Dangerous knowledge

Dangerous knowledge

[Joyal, André]

Dear all,

I wonder if you have seen the BBC "documentary" called "Dangerous knowledge"? 
It is divided in ten parts:

1) 
http://www.youtube.com/watch?v=Cw-zNRNcF90&feature=related

2)
http://www.youtube.com/watch?v=wpWXT9yMBnw&feature=related

3)
http://www.youtube.com/watch?v=1AAvWb5wYNk&feature=related

4)
http://www.youtube.com/watch?v=qUL-x8Gm1h4&feature=related

5)
http://www.youtube.com/watch?v=So9RAbBy1ps&feature=related

6)
http://www.youtube.com/watch?v=fqKQ0-T3swY&feature=related

7)
http://www.youtube.com/watch?v=oldUAw2Aux0&feature=related

8)
http://www.youtube.com/watch?v=0ZcErXdR_eQ&feature=related

9)
http://www.youtube.com/watch?v=BkezCyb7Lkw&feature=related

10)
http://www.youtube.com/watch?v=_8dczB1rY-Q&feature=related

What do you think?

André



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Re: Dangerous knowledge

[Mike Stay]

Here's the summary from BBC's site:

In this one-off documentary, David Malone looks at four brilliant
mathematicians - Georg Cantor, Ludwig Boltzmann, Kurt Gödel and Alan
Turing - whose genius has profoundly affected us, but which tragically
drove them insane and eventually led to them all committing suicide.

The film begins with Georg Cantor, the great mathematician whose work
proved to be the foundation for much of the 20th-century mathematics.
He believed he was God's messenger and was eventually driven insane
trying to prove his theories of infinity.

Ludwig Boltzmann's struggle to prove the existence of atoms and
probability eventually drove him to suicide. Kurt Gödel, the
introverted confidant of Einstein, proved that there would always be
problems which were outside human logic. His life ended in a
sanatorium where he starved himself to death.

Finally, Alan Turing, the great Bletchley Park code breaker, father of
computer science and homosexual, died trying to prove that some things
are fundamentally unprovable.

The film also talks to the latest in the line of thinkers who have
continued to pursue the question of whether there are things that
mathematics and the human mind cannot know. They include Greg Chaitin,
mathematician at the IBM TJ Watson Research Center, New York, and
Roger Penrose.

Dangerous Knowledge tackles some of the profound questions about the
true nature of reality that mathematical thinkers are still trying to
answer today.
-- 
Mike Stay - metaweta@gmail.com
http://math.ucr.edu/~mike
http://reperiendi.wordpress.com


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Re: Dangerous knowledge

[Dana Scott]

I think the premise of the work is silly.  I knew Gödel personally
and many people who knew him.  My long-time friend Robin Gandy was
a close friend and associate of Turing.  I think it is true that
Godel was very frustrated by not being able to settle the status of
the Continuum Hypothesis, but to say that his mathematics drove him
mad is terrible pop psychology.  In the case of Turing, the matter
is even less clear.  For him, persecution may have been a big factor
in his suicide -- which also could have been an accident.  Gödel
did suffer from paranoia, and Cantor was oppressed by religious
questions, which he did relate to his theories of the infinite.
But to conclude cause and effect seems pretty hard to prove.
And what is the point?

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Re: Dangerous knowledge

[Alex Hoffnung]

Hi -

I think I watched this documentary a while ago.  I watched only a few
minutes of it today and then realized that I should probably be doing
something else.  However, I was interested and want to comment briefly.


> In this one-off documentary, David Malone looks at four brilliant
> mathematicians - Georg Cantor, Ludwig Boltzmann, Kurt Gödel and Alan
> Turing - whose genius has profoundly affected us, but which tragically
> drove them insane and eventually led to them all committing suicide.
>

I am not sure what it means for one's genius to drive him or her insane.
>From what I can gather in this summary and my recollection of the film, the
director seems to exploit the illnesses of some of these men to provide some
theatrical drama to the story.  If this is so, then it seems rather
irresponsible.  If I am mistaken and have not watched enough of the video,
then my apologies to the director.


> The film begins with Georg Cantor, the great mathematician whose work
> proved to be the foundation for much of the 20th-century mathematics.
> He believed he was God's messenger and was eventually driven insane
> trying to prove his theories of infinity.
>

This statement does not directly blame the illness on his struggle with
mathematics, but it seems dangerously suggestive of this conclusion.  Here
is a quote from Wikipedia:

Cantor's recurring bouts of
depression<http://en.wikipedia.org/wiki/Clinical_depression>from 1884
to the end of his life were once blamed on the hostile attitude of
many of his contemporaries,[9]<http://en.wikipedia.org/wiki/Georg_Cantor#cite_note-daub280-8>but
these episodes can now be seen as probable manifestations of a bipolar
disorder <http://en.wikipedia.org/wiki/Bipolar_disorder>.[10]<http://en.wikipedia.org/wiki/Georg_Cantor#cite_note-bipolar-9>

This seems like the more reasonable, albeit possibly less glamorous
description of the causes of Cantor's illnesses.  Since I did not watch
further I cannot comment on the others, except that I did not know of any
mental disorders associated to Turing.

Best,
Alex Hoffnung

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Re: Dangerous knowledge

[jim stasheff]

Mike Stay wrote:
> Here's the summary from BBC's site:
>   

At least the Turing implication is very misleading - see below.

> In this one-off documentary, David Malone looks at four brilliant
> mathematicians - Georg Cantor, Ludwig Boltzmann, Kurt Gödel and Alan
> Turing - whose genius has profoundly affected us, but which tragically
> drove them insane and eventually led to them all committing suicide.
>
> The film begins with Georg Cantor, the great mathematician whose work
> proved to be the foundation for much of the 20th-century mathematics.
> He believed he was God's messenger and was eventually driven insane
> trying to prove his theories of infinity.
>
> Ludwig Boltzmann's struggle to prove the existence of atoms and
> probability eventually drove him to suicide. Kurt Gödel, the
> introverted confidant of Einstein, proved that there would always be
> problems which were outside human logic. His life ended in a
> sanatorium where he starved himself to death.
>
> Finally, Alan Turing, the great Bletchley Park code breaker, father of
> computer science and homosexual, died trying to prove that some things
> are fundamentally unprovable.
>   

Certainly his suicide was because of his treatment as a homosexual and 
not that irrational - not `crazy'.

> The film also talks to the latest in the line of thinkers who have
> continued to pursue the question of whether there are things that
> mathematics and the human mind cannot know. They include Greg Chaitin,
> mathematician at the IBM TJ Watson Research Center, New York, and
> Roger Penrose.
>
> Dangerous Knowledge tackles some of the profound questions about the
> true nature of reality that mathematical thinkers are still trying to
> answer today.
>   



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Dangerous ignorance

[Joyal, André]

Many thanks to Dana Scott, Alex Hoffnung and Jim Stasheff
for expressing their view on the BBC "documentary".

I also think that the documentary is a big distorsion of the truth.  
Georg Cantor, Ludwig Boltzmann, Kurt Gödel and Alan Turing were fighting ignorance.
They knew that knowledge is liberating and ignorance dangerous.

AJ


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Re: Dangerous knowledge

[Charles Wells]

The graphic novel Logicomix by Apostolos Doxiadis and Christos H.
Papadimitriou has the relation between being logicians and madness as
one of its themes.  The novel is actually quite good, and I recommend
it, but they make too much of the insanity stuff.  One saving grace is
that the novel has interludes featuring the authors and the artists
arguing about that theme and other aspects of the novel.

