Just to be clear, programming is the _act_ of constructing a program.
As an act, it is not a formalism.  However, the program produced is a
construct within a particular formalism.  To boot, that formalism is a
mathematical formalism.

Hmmm.... not sure about that Glen. Seems to me that your "formalism" can be pretty freely applied. So give me a specific example - when I'm coding Python what is the specific formalism that I am using? Please feel free to use equations.

Or does your formalism just mean "something with a syntax"? In which case French is math as well, as is English, as is music as is (continue ad nauseam)...

R

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[glen ep ropella]

Thus spake Russ Abbott circa 10/01/2008 12:23 PM:
> I would liken a syntax error to tripping while going after a ball. Neither
> is really what we are talking about.  It's the semantics of the intended
> action if actually carried out.  No?

I disagree.  Tripping on approach is not a syntax error; it's another
action, albeit an unintended one.  Indeed, you can easily still throw
the ball even if you've tripped.  That's what we're talking about.

All acts and senses _always_ have meaning in context, with or without
symbols.  Syntax is meaningless.  Syntax is very different from acting
or sensing.

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


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[Russell Standish]

Actually a robot would probably do it the same way we do - trial and
error with some kind of feedback loop. Solving differential equations
tends not to work too well in controlling robots.

But is the feedback loop used by the robot maths? The computer code
is, the formal structure of the loop is, a model of something using it
is. The execution of the code, however, is not maths, AFAICS.

Cheers

On Wed, Oct 01, 2008 at 11:56:20AM -0700, Russ Abbott wrote:

> Is catching/throwing a ball math? A robot would do these things using math.
> But we don't, and we don't prove the result.  We just check out the result
> against reality. So why call it math? Or if you wouldn't call it math, how
> does it differ from writing a program, which also produces a
> result/product/effect. We may not treat that result as a mathematical
> object. As with catching/throwing a ball, we often just check it out against
> the reality of its use.
>
> -- Russ
>
>
> On Wed, Oct 1, 2008 at 11:48 AM, glen e. p. ropella
> <[hidden email]>wrote:
>
> > Thus spake Robert Holmes circa 10/01/2008 11:29 AM:
> > > Is programming a mathematical formalism? No. I know that when I'm
> > cranking
> > > out Python scripts I am not doing any math.
> >
> > Just to be clear, programming is the _act_ of constructing a program.
> > As an act, it is not a formalism.  However, the program produced is a
> > construct within a particular formalism.  To boot, that formalism is a
> > mathematical formalism.
> >
> > So, when you are programming, you are doing mathematics, even if you
> > don't realize it.  The same is true of the child counting on her
> > fingers.  She's doing mathematics even though she may not realize it.
> > The same is true of the plumbing contractor when she _figures_ out how
> > to lay pipe in a house.  She's doing math, even though she may not
> > realize it.
> >
> > Programming is (a form of) mathematics.
> >
> > But I don't want to give the impression that _everything_ is math.  When
> > we construct an actual/physical object, the object is not (necessarily)
> > a construct within a particular formalism.  So, when we build something,
> > say, a chair, we may or may not be doing math.  If we did all the
> > figuring prior to the construction, then the construction phase isn't
> > mathematics.  If, however, we use the various pieces to measure the
> > other pieces and figure things out during the construction process, then
> > we're doing math.
> >
> > So, actions (and sensing) are not math.  Of course, Guenther will
> > probably pop back in and say that _if_ the entire universe is a
> > mathematical formalism and all things in the universe are constructs in
> > that formalism, then all actions and sensing are math, as well.  But
> > aside from that pathological ontological conclusion [grin], there are
> > non-math things.
> >
> > I would also posit that general thought (not calculation or "figuring")
> > may be non-mathematical.  But I can't defend that position very well.
> >
> > --
> > 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
> >

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--

----------------------------------------------------------------------------
A/Prof Russell Standish                  Phone [phone] (mobile)
Mathematics                        
UNSW SYDNEY 2052                 [hidden email]
Australia                                http://www.hpcoders.com.au
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[glen ep ropella]

Thus spake Robert Holmes circa 10/01/2008 12:44 PM:
> Hmmm.... not sure about that Glen. Seems to me that your "formalism" can be
> pretty freely applied. So give me a specific example - when I'm coding
> Python what is the specific formalism that I am using? Please feel free to
> use equations.

