Re: cracks and pots

Re: cracks and pots

[John Baez]

Hi -

> I just came across the following pages
>
> http://motls.blogspot.com/2004/11/category-theory-and-physics.html
> http://motls.blogspot.com/2004/11/this-week-208-analysis.html
>
> written by Lubos Motl, a physicist (string theorist). Some of you may find
> these articles interesting and probably revealing.
>
> Are we category theorists as a whole going to quietly accept getting
> discredited by a minority of us presumably applying category theory to
> string theory?

I can't tell if you're kidding.  I'll assume you're not.

There's nothing wrong with applying category theory to string theory.
The papers by Michael Douglas and Paul Aspinwall cited above by Motl
are some nice examples of using derived categories to study D-branes.

Further examples: the Moore-Seiberg relations turn out to be little
more than the definition of a balanced monoidal category, and the
Segal-Moore axioms for open-closed topological strings are nicely
captured using category theory here:

http://arxiv.org/abs/math.AT/0510664

There were a lot of nice talks on the borderline between category
theory and string theory at the Streetfest.

Perhaps more to the point, Lubos Motl is famous for his heated
rhetoric.  He doesn't like me, or anyone else who criticizes
string theory.  The articles you mention above are mainly reactions
to my This Week's Finds.

He's actually being very gentle - for him.  He even says "the
role of category theory can therefore be described as a `progressive
direction' within string theory".

I'm sure you'll all be pleased to know that.  :-)

> It is surely not too late to react and point out that this is
> not what (all of) category theory is about.

I would urge everyone not to react - at least, not until they are
well aware of what a discussion with him is like.  See his blog
and his comments on Peter Woit's blog if you don't understand what
I mean.   For example:

http://pitofbabel.org/blog/?p=51

> Please give a thought about what
> we, as a community, can urgently do to repair this damaging impression.

Since Motl's personality is well known, any damage will be minimal.
I think we should relax and take it easy.

Best,
jb

Re: cracks and pots

[Marta Bunge]

Hi,

I am relieved to learn (from the postings by David Yetter and John Baez)
that Motl's blog on the issue of categories and string theory is based on 1)
(Yetter) Motl's reluctance, as is the case with many string theorists, to
refuse to learn category theory, and 2) (Baez) Motl's personal dislike of
John Baez and of many other people, so that since Motl's personality is
well-known, any damage will be minimal.

I have also been reminded that 1) (Yetter) categorical ideas are central to
several competitors of string theory, and that there is nothing cracked or
crackpotish about them, and 2) (Baez) there is some serious work in the
borderline of category theory and string theory as exemplified by several
speakers at the StreetFest.

I thank David and John for taking the trouble to respond in detail to what
may have seem as a "provocation" on my part (well, perhaps it was...).

But these informative responses do not address my main concern, which is one
that others (publicly, as Eduardo Dubuc, but several others privately) have
expressed to me following my posting. I was aiming at the fact that there is
a certain trend within category theory (when did it start?) to consistely
give center stage to anything that claims to have connections with physics
(in particular string theory).  Is this because (it is believed that) the
state of category theory is now so poor (as "evidenced" by the lack of
grants) that they (the organizers of meetings) want to repair this image at
any cost? Also, by so doing, are we not becomeing vulnerable?  Are we not
pushing students to work on a certain area on the grounds that it is
fashionable and likely to be funded, even if those students may lack the
motivation and sound background knowledge? I feel that this is dangerous for
category theory (and mathematics in general), as it may lead (is leading?)
to narrow developments of any subject that is approached with these
objectives in mind. I did point these concerns of mine already, in response
to the posting by Robert MacDawson, whom I also thank for giving me the
opportunity to make clearer what my real concerns are.

On the subject of what constitutes good mathematics, Ronnie Brown has
pointed out to me a beautiful expose (with Tim Porter) which you can find in
www.bangor.ac.uk/r.brown/publar.html
I urge you to read it.

I end with a quote from the end of David Yetter's posting in reply to mine.
"If (I suspect when) the string theory emperor turns out to have no clothes,
category theory will suddenly become de rigeur in physics".  I share his
optimism.


Most cordially,
Marta Bunge




************************************************
Marta Bunge
Professor Emerita
Dept of Mathematics and Statistics
McGill University
805 Sherbrooke St. West
Montreal, QC, Canada H3A 2K6
Office: (514) 398-3810
Home: (514) 935-3618
marta.bunge@mcgill.ca
http://www.math.mcgill.ca/bunge/
************************************************




>From: "John Baez" <baez@math.ucr.edu>
>To: categories@mta.ca
>Subject: categories: Re: cracks and pots
>Date: Tue, 14 Mar 2006 11:56:09 -0800 (PST)
>
>Hi -
>
> > I just came across the following pages
> >
> > http://motls.blogspot.com/2004/11/category-theory-and-physics.html
> > http://motls.blogspot.com/2004/11/this-week-208-analysis.html
> >
> > written by Lubos Motl, a physicist (string theorist). Some of you may
>find
> > these articles interesting and probably revealing.
> >
> > Are we category theorists as a whole going to quietly accept getting
> > discredited by a minority of us presumably applying category theory to
> > string theory?
>
>I can't tell if you're kidding.  I'll assume you're not.
>
>There's nothing wrong with applying category theory to string theory.
>The papers by Michael Douglas and Paul Aspinwall cited above by Motl
>are some nice examples of using derived categories to study D-branes.
>
>Further examples: the Moore-Seiberg relations turn out to be little
>more than the definition of a balanced monoidal category, and the
>Segal-Moore axioms for open-closed topological strings are nicely
>captured using category theory here:
>
>http://arxiv.org/abs/math.AT/0510664
>
>There were a lot of nice talks on the borderline between category
>theory and string theory at the Streetfest.
>
>Perhaps more to the point, Lubos Motl is famous for his heated
>rhetoric.  He doesn't like me, or anyone else who criticizes
>string theory.  The articles you mention above are mainly reactions
>to my This Week's Finds.
>
>He's actually being very gentle - for him.  He even says "the
>role of category theory can therefore be described as a `progressive
>direction' within string theory".
>
>I'm sure you'll all be pleased to know that.  :-)
>
> > It is surely not too late to react and point out that this is
> > not what (all of) category theory is about.
>
>I would urge everyone not to react - at least, not until they are
>well aware of what a discussion with him is like.  See his blog
>and his comments on Peter Woit's blog if you don't understand what
>I mean.   For example:
>
>http://pitofbabel.org/blog/?p=51
>
> > Please give a thought about what
> > we, as a community, can urgently do to repair this damaging impression.
>
>Since Motl's personality is well known, any damage will be minimal.
>I think we should relax and take it easy.
>
>Best,
>jb
>
>
>
>
>
>
>
>

Re: cracks and pots

[Krzysztof Worytkiewicz]

The blog in question is indeed more than dubious. Besides the
"scientific" manicheism (group good, monoid bad...), what to think
about ranking countries according to a "civilization index"? The
blogger also claims he was mastering differential geometry and
particle physics at age of 15, so he obviously was too busy and
missed the provocative phase. Not a reason however to try to catch it
up as an "adult".

Cheers

Krzysztof

-- my government will categorically deny the incident ever occurred

Re: cracks and pots

[dusko]

when i said

> eg, if you look at grothendieck's work, he started working in
> algebra, and ended up developing foundational structures, because
> he needed them.

i meant that he ended up working on toposes, fibrations, and descent
(as foundational structures). i did not mean that he observed the
grothendieck universes (which are perhaps foundational, but not much
of a structure), as my hasty formulation had suggested to some
people. sorry about the confusion (and about taking bandwidth to
correct it),

-- dusko

Re: cracks and pots

[David Yetter]

I used the word 'faces' to describe the two aspects of category theory. 
  I see no actual separation in content, only a difference in emphasis 
(esp. as regards applications) and public presentation.

Even as Saunders, late in his life, gave lectures entitled 'All 
Mathematics Belongs Together', so all category theory belongs together.

D. Y.

On 28 Mar 2006, at 03:01, dusko wrote:

> i think david yetter's analysis of the dichotomy "categories as 
> foundations" vs "categories as algebra" was spot on ---  with respect 
> to people and the community. indeed, one could split most of our 
> papers into one category or the other. 
>
> but at the end of the day, i think, we'll all agree that the source of 
> the unreasonable effectiveness of categorical algebra is its 
> foundational content (although there is probably a lot of it that we 
> dont understand yet); and the other way around. eg, if you look at 
> grothendieck's work, he started working in algebra, and ended up 
> developing foundational structures, because he needed them. and a lot 
[lengthy further quotation omitted ...]

Re: cracks and pots

[Alex Simpson]

Quoting dusko <dusko@kestrel.edu>:

> but at the end of the day, i think, we'll all agree that the source
> of the unreasonable effectiveness of categorical algebra is its
> foundational content (although there is probably a lot of it that we
> dont understand yet); and the other way around. eg, if you look at
> grothendieck's work, he started working in algebra, and ended up
> developing foundational structures, because he needed them. and a lot
>  on the "algebra" side now is built upon them. ok, then for a while
> it  was thought that he exaggerated with foundations, and that a more
>  direct approach "could have been in better taste" (to cite
> eilenberg). but maby the fermat theorem would have a more useful
> proof if it was developed in grothendieck style. and nowadays, there
> is a lot of foundational content in tannaka duality etc, in TQFT in
> general ...

TQFT!? It seems dusko has finally discovered the shift key
on his keyboard.

Alex

-- 
Alex Simpson, LFCS, School of Informatics, Univ. of Edinburgh, UK
Email: Alex.Simpson@ed.ac.uk             Tel: +44 (0)131 650 5113
Web: http://homepages.inf.ed.ac.uk/als   Fax: +44 (0)131 667 7209

Re: cracks and pots

[dusko]

i think david yetter's analysis of the dichotomy "categories as  
foundations" vs "categories as algebra" was spot on ---  with respect  
to people and the community. indeed, one could split most of our  
papers into one category or the other.

but at the end of the day, i think, we'll all agree that the source  
of the unreasonable effectiveness of categorical algebra is its  
foundational content (although there is probably a lot of it that we  
dont understand yet); and the other way around. eg, if you look at  
grothendieck's work, he started working in algebra, and ended up  
developing foundational structures, because he needed them. and a lot  
on the "algebra" side now is built upon them. ok, then for a while it  
was thought that he exaggerated with foundations, and that a more  
direct approach "could have been in better taste" (to cite  
eilenberg). but maby the fermat theorem would have a more useful  
proof if it was developed in grothendieck style. and nowadays, there  
is a lot of foundational content in tannaka duality etc, in TQFT in  
general, but we only see hints of it at the moment (and i for one  
just see the reflections of these hints in other people's eyes).

i am of course saying things very clear and familiar to many people  
on this list, but maby they are worth saying nevertheless. it might  
be good if the links between "categories as algebras" and "categories  
as foundations" would not boil down just to the greatest of the  
category theorists, leaving the rest of us in two camps.

-- dusko

Re: cracks and pots

[Peter Selinger]

I just returned from a vacation and caught up with this thread, so
please bear with me as I back up to the central question posed by
Marta Bunge. She suggested that

> anything which even remotedly claims to have applications to physics
> (particularly string theory) is given (what I view as) uncritical
> support in our circles.

Is there any evidence to support this claim? I.e., actual examples
where such research was disproportionally supported that was
uncritical and perhaps unwarranted? There have been several posts
seemingly agreeing that this is the case, but none have given concrete
evidence.  I feel that it is necessary to establish that such
practices indeed exist, before discussing what, if anything, needs to
be done about it. Can one rule out another possibility, namely that
such research is supported because it is original, timely, and
interesting?

