Subject: categories: RE: cracks and pots 93

From: "Marta Bunge" <[email-masked]>
Date: Fri, 31 Mar 2006 17:17:26 -0500

Dear Eduardo,

Your message contains many important observations with which I very much
agree, and a few others that need discussing. I may comment on it some time
soon, publicly or privately. Right now, my purpose for replying to you is a
different and more pressing one.

I noticed that in your "cracks and pots 93" you implicitly refer to a lette=
r
which I had sent to categories in reply to Peter Selinger, and which I had
also sent privately to various people, including you. The letter in questio=
n
never appeared!. It contained an attachment (to MacLane's article) which,
according to Bob Rosebrugh, was difficult to include, hence the delay of it=
s
posting, and ultimately my replacing it by a brief message in response to
Bill Lawvere, in which I included the URL, as suggested by Bob. It seems
imperative now that I post the original message, without the attachment.
Thus, portions of your letter may make more sense. It is below this message=
=2E

By the way, by my own count, there are only 75 messages posted in the
"thread", but 183 more that were written privately to me in connection with
it. Maybe you included some private messages in your count? Either way, thi=
s
means a *lot* of messages.

Best,
Marta

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Dear Peter,

You were lucky to have been away on vacation, but perhaps quickly reading
(how else) the mass of postings in the "cracks and pots" has caused you
intellectual indigestion. Your reaction is therefore quite understandable.
For your sake (and that of others in similar situations), I will sum up wha=
t
caused my postings, and be more explicit concerning

>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.

1.
On March 13, I shared with you all a disturbing posting in Motl's blog,
criticizing category theory in its applications to physics, and more
particularly, John Baez. My concern was based on the possibility that any o=
f
this criticism might be justified because I could not failed to notice how
John Baez had become more or less a prominent figure (as speaker/member of
the scientific committee) in recent(ly announced) meetings in CT.
Explicitly, I was thinking of

Firenze, Ramifications of CT, Nov 13-19, 2003,
Sydney, StreetFest, July 11-16, 2005,
Union College, UC Mathematical Conference, December 3-4, 2005,
Chicago, MacLane Memorial Conference (Unni Nambondiri Lectures), April
7,10,11, 2006,
Halifax (near), CT'06, June 25-July 1, 2006.

2.
On  March 14, and in response to some,  I asked more explicitly what caused
organizers of meetings to bring to center stage one aspect of CT over
others, particulaly one which seemed to me not to be in good standing after
Motl's postings. Was it because it is indeed the case that CT is in
disrepute, and if so its reputation needs to be restored, this being the
best way to do it? Was it because it is funding for CT (notoriously lacking
in the USA) that may be more easily secured that way? I wanted to know
myself, but also possibly alert organizers of meetings to reflect on this
issues, since their power and responsibility is indeed enormous in promotin=
g
a certain kind of research over another.

3.
>From the many responses that I got (some public, and many more privately),=
 I
picked on one (March 17) to add some information that I had just come acros=
s
by reading Nature (on our coffee table, along with a dozen or so scientific
journals), in an article which connected Lee Smolin of the Perimeter
Institute with the Templeton Foundation, the latter a promoter of anything
they can in the borderline of science and religion. In the Scientific
American articles by Lee Smolin on Loop Quantum Gravity and the discretenes=
s
of the universe, a paper John Baez is quoted among the few references  give=
n
at the end of the article. This, in turn, led me to research the Templeton
Foundation itself, and with some help from a fellow categorist who seemed t=
o
know a lot about it, I easily located references to Templeton funding to th=
e
Goedel Centenary Symposium in Vienna, and to the A.Connes workshop on NCA a=
t
the Sir Isaac Newton Institute in Cambridge. I was, however, relieved not t=
o
find any direct connection between Templeton and Category Theory. Still, I
meant to warn those unaware of this easy source of funding (with strings
attached). In a subsequengt posting (March 27) I gave explicit references t=
o
these claims in response to some queries.

4.
In short, I do not think that I can be blamed for not being explicit enough
in matters that I could be explicit about. I still do not have all the
answers to my questions. As I mentioned on March 27, I was mistaken in
thinking of John Baez as a promoter of string theory when, in fact, he
promotes a competitor thery, LQG. But the general question of categorical
applications to physics remained. Why are they promoted now? As you, Peter,
kindly offer as a possible explanation,

>Can one rule out another possibility, namely that such research is
>supported because it is original, timely, and interesting?

