BourWiki-iBourbaki-FunctorWiki?

BourWiki-iBourbaki-FunctorWiki?

[Ellis D. Cooper]

Dear André Joyal,

At 01:55 PM 9/25/2008, you wrote:
(i) Some peoples have expressed doubts about the feasability.
(ii) we should make sure that iBourbaki can last for more than one generation.
(iii) We need to conciliate long term duration 
with the rapid developpement of technology.
(iv) My task at this point is to convince peoples 
that the project is worthy and feasable.

  If it will be useful to distinguish between (a) 
mathematicians informally doing mathematics at a 
blackboard or on a shared napkin or pad, and (b) 
formally composing mathematical exposition in, 
say, LaTeX supplemented by software technology 
for diagrams (e.g., xy-pic and Xfig), then my 
project is relevant solely to (a).  It seems to 
me that both (a) and (b) are necessary for the Subject.

Imagine (a) a mathematics discussion forum with a 
conversation like that on the categories 
listserv,  except augmented by the ability to 
draw and edit all kinds of mathematical 
expressions and diagrams (it has been said that 
"The Bourbaki were Puritans, and Puritans are 
strongly opposed to pictorial representations of 
truths of their faith."),  and (b) a Wiki-like 
peer-generated-and-reviewed presentation of 
research, report, and tutorial material 
with  links back to the discussions, arguments, 
and diagrams in (a).  All students of mathematics 
should be allowed to visit the forum, perhaps 
like a virtual Gallery of the Senate Chamber 
combined with the MIT OpenCourseWare initiative.

( (i), (iv) )
Regarding feasibility of (a), last year I 
sketched a possible algorithm intended to 
address  basic issues of presence and 
registration in a paper available at 
http://distancedrawing.com/Napkin071215a.pdf .

A revision of that algorithm substitutes (1) 
webcam USB technology for digital video camera 
technology, and (2) the browser protocol for instant messaging.

Perhaps the AJAX design pattern called HTTP 
Streaming -- a long-lived HTTP connection  with 
each collaborator -- might be worth 
investigating. A merging algorithm for  multiple 
independently generated images to create a single 
"virtual drawing" is described in the aforementioned paper.

The open source project I am proposing would 
combine forum software like 
http://www.yetanotherforum.net/ with webcam software.

( (ii), (iii) )
With regard to (b) there will be not only 
development of computer technology, but also 
development of mathematical technology. Someday 
might there be something that is as much beyond 
category theory as category theory is beyond Bourbaki?

Strictly speaking, the Subject and this project 
are not about categories.  I wonder how you think 
this discussion should be diverted to a separate 
stream and joined just by those keenly interested in (i)-(iv).

Ellis

Re: BourWiki-iBourbaki-FunctorWiki?

[Andre Joyal]

Dear Ellis Cooper,

>Since this project entails substantial programming effort, I would 
>like to measure the
>level of support the project could expect from the category-oriented 
>research community.
>Your judgement is much appreciated.

In addition to the peoples who have expressed their support in public
many have done it privately. None have opposed it yet.
Some peoples have expressed doubts about the feasability.
In a letter to some of my correspondants I wrote:

>The iBourbaki project is by nature a very long term project.
>Mathematics is vast, and it may take a few generations to fully integrate
>the main body of mathematics to iBourbaki.
>Also the potential contributors will refuse to work seriously
>on something that may disappear a few years later.
>They should have the possibility of making lasting contributions.
>Hence we should make sure that iBourbaki can last for more than one generation.
>It will be like building a cathedral!
>Of course, iBourbaki should evolve, since mathematics and the technology evolve.
>But mathematics is also remarquably stable.
>The mathematics of Euclid is still valid today, inspite of the
>fact that we now have non-euclidian geometry.
>I expect that the main corpus of iBourbaki will not change very much over long period of times.
>We need to conciliate long term duration with the rapid developpement of technology.

The realisation of iBourbaki depends on the collaboration of the mathematical community
in large, not only of category theorists. It also depends on the collaboration and support
of a group of computer scientists. My task at this point is to convince peoples that the 
project is worthy and feasable. 