-- Peter

Marta Bunge wrote:
>
> Robert Dawson wrote:
>
> >	It is not clear to me that the majority of theoretical physicists agree
> >with the negative view of categorical string theory held by the cited blog
> >writers; and in the absence of a consensus among the physicists, I for one
> >(with an undergradate degree and some graduate courses in physics) do not
> >feel qualified to take sides; if anything, errors should be on the side of
> >trying out too many ideas, not too few.
> >
>
> I was trying to elicit an open response from those who *do* know about the
> value (or lack of it) of categorical string theory. In particular, I would
> like to have an answer to this question. Why is it that anything which even
> remotedly claims to have applications to physics (particularly string
> theory) is given (what I view as) uncritical support in our circles?
>
> Best,
> Marta
>
>
>
>

Re: cracks and pots

[V. Schmitt]

David Yetter wrote:

> Fellow categorists,
>
> Jim Stasheff has been appealing to me to comment on the role of
> category theory in knot theory in the context of the ‘cracks and pots’
> thread.
>
[lengthy quotations omitted...]

Hi David,
then, i again, to precise my thoughts.

Knot theory is trivially a good thing.
That category has to do with it does
not surprise anybody reading this
thread. You can relax...
Personnaly, and as a matter of taste, i would
not put for instance polymorphic types is the
same bag. But... ok, say.

Now that theoretical physics, computer
science, phylo., a mix of those, or whatever? ,
is used to justify poor "categorical" work is,
in my view, an existing problem. More or less
everyone is conscious of it (come on!...) but so far
that has not been publically debated.  I am happy
that it happens now.

So I am sorry not share the enthusiastic
mood that everything is good in maths
and I wish that our colleagues "categorists"
take categories... humm... seriously.
Again, i should not be the one who says
that.

Best,
Vincent.

PS: since you averted your book - can we get
a good price?

re: cracks and pots

[Urs Schreiber]

Dear Category Theorists,

I have begun trying to compile a list with information (mainly links to
reviews and other literature) on applications of categories in mathematical
physics and string theory. (It is not finished yet, though.) See

http://golem.ph.utexas.edu/string/archives/000775.html .

Best regards,
Urs Schreiber

Re: cracks and pots

[David Yetter]

[-- Attachment #1: Type: text/plain, Size: 7183 bytes --]

Jim Stasheff has been appealing to me to comment on the role of=20
category theory in knot theory in the context of the =91cracks and pots=92=
=20
thread.

In that regard, let me begin with the story I tell in the introduction=20=

to my book:

At a Joint Summer Research conference a number of years back, Moishe=20
Flato at some point offered the usual dismissal of category theory--=91it=20=

is a mere language=92.  Kolya Reshetikhin and I undertook that evening =
to=20
disabuse him of the notion by explaining Shum=92s coherence theorem (the=20=

one-object version, being =91the braided monoidal category with =
two-sided=20
duals compatible with the braiding is monoidally equivalent to the=20
category of framed tangles=92).  This is a remarkable theorem--a=20
structure absolutely natural from the internal structure of category=20
theory is essentially identical to the key geometric sturctures in 3-=20
and 4-manifold topology, framed tangles being simply =91relative =
versions=20
of=92 the framed links on which the Kirby calculi for 3- and 4-manifolds=20=

depend.  It is one of several theorems relating category theory, and=20
with it  a great deal of algebra, to geometric topology, all of which=20
had a =93who ordered that?=94 feel about them.  It is also the only =
basis=20
on which the connection between knot theory and quantum groups can be=20
explained:  the category of representations of a quantum group has the=20=

algebraic structure for which framed tangles are a free model!

I retired before the point had sunk in, leaving Kolya to continue the=20
discussion.  The next morning as I sat in the back of the main lecture=20=

hall, Flato came in, tapped me on the shoulder, and with a thumbs up,=20
said =93Hey! Viva les categories!. . .these new ones, the braided=20
monoidal ones.=94

Now, Shum=92s theorem is merely the first of several, all of which give=20=

one the =93who ordered that?=94 impression, at least once on starts=20
thinking of TQFT=92s.  The other two that come to mind require a bit of=20=

set up to state fully, but I will spare you all now:  they are Abrams=20
theorem that a 2-dimensional TQFT is equivalent to a Frobenius algebra,=20=

and a theorem due to myself and Crane, and Kerler, that in a certain=20
category of cobordisms between surfaces with boundary, the handle (a=20
torus with a hole cut in it) has the structure of a Hopf algebra (CY,=20
K) which is self-dual (CY) and admits a right integral (K), and that=20
every surface with a circle boundary is a Yetter-Drinfel=92d module over=20=

the handle.  (For an ordinary finite dimensional Hopf algebra,=20
YD-modules are modules over the Drinfel=92d double, but they exist more=20=

generally, for infinite dimensional Hopf algebras or Hopf algebra=20
objects in arbitrary monoidal categories, where Drinfel=92d doubles =
don=92t=20
exist.)

All of these are part and parcel of a different face of category theory=20=

than one saw in the old days:  category theory as algebra, rather than=20=

category theory as foundations.

Flato=92s dismissal was directed at category theory as foundations.  It=20=

is easily ignored if one is interested in foundations of mathematics,=20
since most mathematicians really don=92t care about foundations.  For=20
example, many mathematicians pay lip service to the attitude =91set=20
theory is =91the=92 foundation of mathematics=92, but then turn around =
and=20
talk about =91the real numbers=92.  Which =91real numbers=92?  Dedekind =
cuts? =20
equivalence classes of Cauchy sequences? a complete Archimedian field=20
constructed from surreal numbers?  Now we, as categorists, know the=20
question is silly:  one doesn=92t bother asking which of a family of=20
isomorphic structures one means, because they are isomorphic.  It is in=20=

the practical sense of describing the basic structure of what=20
mathematicians actually do, that category theory is a superior=20
=91foundation=92 to set theory.  (Was there ever a time when the epsilon=20=

tree defining an element of a smooth manifold ever mattered to anyone?)=20=

  The dim view of category theory in many mathematical circles is surely=20=

due to mathematicians=92 boredom with foundations--and attitude which=20
might be summed up as =93Set theory was bad enough.  Why open up all=20
those questions again? Just let me do my geometry, algebra, or=20
whatever.=94

I reading this thread, I wonder how much of the concern about public=20
perceptions of category theory is really concern that =91categories as=20=

algebra=92 has become the public face of category theory, concern on the=20=

part of those who are fond of =91categories as foundations=92.

=91Categories as foundations=92 served the subject poorly in relations =
to=20
most mathematicians, but well in relation to computer science:  only=20
categorists were willing to take up the challenge of polymorphic type=20
theory.  If you thought =91set theory is *the* foundation=92, you bashed=20=

your head against Russell=92s paradox and were no help the the folk in=20=

CS. We (really those of *you* who took up the challenge) were the only=20=

mathematicians who had any hope of being helpful.

On the other hand, those of us who set our sights on =91core =
mathematics=92=20
have been better served by =91categories as algebra=92:  the =
applications=20
to knot theory (and geometric topology more generally), homotopy=20
theory, deformation theory, and physics all flow from this =91face=92 of=20=

category theory.

Even if those of us whose love is =91categories as foundations=92 can be =
a=20
little uneasy with the other face of the subject getting applied to=20
physics and drawing fire from outside mathematics, those of us whose=20
love is =91categories as algebra=92 can be uneasy about applications of =
the=20
other face to philosophy (as pointed to in Peter Arndt=92s last post),=20=

which are sure to be vilified (philosophers and humanists always vilify=20=

their rivals, as I am learning from my daughter who is studying=20
philosophy).  =91Categories as algebra=92 at least got a =91Viva!=92 =
from one=20
of the fathers of deformation quantization.

Best Thoughts,
David Yetter



On 23 Mar 2006, at 14:45, Peter Arndt wrote:

> Dear category theorists,
> I would like to support Krzysztof Worytkiewicz's remark that "cat=20
> theory
> needs to be demystified in first place rather than to be sold" from a
> different side: I have recently come across several publications and
> research projects of philosophers who have become over-enthusiastic=20
> with
> category theory. In certain circles category theory seems to have=20
> gained a
> nimbus of an all-encompassing theory of everything, be it part of
> mathematics or not, see for example
> http://lists.debian.org/debian-devel/2000/10/msg02048.html for an=20
> expression
> of such opinions or http://ru.philosophy.kiev.ua/rodin/Endurance.htm=20=

> for a
> crude offspring of them. Such exaggerated propaganda is very likely to=20=

> cause
> railings like the one of Lubos Motl. Has anyone observed the same=20
> phenomenon
> or does it only exist among the people I have to do with?
>
> All the best,
>
> Peter
>

[-- Attachment #2: Type: text/enriched, Size: 6961 bytes --]

<fontfamily><param>Times</param>Fellow categorists,


Jim Stasheff has been appealing to me to comment on the role of
category theory in knot theory in the context of the ‘cracks and pots’
thread.


In that regard, let me begin with the story I tell in the introduction
to my book:  


At a Joint Summer Research conference a number of years back, Moishe
Flato at some point offered the usual dismissal of category
theory--‘it is a mere language’.  Kolya Reshetikhin and I undertook
that evening to disabuse him of the notion by explaining Shum’s
coherence theorem (the one-object version, being ‘the braided monoidal
category with two-sided duals compatible with the braiding is
monoidally equivalent to the category of framed tangles’).  This is a
remarkable theorem--a structure absolutely natural from the internal
structure of category theory is essentially identical to the key
geometric sturctures in 3- and 4-manifold topology, framed tangles
being simply ‘relative versions of’ the framed links on which the
Kirby calculi for 3- and 4-manifolds depend.  It is one of several
theorems relating category theory, and with it  a great deal of
algebra, to geometric topology, all of which had a “who ordered that?”
feel about them.  It is also the only basis on which the connection
between knot theory and quantum groups can be explained:  the category
of representations of a quantum group has the algebraic structure for
which framed tangles are a free model!


I retired before the point had sunk in, leaving Kolya to continue the
discussion.  The next morning as I sat in the back of the main lecture
hall, Flato came in, tapped me on the shoulder, and with a thumbs up,
said “Hey! Viva les categories!. . .these new ones, the braided
monoidal ones.”


Now, Shum’s theorem is merely the first of several, all of which give
one the “who ordered that?” impression, at least once on starts
thinking of TQFT’s.  The other two that come to mind require a bit of
set up to state fully, but I will spare you all now:  they are Abrams
theorem that a 2-dimensional TQFT is equivalent to a Frobenius
algebra, and a theorem due to myself and Crane, and Kerler, that in a
certain category of cobordisms between surfaces with boundary, the
handle (a torus with a hole cut in it) has the structure of a Hopf
algebra (CY, K) which is self-dual (CY) and admits a right integral
(K), and that every surface with a circle boundary is a
Yetter-Drinfel’d module over the handle.  (For an ordinary finite
dimensional Hopf algebra, YD-modules are modules over the Drinfel’d
double, but they exist more generally, for infinite dimensional Hopf
algebras or Hopf algebra objects in arbitrary monoidal categories,
where Drinfel’d doubles don’t exist.)


All of these are part and parcel of a different face of category
theory than one saw in the old days:  category theory as algebra,
rather than category theory as foundations.


