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gottago


Total Posts: 21
Joined: Feb 2008
 
Posted: 2008-02-23 14:22
Hi,

if your interested in maths and music I've got good news for you. There is now a more or less complete mathematical music theory (ToM).

The theory uses topology of logic (Topoi), category theory and algebraic geometry. It will take perhaps 20 years until this work will become wider known - only 24 citations of the book as of now. The theory has some very astonishing features, because it provides an architecture of concepts, where points in space (sets), become addressed points (so called forms and denotators). The theory is availabe as software at http://www.rubato.org .

polysena


Total Posts: 1038
Joined: Nov 2007
 
Posted: 2008-02-26 22:15

Dear Gottago, can you say more? The link you give is an appetizer but difficult to judge all the book..Have you personnally read this book? What do you think about it?  Are you musician? Compositor?

 I am wondering.. sounds it could be a good present for one of my coauthors. would just excite his curiosity ...he isn't musician.. he can watch stupid films on tv especially with pretty/giggly girls, but  when it comes to his work field..he is a little of an intellectual snob... would you say the book is " deep"? or challenging? Or thought provoking?

 


Люди - леди, джентльмены - Да, конечно, разумеется, Мир далёк от совершенства, А местами просто плох.

Nonius
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Nonius Unbound
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Posted: 2008-02-26 22:34

That book sort of reminds of a book my advisor wrote that he affectionally called "The Wild Book" and which proposed the application of Automata/finite state machines/languages to Psychoanalysis, Sociology, and Biology.

anyway, it sounds sort of interesting, but I'm sceptical.  I'll take a look this weekend and may have some useful comments.


Chiral is Tyler Durden

Martingale
NP House Mouse

Total Posts: 2629
Joined: Jun 2004
 
Posted: 2008-02-26 22:46
one of my college buddy ( who's a geometican) spent several months research work with some guy from psychology dept, don't know what exactly they worked on, but it is felt kind of fun though.. also one of my other budy who's a pure number theory guy told me DE shaw asked him to work for them... man...math dudes are powerful, except me Cry

polysena


Total Posts: 1038
Joined: Nov 2007
 
Posted: 2008-02-27 09:42

anyway, it sounds sort of interesting, but I'm sceptical.  I'll take a look this weekend and may have some useful comments.

 

I am also slightly hesitant, after browsing what I can see.. but indeed could be entertaining book, so looking forward to your comments if any.. no chance for me to see this book in a library from where I operate..

 


Люди - леди, джентльмены - Да, конечно, разумеется, Мир далёк от совершенства, А местами просто плох.

doctorwes


Total Posts: 576
Joined: May 2005
 
Posted: 2008-02-27 10:39
I own this book and have not been able to make head nor tail of it. Peter Johnstone (who's one of the early topos theory gurus and also a music buff) says he doesn't understand the details either. The idea's plausible, though. The Zentralblatt review gives the gist of it: basically musical objects are subject to affine transformations which can be modeled in categories of modules. It turns out that concepts such as pitch inversion, modulation, counterpoint and even aspects of performance can all be understood in this framework.



gottago


Total Posts: 21
Joined: Feb 2008
 
Posted: 2008-02-27 11:15
> Have you personally read this book?

I'll give you an example of what things you will find there. Chapter 19 is a good example. It's starts off with a quote by Grothendieck, who commented on the precursory book: "That is, so it seems, the mathematics of the new age". (my translation)



It is quite surreal to contemplate the fact that Mr. Mazolla lectured in front of 4-5 people explaining what complex numbers are :D I went on to attend a PhD course until GM went off to Minnesota's school of music. He had great problems with the reactionary environment in Switzerland. In fact he is often despised by musicologists.


> can you say more?

ToM is in fact the most complete theory of music ever devised. It is the first time music becomes accessible to a formal language. It breaks up the traditional idea of mathematics (until 1950-60), i.e. the idea of Russell/Whitehead to reduce mathematics to logic/set theory.

I should rather say the idea is due to MacLane, Eilenberg Grothendieck and Lawvere, but ToM does deliver a wealth of ideas through the application of category theory/topoi to music.

