Re: Publicity

Re: Publicity

[Fred E.J. Linton]

Vaughan Pratt <pratt@cs.stanford.edu> suggested:

>   From Rehmeyer's article:
> 
> "It?s even proving valuable in developing rigorous models of music theory."
> 
> " 'If people adopt the level of rigor of category theory,' [Spivak]
> says, 'it will provide a precise language for science as a whole, and it
> will help individual scientists to clarify their thinking.' "
> 
> I don't know what "rigor" is, but if we identify it with consistency
> then there is a limit to the rigor of category theory: Goedel's second
> incompleteness theorem shows that category theory cannot be rigorous
> enough to establish its own rigor.

In my estimation, the "rigor" in Rehmeyer's adjective "rigorous" and
the "rigor" in Spivak's quote have about as little to do with each other
as either has to do with the one in the phrase "rigor mortis" :-) . 

Cheers, -- Fred



[For admin and other information see: http://www.mta.ca/~cat-dist/ ]

Re: Publicity

[Tom Hirschowitz]

Dear Steve,

Nice metaphor!

But I'm afraid my point carries over to the new setting, as:

Category-land looks wild and scary from the surrounding fortresses, so
maybe we should be softer towards people trying to make it look
attractive, open, and, above all, safe.

I'll stop bugging the list with this all now, sorry for the noise.
Tom

On 06/13/2013 09:25 AM, Steve Vickers wrote:
> Dear Tom,
>
> That's the wrong way to look at it. Category-land is really the land _between_ the fortresses. The courage to enter Category-land is the courage to leave the supposed protection of the city walls.
>
> I was lucky enough to do my PhD in a region (Ringland) where they were already getting used to life without having those walls, but for for many of the city dwellers the idea that maths has anything to do with categories is as alien as the idea that milk comes from cows.
>
> Steve.
>
>
> On 11 Jun 2013, at 13:40, Tom Hirschowitz<tom.hirschowitz@univ-savoie.fr>  wrote:
>
>> ...
>> Category-land, as Jean B?nabou calls it, may look like a fortress from
>> the outside. So maybe we should be softer towards people trying to make
>> it look attractive and open.
>>
>> ...
>>
>> (*) It was John Baez, `making a fool of himself' as usual, who made me
>> think I could enter the fortress back in 2006. I'll probably never be as
>> fluent as native category theorists, but I nevertheless think my
>> research has improved since then.
>>


[For admin and other information see: http://www.mta.ca/~cat-dist/ ]

Re: Publicity

[Steve Vickers]

Dear Tom,

That's the wrong way to look at it. Category-land is really the land _between_ the fortresses. The courage to enter Category-land is the courage to leave the supposed protection of the city walls.

I was lucky enough to do my PhD in a region (Ringland) where they were already getting used to life without having those walls, but for for many of the city dwellers the idea that maths has anything to do with categories is as alien as the idea that milk comes from cows.

Steve.


On 11 Jun 2013, at 13:40, Tom Hirschowitz <tom.hirschowitz@univ-savoie.fr> wrote:

> ...
> Category-land, as Jean B?nabou calls it, may look like a fortress from
> the outside. So maybe we should be softer towards people trying to make
> it look attractive and open.
> 
> ...
> 
> (*) It was John Baez, `making a fool of himself' as usual, who made me
> think I could enter the fortress back in 2006. I'll probably never be as
> fluent as native category theorists, but I nevertheless think my
> research has improved since then.
> 


[For admin and other information see: http://www.mta.ca/~cat-dist/ ]

Re: Publicity

[Tom Hirschowitz]

Dear Marta,

Thanks very much for your detailed answer.

First, I agree with you that it is wrong to equate category theory with
logic and computation. I don't know whose mistake this is, but it
certainly is one.

However, it seems to me that people may be led to category theory, or
more generally any interesting subject matter, for bad reasons --- and
that this is sometimes good. (*)

Category-land, as Jean B?nabou calls it, may look like a fortress from
the outside. So maybe we should be softer towards people trying to make
it look attractive and open.

What do you think?

Best wishes,
Tom

(*) It was John Baez, `making a fool of himself' as usual, who made me
think I could enter the fortress back in 2006. I'll probably never be as
fluent as native category theorists, but I nevertheless think my
research has improved since then.




