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4 March 2024 | Draft

Eliciting a Pattern that Connects with AI?

Experimental exchange with ChatGPT in quest of memorable integrative configuration

-- / --

Eliciting integrative insight via ChatGPT
Pattern connectivity and memorability
Unexpected AI aberration -- modelling irrational democratic discourse?
Contrasting preferences for N-fold organization in disconnected patterns
Aesthetic connectivity of patterns in music
Visualizing exponents of factors characterizing larger sets
Monochord ratios, tone frequencies and psychosocial implications
Standard pitch imposition and its analogues: 440Hz vs 432Hz
Requisite strategic attunement when "out of tune" with the times?
Embodying patterns of dance and strategic drama?
Strategic synaesthesia through multisensory pattern recognition


This is written following the conclusion of the annual Munich Security Conference and the publication of its introductory report Munich Security Report 2024. This recognized that: At the moment, there is a real risk that more and more countries end up in a lose-lose situation, which is no longer about who gains more, but only about who loses less (Lyse Doucet, Munich security talks marked by global 'lose-lose' anxiety, The Guardian, 19 February 2024).

It is far from clear in what manner the prestigious event was indicative of deep strategic thinking. With respect to new ideas, the focus would appear to have been on: Stop Putin! Support Netanyahu! Arm Ukraine! Arm Israel! Protect Taiwan! Bomb Houthis! Constrain AI!

The tragedy of Gaza has seemingly been accompanied by authoritative cease fire appeals -- knowing they will be ignored. This echoes the pattern caricatured by Greta Thunberg with respect to recent climate change summits: ‘Blah, blah, blah’: Greta Thunberg lambasts leaders over climate crisis (The Guardian, 28 September 2021; Greta was right about COP blah blah blah, The Malaysian Reserve, 7 December 2023).

From a historical perspective, the "lose-lose" conclusion of Munich 2024 is reminiscent of the poetic assessment of W. B. Yeats a century ago (Dorian Lynskey, 'Things fall apart': the apocalyptic appeal of WB Yeats's The Second Coming, The Guardian, 30 May 2020):

Turning and turning in the widening gyre
The falcon cannot hear the falconer;
Things fall apart; the centre cannot hold;
Mere anarchy is loosed upon the world.

The blood-dimmed tide is loosed, and everywhere
The ceremony of innocence is drowned;
The best lack all conviction, while the worst
Are full of passionate intensity...

Who would now be characterized as "the best", and who "the worst" -- and by whom?

It is in this context that the question of how unity, integration and coherence are to be understood merits ever increasing consideration, as with the assumptions by which they are conventionally framed. Achieving unanimity is recognized as a major challenge for the EU, for example. A contrast can be usefully made with the popular movie theme of The Highlander (1986), as exemplified by the curious inability of the USA and Israel to count beyond one in their aspirations for hegemony (There Can be Only One,

In this period artificial intelligence, exemplified by ChatGPT, can be variously appreciated as a skilled aggregator of accessible information and its configuration into meaningful patterns -- a facility that might have informed the considerations of the Munich debates. With respect to any new form of "unity", it is therefore appropriate to explore the use of such a facility to elicit a "pattern that connects". As a focus of continuing comment, the term famously originated from  Gregory Bateson in clarifying the nature of a meta-pattern in the following context:

The pattern which connects is a meta-pattern. It is a pattern of patterns. It is that meta-pattern which defines the vast generalization that, indeed, it is patterns which connect. (Mind and Nature: a necessary unity, 1979)

And it is from this perspective that Bateson warned: Break the pattern which connects the items of learning and you necessarily destroy all quality (1979, pp. 8-11). The meme continues to evoke commentary (Merlyn Driver, The Pattern that Connects: Gregory Bateson and the Ecology of Mind, Journal of Wild Culture, 27 October 2019; Jeffrey W. Bloom, Patterns That Connect: Rethinking Our Approach to Learning and Thinking, Annual Meeting of the American Educational Research Association, April 1999; Paul Andersen and David Salomon, The Pattern That Connects, Acadia 2010; Søren Brier, Bateson and Peirce on the Pattern that Connects and the Sacred, Biosemiotics, 2008; Helene Finidori, Patterns that Connect, Proceedings of the 60th Annual Meeting of the International Society for the Systems Sciences, 1, 2016, 1).

With the strategic emphasis given to the political slogan -- It's the economy stupid (and its adaptations) -- does the focus on patterns invite yet another adaptation: It's the pattern stupid ? Paradoxically any implication of "stupidity", through failure of pattern recognition, is itself necessarily problematic in a cancel culture.

Previous reflections on its implications are presented separately: Riddle for global civilization of the pattern that connects (2021); Psychosocial "global implication" of a "pattern that connects"? (2020); Cognitive dynamics sustaining the meta-pattern that connects (2013). These variously call into question assumptions regarding the singularity of "the" pattern, the meaning to be associated with "pattern", as with any sense of "connectivity".

There is indeed a fundamental challenge to the connectivity of any such pattern, namely the question of its widespread memorability and comprehensibility. Bateson offers a valuable aesthetic insight in that regard in explaining why "we are our own metaphor" to a conference on the effects of conscious purpose on human adaptation:

One reason why poetry is important for finding out about the world is because in poetry a set of relationships get mapped onto a level of diversity in us that we don't ordinarily have access to. We bring it out in poetry. We can give to each other in poetry the access to a set of relationships in the other person and in the world that we are not usually conscious of in ourselves. So we need poetry as knowledge about the world and about ourselves, because of this mapping from complexity to complexity. (Cited by Mary Catherine Bateson, 1972, pp. 288-9)

The challenge of memorability is articulated otherwise by Doris Lessing in a devastating commentary on communication of insight by a "galactic agent" with a representative of those facing planetary disaster:

To say that he understood what went on was true. To say that he did not understand -- was true. I would sit and explain, over and over again. He listened, his eyes fixed on my face, his lips moving as he repeated to himself what I was saying. He would nod: yes, he had grasped it. But a few minutes later, when I might be saying something of the same kind, he was uncomfortable, threatened. Why was I saying that? and that? his troubled eyes asked of my face: What did I mean? His questions at such moments were as if I had never taught him anything at all. He was like one drugged or in shock. Yet it seemed that he did absorb information for sometimes he would talk as if from a basis of shared knowledge: it was as if a part of him knew and remembered all I told him, but other parts had not heard a word. I have never before or since had so strongly that experience of being with a person and knowing that all the time there was certainly a part of that person in contact with you, something real and alive and listening -- and yet most of the time what one said did not reach that silent and invisible being, and what he said was not often said by the real part of him. It was as if someone stood there bound and gagged while an inferior impersonator spoke for him. (Re: Colonised Planet 5 - Shikasta, 1979, pp. 56-57).

Faced with global strategic insanity and civilizational collapse -- as many now argue -- it could be asked whether these trends are indicative of a form of collective dementia for which Lessing's speculative framing is appropriate. With "everything connected to everything", is any pattern that connects -- of relevance to governance -- then inherently incomprehensible in practice?

The approach here follows from previous consideration of the role of "pillars" in relationship to the patterned configuration of strategic principles -- and their interconnection as "ways of looking" (Principles, pillars, projectives and metaphorical geometry, 2024). Of relevance to reference to the pillar metaphor is its use in distinguishing the 16 pillars of the Earth Charter.

The question previously addressed is the Use of AI in enabling configuration of psychosocial pillars (2024). This concluded with a focus on the possibility of comprehending unification and integration coherently by other means (Higher Dimensional Reframing of Unity and Memorable Identity, 2024). The argument offered the suggestion that any quest for "unity" is more appropriately envisaged in 4D (or more) rather than in 3D -- or through conventional framing of territorial conflicts in 2D (Neglect of Higher Dimensional Solutions to Territorial Conflicts, 2024). Obvious challenges are Russia-Ukraine, the Koreas, China-Taiwan, and Israel-Palestine.

Rather than the previous focus on visual recognition of a pattern that connects, the argument here envisages how such connectivity may well be only comprehensible and credible through a combination of senses -- most notably including sound. There is a delightful irony to the possibility that traditional musical insights regarding the "monochord" may be fundamental to widespread comprehension of "unity" thereby reframed in terms of the numeric "proportions" through which strategic patterns tend to be articulated. This is notably suggested by revisiting the lambda arrangement of numbers in early Greek mathematics. There is every probability that strategic articulations may then be "consonant" with tuning in some manner -- inhibiting uptake if they are experienced as "out of tune"

It is from that perspective that the question is raised as to whether conventional strategic articulation is fundamentally "out of tune" through its controversial standardization of "pitch" -- strangely analogous to the rapidly developing imposition of a narrative "pitch" by mainstream media.