André



-------- Message d'origine--------
De: Ellis D. Cooper [mailto:xtalv1@netropolis.net]
Date: mar. 23/09/2008 09:33
À: Joyal, André; categories@mta.ca
Objet : categories: BourWiki-iBourbaki-FunctorWiki
 
Dear Andre Joyal and categorists,

Various networking models for collaborating on mathematics have been 
alluded to or suggested on this
list (which is itself based on the listserv networking model).

*********************************************************************************************************
Patrik Eklund on 7 Oct 2007 wrote:
"Sound-video" is nothing but Skype, but adding whiteboards, that can be
saved and worked with also offline, you have very good possibilities.
The whiteboard mainly accepts non-formatted text, drawings and images. You
can read doc and ppt file which are "pasted" as bitmaps on the whiteboard.
They include desktop sharing if that would be required. Mathematical text
I add through LaTeX, compiling, converting to pdf, and using the snapshot
tool to paste bitmapped formulas on the whiteboard.
*********************************************************************************************************
Dusko Pavlovic on 15 Sep 2008 wrote:
an improved process, combining the integrity,
and perhaps the structure of the categories@mta community with the
available wiki-methods may bring categorical methods into a dynamic
environment, perhaps more natural for them than books and papers.
*********************************************************************************************************
Andrej Bauer on 16 Sep 2008 wrote:
the usual kind of wiki is not suitable for collaborative science, but
recently there has been news of a special wiki for scientists which has
good support for references, keeps track of who said what, and has a
rating system.
*********************************************************************************************************
Meredith Gregory on 21 Sep 2008 wrote:
    - What is missing in most mathematical presentations is a view into the
    often very human and very messy process of getting to the presentation.
<snip>
Ever since Andre Joyal  mentioned a 2nd life for Bourbaki i can't 
stop thinking about a
Bourbaki  colloquium run in Second Life <http://secondlife.com/>
*********************************************************************************************************
Jacques Carette on 22 Sep 2008 wrote:
I hereby volunteer my time and the technical resources I have at my
disposal to 'host' a "New Bourbaki based on CT" project.
*********************************************************************************************************
John Baez on 22 Sep 2008 wrote:
Mathematics may be too much in a state of foundational
flux for a systematic approach to be successful right now.  Maybe
the best we can hope for is something a bit more like Wikipedia,
where different people contribute different portions of text, and
they don't cohere in a polished whole.  But presumably anyone calling
for a new Bourbaki wants something different from Wikipedia.
<snip>
I would like to see lots of people try lots of different things.
*********************************************************************************************************

A network model not yet mentioned is the multiple-thread technical 
support forum. See,
for example

http://www.theimagingsourceforums.com/forumdisplay.php?f=6
http://www.essentialobjects.com/Forum/Default.aspx
http://www.codeproject.com/KB/ajax/
http://www.codeproject.com/Lounge.aspx?msg=2730104#xx2730104xx

Technical support forums centralize expertise, whereas collaborative 
mathematics would
best have mutually supportive distributed expertise. Each thread 
would be moderated
to maintain topic and civility, like the categories listserv.

Crucial to much mathematical collaboration is sharing of diagrams 
alongside mathematical
expressions and natural language text. A webcam over a pad provides 
this important
function. I myself have used Skype to discuss one-sided limits with 
my son who is away
at college, where instead of looking at each other's face  we aimed 
our webcams at pads.

One step beyond separate pads beneath webcams is the idea of a 
"virtual drawing" which
per discussion thread would overlay appropriately transparent images 
from multiple
collaborators: a shared blackboard in your web browser.

A web-site for collaborative mathematics could combine the secure 
multiple-thread forum model
with virtual drawing. Every participant would have the option to 
record part or all of a thread
for off-line review. Combined with video-conferencing via Skype or 
the like, real-time
collaboration is an option.

Since this project entails substantial programming effort, I would 
like to measure the
level of support the project could expect from the category-oriented 
research community.
Your judgement is much appreciated.

Ellis D. Cooper