Charles Wells

2009/11/30 Mike Stay <metaweta@gmail.com>:
> Here's the summary from BBC's site:
>
> In this one-off documentary, David Malone looks at four brilliant
> mathematicians - Georg Cantor, Ludwig Boltzmann, Kurt Gödel and Alan
> Turing - whose genius has profoundly affected us, but which tragically
> drove them insane and eventually led to them all committing suicide.
>
> The film begins with Georg Cantor, the great mathematician whose work
> proved to be the foundation for much of the 20th-century mathematics.
> He believed he was God's messenger and was eventually driven insane
> trying to prove his theories of infinity.
>
> Ludwig Boltzmann's struggle to prove the existence of atoms and
> probability eventually drove him to suicide. Kurt Gödel, the
> introverted confidant of Einstein, proved that there would always be
> problems which were outside human logic. His life ended in a
> sanatorium where he starved himself to death.
>
> Finally, Alan Turing, the great Bletchley Park code breaker, father of
> computer science and homosexual, died trying to prove that some things
> are fundamentally unprovable.
>
> The film also talks to the latest in the line of thinkers who have
> continued to pursue the question of whether there are things that
> mathematics and the human mind cannot know. They include Greg Chaitin,
> mathematician at the IBM TJ Watson Research Center, New York, and
> Roger Penrose.
>
> Dangerous Knowledge tackles some of the profound questions about the
> true nature of reality that mathematical thinkers are still trying to
> answer today.
> --
> Mike Stay - metaweta@gmail.com
> http://math.ucr.edu/~mike
> http://reperiendi.wordpress.com
>



-- 
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blog: http://sixwingedseraph.wordpress.com/
abstract math website: http://www.abstractmath.org/MM//MMIntro.htm
astounding math stories: http://www.abstractmath.org/MM//MMAstoundingMath.htm
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sixwingedseraph.facebook.com


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Re: Dangerous knowledge

[jim stasheff]

recurring bouts of
depression is not indicative of  a bipolar disorder

were there also manic episodes?

jim




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Re: Dangerous knowledge

[Ronnie Brown]

Hi,

A while ago, I started to watch a BBC programme on a mathematical 
Olympiad camp, but gave up when it was clear that they were concentrating
on a participant  with peculiar behaviour and hardly noticed the several 
pretty girls around! That also sounds like peculiar behaviour.

Perhaps we need a TV programme about producers of TV programmes?

Ronnie Brown


Alex Hoffnung wrote:
> Hi -
>
> I think I watched this documentary a while ago.  I watched only a few
> minutes of it today and then realized that I should probably be doing
> something else.  However, I was interested and want to comment briefly.
>
>
>   
>> In this one-off documentary, David Malone looks at four brilliant
>> mathematicians - Georg Cantor, Ludwig Boltzmann, Kurt Gödel and Alan
>> Turing - whose genius has profoundly affected us, but which tragically
>> drove them insane and eventually led to them all committing suicide.
>>
>>     
>
> I am not sure what it means for one's genius to drive him or her insane.
> >From what I can gather in this summary and my recollection of the film, the
> director seems to exploit the illnesses of some of these men to provide some
> theatrical drama to the story.  If this is so, then it seems rather
> irresponsible.  If I am mistaken and have not watched enough of the video,
> then my apologies to the director.
>
>
>   
>> The film begins with Georg Cantor, the great mathematician whose work
>> proved to be the foundation for much of the 20th-century mathematics.
>> He believed he was God's messenger and was eventually driven insane
>> trying to prove his theories of infinity.
>>
>>     
>
> This statement does not directly blame the illness on his struggle with
> mathematics, but it seems dangerously suggestive of this conclusion.  Here
> is a quote from Wikipedia:
>
> Cantor's recurring bouts of
> depression<http://en.wikipedia.org/wiki/Clinical_depression>from 1884
> to the end of his life were once blamed on the hostile attitude of
> many of his contemporaries,[9]<http://en.wikipedia.org/wiki/Georg_Cantor#cite_note-daub280-8>but
> these episodes can now be seen as probable manifestations of a bipolar
> disorder <http://en.wikipedia.org/wiki/Bipolar_disorder>.[10]<http://en.wikipedia.org/wiki/Georg_Cantor#cite_note-bipolar-9>
>
> This seems like the more reasonable, albeit possibly less glamorous
> description of the causes of Cantor's illnesses.  Since I did not watch
> further I cannot comment on the others, except that I did not know of any
> mental disorders associated to Turing.
>
> Best,
> Alex Hoffnung
>

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Re: Dangerous knowledge

[Alex Hoffnung]

To Jim -

I have not read the source material on this quote, but the footnote  which
accompanies the quote says his physician (a psychiatrist) diagnosed Cantor
with "cyclic manic-depression".  I do not know of any further evidence of
manic behavior, but also have not looked.

Best,
Alex

On Tue, Dec 1, 2009 at 6:26 AM, jim stasheff <jds@math.upenn.edu> wrote:

> recurring bouts of
> depression is not indicative of  a bipolar disorder
> were there also manic episodes?
>
> jim
>
>

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Re: Dangerous knowledge

[Robert Seely]

Actually, I think Dana understates the problem with this program.  It
suffers from what I call the "PBS documentary syndrome" (equally
afflicting the BBC, however, so the name is not universal enough!):
it repeatedly tells you what's cool about its topic, without ever
actually telling you what the topic really is.  Afraid to scare
viewers away with the actual details of the topic, it just talks about
it in terms so general (and often over-inflated or sensationalized,
which was Dana's point) they are really quite meaningless.

Though not perfect by any means, I think a recent 4-part series "The
Story of Maths" narrated by Marcus du Sautoy does better - he even
tries to sketch some proofs.  (The episode closest to "Dangerous
Knowledge" would be the fourth.)  Even better is an old series (but
still to be found on Youtube!) called Mathematical Mystery Tour.

But generally, science documentaries are disappointing, and maths ones
even more so.  It's a pity, because you actually can get an audience
of non-specialists to understand (at least a little) what mathematical
results etc are about.  I teach an honours Liberal Arts maths & logic
class, and a surprisingly large percentage can actually appreciate the
beauty of (eg) natural deduction proofs in predicate logic, basic
theory of natural numbers (infinitude of primes, irrationality of
primes, the fundamental theorem of arithmetic, ... ), simple
axiomatics (we do Boolean algebras as an example), and even Godel's
theorems, and the "Lambek calculus" for linguistics (even a bit of
category theory there!).  This isn't a mickey mouse course (sample
class tests available on request!), and it's a challenge to many of
the students.  The point is: they are willing to make the effort if
they know you're not being condescending, and that you are giving them
"the real thing", not some pablum that only looks good in the box.

I wish more TV documentary producers took that attitude - they might
get a slightly smaller audience, but their audience will appreciate
their efforts more.