On 06/08/2013 11:39 AM, Marta Bunge wrote:
> Dear Tom,
>
> I will do my best to answer your question writing on mi iPad - my
> only tool here in Greece for the summer.
>
> The first part of the article by Julie Rehmayer is standard and I
> find no fault with it. It is in the second part that the author
> reveals her ignorance of the subject. The assertion  "the theory of
> programming languages and the field of logic can be seen as
> essentially identical to category theory " is pure nonsense, even
> more so as it is given an outrageous name - "computational
> trinitarianism" even if spoken in jest.
>
> Why is this assertion wrong? Because it distorts completely the
> nature and role of category theory.
>
> Firstly, category theory is a field in itself, its main virtue being,
> not to compute but to better understand, simplify, unify several
> mathematical fields and in turn their applications. Secondly,
> category theory serves as a foundation of mathematics that is closer
> to mathematical practice than set theory ever was.
>
> Within category theory there are, as you know, several distinct but
> related areas - fibered categories, algebraic theories  monads and
> their algebraic, topos theory, model structures, 2-categories ( and
> reasonably beyond without falling into science fiction). These in
> turn have been succesfully employed in several areas in mathematics,
> such as algebraic geometry, homotopy theory, differential geometry
> and topoly, functional analysis, as well as in computer science,
> logic, model theory, physics, linguistics. Some of those applications
> have promoted further developments of the theory of categories
> itself.
>
> Instead of pointing this out, the author of this article jumps to
> mention solely applications which are sure to impress the naive
> reader, such as quantum information theory, biological systems,
> linguistics, even music, as if the fundamental role of category
> theory in mathematics were not as important or even more so. In
> short, her report on category theory is more typical of a tabloid
> than of serious scientific journalism.
>
> The last part is an instance of what I mean by doing more harm than
> good. Instead of directing the reader to the best texts for
> introducing the subject of category theory to a wide audience, she
> implicitly recommends a book by David Spivak, " published" in
> Arxives. This book. which I perused solely on account of the article
> by Julie Rehmeyer, promotes category theory mostly as a language for
> recording data bases in an efficient way. It dismisses the far
> superior text by F. W. Lawvere and S. Schanuel, Conceptual
> Mathematics, Cambridge University Press, 1997. The latter not only
> instructs but motivates. Even for an expert in the subject, to read
> it is pure pleasure. Another valuable elementary textbook is one by
> M. Barr and C. Wells, Category Theory for Computing Science, CRM,
> Third edition, 1999.
>
> I hope that this partially answers your question.
>
> Kind regards, Marta


[For admin and other information see: http://www.mta.ca/~cat-dist/ ]

Re: Publicity

[Patrik Eklund]

These discussions on trinity and similar seem to raise only irritation
where there would be opportunity to provide constructive discussions.

CT has done a good job in explaining and providing rigour. Some like it,
some don't. Type theory is a typical example where computer science is "on
its own", unless trying to understand trinity like suggestions. Take
'lambda', for instance. Church said already back in 1940 that 'lambda' is
an "improper symbol" and that his 'o' type for something in direction of
propositions, but Church says:

"We purposely refrain from making more definite the nature of the types o
and iota" (peklund: the 'type' type!) ", the formal theory admitting of a
variety of interpretations in this regard. Of course the matter of
interpretation is in any case irrelevant to the abstract construction of
the theory, and indeed other and quite different interpretations are
possible (formal consistency assumed)."

'Trinity' also raises irritation and even fear as it refers to the Holy
Trinitiy, and many feel very uncomfortable even talking about these
things.

The wordpress blog mentioned is also very shallow in its introduction,
just mentioning "manifest in three persons". Some may be interested to
look more into the relation of "the three" as it has been part of history
and e.g. the split of the Latin and Greek Churches. The so called Filioque
addition and why it happened, and how it appears in the Latin language is
far beyond just saying "manifests". The way Augustinus opposed Arianism
and his choices of 'language' is, I think, a bit interesting in this
context. Or maybe not.

Rigour to me is just being clear about what is what. For instance,
sentences build upon terms, and satisfaction/entailment needs sentences.
This shold mean we need to be precise about terms, and then closing that
door. Then we are precise about sentences, and closing that door, and so
on. We should somewhere along that path, e.g. after having closed the
"sentences door", come up with new and nice sentences still to be used.
G?del was doing that all the time.

We shouldn't, I think, allow "circadian rhythms" into science and
mathematics, in particular in type theory concerning how types and
propositions are "manifested" in each other.