Eliciting integrative insight via ChatGPT

As with the earlier presentations, the following argument makes extensive use of ChatGPT as an experimental "cognitive prosthetic" -- anticipating future assistance from AI as it is developed. The deliberate ambiguity of the title offers the implication of a possible future "connection" of a "pattern that connects" with AI such as to engender integrative responses.

Relevant precautions and reservations were previously indicated, including concerns with so-called "hallucinations" and the reinforcement of confirmation bias through what could be described as leading questions. Curiously, in the widespread concern with the dangers of AI, there is little corresponding concern with the "hallucinations", "bias" and "leading questions" which could be recognized as characteristic of conventional global governance and its summits.

A particular concern in reproducing the ChatGPT responses in this document -- as the outcome of an experiment -- is the question of the degree to which they could be considered excessive in length. They have not been substantively edited, meaning that readers could ask the same questions to observe how the responses may evolve with later development of the model. The responses, however excessive, have the merit of providing context and aggregating insight from the web -- a didactic function. Their length usefully highlights the assumption about the appropriate length of any adequate articulation with regard to the "pattern that connects".

The issue of length helps to frame the question how succinct any articulation of a pattern that connects could possibly be -- and for whom? Of relevance to any answer is the current appropriateness of indicating the time required to read many web documents. Could such an articulation be presented in "3 minutes", for example? As an equation? As an image? As sound? How much needs to be "ex-planed" -- for whom -- from the "meta-plane" at which it is meaningful in Bateson's terms.

How does the rate of "insight comprehension" contrast with the assumption that comprehension of a spiritual message of connectivity calls for reading of sacred scripture repeatedly -- the Bible, the Quran, the Torah, the Bhagavad Gita -- given the time required? As noted by Daniel Diffey, with the objective of reading the Bible in a year: The average reader can read the Bible through in about 65 to 75 hours. So if you read the Bible for less than 15 minutes a day, you would accomplish your goal (7 Tips for Reading the Bible in a Year, Grand Canyon University, 22 August 2016). With respect to reading of the Torah, some Conservative congregations use a triennial cycle, reading approximately a third of the Torah every year and completing the reading in three years. In the case of the Quran, a rough estimate would be around 30-40 hours for a complete reading with all the necessary breaks in between (How Long Does It Take to Read the Quran? Quran Spirit).

A related constraint is evident in assumptions regarding the years of formal education that may be required in order to comprehend the nature of any pattern that connects. Such an assumption is called into question by cases such as Srinivasa Ramanujan.

Notably questionable in the framing of responses by ChatGPT is a degree of preliminary "artificial appreciation" -- even "artificial validation" -- seemingly designed to encourage user engagement, however speculative the request. As with use of personal pronouns, this renders responses somewhat less appropriate in a document of this kind. With respect to assistance from ChatGPT in eliciting a hypothetical pattern that connects, especially questionable is the "pattern" through which its responses tend to be presented -- echoing conventional patterns which reinforce the prevailing "disconnect". Others have noted the recourse to platitudes, especially when avoiding controversial issues -- platitudes and banalities of little strategic relevance or feasibility (Peter Isackson, Outside The Box: ChatGPT sinks in the Gulf of Tonkin, Fair Observer, 19 February 2024. What other presentational patterns could be meaningfully considered?

In the presentation here the responses have been placed in shaded areas for clarity -- and to enable them to be readily skipped by the reader. However when the documents are presented as PDFs, this shading may be lost (as with hyperlinks). Future possibilities for inclusion of AI include offering readers the capacity to switch between showing and hiding such responses -- as a means of focusing only on the prompts and other commentary. The responses could then be rendered accessible like the footnotes of an academic paper -- to be selectively ignored. Given the length of this document (when responses from ChatGPT are integrated into its presentation), and as part of the experiment in the use of AI, consideration was given to making it available in two versions: a version without responses (as with the separate treatment of supporting data in some studies), and a version with ChatGPT responses.

With respect to the potential future value for governance of AI in enabling recognition of a pattern that connects, there is however the sobering possibility that its communication with global leadership may be as constrained and irrelevant as that of Doris Lessing's "galactic" advisor (as noted above).

Pattern connectivity and memorability

At the time of writing there is exceptional media focus on the cognitive capacity of Joseph Biden, as President of the USA -- given his acclaimed role as leader of the free world. (Tim Reid, Age, mental capacity dominate campaign trail after report questions Biden's memory, Reuters, 11 February 2024; Rachel Sharp, Biden’s Biggest Gaffes: muddling up wars, forgetting names and dozing off mid-event, The Independent, 9 February 2024; 6 takeaways from the special counsel’s report on Biden’s classified documents, PBS, 8 February 2024; List of Joe Biden gaffes, RationalWiki).

Confusing the names of countries clearly has implications for ordering military strikes (Biden mixes up presidents of Mexico and Egypt in speech defending memory, The Guardian, 9 February 2024; Joe Biden confuses Gaza with Ukraine in airdrop announcement, The Guardian, 2 March 2024).

The challenge of memory and cognitive capacity is of course far more general -- given widespread recognition of ageing populations (Kenneth Langa, Cognitive Aging, Dementia, and the Future of an Aging Population, National Academy of Sciences, 2018; Daniel Murman, The Impact of Age on Cognition, Seminars in Hearing, 36, 2015, 3). This will notably have major implications for the use of information technology in a society increasingly dependent upon it -- whether or not many can be adequately assisted by AI in their daily need for pattern recognition. Uncritical dependence on AI may well exacerbate the challenging erosion of collective memory (Societal Learning and the Erosion of Collective Memory, 1980).

To the extent that recognition of a pattern that connects may be associated with recognition of symmetry, it is sobering to note that symmetry of the highest order discovered -- caricatured as the Monster group -- required some 15,000 pages for its proof (Potential Psychosocial Significance of Monstrous Moonshine, 2007).

Question to ChatGPT: Different types of memory are recognized (4 or more). How much (how many items) can be remembered in each case? What are the constraints?

# Show/Hide AI response #

The issue of constraints on conceptual clustering emerges from assessments of problematic-strategic complexity, as with the Situational Complexity Index (SCI) of the Institute for 21st Century Agoras (Cognitive limitations and reductionism in response to global challenges, 2017). Key constraints include:

Question to ChatGPT: This response avoids consideration of constraints such as Dunbar's number. How many plant or animal names can be typically remembered. What are the memory constraints for a lawyer (precedents?), sports fanatic, historian, music enthusiast, etc -- accepting that there are mnemonic tricks to enhance such capacity

# Show/Hide AI response #

Question to ChatGPT: A general question would take the form of how many "things" people tend to be able to remember -- with whatever qualifications. A related question is whether that capacity is now eroded or enhanced by information technology. The question could focus on the size of the vocabulary readily used. Indicative challenges are the number of countries, species, foodstuffs, or chemical elements which can be remembered

# Show/Hide AI response #

There is a strong case for visual indication of the challenge of comprehension and memorability of any progressively larger, interconnected array, most notably its "erosion" as a consequence of aging. This might best be illustrated by a network arrayed around a central point -- becoming progressively less dense (even evanescent) towards a surrounding periphery. Such an image was requested from ChatGPT, but the results were unsatisfactory.

The following images are somewhat suggestive, but also unsatisfactory. They are reproduced from an earlier exercise (Global communication patterns in a hyperbolic space of negative curvature, 2016). The animations could be improved by having the lines fade to invisibility towards the periphery -- with the fading occurring progressively as an indication of erosion over time. Use could be made of concentric shading to indicate the relative number of elements remembered or forgotten -- with the larger numbers in the outer concentric zones.

Animations suggestive of erosion of comprehension and memorabilty from a centre to a periphery
Animation of set of regular tilings Animation of set of quasiregular tilings Poincaré Disk
(adapted from Wolfram Demonstration Project)
Animation of set of regular tilings Animation of set of quasiregular tilings
Image reproduced from Global communication patterns in a hyperbolic space of negative curvature (2016)

Further consideration could be given to representation of connectivity erosion. The outer zones of the images could, for example, suggest the challenge of recognizing and remembering an array of natural species (1.2 million formally described), intergovernmental organizations (5,000), US military bases in foreign countries (approximately 700 bases), elected representatives of a country (approximately 500), countries and territories (195-250).

