Thanks to Masoud for keeping the blog alive in the middle of all these trips to conferences. The last one I attended ended today and was dedicated to Pauli's philosophical ideas. It was quite interesting and gave me a great occasion to get a better knowledge of these ideas. An interesting talk was given by Rafael Nuñez "Where does mathematics come from? Pauli, Jung, and contemporary cognitive science" with a brave attempt to dismiss platonism (and in particular Pauli's view) using "contemporary cognitive science". The talk was very entertaining, in particular on the representation of the future as relative motion as in expressions of the form "winter is coming" or "we are arriving at the end of the year". Or when the infamous Chilian dictator, after the coup, said successively:"Communism has taken us at the edge of the abyss" and "today we took a big step forward". Unfortunately I missed the talk of Arthur Miller "When Pauli met Jung - and what happened next"... but I could talk to him directly and got very interested with these images Jung was showing to Pauli after hearing his dreams. I had to give a rather improvised talk on Wednesday morning (about the nature of mathematical reality and also the relations with physics) and barely made it in time, since my plane to Milan had been canceled the day before (strike of Air Control) and I had to go there by train. This took the whole day and the only possible way to reach Ascona in time was to rent a car in Milan and drive there in the middle of the night. I did it since I really hate to accept giving a talk somewhere and not be able to make it at the last moment, but there was definitely a kind of "Pauli effect"making it quite difficult to reach the place in time...
Jürg Fröhlich was prevented to come for family reasons and the talk on Pauli's work was given by Harald Atmanspacher who replaced Fröhlich at the last minute. What was really striking in this meeting was that all talks were followed by long and passionate discussions which usually lasted for almost half an hour and one could learn a lot just because there was so much interaction.
Thanks for this post. I am very intersted to know more about these images Jung was showing to Pauli after hearing his dreams....
I recently heared that Grothendieck have also written about his dreams and his interpretaions. Any relations here?
Did they talk about Rafael Nunez's research on South America's indigenous Aymara and their "radically diferent metaphorical mapping of time"? The past is in front of them and the future behind them. The same word is used for "eye", "front", "sight", and "past". They gesture over their shoulder when talking about what will happen in the future. It's a beautiful idea: of course we can't see the future, but we can see the past.
Dear nic, yes and this was a very nice point in the talk. I completely share this view that the past is the only thing we control and in fact I believe we just keep trying to rearange the past in order to cope with whatever the present gives us...
Anonymous, the lecture of Arthur Miller was based on a book which is scheduled for publication next year. So one will have to wait for that one.
As far as I know it is true that Grothendieck has been writing a lot about dreams, but my information is not reliable and the only source is the "Grothendieck Circle" website at
from which you can get better information.
ac, yes, "cope" is the right word. I think we have much to learn from indigenous people. Perhaps from animals as well. There is a primatologist, Frans de Waal, who studies conflict resolution among chimpanzees. He also wrote a wonderful book called "Our Inner Ape".
I follow the advice of Mr A.C, and I post a thought on reality in mathematics.
I was writing down the Newton's principle m.a = F when I remembered a question I asked my teacher: "Ms, what does mass represent exactly ?". Her answer was quite vague, but I
clearly understood that I was bothering her.
Now, I'm not even sure I could define it clearly, without refering to the Newton's principle. But, finally, I realised that the mass is just a number we stick to the object in order to quantify the relation between its movement and the forces applying to it.
Then I also realised that Mr Newton had a really keen brain to write such a law.
In addition, the philosophical topic this year was "the powers of imagination", and the french teacher quoted Descartes explaining (I don't remember the right quote, so I could be mistaken), the notion of force is just a product of our imagination. Then a strange thought went through my mind. All the physical principles, masses, forces etc... are just products of our imagination. Yet, when I'm told about the structure of the matter, I can't help refering to this by talking about atoms, electrons, etc... as if these products of the imagination were actually (really?) inside the functioning of the object.
Then I wondered how a physical theory is validated. The few I know took me to conclude, roughly speaking, that a physical theory, to be validated, have to predict results and prepare experiments allowing to validate theses predictions. So the comparison with the world come in 2d place. I mean, the theoricist first build the object in his mind, and after that, he checks the correspondence between this mind-object"
and the physical object. And once again, I realised that Mr Newton was quite amazing: his mind-object fits the physical object so well that nowadays, it is hard to make the difference between the two. If I ask my physics teacher why an apple fall down, he will certainly answer that the apple is subject to the gravity force which implies its movement. And asking him if he is sure might get me into troubles ...
The quantic physics is quite popular nowadays, and even if the topic is completely out of my reach, I wanted to have a glance in it. What has first astonished me was the non natural aspect of its principles. I encountered hilbert spaces, eigenvalues, ... just this year, and I recognize I was bit shocked to see such objects occur in a physical theory. But, if we get to the bottom of the thing, these principles are not less
natural than the notion of force from Newton: I was presented the forces like arrows that push or pull objects ... it sounds quite estoric.