-= rags =-


On Mon, 30 Nov 2009, Dana Scott wrote:

> I think the premise of the work is silly.  I knew Gödel personally
> and many people who knew him.  My long-time friend Robin Gandy was
> a close friend and associate of Turing.  I think it is true that
> Godel was very frustrated by not being able to settle the status of
> the Continuum Hypothesis, but to say that his mathematics drove him
> mad is terrible pop psychology.  In the case of Turing, the matter
> is even less clear.  For him, persecution may have been a big factor
> in his suicide -- which also could have been an accident.  Gödel
> did suffer from paranoia, and Cantor was oppressed by religious
> questions, which he did relate to his theories of the infinite.
> But to conclude cause and effect seems pretty hard to prove.
> And what is the point?
>

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Re: Dangerous knowledge

[John Baez]

The BBC wrote:

 In this one-off documentary, David Malone looks at four brilliant
>> mathematicians - Georg Cantor, Ludwig Boltzmann, Kurt Gödel and Alan
>> Turing - whose genius has profoundly affected us, but which tragically drove
>> them insane and eventually led to them all committing suicide.
>>
>
Jim Stasheff wrote:

At least the Turing implication is very misleading - see below.
>

It's also not true that George Cantor committed suicide!

And I would not call Ludwig Boltzmann a mathematician.  I'd call him a
physicist.

But the documentary seems a bit more accurate than this summary.
And it could be good to have documentaries that sensationalize mathematics
and make it seem "edgy" and "dangerous".  We oldsters can tut-tut about the
inaccuracies and lack of serious content, but as a kid I would have enjoyed
it - and if it makes one youngster pursue a career in mathematics instead of
crime, that may justify its existence.

Best,
jb


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RE : categories: Re: Dangerous knowledge

[Joyal, André]

Dear Robert,

The "The Great Global Climate Swindle" is an example of 
anti-scientific propaganda in the name of science:

http://en.wikipedia.org/wiki/The_Great_Global_Warming_Swindle

You can watch it on youtube:

http://www.youtube.com/watch?v=xzSzItt6h-s

The "documentary" is full of errors: 

http://www.realclimate.org/index.php/archives/2007/03/swindled/

http://www.climateofdenial.net/?q=node/3

André


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Dangerous times

[Joyal, André]

[Note from moderator: this is posted following the context of recent
messages, but is quite far off-topic, so further discussion should be
off-list.  Thanks, Bob ]


Dear fellow category theorists,

The following message will probably surprise you.
You may not be aware that we are presently living extraordinary times.
The time when the fate of humanity was decided.

You probably know that climate warming is posing a serious threat to the biosphere and to our civilisation.
The danger is particulary insidious because the warming is imperceptible when
compared to the everyday variation of the weather and to the yearly variation of the seasons.
The scary thing is that the climate may cross an unpredictable tipping point leading to
irreversible catastrophic consequences. 
Of course, we all hope that the problem will be attacked vigorously this month in Copenhagen:

http://en.cop15.dk/

However, there are reasons to be pessimistic about the Copenhagen meeting. 
Please, read the piece "Never-Give-Up-Fighting-Spirit", recently posted by Jim Hansen:

http://www.columbia.edu/~jeh1/

You can also watch a video:

http://vimeo.com/7908590

It is becoming quite clear that the problem of climate warming 
cannot be solved by cap and trade mechanisms, or by ordinary political actions.
The usual "wait and see" strategy can only lead to more serious problems.

The real solution may require deep social transformations involving cultural changes. 
We the scientists, may have a responsability in discovering, inventing and making the changes.
We may need to develop a new wisdom for ourselves, our science and our societies.
This can be a very exciting time.

What do you think?

André
 

 


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Re: Dangerous knowledge

[Ronnie Brown]

It is easy to criticise others but I think there is a general problem 
with mathematics teaching (in my limited experience in the UK)
of mathematicians not explaining what the subject is about, or even 
thinking that this is necessary, or useful. I would like to direct 
attention to our
`Knot exhibition'
http://www.popmath.org.uk/exhib/knotexhib.html
and the discussion of what we were trying to achieve in
http://www.bangor.ac.uk/~mas010/icmi89.html  :
in broad terms, this was to show through the medium of knots some of the 
methodology of mathematics. The advantages of knots for this aim are many.

In some ways the spirit of this exhibit is expressed by the slogan
`advanced mathematics from an elementary viewpoint'.
So how much of the baggage can you throw away and still get to, say, a 
real calculation?
I once did a sample Todd-Coxeter enumeration of a presentation of a 
finite group of order 8  to a class of unprepared 14 year olds, 
(fortunately
I was prepared to do this!) and had them helping me  fill in the table 
(just as well , too) and draw the Cayley graph.

I feel there is a real hunger in the public and in other sciences to 
find out what is going on in mathematics which has some kind of excitement,
preferably in terms of new ideas, rather than solving say the Goldbach 
Conjecture. Higher dimensional algebra is quite useful in this respect.
One can discuss what is or should be a higher dimensional formula, and 
why the idea  might, or might not, be relevant to brain function! (I've 
done this too for an audience of neuroscientists.)

Also discussed  in
http://www.bangor.ac.uk/~mas010/promotingmaths.html
is the heretical idea of `promoting mathematics' to students of 
mathematics!

The point I am getting at is that there may be  something we can do about
`But generally, science documentaries are disappointing, and maths ones
even more so.' as suggested by Robert, and the start may be conveying 
certain attitudes to the many
students studying mathematics seriously. Is this done enough?

Perhaps those interested in category theory are in a better position to 
deal with these problems than those with no such interest!!???


Ronnie Brown



Robert Seely wrote:
> Actually, I think Dana understates the problem with this program.  It
> suffers from what I call the "PBS documentary syndrome" (equally
> afflicting the BBC, however, so the name is not universal enough!):
> it repeatedly tells you what's cool about its topic, without ever
> actually telling you what the topic really is.  Afraid to scare
> viewers away with the actual details of the topic, it just talks about
> it in terms so general (and often over-inflated or sensationalized,
> which was Dana's point) they are really quite meaningless.
>
> Though not perfect by any means, I think a recent 4-part series "The
> Story of Maths" narrated by Marcus du Sautoy does better - he even
> tries to sketch some proofs.  (The episode closest to "Dangerous
> Knowledge" would be the fourth.)  Even better is an old series (but
> still to be found on Youtube!) called Mathematical Mystery Tour.
>
> But generally, science documentaries are disappointing, and maths ones
> even more so.  It's a pity, because you actually can get an audience
> of non-specialists to understand (at least a little) what mathematical
> results etc are about.  I teach an honours Liberal Arts maths & logic
> class, and a surprisingly large percentage can actually appreciate the
> beauty of (eg) natural deduction proofs in predicate logic, basic
> theory of natural numbers (infinitude of primes, irrationality of
> primes, the fundamental theorem of arithmetic, ... ), simple
> axiomatics (we do Boolean algebras as an example), and even Godel's
> theorems, and the "Lambek calculus" for linguistics (even a bit of
> category theory there!).  This isn't a mickey mouse course (sample
> class tests available on request!), and it's a challenge to many of
> the students.  The point is: they are willing to make the effort if
> they know you're not being condescending, and that you are giving them
> "the real thing", not some pablum that only looks good in the box.
>
> I wish more TV documentary producers took that attitude - they might
> get a slightly smaller audience, but their audience will appreciate
> their efforts more.
>
> -= rags =-
>

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Re: Dangerous knowledge

[Vaughan Pratt]

Aren't artistic types alleged to be more prone to mental illness than
say sales clerks, real estate agents, auto mechanics, farmers,
lumberjacks, etc?   More generally, creative people?  On that basis
would one expect a higher prevalence of mental disorders among
theoretical physicists (Boltzmann) than experimental ones (Rutherford),
or among mathematicians than engineers, or among top chefs than short
order cooks?

