Re: Good article for promoting pure math research
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 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
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 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
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 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
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
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
On 7/19/11 5:24 AM, Ronnie Brown wrote:
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."
There was once a marvelous satire purporting to be Isaac Newton's grant application. jim [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
I would greatly appreciate it if someone on the list, Andre or Tim, perhaps, could send me a pdf file of the "impact" article in Nature. The University of Minnesota has an electronic subscription to Nature, but issues less than a year old are not made available and I am, for obvious reasons, unwilling to pony up $32 to read the article. Thanks very much in advance. Bill Messing [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
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 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
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 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
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 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
participants (9)
-
André Joyal -
David Roberts -
Ellis D. Cooper -
JeanBenabou -
jim stasheff -
Ronnie Brown -
Sergei SOLOVIEV -
Timothy Porter -
William Messing