Applications always bring new ideas. We are used to this because of applications of mathematics to physics, linguistics and biology, not so much economics surprisingly. So this work opens up a whole new door in my opinion, because for the first time since Pythagoras music becomes an inspiration for mathematics. Music is not educible in standard mathematics, because the consituents of music are recursive concepts, not points (element of a set). Remember that the Pythagoreans were a mathematical religious group who, so the legend goes, threw Hippasus into the sea for discovering the irrational numbers. Their world view depended on numbers as harmony, which in turn have influenced Plato. So when we allude to Platonic ideas, we really are referencing the Pythagorean concept of numbers as objects (atoms if you will, called cosmoi). In fact this concept of cosmoi is very similiar to function spaces.

> Have you personally read this book?

Reading the book is quite impossible. The German book GdT is a better start. Perhaps I should translate parts of it as an introduction.

> What do you think about it? would you say the book is " deep"? or challenging? Or thought provoking?

I am very enthusiastic about the theory. It is certainly very hard or rather impossible to follow all of it. I would say it's as deep as a black hole ;)

> Are you musician? Compositor?

A mediocre classical pianist. I plan to devote a good portion of my time to the theory and it's applications. As of now the theory is mostly concerned with music up to 1950 (traditional notes), but is easily extendible to sound. That is what I am especially interested in, because it relates to music cognition and language.

Johnny
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Total Posts: 4333
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Posted: 2008-02-27 11:47
> Have you personally read this book?

Reading the book is quite impossible.

I struggle to think of many things more pretentious than recommending a book which you don't think it is possible to read.


From the subprime to the ridiculous

polysena


Total Posts: 1038
Joined: Nov 2007
 
Posted: 2008-02-27 11:49

DrWes thank you und  Gottago herzlichen Dank,

 for your very interesting comments..

After reading your posts the book sounds really to be quite a non
trivial piece..

which also means that one might be unable to make sense of it (sadly
obviously)...  Grothendieck writes in Recoltes and Semailles that he is irritated when he sees his students don't see what he sees or follow him.. this to the point that it is deemed  unreadable by both DrWes and Gottago...

And you say Gottago that the great Grothendieck himself commented on
the preliminary version of the book, this is truely extraordinary...

Do you suggest the translation from German to English is not of your
taste? or is it because the book has become too big, to complex (after its revamping in English ?) (the german link says Englische, erweitere und aktualisierte Neufassung erscheint)

Re: point on conformism... Conformism is unfortunately no less prevalent in the scientific
circles than elsewhere..


Люди - леди, джентльмены - Да, конечно, разумеется, Мир далёк от совершенства, А местами просто плох.

gottago


Total Posts: 21
Joined: Feb 2008
 
Posted: 2008-02-27 12:16
> do you think the translation from German to English is not of your taste?

The second book is not really a translation. It encompasses all the developments since 1990.

> I struggle to think of many things more pretentious than recommending a book which you don't think it is possible to read.

I didn't recommend the book as you have failed to notice. There is a nice word in German for this kind of statement: Vor-Urteil (pre-judice). I suppose that knowledge for you is mostly a matter of status. Well, I profoundly disagree. This attitude is a good reason to dislike the whole idea of science as a profession. What do you think science is for? Not for the public good?

FDAXHunter
Founding Member

Total Posts: 8333
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Posted: 2008-02-27 12:17
Dude, gottago, are you paranoid?

The Figs Protocol.

polysena


Total Posts: 1038
Joined: Nov 2007
 
Posted: 2008-02-27 12:36

Johnny to be fair, I do not feel  Gottago recommended reading the book, he brought it to attention only.

It is  really my fault for asking that question about readability... .. for as I said I might be thinking of perhaps buying it as a gift for my people ...both are non German/non English native speakers. Both do not read German, and my Russian colleague's command of English is not too exceptional.. this is why I am trying from afar.. to assess whether the content interest would exceed the other difficulties (huge thick book, music oriented but with a lot of the stuff (topos cat..) that they both are very fond of....English and wordy.. etc..). Dr Wes's assessment was quite useful and Gottago was detailed in his reply, I both thank them.

