[1]
ABSTRACT

In his comment 'Wholes and Their Aspects' Chris Lofting wants to 'show the source of mathematical descriptions and so their proximity to 'reality' based purely from 'in here' '. He deals with a topic of central importance for mental activity, the function of mental structures (which he calls 'templates'). However, these structures (including mathematics) arise within undivided mind-nature experience, and therefore they are both 'inside' and 'outside', rather than arising only from 'in here' as Lofting proposes. If experience, reality, and truth are understood as primarily undivided, the unification of experience, on which Lofting spends much effort, is a less difficult problem: early experiene includes 'meanings' which may then be encoded in various ways; problems may arise chiefly at the point of de-coding back into meanings. This differs from Lofting's description of 'templates' themselves being the source of meaning. 'Wholes' are the elements of mental structuring, and not mainly a product of teaching methods, as Lofting seems to suggest. They are at times, particularly in early stages of usage, employed in an inflexible fashion, if they are understood as parts of a mind-independent reality rather than as tools. But individual and cultural developments have often resulted in greater flexibility and openness of the structures, which then no longer prevent access to more original, less structured experience. 'Aspects' are potentially also such 'wholes'. - In an appendix, three historical examples of mental structuring are discussed with respect to some of these and related properties.


[2]
SUMMARY OF LOFTING'S ARGUMENT

In his commentary (TA1,C11) Chris Lofting wants to 'show the source of mathematical descriptions and so their proximity to 'reality' based purely from 'in here' '. He discusses brain functions in the task of seeing wholes and their aspects, the latter of which, he proposes, exist in 3 basic categories: parts, static, and dynamic relationships. He then goes into the relations of parts to wholes, suggesting among other things (C11<12>) that our culture teaches wholes, then static relations, then detailed parts, and only finally dynamic relations: 'we don't get into complex numbers until our teens'. He writes <9ff> that there is a 'basic template' which leads us into eight possible basic elements, and <15> that this is related to the derivation of the number systems. <16> '... we can in fact create anything using mathematical terms since they are directly related to whole/aspects mappings since that is where they come from'. <17> '... words are more 'cultural' in that in maths '1' is '1' whereas in spoken language there are many terms for '1'.'

[3]
From here he wants <19> to 'elicit 'meaning' ': 'there seems to be a sense of 'feel' that is describable and directly linked to the wholes/aspects template and it is from here that develops our sense of meaning.' Subsequently, Lofting emphasizes the role of dichotomization, and proposes four ways of mixing elements, which can be expanded into eight. Then <26f> he discusses the I Ching which he states expands the analysis further, including 'persona types'. And <29> 'My point is that this 'middleware' (the whole/aspects template <18> between neurology and psychology) is shared by all humans and it is what enables us to get around 'local' expressions and so understand each other'. <30> 'The presence of a whole/aspects template 'in here' enables the abstract distinction of 'out there' together with developing a 'feel' for these distinctions and so a sense of 'meaning' both at the abstract level and at the 'gut' level'. <34> 'In modern times, ... consensus has arisen about 'out there'... and so there is no need for believing in 'external' forces to describe the origins of mathematics ...'

[4]
(text b) 'we have been able to determine the very process in which we go about making choices based on classifications previously made. We introduce a template from which all symbol and metaphor seems to emerge ... of elements for processing information, and by reviewing ancient (I Ching) as well as modern ... categorization systems so is demonstrated the 'chemistry' of information and thus the source of meaning.'


[5]
DISCUSSION

In my reply to these points I will have to limit myself to a few topics.


(A) MIND-INDEPENDENT REALITY

A central point for discussion has to be Lofting's use of terms like 'in-here' and 'out-there' which suggests that he believes in mind-independent reality or MIR (I apologize for repeating myself here, it is a point which I have made several times in the past, but I think it is crucial). He claims (TA1 C11,<34>) that 'due to the whole/aspects template and the development of mathematics so a degree of global consensus has arisen about 'out there' ... and so there is no need for believing in 'external' forces to describe the origins of mathematics'. Templates (including mathematics) are inside, reality and truth are outside, he says in effect. Thereafter he has a problem in bringing the two together, on which task he spends much effort.