It is pretty free because it's a turing complete formal system.  Here
are the general categories of the alphabet:

None, NotImplemented, Ellipsis, Numbers, Sequences, Set types, Mappings,
Callable types, Modules, Classes, Class instances, Files, Internal types


And here are some of the inferential operators for deducing one
statement from previous statements:

+, -, /, *, %, <<, >>, lambda, if, for, while, try, etc.

It would take quite a bit of space to outline the entire formal system.
 Feel free to consult:

   http://docs.python.org/ref/ref.html

> Or does your formalism just mean "something with a syntax"? In which case
> French is math as well, as is English, as is music as is (continue ad
> nauseam)...

Excellent point.  However, neither English nor French have a strict
syntax.  For example, I can say something like "You an apple, have." and
you will understand what I'm saying.  That's why we found Yoda to be
such a cute character in those movies... well, that and because he's
ugly, short, and green... and can kick ass with a light saber.

No syntax error arises when I speak such "incorrect" sentences.  That's
because English is a language for describing reality/thoughts.
Mathematics, too, is a language.  And one can formulate incorrect
sentences in math, too.  Similarly, a good math teacher can even read
the correct implication from an incorrectly stated mathematical sentence
(math teachers do this all the time to determine how to teach their
ailing students).

However, in any _particular_ formalism (formulated mathematically), an
incorrect sentence will be undoubtably incoherent.  That's different
from a _false_ sentence.  E.g. "1 + 1 = 3" is a false sentence.  But
"1/inf" is an incoherent sentence (statement of existence) -- i.e. it is
undefined.

Is it coincidence that an incorrect Python sentence immediately halts
the whole process, too?  No, it's not a coincidence.  It's because
Python is a formalism and every statement is either parsable or not.
There is no middle ground.... like tripping when winding up a pitch or
putting the verb at the end of an English sentence.

Python is a formal system and correct programs written in Python are
valid mathematical transformations (deductions) from initial to final
conditions.

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


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[Marcus G. Daniels]

Russell Standish wrote:
> Actually a robot would probably do it the same way we do - trial and
> error with some kind of feedback loop.
>  
Excuse a side remark on ABM toolkit stuff.

I hadn't played with Breve (http://breve.sf.net) until recently.  Some
relevant features:

1) 3d with collision detection, and event callbacks on collisions.

2) Native code / C++ implementation

3) Several language options, including Python, Steve, Lisp, and Push.
Push is a language intended for evolution of code (genetic programming).
(overhead of these seem not to be an obstacle for the 3d models, which
are bottlenecked on physics and 3d operations, much of that accelerated
by GPU hardware by way of OpenGL)



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[Kenneth Lloyd]

Russell,

You are absolutely right.  BioDynamic's Big Dog learned to walk over uneven
ground using evolutionary neural networks. So are ANN's math?  Well, yes (my
answer) and no.  Actually, it depends on your concept of math - which I
sense is rather rigidly defined within this discussion.  ANN's can solve
non-analytic equations, which are beyond differential equations.