 

 


Люди - леди, джентльмены - Да, конечно, разумеется, Мир далёк от совершенства, А местами просто плох.

gottago


Total Posts: 21
Joined: Feb 2008
 
Posted: 2008-02-27 13:00
I'll phrase it differently. Reading the whole book is quite impossible. One can understand and appreciate parts of it if one heard a lecture on it and has a basic training in mathematics. It is not meant to be read in the literal sense of the word. I spoke with different PhD students of the author, who can't read it either. Therefore I conclude I am not paranoid and all that stupid either. Because I am one of there very few students and plan to spend years studying the theory, it is not very fair to say I am pretentious. I'm glad that a few people here are interested and somebody even owns the book. PM me if you want to exchange ideas, are interested, etc.

nuno


Total Posts: 277
Joined: Jul 2006
 
Posted: 2008-02-27 15:08
Hi,

if your interested in nuclear and phynancs I has a good news for you. There is now a more or less complete Taxonomy of Trolls (ToT).

The taxonomy uses FrontPage 4.0 (Microsoft), blockquotes, and several colorful expletives. It will take perhaps 20 seconds to scan this taxonomy -- I can only speculate (or ask you to speculate for me) on how many pages link to this page as of now. The taxonomy has some astonishing features, particularly section 3.1. I attempted to read it but found it quite impossible, although there might be those who would say that 185 characters is nothing, but I would say that 185 characters is impossible.

Off-topic (but then, all of a troll's posts are off-topic): has anyone read the Vayner/Adidas theorem (2004) relating quite impossible and nothing? If so please summarize and translate it for me. My native language is troll.

Johnny
Founding Member

Total Posts: 4333
Joined: May 2004
 
Posted: 2008-02-27 15:15
ROFL Big Smile

From the subprime to the ridiculous

gottago


Total Posts: 21
Joined: Feb 2008
 
Posted: 2008-02-27 15:19
I will use the method suggested under 5.1:

"Ignore them and they will go away.


This is the traditional usenet method of dealing with Trolls, and is regularly suggested.

It is similar to the method use to train dogs, and very young children, ignore bad behaviour and reward good behaviour."

Edit: just because you don't understand what somebody else is saying doesn't mean she or he is stupid. And: 5/8 people are interested so please stop spaming.

gottago


Total Posts: 21
Joined: Feb 2008
 
Posted: 2008-02-29 18:28
@Nonius, doctorwes, polysena: thanks for you interest. I have created a preliminary forum where I hope to bundle people with interest in the theory, from all kinds of different perspectives (music or mathematics or both). I can also ask Mr. Mazolla or students of his to address general open questions.

silverside


Total Posts: 1399
Joined: Jun 2004
 
Posted: 2008-02-29 18:33

there is an Irish saying which i think is appropriate

f**k the begrudgers

 


kr
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Posted: 2008-03-01 09:37
if I might ask a a couple of naive questions:

1 what is the objective of this theory?
2 what use is that to a musician?

The example I have in my head is a guy like Krenek, whose examples of 'serial music' (even pre-1950) demonstrate that it is easy enough to create music which previously didn't fit the definition of music, and still, some of it is pretty good and some of it less so. Additionally, what separates the first category from the second doesn't really have much to do with the 'serial' composition strategy, it's more the type of intriguing fuzzy parallels that crop up - possibly random chance, possibly not.

Beyond that I'd argue that similar criticism is probably due to topos theory more generally.... i.e. nice framework but did it solve any interesting problems? At least sheaves can claim this, with a lot of mods strapped on, but I never saw anybody studying topoi because they could get a better bound on an character sum over an arithmetic variety.

Anyhow I will be sure to crack this one open for the perusal of a few paragraphs before cranking up the VAN HALEN. Does that make me a begrudger?

my bank got pwnd

gottago


Total Posts: 21
Joined: Feb 2008
 
Posted: 2008-03-01 12:17
> 1 what is the objective of this theory?

Generally musicologists try to explain music with its historic appearances. This theory however is more or less independent, i.e. it explains music in its generality. Without the use of this or a similar mathematical theory it is in my view impossible to have a general theory. If you pick a music-theory book you will be astonished with what kind of imprecisions music-theorists are willing to live with.