Everyone seems to be a mental health expert today, just as everyone is
an expert on evolution and global warming (but not quantum mechanics or
ecology or anesthesiology, funny how that works).  I'd be uncomfortable
with any innuendos of this kind about theoreticians vs. practitioners,
or creatives vs servants, or prima donnas vs. choristers, without some
solid independent evaluation of this question by professionals with a
substantial track record in mental health.  Has any such evaluation been
made?

Vaughan Pratt


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Re: Dangerous knowledge

[Joyal, André]

Perhaps, Paul Dirac is another example of a strange character.
See his biography: 

Strange Genius: The Life and Times of Paul Dirac 

http://physicsworld.com/cws/home

AJ

-------- Message d'origine--------
De: categories@mta.ca de la part de Vaughan Pratt
Date: dim. 06/12/2009 13:46
À: categories list
Objet : categories: Re: Dangerous knowledge
 
Aren't artistic types alleged to be more prone to mental illness than
say sales clerks, real estate agents, auto mechanics, farmers,
lumberjacks, etc?   More generally, creative people?  On that basis
would one expect a higher prevalence of mental disorders among
theoretical physicists (Boltzmann) than experimental ones (Rutherford),
or among mathematicians than engineers, or among top chefs than short
order cooks?

Everyone seems to be a mental health expert today, just as everyone is
an expert on evolution and global warming (but not quantum mechanics or
ecology or anesthesiology, funny how that works).  I'd be uncomfortable
with any innuendos of this kind about theoreticians vs. practitioners,
or creatives vs servants, or prima donnas vs. choristers, without some
solid independent evaluation of this question by professionals with a
substantial track record in mental health.  Has any such evaluation been
made?

Vaughan Pratt


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Re: Dangerous knowledge

[jim stasheff]

Vaughan Pratt wrote:
> Aren't artistic types alleged to be more prone to mental illness than
> say sales clerks, real estate agents, auto mechanics, farmers,
> lumberjacks, etc?   More generally, creative people?  On that basis
> would one expect a higher prevalence of mental disorders among
> theoretical physicists (Boltzmann) than experimental ones (Rutherford),
> or among mathematicians than engineers, or among top chefs than short
> order cooks?
>
> Everyone seems to be a mental health expert today, just as everyone is
> an expert on evolution and global warming (but not quantum mechanics or
> ecology or anesthesiology, funny how that works).  I'd be uncomfortable
> with any innuendos of this kind about theoreticians vs. practitioners,
> or creatives vs servants, or prima donnas vs. choristers, without some
> solid independent evaluation of this question by professionals with a
> substantial track record in mental health.  Has any such evaluation been
> made?
>
> Vaughan Pratt
>

I seem to recall some such work on Asperger's
see book by Ioan James and a benefides neuroscientist

jim



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A well kept secret

[Joyal, André]

Category theory is a powerful mathematical language.
It is extremely good for organising, unifying and suggesting new directions of research.
It is probably the most important mathematical developpement of the 20th century.

But we cant say that publically.

André Joyal


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Re: Dangerous knowledge

[Steve Vickers]

Dear Vaughan,

I haven't looked at the programmes, but I mentioned the general drift of
the categories discussion to my wife Dr Camilla Haw. She is a practising
psychiatrist and has also done a lot of research with the Oxford Centre
for Suicide Research. Her comments were (i) academics in general have a
low suicide rate (high rates are for health professionals and
agricultural workers), and (ii) 4 cases over a century or more don't in
themselves add up to risk factor.

Best wishes,

Steve.

Vaughan Pratt wrote:
> Aren't artistic types alleged to be more prone to mental illness than
> say sales clerks, real estate agents, auto mechanics, farmers,
> lumberjacks, etc?   More generally, creative people?  On that basis
> would one expect a higher prevalence of mental disorders among
> theoretical physicists (Boltzmann) than experimental ones (Rutherford),
> or among mathematicians than engineers, or among top chefs than short
> order cooks?
>
> Everyone seems to be a mental health expert today, just as everyone is
> an expert on evolution and global warming (but not quantum mechanics or
> ecology or anesthesiology, funny how that works).  I'd be uncomfortable
> with any innuendos of this kind about theoreticians vs. practitioners,
> or creatives vs servants, or prima donnas vs. choristers, without some
> solid independent evaluation of this question by professionals with a
> substantial track record in mental health.  Has any such evaluation been
> made?
>
> Vaughan Pratt
>


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re: A well kept secret

[David Spivak]

I think we should say it publicly.  Gays get to have gay pride, why
shouldn't categorists get to have category-theory pride?  Perhaps
we've just been in the closet too long.  I think it's the right thing
to do to explain to people that this stuff is interesting and
worthwhile to us.

Worst of all would be to let the fear of shame keep us from saying
what we hold as true.  If I consider category theory to be good,
beautiful, valid math, then I shouldn't be shy about saying as much.
If someone else doesn't consider it to be "real math," he or she can
challenge me -- I'm up for that discussion.  The worst they can do is
not give me a job, but this is not an issue because I don't belong at
a place that doesn't respect category theory.

Andre is right -- category theory is probably the most important
mathematical developpement of the 20th century.

David


On Mon, Dec 7, 2009 at 6:13 AM, Joyal, André <joyal.andre@uqam.ca> wrote:
> Category theory is a powerful mathematical language.
> It is extremely good for organising, unifying and suggesting new directions of research.
> It is probably the most important mathematical developpement of the 20th century.
>
> But we cant say that publically.
>
> André Joyal


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re: A well kept secret

[Robert Seely]

Well, we might not say that, but Voevodsky did.  Link on the triples
page: http://www.math.mcgill.ca/triples/  (or directly
http://claymath.msri.org/voevodsky2002.mov) where he says "Categories:
one of the most important ideas of 20th century mathematics".

BTW - the Farmelo book, The Strangest Man, is one I recommend to my
students - it's well worth looking at.  But one thing that struck me
was how *little* Farmelo plays the "strange man" theme - Dirac was
indeed strange, but that's not what makes him worth reading about, nor
was it what made him a great theoretician.  Farmelo doesn't (IMO) make
the same mistake so many documentary producers do ...

-= rags =-


On Mon, 7 Dec 2009, Joyal, André wrote:

> Category theory is a powerful mathematical language.
> It is extremely good for organising, unifying and suggesting new directions of research.
> It is probably the most important mathematical developpement of the 20th century.
>
> But we cant say that publically.
>
> André Joyal

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Re: A well kept secret

[Steve Vickers]

Dear Andre,

I think category theorists have done an excellent job at publicizing the
secret. I am very much struck at category meetings what a variety of
backgrounds the participants come from, lots from computer science of
course, and now increasingly many physicists. It seems to me this is
exactly because category theory has the qualities you describe. It
enables the pure category theorists, the computer scientists, the
physicists to meet and talk together with a high degree of mutual
understanding.

I don't think of myself as a pure category theorist, but I can't imagine
trying to do what I do without it.

All the best,

Steve.

Joyal wrote:
> Category theory is a powerful mathematical language.
> It is extremely good for organising, unifying and suggesting new directions of research.
> It is probably the most important mathematical developpement of the 20th century.
> 
> But we cant say that publically.
> 
> André Joyal
> 



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Re: Dangerous knowledge

[Vaughan Pratt]

[Note from moderator: while interesting, this thread has strayed well
off-topic; to be posted further submissions must be relevant to
categories.]