Cheers,

Patrik



[For admin and other information see: http://www.mta.ca/~cat-dist/ ]

Re: Publicity

[Urs Schreiber]

On 6/8/13, Marta Bunge <martabunge@hotmail.com> wrote:

> The assertion  "the theory of programming
> languages and the field of logic can be seen as essentially identical to
> category theory " is pure nonsense, even more so as it is given an
> outrageous name - "computational trinitarianism" even if spoken in jest.

The term "computational trinitarianism"

   http://ncatlab.org/nlab/show/computational+trinitarianism

refers to the theorem relating category theory and type theory

   http://ncatlab.org/nlab/show/relation+between+type+theory+and+category+theory

The further relation between type theory to logic and programming
languages is similarly well established. The term "computational
trinitarianism" was invented by Bob Harper in an expositional blog
post

  http://existentialtype.wordpress.com/2011/03/27/the-holy-trinity/

designed to alert an unspecialized public about these nice and useful
facts. I guess that's what the author of that article about Spivak's
paper picked up.


[For admin and other information see: http://www.mta.ca/~cat-dist/ ]

Re: Publicity

[Jeremy Gibbons]

On 8 Jun 2013, at 10:39, Marta Bunge wrote:

> It is in the second part that the author reveals her ignorance of the subject. The assertion  "the theory of programming languages and the field of logic can be seen as essentially identical to category theory " is pure nonsense, even more so as it is given an outrageous name - "computational trinitarianism" even if spoken in jest. 

Don't blame Rehmayer for the "computational trinitarianism" line; that's Bob Harper's invention, tongue in cheek. 

But I don't think Harper is to blame for equating CT with PL and logic. He does say

> The doctrine of computational trinitarianism holds that computation manifests itself in three forms: proofs of propositions, programs of a type, and mappings between structures.  These three aspects give rise to three sects of worship: Logic, which gives primacy to proofs and propositions; Languages, which gives primacy to programs and types; Categories, which gives primacy to mappings and structures.  The central dogma of computational trinitarianism holds that Logic, Languages, and Categories are but three manifestations of one divine notion of computation.

   http://existentialtype.wordpress.com/2011/03/27/the-holy-trinity/

All I take him to mean is that logic, languages, and categories offer three complementary perspectives on computation. I don't think you can read this as "computation subsumes category theory".

Jeremy

Jeremy.Gibbons@cs.ox.ac.uk
Oxford University Department of Computer Science,
Wolfson Building, Parks Road, Oxford OX1 3QD, UK.
+44 1865 283521
http://www.cs.ox.ac.uk/people/jeremy.gibbons/



[For admin and other information see: http://www.mta.ca/~cat-dist/ ]

Re: Publicity

[Ross Street]

On 08/06/2013, at 12:40 AM, Ronnie Brown wrote:

> `Category Theory: an abstract setting for
> analogy and comparison', In: What is Category Theory? Advanced
> Studies in Mathematics and Logic, Polimetrica Publisher, Italy,
> (2006) 257-274.  ([141] on my publication list. pdf available)


That should be [146].
Thanks Ronnie,
Looking forward to reading it.
==Ross



[For admin and other information see: http://www.mta.ca/~cat-dist/ ]

Re: Publicity

[Vaughan Pratt]

  From Rehmeyer's article:

"It?s even proving valuable in developing rigorous models of music theory."

" 'If people adopt the level of rigor of category theory,' [Spivak]
says, 'it will provide a precise language for science as a whole, and it
will help individual scientists to clarify their thinking.' "

I don't know what "rigor" is, but if we identify it with consistency
then there is a limit to the rigor of category theory: Goedel's second
incompleteness theorem shows that category theory cannot be rigorous
enough to establish its own rigor.

Vaughan


On 6/5/2013 5:28 PM, Ross Street wrote:
> http://www.sciencenews.org/view/generic/id/350567/description/One_of_the_most_abstract_fields_in_math_finds_application_in_the_real_world
>
> Perhaps the above article is more good than harm.
>
> Ross
> www.math.mq.edu.au/~street
>
>

[For admin and other information see: http://www.mta.ca/~cat-dist/ ]

Re: Publicity

[Ronnie Brown]

This brings up one of my hobby-horses, that the virtues of abstraction
are not marketed, even to mathematics students.  After I gave a
presentation to teachers and pupils on knots, including prime knots, in
1987 or so a teacher came up to me and said: "That is the first time in
my mathematical career that anyone has used the term `analogy' in
relation to mathematics!" Who is responsible for this?

Of course *abstraction* is about *analogies*.  I will comment  this on
the given web site, but my registration awaits approval. The word
`analogy' does occur 9 times in Spivak's book, but not I think with this
force.