As widely disseminated, two typical approaches to the visualization of the European Parliament are reproduced below. Is their simplicity worthy of the complex challenges of governance for which the European Parliament claims responsibility? Or is it fundamentally misleading, effectively cultivating an illusion of coherence which is totally questionable in practice?

Missing from such images is any sense of how the 700-plus MEPs communicate with each other in this configuration, given obvious time constraints -- even if person-to-person and person-to-groups, as well as group-to-group communications, are facilitated electronically. These are of course clearly possible even when MEPs are not assembled together physically. It is unclear whether these different modes of communications are subject to continuing assessment with regard to their efficacy. Of some concern would obviously be the dominance of speaking time by some MEPs, for whatever reason, and the marginalization of others.

Indications challenges to comprehension, memorability and communication
Representtion of degrees of memorability Hemicycle (debating chamber) of the European Parliament
during a plenary session in Strasbourg.
Indication of composition of the European Parliament
by political groups (Elections to the Parliament)
Pope addressing European Parliament Indication of composition of the European Parliament
  European Union, 2014 EP-012763 User:Glentamara [CC BY-SA 4.0], via Wikimedia Commons

Question to ChatGPT: With the constraints on the number of "things" that can be remembered, there is necessarily a further constraint on memorability of their connectivity. It is one thing to recognize 1,000 birds, songs, laws, chemicals, etc -- but quite another to recall how those bird species may relate to one another (or the songs, etc). This suggests the need for a measure of connectivity and how diminishing connectivity may be associated with increasing "things" in a set -- to say nothing of the connectivity between things in different sets

# Show/Hide AI response #

Question to ChatGPT: Whilst the response is necessarily appropriate, it is useful to recognize that the knowledge architecture exploited by search engines does not necessarily facilitate a response to questions of the form: of what set is that an instance -- or to what is that systemically related

# Show/Hide AI response #

As variously discussed, whether with respect to ageing or information overload, the constraint on pattern connectivity is usefully framed by the horizon effects on a sphere, rather than on a circular disk:

Unexpected AI aberration -- modelling irrational democratic discourse?

In the midst of the experimental exchange with ChatGPT, in response to a "serious" question, it switched into a curiously "lyrical" mode. The aberration over several days was reported by others (Benj Edwards, ChatGPT goes temporarily "insane" with unexpected outputs, spooking user, Ars Technica, 22 February 2024; ‘ChatGPT going crazy’: OpenAI identifies issue causing malfunction of chatbot, The Indian Express, 22 February 2024). An explanation was offered after it had been fixed (Unexpected responses from ChatGPT: Incident Report for OpenAI, February 2024)

The responses in that erroneous mode are included as a potentially useful indication of how democratic discourse might be variously "distracted", as with the "gaffes" of world leaders. The temporary issue is consistent with the "imaginative errors" of ChatGPT in the current state of development of its DALL-E image generation facility -- as previously noted.

Question to ChatGPT: Given current concerns regarding the memory capacity of leadership, and democratic representatives -- faced with information overload -- how might this be challenged by the complexity of strategic articulations which are not specifically designed to be readily remembered? How would this constrain effective governance, oversight, and resilient adaptation?

# Show/Hide AI response #

Question to ChatGPT: That response, especially the conclusion, is of unusual style. Do you have an explanation for that

# Show/Hide AI response #

Question to ChatGPT: The style of response is interesting but seems to have drawn on a very particular source which would be alienating to many -- even rejected as a form of "hallucination". It remains unclear to me how and why you switched into that style

# Show/Hide AI response #

Question to ChatGPT: I would still like clarification as to how or why your lyrical style was triggered since from an IT perspective it could be considered indicative of a bug. Some of the language of the response reminded me of Lewis Carroll's Jaberwocky: ’Twas brillig, and the slithy toves, Did gyre and gimble in the wabe: All mimsy were the borogoves, And the mome raths outgrabe.

# Show/Hide AI response #

Contrasting preferences for N-fold organization in disconnected patterns

Although there is widespread appreciation of number symbolism (irrespective of its corresponding deprecation as superstition), the concern in the earlier papers was the justification for popular appreciation of larger sets, deemed fundamental to the symbolism valued by particular cultures and belief systems -- and to their memorability in offering a sense of identity. The question focused on sets variously composed of prime numbers raised to various exponents.

The following examples include sets engendered and valued by traditions, as well as those variously encompassing understandings of human rights, together with some deemed fundamental by science. The first column indicates numbers from the table of Nicomachus (dicussed below), registered as A036561 in the On-Line Encyclopedia of Integer Sequences.

Indication of conventionally unrelated patterns
OEIS A036561 (nearest integers) Factors Elements
in set
Key sets of potential cultural or strategic relevance
108 [22x33] 108 a characteristic number of prayer beads in circlets (Designing Cultural Rosaries and Meaning Malas to Sustain Associations within the Pattern that Connects, 2000); celebration of Japanese New Year according to Buddhist/Shinto tradition (Why Do Japanese Bells Ring 108 Times on New Year’s Eve? National Bell Fesitval; Joya no Kane: Purify Yourself With This Episode, Uncanny Japan, 28 December 2023); names of deity variously chanted, as separately discussed (Embodiment of 108-foldness as ultimate spiritual challenge? 2024)
96 [2x47] 94* chemical elements organized in the Periodic Table, 94 of the 118 elements are found naturally on Earth; the remaining 24 are synthetic
81 [34] 81 classical Chinese philosophy organized in terms of the 81-fold sets of the Taixuanjing ("The Canon of Supreme Mystery") and the Tao Te Ching, discussed separately (Indications of strategic coherence from 81-fold patterns in 4D, 2024); the American Convention on Human Rights is composed of 82 articles
72 [23x33] 72 71 Articles of the UN Convention against Corruption; mnemonic clues to 72 modes of viable system failure -- and integrity -- through a "demonic" and "angelique" pattern language (Variety of System Failures Engendered by Negligent Distinctions, 2016)
64 [26] 64 64-fold set of hexagrams of the I Ching ("The Book of Changes"); 63 Articles of the African Charter on Human and Peoples' Rights
54 [2x33] 53* 53 Articles of the Arab Charter on Human Rights and of the UN Convention on the Rights of the Child
* [2x52] 50 50 Articles of the UN Convention on the Rights of Persons with Disabilities
* [2x23] 46 46 Articles of the UN Declaration on the Rights of Indigenous Peoples
36 [22x32] 36 Georges Polti (The Thirty-Six Dramatic Situations, 1916); Yuan Gao: Lure the Tiger Out of the Mountains: how to apply the 36 stratagems of Ancient China to the Modern World (1993)
32 [2x3x5] 30* 30 Articles of the Universal Declaration of Human Rights
27 [22x7] 28* 28 Articles of the Universal Declaration on Bioethics and Human Rights; 28 Articles of the UN Declaration on the Rights of Peasants and Other People Working in Rural Areas
[33] 27 27 Articles of the Declaration of the Rights of Man and of the Citizen
24 [52] 25* 25 Articles of the International Convention on the Elimination of All Forms of Racial Discrimination
* [22x5] 20 Checklist of web resources on 20 strategies, rules, methods and insights (2018).
18 [2x32] 18 18 Articles of European Convention of Human Rights
16 [24] 16 16(+1) Sustainable Development Goals of the UN; (Eliciting Potential Patterns of Governance from 16 Sustainable Development Goals, 2022)
[2x7] 14 (Pattern of 14-foldness as an Implicit Organizing Principle for Governance? Web resources, 2021)
12 [22x3] 12 (Checklist of 12-fold Principles, Plans, Symbols and Concepts: web resources, 2011)
* [2x5] 10 10 Articles of the UN Declaration on the Right to Development
8 [23] 8 8 Millennium Development Goals

Despite the widespread popular appreciation of many of them, their value is seen as distinct from those of much smaller sets, especially valued in relation to psychosocial organization and governance -- a form of "disconnect". Issues are highlighted by the 16-fold Earth Charter and the 16(+1) Sustainable Development Goals of the UN:

Question to ChatGPT: Contrasting examples, seemingly with a degree of concordance with the monochord pattern, are the various international human rights charters: American Convention on Human Rights (82 articles), African Charter on Human and Peoples' Rights (63); Arab Charter on Human Rights (53), Convention on the Rights of the Child (54), Universal Declaration of Human Rights (30), European Convention of Human Rights (18). How might their preoccupations be reconciled, if they are each an indication of a distinctive "musical" culture

# Show/Hide AI response #

Question to ChatGPT: How might any such concordance with an expression of tones be explored -- with some insight into the extent to which a given charter might be "in tune" or "out of tune" -- thereby affecting its memorability and uptake

# Show/Hide AI response #

Question to ChatGPT: This exchange has previously highlighted sets from 81-fold (Tao Te Ching) to 36-fold (Polti, etc). Do you have access to an array of such larger sets distinguished by their factors and exponents

# Show/Hide AI response #

Question to ChatGPT: How does that response -- and the role of exponents -- relate to the importance of "power laws" in a variety of domains.