Flato’s dismissal was directed at category theory as foundations.  It
is easily ignored if one is interested in foundations of mathematics,
since most mathematicians really don’t care about foundations.  For
example, many mathematicians pay lip service to the attitude ‘set
theory is ‘the’ foundation of mathematics’, but then turn around and
talk about ‘the real numbers’.  Which ‘real numbers’?  Dedekind cuts? 
equivalence classes of Cauchy sequences? a complete Archimedian field
constructed from surreal numbers?  Now we, as categorists, know the
question is silly:  one doesn’t bother asking which of a family of
isomorphic structures one means, because they are isomorphic.  It is
in the practical sense of describing the basic structure of what
mathematicians actually do, that category theory is a superior
‘foundation’ to set theory.  (Was there ever a time when the epsilon
tree defining an element of a smooth manifold ever mattered to
anyone?)  The dim view of category theory in many mathematical circles
is surely due to mathematicians’ boredom with foundations--and
attitude which might be summed up as “Set theory was bad enough.  Why
open up all those questions again? Just let me do my geometry,
algebra, or whatever.” 


I reading this thread, I wonder how much of the concern about public
perceptions of category theory is really concern that ‘categories as
algebra’ has become the public face of category theory, concern on the
part of those who are fond of ‘categories as foundations’.  


‘Categories as foundations’ served the subject poorly in relations to
most mathematicians, but well in relation to computer science:  only
categorists were willing to take up the challenge of polymorphic type
theory.  If you thought ‘set theory is *the* foundation’, you bashed
your head against Russell’s paradox and were no help the the folk in
CS. We (really those of *you* who took up the challenge) were the only
mathematicians who had any hope of being helpful.


On the other hand, those of us who set our sights on ‘core
mathematics’ have been better served by ‘categories as algebra’:  the
applications to knot theory (and geometric topology more generally),
homotopy theory, deformation theory, and physics all flow from this
‘face’ of category theory.  


Even if those of us whose love is ‘categories as foundations’ can be a
little uneasy with the other face of the subject getting applied to
physics and drawing fire from outside mathematics, those of us whose
love is ‘categories as algebra’ can be uneasy about applications of
the other face to philosophy (as pointed to in Peter Arndt’s last
post), which are sure to be vilified (philosophers and humanists
always vilify their rivals, as I am learning from my daughter who is
studying philosophy).  ‘Categories as algebra’ at least got a ‘Viva!’
from one of the fathers of deformation quantization.


Best Thoughts,

David Yetter</fontfamily>




On 23 Mar 2006, at 14:45, Peter Arndt wrote:


<excerpt>Dear category theorists,

I would like to support Krzysztof Worytkiewicz's remark that "cat
theory

needs to be demystified in first place rather than to be sold" from a

different side: I have recently come across several publications and

research projects of philosophers who have become over-enthusiastic
with

category theory. In certain circles category theory seems to have
gained a

nimbus of an all-encompassing theory of everything, be it part of

mathematics or not, see for example

http://lists.debian.org/debian-devel/2000/10/msg02048.html for an
expression

of such opinions or http://ru.philosophy.kiev.ua/rodin/Endurance.htm
for a

crude offspring of them. Such exaggerated propaganda is very likely to
cause

railings like the one of Lubos Motl. Has anyone observed the same
phenomenon

or does it only exist among the people I have to do with?


All the best,


Peter


</excerpt>

re: cracks and pots

[Marta Bunge]

Hi,

I thought that my intention in raising the issues that I did in my original
posting of March 12 were clear enough. Now it seems that they were not, to
some.

1.
I find ridiculous the suggestion put forward by Robert Dawson (March
23)  that my presumed "call for collective action against an entire field
of research seems uncomfortably close to an organized boycott, an extreme
breach of tradition that only an emergency -if that - could justify it".

The invention of an alleged "boycott" plot seems aimed at dismissing the
questions that I (and other concerned mathematicians who joined the
discussion) have raised. Anybody who, like Robert Dawson, resorts to such
inventions appears to be panicking in that he is trying to divert attention
from, rather than help, a healthy discussion.


2.
Eduardo Dubuc writes: "I do not agree necessarily with Marta's implicit
views". There is nothing implicit in my views. Just take a second look at my
various postings of March 14, 15, and 17 in reply to some people. If Eduardo
refers to my bringing in the Templeton Foundation into the discussion, then
I would like to add some comments, partly expanding (and correcting) my
reply to Vincent Schmitt (March 17).

I can back up my contentions in reference to the the Goedel Centenary
Symposium in Vienna

http://www.logic.at/goedel2006/

and the workshop organized by A. Connes at the Sir Isaac Newton Institue in
Cambridge (Non Commutative Algebra)

http://www.newton.cam.ac.uk/programmes/NCG/ncgw02


I should, however, make more precise my reference to the Perimeter Institute
for Mathematical Physicts. What sems clear is that one of its most prominent
long-term researchers is at the same time one of the prominent particpants
in Templeton funding and activties, for instance the Foundational Questions
Institute. I quote from the last issue of Nature

http://www.fqxi.org/about.html

"Phycists to confront those big questions. Time travel, multiple universes
and extraterrestrial intelligence seem more the purview of Star Trek
scriptwriters than of serious researchers. (...) The FQI was set up last
October with a grant from the Templeton Foundation, which promotes research
at the boundary of religion and science. With US$8 million in seed money,
the FQI will fund dozens of researcher's part-time work on these questions.
(...) "I am very happy to see that a project has started to address these
needs" says Lee Smolin of the Perimeter Institute for Theoretical Physics in
Waterloo, Ontario, who is also on the FQI's scientific advisory board.  --
Geoff Brumfield. Nature.
2 March 2006."

I stated incorrectly that the Pi is devoted to String Theory, when it seems,
judging from the work of Lee Smolin, that Pi rather promotes Loop Quantum
Gravity, a competitor to String Theory. By the way, an article by Lee Smolin
entitled "Atoms of Space and Time" on LQG has been issued already three
times (with minor variations) in Scientific American (200, 2004, 2006), so
many of you must have seen it.

3.
I have never suggested that "an entire field of research" should be suspect
of constituting bad mathematics. If by this entire field of research it is
meant n-categories, theta-categories, operads, topological quantum theories,
and so on, there is, as in any other field, good and bad mathematics.
Perhaps I should bring to your attention my comments to the organizers of
the StreetFest, requested
by them of all participants, and posted in their website as

http://streetfest.maths.mq.edu.au/feedback?lastname=Bunge&firstname=Marta

I stand by this, and only hope that my remarks in the "cracks and pots"
postings have not been misinterpreted by the people mentioned in my comment
above, and by others, like Ieke Moerdijk, not mentioned in it since they
were not there.

4.
I also think that a problem persists in the emphasis given to the "you do
not want to know" general message in Baez postings, not because of them
intrinsically, or of himself, but of the use others (for what purposes, I do
not know) are making of this general trend. One instance of this trend
(although in a different casting) is the following

http://www.math.uchicago.edu/~eugenia/morality/

of a lecture that Eugenia Cheng gave in Cambridge last year.


With best wishes for (and absolute faith in) category theory,
Marta

************************************************
Marta Bunge
Professor Emerita
Dept of Mathematics and Statistics
McGill University
805 Sherbrooke St. West
Montreal, QC, Canada H3A 2K6
Office: (514) 398-3810
Home: (514) 935-3618
marta.bunge@mcgill.ca
http://www.math.mcgill.ca/bunge/
************************************************




>From: Eduardo Dubuc <edubuc@dm.uba.ar>
>To: categories@mta.ca
>Subject: categories: re: cracks and pots
>Date: Thu, 23 Mar 2006 13:50:45 -0300 (ART)
>
>Hi
>
>To follow are the contents of two postings that Bob (always vigilant, ja!)
>thought best to concatenate in only one.
>
>On spite of Robert's erudition and his knowledgeable discourse, I still
>think Einstein using differential geometry to develop general relativity
>is not at the same level that John Baez using category theory to develop
>and/or understand string theory. His arguments are valid in a court of
>law, but do not convince me. I imagine John himself is probably the first
>to laugh at such a comparison.
>
>But this is not the issue of my present posting. He touches also some
>pertinent points that go more to the core of the "cracks_and_pots" debate.
>
>(In between ** are Robert  words)
>
>What Motl says certainly does not make people using category theory in
>string theory laugh. Applications of category theory to string (or to
>other physical theories competing with string theory ?, see Yetter's
>posting, it is all very confusing !!) may be valuable or may not. I (and a
>lot of us) can not tel.
>
>** In which case demands that they ($) be read out of the meeting are
>premature.
>($) papers that claim applications to physics **
>
>This is a difficult question.
>
>Marta was saying (and Bob Walters and others agree) that when a paper was
>claiming applications to physics it was easily accepted without
>knowledgeable and close examination, and that there were a lot of them.
>
>Probably a lot of them should be read out, but not by policy against (as
>it was erroneously interpreted in these postings). Serious refereeing is a
>healthy practice that should not be equaled with censorship.
>
>**Remember - in mathematics it's a matter of "In God We Trust,
>everybody else must provide a proof."**
>
>This is not so much so. Speculations in math are very difficult. If not
>well founded they are vacuous. Only great mathematicians can do them
>(example close to us, Grothendieck), the rest of us must provide a proof.
>
>**If the math itself meets mathematical standards of rigor, its
>application to physics need surely only meet the standards appropriate to
>that subject.**
>
>The math itself must also meet standards of quality, not only of rigor.
>Besides that, "standards appropriate to that subject" does not mean "free
>for anything". Motl writes:
>
>"I always feel very uneasy if the mathematically oriented people present
>their conjectures about physics, quantum gravity, or string theory as some
>sort of "obvious facts."
>
>Clearly he is  saying that these standards are not being fulfilled (in his
>opinion of course) by claimed applications of math to physics.
>
>Motl  may be wrong or he may be right, what we have not seen yet in these
>postings is a convincing or clear answer to the questions he arises. I
>would say, not even an answer at all.
>
>These questions triggered Marta's original posting, which in turn was
>arising other (not exactly the same) questions. I do not agree necessarily
>with Marta's implicit views, what I support is her courage to point out
>that they are serious problems in the category theory community (for
>example, quality of the publications, abuse of fashionable topics to get
>grants, invited speakers in CT meetings).
>
>Best wishes    e.d.
>
>
>
>
>
>
>
>

Re: cracks and pots

[Peter Arndt]

Dear category theorists,
I would like to support Krzysztof Worytkiewicz's remark that "cat theory
needs to be demystified in first place rather than to be sold" from a
different side: I have recently come across several publications and
research projects of philosophers who have become over-enthusiastic with
category theory. In certain circles category theory seems to have gained a
nimbus of an all-encompassing theory of everything, be it part of
mathematics or not, see for example
http://lists.debian.org/debian-devel/2000/10/msg02048.html for an expression
of such opinions or http://ru.philosophy.kiev.ua/rodin/Endurance.htm for a
crude offspring of them. Such exaggerated propaganda is very likely to cause
railings like the one of Lubos Motl. Has anyone observed the same phenomenon
or does it only exist among the people I have to do with?

All the best,

Peter

re: cracks and pots

[Eduardo Dubuc]

Hi

To follow are the contents of two postings that Bob (always vigilant, ja!)
thought best to concatenate in only one.

On spite of Robert's erudition and his knowledgeable discourse, I still
think Einstein using differential geometry to develop general relativity
is not at the same level that John Baez using category theory to develop
and/or understand string theory. His arguments are valid in a court of
law, but do not convince me. I imagine John himself is probably the first
to laugh at such a comparison.

But this is not the issue of my present posting. He touches also some
pertinent points that go more to the core of the "cracks_and_pots" debate.

(In between ** are Robert  words)

What Motl says certainly does not make people using category theory in
string theory laugh. Applications of category theory to string (or to
other physical theories competing with string theory ?, see Yetter's
posting, it is all very confusing !!) may be valuable or may not. I (and a
lot of us) can not tel.

