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Category: stories

writing

A long
time ago Don Passman
told me the simple “secret” for writing books : “Get up and,
before you do anything else, try to write 2 or 3 pages. If you do this
every day, by the end of the year you’ll have a pretty thick book.”

Probably the best advice ever for those who need to get a thesis or book
finished. I’ve managed to live by this rule for several months in a
row (the first half of 2000 leading to version 2 and the winter of 2001-2002
resulting in version 3) and I can recommend it to
anyone in need for some (self)dicipline. It feels just like training,
hard in the beginning but after a couple of weeks you’re addicted.
Also the pitfalls are similar. On certain days you have so much energy
that it is easy to write 10 or more pages (or in the revision process,
to revise 30 or more pages). Don’t do it! Tomorrow you will be
exhausted and you will not be able to do a single page but you will
convince yourself that it is not needed as you did more than enough the
day before. And you’ll feel and say the same thing the day after, and
the next day! and before you realize it you’ll be way behind
schedule. So, rule 1 : do 2 pages mimimun, 3 or 4 if possible but never
more than 5!

Another useful bit of advice comes from
Lewis Caroll’s ‘Through the looking glass’
in which the Red
King says

Start at the beginning, then continue until
you reach the end. Then stop.

Too many bookprojects
never get past the planning stages. It is much more fun to dream up the
perfect book than it is to write the first paragraph. Also, when the
writing on chapter X goes slow, it is tempting to begin with chapter X+1
or any other chapter that seems like more fun, and before you know
you’ll end up with a complete mess (and believe me, I know what I’m
talking about here).

Armed with these two guiding rules I began
the new year writing version pi of my book. (Oh, a marginal note : some
people seem to think that I set up ‘NeverEndingBooks’ to get my
book published. It may surely be the case that I’ll get _a_
book published there, but _the_ book I promised already a long
time ago to the EMS-publishing
house
! So, if you have an interesting bookproject for
‘NeverEndingBooks’ please contact us.) Anyway, the writing goes
slow! I’m already far behind schedule. So far I produced just over 20
pages! Part of the problem is that I want the book to be self-contained
and from past experiences with our ‘masterclass non-commutative
geometry’ I know that this means including a lot of elementary
material (it seems that sudents are eager on entering a masterclass on
non-commutative geometry without knowing the basics of either
non-commutative algebra or algebraic geometry). So. I started out with
believe it or not the definition of matrix-multiplication! But the book
has a pretty steap learning curve, by page 3 I’m already using
Grassmannians to classify left ideals in matrix-algebras! But I was
surprised how long it took me to come up with my own proofs of all this
‘trivial’ material. But the main problem is : lack of motivation.
I’m no longer convinced that one has to write technical books to aid
the younger generation. They are already far too technical!Perhaps it
would be far better to write books helping to develop creativity? But
how? And why are there so few of such books around. In fact, I know of
only one book trying to achieve this : An Invitation to General
Algebra and Universal Constructions
By George Bergman. His chapter 0
‘about the course and these notes’ comes very close to how I would
like to teach masterclass courses or how I’d love to write books if
only I’d know how. Perhaps, over the next couple of weeks, I’ll use
this weblog again to write up a micro-course on noncommutative geometry,
some people tell me they begin to miss the mathematics on this
site.

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changes

Tomorrow
I’ll give my last class of the semester (year?) so it is about time to
think about things to do (such as preparing the courses for the
“master program on noncommutative geometry”) and changes to make to
this weblog (now that it passed the 25000 mark it is time for something
different). In the sidebar I’ve added a little poll to let you guess
what changes 2005 will bring to this blog (if I find the time over
Christmas to implement it). In short, @matrix will
become the portal of a little company I’ll start up (seems
_the_ thing to do now). Here are some possible names/goals. Which
one will it be? Vote and find out after Christmas.

