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Category: stories

capita selecta


Rather than going to the NOG
III Workshop
I think it is more fun to give a talk for the Capita
Selecta
-course for 2nd year students on “Monstrous Moonshine”. If
I manage to explain to them at least something, I think I am in good
shape for next year\’s Baby Geometry (first year) course. Besides,
afterwards I may decide to give some details of Borcherds\’ solution next year in my 3rd year
Geometry-course…(but this may just be a little bit
over-optimistic).
Anyway, this is what I plan to do in my
lecture : explain both sides of the McKay-observation
that

196 884 = 196 883 + 1

that is, I\’ll give
the action of the modular group on the upper-half plane and prove that
its fundamental domain is just C using the modular j-function (left hand
side) and sketch the importance of the Monster group and its
representation theory (right hand side). Then I\’ll mention Ogg\’s
observation that the only subgroups Gamma(0,p)+ of SL(2,Z)
for which the fundamental domain has genus zero are the prime divisors
p of teh order of the Monster and I\’ll come to moonshine
conjecture of Conway and Norton (for those students who did hear my talk
on Antwerp sprouts, yes both Conway and Simon Norton (via his
SNORT-go) did appear there too…) and if time allows it, I\’ll sketch
the main idea of the proof. Fortunately, Richard Borcherds has written
some excellent expository papers I can use (see his papers-page and I also discovered a beautiful
moonshine-page by Helena Verrill which will make my job a lot
easier.
Btw. yesterday\’s Monster was taken from her other monster story…

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25 years monstrous moonshine

Writing a survey paper is a highly underestimated task. I once
tried it out with \’Centers of generic division algebras : the
rationality problem 1965-1990\’ and it took me a lot of time and that
was on a topic with only 10 to 15 key papers to consider… The task of
writing a survey paper on a topic with any breadth must be much more
difficult. Last week, Terry Gannon posted a survey paper on the arXiv :
Monstrous Moonshine : The first twenty-five years
which gives a very readable introduction to this exciting topic. It has
a marvelous opening line :

It has been approximately
twenty-five years since John McKay remarked that

196 884 = 196 883 +
 1

Anyone who is puzzled by this line (“So what?”)
should definitely have a go at this paper! Still not convinced? Here is
the second sentence :

That time has seen the discovery of
important structures, the establishment of another deep connection
between number theory and algebra, and a reinforcement of a new era of
cooperation between pure mathematics and mathematical
physics.

For the remaining sentences (quite a few, the paper
is 33 pages long) I happily refer you to the paper.

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artistic and other frustrations


Yesterday, PD1 exhibited some of her paintings in the Antwerp Museum for
Photography
. Over breakfast this morning she was in a rare angry
mood. No, she was satisfied with the responses she got on her work, the
room was not ideal (lighting etc.) but that was not what mattered…
Me : So?
She : There was this other work, a
video-performance. I once saw by accident on Arte a short-film and this
performance stole the whole idea of that film, from start to finish! The
whole idea was nicked!
Me : Wake up! That\’s the majority way
of creating art, or science for that matter.
She : But it is so
unfair! Why do people steal ideas ?
Me : Maybe they don\’t see
it as stealing. Maybe they believe they do a better thing with the
original idea than the person who invented it.
She : Nothing
can beat the original! Anyway, I find the most rewarding thing about art
to come up with an original idea and work it out. It cannot be rewarding
to steal other people\’s ideas.
Me (dry) : I think such people
are after other rewards…
She : The same thing happens at
school. Sometimes I come up with a suggestion to use a different
technique or material and then a few weeks later, half of my class seems
to have worked this out too.
Me : So ? You still had the
idea.
She : Yes, but the Jury doesn\’t know that!
Me :
So ? After the Jury you can still be confident to come up with new
ideas, these others may fear they will only be able to repeat
themselves.
She : But is it so unfair!
Me : What\’s
the alternative ? Are you going to lock yourself up in your room to
paint and let nobody see the result?
She : No, but I prefer to
do my painting here at home, on my own with nobody looking over my
shoulder constantly to see whether they can use some of my ideas. I will
paint on my own and only when it is fully finished they may see the
result!
Me : That\’s the spirit girl! You are much cleverer
than I will ever be…