[6]
In my opinion (TA1[1-30]) the MIR position is not tenable, although it is very prevalent in discussions about mind and brain. MIR views can serve adequately for thinking about brain-neurophysiology, and about information processing, but not about subjective experience, which it automatically excludes. The resulting problems can, I suggest, be avoided with adoption of an experience-centered view, such as the one of responsive reality formation (RRF, cf. TA1,R1[5-8]), in which the fixation of ontological structures is seen to be a technical procedure involving temporary working structures, rather than the establishment of mind-independent facts.

[7]
In a later text, Lofting presents a somewhat different account. (TA6,C1, abstract:) 'The consideration of Quantum Mechanics as something 'independent' of humans sometimes leads to the failure to recognise that it is a 'mapping' system created by 'in here' to help describe specific processes 'out there' and it is the structure of the system that can help ...'. I have difficulties determining the meaning of this sentence. Perhaps it would be helpful if Lofting could provide clear statements about a few key concepts, for instance: does he or does he not believe that reality and truth are mind-independent ? Are in-here' and 'out-there' the same as 'subject' and 'object', or as 'I' and 'the world', and if not, how do they differ from those terms ? Perhaps he could provide operational definitions for his terms. Also, when, in such an epistemological context, he says 'is', he sometimes means 'we can create'; this point is fairly clear in his just quoted statement, but in other places it is more ambiguous, for instance when he writes (in text a) that 'we interpret the I Ching as a metaphor for the brain's way of dealing with wholes and their aspects'; what can that mean ?


[8]
(B) MEANING

Lofting's discussion of meaning faces problems which are closely related to those just discussed. Roughly speaking, he has the question upside down, I would suggest. Meaning comes before any 'templates', particularly of the type which he discusses. Consider a cat catching a mouse. The meaning of this is immediately evident to both of them, together with the gut feelings as well as the gestalt templates, which mediate what happens. However, if we communicate meanings with the aid of codified mental structures of various kinds, problems may arise in decoding, back into meanings. The codes (such as words, gestures, etc.) stand in for ('as-if they were') the meanings. Lofting emphasizes (C11<17>) that mathematical expressions are more universally understood; this is true, but it is because the Arabic etc., notation system was widely accepted by a specialized community or school of (commercial, scientific, etc.) knowledge, which became more and more international. One should also not forget that originally numbers stand in for 'counting' activity, which is easily communicable because it is simple and unequivocal, at least at the elementary stages.

[9]
'Local' codes or expressions <18> which have been developed to encode meanings may limit communication. Suppose you talk or gesture to someone of a different culture and he misunderstands you - he might conceivably even kill you, in case there are important differences between your and his understanding (meaning) of the situation, or of the message which you try to convey with the help of words or gestures (it appears something like that happened to Giovanni Verrazano when, after having discovered the Hudson River, he landed on a Caribbean island). Some meanings may actually lie outside the range of experience of one of the participants. To assume that the mental structures in themselves have meanings or truths, or that meaning results from symbol manipulation is, I would think, a misunderstanding, albeit a very common one, and even though this has in the past been scientifically (logically-mathematically) elaborated.


[10]
(C) 'TEMPLATES' AND 'MIDDLEWARE'

What and where are Lofting's 'templates' ? It seems to me that these mind-nature structures have, among others, the following properties:
(i) They originate ad-hoc, that is as responses to needs for structuring. Usually, individuals conceive of them first, but their main importance is often social. One prominent source of this need for structure is the under-determination of human thinking (as compared to animals which rely more on genetically built-in behavior patterns), in combination with increased needs for communication and cooperation, which first became prominent after the invention of agriculture.
(ii) They may to varying degree become secondarily reinforced by beliefs - which either remain mostly functional, or become more absolute. To the extent that the beliefs are absolute, they transcend experience and imply persistent metaphysics (that is, ontology, MIR). Absolute belief is not indispensable for the use of patterns, as illustrated for instance by the practices of counting, mathematics, the I Ching, use of proverbs, card playing, or of crystal gazing, although all sorts of structures ('templates'), including those just mentioned, can be made the center of cults and of more or less absolute beliefs.
(iii) The templates structure mind-nature experience before any subject-object split. Thus they are not only 'in-here', as Lofting suggests, but both in and out simultaneously. This point is not compatible with an MIR view of things.
(iv) Lofting's idea of 'middleware' may be helpful; it would correspond to an ability (including the needed brain hardware) such as the human pre-disposition to speech, to gestalt perception, to counting, etc. This phylogenetic development has resulted in an enormous enlargement of the mental and behavioral tool arsenal in humans (with the help of genetically mediated anatomical changes and corresponding increase in functional abilities, in particular learning ability), as compared with the one of chimpanzees, whose genetic endowment is in other respects quite similar to that of humans. The development has also resulted in the genetic under-determination of human thinking, which makes the (less or more deliberate) creation of stable mental structures necessary.
(v) In a recent communication (c) Lofting writes that: 'the potential price of discovering algorithms (for neuro-linguistic patterns and programming) is the 'death' of self-identity.' This loss of subjectivity happens, it seems to me, in all attempts which try to deal with subjective experience objectively (that is, via MIR). It also shows the problem of trying to understand 'patterns' as being 'inside': because the objective theorizing, in this case concerning patterns, can only be done (as-if it were) outside. This is the chief argument for abandoning MIR views.