http://www.youtube.com/watch?v=W1czBcnX1Ww 

Ken

> -----Original Message-----
> From: [hidden email]
> [mailto:[hidden email]] On Behalf Of Russell Standish
> Sent: Wednesday, October 01, 2008 3:50 PM
> To: [hidden email]; The Friday Morning Applied
> Complexity Coffee Group
> Subject: Re: [FRIAM] Is programming a mathematical formalism
>
> Actually a robot would probably do it the same way we do -
> trial and error with some kind of feedback loop. Solving
> differential equations tends not to work too well in
> controlling robots.
>
> But is the feedback loop used by the robot maths? The
> computer code is, the formal structure of the loop is, a
> model of something using it is. The execution of the code,
> however, is not maths, AFAICS.
>
> Cheers
>
> On Wed, Oct 01, 2008 at 11:56:20AM -0700, Russ Abbott wrote:
> > Is catching/throwing a ball math? A robot would do these
> things using math.
> > But we don't, and we don't prove the result.  We just check out the
> > result against reality. So why call it math? Or if you
> wouldn't call
> > it math, how does it differ from writing a program, which also
> > produces a result/product/effect. We may not treat that result as a
> > mathematical object. As with catching/throwing a ball, we
> often just
> > check it out against the reality of its use.
> >
> > -- Russ
> >
> >
> > On Wed, Oct 1, 2008 at 11:48 AM, glen e. p. ropella
> > <[hidden email]>wrote:
> >
> > > Thus spake Robert Holmes circa 10/01/2008 11:29 AM:
> > > > Is programming a mathematical formalism? No. I know
> that when I'm
> > > cranking
> > > > out Python scripts I am not doing any math.
> > >
> > > Just to be clear, programming is the _act_ of
> constructing a program.
> > > As an act, it is not a formalism.  However, the program
> produced is
> > > a construct within a particular formalism.  To boot, that
> formalism
> > > is a mathematical formalism.
> > >
> > > So, when you are programming, you are doing mathematics,
> even if you
> > > don't realize it.  The same is true of the child counting on her
> > > fingers.  She's doing mathematics even though she may not
> realize it.
> > > The same is true of the plumbing contractor when she
> _figures_ out
> > > how to lay pipe in a house.  She's doing math, even
> though she may
> > > not realize it.
> > >
> > > Programming is (a form of) mathematics.
> > >
> > > But I don't want to give the impression that _everything_
> is math.  
> > > When we construct an actual/physical object, the object is not
> > > (necessarily) a construct within a particular formalism.  
> So, when
> > > we build something, say, a chair, we may or may not be
> doing math.  
> > > If we did all the figuring prior to the construction, then the
> > > construction phase isn't mathematics.  If, however, we use the
> > > various pieces to measure the other pieces and figure things out
> > > during the construction process, then we're doing math.
> > >
> > > So, actions (and sensing) are not math.  Of course, Guenther will
> > > probably pop back in and say that _if_ the entire universe is a
> > > mathematical formalism and all things in the universe are
> constructs
> > > in that formalism, then all actions and sensing are math,
> as well.  
> > > But aside from that pathological ontological conclusion [grin],
> > > there are non-math things.
> > >
> > > I would also posit that general thought (not calculation or
> > > "figuring") may be non-mathematical.  But I can't defend
> that position very well.
> > >
> > > --
> > > 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
>
> --
>
> --------------------------------------------------------------
> --------------
> A/Prof Russell Standish                  Phone [phone] (mobile)
> Mathematics                        
> UNSW SYDNEY 2052                 [hidden email]
> Australia                                http://www.hpcoders.com.au
> --------------------------------------------------------------
> --------------
>
> ============================================================
> 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

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[Kenneth Lloyd]

Sorry, that was Boston Dynamics.  My bad.