Jim Stasheff wrote:
> I seem to recall some such work on Asperger's
> see book by Ioan James and a benefides neuroscientist

Ioan James held the Savilian Chair of Geometry at Oxford during 1970-95,
and seems to be the only author.  Where does the neuroscientist come
into it?

Autism is a pretty disabling condition.  The 20 individuals James writes
about seem at worst to be only mildly autistic and surely would be
better described as having Asperger syndrome if even that.  In 1944 Hans
Asperger described a behavioral pattern that, according to the Wikipedia
article on him, included "a lack of empathy, little ability to form
friendships, one-sided conversation, intense absorption in a special
interest, and clumsy movements."

Anyone who's gone overtime in a conference talk at the expense of the
next speaker could be judged as having at least three of the first four
of these, and the audience would then be riveted on the speaker's
movements to assess their clumsiness.  And how does one judge "ability
to form friendships?"  By the number of the speaker's coauthors?  Some
people are by nature private, others compartmentalize their time into
private and social periods so that they can get some work done in their
private time.  How is someone to be judged when their social time is
only say 10% or 20% of their private time?

Wikipedia has the following article:

http://en.wikipedia.org/wiki/People_speculated_to_have_been_autistic

whose introduction reads

---
Famous historical people have been speculated to have been autistic by
journalists, academics and autism professionals. Such speculation is
controversial and little of it is undisputed. For example, several
autism researchers speculate that Wolfgang Amadeus Mozart had autism and
other diagnoses, while other researchers say there is not sufficient
evidence to draw conclusions that he had any diagnoses
---

The body of the article includes "Speculation about their diagnoses is
based on reported behaviors rather than any clinical observation of the
individual. Fred Volkmar, a psychiatrist and autism expert and director
of the Yale Child Study Center says, 'There is unfortunately a sort of
cottage industry of finding that everyone has Asperger's.' "

Here's the Amazon product description of James' book, and two customer
reviews.

---
This fascinating collection identifies famous figures from the past,
whose behaviour suggests they may have had autism, a disorder that was
not defined until the mid - 20th century. James looks at the lives of 20
individuals - scientists, artists, politicians and philosophers -
examining in detail their interests, successes, indifferences and
shortcomings. Among the profiles are those of mathematician and
philosopher Bertrand Russell, who wondered in his autobiography how he
managed to hurt the people around him quite without meaning to;
biologist Alfred Kinsey, who excelled in academia but was ill at ease in
social situations; and the writer Patricia Highsmith, who had very
definite likes (fountain pens and absence of noise) and dislikes
(television and four-course meals). From Albert Einstein to Philip of
Spain, these intriguing individuals all showed clear evidence of
autistic traits. This book will be of interest to general readers and
anyone with a personal or professional interest in autism.
---

---
FIRST REVIEW: "Offers opportunity for personal insight"

This book is not what I expected, yet I appreciate its contribution to
the literature on this topic.

Twenty biographical accounts are arranged chronologically. Each offers
basic facts about the life and accomplishments of the individual, and
includes accounts of their behaviors, their own views of their
challenges and accomplishments as well as the perceptions of their
contemporaries.

Taken together, these twenty biographies offer me insights into human
diversity and the importance of accepting ourselves and others for our
strengths as well as our idiosyncrasies. As a teacher it helps me both
understand and appreciate unique children.
---

---
SECOND REVIEW: "Not another book about famous people who might have had
Asperger Syndrome!"

I have to say, this genre is getting rather tired, and there is a lot of
overlap between all the books on this subject, of which there are many.
If you already own one of the other books on this subject, you don't
need to buy this one, and if you don't already own a book on this
subject, this one is as good as any. What else can I say? It's 20 mini
biographies of people the author has researched and considers to show
signs of having had Asperger Syndrome. Interesting enough, and probably
succeeds in the stated aim of raising the self esteem of people with AS.
---

Vaughan


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Re: A well kept secret

[Charles Wells]

To add to Steve Vickers' remarks:  Category theory is definitely out
of the closet.  A substantial number of the questions on MathOverflow
involve categorical concepts and many of them are questions about
category theory itself, not merely applications.  The n-category café
blog and its ancillary n-labs has lots of category stuff, both
applications to physics and about category theory itself.

Charles Wells



-- 
professional website: http://www.cwru.edu/artsci/math/wells/home.html
blog: http://sixwingedseraph.wordpress.com/
abstract math website: http://www.abstractmath.org/MM//MMIntro.htm
astounding math stories: http://www.abstractmath.org/MM//MMAstoundingMath.htm
personal website:  http://www.abstractmath.org/Personal/index.html
sixwingedseraph.facebook.com


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re: A well kept secret

[Mehrnoosh Sadrzadeh]

I have read that  Dirac had no empathy, not even for his family. I think the
story goes the same  for many other famous mathematicians/scientists. Why is
it being so promoted that being a good mathematician and a good human being
is impossible? Is it really true?

-Mehrnoosh

On Tue, Dec 8, 2009 at 5:23 AM, Robert Seely <rags@math.mcgill.ca> wrote:

> Well, we might not say that, but Voevodsky did.  Link on the triples
> page: http://www.math.mcgill.ca/triples/  (or directly
> http://claymath.msri.org/voevodsky2002.mov) where he says "Categories:
> one of the most important ideas of 20th century mathematics".
>
> BTW - the Farmelo book, The Strangest Man, is one I recommend to my
> students - it's well worth looking at.  But one thing that struck me
> was how *little* Farmelo plays the "strange man" theme - Dirac was
> indeed strange, but that's not what makes him worth reading about, nor
> was it what made him a great theoretician.  Farmelo doesn't (IMO) make
> the same mistake so many documentary producers do ...
>
> -= rags =-
>
>
>
> On Mon, 7 Dec 2009, Joyal, André wrote:
>
>  Category theory is a powerful mathematical language.
>> It is extremely good for organising, unifying and suggesting new
>> directions of research.
>> It is probably the most important mathematical developpement of the 20th
>> century.
>>
>> But we cant say that publically.
>>
>> André Joyal
>>

-- 
Mehrnoosh Sadrzadeh
EPSRC Postdoctoral Research Fellow
Oxford University Computing Laboratory
Research Fellow of Wolfson College
http://web.comlab.ox.ac.uk/people/Mehrnoosh.Sadrzadeh/


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re: A well kept secret

[Robert Seely]

On Wed, 9 Dec 2009, Mehrnoosh Sadrzadeh wrote:

> I have read that  Dirac had no empathy, not even for his family. I think the
> story goes the same  for many other famous mathematicians/scientists. Why is
> it being so promoted that being a good mathematician and a good human being
> is impossible? Is it really true?

Certainly Farmelo's book gives that impression - Dirac wasn't exactly
warm and cuddly.  But I'd say that from my experience with
mathematicians, there's no reason to assert that one cannot be both a
good mathematician and a good human being - but maybe that's just
because most mathematicians I know are category theorists ...

... (there are exceptions, of course) ...