# Show/Hide AI response #

The question seemingly calling for explanation is whether the choice of such clustering is totally arbitrary in contrast with the possibility that it may be indicative of other considerations of potentially vital significance for the elaboration, comprehension and memorability of future strategies, as previously discussed (Patterns of N-foldness: comparison of integrated multi-set concept schemes as forms of presentation, 1980; Representation, Comprehension and Communication of Sets: the role of number, 1978).

This contrast frames the question as to whether it is assumed that global governance can be effectively managed through strategic sets articulated with "smaller" numbers.

Aesthetic connectivity of patterns in music

As noted above, it is potentially fruitful to challenge the tendency to restrict pattern recognition to the visual modality, extending the possibility to the contribution of the other senses -- hearing, tasting, touching, smelling -- singly or in combination. The visual mode lends itself most readily to mathematical analysis in support of governance. The other senses, with the exception of music, tend to feature primarily in design for marketing purposes. With respect to the "pattern that connects", little is said regarding "patterns of taste", "patterns of odour", or "patterns of touch" -- despite considerable attention to "aesthetic patterns".

The potential future implications have been discussed separately (Aesthetics of Governance in the Year 2490, 1990; Poetry-making and Policy-making: arranging a Marriage between Beauty and the Beast, 1993; A Singable Earth Charter, EU Constitution or Global Ethic? 2006; Future challenge of problematic sets for governance -- strategic sonnets? 2021; Aesthetics and Informatics: the art of information for policy-making and community-building, 1999).

For Darrell Conklin:

Pattern in music, referring to the discovery, representation, selection, and interpretation of repeated structures within single pieces (intra-opus) or corpora (inter-opus), is a central part of music analysis, musical style and genre, improvisation, music perception, and composition. This special issue of the Journal of Mathematics and Music presents a diverse selection of papers on the topic of pattern in music from computational and mathematical perspectives. The following overview will introduce the papers considering three facets: representation, discovery, and evaluation and interpretation. (Pattern in Music, Journal of Mathematics and Music, 15, 2021, 2)

In considering patterns in music, a traditional point of departure is the monochord -- with the insight it offers into proportion in relation to musical scales. As noted by David Creese (The Monochord in Ancient Greek Harmonic Science, 2010): With its single string, movable bridge and graduated rule, the monochord... straddled the gap between notes and numbers, intervals and ratios, sense-perception and mathematical reason.

Potentially especially relevant, in a period challenged by polarities, is their recognition as a tonal counterpart to "string theory" -- through insights from the monochord (Polarities as Pluckable Tensed Strings, 2006). This earlier exploration focused speculatively on  "hypercomprehension through harmonics of value-based choice-making".

The work of musicologist Ernest McClain is especially significant in the exploration of engagement with larger sets (The Myth of Invariance: the origin of the gods, mathematics and music from the Rg Veda to Plato, Journal of Aesthetics and Art Criticism, 36, 1976, 1) as notably clarified by F. Leighton Wingate (The Published Writings of Ernest McClain through Spring 1976, North Texas State University, 1977). Highlighting the interplay of factors and exponents, this featured several indicative matrices, as reproduced below. The relevance is further clarified in a compilation by Bryan Carr and Richard Dumbrill (Music and Deep Memory: speculations in ancient mathematics, tuning, and tradition in memoriam Ernest McClain, 2018).

In Ernest McClain's work, the generative matrix is a conceptual tool that helps illustrate the relationships between musical intervals within a scale or tuning system. The idea of rings in this matrix is more about visualizing the mathematical relationships between intervals (ratios of frequencies) than about literal spatial arrangements. These intervals can include octaves, fifths, fourths, thirds, etc., each represented by specific ratios (e.g., 2:1 for an octave, 3:2 for a perfect fifth). The goal would be to see if the article counts (above) can be expressed in a way that mirrors the harmonic or mathematical relationships found in music theory, specifically in the context of just intonation as McClain explores.

In reality, McClain's rings are about the relationships between musical intervals as they expand outwards from a fundamental tone, with each ring potentially representing a set of intervals that share a common mathematical relationship. Applying this to the number of articles in human rights charters is an imaginative leap, using the structure and harmony of music as a lens to view the structure of these charters in a new light.

The work of McClain has been explicitly celebrated in a study of the statuette of the so-called Venus of Lespugue (dating back 25,000 years) -- from an archaeomusicological perspective (The Canon of Lespugue, Epigraphic Society Occasional Papers, 24, 1994). The study's purported embodiment of a musical canon resulted from collaboration between cultural historian William Irwin Thompson (Coming into Being: artifacts and texts in the evolution of consciousness, 1996) and mathematician Ralph Abraham (Dynamics, the Geometry of Behavior, 1992).

Insights from an archeomusicological perspective

Venus of Lespugue
(front and back views)

The Canon of Lespugue
alongside the Greek Dorian mode
Aulos and monochord tuned to the Hindu-Greek scale
(McClain, 1976, Chart 1)
The Canon of Lespugue Aulos and monochord tuned to the Hindu-Greek scale
Redrawn Venus of Lespugue (Flutopedia) Reproduced from The Canon of Lespugue (Epigraphic Society Occasional Papers, 24, 1994)

Of some relevance, that earlier study was followed by a second collaborative study (The Geometry of Angels, 1998), as previously indicated (Paradoxical existence of global cognitive constructs, 2024). The framing offered by "geometry" featured in an unpublished contextual overview by Abraham, emphasizing the role of "dynamics" (The Geometry of the Soul, Stanford University, 1991). However, given the significance of the breasts in the statuette, it is curious that their dynamics as a major "attractor" was not recognized. Arguably any pattern that connects calls for understanding in dynamic terms. The evocation of the angel metaphor at that time is consistent with the study by Gregory Bateson and Mary Catherine Bateson (Angels Fear: towards an epistemology of the sacred, 1988; Mary Catherine Bateson, Angels Fear Revisited: Gregory Bateson's Cybernetic Theory of Mind Applied to Religion-Science Debates, Biosemiotics, 2008).

The Flutopedia presentation of the study by Thompson and Abraham is introduced as follows (with a redrawn version of the statuette):

There are many challenges to interpreting ancient artifacts in the context of music. One challenge is that many aspects of music relate closely to fundamental mathematical ratios. Octave intervals have frequency ratios of 2:1, intervals of fifths are (or are close to) 3:2, fourths are 4:3, and most other intervals can be rendered as simple ratios. Those ratios appear in many disciplines, especially in art and archetecture. This makes it difficult to distingush the intent of a written text: does it refer to music, mathematics, or architecture? (Venus of Lespugue, Flutopedia)

Question to ChatGPT: There is an extensive literature on culturally meaningful number symbolism. Typically this focuses on smaller numbers. Potentially more intriguing is popular appreciation of larger numbers, as with 36, 64, 72, 81, 108. These numbers may indeed be reframed in terms of their factors and their exponents, as illustrated by the work of McClain as a musicologist. To what extent are such sets associated with music and tuning systems. Is it the musical associations which render the sets popularly attractive -- possibly from a cognitive perspective. Is there a pattern to the relation between such larger sets

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Question to ChatGPT: Expressed as integers, Ernest McClain indicates correspondences between tone frequency ratios (60, 54 48, 45, 40, 36, 32, 30) and length ratios (72, 80 90, 99, 108, 120, 135, 144). Citing McClain, Abraham and Thompson present a corresponding pattern of Dorian frets (144, 135, 120, 108, 96, 90, 86, 80, 72). Many of these numbers can be recognized as characterizing sets highly valued by particular cultures, notably 108, 72, and 36. Notably absent is 64. Is there an appropriate comparison to be made between the ratios and cultural sets, given what may be missing

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Question to ChatGPT: Further to the previous question, is there an appropriate comparison to be made between the ratios and cultural sets, given what may be missing. Is there a more comprehensible way to juxtapose such information in different "languages" with the number of elements in the sets.

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Visualizing exponents of factors characteristic of larger sets

The argument frames the question as to how the distribution of tones -- variously denoted by factors with exponents -- can be coherently represented in order to explore the degree to which this is indicative of the articulation of cognitive sets (charters, symbolic sets, etc).