> -----Original Message-----
> From: [hidden email]
> [mailto:[hidden email]] On Behalf Of Kenneth Lloyd
> Sent: Wednesday, October 01, 2008 5:15 PM
> To: 'The Friday Morning Applied Complexity Coffee Group'
> Subject: Re: [FRIAM] Is programming a mathematical formalism
>
> Russell,
>
> You are absolutely right.  BioDynamic's Big Dog learned to
> walk over uneven ground using evolutionary neural networks.
> So are ANN's math?  Well, yes (my
> answer) and no.  Actually, it depends on your concept of math
> - which I sense is rather rigidly defined within this
> discussion.  ANN's can solve non-analytic equations, which
> are beyond differential equations.
>
> http://www.youtube.com/watch?v=W1czBcnX1Ww 
>
> Ken
>
> > -----Original Message-----
> > From: [hidden email]
> > [mailto:[hidden email]] On Behalf Of Russell Standish
> > Sent: Wednesday, October 01, 2008 3:50 PM
> > To: [hidden email]; The Friday Morning Applied Complexity
> > Coffee Group
> > Subject: Re: [FRIAM] Is programming a mathematical formalism
> >
> > Actually a robot would probably do it the same way we do -
> trial and
> > error with some kind of feedback loop. Solving differential
> equations
> > tends not to work too well in controlling robots.
> >
> > But is the feedback loop used by the robot maths? The computer code
> > is, the formal structure of the loop is, a model of
> something using it
> > is. The execution of the code, however, is not maths, AFAICS.
> >
> > Cheers
> >
> > On Wed, Oct 01, 2008 at 11:56:20AM -0700, Russ Abbott wrote:
> > > Is catching/throwing a ball math? A robot would do these
> > things using math.
> > > But we don't, and we don't prove the result.  We just
> check out the
> > > result against reality. So why call it math? Or if you
> > wouldn't call
> > > it math, how does it differ from writing a program, which also
> > > produces a result/product/effect. We may not treat that
> result as a
> > > mathematical object. As with catching/throwing a ball, we
> > often just
> > > check it out against the reality of its use.
> > >
> > > -- Russ
> > >
> > >
> > > On Wed, Oct 1, 2008 at 11:48 AM, glen e. p. ropella
> > > <[hidden email]>wrote:
> > >
> > > > Thus spake Robert Holmes circa 10/01/2008 11:29 AM:
> > > > > Is programming a mathematical formalism? No. I know
> > that when I'm
> > > > cranking
> > > > > out Python scripts I am not doing any math.
> > > >
> > > > Just to be clear, programming is the _act_ of
> > constructing a program.
> > > > As an act, it is not a formalism.  However, the program
> > produced is
> > > > a construct within a particular formalism.  To boot, that
> > formalism
> > > > is a mathematical formalism.
> > > >
> > > > So, when you are programming, you are doing mathematics,
> > even if you
> > > > don't realize it.  The same is true of the child
> counting on her
> > > > fingers.  She's doing mathematics even though she may not
> > realize it.
> > > > The same is true of the plumbing contractor when she
> > _figures_ out
> > > > how to lay pipe in a house.  She's doing math, even
> > though she may
> > > > not realize it.
> > > >
> > > > Programming is (a form of) mathematics.
> > > >
> > > > But I don't want to give the impression that _everything_
> > is math.  
> > > > When we construct an actual/physical object, the object is not
> > > > (necessarily) a construct within a particular formalism.  
> > So, when
> > > > we build something, say, a chair, we may or may not be
> > doing math.  
> > > > If we did all the figuring prior to the construction, then the
> > > > construction phase isn't mathematics.  If, however, we use the
> > > > various pieces to measure the other pieces and figure
> things out
> > > > during the construction process, then we're doing math.
> > > >
> > > > So, actions (and sensing) are not math.  Of course,
> Guenther will
> > > > probably pop back in and say that _if_ the entire universe is a
> > > > mathematical formalism and all things in the universe are
> > constructs
> > > > in that formalism, then all actions and sensing are math,
> > as well.  
> > > > But aside from that pathological ontological conclusion [grin],
> > > > there are non-math things.
> > > >
> > > > I would also posit that general thought (not calculation or
> > > > "figuring") may be non-mathematical.  But I can't defend
> > that position very well.
> > > >
> > > > --
> > > > 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
> >
> > --
> >
> > --------------------------------------------------------------
> > --------------
> > A/Prof Russell Standish                  Phone [phone] (mobile)
> > Mathematics                        
> > UNSW SYDNEY 2052                 [hidden email]
> > Australia                                http://www.hpcoders.com.au
> > --------------------------------------------------------------
> > --------------
> >
> > ============================================================
> > 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
>
>
> ============================================================
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[Owen Densmore]

Nick: I'm a bit confused about what you'd like from this.

Paragraph 1: The observation that there may be Math-envy amongst  
programmers.
Paragraph 2: A reference to the prior threads on the philosophy of  
math along with a correct observations on silos .. or possibly a depth/
breadth contrast.
Paragraph 3: A nice statement on degree of formalism as pertains to  
computing and mathematics.

If you want an agreement to Paragraph 3, I'd have to be in the  
negative.  I'd also say that Math is beginning to have Computer-Envy,  
and to realize their notation is in the same state is Roman Numerals  
were before modern positional number formats.

Here's why.  After pondering the division between the practice of  
mathematicians and computer scientists, I came to the rather obvious  
that CS is a branch of Math.  I will be somewhat reductionist here by  
reducing "computing" to "algorithms".

So I don't have math envy as a CS guy, I just am aware how rich all  
the rest of Math is as Glen so nicely pointed out.  Your silo  
reference is germane here too: like in many disciplines, we tend to  
depth rather than breadth.

Now to get into really hot water.  Much of the division is the  
difference in syntax of mathematics .. called Mathematical Notation  
(MN) .. and the syntax of algorithms .. Scripts (or code).  This  
really is a bear when one tries to cross the boundaries.