WebMathNess is a Web-service company helping lazy
mathematicians to set up their website and make it LaTeXRender savvy
(free restyling every 6 months).

iHomeEntertaining is a
Tech-company helping Mac-families to get most out of their valuable
computers focussing on Audio-Photo-Video streaming along their Airport-network.

SnortGipfGames is a Game-company focussing on the
mathematical side of the Gipf project
games
by distributing Snort-versions of them.

NeverendingBooks is a Publishing-company specializing
in neverending mathematical course- and book-projects offering their
hopeless authors print on demand and eprint services.

QuiverMerch is a Merchandising-company specializing in
quivers. For example, T-shirts with the tame quiver classification,
Calogero-Moser coffee mugs, Lego-boxes to construct local quivers
etc.

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Jacobian update 2

Yesterday
a comment was made to the Jacobian update post saying :

The
newest thing I heard was that the proof unfortunately was incorrect at
some point – The jacobian conjecture strikes again..?? Comment by Stefan
12/6/2004 @ 4:16 pm

Clearly I was intrigued and I
asked for more information but (so far) got no reply. Some people
approach me for the latest on this issue (I don’t know a thing about the
‘proof’ but if you do a Google on Carolyn Dean Jacobian this weblog turns up third on
the list and therefore people assume I have to know something…)
so I did try to find out what was going on. I emailed Harm Derksen who is
in Ann Arbor _and_ an expert on polynomial automorphisms, so if
someone knew something about the status of the proof, he definitely
would be the right person. Harm replied instantly, unfortunately with
sad news : it seems that the announced seminar on Carolyn’s proof is
canceled because an error has been found… For the moment at
least, the Jacobian conjecture seems to be entirely open again in two
variables (of course most people expect it to be false in three or more
variables).

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blog-stress


What would you do if 80% of your blog is owned by the
_companies_ of your Ph.D. students? First, try to talk them into
selling some of their blogshares back to the public. If this fails,
threaten never to post on your blog again until the share-price has sunk
deep enough to force them into selling. If this fails also and if you
see that the price only goes up no matter how long you remain silent, it
is time for more drastic measures. Luckily, blogshares allows the owner of a
blog to issue new shares, thereby flooding the market and stabilizing
the price. I was forced into this twice this week (the two horizontal
lines in the diagram) : on monday I issued another 5000 shares dropping
their 80% to 40% but today they acquired again 50.1% forcing me into
issuing another 1000 shares… Clearly it would be fun if more of
you out there would be buying shares of this blog (I will stick to the
1000 shares I got by claiming the blog) but I will keep on issuing new
shares whenever one player acquires more than 50%. All of this
blogshares-stuff is a bit surrealistic. In less than one week the
share-value went from 0.76 to 62.73 and the total value of all public
owned shares from 0.00 to 377383.00 and at best I wrote one reasonable
post in the same period. Oh, the stress of having to maintain an
acceptable level of postings in order to preserve the property of the
shareholders of your blog…
As if this is not enough, some
bloggers start feeling guilty because they cannot maintain their rhytm
of updates in times that they feel sick or tired. Here's what Bitch Ph.D. wrote yesterday

I think I need a break from blogging. Well,
actually I need a break from a lot of things, but blogging is optional.
Plus, I really just have nothing of substance to say right now. I hate
to be all drama-queeny, and fuck, maybe I'll change my mind if the
meds kick in tomorrow. Though actually I think they're working in
that I still feel shitty and anxious but
it's—just—manageable enough for me to function at a sort
of minimal level. Or maybe that's a placebo effect. Who the hell
knows.

Anyway , the point of this post other than to just
say I feel incredibly shitty is to be giving myself public permission to
be a shitty blogger for however long it takes until I actually want to
talk again.