** In which case demands that they ($) be read out of the meeting are
premature.
($) papers that claim applications to physics **

This is a difficult question.

Marta was saying (and Bob Walters and others agree) that when a paper was
claiming applications to physics it was easily accepted without
knowledgeable and close examination, and that there were a lot of them.

Probably a lot of them should be read out, but not by policy against (as
it was erroneously interpreted in these postings). Serious refereeing is a
healthy practice that should not be equaled with censorship.

**Remember - in mathematics it's a matter of "In God We Trust,
everybody else must provide a proof."**

This is not so much so. Speculations in math are very difficult. If not
well founded they are vacuous. Only great mathematicians can do them
(example close to us, Grothendieck), the rest of us must provide a proof.

**If the math itself meets mathematical standards of rigor, its
application to physics need surely only meet the standards appropriate to
that subject.**

The math itself must also meet standards of quality, not only of rigor.
Besides that, "standards appropriate to that subject" does not mean "free
for anything". Motl writes:

"I always feel very uneasy if the mathematically oriented people present
their conjectures about physics, quantum gravity, or string theory as some
sort of "obvious facts."

Clearly he is  saying that these standards are not being fulfilled (in his
opinion of course) by claimed applications of math to physics.

Motl  may be wrong or he may be right, what we have not seen yet in these
postings is a convincing or clear answer to the questions he arises. I
would say, not even an answer at all.

These questions triggered Marta's original posting, which in turn was
arising other (not exactly the same) questions. I do not agree necessarily
with Marta's implicit views, what I support is her courage to point out
that they are serious problems in the category theory community (for
example, quality of the publications, abuse of fashionable topics to get
grants, invited speakers in CT meetings).

Best wishes    e.d.

Re: cracks and pots

[Steve Vickers]

On 17 Mar 2006, at 09:36, George Janelidze wrote:
> ... I think if we really care about
> relations between category theory and "other foundational
> disciplines", we
> should begin by explaining that category theory is not just a language
> allowing one to call homology a functor, but that category theory has
> beautiful constructions and results (some already from 1940s and 50s!)
> making enormous simplifications/applications/illuminations in
> neighbour
> areas of pure mathematics, such as abstract algebra, geometry, and
> logic.

Dear George,

I think the straight answer is that it is genuinely difficult.

Even for elementary applications it is not easy. Try asking non-
categorical topologists how they explain the product topology to
students. Many will say, "This definition may look odd, but it turns
out to work best." Others will produce various ad hoc justifications,
such as "It's the definition that makes Tychonoff's theorem
true." (Though that may be at least historically correct.)   You
point out that the product topology is the unique one such that
projections are continuous and tupling preserves continuity,  but
they still don't see that as anything special.

But with regard to certain advanced applications, there are pictures
in the minds of the category theorists that do not translate at all
easily to paper. Even the master expositors find it hard. I'm
thinking for example of the idea of topos as generalized space.

I have been working seriously with toposes (usually as generalized
spaces) for about 15 years now and in some respects my understanding
of them is quite deep. Yet there is still a huge gap in my
understanding when it comes to their applications in algebraic
geometry, Galois theory and algebraic topology, the kind of fields
that gave rise to toposes in the first place. Somehow when I read the
accounts I see a mass of machinery but no clear intuitions for what
it is doing. This surprises me. A characteristic strength of category
theory is that it is particularly good at explaining the underlying
meaning of constructions, with its notion of universal properties,
and with some beautiful tricks of categorical logic.

So is it possible to explain, or illuminate, those particular
categorical applications to someone like me? (Perhaps the challenge
has already been met, and I've just missed the right book; and of
course I eagerly await vol. 3 of the Elephant.)

Here's a sample question where my categorical understanding falls
short of the applications.

If A is an Abelian group, then the space ^A of A-torsors is also a
group (modulo canonical isomorphisms - the equational laws of group
theory do not necessarily hold up to equality). The identity element
is the regular representation of A on itself, group multiplication is
"tensor product" of torsors, and inverses are got by inverting the A-
action.

It follows that if X is any space, then the collection of continuous
maps from X to ^A is also a group, and this construction is self-
evidently contravariant in X.

Obviously it takes topos theory to formalize this, but already we can
paint a picture.

For example, suppose A is the cyclic group C_2 of order 2 and X is
the circle. Then there are (classically) two isomorphism classes of
maps T: X -> ^A, essentially because in going once right round the
circle the variable torsor T(x) can come back either just how it
started or with an automorphism swapping its two elements. The
corresponding group is C_2.

This looks like some kind of cohomology, so is it already part of the
standard theory? I've never managed to follow all the machinery through.

All the best,

Steve Vickers

Re: cracks and pots

[Mamuka Jibladze]

> Category theory, and for that matter modern (as opposed to elementary)
> algebra, is to mathematics as mathematics is to physics, and for that
> matter to computer science.  Whereas mathematics organizes reasoning
> about the phenomena studied by physicists and computer scientists,
> algebra and category theory perform a similar function for mathematics.
>
> In any setting organization is desirable, and arguably necessary on
> occasion.  But the use of algebra and category theory to organize
> physics and computer science is a double whammy here.  One should
> therefore be doubly sympathetic of those physicists and computer
> scientists who want to know what substantive contribution is being made
> to their subject and can't evaluate the answers because they are one if
> not two levels removed from the necessary abstractions.
>
> Vaughan Pratt

It just occurred to me that to justify such viewpoint we might have to look
at the point in time when mathematics began to become abstracted out from
natural sciences to see whether category theory is already in the same
position with respect to the rest of mathematics.

Although I certainly do not know enough history of science, I will still
dare to speculate that the situation now is completely different from what
it was then. I believe mathematics as a substantial part of the body of
scientific knowledge did exist and evolve long long before it began to be
considered as some separate entity which can be used to organize the rest -
in fact many people still think of mathematics as just another science on
completely equal footing with, say, biology or physics.

Whereas birth and development of category theory has been, I think, much
more deliberate, abrupt and discontinuous in comparison. If this is so, one
possible conclusion might be that probably category theorists simply want
too much too soon. Maybe they should be more patient and let their
discipline become stronger within the body of mathematics before forcibly
declaring it a new organizing force outside the rest of mathematics. This is
as if a child would be forced to care for its parents shortly after being
born.

Mamuka Jibladze

Re: cracks and pots

[James Stasheff]

I think knot theory is particularly helpful here but I'll let Yetter and
Freyd reply further.

	Jim Stasheff		jds@math.upenn.edu

		Home page: www.math.unc.edu/Faculty/jds

On Thu, 16 Mar 2006, Vaughan Pratt wrote:

> Category theory, and for that matter modern (as opposed to elementary)
> algebra, is to mathematics as mathematics is to physics, and for that
> matter to computer science.  Whereas mathematics organizes reasoning
> about the phenomena studied by physicists and computer scientists,
> algebra and category theory perform a similar function for mathematics.
>
> In any setting organization is desirable, and arguably necessary on
> occasion.  But the use of algebra and category theory to organize
> physics and computer science is a double whammy here.  One should
> therefore be doubly sympathetic of those physicists and computer
> scientists who want to know what substantive contribution is being made
> to their subject and can't evaluate the answers because they are one if
> not two levels removed from the necessary abstractions.
>
> Vaughan Pratt
>
>

RE: cracks and pots

[James Stasheff]

Dear all,
	Picking up on the funding issue.  I've served on the
NSF Advisory panel, though many years ago, so I'm familiar with some
of the issues with federal funding.

The worst of it from my experience is that it takes universities
off the hook as to supporting research directly, as opposed to being only
a channel for external funds.  Worse yet, tenure and promotion decisions
are increasingly based on external support (at least in the US)
thus the university doesn't trust its own faculty.

Also involved is a bureaucratic aspect: it's more efficient to
process a large grant with multiple researchers.

In the ``good ole days'', math in the US has essentially NO post-docs.

	Jim Stasheff		jds@math.upenn.edu

		Home page: www.math.unc.edu/Faculty/jds


On Fri, 17 Mar 2006, Marta Bunge wrote:

> Dear Vincent,
>
> I am glad that you posted your reply to me. You raise questions that many of
> us have and that really relate to what I was trying to convey.  I hope that
> your letter is widely read. I will only comment on one aspect of it.
>
> >Of course the problem is the way research is sponsored.
> >Leading researchers are not so much good mathematicians
> >but good salesmen. Category theory is just not very trendy at the
> >minute and to get the money one needs to do theoretical physics
> >(there had been also Computer Science at some point - that was poor
> >is not it?).
> >There were a couple of Fields medals and  a new train called
> >TQFT that everybody just jumps in to get funded.
>
> I see nothing wrong in seeking funding for serious and well-motivated
> research. Young people have to eat too! What I worry about (this I did not
> say before) is that this craze for funding may drive researchers to accept
> *any* kind of funding, thinking naively that there are no strings (no pun
> intended) attached. When I was young, I once rejected NATO funding and,
> since there was no other source of funding for me at the moment, I had to
> go back to Argentina for two years and thus interrupt my graduate studies
> at Penn. Nowadays, it is the turn of organizations such as the Templeton
> Foundation (seeking to conciliate science with religion) which offer
> "graciously" to fund (and lavishly so) many projects in philosophy,
> physics and mathematics.
>
> Examples of Templeton funding are increasingly found: take the Perimeter
> Insitute (String Theory), the Godel Centennary Symposium in Vienna (Logic
> and Foundations), the workshop organized by A. Connes at the Sir Isaac
> Newton Insititue in Cambridge (Non Commutative Algebra), and others that
> are mentioned in Nature, for instance. This is all for public consumption
> -- just look at their web sites. Some of us find this really scary. That
> is why I do not put the getting of grants as a priority-- good science and
> good mathematics should always be the main priority.
>
> But then, you will ask, how do we feed graduate students, postdocs and
> unemployed category theorists? I do not know, but certainly not by resorting
> to dubious sources of funding. Not that it has happened yet! Forgive my
> "using" your comment to give way to a deep source of worry, certainly not
> unrelated to what I have been saying since the beginning of this discussion.
>
>
> As for
>
> >2/ Will be the rebirth of category - I bet!
>
>
> This is partly what I was asking -- are we (CT) in such a poor state that we
> need to be reborn in another guise? Maybe so, but I am just too immersed in
> my own (certainly not main stream) work to really judge. You are not the
> only one to suggest that we need an uplift. That may be so, but is it the
> reason for thinking it merely that there are no grants coming our way these
> days --  except when we (say that we) work in matters of interest to
> physics?
>
> It seems that I have only questions to ask -- not solutions to give. I
> apologize for that.
>
>
> Best wishes,
> Marta
>
> >From: "V. Schmitt" <vs27@mcs.le.ac.uk>
> >To: categories@mta.ca
> >Subject: categories: Re: cracks and pots
> >Date: Thu, 16 Mar 2006 09:51:00 +0000
> >
> >Dear Marta,
> >My english is so, so. I am french.
> >But this is to give briefly my opinion (I agree with you
> >more or less).
> >
> >I know a little of category and mathematics in general.
> >I love the category theory developped in the 70's and
> >I would have appreciated some category meetings at the
> >time.  But i am too young.
> >
> >Category theory like any good mathematics will never
> >die - but may "our" category community will.
> >
> >Of course the problem is the way research is sponsored.
> >Leading researchers are not so much good mathematicians
> >but good salesmen. Category theory is just not very trendy at the
> >minute and to get the money one needs to do theoretical physics
> >(there had been also Computer Science at some point - that was poor
> >is not it?).
> >There were a couple of Fields medals and  a new train called
> >TQFT that everybody just jumps in to get funded.
> >
> >Now as a *community* what shall *we* do?
> >
> >First the question regards mainly the established
> >people in the community (not me!).
> >1/ One can try to sell category theory  in a better way.
> >This is a bit like tomato sauce that you can put everywhere.
> >And try to make new friends - inviting them to give talks... -
> >from different disciplines.
> >2/ We may claim loudly that cat theory is real mathematics
> >and really try hard to do good mathematics. There are
> >certainly good mathematicians definitely willing to use
> >cat theory.  I saw many coming to category theory to develop
> >their own maths (- this happens for instance in France with Berger who
> >will never claim that he is a "categorician". Though he is completely
> >in it!)
> >
> >My feeling is the attitude 1/ pushed to the extreme may be
> >very damaging.  These talks about category everywhere and
> >for everything are just poor and sound really stupid.
> >They do not serve the cause.
> >
> >2/ Will be the rebirth of category - I bet!
> >
> >Sorry for the message written in haste
> >and the poor english. Good e-mails from you
> >on the list!
> >
> >best regards,
> >Vincent.
> >
> >
> >
> >
>
>
>
>

Re: cracks and pots

[Robert J. MacG. Dawson]

jim stasheff wrote:
>
>
> Robert J. MacG. Dawson wrote:
>
> And, as you know, there are
> still scales, almost a century later,  on which its predictions are
> unsatisfactory.
>
> For us ignorant of these, please explicate.