In the past these 'templates' had many different names. Plato called them 'ideas' or 'forms' and, in contrast to Chris Lofting, saw them outside. In my opinion, exclusive inside as well as outside locations are both untenable. Structures are always in both simultaneously, that is they reside in primarily undivided mind-nature experience.


[11]
(D) WHOLES AND ASPECTS

Wholes (or entities) are the building blocks of structured thinking. If we discuss experience rather than brain function or mathematical procedures: structure (gestalt) formation from no structure is the elementary process, which produces the units we deal with, and in humans the units include words and numbers. Teaching (C11<12>) can play a role but is not the main reason for the precedence of wholes. 'Aspects' are not the results of mathematical procedures. They too are such structured elements, obtained by turning attention to a part (of a more encompassing structure) which then functions as a structure in itself. For instance, a flat tire may suddenly become an all-absorbing central object (or 'aspect', which means 'way of looking').

[12]
To assume that numerical or other templates, or knowledge of brain function, etc., are earlier than the original (unstructured) experience is in my opinion a fundamental error, because (please excuse my repetition) assuming that such procedures get to the foundations obstructs access to experience. The procedures are tools we can use for structuring, investigation, communication, and expansion of experience. Now, when one uses a new concept (or tool) there may be a tendency to overestimate its importance, and it may be believed to be, by itself, a part of nature (or even a god). Thus the use of numbers was at times turned into a religion of number-worship by the Pythagoreans. Chris Lofting' enthusiasm leads him to claim <16> that 'we can in fact create ANYTHING using mathematical terms'. This obviously refers to the great usefulness which mathematical tools have in the sciences; however, I would challenge him to create the experience of the smell of roses in this way (that is, the subjective experience, and NOT the structural patterns of the chemical compounds or the neuronal firing patterns which are involved in this).



[13]
APPENDIX:
AD-HOC ORIGIN OF TEMPLATES IN MIND-NATURE EXPERIENCE,
WITH SECONDARY FIXATION BY BELIEF (EXAMPLES)

In this appendix I try, for my own benefit, to evaluate some of the points raised by Lofting's proposal, with respect to three historical 'template systems', of which I have chosen two more or less randomly, the third one is the I Ching which Lofting cites. I reproduce this material here in the assumption that it may interest some readers, and would appreciate comments by those who know more about this than I do.


[14]
(A) EARLY NUMBER SYSTEMS

The development of an early number system is described in a paper by Friberg (1984-97). He points out (p.35) that there has been 'a continuity of representation of numbers and measures from the time of the rise of the city-states in southwest Asia backwards in time to the early Neolithic, as long as 10,000 years ago.' '... a variety of clay 'tokens' served in the region continually from the ninth millennium BC to the end of the fourth millennium to designate numbers, measures and perhaps categories of objects. ... late in the fourth millennium ... selected symbols (were enclosed) in protective envelopes of clay, many of them bearing surface impressions resembling the enclosed tokens. The envelopes in turn seem to have inspired the invention of 'impressed tablets' ' (in cuneiform writing, with number notations but lacking abstract or pictographic word signs). Depending on what was counted, a decimal or sexagesimal number system was used, a practice which has persisted to some extent from Mesopotamian usage until now (cf. sixty minutes per hour).