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versions e and pi


Once again, it may take a while before you know why there is a
[spooks]-logo next to this message… Thanks so much for the
abundant support I received when I mentioned that I might rewrite my
'forgotten' book! There was one (1) comment

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Scottish solids

John McKay
pointed me to a few interesting links on ‘Platonic’ solids and monstrous
moonshine. If you thought that the ancient Greek discovered the five
Platonic solids, think again! They may have been the first to give a
correct proof of the classification but the regular solids were already
known in 2000BC as some
neolithic stone artifacts
discovered in Scotland show. These
Scottish solids can be visited at the Ashmolean Museum in Oxford. McKay
also points to the paper Polyhedra in physics,
chemistry and geometry
by Michael Atiyah and Paul Sutcliffe. He also
found my posts on a talk I gave on monstrous moonshine for 2nd year students earlier this year and
mentionted a few errors and updates. As these posts are on my old weblog
I’ll repost and update them here soon. For now you can already hear and
see a talk given by John McKay himself 196884=1+196883, a monstrous tale at the Fields Institute.

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Jacobian update

One way to increase the blogshare-value of this site might be to
give readers more of what they want. In fact, there is an excellent
guide for those who really want to increase traffic on their site
called 26
Steps to 15k a Day
. A somewhat sobering suggestion is rule S :

“Think about what people want. They
aren't coming to your site to view “your content”,
they are coming to your site looking for “their
content”.”

But how do we know what
people want? Well, by paying attention to Google-referrals according
to rule U :

“The search engines will
tell you exactly what they want to be fed – listen closely, there is
gold in referral logs, it's just a matter of panning for
it.”

And what do these Google-referrals
show over the last couple of days? Well, here are the top recent
key-words given to Google to get here :

13 :
carolyn dean jacobian conjecture
11 : carolyn dean jacobian

9 : brauer severi varieties
7 : latexrender

7 : brauer severi
7 : spinor bundles
7 : ingalls
azumaya
6 : [Unparseable or potentially dangerous latex
formula Error 6 ]
6 : jacobian conjecture carolyn dean

See a pattern? People love to hear right now about
the solution of the Jacobian conjecture in the plane by Carolyn Dean.
Fortunately, there are a couple of things more I can say about this
and it may take a while before you know why there is a photo of Tracy
Chapman next to this post…

First, it seems I only got
part of the Melvin Hochster
email
. Here is the final part I was unaware of (thanks to not even wrong)

Earlier papers established the following: if
there is
a counterexample, the leading forms of $f$ and $g$
may
be assumed to have the form $(x^a y^b)^J$ and $(x^a
y^b)^K$,
where $a$ and $b$ are relatively prime and neither
$J$
nor $K$ divides the other (Abhyankar, 1977). It is known
that
$a$ and $b$ cannot both be $1$ (Lang, 1991) and that one
may
assume that $C[f,g]$ does not contain a degree one
polynomial
in $x, y$ (Formanek, 1994).

Let $D_x$ and $D_y$ indicate partial differentiation with respect

to $x$ and $y$, respectively. A difficult result of Bass (1989)

asserts that if $D$ is a non-zero operator that is a polynomial

over $C$ in $x D_x$ and $y D_y$, $G$ is in $C[x,y]$ and $D(G)$

is in $C[f,g]$, then $G$ is in $C[f,g]$.

The proof
proceeds by starting with $f$ and $g$ that give
a
counterexample, and recursively constructing sequences of
elements and derivations with remarkable, intricate and
surprising relationships. Ultimately, a contradiction is
obtained by studying a sequence of positive integers associated
with the degrees of the elements constructed. One delicate
argument shows that the sequence is bounded. Another delicate
argument shows that it is not. Assuming the results described
above, the proof, while complicated, is remarkably self-contained
and can be understood with minimal background in algebra.

  • Mel Hochster

Speaking about the Jacobian
conjecture-post at not even wrong and
the discussion in the comments to it : there were a few instances I
really wanted to join in but I'll do it here. To begin, I was a
bit surprised of the implicit attack in the post

Dean hasn't published any papers in almost 15 years and is
nominally a lecturer in mathematics education at Michigan.