Now, here is how I understand the reality of mathematics. The "mind-objects" produced by mathematics
don't have less consistency than physical objects, since we sense these latters through "mind-objects". Precisely, I can't see a line that could be drawn between physical objects and "mind-objects", since we sense the world through "mind-objects". I can't see the line between the reality of mathematics and the reality of physics. Thus the consistency of one is equivalent to the consistency of the other.
(I might have mispelled some words since english isn't my native language, I apologize)
Thanks for your report from Ascona. The Pauli/Jung correspondence has generated a lot of interest since they were published in 2000 and I must confess that I fully agree that they make a fascinating read! There are a few books out about them such as those by Suzanne Gieser and by David Lindolff but I found these rather diappointing since these authors can't make much out of Pauli's extensive scientific references that mix freely with both the mystical and the banal in his dream accounts! I went through these last year while preparing a poster I delivered last year on the issue of Mathematics and Dreams. (I picked because there is precious little written on the subject so even a complete outsider might have something relevant to say!) I also read the whole of Grothendieck remarkable "Cle' des Songes" which is posted in the circle site you mention. Unfortunatelly his dreams (unlike those of Ramanujan aparently) have very little to do with math!
Funny you mention it, though, because I have also made some use of your own statements in "Matiere a Penser" which I found extremely insightful namely the one on page 112 (I have the old paperback edition from Points-Seuil) about how the whole process of approaching a problem has an angusih ridden verification stage that is "somewhat like a dream" (your words)! Maybe you would not mind me asking if you ever had dream experiences involving math that you remember? (Hadamard dismisses these in his famed book but not before he tells a delightful anectode about a case related by Leonard Dickson...) I'd rather not bore you with any details on why this interests me.
There was in Chicago last month what was possibly one of the most interesting conferences in noncommutative geometry that happened in recent years. Strangely enough, it left no trace on your blog. Obviously, obscure speculations about synchronicity by Wolfgang Pauli and Carl Gustav Jung are considered to have more relevance to the field than a lot or really interesting and new mathematics. Weird.
Thanks for your comment. As for the Chicago conference that you mentioned and your statement that " it left no trace on your blog" I draw you attention
to this piece http://noncommutativegeometry.blogspot.com/2007/05/update-on-vanderbilt-conference.html where the conference is mentioned. The link to the conference page also appeared under the events section before the conference and has now moved
to the past events section. Unfortunately there is no information on talks or abstracts publicly available online. So that is all that we could do. You refer to the conference as ``possibly one of the most interesting conferences in noncommutative geometry". Fine- and it seems you were there. Then why don't you drop a line or two for this blog to bring it to the attention of the community at large? and for that matter all are welcome to notify us and put comments in the blog about the activities that are happening around them and have some inside information.
That brings us to a bigger issue: what is the role of this blog? I am not sure what to say but I can say one thing and hint at what we are not: we are not science journalists and don't aspire to be one! Please note that no judgment is intended here
and I just think that that is a personal choice that reflects our interests best.That is all. To give more extensive coverage to NCG events worldwide needs the cooperation and help of all the people working in NCG and is a joint responsibility! Thanks again for your concern and comment.
I was about to leave a message along the lines of Masoud's response.
a) being a non-traveler myself, I'd welcome more info on new things happening in noncommutative geometry at Chicago (or any other place), or a link to papers or other online material.
b) the present blog has (at least to me) a clear purpose. Anyone disagreeing with it is invited to start a noncommutativegeometry.wordpress.com blog or any other blog to make their point.
c) i dont like anonymous comments too much...
Thanks for your comment, it is quite difficult to "maintain" the blog just Masoud and me. We really welcome comments like yours and would be happy to have you as a "guest" blogger. One basic concern I have is to try and bridge the gap between the various aspects of NCG. I really like the purely algebraic aspect (and did a bit of work with Michel Dubois-Violette on that). Both the purely algebraic noncommutative geometry as well as the more "operator theoretic" differential noncommutative geometry are mature enough now not to be frightened to interact more openly. When a theory is at its beginning I believe it is important to leave it a chance to grow by itself and "protect" it somehow, but obviously time is ripe now for a broader perspective and attitude. That's pretty much what is going on with the new Journal and the organized meetings such as the Newton Institute program of last fall or precisely the Chicago meeting. Since I was there only briefly it is difficult for me to write a full report but I'll do what I can (after doing that for the vanderbilt meeting) and will try to get a "volunteer" to give a better account than my partial one (because of the small number of talks I could attend, being quite tired after the many classes I had to give in Vanderbilt).
thank you (and also Matilde) for keeping us updated on events in the NCG-conference circuit.
thanks also for the 'guest-blog' offer. i'll email you about it soon.
i agree there is a need for more communication across the algebraic/differential divide in noncommutative geometry and perhaps a group blog can make a contribution to it.
for now i'll continue to follow things here with interest and will contribute when i can.
all the best :: lieven.
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