It's horrid to express MN in Scripts.  The impedance mismatch is  
wild.  And much of MN is "ambiguous" in the sense that ab + 1 could  
mean the variable "ab" incremented by 1, or the product of the  
variable "a" and "b" then incremented.  Conventions are used for  
disambiguation. Math folks are now attempting to reconcile the  
differences, but its my guess that 2 centuries on, most of current MN  
will have been replaced by something more like APL or J syntax.

There is one other interesting difference, one that Knuth has done a  
superb job of discussing: the distinction between the continuous and  
discrete.  This is not strictly due to limitations in the precision of  
computer numbers.  It is a mindset.  Most Math folks tend to the  
"asymptotic" leap: presuming at some point moving from Sigma's to  
Integrals is appropriate.  Knuth begs to differ, and one of his best  
books, Concrete Mathematics, is about the joint of Cont[inuous and  
Dis]Crete mathematics.

    -- Owen


On Oct 1, 2008, at 11:01 AM, Nicholas Thompson wrote:

> Ever since I first came to Santa Fe, and joined the extensive  
> computation
> culture here, I felt I have detected in the software people here  
> something
> equivalent to the physics- envy that we psychologists are prone to:  
> let's
> call it math-envy.  Math-Envy seems to be that while programming is  
> subject
> to the vicissitudes of any linguistic enterprise, mathematics  
> displays true
> formalism.... "you always know where you stand" in mathematics.
>
> The more I have read ... most recently Rosen, Reuben Hersh, George  
> Laykof,
> Monk's biolography of Wittgenstein --- the more it seems that the  
> best one
> can say of mathematics is that "If you know where you are standing in
> mathematics, you know where you stand" in mathematics.  Take Zero for
> instance, and minus numbers, and roots of minus numbers, etc., etc.  
> All of
> these things are metaphoric extensions and, as Laykof points out,  
> in fact
> zero is different depending on which of several metaphors one has in  
> mind
> when one is using it.  Thus, the sense of safety one gets in  
> mathematics
> comes from the tendancy of mathematicians to hide out in deep silos,  
> rather
> than from a greater power or universality of their inter-silo  
> discourse.
> It is the same sense of safety that one gets in any monastery.  Or, I
> imagine, that one gets from deep involvement in any programming  
> language.
>
> Now, the proposition having been stated so baldly -- and no doubt  
> ineptly
> -- by an outsider, I suspect that ALL mathematicians on the list  
> will now
> agree that the case has been OVER stated and that, whatever the  
> differences
> in degree of formalism within the various forms of mathematics, all
> mathematics is clearer than other forms of argument, such as plain old
> vanilla philosophy,  or, say,  experiment and proof in psychology.  
> Getting
> you all to agree in this way will have been my highest achievement  
> of the
> day.
>
> Nick

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[Phil Henshaw-2]

Observing how the present diverges from the past should be useful, both for
becoming better able to control or capitalize on how nature works, but also
for better controlling ourselves to stop repeating past choices that would
be in error.  

I'm trying to share something of my experience and verifiable knowledge of
that, that is of some importance.   Some only see a fine line between
learning someone's tricks for making your own discoveries, and repeating
back the words they use to describe their own discoveries, but there's a
world of difference, of course.   I don't want to hear my empty words back,
I want to hear your full words reflecting your having made some of the same
observations.  Words are only meaningful if they represent shared
experience.  I think science can help us compare notes on our independent
observations of the divergent processes in nature, and to really learn
something by that.  

Growing rates and kinds of learning occur within relationship networks as
they multiply their organizational scale and complexity.  That applies to
projects that start small at home or work, to software, building plans or
businesses, industries, societies, etc, that get endlessly bigger in scale
and incorporate changes in kind ever faster.  I observe that when a complex
multiplication of relationships like that runs into an unexpected rush of
complications, it's often just before serious widespread failures occur.
It looks to me to be a signal that marks crossing a line toward
unmanageability for the system as a whole, marking an internal 'breaking
point'.  

Do any of you notice that rush of complications as a signal of self-controls
becoming, overextended, unresponsive and systems about to go "out of
control", like over driving the slop in your steering system?   It's also a
little like a juggler being thrown just one too many balls to keep in the
air all at once, and not dropping just the one but nearly all of them.  I
think it's a general property of divergent learning systems.   Do you guys
recognize any cases where organizational instability arises due to exceeding
the learning responses of the parts?  