	(1) At the very small scale, nobody has really managed to unify quantum
mechanics (which is as thoroughly tested on its home turf as relativity
is on its own) with general relativity. QM works astonishingly  well on
the atomic scale, GR works astonishingly well on the astronomical scale,
but there is a big gap, "in which we live", in which neither is
particularly evident and classical Newtonian mechanics   works pretty
well for most purposes.

	(2) At very large scales there is some question as to whether
additional forces, not predicted by general relativity, are needed to
explain some cosmological observations. This is more speculative, but a
lot of physicists seem to think *something* needs to be done.

	-Robert

Re: cracks and pots

[Eduardo Dubuc]

Well Robert, you are right in every particular fact and detail about
Einstein and about relativity, there is not question about this. But there
is not question either that is not Einstein or relativity that concern us
here.

I am right about the fact that introducing Einstein and differential
geometry into our present discussion on the interaction of string theory
and category theory was an infantile attempt to attack Motl's views. Worst
than that, it introduces a distraction to Marta's principal issues.

I can not be on the side of Motl, neither on the side of Baez, since I am
ignorant about string theory. I point out that the Motl-Baez interaction
gives rise to important issues that concern what it is good and what is
bad mathematics or physics. In particular, what is good and what is bad
category theory. Also, the meaning and profitable consequences of being in
a fashionable subject. These issues were clearly exposed in Marta's
postings, and we should be ready to talk about them publicly.

In March 16 we got very good and pertinent postings that make us see other
angles, think and learn: Baez's, Paul Taylor's, Dusko's and Vincent
Shmitt's postings.

Silences are also meaningful.

e.d.

Re: cracks and pots

[Krzysztof Worytkiewicz]

Vincent, you sound like this Beatles song, you know, in the White
Album... Fully agree with you on the essentials of point 2 (you know
that). However,  uncritically referring to vociferations out of a
some hate blog only because the blogger is labeled "string theorist"
is not unlike point 1, at least in my modest opinion.

Among the problems with the way research is sponsored there is this
particularly modern one:  the commitment to the short-term. It is
quite similar to what happens in other sectors of the globalised
society (of "high civilisation index" as L.Motl would presumably say
-:( ) and leads to a growing disbalance in the allocation of
resources. Cats are a very fine tool to organise concepts and proofs.
Surprisingly enough, most mathematicians are quite reluctant or
openly hostile. On the high-end, cat theory is crucial when it comes
down to unify seemingly disparate areas of maths (which is unlikely a
goal for itself) and this kind of work is quite clearly long-term.

My 2 p: cat theory needs to be demystified in first place rather than
to be sold. In particular, I think that the (still somehow ongoing)
debate if it is a better foundation for maths or not is absolutely
pointless.

>  Category theory is just not very trendy at the
> minute and to get the money one needs to do theoretical physics
> (there had been also Computer Science at some point - that was poor
> is not it?).

Now we have the best of both worlds: quantum computing :-))

Cheers

Krzysztof

-- my government will categorically deny the incident ever occurred

Re: cracks and pots

[jim stasheff]

Robert J. MacG. Dawson wrote:

And, as you know, there are
still scales, almost a century later,  on which its predictions are
unsatisfactory.

For us ignorant of these, please explicate.

thanks

jim

> Eduardo Dubuc wrote:
>> Well Robert,
>>
>> 1)
>>
>>
>>> Well, Einstein was not "trying to"; he was using it, and presented this
>>> use as an accomplished fact.
>
> ...
>
>> General relativity was born with differential geometry; it has no meaning
>> without differential geometry. String theory was already there when a
>> category theory approach began.
>
>     Sorry, Eduardo! That's a little oversimplified.   See, for instance,
> section 17.7 of Misner, Thorne, and Wheeler's "Gravitation", among other
> references.
>
>      General relativity (though of course not in its modern form) goes back
> to Einstein's formulation of the equivalence principle in 1907 (only two
> years after special relativity), and the prediction of the gravitational
> red shift. In 1911 Einstein also predicted the bending of light by
> massive bodies; this too is intrinsically part of GR.
>
>     But it was only in 1912 that he realized that Euclidean geometry awas
> not compatible with this, and (encouraged by Grossmann and Levi-Civita)
> started looking at differential geometry as a way to handle
> non-Euclidean spacetime.  Einstein and Grossmann's 1913 attempt at a
> general relativity theory was wrong; it did not transform correctly.
> Some time after this,  Planck specifically warned him that the
> differential geometry approach would not work and would not be believed
> if it did.
>
>     In  November 1915 Einstein submitted two papers.  The first of these
> explained some observations such as the precession of the perihelion of
> Mercury, but in other ways made wildly nonphysical predictions
> (essentially ignoring many of the effects of mass -though  this
> "linearized theory" does have some uses as an approximation) He
> corrected this soon with a second paper in which he finally got it
> right. Sort of.
>
>     In 1917 Einstein introduced a cosmological constant into his field
> equations to account for the "fact" that the universe wasn't expanding.
> In the 1920's he took it out again when it turned out that the universe
> *was* expanding.  Now astronomers think there ought to be one, but with
> a value very different from what Einstein originally put forward.
>
>     So GR got by without differential geometry for five years; and it was
> another decade or so before it was a mature theory with enough of  the
> bugs out to do what was expected of it.  And, as you know, there are
> still scales, almost a century later,  on which its predictions are
> unsatisfactory.
>
>     -Robert
>
>
>
>

Re: cracks and pots

[George Janelidze]

I join Bob in saying that I fully agree with Marta, and I fully agree with
Bob's second sentence. However, I have a problem with "look the gift horse
in the mouth", since the horses we get are so often headless...

I would also like to make just one comment to Paul's message (although I
disagree with most of it; sorry!). Paul says:

"Which generation was it that alienated other mathematicians by making
outrageous claims about the foundations of mathematics that it never
backed up with theorems?   Which generation actually got its hands dirty
and proved the theorems that relate category theory to other foundational
disciplines?"

Well, our colleagues active in the 1960s and 70s invented elementary
toposes, for example, and proved many theorems about them. Those theorems
did not convince set-theorists to forget sets, but are they convinced now?
On the other hand those theorems were very beautiful, along with many others
from several areas of category theory; I would describe 1960s and 70s as
Golden Age of category theory. I am not saying of course that nothing
important was discovered after 70s, but I see problems, and growing chaos,
often created by ambitiously presented pseudo-relations with "other
foundational disciplines".

Moreover, talking about "relations": According to the classical work of
Sammy and Saunders, the first "relation" was with algebraic topology. As we
all know, there are various (co)homology/homotopy functors from topological
spaces to groups, or to more complicated algebraic (or coalgebraic, Hopf,
etc.) structures. There are also simplicial sets and other combinatorial
intermediate players, and the relationship between geometric and
combinatorial objects goes back to Euler (if not to Plato...). As we know
from 1960s, the universal property of Yoneda embedding yields various
adjoint functors, including those between simplicial sets and topological
spaces - and this is why combinatorial objects are there! And what do recent
algebraic topology text books do instead of explaining this? They are still
talking about gluing cells instead. I think if we really care about
relations between category theory and "other foundational disciplines", we
should begin by explaining that category theory is not just a language
allowing one to call homology a functor, but that category theory has
beautiful constructions and results (some already from 1940s and 50s!)
making enormous simplifications/applications/illuminations in neighbour
areas of pure mathematics, such as abstract algebra, geometry, and logic.

George Janelidze

----- Original Message -----
From: "RFC Walters" <robert.walters@uninsubria.it>
To: <categories@mta.ca>
Sent: Wednesday, March 15, 2006 3:35 PM
Subject: categories: Re: cracks and pots


> I also would like to support the remarks of Marta with which I am in
> full agreement.
> The category theory community seems happy to accept uncritically, and
> give centre-stage to, any interest shown by an external field. In this
> context one should certainly look the gift horse in the mouth.
>
> Bob Walters

RE: cracks and pots

[Marta Bunge]

Dear Vincent,

I am glad that you posted your reply to me. You raise questions that many of
us have and that really relate to what I was trying to convey.  I hope that
your letter is widely read. I will only comment on one aspect of it.

>Of course the problem is the way research is sponsored.
>Leading researchers are not so much good mathematicians
>but good salesmen. Category theory is just not very trendy at the
>minute and to get the money one needs to do theoretical physics
>(there had been also Computer Science at some point - that was poor
>is not it?).
>There were a couple of Fields medals and  a new train called
>TQFT that everybody just jumps in to get funded.

I see nothing wrong in seeking funding for serious and well-motivated
research. Young people have to eat too! What I worry about (this I did not
say before) is that this craze for funding may drive researchers to accept
*any* kind of funding, thinking naively that there are no strings (no pun
intended) attached. When I was young, I once rejected NATO funding and,
since there was no other source of funding for me at the moment, I had to
go back to Argentina for two years and thus interrupt my graduate studies
at Penn. Nowadays, it is the turn of organizations such as the Templeton
Foundation (seeking to conciliate science with religion) which offer
"graciously" to fund (and lavishly so) many projects in philosophy,
physics and mathematics.

Examples of Templeton funding are increasingly found: take the Perimeter
Insitute (String Theory), the Godel Centennary Symposium in Vienna (Logic
and Foundations), the workshop organized by A. Connes at the Sir Isaac
Newton Insititue in Cambridge (Non Commutative Algebra), and others that
are mentioned in Nature, for instance. This is all for public consumption
-- just look at their web sites. Some of us find this really scary. That
is why I do not put the getting of grants as a priority-- good science and
good mathematics should always be the main priority.

But then, you will ask, how do we feed graduate students, postdocs and
unemployed category theorists? I do not know, but certainly not by resorting
to dubious sources of funding. Not that it has happened yet! Forgive my
"using" your comment to give way to a deep source of worry, certainly not
unrelated to what I have been saying since the beginning of this discussion.


As for

>2/ Will be the rebirth of category - I bet!


This is partly what I was asking -- are we (CT) in such a poor state that we
need to be reborn in another guise? Maybe so, but I am just too immersed in
my own (certainly not main stream) work to really judge. You are not the
only one to suggest that we need an uplift. That may be so, but is it the
reason for thinking it merely that there are no grants coming our way these
days --  except when we (say that we) work in matters of interest to
physics?