-= rags =-


> -Mehrnoosh
>
> On Tue, Dec 8, 2009 at 5:23 AM, Robert Seely <rags@math.mcgill.ca> wrote:
>
>> Well, we might not say that, but Voevodsky did.  Link on the triples
>> page: http://www.math.mcgill.ca/triples/  (or directly
>> http://claymath.msri.org/voevodsky2002.mov) where he says "Categories:
>> one of the most important ideas of 20th century mathematics".
>>
>> BTW - the Farmelo book, The Strangest Man, is one I recommend to my
>> students - it's well worth looking at.  But one thing that struck me
>> was how *little* Farmelo plays the "strange man" theme - Dirac was
>> indeed strange, but that's not what makes him worth reading about, nor
>> was it what made him a great theoretician.  Farmelo doesn't (IMO) make
>> the same mistake so many documentary producers do ...
>>
>> -= rags =-
>>

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A well kept secret

[Paul Taylor]

I'm not too sure what the context was, but Andre' Joyal said on 7
December,

 > Category theory is a powerful mathematical language.  It is extremely
good
 > for organising, unifying and suggesting new directions of research.

I completely agree.

 > It is probably the most important mathematical developpement of
 > the 20th century.

It is too early to tell.

[Comment attributed to Zhou Enlai (Chinese Communist leader 1949-76)
when asked his opinion of the French Revolution.]

 > But we cant say that publically.

I think we should be wary of slapping ourselves on the back too much.

The fact is that category theory alienated the rest of the mathematical
world.   Since the damage had been done in the 1970s, well before my
time,
I have never managed to work out how this happenned, or who was
responsible.

Probably it was the result of haughty claims about being the "most
important mathematical development",  and about being the foundations
of mathematics before any serious technical work was done to justify
this.
Of course the ignorance and arrogance of mathematicians outside our
subject
had a lot to do with it too.

Indeed, I believe that there is nothing wrong with pre-1980 category
theory that cannot be attributed to the fact that it was done by pure
mathematicians,  and nor is there anything wrong with the post-1980
subject that is not the result of its having been done by computer
scientists.

However,  discussion on that is not going to get us very far.  What is
more relevant and able to be fixed is the point in Andre's title, that
category theory is a
       WELL KEPT SECRET.

Secrecy, like charity, begins at home.   For example, the notion of
       ARITHMETIC UNIVERSE
was one of the most insightful developments of 1970s categorical logic.

It captures exactly what is taught as "discrete mathematics" to
computer science students (and is relevant to combinatorial
mathematics),
namely products, equalisers, stable disjoint sums, stable effective
quotients of equivalence relations and FINITE powersets.  It is the
least structure that is capable of constructing the free internal gadget
of the same kind,  so the original idea was to prove Godel's
incompleteness
theorem categorically.

Recently I was looking though the archives of the "Foundations of
Mathematics" (FOM) mailing list at   cs.nyu.edu/pipermail/fom/
and, amongst all of the personal abuse directed at Colin McLarty and
Steve Awodey, came across an interesting argument against category
theory, namely that the notion of elementary topos was merely an
aping of the axioms of set theory.   Arithmetic universes answer that
objection extremely well.

The work on arithmetic universes was done THIRTY SIX YEARS AGO, and
many people since then have been nagging the author to write it up,
indeed I myself have been doing so for half of that time now.

I don't want anybody to read this as a personal attack -- it is
simply an example of a general phenomenon, albeit an important example
because of the importance of the material.   Anybody in my generation
or younger can cite lots of examples of "well known"  "folklore"
results that were supposedly discovered in the 1970s but have never
been written up.   The worst thing is that any younger person who
is so impertinent as to write out a proof of one of these results
has their paper rejected.

To give another example, the theory of continuous lattices is crucial
as background for my work on Abstract Stone Duality.   I asked exactly
the people who should have written it whether there was an introduction
to continuous lattices suitable for analysts.   There isn't, so
I had to write my own.   In this, I stated without proof that the
evaluation map   Sigma^X x X --> Sigma   is continuous (when the
topology Sigma^X is itself given the Scott topology)   iff  X is locally
compact,  and in this case Sigma^X is itself locally compact and
obeys the adjunction   Yx(-) -| Sigma^(-).    The referee quite
reasonably asked for a reference to a proof, but, so far as I can
gather, no such proof exists in the literature.

Two more examples: when is some Australian going to write
"2-categories for the working categorist"?
Where is the textbook on universal algebra based on monads?

So, to answer Andre's question about why category theory is such a well
kept secret -- it is because category theorists KEEP it as a secret.

Each of us can help to leak this secret by doing two things:

PUBLISH (= make freely available on the Web) all of the papers that
you PRIVATISED by handing them over to commercial journals.

WRITE textbook or encyclopedia accounts of your work for resources
like the "n-cat lab",   ncatlab.org/nlab/show/HomePage

Paul Taylor



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RE : A well kept secret

[Joyal, André]

Dear Paul,

I thank you very much for your insightful comments.

>Anybody in my generation or younger can cite lots of examples of "well known" 
> "folklore" results that were supposedly discovered in the 1970s but have 
> never been written up.  

You are completely right. 
I have my share of responsabilities here.
I will not try to explain what happened, because it may be counterproductive.
I apologise to you and to everyone who may have suffered from not getting 
access to the information they wanted from me.
I am planning to correct the problem by publishing all my "secret" notes, 
papers and books during 2010, starting this December. 

Best, 
André



-------- Message d'origine--------
De: Paul Taylor [mailto:pt09@PaulTaylor.EU]
Date: jeu. 10/12/2009 09:49
À: categories list
Cc: Joyal, André
Objet : A well kept secret
 
I'm not too sure what the context was, but Andre' Joyal said on 7 
December,

 > Category theory is a powerful mathematical language.  It is extremely 
good
 > for organising, unifying and suggesting new directions of research.

I completely agree.

 > It is probably the most important mathematical developpement of
 > the 20th century.

It is too early to tell.

[Comment attributed to Zhou Enlai (Chinese Communist leader 1949-76)
when asked his opinion of the French Revolution.]

 > But we cant say that publically.

I think we should be wary of slapping ourselves on the back too much.

The fact is that category theory alienated the rest of the mathematical
world.   Since the damage had been done in the 1970s, well before my 
time,
I have never managed to work out how this happenned, or who was 
responsible.


...



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Re: Dangerous_knowledge

[Joyal, André]

Dear John,

you wrote:

> We oldsters can tut-tut about the
>inaccuracies and lack of serious content, but as a kid I would have enjoyed
>it - and if it makes one youngster pursue a career in mathematics instead of
>crime, that may justify its existence.

Perhaps, a better and more exciting model for the youngster 
is Richard Feynman, a "genious" with common sense:

http://www.lhup.edu/~DSIMANEK/cargocul.htm

Best,
André


-------- Message d'origine--------
De: categories@mta.ca de la part de John Baez
Date: mar. 01/12/2009 21:16
À: categories@mta.ca
Objet : categories: Re: Dangerous knowledge
 
The BBC wrote:

 In this one-off documentary, David Malone looks at four brilliant
>> mathematicians - Georg Cantor, Ludwig Boltzmann, Kurt Gödel and Alan
>> Turing - whose genius has profoundly affected us, but which tragically drove
>> them insane and eventually led to them all committing suicide.
>>
>
Jim Stasheff wrote:

At least the Turing implication is very misleading - see below.
>

It's also not true that George Cantor committed suicide!

And I would not call Ludwig Boltzmann a mathematician.  I'd call him a
physicist.

But the documentary seems a bit more accurate than this summary.
And it could be good to have documentaries that sensationalize mathematics
and make it seem "edgy" and "dangerous".  We oldsters can tut-tut about the
inaccuracies and lack of serious content, but as a kid I would have enjoyed
it - and if it makes one youngster pursue a career in mathematics instead of
crime, that may justify its existence.