Unrelated to music, the possibilities of visualizing factor exponentiation are the subject of various suggestive indications and animations, including:

Potentially the most elaborate explanation, without reference to musical tones, is offered by FasterCapital (Geometry and a 2: investigating the geometric interpretation of exponents, 17 December 2023).

By contrast, an extensive commentary on musical modes (with suggestive illustrations) is articulated by John Carlos Baez for the Azimuth Project (1 November 2022) as:

• Part 1: modes of the major scale.
• Part 2: minor scales, and a cube of modes.
• Part 3: all 7-note scales drawn from the 12-tone chromatic scale...
• Part 4: modes of the major and melodic minor scale.

• Part 5: modes of the Neapolitan major scale.
• Part 6: the special role of the Lydian mode, and the circle of fifths.
• Part 7: cycling through all 84 modes of the major scale in all keys.
• Part 8: how the group x acts on the set of all 84 modes of the major scale in all keys.

Other possibilties could be explored in terms of:

Question to ChatGPT: Other than the matrix configurations of McClain, can the relation between those larger sets be visualized. It might be assumed that their significance would be rendered explicit in magic squares, cubes or circles -- framing factors and exponents in some way. Do Chladni patterns in 2D or 3D offer another possibility

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Another possibility could be explored in terms of power laws

However that approach seems only to have been applied to musical success by Andrew Gustar (The Laws of Musical Fame and Obscurity, Significance: Royal Statistical Society, 17, 2020, 5; Fame, Obscurity and Power Laws in Music History, European Musicological Review, 14, 2019, 3-4). Of greater relevance to the argument here is the study by Dimitrios Rafailidis and Yannis Manolopoulos (The Power of Music: searching for power-laws in symbolic musical data, 12th Panhellenic Conference on Informatics (PCI'08), 2008). There is noted that all previous works regarding power-laws in musical data, discovered scale free distributions based on variables -- but with low musicological meaning.

Ironically it would appear that the most relevant approach to visualization is through the polgonal patterns traditionally explored by the Pythagoreans, known as pebble diagrams and now presented as polygonal numbers (David Nirenberg and Ricardo Nirenberg, Knowledge from Pebbles, KNOW: A Journal on the Formation of Knowledge, 2, 2018, 1; Vera Stevens, Pebble Maths: Teacher Training Manual, 2015).

Traditionally these featured as the tetractys as extensively described by Siemen Terpstra (An Introduction to the Monochord, Alexandria: the Journal of the Western Cosmological Traditions, 2, 1993). For Terpstra:

It would be a useful tool to be able to designate the harmony itself, independent of the method of generating it, or the particular sequence with which it is expressed. The Pythagoreans did this by the use of a simple matrix of tuning operations, called the "pebble arithmetic". It was so named because in its most abstract form it appears simply as an array of pebbles in triangular patterns. This is the shape of the Tetraktys! This "notation"” is a practical device which helps the tuner know what particular harmony he or she has produced. It is also an indispensible morphological model of the structure of harmony, eliminating redundancies in the expression of scale elements, and “mapping” the regions of the harmony matrix in an unambiguous way. Each type of musical scale has a unique and defining “pebble” pattern.

As Terpstra indicates separately:

The Tetractys symbol is an exquisite example of how a simple visual pattern can have multi-varied meanings and "levels" of interpretive significance. The famous Pythagorean oath refers to the Tetractys, praising it as the source "which contains the fount and root of eternal nature". A profusion of insights can be derived from the image, concepts which are relevant to arithmetic (number relations), harmonics (musical tuning theory), and geometry (number relations in space). Only a pitifully small amount of ancient commentary has been preserved; but the study of the above disciplines uncovers more and more relevance for the symbol... The Pythagoreans sav in Number the eternal archetypes of order in nature, the mind, and the metaphysical realm. Hence statements of simple arithmetical relations are imbued vith religious import. Mathematics is still the most abstract language of mankind, and the best suited to describe the laws which govern the universe. (The Meaning of the Tetractys: musical symbolism in Pythagorean arithmology, 1993, diagrams)

Ironically the traditional focus on pebble diagrams has recently evolved into a mathematical game, knowng as pebbling, with similarities the Chinese game of Go.

Question to ChatGPT: In An Introduction to the Monochord (1993) Siemen Terpstra illustrates the use of the tetractys by Pythagoreans, indicating it would be a useful tool to be able to designate the harmony itself, independent of the method of generating it, or the particular sequence with which it is expressed. The Pythagoreans did this by the use of a simple matrix of tuning operations, called “pebble arithmetic.” It was so named because in its most abstract form it appears simply as an array of pebbles in triangular patterns. How could this be adapted to the indication of the "harmony" between sets -- such as those of human rights

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Question to ChatGPT: That response reframes the matter in qualitative terms -- typically a long-term challenge. The question is whether the numeric characteristics could be more readily configured -- using factors and their exponents -- to imply qualitative relationships through the memorability of the presentation

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The above responses of ChatGPT are typical of a degree of avoidance and an optimistic recourse to inoperable generalities -- however appropriately formulated.

Pythagorean music theory is based on the idea that musical intervals can be described with ratios of small positive integers. In antiquity these ratios refer to string lengths on a monochord (Daniel Muzzulini, Isaac Newton's Microtonal Approach to Just Intonation, European Musicological Review, 15, 2020, 3-4). Just intonations are a system of musical tuning in which the frequencies of notes are related by ratios of small whole number. This system creates harmonies that are perceived as consonant due to their simple mathematical relationships. They are categorized by the notion of limits. The limit refers to the highest prime number fraction included in the intervals of a scale. All the intervals of any 3-limit just intonation will be multiples of 3 (List of pitch intervals, Wikipedia; Harmonic series, Wikipedia):

All of the ratios which are inherent in a given monochord series can be expressed by using an interval triangle as shown below. The approach is now described more generally in terms of polygonal number -- indicated below in the case of a hexagonal number pattern used by Ernest McClain, as discussed by F. Leighton Wingate (The Published Writings of Ernest McClain through Spring 1976, 1977). The succession of concentric bands therein are associated with increasing exponents.

Tetractys Interval triangle
Tetractys 3-limit interval triangle
Reproduced from Siemen Terpstra (1993)
Tetractys as 3-limit matrix of tones
Plato lambda Prime factors Crantor lambda Harmonic series (monochord)
3-limit just intonation Plato lambda 3-limit just intonation prime factors 3-limit just intonation Crantor 3-limit just intonation harmonic series
Reproduced from (The Meaning of the Tetractys, 1993; diagrams)
Tetractys (rotated) as 5-limit matrix of tones
Source Prime factors Numbers Pitch names (harmonics)
5-limit just intonation source 5-limit just intonation prime factors 5-limit just intonation numbers 5-limit just intonation harmonics
Reproduced from (The Meaning of the Tetractys, 1993; diagrams)

Nicomachus of Gerasa has gained a position of importance in the history of ancient mathematics due in great measure to his Introduction to Arithmetic, one of the only surviving documentations of Greek number theory. Jay Kappraff discusses a pair of tables of integers (below) found in the Arithmetic and shows how they lead to a general theory of proportion (The Arithmetic of Nicomachus of Gerasa and its Applications to Systems of Proportion, Nexus Network Journal, 2, 2000). As reproduced below, Kappraff interpolates tone names in a later study (Ancient Harmonic Law, 2007). The numbers are presented as the Nicomachus triangle in the On-Line Encyclopedia of Integer Sequences (as shown below right) with multiple commentaries and references. The triangle pertaining to this sequence has the property that every row, every column and every diagonal contains a nontrivial geometric progression. More interestingly every line joining any two elements contains a nontrivial geometric progression.

Integers from the Arithmetic of Nicomachus
(as string lengths, and with modern tone names interpolated from Kapraff in one case)
Tables Table for expansions of the ratio 3:2 OEIS Triangular array of Nicomachus
Reproduced from Kappraff (2000) Reproduced from Kappraff (2007) Reproduced from OEIS (A036561)

A compilation by A. Volkov and V. Freiman on Computations and Computing Devices in Mathematics Education Before the Advent of Electronic Calculators (2019) includes a study by Athanasia Megremi and Jean Christianidis (Interpreting Tables of the Arithmetical Introduction of Nicomachus through Pachymeres’ treatment of Arithmetic: preliminary observations, 2019).