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the cpu 2 generation

Never
ever tell an ICT-aware person that you want to try to set up a
home-network before you understand all 65536 port-numbers and their corresponding
protocols. Here is what happened to me this week. Jan Adriaenssens returned from an extended vacation in New Zealand and I told him
about my problems with trying to set up WebDAV securely. He
stared at me with that look that teenage children have if they
find out their parents dont know how to handle the simplest things on a
mobile such as saving a number, writing an SMS let alone use the
dictionary… and asked ‘now why would you want to do that??? I just
use AppleTalk to connect to my computer securely’. Now I’m not such a
fool that I didnt try this out but I didnt manage to get matrix
mounted on my Desktop. ‘Oh, but thats probably because of the
firewall’ Jan said ‘just send an email to Peter (the guy running the
defenses here) and ask him to open up ports 548 and
427…’ And sure enough five minutes later the problem was
solved and I could trow my WebDAV-plans in the dustbin (although, I
think Ive found a use for WebDAV but will keep this a bit longer to
myself until I checked it out). If you think that was the end of it,
think twice. Never ever point an ICT-professional to your
computer. They then start looking at its firewall-logs and find all
sorts of things such as : ‘I noticed that traffic from port 53
was dropped to the firewall, could it be that you configured the
firewall as DNS-server. If this is the case, you better remove it and it
will increase your network-speed, I think.’ And sure enough that
IP-address was set on my machine as one of two possibilities for the
DNS-server so I quickly removed it and in the process thought that maybe
I should also remove the other one so I did send Peter another email
asking whether that was ok. It turned out that the second IP address was
the genuine DNS-server so I got a sec answer back ‘You better leave
this as it is otherwise not much will work…’ Oh, shame, shame eternal
shame on me!

My only defense is that I still belong
to what I would call the cpu 2 generation (I’m a few years too
old to belong to the more computer-aware generation X). When I
started out doing research in 1980 the single most important command was

cpu 2

which you had to type before you could run any program.
By typing this you asked to be given 2 minutes of central processing
time, so you had to write all your programs in such a way that either
they gave a result back within 2 minutes or to include lots of
output-commands giving you a chance to determine at which parameters you
would restart the program for your next cpu 2. I once computed in
this way all factorial maximal orders in quaternion algebras by spending
a couple of days in the computer room. These days any desktop computer
would finish this task in half a minute. Perhaps the younger generations
will appreciate all the hard computer-work we had to do back then if
they read a bit from the computer history museum page!

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one week blogging

So far I
found it rather easy to post one or more messages a day as I was
installing a lot of software or trying to get things working and was
merely logging my progress for future reference. These notes are useful
to me but probably not to the rest of the world. Another thing I noticed
is that I’m using this blog sometimes as a replacement for my
Bookmarks, merely listing interesting web-pages without too much
personal comments. I will continue to post both install-logs and
bookmark-logs but in addition I want to write (say weekly) a lengthier
post on a specific topic with more background, more details (such as
screenshots) and more personal comments. We will see how this works out
in the coming weeks…

Another thing that slightly
worried me is that people visiting my homepage and clicking on to my
blog may expect entirely different things there. But this cant be
helped, I’m sitting on an OSX-cloud at the moment but no doubt this
will change quickly. Beginning of february I have to give a talk on
Combinatorial Game Theory and soon afterwards the
Non-commutative Geometry Master Class starts in which I’m giving
a couple of courses, so mathematics will become more dominant in this
blog from next month on…

On a
blog-tech matter : I found a quite good editor pMpost
which is meant to write pMachine-blogs offline and upload them by one
click. It also synchronizes categories etc. on login. Further, it has a
spelling-checker but the thing I really like about it is that you can
save texts as a draft and continue at a later time (sadly, it remember
the date/hour when you start your post so when you finally submit it it
will be posted at the starting- rather than the posting-day. Still,
there is nothing that copy/paste cannot solve. I hope to use this
facility when (read if) I’m going for a more in-depth post. Another
matter that I will address to as quickly as possible (probably over the
weekend) is teh layout of this site. The main annoying thing is that the
text doesnt resize when you increase/decrease window width. So I will
address this matter first and probably leave a personal layout and
color-scheme to later. Fortunately, I did find a good site containg a
lot of CSS templates for pMachine weblogs. Another site I’ll have to
investigate over the weekend is pMtemplates. But don’t expect too much from the
layout-side, I still have other projects to worry about : SSL, WebDAV,
streaming iTunes, getting on Ethernet-DVD player to work and so
on.

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