If there were such a property of instability in growth, and if you
considered cybernetics to be the science of control, a principle of
self-control to avoid pushing learning responses out of control could be
called its "principal principle", i.e. don't overshoot.   That's what I
dubbed it anyway, the prudent choice to not push the learning demands of a
system beyond the responsiveness of its parts.  Does that make any sense in
terms of what you observe?



Phil Henshaw                                  ¸¸¸¸.·´ ¯ `·.¸¸¸¸
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
680 Ft. Washington Ave NY NY 10040                      
tel: [phone]   e-mail: [hidden email]     explorations:
www.synapse9.com   
"it's not finding what people say interesting, but finding the interest in
what they say"






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[Carl Tollander]

Nick,

Leave us not conflate clarity, concision and expressiveness.   One may
make tradeoffs, for example one may choose one computer language for its
large number of libraries and ability to say a great many things in many
ways, at the expense of concision and clarity.

As to envy, I think there is a kind of envy of the different kinds of
communities.  Compare, for example, the N-Category cafe with, say,
Slashdot.   In the latter, a CS person may begin to feel after a short
while that one is wasting one's time, in a way one does not in the
former, even if one does not consistently feel entirely sure of what is
being said in the former.

In contrast to the statement  "If you know where you are standing in
mathematics, you know where you stand", I would say "If you know where
you are standing in mathematics, you can appreciate better where you
*might* stand".  One can certainly have this appreciation in a CS world,
though I have a sense that in Mathematics there is a closer sense of the
history of one's particular community and therefore why people talk
about  particular mathematical subjects the way they do - the frames (as
Lakoff would use the term) are both more transparently indigenous and
explicit.  This seems to me particularly the case wrt algebra and
topology (oh yes and category theory); oddly, the more universal
something seems (e.g. Euclidean geometry), the less historically
grounded it feels.

I'm not sure of the origins of the notion that mathematical formalisms
convey "safety".  Surely one's appreciations are open to challenge;
somebody else drills a hole through one's cherished mappings, or opens
up some new field that in retrospect seems obvious to all in the midst
of  what one thought were  fundamental truths.   Mathematics seems a
more dangerous approach to reality; there are fewer "Turing Machine"
like constructs upon which one may rely.  It seems again that "safety"
is more a matter of taking refuge in the nature of the mathematical
community and its history.  This community and its history is not as
anecdotal as in many areas of science.  There is a kind of "mathematics
of the silos" that lets you explore one silo while also mapping it into
the others.  Both highly focused and highly open.

So, envy; I suppose so.   And if we can find ways to rationally bind our
model of how CS is done closer to the way Mathematics is done, Make The
Most Of It.

Unlike sausage and law, one can only love formalisms if one loves
watching them being made.

Carl



Nicholas Thompson wrote:

> Ever since I first came to Santa Fe, and joined the extensive  computation
> culture here, I felt I have detected in the software people here something
> equivalent to the physics- envy that we psychologists are prone to: let's
> call it math-envy.  Math-Envy seems to be that while programming is subject
> to the vicissitudes of any linguistic enterprise, mathematics displays true
> formalism.... "you always know where you stand" in mathematics.  
>
> The more I have read ... most recently Rosen, Reuben Hersh, George Laykof,
> Monk's biolography of Wittgenstein --- the more it seems that the best one
> can say of mathematics is that "If you know where you are standing in
> mathematics, you know where you stand" in mathematics.  Take Zero for
> instance, and minus numbers, and roots of minus numbers, etc., etc.  All of
> these things are metaphoric extensions and, as Laykof points out,  in fact
> zero is different depending on which of several metaphors one has in mind
> when one is using it.  Thus, the sense of safety one gets in mathematics
> comes from the tendancy of mathematicians to hide out in deep silos, rather
> than from a greater power or universality of their inter-silo discourse.
> It is the same sense of safety that one gets in any monastery.  Or, I
> imagine, that one gets from deep involvement in any programming language.  
>
> Now, the proposition having been stated so baldly -- and no doubt ineptly
> -- by an outsider, I suspect that ALL mathematicians on the list will now
> agree that the case has been OVER stated and that, whatever the differences
> in degree of formalism within the various forms of mathematics, all
> mathematics is clearer than other forms of argument, such as plain old
> vanilla philosophy,  or, say,  experiment and proof in psychology.  Getting
> you all to agree in this way will have been my highest achievement of the
> day.  
>
> Nick  
>
> 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
>
>  

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