The Arithmetical Introduction is indeed an introduction to the study of the properties of numbers, that is, an introduction concerning the theory of numbers. Is theoretical arithmetic all that we can learn from this work though? We will argue that a textual analysis of the work suggests otherwise. For this purpose, the aspect of representation and organization of the content of the text will be elaborated. It concerns more specically the meticulously detailed instructions provided by Nicomachus towards reading, constructing and using some of the tables included in the printed edition of his text bearing on pairs of numbers in relation. The presence of such textual units in Nicomachus’ treatise gives rise to several questions. Could it be possible to produce a case study where such textual units could be studied through the prism of a certain functionality? Do the surrounding text and accompanying tables have any heuristicvalue, and, if so, of what sort? Finally, could tables and text together be viewed as portraying underlying teaching purposes, and, if so, of what sort? [emphasis in original]

In that light, inspection of the triangular array of Nicomachus (right above) suggests a suspicious degree of correspondence with the size of the sets (as presented earlier), notably the number of articles in human rights charters and global strategic initiatives. In statistical terms, there appears to be a remarkable degree of correlation. Given the musical perspective clarified above, this is suggestive of an unexplored degree of "consonance" between the seemingly disparate sets of human rights-related charters. This calls for careful exploration of the cognitive implications governing preferences for the sets presented. Any consonance could then be understood as a characteristic of the elusive pattern that connects.

Whilst the focus in the interaction with ChatGPT is on the human rights charters, the sets presented earlier also include those of considerable cultural importance, numbering 108, 81 and 72 -- which aso feature in the Nicomachus pattern. This reinforces the case for a more systematic study of sets with potential cognitive implications as noted separately (Patterns of N-foldness: Comparison of integrated multi-set concept schemes as forms of presentation, 1980).

Question to ChatGPT: Given the correlation recognized in this exchange between the number of articles in human rights charters and the numbers which emerge from 3-limit or 5-limit just intonation (possibly with a tolerance of plus-or-minus 2) in the classical table from Nicomachus (OEIS A036561), including: 81, 72, 64, 54, 32, 27, 24, 18, 16, 8, could you present the following in those terms: American Convention on Human Rights (82 articles), UN Convention against Corruption (71), African Charter on Human and Peoples' Rights (63), Arab Charter on Human Rights (53), Universal Declaration of Human Rights (30), Universal Declaration on Bioethics and Human Rights (28), Declaration of the Rights of Man and of the Citizen (27), International Convention on the Elimination of All Forms of Racial Discrimination (25), European Convention of Human Rights (18), Sustainable Development Goals of the UN (17), Millennium Development Goals (8)

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Indicative atribution of human rights related articulations (indicated above) to Nicomachus table of integers
(near misses in italics; no account of lower numbers; non-human rights in quotes)
    2 22 23 24 25 26
    [2] [4] 8 (MDGs) 16 (SDGs) 32 (UNDHR) 64 (Africa)
3 [3] [6] [12] 24 (Racism) 48 (Indig.) 96 ("Period.") 192 ("Sea")
32 [9] 18 (Europe) 36 72 ("Corrup.") 144 288 576
33 27 (Citizen) 54 (Arab) 108 ("Bells") 216 432 864 1728
34 81 (America) 162 (SDG tasks) 324 648 1296 2592 *

Issues for further exploration:

Of particular interest in the light of any connecting pattern, as evident from the Nicomachus triangle and McClain's matrix configurations, is the variety of "voices" appropriate to sustainability, as discussed separately (Requisite variety of "voices" for psychosocial wholth: 6, 8, 12, 20, 30?, 2015; Music and aesthetics as mnemonic aids to governance, 2022). At least for some cultures, the requisite coherence may be particularly evident through a musical lens (Knowledge Gardening through Music patterns of coherence for future African management as an alternative to Project Logic, 2000).

Indicative matrix configurations of tones by Ernest McClain
Generative matrix with exponents Star-hexagon matrix for Just tuning
, with tonal interpretation
Cubic lattice as "Holy Mountain" Tonal values in hexagonal lattice array
Generative matrix Star-hexagon matrix for Just tuning Cubic lattice as "Holy Mountain" 37 Tonal values in hexagonal lattice array
Images reproduced from Wingate (The Published Writings of Ernest McClain through Spring 1976, 1977) Reproduced from McClain, Meditations Through the Quran: tonal images in an oral culture, 1981, p. 95)

The array of tones presented by McClain, following that of the Pythagoreans, has since been explored as a "tone space" characterized by a "tone net" or Tonnetz. A variety of visual representations of the Tonnetz, notably in the light of graph theory,  are now explored to show traditional harmonic relationships in European classical music (Giovanni Albini and M. P. Bernardi, Graph Theory and Music: A Mathematical Tool for Musicians, Advances in Intelligent Systems and Computing, 2018; Kenneth M. Smith, The Transformational Energetics of the Tonal Universe: Cohn, Rings and Tymoczko, Music Analysis, 33, 2014, 2). As reviewed by Richard Cohn (Graph-theoretic and Geometric Models of Music, Mathemusical Conversations: mathematics and computation in music performance and composition, 2016):

Graph-theoretic models are mathematical structures that model pairwise relationships between objects (such as pitches and chords) in terms of networks of vertices connected by edges. Geometric models are mathematical models based on the notion of space and concepts such as distance, neighborhood, and connectivity. Cohn begins in Ancient Greece with Crantor’s lambda, continues with Nicomachus’s triangle, Torkesey’s triangle, Euler’s Tonnetz and its various adaptations, Douthett’s Cube Dance, and finally concludes with Tymoczko’s orbifold. The juxtaposition of so many models in such a short space could have produced chaotic results, but Cohn successfully draws a common historical thread throughout these models, describing how each model was a natural response to contemporaneous developments in musical practice. This chapter could serve well as a first introduction to this area of music modelling, perhaps as part of a university course in music theory or music psychology. (Peter M. C. Harrison, Empirical Musicology Review, 12,2017, 1-2 )

Such articulations frame the question as to whether arrays of strategies call for analogous geometrically enhanced exploration. The association of individual strategic articulations with tones, if only for mnemonic purposes, offers the curious possibility that as a pattern of sets they together invite the possibility of melodic compositions being "played" within the context of an AI-enabled "global brain" (Envisaging a Comprehensible Global Brain -- as a Playful Organ, 2019). Such a framing invites speculation on missing notes, attunement of the pattern, and the challenge to "sacred music" exemplified historically by the tritone (diabolus in musica).

Monochord ratios, tone frequencies and psychosocial implications

There are many accessible references to the significance of the number 432 -- variously questionable (Robert Edward Grant, Flower of Life and 432, 10 January 2021)

Question to ChatGPT: With new measurement technology, the switch from monochord length ratios to frequencies has added interest to the symbolic significance of the number of 432, variously speculative and questionable. Could you comment on this including reference to the properties of 432 as a number and recognition of its relevance in traditional architecture, less vulnerable to deprecation as pseudoscience

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Given the symbolic importance widely associated with circlets of 108 prayer beads, of particular interest is the relation between string length ratios and frequency in a monochord (Liutaio Mottola, Pitch Frequency of Vibration), String Tension, String Length, and String Weight, Lutherie Information Website)

Question to ChatGPT: How do the traditional length ratios of monochord analysis relate to the measure of tone frequencies in Hertz, in particular how is this illustrated by 108 versus 432 Hz

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Question to ChatGPT: With respect to your reservation with regard to 108, it nevertheless features in the analysis by Abraham and Thompson (1994), based on that of McClain (1976), as corresponding to G. 432 Hz features in the continuing controversy as "Verdi's A" in contrast with the pitch standard of 440 Hz. Could you clarify this

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Question to ChatGPT: You indicate that the relationship between length ratios and frequencies in a monochord is governed by the length of the string, its tension, and its linear density. Does this indeed suggest that the frequency of 432 Hz can be variously obtained -- through tuning -- in order to obtain the note with which 432 Hz is associated. Could this point be presented more clearly

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Question to ChatGPT: This exchange has focused on eliciting the elusive "pattern that connects". Your response suggests that if 432 Hz is somehow associated with that connectivity, then the response calls for metaphorical interpretation of psychosocial relevance -- both with respect to memorability and governance. Length as suggested by survey baseline? Tension as a feature of the relation between opponents? Linear density (thick or thin)? Could you suggest the development of that possibility

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Of curious relevance to this argument is the appreciation of the so-called Yellow Bell in Chinese music theory and its implications for governance (Bei Peng, Listen, Measure, Calculate: in search of the Urton of the "Yellow Bell" in Chinese Music Theory, EASA Colloquium Science Meets Art, 18 March 2022):

Put simply: the length of the Yellow Bell musical pipe determined the economic measuring units of the whole country! It was the basis for the political decisions, which therefore also had a foundation in music theory. As such, it also became the primary concern of every dynasty. In turn, each dynasty wanted to use the length of the Yellow Bell pipe in accordance with its own general “cultural orientation” and therefore always chose to revise it, especially to show that they were in charge of defining this most basic measure.