No, of course not -- one cannot rule it out. Here, I am ignorant of physics
so I cannot answer this question (David Yetter has supported the view that
they are original, timely and interesting, and has contrasted "algebraic" t=
o
"foundational" aspects of CT).  But even if the answer were "yes", I would
welcome responses  to the question which still remains unaswered (except
that most of us surely have a formed opinion) -- is CT in such a poor state
that it needs revamping? Sould we not wait a few years until several
original and interesting (maybe not timely) contributions to CT in
connection with other fields of mathematics are appreciated and incorporate=
d
into the mainstream? What do we gain by pushing those under the rag? To
imply, perhaps, that we ourselves do not value them? These, I believe, are
crucial and timely questions, and I do not regret unwilingly having brought
them up

5.
I take this opportunity to thank Bill Lawvere for his first posting "Why ar=
e
we concerned? I", in which the lucid article by Saunders MacLane (Synthese,
1997) is recalled in connection with the discussions that arose in the
"cracks and pots" so-called-thread (why "thread"?). I am sure that most of
you have read it, but just in case you have not, I attach it here it in pdf
form. This is very timely in view of the upcoming MacLane Memorial
Conference in Chicago.

Peter, I hope that I have answered your questions. I can't speak for the
others who have contributed to this "thread". Unlike what has been
suggested, what I originated on March 13 was far from a "complot". It was a
genuine concern of mine and I see now, by many of the responses, that it is
also a concern of others. On the other hand, getting personally attacked
(for the wrong reasons, to boot) is a necessary price that I have to pay an=
d
it does not concern me as much.

