Mathematics VS? Agent Based Modeling

[Nick Thompson]

Dear Friamers,

I have been engaged with a long correspondence with one of my friends at Clark, a mathematicain.  I was trying to entice him into teaching a Net Logo course with me next semester, and after some throat clearing, here was his response.  I find the debate so very interesting that I wanted to hear what you-all thought of it, and I got his permission to post it.    I will identify him as ( Mathematicial Colleague).   MC and I are old friends and those of you who know me know that I am given to .... uh.... rambunctious discourse.  So the tone here is my tone, not really his.  I think you will enjoy it.  

MC --More seriously, is there anything *mathematical* about
NetLogo modeling? My impression (without having gone to
the links below) is that it is just another--nicer looking,
easier-to-program, even conceptually cleaner--way to make
black boxes, and to that extent is no different from the Excel
spreadsheets that John Kennison occasionally pushes on people,
or the Java applets Dave Joyce programmed for you. Mathematics
may be *consumed* in the programming of the simulation, but there is
no mathematical analysis (and probably can't be), just an opaquely
imperspicuous *thing* with some toggles that can be adjusted so
as to create different--sometimes strikingly different--outputs.
So what, from a mathematical point of view? A mathematician,
when not acting as an engineer on hire, wants to *understand*
formal structures by formal means. Where's the understanding,
here? How is this different--from the point of view of a
mathematician who wants to do mathematics--from programs that
produce fractal images? Look, a cloud! Look, waves! Look,
a tiger's pelt! Pretty!

Even partial answers to the questions embedded in this bitter
rant are welcome, and of course counterrants are good, too.

(signed, MC)

P. S. . I think NetLogo would be perfect
for exploring the Heider-Michotte Phenomenon. If I had the
time (if, say, I were on sabbatical...), I would probably
re-learn Logo by learning NetLogo and then program some
Heideresque scenes. *That* box wouldn't be black; there
wouldn't necessarily be all that much mathematics in it,
but what there was would be pretty clear.


On 10 Mar 2005 at 12:57, Nicholas Thompson wrote:

NT> Well, WELL!
>
> May I have your permission to post your comments (anonymously, if you
> prefer) to the friam list. I would LOVE to see what they do with it.

> Here is what I would do with it.
>
> Development has two problems; how do you get simple (convergent) results
> out of complex imputs; and how do you get complex (divergent) outcomes out
> of simple imputs. Agent based model provides us with a way of
> illustrating both effects.

MC--It illustrates "that". Does it illustrate "how"?

> Following Fox-keller for a beat or two, I
> guess I would say that , a model is an aid to understanding only one
> understands the model.

MC-- Following Fox-Keller myself, now that you've reminded me of her
name, why is "agent based modeling" not exactly similar to making
crystal gardens and saying you've modeled Life Itself?

NT> I am under the illusion that working with agent
> based modeling will help me get a grip on emergence, in both its divergent
> and convergent forms.
>
> Can mathematics do that for me?

MC -- I dunno.  ....  It well may be that "working
with agent based modeling will help" you "get a grip on emergence,
in both its divergent and convergent forms". My expressed doubts
were that it will help you, or anyone, get a *mathematical* grip
(on anything). There are presumably as many ways of getting a grip
as there are ways of knowing (or constructing tribal lays). When
it's working for me, gnosis beats mathematics all hollow. But I
don't count on gnosis, and even if I could, it wouldn't be sensible
of me to conflate gnosis with the practice of mathematics--unless,
indeed, I had not only its power for myself, but also the additional
power (perhaps mediated by a peacock feather like Sri Wozzname used
to use) to cause it to strike everyone else with whom I wished to
share my new knowledge.

Here's a self-quotation from one of the two papers I'm trying to
finish for .... this week .... .

""Qualitative psychological research makes very little use
of mathematics as such: certain statistical methods may be
applied, and bits of jargon are occasionally appropriated
from mathematics for (what appears to mathematicians to be)
purely metaphorical use; but the concrete mathematical
structures and deductive processes characteristic of the
actual practice of mathematics, the ends to which working
mathematicians have coined their jargon, are neglected.

"(The following paragraph is an almost equally snarky description
of "quantitative psychological research".) I'm not going to
accuse you, FRIAM, or the NetLogo fans of being "qualitative".
What I haven't seen (and haven't looked for, today; so maybe
it's all there in the NetLogo website you pointed at, and I
will apologize profusely in a few weeks) are any of those
"concrete mathematical structures and deductive processes
characteristic of the actual practice of mathematics".

Just between the two of us, I keep having fears that the general
run of qualitative types ...  are cargo cultists (mathematically). ..."

signed MC
-------------- next part --------------
An HTML attachment was scrubbed...
URL: /pipermail/friam_redfish.com/attachments/20050310/24d628e3/attachment.htm

[Russell Standish]

I think mathematics is the study of formal systems, period. Therefore
an ABM system is as much mathematics as say computer algebra, or
solving a differential equation, whether numerically or symbolically.

That it can be quite difficult to actually understand what is
happening with an ABM shouldn't count against its formal
character. After all, who said mathematics was easy?

Cheers

PS - I'm aware my position contrasts with Stephen Wolfram's in NKS.

On Thu, Mar 10, 2005 at 06:17:09PM -0700, Nicholas Thompson wrote:

> Dear Friamers,
>
> I have been engaged with a long correspondence with one of my friends at Clark, a mathematicain.  I was trying to entice him into teaching a Net Logo course with me next semester, and after some throat clearing, here was his response.  I find the debate so very interesting that I wanted to hear what you-all thought of it, and I got his permission to post it.    I will identify him as ( Mathematicial Colleague).   MC and I are old friends and those of you who know me know that I am given to .... uh.... rambunctious discourse.  So the tone here is my tone, not really his.  I think you will enjoy it.  
>
> MC --More seriously, is there anything *mathematical* about
> NetLogo modeling? My impression (without having gone to
> the links below) is that it is just another--nicer looking,
> easier-to-program, even conceptually cleaner--way to make
> black boxes, and to that extent is no different from the Excel
> spreadsheets that John Kennison occasionally pushes on people,
> or the Java applets Dave Joyce programmed for you. Mathematics
> may be *consumed* in the programming of the simulation, but there is
> no mathematical analysis (and probably can't be), just an opaquely
> imperspicuous *thing* with some toggles that can be adjusted so
> as to create different--sometimes strikingly different--outputs.
> So what, from a mathematical point of view? A mathematician,
> when not acting as an engineer on hire, wants to *understand*
> formal structures by formal means. Where's the understanding,
> here? How is this different--from the point of view of a
> mathematician who wants to do mathematics--from programs that
> produce fractal images? Look, a cloud! Look, waves! Look,
> a tiger's pelt! Pretty!

--
*PS: A number of people ask me about the attachment to my email, which
is of type "application/pgp-signature". Don't worry, it is not a
virus. It is an electronic signature, that may be used to verify this
email came from me if you have PGP or GPG installed. Otherwise, you
may safely ignore this attachment.

----------------------------------------------------------------------------
A/Prof Russell Standish             Director
High Performance Computing Support Unit, Phone [phone] (mobile)
UNSW SYDNEY 2052                     Fax   [phone] (")
Australia             [hidden email]            
Room 2075, Red Centre                    http://parallel.hpc.unsw.edu.au/rks
            International prefix  +612, Interstate prefix 02
----------------------------------------------------------------------------