But this was immediately addressed and retracted in
the comments :

Just curious. What exactly did
you mean by “nominally a lecturer”?
Posted by mm
at November 10, 2004 10:54 PM

I don't know
anything about Carolyn Dean personally, just that one place on the
Michigan web-site refers to her as a “lecturer”, another
as a “visiting lecturer”. As I'm quite well aware from
personal experience, these kinds of titles can refer to all sorts of
different kinds of actual positions. So the title doesn't tell you
much, which is what I was awkwardly expressing.
Posted by Peter
at November 10, 2004 11:05 PM

Well, I know a few things
about Carolyn Dean personally, the most relevant being that she is a
very careful mathematician. I met her a while back (fall of 1985) at
UCSD where she was finishing (or had finished) her Ph.D. If Lance
Small's description of me would have been more reassuring, we
might even have ended up sharing an apartment (quod non). Instead I
ended up with Claudio
Procesi
… Anyway, it was a very enjoyable month with a group
of young starting mathematicians and I fondly remember some
dinner-parties we organized. The last news I heard about Carolyn was
10 to 15 years ago in Oberwolfach when it was rumoured that she had
solved the Jacobian conjecture in the plane… As far as I recall,
the method sketched by Hochster in his email was also the one back
then. Unfortunately, at the time she still didn't have all pieces
in place and a gap was found (was it by Toby Stafford? or was it
Hochster?, I forgot). Anyway, she promptly acknowledged that there was
a gap.
At the time I was dubious about the approach (mostly
because I was secretly trying to solve it myself) but today my gut
feeling is that she really did solve it. In recent years there have
been significant advances in polynomial automorphisms (in particular
the tame-wild problem) and in the study of the Hilbert scheme of
points in the plane (which I always thought might lead to a proof) so
perhaps some of these recent results did give Carolyn clues to finish
off her old approach? I haven't seen one letter of the proof so
I'm merely speculating here. Anyway, Hochster's assurance that
the proof is correct is good enough for me right now.
Another
discussion in the NotEvenWrong-comments was on the issue that several
old problems were recently solved by people who devoted themselves for
several years solely to that problem and didn't join the parade of
dedicated follower of fashion-mathematicians.

It is remarkable that the last decade has seen great progress in
math (Wiles proving Fermat's Last Theorem, Perelman proving the
Poincare Conjecture, now Dean the Jacobian Conjecture), all achieved
by people willing to spend 7 years or more focusing on a single
problem. That's not the way academic research is generally
structured, if you want grants, etc. you should be working on much
shorter term projects. It's also remarkable that two out of three
of these people didn't have a regular tenured position.

I think particle theory should learn from this. If
some of the smarter people in the field would actually spend 7 years
concentrating on one problem, the field might actually go somewhere
instead of being dead in the water
Posted by Peter at November
13, 2004 08:56 AM

Here we come close to a major problem of
today's mathematics. I have the feeling that far too few
mathematicians dedicate themselves to problems in which they have a
personal interest, independent of what the rest of the world might
think about these problems. Far too many resort to doing trendy,
technical mathematics merely because it is approved by so called
'better' mathematicians. Mind you, I admit that I did fall in
that trap myself several times but lately I feel quite relieved to be
doing just the things I like to do no matter what the rest may think
about it. Here is a little bit of advice to some colleagues : get
yourself an iPod and take
some time to listen to songs like this one :

Don't be tempted by the shiny apple
Don't you eat
of a bitter fruit
Hunger only for a taste of justice

Hunger only for a world of truth
'Cause all that you have
is your soul

from Tracy Chapman's All
that you have is your soul

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congrats carolyn


Rumour has it (see for example here or here)
that Carolyn Dean proved the Jacobian
conjecture
in two variables!!!
Melvin Hochster seems to have
checked the proof and is convinced it is ok. Here is what he mailed to
seminar participants

The Jacobian conjecture
in the plane has been an open problem since 1939 (Keller). The simple
statement is this: given a ring map $F$ of $C[x,y]$ (the polynomial ring
in two variables over the complex numbers $C$) to itself that fixes $C $
and sends $x, y$ to $f, $g, respectively, $F$ is an automorphism if and
only if the Jacobian determinant $f_x g_y – f_y g_x$ is a nonzero
element of $C$. The condition is easliy seen to be necessary.
Sufficiency is the challenge.