Tim and I have a paper:

   `Category Theory: an abstract setting for
analogy and comparison', In: What is Category Theory? Advanced
Studies in Mathematics and Logic, Polimetrica Publisher, Italy,
(2006) 257-274.  ([141] on my publication list. pdf available)

The other side to category theory is that is has stimulated the
development of new algebraic/mathematical  structures.

Ronnie

On 06/06/2013 16:46, Eduardo J. Dubuc wrote:
> On 05/06/13 21:28, Ross Street wrote:
>> http://www.sciencenews.org/view/generic/id/350567/description/One_of_the_most_abstract_fields_in_math_finds_application_in_the_real_world
>>
>>
>> Perhaps the above article is more good than harm.
>>
>> Ross
>> www.math.mq.edu.au/~street
>>
>>
>>
>
> I just read the article. It seems to me that it is empty marketing. But,
> anyway, marketing has been extensively used in mathematics, to witness,
> Thom's theory of catastrophes (hiding that there was good mathematics
> underneath).
>
> e.d.
>

[For admin and other information see: http://www.mta.ca/~cat-dist/ ]

Re: Publicity

[Fred E.J. Linton]

On Thu, 06 Jun 2013 09:26:15 AM EDT Ross Street <ross.street@mq.edu.au>
wrote:

>
http://www.sciencenews.org/view/generic/id/350567/description/One_of_the_most_abstract_fields_in_math_finds_application_in_the_real_world
> 
> Perhaps the above article is more good than harm.

Over the years, author Julie Rehmeyer has given birth to quite a litter,

http://www.sciencenews.org/view/authored/id/43/name/Julie_Rehmeyer ,

of mathematically literate news articles, including, for example, a report
on the claim of "Vinay Deolalikar, a computer scientist at Hewlett Packard 
labs in India, [who] sent an email on August 7 [of the year 2010] to a few 
top researchers claiming that P doesn’t equal NP" -- cf.:

http://www.sciencenews.org/view/generic/id/63252/description/Crowdsourcing_peer_review

The piece you point to strikes me as quite reasonable, actually, apart from 
the two pairs of paragraphs reporting on the ... umm ... thinking (?) of
Messrs. Harper and Spivak, which strike me as being probably accurate
depictions of their own cockeyed cocktail-party gibberish.

[But then, what do I know? I'm just a retiree from tiny little Wesleyan, 
after all, not an active respected member of Carnegie Mellon or MIT :-) .]

But all the rest is about as close to the mark as a discussion pitched 
to the interested and sympathetic layperson can possibly be.

Cheers, and thanks for pointing that piece out, -- Fred



[For admin and other information see: http://www.mta.ca/~cat-dist/ ]

Re: Publicity

[Eduardo J. Dubuc]

On 05/06/13 21:28, Ross Street wrote:
> http://www.sciencenews.org/view/generic/id/350567/description/One_of_the_most_abstract_fields_in_math_finds_application_in_the_real_world
>
> Perhaps the above article is more good than harm.
>
> Ross
> www.math.mq.edu.au/~street
>
>
>
> [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

I just read the article. It seems to me that it is empty marketing. But,
anyway, marketing has been extensively used in mathematics, to witness,
Thom's theory of catastrophes (hiding that there was good mathematics
underneath).

e.d.


[For admin and other information see: http://www.mta.ca/~cat-dist/ ]

Re: Publicity

[Marta Bunge]

Dear Ross, 

I find this article not only superficial but misleading. Its presentation of  category theory is not only simplified but distorting. I think that it may do more harm than good  It is important to know how we are seen in some sources, but we need not pay attention to them. Even if (or particularly because)   an article like this one is seemingly laudatory. 

Best regards,
Marta

Sent from my iPad

On 2013-06-06, at 9:24 AM, "Ross Street" <ross.street@mq.edu.au> wrote:

> http://www.sciencenews.org/view/generic/id/350567/description/One_of_the_most_abstract_fields_in_math_finds_application_in_the_real_world
> 
> Perhaps the above article is more good than harm.
> 
> Ross
> www.math.mq.edu.au/~street
> 

[For admin and other information see: http://www.mta.ca/~cat-dist/ ]

Publicity

[Ross Street]

http://www.sciencenews.org/view/generic/id/350567/description/One_of_the_most_abstract_fields_in_math_finds_application_in_the_real_world

Perhaps the above article is more good than harm.

Ross
www.math.mq.edu.au/~street



[For admin and other information see: http://www.mta.ca/~cat-dist/ ]