Yours,
Marta

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>From: Eduardo Dubuc <[email-masked]>
>To: [email-masked]
>Subject: categories: cracks and pots 93
>Date: Thu, 30 Mar 2006 15:31:17 -0300 (ART)
>
>Hi,
>
>The 93 is because I have by now 92 msages in my cracks and pots file.
>
>I apologize for the length of this posting. It is intended to be a (may be
>biased) partial account of the debate, and some comments.
>
>
>Well, by now the "cracks and pots" debate is establishing itself as, in my
>opinion, an interesting and worth-wile event. Congratulations   Marta !!
>
>We are learning about:
>
>a) Understand  (for many of us) better what is mathematics, and what is
>physics, what is rigor and what is buccaneering, and also what is
>bullshit.
>
>b) "Something is rotten in the state of category theory community"
>
>Pay attention that The Bard does not say "category theory", but he says
>"category theory community"
>
>I start from who has made the more refreshing, humorous, down to
>earth, honest and intelligent contributions to this debate:
>
>**Vicent Schmitt: 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 publicly debated.**
>
>Yes Vincent!!, you point right to what it is at the center (or very near
>it) the problem raised in Marta=D5s original "cracks and pots" posting!. A=
nd
>the "(come on!...)", beautiful !.
>
>Now, talking about rigor, conjectures and proofs:
>
>**Maclane : If a result has not yet been given valid proof, it isn't yet
>mathematics. This however does not deny the many preliminary stages of
>insight, experiment, speculation or conjecture, which can lead to
>mathematics. It states simply that a conjectured result is not yet a
>theorem **
>
>It is relevant to compare this with Motl's distinction between physics and
>mathematics:
>
>**Motl: In physics, we propose different conjectures about the real world,
>and it is important that we're not guaranteed that these conjectures will
>be true.
>
>String theory itself is not just a conjecture, but rather a
>seemingly consistent mathematical framework. Once we accept string theory
>as an objectively existing mathematical structure, a structure that we
>treat as a part of "generalized physics" - which is of course what all
>string theorists are doing every day - we can ask a lot of questions about
>its properties.**
>
>He does distinguish between  "physics as conjecture" and mathematics with
>applications to physics. He call this mathematics  "generalized physics"
>
>But "conjecture" to be acceptable is not unrigourous neither buccaneering.
>he says:
>
>**Motl: the statements about string theory are just conjectures, and they
>need to be proved or supported by evidence, otherwise they're irrelevant
>and "wrong", in the physical sense.**
>
>He also says:
>
>** Motl: 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".
>
>He is clearly saying that those "mathematically oriented people" are
>lacking  rigor.
>
>Many postings in this debate confound mathematical rigor with formalism,
>and push forward the idea that a formal and logically correct statement
>has automatically rigor. Even if it is foolish:
>
>**V. Pratt: In axiomatic mathematics, everything that is not forbidden is
>permitted. **
>
>**R. Dawson: If the math itself meets mathematical standards of rigor, its
>application to physics need surely only meet the standards appropriate to
>that subject.**
>
>It seems to me that he is equating here "mathematical standards of rigor"
>with "logically correct", and  "the standards appropriate to that subject"
>(in this case, physics) with " buccaneering "
>
>Nothing more wrong!! . In both cases, failing to convey what it should be
>considered  "rigor in mathematics"  and  "rigor in physics"
>
>But again Saunders and Lubos:
>
>**MacLane: real proof is not simply a formalized document, but a sequence
>of ideas and insights**
>
>** Motl: the primary physical motivation is to locate the right ideas and
>equations that describe the real world. Category theory has been used by
>many to achieve completely wrong physical conclusions - for example, by
>considering the "pompously foolish" quantization functor.**
>
>He however seems to be pushing forward the same misconception of "rigor":
>
>**Motl: It may be nice to be rigorous, but it's always more important to
>be correct: if the specific kind of rigor leads us to stupid conclusions
>in physics, we should avoid it.**
>
>From the original Marta's "cracks and pots"
>
>**M.Bunge:  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?**
>
>**J. Baez: 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.**
>
>Here it is a clear and rigorous answer:
>
>(1) **W. Lawvere: The question is not whether mathematics should be
>applied. Most of us agree that it should. The concern is rather that our
>subject is sometimes being used as a mystifying smoke screen to protect
>pseudo-applications against the scrutiny of the general public and of the
>scientific colleagues in adjacent disciplines. We need to ensure that
>applications themselves be maximally effective, not clouded by
>misunderstanding.**
>
>Now, an example of superficial conclusions:
>
>** J. Baez: 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.**
>
>There is nothing funny about this. Lubos say:
>
>** Motl: One of the fascinating features of string theory is that its
>objects and investigations, even though they've been partially
>disconnected from the daily exchanges with the experimentalists, remained
>extremely physical in character. All of the objects that we deal with are
>analogous to some objects in well-known working physical theories, to say
>the least.**
>
>Bill has made a serious, well fundamented and non-bullshit contribution to
>"crack and pots" (he utilizes a different heading:" WHY ARE WE CONCERNED?"=
)
>
>In contrast to many passages of some contributors that it will be tiresome
>to reproduce here, and where one founds an overwhelming proliferation of
>
>highly technical, sophisticated, difficult and impressively sounding words
>
>such that it becomes impossible to see what they are saying, unless you
>are an expert, in which case you may find out that it is only superficial
>thinking  (I am thinking specially in certain parts of  Davis Yetter's
>postings).
>
>** W. Lawvere: Professors may not consider the possibility of learning
>from undergraduate text books, and some may feel bored that I have once
>again repeated the above basic definitions and observations.**
>
>If you have some real thoughts, you do not need impressive jargon.
>
>See what an original and deep insight:
>
>** W. Lawvere: As quantity includes zero, so structure includes the case
>of no structure, which Cantor considered one of his most profound and
>exciting discoveries**
>
>Superficial thinking  (which could be malicious, but very often is simply
>stupid) has manifested itself in these postings  by pushing forward the
>idea that there are two different  kinds of category theory:
>
>"Categories as Foundation" and  "Categories as Algebra", the first
>implicitly (but not explicitly said) the "bad one", and the second the
>"good" one.
>
>** D. Yetter: 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.**
>
>We have an excellent analysis of this fallacy in Bill's postings, which
>should be read carefully and slowly.
>
>I imagine now to add something that Lawvere himself pointed out a long
>time ago: The laws of logic are a particular instance of the categorical
>concept of adjoint functors, a concept that grew out of mathematical
>experience.
>
>There is any way some explanation to Yetter's prejudice against
>"categories as foundation".  Often very poor category theory has been
>justified by people writing on foundations. Bill's quote (1) above also
>applies to this and related use of category theory in theoretical computer
>science.
>
>Somebody else that does not need either noisy language sees better:
>
>** Dusko: I am of course saying things very clear and familiar to many
>people on this list, but maybe they are worth saying nevertheless.**
>
>** Dusko: 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 **
>
>Then, he passes to consider Grothendiek's  ("the greatest of the
>category theorists") work  on Topos theory as work on foundations, which
>agrees with the analysis of foundations made by Lawvere.
>
>I can not restrain myself to quote the following magnificent piece of
>meaningless  hallucinogenic  discourse:
>
>**V. Pratt: In the millions of years of evolution of primate thinking, no
>productive mathematical mechanism has a higher probability of being
>stumbled on than mathematics founded on the Yoneda axiom. I know of no
>better explanation of how human thought could have evolved to its present
>form than evolution finding and exploiting the Yoneda principle**
>
>Now, some serious business:
>
>In recent years J.Baez and his followers have been occupying more and more
>space in the categorical community (this fact is at the starting point of
>the present debate).
>
>I think this is so because they have some interesting category theory to
>show, but they are occupying more space than their mathematics deserves
>because they bring a refreshing air to a community until now dominated by
>an old guard that has not shown signs of necessary evolution, and that has
>not being able to attract very good and talented young mathematicians to
>the community. There is now not other exiting body of developments within
>the community. The old guard is being pushed out (prone or supine ?), but,
>alas, not by better mathematicians.
>
>Category theory is in good shape (in particular pushed forward by the
>Russian school), and it is now passing over the category community. I
>have lost the information now, but recently it was in Europe an important
>congress that it had two subjects: one was a prestigious subject (that I
>do not remember now), the other was category theory. Not a single name
>(including Baez group) that we see in the category theory community
>meetings was there.
>
>Best wishes to all   e.d.
>
>
>
>
>
>
>
>
>
>