It is no wonder that there is also a very complex connection in the relationship between the Yellow Bell-number Eighty-one and pre-modern calendrics in China. The music theorists were mathematicians and also astronomers at the same time. They were always constantly trying to construct a perfect calendar, using the number 81 as the basic number. This is also inseparable from the Yijing 易經 (Book of Changes) and the philosophical idea of the “unity of heaven and man” (tianrenheyi 天⼈合⼀)...

In conclusion, one can say that the concept of the Yellow Bell is one of the most central concepts in traditional Chinese music theory

Useful context on the relation between Western and Eastern framing is provided by Fred Fisher (The Yellow Bell of China and the Endless Search Music Educators Journal, 59, 1973, 8).

Question to ChatGPT: Given the "Yellow Bell" traditionally considered so fundamental to Chinese music theory and governance, are there further clues to such a metaphorical interpretation

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Question to ChatGPT: The reference to unity in relation to diversity frames the sense in which the Platonic ideal of governance and that of the Yellow Bell are highly problematic and inadequate as a constraining understanding of "unity". The "diabolus in musica" can then be seen as a musical celebration of diversity -- comparable to the contrast between the European Anthem and the Eurovision Song Contest. Missing is the nature of the elusive balance and harmony between them -- enabling their reconciliation as models of governance

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Standard pitch imposition and its analogues: 440Hz vs 432Hz

There is relatively little recognition of the manner in which the "standard" of musical pitch has been surreptiously defined globally -- and especially its implications. As noted by Wikipedia with respect to concert pitch:

Concert pitch is the pitch reference to which a group of musical instruments are tuned for a performance. Concert pitch may vary from ensemble to ensemble, and has varied widely over time. The ISO defines international standard pitch as A440, setting 440 Hz as the frequency of the A above middle C. Frequencies of other notes are defined relative to this pitch... In 1939 an international conference recommended that the A above middle C be tuned to 440 Hz, now known as concert pitch. This was adopted as a technical standard by the International Organization for Standardization in 1955 and reaffirmed by them in 1975 as ISO 16.

Consideration of pitch is further confused by reference to scientific pitch (philosophical pitch, or Verdi tuning)

Particularly in the beginning of the 21st century, many websites and online videos have been published arguing for the adoption of the 432 Hz tuning – often referred to as "Verdi pitch" – instead of the predominant 440 Hz. These arguments have also been associated with claims regarding the therapeutic properties of the 432 Hz pitch, variously held to be questionable:

For example, Brian Collins asks:

The unquestionable focus on 440 Hz has the consequence of precluding consideration of the implications of its imposition. Whilst arguably unrelated, the following merit exploration in systemic terms as instances of analogous processes:

Of particular relevance to the argument here is the controversy regarding the widely commented Platonic ideal of governance as emblematic of appropriate unity -- informed by musical principles -- and the obvious countervailing pressures for appropriate expression of diversity. Disagreements regarding tuning systems exemplify the difficulty of encompassing diversity with its implications for any imposition of identity experienced as required conformity to a norm.

Ironically the poorly explored paradoxes associated with an ideal standard pitch are variously evident, as argued separately (Paradoxes of Durable Peace, Heaven and a Sustainable Lifestyle, 2023). Of particular strategic relevance is whether the imposition of a standard curtails the effective uptake of strategic proposals like the UN's Sustainable Development Goals -- then experienced as "boring" in the light of a musical understanding of diversity.

Requisite strategic attunement when "out of tune" with the times?

Critical evaluations of governance in this period may be framed by a musical metaphor (Herman Lelieveldt, Out of tune or well tempered? How competition agencies direct the orchestrating state, Regulation and Governance, 14, 2020, 3). With any implied sense of deep time, there is a case for exploring the extent to which governance is "out of tune" with the ZeitGeist (Monika Krause, What is Zeitgeist? Examining period-specific cultural patterns, Poetics, 76, 2019, 101352; Bieke Abelshausen, et al, Participation throughout the Decades: how the zeitgeist influences both theory and practice, Procedia - Social and Behavioral Sciences, 191, 2015). The musical framing has been used with respect to corporate social responsibility (Frank Jan De Graaf, CSR as Value Attunement within Governance Processes: stakeholder dialogue, corporate principles and regulation, Business and Society Review, 121, 2016, 3).

Question to ChatGPT: In the light of that response, to what extent does the pattern of length ratios (108, 92 (+/- 2), 80 (+/- 2), 72, 64, 54, 36, etc) then suggest how conceptual and strategic articulations should be structured. Does this suggest the probability that the articulation of concept sets is based on monochord length ratios -- with the possibility that choices unthinkingly made for such articulations may then be "out of tune"

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Question to ChatGPT: That response suggests that the challenge of any "tuning" may depend on a degree of subtle discernment. The issue is most notably illustrated with respect to strategic articulations of 16 (+/- 2) elements,, as with the UN's Sustainable Development Goals, in contrast with 14-fold, 15-fold, and 17-fold patterns -- and their relation to the 18-fold length ratio. Can the "strategic ear" distinguish appropriately between these

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Question to ChatGPT: In the light of that response, it could be expected that the strategic challenges of governance might be most beneficially articulated by such means, as envisaged by Plato and noted by McClain. Is there any current indication of this with respect to the articulation of global strategies -- or of failure to do so being recognized as "out of tune"

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Question to ChatGPT: Whilst the response is valuable, a major difficulty is evident in the manner in which lip-service is paid to "harmony" when there is an evident disconnect in practice with the cognitive appeal of patterns articulated in music. This may be evident in the contrasting appeal of the European Anthem and the Eurovision Song Contest. Neither has been explored with respect to its relevance to the elaboration of memorable strategies and their popular uptake

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Question to ChatGPT: Whilst indeed pertinent, that response avoids recognition of the highly problematic and controversial dynamics between advocates of a "classical" understanding of harmony, and that between those favouring what is featured competitively by the Eurovision "contest" -- and between those two extremes. The former has been a focus of Jacques Attali as providing the implicit (problematic) framing of governance in this period (Noise: The Political Economy of Music, 1985). Seemingly no governance model has emerged from the "Eurovision model"

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Question to ChatGPT: It could be argued that the challenge of any reconciliation between these contrasting approaches (and the "irreconcilable" preferences with which they are associated) calls for "aesthetic" resolution as widely framed in cultural epics and sagas. In that respect of relevance is the initiative of the 12 songs of The Globalization Saga: Balance or Destruction, 2004, as a CD accompaniment to a book by Professor Franz Josef Radermacher, FAW - Institute for Applied Knowledge Processing, Ulm, in association with the Global Marshall Plan Initiative.

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Question to ChatGPT: A major difficulty is evident in the competitive claims made for aesthetic works towards that end. Aesthetic models of governance then replicate the current inadequacies of political and ideological models. The challenge has been explored by Robert Graves (Seven Days in New Crete, 1949). It would appear that there is a need to integrate some form of self-reflexivity into the framing of any viable "pattern that connects" -- if only through recognition of the dramatic dynamic of success and failure framed in epic mode, with the associated sacrifice.

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Embodying patterns of dance and strategic drama?

The argument above has noted the seeming absence of any 36-fold pattern in the articulation of human rights strategies in terms of the tonal array of the Nicomachus pattern. It is therefore somewhat striking how a 36-fold pattern has been deemed significant in articulations of relevance to human rights, namely dramatic situations and strategic stratagems.

As queried by Antonio de Nicolas: Which one of these two language criteria, "sound" or "sight", sensitizes the reader more? Whatever the direction of this discussion the true result is that "sound" criteria for language is the original criteria of language, while sight criteria is derived and not original (Meditations through the Rg Veda, 1978). As he indicates:

Therefore, from a linguistic and cultural perspective, we have to be aware that we are dealing with a language where tonal and arithmetical relations establish the epistemological invariances... Language grounded in music is grounded thereby on context dependency; any tone can have any possible relation to other tones, and the shift from one tone to another, which alone makes melody possible, is a shift in perspective which the singer himself embodies. Any perspective (tone) must be "sacrificed" for a new one to come into being; the song is a radical activity which requires innovation while maintaining continuity, and the "world" is the creation of the singer, who shares its dimensions with the song. (p. 57)

Earlier commentary discussed the articulation of 36 "dramatic situations" -- with the implication that "narratives" might interrelate them as suggested by the hypothetical pathways (Thirty-six Dramatic Situations faced by Global Governance? 2022). The titles of the familiar "situations" are those of Georges Polti's 36 Dramatic Situations (Changing Minds), as reproduced and discussed separately (Dramatic situations in narrative and stories -- plus or minus thirty-six? 2022). The discussion explored how these might relate to the Chinese insight into 36 stratagems, a unique collection of ancient Chinese proverbs that describe some of the most cunning and subtle war tactics, presented metaphorically as "luring the tiger" (Yuan Gao, Lure the Tiger Out of the Mountains: how to apply the 36 stratagems of Ancient China to the Modern World, 1993).