Perhaps the underlying question is, why should one be interested in understanding music at all?
Now, mathematics has always drawn a lot from physics. Everybody knows that, to an extent that it is overlooked most of the time. Consider on the other and for example the impact of the mathematical studies of language by N. Chomsky. D. Knuth, one of the most important computer scientists of course, cites Chomsky as his main influence. Why should a mathematician be not interested in music as much as in language or physics? Why should he not be interested iff his object of study shows considerable complexity that is.

> 2 what use is that to a musician?

If a musician would want to apply some of the maths he would have to choose a small subset to get somewhere. Perhaps with a very good piece of software (rubato is a beginning) he might be able to access the formal systems without him understanding the underlying theory.

> nice framework but did it solve any interesting problems?

As far as I can judge topos of music demonstrates that. The reason is that music is about concepts (melody, harmony, rhythm) which can not be defined as sets. A note for instance consists of a pitch, a voice, an onset, a duration and a loudness. A transformation in pitch is modulation, in voice a variation, in onset/duration a repetition, in loudness a dynamic. An interpretation could be seen as a transformation of the concept note = limit(pitch,voice,onset,duration,loudness), but then a melody is a powerset of notes, a theme a powerset of melodies and so on. So there is a need for 'bottomless recursion'.

polysena


Total Posts: 1038
Joined: Nov 2007
 
Posted: 2008-03-01 13:22
more and more interesting...but the book indeed seems hard from afar.....

Люди - леди, джентльмены - Да, конечно, разумеется, Мир далёк от совершенства, А местами просто плох. The Dot and the Line: A Romance in Lower Mathematics http://www.youtube.com/watch?v=OmSbdvzbOzY

kr
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Posted: 2008-03-01 14:42
"what kind of imprecisions music-theorists are willing to live with"...

I don't think music is all that different from finance in that the bandwidth available to express an idea is pretty narrow, so the observer is faced with indeterminacy. Maybe that's not the Webster definition of 'more art than science' but I'd argue that the reaction most musicians have to 'imprecisions of music theory' the opposite of astonishment - i.e. the imprecision is an end in itself.

"access the formal systems without understanding the underlying theory"... seems like that's already happening, without a book written in a language that virtually no musician understands.

"a note consists of..." ok but music is a whole lot more than a collection of notes. For one thing, music alludes to other music - for instance, borrowing riffs from others occurred long before the jazz age. I guess my point is I don't see how building up music from its root concepts the way an object-oriented engineer would, will ever get to what a professional musician would ever care about.

for disclosure, before I did finance, I was a mathematician, and before I was a mathematician, I was a pianist. But then again, from what I read, even Robin Hartshorne plays the shakihuchi, so wtf do I know?

my bank got pwnd

AVt


Total Posts: 833
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Posted: 2008-03-01 15:33
shakuhachi ?

gottago


Total Posts: 21
Joined: Feb 2008
 
Posted: 2008-03-01 16:25
> the imprecision is an end in itself.

Or perhaps rather degrees of freedom. A theory should do better than that, or it is really not useful at all. Mazolla in recent years worked a lot on using algebraic topology for free jazz gestures. I believe that description in terms of theory is a natural extension of description in terms of performance.

> will ever get to what a professional musician would ever care about

I agree. But then the most professional (or maybe academic/earnest) musicians are those the public doesn't care about that much, such as modern music, jazz, classical music, etc. The biggest trend from 1950 on was more and more academic music, which alludes a lot to formal systems (such as twelve-tone music, serialism or academic electronic music). Although I do some potential for commercial applications, the main beneficiaries are maths orientated musicologists and pure mathematicians. A proof of concept was a recomposition of Beethoven's Hammerklaviersonata.

kr
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Posted: 2008-03-01 19:08
shakuhachi indeed - I stand corrected

anyhow the car lost its driver during the hairpin but if it continued to another ten laps on the racecourse since that time, I was unaware as I've changed channels and am now watching the swimsuits. now if robots enjoy watching these driverless cars then who am I to complain that they are entertained? i'll get hammered while reposing over a cold one.

what I don't know is if there is a financial news show for the robots to watch after the driverless-indy has finished. optimal portfolio theory for negative-volatility assets in the imaginary plane, anyone?

my bank got pwnd
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