It seems that I have only questions to ask -- not solutions to give. I
apologize for that.


Best wishes,
Marta

>From: "V. Schmitt" <vs27@mcs.le.ac.uk>
>To: categories@mta.ca
>Subject: categories: Re: cracks and pots
>Date: Thu, 16 Mar 2006 09:51:00 +0000
>
>Dear Marta,
>My english is so, so. I am french.
>But this is to give briefly my opinion (I agree with you
>more or less).
>
>I know a little of category and mathematics in general.
>I love the category theory developped in the 70's and
>I would have appreciated some category meetings at the
>time.  But i am too young.
>
>Category theory like any good mathematics will never
>die - but may "our" category community will.
>
>Of course the problem is the way research is sponsored.
>Leading researchers are not so much good mathematicians
>but good salesmen. Category theory is just not very trendy at the
>minute and to get the money one needs to do theoretical physics
>(there had been also Computer Science at some point - that was poor
>is not it?).
>There were a couple of Fields medals and  a new train called
>TQFT that everybody just jumps in to get funded.
>
>Now as a *community* what shall *we* do?
>
>First the question regards mainly the established
>people in the community (not me!).
>1/ One can try to sell category theory  in a better way.
>This is a bit like tomato sauce that you can put everywhere.
>And try to make new friends - inviting them to give talks... -
>from different disciplines.
>2/ We may claim loudly that cat theory is real mathematics
>and really try hard to do good mathematics. There are
>certainly good mathematicians definitely willing to use
>cat theory.  I saw many coming to category theory to develop
>their own maths (- this happens for instance in France with Berger who
>will never claim that he is a "categorician". Though he is completely
>in it!)
>
>My feeling is the attitude 1/ pushed to the extreme may be
>very damaging.  These talks about category everywhere and
>for everything are just poor and sound really stupid.
>They do not serve the cause.
>
>2/ Will be the rebirth of category - I bet!
>
>Sorry for the message written in haste
>and the poor english. Good e-mails from you
>on the list!
>
>best regards,
>Vincent.
>
>
>
>

RE: cracks and pots

[Marta Bunge]

Dear John,

Thanks for your candid and informative letter. I feel that few people who so
far have responded to me (or to others in the discussion that I started)
really understand what my concerns are.


>Anyway, I'm sure these comments won't put your worries to rest!
>They're not really meant to.  I just think it's good to see the
>issue of "category theory and string theory" as part of a much
>bigger and more complicated mess.  :-)
>

Your comments were very interesting and of course they will not put my
worries to rest. I am grateful, though,  for your taking this as part of a
larger issue, on which I could expand more, but will not, since all I wanted
was to raise awareness, not to preach (or even less to police).

Best thoughts,
Marta

--------------------------------------------------------------------------------------------------------

>From: "John Baez" <baez@math.ucr.edu>
>To: categories@mta.ca (categories)
>Subject: categories: cracks and pots
>Date: Thu, 16 Mar 2006 12:47:53 -0800 (PST)
>
>Dear Marta -
>
>You write:
>
> > I am relieved to learn (from the postings by David Yetter and John Baez)
> > that Motl's blog on the issue of categories and string theory is based
>on 1)
> > (Yetter) Motl's reluctance, as is the case with many string theorists,
>to
> > refuse to learn category theory, and 2) (Baez) Motl's personal dislike
>of
> > John Baez and of many other people, so that since Motl's personality is
> > well-known, any damage will be minimal.
>
>Good!

...

[Further repetition deleted by moderator.]

Re: cracks and pots

[Vaughan Pratt]

Category theory, and for that matter modern (as opposed to elementary)
algebra, is to mathematics as mathematics is to physics, and for that
matter to computer science.  Whereas mathematics organizes reasoning
about the phenomena studied by physicists and computer scientists,
algebra and category theory perform a similar function for mathematics.

In any setting organization is desirable, and arguably necessary on
occasion.  But the use of algebra and category theory to organize
physics and computer science is a double whammy here.  One should
therefore be doubly sympathetic of those physicists and computer
scientists who want to know what substantive contribution is being made
to their subject and can't evaluate the answers because they are one if
not two levels removed from the necessary abstractions.

Vaughan Pratt

cracks and pots

[John Baez]

Dear Marta -

You write:

> I am relieved to learn (from the postings by David Yetter and John Baez)
> that Motl's blog on the issue of categories and string theory is based on 1)
> (Yetter) Motl's reluctance, as is the case with many string theorists, to
> refuse to learn category theory, and 2) (Baez) Motl's personal dislike of
> John Baez and of many other people, so that since Motl's personality is
> well-known, any damage will be minimal.

Good!

> I thank David and John for taking the trouble to respond in detail to what
> may have seem as a "provocation" on my part (well, perhaps it was...).

By the way, I should explain why I thought you might be kidding in
your original post.  I had never heard anyone before suggest that
category theory could be discredited by applications to string theory.
It completely surprised me.  I'm used to the opposite complaint:
that category theory is discredited by its *lack* of applications.
Of course, this always comes from people who 1) haven't taken the time
to learn of its applications, 2) don't know enough category theory to
appreciate its *intrinsic* interest.

But it's good to hear your real concern:

> But these informative responses do not address my main concern, which is one
> that others (publicly, as Eduardo Dubuc, but several others privately) have
> expressed to me following my posting. I was aiming at the fact that there is
> a certain trend within category theory (when did it start?) to consistently
> give center stage to anything that claims to have connections with physics
> (in particular string theory).  Is this because (it is believed that) the
> state of category theory is now so poor (as "evidenced" by the lack of
> grants) that they (the organizers of meetings) want to repair this image at
> any cost?

Since I began as a mathematical physicist and got interested in
n-categories for their applications to topological quantum field theory,
only later falling in love with category theory per se, I'm the wrong one
to answer this question.  I don't even know if it's true that applications
to physics are given center stage, much less when this started, or why.

I know a bit more about how people in differential geometry and
differential topology got excited about work with links to physics.
This trend probably started around the time of the Atiyah-Singer
index theorem, which uses characteristic classes to compute the
Euler characteristics of certain chain complexes built using
differential operators.  At the time this result was proved (1962-1965),
it seemed an audacious blend of analysis and topology.  That's
one reason it caught people's interest.

Another reason people liked the index theorem so much was that it
turned out to be related to "anomalies" in quantum field theory,
a phenomenon discovered by Adler, Bell and Jackiw around 1969.
These nasty "anomalies" are actually a very practical issue
in particle physics: they're related to the lifetime of the pion,
and you can rule out field theories that have certain kinds of anomalies.

I guess the relation between the index theorem and anomalies only
became clear in the late 70's.  I guess people were shocked and
excited when it turned out that such sophisticated topology had
practical applications to physics.  Most topologists didn't know
any quantum field theory, and most quantum field theorists didn't
know that much topology.  So, a kind of mutual fascination developed:
both sides began learning about each other.

People gave lots of proofs of the index theorem that illustrated
very different ways of looking at it.  The first proof had used a lot
of K-theory and cobordism theory; later proofs used more facts about
the heat equation, but by the time I was in grad school (1982-86)
Quillen was giving lectures in which he tried to find a proof that
only used multivariable calculus and "super" reasoning - i.e., lots
of Z/2-graded linear algebra.  This was when supersymmetry was just
hitting the shores of mathematics, and Witten was starting to work
his wonders.

Anyway, index theory is just one of the first of many developments
where ideas from physics met ideas from branches of math that seemed
to have nothing to do with physics.

In the heyday of Bourbaki, I guess pure mathematics seemed very
removed from physics.  It's fun to read what Dieudonne says about
mathematical physics in his "Panorama of Pure Mathematics".  By now,
the situation has completely reversed in many fields, starting with
differential geometry and topology, but then moving on to certain
areas of algebra, and algebraic geometry, and now category theory,
especially higher category theory....

This process has caused friction at every stage.  Physicists
don't always enjoy the intrusion of more mathematics into their various
fields!   Mathematicians don't always enjoy the intrusion of more
physics - or the fast-paced, exploratory, sometimes sloppy cognitive
style of physicists.  You may recall Jaffe and Quinn's worries about
the impact of physics on mathematics:

http://www.arxiv.org/abs/math.HO/9307227

and how Atiyah in reply called for mathematicians to adopt the
more "buccaneering" style of physics:

http://www.ams.org/bull/pre-1996-data/199430-2/199430-2TOC.html

which led Mac Lane to respond with the ballad of Captain Kidd:

http://www.math.nsc.ru/LBRT/g2/english/ssk/proof_is_necessary.pdf

The interesting big question is: how has this increased interaction
both helped and hurt mathematics and physics?  Clearly there are
benefits.  But does math become too "trendy" by chasing after links
with the latest ideas of string theory?  Does physics lose sight of
its real purpose by focusing too much on mathematical elegance?

There are lots of issues here.  I've gone on too long already to
want to tackle them now.  But I think it's fair to say that that
mathematics has benefited more than physics.  One reason is that
theories of physics do not need to be correct - i.e., apply to
this particular universe of ours - to be mathematically interesting.

Indeed, the funny thing about string theory is that while leading
to an abundant harvest of rigorous mathematical results, it has
not yet correctly predicted a single result from a single experiment,
even after more than 20 years of work on the part of many smart people.

This is part of a more general malaise in the theoretical side of
fundamental physics, which various people have been commenting on
recently:

http://www.math.columbia.edu/~woit/wordpress/?p=307

http://www.nyas.org/publications/UpdateUnbound.asp?UpdateID=41

http://math.ucr.edu/home/baez/where_we_stand/

So, it's possible that string theory will eventually fall out
of fashion.  This could change the current dynamic between math and
physics.  A lot will depend on the results from the LHC particle
accelerator, due to start operation in 2007.   It may get evidence
for string theory; it may not.

Anyway, I'm sure these comments won't put your worries to rest!
They're not really meant to.  I just think it's good to see the
issue of "category theory and string theory" as part of a much
bigger and more complicated mess.  :-)

Best,
jb

Re: cracks and pots

[Robert J. MacG. Dawson]

Eduardo Dubuc wrote:
> Well Robert,
>
> 1)
>
>
>>Well, Einstein was not "trying to"; he was using it, and presented this
>>use as an accomplished fact.

...

> General relativity was born with differential geometry; it has no meaning
> without differential geometry. String theory was already there when a
> category theory approach began.

	Sorry, Eduardo! That's a little oversimplified.   See, for instance,
section 17.7 of Misner, Thorne, and Wheeler's "Gravitation", among other
references.

	 General relativity (though of course not in its modern form) goes back
to Einstein's formulation of the equivalence principle in 1907 (only two
years after special relativity), and the prediction of the gravitational
red shift. In 1911 Einstein also predicted the bending of light by
massive bodies; this too is intrinsically part of GR.

	But it was only in 1912 that he realized that Euclidean geometry awas
not compatible with this, and (encouraged by Grossmann and Levi-Civita)
started looking at differential geometry as a way to handle
non-Euclidean spacetime.  Einstein and Grossmann's 1913 attempt at a
general relativity theory was wrong; it did not transform correctly.
Some time after this,  Planck specifically warned him that the
differential geometry approach would not work and would not be believed
if it did.

	In  November 1915 Einstein submitted two papers.  The first of these
explained some observations such as the precession of the perihelion of
Mercury, but in other ways made wildly nonphysical predictions
(essentially ignoring many of the effects of mass -though  this
"linearized theory" does have some uses as an approximation) He
corrected this soon with a second paper in which he finally got it
right. Sort of.