Best,
jb


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re: A well kept secret

[Michael Barr]

There are several comments I could make to this posting, but I will
confine myself to two.  First, I was around all through the 70s (and most
of the 60s) and I have no idea what categorists did to earn the opprobrium
described below.  A colleague of mine commented one day maybe 25 years
ago, that it seemed in the 60s that category theory would be important,
but it hasn't turned out that way.  I am not sure what didn't turn out
that way, but that seemed to have been the general opinion.

Second, a couple of papers by Linton and Manes in the Zurich Triples Book
(LNM #80) makes very explicit the connection between triples and universal
algebraic theories.  Although doubtless out of print, a dozen of us put a
lot of effort into retyping it in tex and republishing it as a TAC
reprint.  If someone wants to go ahead and replace every instance of
"triple" by "monad" go ahead.  Also Beck's tripleableness theorem is in
Beck's thesis, another TAC reprint also retyped by volunteers.

Incidentally (although Paul is well aware of this) every paper of mine
later than 1985 and every earlier paper of which I had an electronic
trace, is available on my personal ftp site.  Also incidentally my wife
and I retyped Grothendieck's Tohoku paper and are waiting only for
proof-reading by the Van Osdols to post it (hint, hint, since I know Don
reads this group).

Michael

On Thu, 10 Dec 2009, Paul Taylor wrote:

> I'm not too sure what the context was, but Andre' Joyal said on 7
> December,
>
>>  Category theory is a powerful mathematical language.  It is extremely
> good
>>  for organising, unifying and suggesting new directions of research.
>
> I completely agree.
>
>>  It is probably the most important mathematical developpement of
>>  the 20th century.
>
> It is too early to tell.
>
> [Comment attributed to Zhou Enlai (Chinese Communist leader 1949-76)
> when asked his opinion of the French Revolution.]
>
>>  But we cant say that publically.
>
> I think we should be wary of slapping ourselves on the back too much.
>
> The fact is that category theory alienated the rest of the mathematical
> world.   Since the damage had been done in the 1970s, well before my
> time,
> I have never managed to work out how this happenned, or who was
> responsible.
>
> Probably it was the result of haughty claims about being the "most
> important mathematical development",  and about being the foundations
> of mathematics before any serious technical work was done to justify
> this.
> Of course the ignorance and arrogance of mathematicians outside our
> subject
> had a lot to do with it too.

...

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Re: A well kept secret

[Tom Leinster]

On Thu, 10 Dec 2009, Paul Taylor wrote:

> Two more examples: when is some Australian going to write
> "2-categories for the working categorist"?

This seems like a good candidate:

Stephen Lack, "A 2-categories companion"

http://arxiv.org/abs/math/0702535 (73 pages)

There's also Kelly and Street's excellent "Review of the elements of
2-categories" (1974), but doubtless you know about that, and I guess it's
not as comprehensive as what you're envisaging.

Best wishes,
Tom


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Re: A well kept secret

[Michael Fourman]

On 10 Dec 2009, at 14:49, Paul Taylor wrote:

>    In this, I stated without proof that the
> evaluation map   Sigma^X x X --> Sigma   is continuous (when the
> topology Sigma^X is itself given the Scott topology)   iff  X is locally
> compact,  and in this case Sigma^X is itself locally compact and
> obeys the adjunction   Yx(-) -| Sigma^(-).    The referee quite
> reasonably asked for a reference to a proof, but, so far as I can
> gather, no such proof exists in the literature.

Not in the compendium?

Professor Michael Fourman FBCS CITP
Informatics Forum
10 Crichton Street
Edinburgh
EH8 9AB 
http://homepages.inf.ed.ac.uk/mfourman/
For diary appointments contact :
mdunlop2(at)ed-dot-ac-dot-uk
+44 131 650 2690



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Re: A well kept secret

[Greg Meredith]

Dear Paul,

Two more examples: when is some Australian going to write

"2-categories for the working categorist"?

Where is the textbook on universal algebra based on monads?

Absolutely. The latter would so greatly simplify a number of
cross-disciplinary conversations.

Best wishes,

--greg

On Thu, Dec 10, 2009 at 6:49 AM, Paul Taylor <pt09@paultaylor.eu> wrote:

> I'm not too sure what the context was, but Andre' Joyal said on 7
> December,
>
>
> > Category theory is a powerful mathematical language.  It is extremely
> good
> > for organising, unifying and suggesting new directions of research.
>
> I completely agree.
>
>
> > It is probably the most important mathematical developpement of
> > the 20th century.
>
> It is too early to tell.
>
> [Comment attributed to Zhou Enlai (Chinese Communist leader 1949-76)
> when asked his opinion of the French Revolution.]
>
>

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re: A well kept secret

[jim stasheff]

Michael Barr wrote:
> There are several comments I could make to this posting, but I will
> confine myself to two.  First, I was around all through the 70s (and most
> of the 60s) and I have no idea what categorists did to earn the
> opprobrium
> described below.

I have my suspicions as to what categorists did to earn the opprobrium
described below.

The high density of new vocabulary in many research papers.

Not enough published at the level of Saunders Cats for teh Working
mathematician

Too many papers doing category theory for its own sake

apologies ahead of time to anyone whose ox is being gored

jim



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re: A well kept secret

[jim stasheff]

> this stuff is interesting and
> worthwhile to us.
>
> but that doesn't imply

> category theory is probably the most important
> mathematical developpement of the 20th century.
>   

we need to build that bridge

jim


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Re: A well kept secret

[Zinovy Diskin]

On Thu, Dec 10, 2009 at 9:49 AM, Paul Taylor <pt09@paultaylor.eu> wrote:

> The fact is that category theory alienated the rest of the mathematical
> world.   Since the damage had been done in the 1970s, well before my
> time,
> I have never managed to work out how this happenned, or who was
> responsible.
>

Had it been really  *done*?  It may be just in "the nature of things"
when a community A provides abstract models for community B. Something
similar appears in relations between physicists and mathematicians, or
between physicists/computer scientists and engineers.

When a mathematician is building a math model for some physical
theory, his main driving force is a question "What do they *really*
do?"  As the work is progressing, the question develops into a thesis
"they don't actually understand what they do", and with this attitude,
the mathematician finally brings something structurally neat to
physicists. In a typical good case, the reaction would be like Manin
recently formulated in his interview "we always knew that but thank
you for attention". In a bad case, ... you know.

Isn't it similar to the math vs.category theory case?  For some people
structural clarity and elegance is a matter of life and death, for
others it's a dispensable luxury (it's a rephrasing of Edsger Dijkstra
if I remember right).

zd






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RE: A well kept secret

[Wojtowicz, Ralph]

Jim Stasheff wrote:
> we need to build that bridge

The paper linked below is an example of a "success story" that I have recently described to sponsors who want to know what use category theory has been to other parts of mathematics.  In my opinion, the fact that category theory provided not only new insights into semantics of full first-order S4 modal logic but also semantics of higher-order S4 helps build the bridge mentioned above.
http://www.andrew.cmu.edu/user/awodey/preprints/FoS4.phil.pdf

One sponsor had his own example (see the link below which he brought to my attention) which has generated a lot of interest among my colleagues at work since "network analysis" is one of our primary business areas.
http://comptop.stanford.edu/preprints/clust-functorial.pdf

I am still working through the following but think it also contributes to the bridge.
http://www.andrew.cmu.edu/user/awodey/preprints/homotopy.pdf

Ralph Wojtowicz
Metron, Inc.
1818 Library Street, Suite 600
Reston, VA  20190
www.metsci.com


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Re: A well kept secret

[Zinovy Diskin]

On Mon, Dec 7, 2009 at 9:13 AM, Joyal, André <joyal.andre@uqam.ca> wrote:
> Category theory is a powerful mathematical language.
> It is extremely good for organising, unifying and suggesting new directions of research.

one important point is missing: design and design patterns. Design
from scratch is for geniuses while ordinary people design by adapting
and developing preexisting patterns. Category theory created a
powerful system of design patterns for math and beyond (computer
science, physics, engineering). It seems it changed the very
nature of mathematical design.

