Fwd: Good article for promoting pure math research

Fwd: Good article for promoting pure math research

[André Joyal]

Dear All,

An article on

THE UNPLANNED IMPACTS OF MATHEMATICS

was recently published in Nature:

http://www.nature.com/nature/journal/v475/n7355/full/475166a.html

andré



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Re: IMPACT

[Timothy Porter]

On 17/07/2011 16:51, Andr=E9 Joyal wrote:
> Dear All,
>
> An article on
>
> THE UNPLANNED IMPACTS OF MATHEMATICS
>
> was recently published in Nature:
>
> http://www.nature.com/nature/journal/v475/n7355/full/475166a.html
>
> andr=E9
>
>
>
> [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

Dear All,

Let me put this in a context for non-UK readers of this list.  Various=20
bodies in the UK are asking for `impact' as part of their assessment of=20
research.  This is in particular true of the REF exercise. (Perhaps=20
someone else can comment on this as well as I am `out of this', having=20
been a victim of a previous round of such `exercises'.) We all know that=20
mathematics is central to modern technological developments, but pure=20
mathematics finds itself in the position of having  little direct IMPACT=20
as measured in the way that the nebulous THEY (i.e. the bean counters)=20
have defined it. We thus have that a sociologist can say that their=20
research resulted in  (whatever), a physicist can point to a new=20
technical development, whilst a pure mathematician is left saying=20
`doh!'. This may have, unless watched, very serious implications for=20
category theory as between us and the areas with IMPACT there seems to=20
be a wide gulf, at least to the outsider. (When money is short, people=20
fight over what little there is with enthusiasm!)

This may have also an impact on the recrutement of new researchers, so=20
someone working in PDEs is likely to be viewed as potentially having=20
more impact than someone working in category theory. (If you think that=20
as you are not in the UK then you need not worry, and that your research=20
organisations are not going to behave so stupidly,..... )

There is a wiki (at lmsrefresponse dot wordpress dot com <- and I hope=20
this is ok with the list rules about links replace dot by . of course)=20
which some of you may want to look at. The London Math Soc does not seem=20
that sure as to how to best treat the situation.

(I would request, that if someone on the list wants to discuss IMPACT,=20
that they look at the lms pages first. If they go to the LMS main page=20
then to `policy' and look for impact they should find it and various=20
related documents. Please restrict attention to category theory, as that=20
is very vulnerable as quite a few other mathematicians have a negative=20
attitude to it.)

Tim







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Re: IMPACT

[JeanBenabou]

Dear Tim,

Your mail begins with:

> Let me put this in a context for non-UK readers of this list.

I think I qualify on both counts, I am a non-UK reader, and still on
this list.
But then you continue with:

> Various=20 bodies in the UK are asking for `impact' as part of
> their assessment of=20
> research.  This is in particular true of the REF exercise.

I'm afraid I don't know what is=20 research and REF exercise. It
seems very important since you say:

> (Perhaps=20 someone else can comment on this as well as I am `out
> of this', having=20 been a victim of a previous round of such
> `exercises'.)

This importance is attested by:

> We all know that=20 mathematics is central to modern technological
> developments,

And=20 occurs in  your mail more than 20 times.

Could you, or any one on the list, please explain briefly to a french
mathematician what=20 mathematics, pure and applied, and REF
exercises are?

Many thanks, and best regards,

Jean



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Re: IMPACT

[Timothy Porter]

Dear All,

The message  got extremely garbled by having some =20 added.  (I presume
these were translated from one text format to another and were end of
line symbols!)

The term REF is a research evaluation.  I quote from our HEFCE website.
(HEFCE= Higher education funding council for England. It also
coordinates these sorts of exercises for Wales, Scotland and Northern
Ireland.)

The Research Excellence Framework (REF) is the new system for assessing
the quality of research in UK higher education institutions.

I will try to send the message again, hoping that the =20s, which I will
delete, do not reappear!!!!!!

Tim

Thanks to Jean for pointing out the =20s!


Here is the original:

______________

Dear All,

Let me put this in a context for non-UK readers of this list.  Various
bodies in the UK are asking for `impact' as part of their assessment of
research.  This is in particular true of the REF exercise. (Perhaps
someone else can comment on this as well as I am `out of this', having
been a victim of a previous round of such `exercises'.) We all know that
mathematics is central to modern technological developments, but pure
mathematics finds itself in the position of having  little direct IMPACT
as measured in the way that the nebulous THEY (i.e. the bean counters)
have defined it. We thus have that a sociologist can say that their
research resulted in  (whatever), a physicist can point to a new
technical development, whilst a pure mathematician is left saying
`doh!'. This may have, unless watched, very serious implications for
category theory as between us and the areas with IMPACT there seems to
be a wide gulf, at least to the outsider. (When money is short, people
fight over what little there is with enthusiasm!)

This may have also an impact on the recrutement of new researchers, so
someone working in PDEs is likely to be viewed as potentially having
more impact than someone working in category theory. (If you think that
as you are not in the UK then you need not worry, and that your research
organisations are not going to behave so stupidly,..... )

There is a wiki (at lmsrefresponse dot wordpress dot com <- and I hope
this is ok with the list rules about links replace dot by . of course)
which some of you may want to look at. The London Math Soc does not seem
that sure as to how to best treat the situation.