	In 1917 Einstein introduced a cosmological constant into his field
equations to account for the "fact" that the universe wasn't expanding.
In the 1920's he took it out again when it turned out that the universe
*was* expanding.  Now astronomers think there ought to be one, but with
a value very different from what Einstein originally put forward.

	So GR got by without differential geometry for five years; and it was
another decade or so before it was a mature theory with enough of  the
bugs out to do what was expected of it.  And, as you know, there are
still scales, almost a century later,  on which its predictions are
unsatisfactory.

	-Robert

Re: cracks and pots

[Eduardo Dubuc]

Well Robert,

1)

> Well, Einstein was not "trying to"; he was using it, and presented this
> use as an accomplished fact.

I just wanted to put in evidence the following fallacy that you are
pushing forward:

To attack the use of category theory (by some people) in string theory is
at the same level that it would have been to attack the use (by Einstein)
of differential geometry in general relativity.

General relativity was born with differential geometry; it has no meaning
without differential geometry. String theory was already there when a
category theory approach began.

It is not the same thing.

Putting everything in the same bag is a well-known strategy to confuse an
issue.

Also, to have a poor opinion of many papers on applications of category
theory to physics is one thing, to say that category theory has no future
in physics is a completely different one. Nobody (including Motl's writing
I am discussing (*)) has said the latter!!

Quoting now from David Yetter:

** If (I suspect when) the string theory emperor turns out to have no
clothes, Category theory will suddenly become de rigeur in physics". **

I start to believe that independently from what it finally happens with
string theory; it is possible, even with the emperor well dressed, that
category theory will with time become the rigeur in physics.

2)

> Also, you forgot to mention that he flunk a high-school exam or
> something of the sort proving by this very fact that a lot of people
> were stupid, just as they are those which have doubts about the real
> value of some applications of category theory to physics !

I can only say that I am sorry about your reaction to this. It was just an
irony, and I thought this was evident.

e.d.

(*) Motl said (if I remember correctly) something of the sort that he
thinks that to reach some goals of string theory certain category theory
approach will not be helpful.

Re: cracks and pots

[Robert J. MacG. Dawson]

Eduardo wrote:

> Well, Einstein was not "trying to", he was using it, and presented this
> use as an accomplished fact.

	He didn't just wake up one morning with the whole thing in finished
form.  Moreover, it was some time before it was experimentally verified;
some details, such as the presence or absence of a cosmological
constant, took some time to settle; some predictions (black holes,  Big
Bang) were not generally accepted for some time;  and even now it is
known *not* to be a good description of the universe at a very small scale.

> Also, you forgot to mention that he flunk a high-school exam or something
> of the sort proving by this very fact that a lot of people were stupid,
> just as they are those which have doubts about the real value of some
> applications of category theory to physics !

	I did not "forget" to, it never occurred to me to do so, for two good
reasons.

  	Firstly, I don't see the relevance.  Are you suggesting that

(1) Einstein must have been stupid to flunk an exam, or that

(2) his teacher and N-1 unspecified others were stupid because

	(2a) an exam was set that Einstein could flunk, or
	(2b) Einstein having flunked the exam, they did not recognize his
future genius & change the grade?

	None of these conclusions seem justified to me... as my records   at
Dalhousie and Cambridge will show,   people can flunk exams on bad days;
I don't *think* I'm stupid, and I know the instructors who set the exams
were not.

    But, secondly and more to the point, recent research suggests that
the story of Einstein's failing grades is apocryphal. What seems to have
happened is that  his school changed over from a grading scheme with 1
high and 6 low to one with 6 high and 1 low, and a surviving report card
had been misinterpreted.  See for instance:

	http://www.abc.net.au/science/k2/moments/s1115185.htm

	-Robert

Re: cracks and pots

[dusko]

On Mar 15, 2006, at 5:35 AM, RFC Walters wrote:

> The category theory community seems happy to accept uncritically, and
> give centre-stage to, any interest shown by an external field. In this
> context one should certainly look the gift horse in the mouth.

i think this is a very nice metaphor. but i am not sure that being
critical about science is as easy as looking in horses mouth. already
hilbert was largely wrong when he tried to prescribe a shape of a
science. and nowadays it is a much harder task. everyone sees just a
very small fragment. research advances by evolution, not by
intelligent design.

the division between pure and applied mathematics is not as simple as
it used to be. 20 years ago, if you wanted to work on something that
would never ever degrade into applications, then algebraic geometry
probably seemed like a good bet. nowadays, at each moment, millions
of transactions on the internet are secured using elliptic and
hyperelliptic curves; the structure of their picard groups is
discussed in standardisation bodies. if a bank protects its customers
from phishing by identity-based keys, they are using weil or tate
pairing...

so the purest math has become the most applied; the most spiritual
the most concrete. the other way around, these applications put a
babylonian library on everyone's desk. what was picard group again?
google for it. biology research is based on large public databases.
physics is documented (driven?) by blogs. even category theory is
discussed online.

so i think it is great that people get nasty, or personal about
category theory. the landscape of babylon: "the dog barks while the
caravan goes by."

just my 2p,
-- dusko

Re: cracks and pots

[V. Schmitt]

Dear Marta,
My english is so, so. I am french.
But this is to give briefly my opinion (I agree with you
more or less).

I know a little of category and mathematics in general.
I love the category theory developped in the 70's and
I would have appreciated some category meetings at the
time.  But i am too young.

Category theory like any good mathematics will never
die - but may "our" category community will.

Of course the problem is the way research is sponsored.
Leading researchers are not so much good mathematicians
but good salesmen. Category theory is just not very trendy at the
minute and to get the money one needs to do theoretical physics
(there had been also Computer Science at some point - that was poor
is not it?).
There were a couple of Fields medals and  a new train called
TQFT that everybody just jumps in to get funded.

Now as a *community* what shall *we* do?

First the question regards mainly the established
people in the community (not me!).
1/ One can try to sell category theory  in a better way.
This is a bit like tomato sauce that you can put everywhere.
And try to make new friends - inviting them to give talks... -
from different disciplines.
2/ We may claim loudly that cat theory is real mathematics
and really try hard to do good mathematics. There are
certainly good mathematicians definitely willing to use
cat theory.  I saw many coming to category theory to develop
their own maths (- this happens for instance in France with Berger who
will never claim that he is a "categorician". Though he is completely
in it!)

My feeling is the attitude 1/ pushed to the extreme may be
very damaging.  These talks about category everywhere and
for everything are just poor and sound really stupid.
They do not serve the cause.

2/ Will be the rebirth of category - I bet!

Sorry for the message written in haste
and the poor english. Good e-mails from you
on the list!

best regards,
Vincent.

Re: cracks and pots

[Eduardo Dubuc]

Hi:

I will put quotations from different postings or Molt's writing in between
two "**"

Well, I can see the classical reaction of some groups when one of its
members points out that something is really wrong with the group.

Marta will suffer all kind of "polite" (nothing of the sort of the
Benabou-Taylor confrontation) attacks, but not for this less devious or
sanguine. Typically she will be taken out of context, or get answers to
questions she never had asked, or be treated ironically or in disbelief
(**I can't tell if you're kidding.  I'll assume you're not **)


There are two principal points here:

1. The real value of some contributions of category theory to physics.

2.  The lot of rubbish written using category theory and which is
fashionable because it claims to have applications to physics.


Marta was forced to explicit some of the questions we can clearly see in
between lines in her original posting:

** I was trying to elicit an open response from those who *do* know about
the value (or lack of it) of categorical string theory. In particular, I
would like to have an answer to this question. Why is it that anything
which even remotely claims to have applications to physics (particularly
string theory) is given (what I view as) uncritical support in our
circles?

Best,
Marta **

I will like to see a clear answer to this question. Or a clear refutation
proving that it is not the case.

Notice that the existence of point 2. above is perfectly consistent with
the existence of really valuable contributions of category theory to
string theory, which is one of the points treated by Motl.

** There's nothing wrong with applying category theory to string theory.
The papers by Michael Douglas and Paul Aspinwall cited above by Motl
are some nice examples of using derived categories to study D-branes.**

This make us think that they may be some valuable contributions, but this
possibility is also left open by Motl himself.

Quoting myself:

** I will like to see here a debate about Motls's writing quoted above.

Just about this writing, NOT ABOUT Motls himself or other things he may
have done or represent !! **

No luck, just discredit Motl, not refute his sayings:

**  Perhaps more to the point, Lubos Motl is famous for his heated
rhetoric.  He doesn't like me, or anyone else who criticizes
string theory.  The articles you mention above are mainly reactions
to my This Week's Finds. **

** My reaction to the blog posts you cite is that this is a sting theorist
holding his breath and refusing to learn category theory. My guess is that
Motl wouldn't want to learn the heavily categorical formulations of mirror
symmetry that Yan Soibelman uses, even though they are motivated by string
theory.**

The following is  better in answering Motl:

** Categorical ideas are absolutely central to several competitors to
string theory: the Barrett-Crane model of quantum gravity (and to a lesser
extent 'loop quantum gravity' with which the BC model is often
conflated) and Connes' recovery of the Standard Model from non-commutative
geometry (a part of mathematics which has obliged reluctant mathematicians
to think about categorical ideas deeper than they originally were
comfortable with). There is nothing cracked or crackpot about either. **

I am unable to judge, but it seems to me this gives category theory strong
support But does not go against what Motl says concerning category
theory. Neither against Marta's warning that category theory is being
discredited by many (she says a minority) category theory people.

Motl writes:

** I've asked the same elementary questions to many people who've been
trying to explain me derived categories - some of them with some success,
most of them with no success whatsoever: Are these notions and statements
of category theory something that you can prove - or at least check in
many situations - to be valid for string theory as we know it, or is it
just an unproven conjecture that derived categories describe D-branes? **

Can somebody give a an answer ?

He also writes:

** I always feel very uneasy if the mathematically oriented people present
their conjectures about physics, quantum gravity, or string theory as some
sort of "obvious facts". **

I would say that any serious scientist or mathematician would feel the
same way !!, and also that this seems to be a common practice in many
papers that claim applications of category theory to physics.

** I have this image of differential geometers saying to each other, a
century ago, "Don't you think somebody ought to tell that Einstein to
stop trying to use differential geometry to explain gravity, before our
whole field gets a bad name?" **

Well, Einstein was not "trying to", he was using it, and presented this
use as an accomplished fact.

Also, you forgot to mention that he flunk a high-school exam or something
of the sort proving by this very fact that a lot of people were stupid,
just as they are those which have doubts about the real value of some
applications of category theory to physics !

** I do not see how anybody can possibly discredit category theory by
applying it to string theory, even inappropriately, any more than "The
da Vinci Code" discredits classical geometry and number theory. **

** Since Motl's personality is well known, any damage will be minimal.
I think we should relax and take it easy.**

Well, rubbish category theory always discredits the whole of category
theory, specially given the fact that it is not yet a prestigious and
established subject (think in SGA4 and the introduction of SGA41/2)

It will be nice to relax and take it easy.

Will all of us do so  ?

I hope we will read in this cat-list some valuable considerations about
Motl's questions and doubts, and about Marta's courageous warnings.

e.d.

Re: cracks and pots

[RFC Walters]

I also would like to support the remarks of Marta with which I am in
full agreement.
The category theory community seems happy to accept uncritically, and
give centre-stage to, any interest shown by an external field. In this
context one should certainly look the gift horse in the mouth.