Z.


> It is probably the most important mathematical developpement of the 20th century.
>
> But we cant say that publically.
>
> André Joyal
>


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re: A well kept secret

[Vaughan Pratt]

Michael Barr wrote:
>  First, I was around all through the 70s (and most
> of the 60s) and I have no idea what categorists did to earn the opprobrium
> described below.

My experience with CT may give some insight here.

When I joined the MIT faculty in 1972 it was already 8 years since I'd
taken Max Kelly's category theory class, and the only bit of it that I
had retained by that time was that categories weren't required to have
an underlying set functor (and I couldn't in 1972 even phrase that much
of my recollection in the language of CT I used just now).

Now skip the next two paragraphs (which are only there to preserve
chronological order) unless you want all the boring details.

In between I spent a year taking mathematics honours (fourth year), in
which Max taught us topology (he had planned to teach us algebraic
topology but realized we weren't prepared for it) and we got many other
courses from John Mack (number theory), T.G. Room (axiomatic geometry),
Bruce Barnes (group theory), etc.  I then spent a year doing physics
honours (a second fourth year, I did maths honours first because I
wanted to be a theoretical physicist and had sensed that without maths
honours the physics honours year would be insufficient grounding for a
theoretical physicist).

But then the next year I noticed that computer science was an
as-yet-untapped gold mine of important yet easily solved problems,
whence my career move from physics into CS.  (A pity in some respects
since I've always been good at solving hard problems once they engage my
interest and the problems in physics had by then become quite hard and
therefore should have been right up my alley.)  So I became a CS grad
student at Sydney then Berkeley then Stanford, and then Don Knuth's
postdoc in 1971-72, and then spent a few months at IBM Yorktown Heights
in a visiting faculty position in 1972.

In 1972 the only person in the whole of 545 Technology Square (a 9-story
building on the "other side of the tracks" from the main body of MIT)
who talked about categories was Mitch Wand.  Mike Fischer was his
advisor.  I lived out Mike's way and commuted to work with him much of
the time, a half hour ride each way, so we got to discuss many things,
but I don't recall category theory ever coming up.  We mostly talked
about algorithms and program verification and programming language
design and group theory and other technical things, along with the
vegetable gardens we were growing in our back yards as a joint project
that also involved Albert Meyer.  We both were totally oblivious to
politics, which never came up.  And it never occurred to either of us
that we should discuss CT.

While still a grad student Mitch gave a graduate course on CT.  I didn't
attend any of it, being rather busy as a junior faculty and having no
occasion to, but I would occasionally hear feedback from those who did.
  The general feeling seemed to be that this was "mathematics made
difficult," a way of obfuscating the obvious.  I had no reason to defend
CT at the time and simply accepted these reports as putting CT in the
same ballpark that Rene Thom's chaos theory was later put by some of its
detractors.

In 1979, finding logic problems becoming more challenging, I
(re)discovered algebra by way of universal algebra.  I learned UA from
Rasiowa and Sikorski, which I found to my surprise I could speed-read
(must have been the excellent Sydney algebra courses), and successfully
applied it to the logic problem I'd previously been stuck on.

In 1983 I realized that category theory was the algebra of functions.  I
tried very very hard to understand Chapter 1 of CWM, which seemed far
more obscure than universal algebra.  Speed-reading that chapter was out
of the question for me.

Eventually I gave up and moved on to Chapter 2 and beyond, and after
that it was just as easy as universal algebra.

----------
So I would say that the opprobrium could well have originated from the
impression that CT was obfuscation, which Chapter 1 of CWM did nothing
to dispel.  Two four-syllable words beginning with the same letter, one
leading to the other.
----------

So what do I think today?  Well, I would rank three related concepts as
being of fundamental but not equal importance, in the following order,
most important first.

1.  2-categories

2.  Dense functors

3.  Natural transformations

The algebra of 2-categories is barely algebra, it is really the
associativity intrinsic to geometry.  If you cut a string, even one with
colored ink marks on it, in two places you can't tell after the fact in
which order the cuts were made.  If you cut a painting by Picasso
vertically then horizontally into four pieces, the same holds even
though the painting has depreciated.  These are respectively
associativity and middle-interchange.  I hardly recognize these as
algebra, they're geometry as far as I'm concerned, but they're the
algebra of 2-categories.  They suck, e pur si muove.

Dense functors are important because they expose what is "natural" about
natural transformations as an instance of 2-cells.  To see how this
works see http://boole.stanford.edu/pub/yon.pdf , "The Yoneda lemma as a
foundational tool for algebra."  I imagine Steve Lack et al have some
equivalent way of describing this viewpoint which I'm still waiting to
hear about (my 1962-1965 classmate Ross Street promised he'd get back to
me on this but that was a while back).  Meanwhile I've received
enthusiastic feedback about it from Ronnie Brown and also a response
from William Boshuk ("very enjoyable pamphlet"), though that's it so far.

I've felt for at least 15 years that the notion of natural
transformation as traditionally defined is a complicated concept.  This
I believe whether one thinks of them as a category theorist or (in their
manifestation as homomorphisms) as an algebraist.  Either way the idea
is subtle.  This subtlety of the concept is why I don't rank it higher.

My ranking makes it ironic that transformations that are called
"natural" should end up third.  But then that's just my ranking, YMMV as
they say.

Vaughan

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Re: Dangerous knowledge

[Eduardo J. Dubuc]

yes, but be careful, the option is not mathematics or crime, it is
mathematics or somenthig else

pursue a career in mathematics by (or because) wrong reasons can only
lead to a bad mathematician and/or a frustrated man

a waste, not a criminal but ... ?




jim stasheff wrote:
>> and if it makes one youngster pursue a career in mathematics instead of
>> crime, that may justify its existence.
>>
>> Best,
>> jb
>>
> at least one or more episodes of Numb3ers
> made that point
>
> jim
>


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Re: Dangerous knowledge

[jim stasheff]

> and if it makes one youngster pursue a career in mathematics instead of
> crime, that may justify its existence.
>
> Best,
> jb
>
at least one or more episodes of Numb3ers
made that point

jim




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Re: Dangerous knowledge

[Mike Stay]

On Mon, Nov 30, 2009 at 3:37 PM, Dana Scott <dana.scott@cs.cmu.edu> wrote:
> I think the premise of the work is silly.

I agree; it seems to be an urban legend that to be a great
artist--whether a musician, painter, mathematician, or what have
you--one has to be mentally unstable.  Perhaps it's a way for people
to excuse themselves for never creating a work of great beauty.
-- 
Mike Stay - metaweta@gmail.com
http://math.ucr.edu/~mike
http://reperiendi.wordpress.com


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