[15]
Thus the systems were developed ad hoc, that is to say for purposes: such as of dealing with daily problems, in the developing agricultural economies; for instance: how much seed is needed for a field of a certain size with a certain number of furrows and with a standard spacing between seeds; or: how much food is needed daily for a group of so and so many field workers ? The clay tablets are in part mathematical texts, which were apparently copied by younger scribes who in this way accumulated a little library, 'a Sumerian Farmer's Almanach' (p.32) of their own. In Friberg's paper there is no mention of the role of worldly or ecclesiastic authorities, although I would guess they probably played a role.


[16]
(B) THE I CHING

The latter type of information is somewhat clearer in the Chinese system called the I Ching which Chris Lofting mentions on a number of occasions. Since I am not familiar with the I Ching and its related literature, I have consulted a book by R Siu, which presents the historical background as well as a guide to the interpretations of its hexagrams (and I would appreciate comments on whether my resulting understanding of this system is adequate). The following are some quotations from this book, with page numbers in brackets.

[17]
(p.2) ' From (the) biphasic cycle of peasant life arose the fundamental conception of the universe in the Chinese mind. Affairs were grouped according to their tendencies into two general categories. These correspond to the season dominated by female work, namely the weaving during the closed winter months in the huts, and to the season dominated by male work, namely the hard agricultural labor in the fields. Everything was divided into the two respective modalities of the yin and the yang. Yin originally pertained to shade and yang to light. In later development, the terms became expanded to encompass the two cosmic principles. Yin stood for cold, softness, contraction, wetness, femininity, and the like. Yang stood for heat, hardness, expansion, dryness, masculinity, and the like. The opposition, alternation, and interaction of these two forces give rise to all phenomena in the universe ... nothing remains static. ... As Lao-tzu summed it up, 'reversal is the nature of the Tao' ' (the Tao is the 'way of good living').

[18]
(p.2f) ' The simple interaction of the two influences is schematically represented by pairs of divided and/or undivided lines, representing the yin and the yang, respectively.' Using two lines, reading from bottom to top, this results in four permutations: yang-yang, yang-yin, yin-yang, and yin-yin. ' The next-higher yin-yang series consists of the eight trigrams of three lines each. According to legend, these were devised by Emperor Fu Hsi in 2852 B.C. A name was given to each trigram ... Doubling of these three lines into six yields sixty-four ... hexagrams of the I Ching ... The array is supposed to be inclusive of all human situations in which a person might find himself. The yin-yang series can be expanded geometrically to provide an infinite progression, namely 128, 256, 512, 1024, ad infinitum. The originators of the I Ching judiciously stopped at the practical limit of sixty-four. This number constitutes a classification sufficiently fine so as to provide useful types of situations, against which specific cases can be matched. Yet the subdivisions are not so numerous as to be too cumbersome for a single scheme ...'

[19]
(p.3f) 'In 1143 B.C., King Wen systematically organized the sixty-four hexagrams into the cohesive scheme as we know it today ... to each he gave a name and a thematic text, called the T'uan. The T'uan presents a summary of the hexagram's chief attributes ... The King's son, the Duke of Chou, added the Yao, which is a set of succinct statements concerning the respective constituent lines ... (which) represent the evolving behavioral events within the T'uan ... At times, a leitmotiv is carried throughout the six passages of the Yao. But frequently the relevancy of the meaning of one line to that of the next, or even of the T'uan itself, is not quite clear. ... Many other additions were made over the next 1500 years ...' It was used for prophecies ... ' two popular techniques ... were sorting 49 yarrow stalks and the tossing of three coins. He then looked up the oracular message in the corresponding section of the text. ... No prophet, priest, or oracle is involved in the exercise, ... the person approached the I Ching ... for the sense of the universal movement itself.'

[20]
However (p.5f) ' The divinational aspects of the I Ching do not concern us in this book ... (but) the text (also) became a valuable synopsis for meditations on human relationships. It formed the basis of statecraft ... (and) provided the precepts for success and tranquillity ... manual on ethics ... source of proverbs ... Its central emphasis is on the intuitive grasping of the totality. Specific facts and figures are not constants to be searched out for their own sakes. The whole is ever in continuous flux. No single constituent is without impact upon the others and vice versa. ... Depending upon their respective positions and contexts, the individual lines vary greatly in their contributions to the total message of the hexagram. ... (p.8) If one has an intuitive appreciation of universal movements during their instants of change, the art of good living is within one's reach. ... (p.9) Being one with nature, he apprehends the all - totally, instantaneously, ineffably. This is the ultimate lesson of the I Ching.'

