[Fis] Music in group-theoretic biology

John and Pedro,

Both in group theory as applied to biology and in music as concurrent,
recurring processes we see NEIGHBORHOOD AND CYCLICITY relations. The rhythm
is a (temporally) longitudinal process (just like the DNA has a sooner and
later, a beginning and an end). The accord (the musical tutti) is a
temporally transversal information, a cross-sectional composition, where
one cannot state that the flutes are before (sooner) than the violins or
the brass. These are all at the same time. Here, group relations are useful.

What we have to discuss is HOW MANY TEMPORAL SEQUENCES can combine into HOW
MANY GROUP STRUCTURES. Relative to how the history of this melody, it is a
surprise, a satisfaction or a suspenseful tension that this specific accord
has been chosen by the composer. Among how many accords can a composer
choose if he uses n instruments k ticks long?

Best regards to Scott Muller and please give him the hint that he should
count how many multidimensional partitions are possible on n objects (that
is: how many distinct group relations can be generated on a set of n
objects). Once he has this, he will no doubt compare this upper limit (of
information carrying capacity) to the number of distinct sequences one can
generate on a set of n objects. Then, the surprise will be perfect. He shall
tell you that he will have found the mechanism by which theoretical
genetics works. Then, we shall all rejoice!

If anyone is seriously interested in the fundamentals of information theory
and music, I may suggest some work that has been done in this field.

Karl

-----Urspr�ngliche Nachricht-----
Von: fis-bounces@listas.unizar.es [mailto:fis-bounces@listas.unizar.es]Im
Auftrag von John Collier (by way of "Pedro C. Mariju�n"
<marijuan@posta.unizar.es>)
Gesendet: Montag, 2. Juni 2003 13:53
An: fis-listas.unizar.es
Betreff: Re: [Fis] Group-theoretic biology

I realize that it is way off the music topic, but my student, Scott Muller
has been applying group theory to the foundations of information theory. He
has some nice arguments to the effect that though people like jaynes have
argued that the information mapping is arbitrary, if one actually considers
the physical transformation that one can perform on a structure, the result
is fully determined (and gives, incidentally, exactly the information
content I would calculate from my paper Causation is the Transfer of
Information). I tried to convince Scott to come to the Symmetry Festival in
Budapest, but I didn't get very far. He makes his income as a computer
(databse) programmer, and that is on hard times right now (my brother is
having the same problem). Anyway, Scott shows very clearly the central
connections between group theory and information theory, and has some
really original ideas concrning the physical interpretation of information.

As I said, these recent postings just prompted me to remark on this, and I
don't really have anything to add. If anyone wants to get in touch with
Scott, they can ask me, or lese go to the Complex Adaptive Systems research
Group site at the University of Newcastle in OZ. I don't have my address
book here, but a search on CASRG Newcastle, or Hooker Complexity will turn
it up. It is also addressed on my own web site here.

John

Professor John Collier
Philosophy, University of Natal
Durban 4041 South Africa
T: +27 (31) 260 3248 / 260 2292
F: +27 (31) 260 3031
email: collierj@nu.ac.za

>>> "Pedro C. Mariju�n" <marijuan@posta.unizar.es> 05/30/03 14:24 PM >>>
Dear FIS colleagues,

Thanks to Sergei and Michael for their recent exchanges on theoretic
biology. Let me add that there is now included among the fis papers a
contribution of mine on the informational phenomena of the cell ('From
inanimate molecules to living cells: the informational scaffolding of
life'). It is a chapter of a whole book the editor of which is Franco
Musumeci (in this list too): his 'Foreword' for that very interesting book
can also be visited in our web (let us thank Rey Abe for his accurate
maintenance of our site!!).
http://fis.iguw.tuwien.ac.at/resources/papers..html

I am reluctant to get into depth about this discussion right now, in spite
of its centrality... Mixing that group-theoretic biology with the
generative-structural and communicational fis categories, and the insights
we gained about molecular recognition and cellular 'abduction' and
'constraints' in fis 2002 will be a challenging experience (this Summer,
this Autumn?). Perhaps we will be lead to re-discuss some of Ted's and
Jerry's postings months ago about fis theoretical options: the elegant
tools proposed from group theory, so useful for rationalization of
'computational fields', could they do a similar job for the central
'informational fields' (in my opinion, the triad bio & neuro & socio)?
Indeed we will have to examine very carefully the phenomenology of the cell
(what I tried to do in my above paper).

And about music? Someone attempting to build a bridge in between the
different levels recently addressed here would do a great job. For my
taste, Michael and Andrei have gone for the 'syntactic analysis' while Juan
focuses on 'word structure' (and I was heading towards the 'emotional
utterance'--or the 'semiotics' of music?). Along this very text metaphor,
some reflection on the origins of the Western musical notation itself could
be illuminating... the accurate alphabetic 'picture of the voice' by the
Greeks, the Medieval 'picture of the song' achieved in the monasteries
(curious, Why in the monasteries?).

About some of Juan's questions, the auditory perception would be caught
into similar enigmatic processes as other sensory infos. For instance, the
Weber-Fechner logarithmic law, that (in Rodolfo Llin�s' opinion--2001)
underlies the octave tonal structure. The preference for '7' in quite many
of our sensorimotor categorizations could be linked to aspects of musical
representation too (the seven basic notes, but also seven colors, seven
vowels.... again see Llin�s, and the classical work of G. Miller). Some of
my paper interpretations on 'cellular and tissular measurement problems'
could also be pertinent in this regard, and also would be, I think, Karl's
funny 'partitional constancy' of 7 (it is the only number with that
property!). Again, we are lead to discuss the formal grounding that
underlies the biological strategies of 'info optimization': rather
confussing.

all the best

Pedro

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Received on Tue Jun 3 10:35:57 2003