Bob Walters

Re: cracks and pots

[Dominic Hughes]

Roger Penrose, page 960 of "The Road to Reality - A Complete Guide to the
Laws of the Universe":

  Another idea that may someday find a significant role to play in
  physical theory is *category* theory and its generalisation to
  n-category theory.  [...]  It would not altogether surprise me to find
  these notions playing some significant role in superseding conventional
  spacetime notions in the physics of the 21st century.

Dominic

http://boole.stanford.edu/~dominic

Re: cracks and pots

[Robert Seely]

I just posted a notice of a special session on Categorical Logic and
Quantum Computation in the upcoming ASL meeting at UQAM - although the
preparation for that session goes back many months, and it was always
my intention to post a schedule for the session here, I was reminded
to do so upon reading Marta's message; in a sense I see it as a
partial reply (even if the applications to physics are not those of
the postings Marta quoted).  I think the mathematics of that session
will be of a high standard - we hope many of you will attend to judge
for yourselves!

-= rags =-

-- 
<rags@math.mcgill.ca>
<www.math.mcgill.ca/rags>

Re: cracks and pots

[Marta Bunge]

Robert Dawson wrote:

>	It is not clear to me that the majority of theoretical physicists agree
>with the negative view of categorical string theory held by the cited blog
>writers; and in the absence of a consensus among the physicists, I for one
>(with an undergradate degree and some graduate courses in physics) do not
>feel qualified to take sides; if anything, errors should be on the side of
>trying out too many ideas, not too few.
>

I was trying to elicit an open response from those who *do* know about the
value (or lack of it) of categorical string theory. In particular, I would
like to have an answer to this question. Why is it that anything which even
remotedly claims to have applications to physics (particularly string
theory) is
given (what I view as) uncritical support in our circles?

Best,
Marta

Re: cracks and pots

[Robert J. MacG. Dawson]

Marta Bunge wrote;


	This [inviting researchers in fashionable applied areas to speak at
	category theory meetings] may lead to narrow
> developments of any subject that they approach with this objective in
> mind, and that is dangerous for the future of category theory (of
> mathematics, in general). That is my main concern. My posting tried to
> call attention to what I think is a sad state of affairs in category
> theory, when it need not be.

	It is not clear to me that the majority of theoretical physicists agree
with the negative view of categorical string theory held by the cited
blog writers; and in the absence of a consensus among the physicists, I
for one (with an undergradate degree and some graduate courses in
physics) do not feel qualified to take sides; if anything, errors should
be on the side of trying out too many ideas, not too few.

	I have this image of differential geometers saying to each other, a
century ago, "Don't you think somebody ought to tell that Einstein to
stop trying to use differential geometry to explain gravity, before our
whole field gets a bad name?"

	Of course, the pioneering knot theorists probably thought that Lord
Kelvin ought to stop trying to explain atomic nuclei as knotted loops of
ether, too.  But I think Einstein did differential geometry more good
than Kelvin did harm to knot theory.  A mathematical technique  powerful
enough to show that a physical theory does *not* work has shown its own
value.

	What has sometimes gone on, at least for a while, is that very abstract
physical theories have continued to be studied after it had become
obvious that their predictions were wildly at variance with observation,
or that they would never make any predictions. Even then I don't think
the reputation of the mathematical theory being abused suffers, though
that of the neighboring theoretical physicists may. I don't think this
is the case with string theory yet, though I could be wrong.

	Cheers,
	      Robert Dawson

Re: cracks and pots

[Marta Bunge]

Dear Robert,

I agree with most of what you say, and I was not suggesting that we police
how categorists choose to apply their field. Nothing further from my mind.

>	Mathematics, like the phone service, is a "common carrier". We develop it;
>we use it; but we have neither the right nor the obligation to police how
>others apply it (unless they get the mathematics itself wrong?).  Moreover,
>given the historical difficulty of recognizing good physical theories ahead
>of time, it would be impossible to do so wisely even if we had the right.

But organizers of meetings in category-related subjects can certainly direct
attention to certain trends in category theory, thereby promoting certain
areas over others, and this they can easily do by their choice of invited
speakers of (series of) lectures. They may have neither the right nor the
obligation to do so, but they certainly have the power to do so. If this
happens consistently, then the outcome is predictable. Students (and their
advisors) might flock to certain areas of research just because they are
fashionable and can thus get funding that otherwise will not be easily
obtained. This may lead to narrow developments of any subject that they
approach with this objective in mind, and that is dangerous for the future
of category theory (of mathematics, in general). That is my main concern. My
posting tried to call attention to what I think is a sad state of affairs in
category theory, when it need not be.

Best wishes,
Marta

Re: cracks and pots

[Robert J. MacG. Dawson]

Marta Bunge wrote:
> Hi,
>
> I just came across the following pages
>
> http://motls.blogspot.com/2004/11/category-theory-and-physics.html
> http://motls.blogspot.com/2004/11/this-week-208-analysis.html
>
> written by Lubos Motl, a physicist (string theorist). Some of you may find
> these articles interesting and probably revealing.
>
> Are we category theorists as a whole going to quietly accept getting
> discredited by a minority of us presumably applying category theory to
> string theory? It is surely not too late to react and point out that
> this is not what (all of) category theory is about.

	I don't see that we have any more need to do this than (for instance)
algebraic topologist, group theorists, or differential geometers have
when somebody floats a perhaps-too-conjectural theory using those
branches of mathematics. Heck, physicists have managed to come up with
what are now generally seen as dubious theories using nothing more than
elementary arithmetic (Dirac's Big Numbers hypothesis, say.)  Do the
number theorists have to protest this?

	Big problems in physics have tended to be solved only after a lot of
attempts that look pretty strange in retrospect (think of some of the
early models of the atom!)   But correct theories (or at least theories
that represent a major improvement in understanding and prediction) can
also look pretty strange;  think how general relativity, or even special
relativity, must have looked in their day.  I seem to recall that the
periodic table was originally considered at least as dubious as Bode's
Law - and if they had been able to measure molecular masses more
accurately in Mendeleev's day, they would have seen that the main idea
was actually _wrong_, and its acceptance would probably have had to
await the technology to separate individual isotopes, which do have
(reasonably) predictable masses.  Quaternions were fashionable in
Victorian days to represent motions in space, dropped out of fashion
when people decided that the restriction of their applicability to
three-dimensional space was parochial, and dropped back in again when
people realized that in fact a three-plus-one-dimensional spacetime had
some rather special properties.

	Mathematics, like the phone service, is a "common carrier". We develop
it; we use it; but we have neither the right nor the obligation to
police how others apply it (unless they get the mathematics itself
wrong?).  Moreover, given the historical difficulty of recognizing good
physical theories ahead of time, it would be impossible to do so wisely
even if we had the right.

	I do not see how anybody can possibly discredit category theory by
applying it to string theory, even inappropriately, any more than "The
da Vinci Code" discredits classical geometry and number theory.

	-Robert Dawson

Re: cracks and pots

[Eduardo Dubuc]

I congratulate Marta for her posting, I just read Motls's

http://motls.blogspot.com/2004/11/category-theory-and-physics.html

and find it very revealing as Marta said, and more than that, I find it a
very clear exposition (by way of philosophy and by way of examples)
about what is good science and mathematicas and about what it is not.

Marta is right about that it concerns all of us category theoricist.

I will like to see here a debate about Motls's writing quoted above.

Just about this writing, NOT ABOUT Motls himself or other things he may
have done or represent !!

I do not feel capable to say something because in particular am ignorant
of physics, but many of you are not. I think in Bill for example.

So long    Eduardo Dubuc

Re: cracks and pots

[David Yetter]

Dear Marta,

My reaction to the blog posts you cite is that this is a sting theorist
holding
his breath and refusing to learn category theory. My guess is that Motl
wouldn't
want to learn the heavily categorical formulations of mirror symmetry
that Yan
Soibelman uses, even though they are motivated by string theory.
Basically
categorical ideas aren't part of the standard bag of tricks physicists
use (even
though they often give much more elegant, concise, and insightful
formulations of some of those tricks), and the proverb about 'old dogs'
and
'new tricks' applies to physicists as well.

His attack on Baez is fairly standard stuff:  in the mode of "string
theory
is the theory of nature, so we don't want to think about alternatives
like
loop quantum gravity."  It is a polemical defense of a scientific
theory that
hasn't produced a testable prediction in the 40 plus years since its
inception,
and worse than that, unless one adds bells and whistles to fix it (in
the manner
of 'gaseous Vulcan' or Ptolemaic epicycles), predicts the existence
of a massless scalar field *not observed in nature*.  It really has
nothing at
all to say about category theory, which is after all a mathematical
theory
which stands irrespective of its extra-mathematical applications.

Categorical ideas are absolutely central to several competitors to
string theory:
the Barrett-Crane model of quantum gravity (and to a lesser
extent 'loop quantum gravity' with which the BC model is often
conflated)
and Connes' recovery of the Standard Model from non-commutative geometry
(a part of mathematics which has obliged reluctant mathematicians to
think about
categorical ideas deeper than they originally were comfortable with).
There is nothing
cracked or crackpot about either.

It is simply a fact we have to live with that our subject has found
legitimate uses
in physics, but uses which are unpopular with the dominant school of
physics in
the North America.  If (I suspect when) the string theory emperor turns
out
to have no clothes, category theory will suddenly become de rigeur in
physics.  (As it should, since categorical expressions of physical
ideas are the logical conclusion of 20th century physics drive to
express
everything in coordinate-free terms.)

Best Thoughts,
David Yetter









On 12 Mar 2006, at 17:29, Marta Bunge wrote:

> Hi,
>
> I just came across the following pages
>
> http://motls.blogspot.com/2004/11/category-theory-and-physics.html
> http://motls.blogspot.com/2004/11/this-week-208-analysis.html
>
> written by Lubos Motl, a physicist (string theorist). Some of you may
> find
> these articles interesting and probably revealing.
>
> Are we category theorists as a whole going to quietly accept getting
> discredited by a minority of us presumably applying category theory to
> string theory? It is surely not too late to react and point out that
> this is
> not what (all of) category theory is about. Please give a thought
> about what
> we, as a community, can urgently do to repair this damaging impression.
> Unless we are prepared to wait until things change by themselves
> within our
> lifetime.
>
>
> Hopefully disturbing your weekend,
> Cordially,
> Marta
>
>
>
> ************************************************
> Marta Bunge
> Professor Emerita
> Dept of Mathematics and Statistics
> McGill University
> 805 Sherbrooke St. West
> Montreal, QC, Canada H3A 2K6
> Office: (514) 398-3810
> Home: (514) 935-3618
> marta.bunge@mcgill.ca
> http://www.math.mcgill.ca/bunge/
> ************************************************
>
>

cracks and pots

[Marta Bunge]

Hi,

I just came across the following pages

http://motls.blogspot.com/2004/11/category-theory-and-physics.html
http://motls.blogspot.com/2004/11/this-week-208-analysis.html

written by Lubos Motl, a physicist (string theorist). Some of you may find
these articles interesting and probably revealing.

Are we category theorists as a whole going to quietly accept getting
discredited by a minority of us presumably applying category theory to
string theory? It is surely not too late to react and point out that this is
not what (all of) category theory is about. Please give a thought about what
we, as a community, can urgently do to repair this damaging impression.
Unless we are prepared to wait until things change by themselves within our
lifetime.


Hopefully disturbing your weekend,
Cordially,
Marta



************************************************
Marta Bunge
Professor Emerita
Dept of Mathematics and Statistics
McGill University
805 Sherbrooke St. West
Montreal, QC, Canada H3A 2K6
Office: (514) 398-3810
Home: (514) 935-3618
marta.bunge@mcgill.ca
http://www.math.mcgill.ca/bunge/
************************************************