[21]
As an example, the characteristics of the (according to King Wen and the Duke of Chou) fifty-first hexagram, called Chen ('Shock'), which Chris Lofting depicts in his paper (a) on his own Book of Changes are as follows. It reads, from bottom to top: yang yin yin yang yin yin (this I would think may be written in binary code as 100100, or 011011, depending on selection of symbols). (p.329:) The overall judgment of this hexagram (T'uan, written by the king): 'the superior man understands the nature of shocks and so remains sufficiently self- confident and self- possessed to take appropriate action. He concentrates on the service in which he is engaged.' There are also 5 constitutive events (Yaos, written by the Duke) which describe the principal nuances, but which would take too much space to reproduce here.

[22]
The contents of the I Ching have developed over many centuries, and form a core of Chinese religion and philosophy, even though the advent of Buddhism since about 500 B.C. has weakened its influence. I will briefly discuss here only one aspect, the hexagrams' role in mental structuring. From Siu's description it seems to me that this set of structures developed in response to individual needs for mental structure, as well as to communal needs for acceptable, communicable, and standardized structures. It responded to the uncertainties of human thinking and life in general, by providing a set of structures, thus fulfilling a role similar to that offered by the sacred texts of other traditions. It was developed according to practical requirements: the earlier forms with two, four, and eight alternatives were regarded as too few (presumably they were too inflexible), sixty- four as adequate, more than that as impractical. In addition, the 64 items became very flexible due to the (secondary) interpretation of their internal structure as well as the interpretations ascribed by authority of the king, and in addition the need for their interaction with nature was emphasized.

[23]
Thus the I Ching became the Book of Change (rather than, say, a source of invariable or holy structure which must not be tampered with because it has to remain 'whole' as it is - but of course even 'holy' texts are subject to interpretation). Siu emphasizes (p.4) that each person deals directly with the array of hexagrams, without intervention of a religious or other authority, although evidently the authorities of emperors and kings played a role, and the royal interpretations were widely accepted. Thus we can see here the development of a communal structure for thinking about problems (divination, interpersonal relations, practical planning, as well as religious needs). This structure has an ad-hoc aspect (it is designed because it is needed for thinking and communication), a communal aspect (with the help of political and religious powers), a random aspect (casting yarrow stalks, or dice, etc., and this not only for prophecy but also for policy and for daily decisions), and an additional non-mathematical interpretation aspect both within the hexagrams and according to individual situations.

[24]
But probably the most central aspect is the role of intuition. In my understanding, this opens a way to a return to the origin, which had been unstructured; now the mind is structured, individually and collectively, providing some stability, but in such a flexible way that intuition is not necessarily inhibited by the created structures. Thus there is always a considerable margin for interpretation, which in effect renders the method and its results un-falsifiable in the scientific (Popper's) sense, and there is room for idiosyncrasies and superstition as well. (A corresponding feature in revealed religion would be the possibility of mysticism which allows intuition, by going beyond scripture.)

[25]
Despite its authoritative effect when dealing with assessment of attitudes and with decision making, the use of the hexagrams does not appear to involve claims of ontological (MIR) truths, but rather deals with practical aspects like attitudes and decisions. This point is relevant because at times Lofting makes statements which appear to postulate ontological validity, such as when talking about 'maps of reality', as opposed to illusions'. (Please let me know if this opinion is erroneous; at any rate, an operational definition of Lofting's terms 'reality' and 'illusion' would be helpful).


[26]
(C) FUNCTIONS OF UNIVERSAL RELIGIONS

The practical effects of a universal religion involve initially an acceptance of a different way of life, of a superior authority and of rites (Moore, on Fletcher, 1998). In the conversion of Europe to Christianity (apart from the Near East and Rome, starting AD 371 in France and ending 1386 in Lithuania) an 'upgrading' of the territories was involved, in an economic and cultural sense. There was, for each kingdom or territory, 'increasing wealth, stability, and standing which it gained from the know-how and contacts of the missionaries' ... 'Christian societies, not so much because they were Christian as because they were developed, were highly destabilizing neighbours'. And the same happened elsewhere, with the advent of Islam and Buddhism, for instance.