Carolyn Dean has
proved the conjecture and will give a series of talks on it beginning
Thursday, December 2, 3-4 pm, continuing on December 9 and December 16.
Because there have been at least five published incorrect proofs and
innumerable incorrect attempts, any announcement of a proof tends to be
received with skepticism. I have spent approximately one hundred hours
(beginning in mid-August) checking every detail of the argument. It is
correct.

Many congratulations Carolyn and I hope to see you once
again somewhere, sometime.

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version pi

Now
that versions 2 and 3 of my abandoned book project
noncommutative~geometry@n are being referenced (as suggested) as
“forgotten book” (see for example Michel's latest paper) it is
perhaps time to consider writing version $\\pi$. I haven't made up
my mind what to include in this version so if you had a go at these
versions (available no longer)
and have suggestions, please leave a comment. An housekeeping-note :
this blog is flooded with link-spammers recently so I did remove the
automatic posting of comments. I use the strategy proposed by Angsuman to combat
them. This sometimes means that I overlook a comment (this morning I
discovered a lost comment while cleaning up the spam-comments, sorry!)
but it is the only way to keep this blog poker-casino-sex-etc free. It
goes without saying that any relevant comment (positive or negative)
will be approved as soon as I spot it.

At the moment I
haven't the energy to start the writing phase yet, but I am slowly
preparing things

  • Emptied the big antique table upstairs
    to have plenty of place to put things.
  • Got myself a laser
    printer and put it into our home-network using AirportExpress which
    allows to turn any USB-printer into a network-printer.
  • Downloaded the Springer Verlag Book Stylefiles svmono.zip. This
    does not mean that I will submit it there (in fact, I promised at least
    one series-editor to send him a new version first) but these days I
    cannot bring myself to use AMS-stylefiles.
  • Accepted an
    invitation to give a master-course on noncommutative geometry in Granada in 2005 which, combined with
    the master-class here in Antwerp next semester may just be enough
    motivation to rewrite notes.
  • Bought all four volumes of the
    reprinted Winning Ways for your
    Mathematical Plays
    as inspiration for fancy terminology and notation
    (yes, it will be version $\\pi$ and _not_ version $e$).
  • etc.
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on fundamentalism


Politicians have a tendency to jump on bandwagons. After Theo Van
Gogh was murdered by a Dutch-Maroccan there has been a unanimous outcry
to tackle 'Muslim Fundamentalists' both in the Netherlands and
Belgium. The Belgian interior minister came on television assuring the
public that he will shut down all fundamentalist internet sites…
His teenage children should tell him some basic facts of life.
In
Belgium all politicians stumble over each other to convince us how tough
they will act against extremism (they mean of course Islamic
fundamentalism), well let us see what they will do now with the extreme
right party 'Vlaams Blok' which was convicted today (in appeal)
for racism! Nothing of course, we can all easily see fundamentalism in
other people but rarely in ourselves.
It is not a big secret that
I admire Jeanette Winterson, but rarely did I agree more with one of her
montly columns than her november column. Just one paragraph :

There is very little difference between Islamic Fundamentalism and
Christian Fundamentalism. Both groups will use holy text to justify
their murders and their misogyny. Both groups believe that they are
right and that everyone else is wrong. Both groups are anti-science,
both prefer faith over facts. Ironically, both are united against the
values of liberal Western culture.

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