(I would request, that if someone on the list wants to discuss IMPACT,
that they look at the lms pages first. If they go to the LMS main page
then to `policy' and look for impact they should find it and various
related documents. Please restrict attention to category theory, as that
is very vulnerable as quite a few other mathematicians have a negative
attitude to it.)

Tim




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Re: IMPACT

[Ronnie Brown]

In this context, I would like to give a quotation from the the
Autobiography of Thomas Young (1773-1829), referred to in the book `The
last man who knew everything', Andrew Robinson, Pearson Education Inc,
2006, p.224.

"It is indeed so impossible to forsee the capabilities of improvement in
any science, that it is idle to form any general opinion of what would
be the comparative advantage of the employment of time in any one
investigation rather than another, for almost all the authors of
important discoveries and even of inventions, are led as much by
accident as by system to their success."

Thomas Young  was the person who developed the wave theory of light, and
many other things. See for example
http://en.wikipedia.org/wiki/Thomas_Young_%28scientist%29

However the Government has long enjoined its research assessment panels
to predict the future, without being completely clear on the methodology
for this.

All this does reinforce the good sense in trying to make clear the
(current!)  role of category  theory, and its wide ranging influence.

Ronnie Brown

On 18/07/2011 07:51, Timothy Porter wrote:
> On 17/07/2011 16:51, Andr=E9 Joyal wrote:
>> Dear All,
>>
>> An article on
>>
>> THE UNPLANNED IMPACTS OF MATHEMATICS
>>
>> was recently published in Nature:
>>
>> http://www.nature.com/nature/journal/v475/n7355/full/475166a.html
>>
>> andr=E9
>>

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an old paper

[Sergei SOLOVIEV]

To all, and in particular Peter Freyd,

Dear Peter,

I could not find your old paper on diagrammatic reasoning (it was
published in some collection
in 70-es, but I could not find it via google). Maybe somebody can
provide me some
information how to get a copy.

All the best

Sergei Soloviev


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distributors for 2-categories

[David Roberts]

Hi all,

==Background==

I have finally read Jean Benabou's Louvain lectures on distributors, which he
was kind enough to send me earlier this year. In them he describes the following
bicategories of distributors (some paraphrasing/simplification may occur,  and
modernisation of terms - all errors are mine):

Dist
  objects: categories C,D,...
  arrows: functors C^op x D--> Set (equiv. opfibrations H --> C^op x D)
  2-arrows: natural transformations (equiv. cartesian functors over C^op x  D)

Dist(V), for V a symmetric closed monoidal category
  objects: V-enriched categories C,D,...
  arrows: V-functors C^op x D--> V
  2-arrows: V-natural transformations

Dist(E), for E a regular category
  objects: categories internal to E  C,D,...
  arrows: internal opfibrations H --> C^op x D
  2-arrows: internal (cartesian) functors over C^op x D

Dist(K), for K a bicategory
  objects: monads in K . . . .

And here it seems to me the pattern breaks down, as taking as input the
bicategories Cat, V-Cat and Cat(E), we do not arrive at any of the examples on
the previous list.

I understand the motivation behind Dist(K), namely that one considers the
process

E |--> Span(E) |--> Dist(Span(E)) = Dist(E)    (E regular category)

as Cat(E) = Monads(Span(E)). I'm not worried about that too much.

==Question==

1) Has anyone done any work on distributor-like constructions for bicategories
that recover the processes

Cat |--> Dist,
V-Cat |--> Dist(V),
Cat(E) |--> Dist(E)?

Something like universally adding adjoints to all 1-arrows in a bicategory, I
would imagine.

I'm asking this in the context of the equivalence between representable
distributors and anafunctors, so I suppose a secondary question is:

2) Given 1) above, is there a notion of 'representable 1-arrow' in this
universal construction?

Thanks,

David



------------------------------
David Roberts

david.roberts@adelaide.edu.au
University of Adelaide



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IMPACT

[Ellis D. Cooper]

Understanding and maybe even solving problems in energy conservation,
energy transduction and global warming depend in part on advances in
chemical thermodynamics. But chemical thermodynamics is an old and
difficult branch of mathematical science. My book on mathematical
mechanics tries to take baby steps towards a categorical chemical
thermodynamics.

For example, there exists a monoidal functor ("Hess's Law") which
assigns enthalpy of formation to mixtures and enthalpy of
transformation to reactions. One-, two-, or three-dimensional bodies
are connected by bodies that conduct certain substances, and which
may themselves be connected by bodies conducting other substances.
Substances include chemicals, charge, volume, momentum, and entropy,
and any flowing substance carries energy. The theory of substances is
an axiomatic theory including an Energy Axiom ("First Law of
Thermodynamics") and an Entropy Axiom ("Second Law of Thermodynamics").

In my dreams a grown up categorical chemical thermodynamics may
invoke higher-dimensional categories and other areas of current
seemingly abstract research.

Ellis D. Cooper



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