[27]
The interesting point here is, in my opinion, again the starting feature of new mental structures which have a communal and practical, technical and economic effect. Furthermore, because of their claim to universal validity, they had also implications of wide-ranging political power. In this respect, the universal religions had a function similar to that of the United Nations of today. The new religions also provided an anchor structure for the new way of life. This anchor was more often a positive doctrine with a paradoxical center, rather than negative in the zero-reference sense. We may ask here what the relation is between the individual internal conversion and this functional cultural and organizational role of the new religion. Which comes first, and which is the more central ?

[28]
Moore gives the following, historically early, example of the conversion efforts: '...around 240 ... Gregory the Wonderworker' (Gregorios Thaumaturgos) ' became Bishop of Neocaesarea in Pontus, deep in Anatolia, and set about converting his parishioners ... guided by visions, building a cathedral which stood firm when an earthquake flattened almost everything else, drying up a lake which armed gangs led by quarreling brothers were about to do battle over, and in short using every device in the natural and supernatural repertoire to display the awesome superiority of his God. ... he was one of the first of a series of Roman landowners and civic leaders, who, for three centuries and more, battled to impose Christianity on their tenants and dependants, and on the inhabitants of the largely untamed countryside around them.'

[29]
The belief in this God thus acted as a positive anchor (cf.TA1[30,45-49]) for the acceptance and stabilization of the organizational-cultural envelope, and as motivation for the missionary activity. This means that in the process of this conversion, historically the ad-hoc functional aspect came first but that thereafter the religious conviction became the central point. Indeed the latter came to constitute acceptance of a positive ontological (metaphysical and exclusive) anchor for all of the subject's and the community's thinking and action. Because the new God claimed exclusive validity, he did not tolerate competition, the old gods were to be declared false, and non-believers should be forced to agree, as even Augustinus agreed, somewhat reluctantly.

[30]
However, this interpretation leaves open the question why Christianity was initially attractive, when confronted with the superior organization of the Roman state which was still pagan. The answer may lie (I speculate) in its promise of universal and permanent validity, both in terms of a stable and comprehensive belief (for which there was a need in view of the instability, and thus unreliability, of the Roman pantheon, with emperors declaring themselves to be gods, as well as new gods being imported from abroad) including all aspects of life, and in principle open to everyone on an egalitarian footing, not being limited to one ethnic group, state, etc.

[31]
The need for central structures is present in all of us. The needs which have led to the positive religious and philosophical anchor structures are essentially the same as the ontological needs of scientists who want to pursue a search for a 'truth' which is thought (a) to exist mind-independently and (b) to act as a positive anchor. If we want to understand mind-nature experience analytically - rather than safely (i.e., guarded by taboos, such as implied in many religious creeds, or in exclusive objectivism, or in exclusive empiricism), function is the point of start and remains the point of reference (i.e., as a negative, non-structured, anchor). The difference is that in religion one can to some extent afford to 'credere quia absurdum' (and in the case of positive anchors one must actually do so); but this does not really work in science - even though it is obviously done all the time, as implied in a belief in MIR. Scientists who accept positive anchors find themselves ipso facto in a blind alley in case they try to deal with experience per se.

-----------------------------------------------------------------

REFERENCES

Friberg J (1997), Numbers and Measures in the Earliest Written Records. Scientific American, The Origins of Technology, pp. 28-35 (originally published in Scientific American, February 1984).

Lofting CJ (1997-8)
Some texts by Lofting which are not available from this Forum can be obtained from his web site:
http://www.ozemail.com.au/~ddiamond
(a) Welcome to Chris Lofting's Book of Changes (IC+)
(b) Symbols and Metaphors; Creating Reality
The following was posted in 'Dialogues':
(c) On Neuro-linguistic Programming, 25 Febr. 1998, to the 'Philosophical Psychology Group'.

Moore RI (1998), A new way of doing things. How pagan Europe was converted - and upgraded. (Discussion of a book by R Fletcher, 'The Conversion of Europe, from paganism to Christianity, 371-1386 AD', Harper Collins), Times Literary Supplement, 8 Febr.1998, p.24.

Siu RGH (1968), The Man of Many Qualities, A Legacy of the I Ching. Cambridge, Mass., MIT Press.

[Author: Herbert F J Muller
e-mail <mdmu@musica.mcgill.ca>]