Question to ChatGPT: In an earlier phase of this exchange, reference was made to Polti's 36 dramatic situations, as well as to the traditional 36 Chinese stratagems. Your response suggests that the requisite self-reflexivity calls for more explicit recognition (as a "lens") of how those conditions play out in the saga of any governance dynamic -- rather than leaving any such recognition to historical commentary.

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Question to ChatGPT: It is then appropriate to ask whether any detectable efforts have been made to give musical expression to either set of 36 -- given the long tradition of using musical accompaniment to any dramatic presentation. The question is then whether the organization of the music accords to a meaningful degree ("resonates") with the requisite cognitive insight -- or whether the failure to do so is indicative of a fundamental disconnect typically ignored

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Question to ChatGPT: That response necessarily focuses on the cognitive embodiment in music of the dramatic dynamics of governance. A more feasible approach might be evident with respect to dance -- also used to enhance governance "receptions". There is indeed a literature on cognitive embodiment in movement (Mark Johnson, Philosophy in the Flesh: The Embodied Mind and Its Challenge to Western Thought, 1999). Presumably Eastern traditions of dance have embodied an equivalent of Polti's situations, and Chinese traditions may have embodied the 36 stratagems in dragon dances

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Of relevance to this argument is the distinction by René Thom of a set of " archetypal morphologies" as presented below and discussed by Wolfgang Wildgen (René Thom's contribution to linguistics and his semiophysics applied to art and music, 2023). Wildgen notes that the earliest version of Thom’s list contained 18 elements and in some cases different names (Topologie et linguistique, 1970). Additional archetypes are: Unir (unite) , Séparer (separate), Le Suicide (suicide). This offers another instance in which the capacity for discernment -- in this case between 16 and 18 -- merits consideration.

Changes: the locus of principal changes of topological type
reproduced from René Thom, Structural Stability and Morphogenesis, 1972
Changes: the locus of principal changes of topological type 1. curve with cusp pointing downward
2. appearance of new point at origin, where lip formation begins --
3. this grows... .
4. pierces the cusp..
5. and crosses it form the phallic mushroom... characteristic of the parabolic umbilic...
6. the cusp meets the lower branch of the lip in a hyperbolic umbilic...
7. and then the two branches cross to form a curvilnear triangle piercing laterally a convex curve
8. the triangle shrinks, first touching the curve
9. and then shrinking inside it
10. to form a hypercycloid with three cusps, and finally vanishes in an elliptic umbilic..
11. reappearing immediately with the same orientation
12. its lower cusp meets the curve
13. and pierces it
14. the curve and upper edge of the triangle touch in beak-to-beak singularity, which separates
15. producing two symmetric swallowtails, reabsorbed into the curve
16. leading to the original configuration

Question to ChatGPT: Any effort to give mathematical expression to dance and its strategic implications could also benefit from the work on catastrophe theory by Rene Thom and his later focus (Traces of Dance: Choreographers' Drawings and Notations, 1994). How might Polti's set and the 36 stratagems then relate to Thom's Structural Stability and Morphogenesis (1972)

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Question to ChatGPT: Ernest McClain, In his study, Meditations Through the Quran: tonal images in an oral culture (1981), produces a hexagonal lattice array of 37 tonal values [reproduced above] as a development of his generative matrix mentioned in this exchange -- framing his commentary on the musical implications of Plato's Laws and the construction of the ideal city of Magnesia. Of interest is the potential correspondence of this 37-fold pattern to the 36-fold pattern of Chinese stratagems and the 36-fold pattern of Polti's dramatic situations. Could either of the latter be explored in tonal terms [Sophie Bourgault, Music and Pedagogy in the Platonic City, The Journal of Aesthetic Education, 46, 2012, 1]

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Strategic synaesthesia through multisensory pattern recognition

Question to ChatGPT: In the light of that response, the quest for the "pattern that connects" -- as yet unsuccessful -- may be inadequately framed through the focus on patterns perceived visually or through sound. The archetypal pattern may only be comprehensible as a whole through the pattern recognition facilities of the five sense in combination: vision, sound, taste, smell, touch. A key to their combination may be in the role of number in each case, as mathematicians could readily argue

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Question to ChatGPT: The response suggests that recognition and comprehension of the "pattern that connects" may be intimately related to the controversial recognition of synaesthesia -- and how it is entangled with number. This possibility could be reinforced by the as yet unexplained skills of Ramunajan, given his "sensual" relation to number.

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Question to ChatGPT: In the light of Ramanujan's creativity, there is a case for calling into question some constraining implications of pattern recognition. There is a misleading sense in which the "pattern that connects" can be experienced through detached observation. Its comprehension may by contrast require some form of dynamic engagement -- as suggested by musical improvisation (rather than repetition). Speculatively it might be imagined that meaningful engagement with such "organization" might be more comparable to playing an instrument, as discussed separately: Envisaging a Comprehensible Global Brain -- as a Playful Organ (2019). Should fruitful engagement with AI be more appropriately understood in such terms

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Question to ChatGPT: The response could be understood as overly general and lacking in guidance on the modalities suggested by understandings of the theory of harmony. In the base of such insight, the failure of conventional approach is illustrated by the World Parliament of Religion's unsuccessful initiative with respect to articulating and eliciting support for a Global Ethic

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The elusive pattern that connects may well be usefully understood as a pattern language most readily recognized by many through music, as implied by the work of Takashi Watanabe (Music Composition Patterns: a pattern language for touching music, Proceedings of the 27th European Conference on Pattern Languages of Programs, 2022, Article 31) and the approach of Thomas Schlechte (A Pattern Language For Composing Music, 2019).

Rather than the restrictive focus on the pattern that connects as an externality, the cognitive relation to music -- given its relation to mathematics -- merits exploration in the light of the arguments of George Lakoff and Rafael Nuñez (Where Mathematics Comes From: how the embodied mind brings mathematics into being, 2001). The case is all the stronger from any multisensory recognition of that pattern.

Ironically there is a case for recognizing a degree of analogy between the monochord and the spinal cord, as explored from the perspective of an osteopath by Antonio Ruiz de Azúa Mercadal (The Human Monochord, November 2017):

An analogy between osteopathic treatments and playing the guitar is presented by using and comparing the physical elements of both activities. The complex brain-spinal cord and filum terminate is compared to the string of a guitar and the human emotions are compared to the music being played by such an instrument.

Such an understanding is consistent with traditional understandings of the subjective implications of music as variously reviewed (Isabel da Rocha, Music, the Phenomena of the Universe and the Human Being in the Pythagorean tradition, International Lusophone Congress on Western Esotericism, 2016; Anthony Peter Westbrook, The Divine Vina and the World Monochord: musical cosmology from the Rg Veda to Robert Fludd, 2001). In contrast to the considerable interest in the monochord in relation to meditation and therapy on the chakras of Eastern traditions, the question is the future relevance of such metaphors to remedial strategies for the collective (Global Insight from Crown Chakra Dynamics in 3D? 2020).


Ralph Abraham:

Ralph Abraham and Christopher D. Shaw :

Gregory Bateson. Mind and Nature; a necessary unity. Dutton, 1979

Gregory Bateson and Mary Catherine Bateson. Angels Fear: towards an epistemology of the sacred. University of Chicago Press, 1988

Joachim E. Berendt. Nada Brahma -- the World is Sound: Music and the Landscape of Consciousness. Destiny Books, 1991

Bryan Carr and Richard Dumbrill (Eds). Music and Deep Memory: speculations in ancient mathematics, tuning, and tradition in memoriam Ernest McClain. Iconea Publications, 2018) [text]

Julyan Cartwright. Dynamical Systems, Celestial Mechanics, and Music: Pythagoras Revisited. 2020 [text]

Thomas Christensen (Ed.). The Cambridge History of Western Music Theory. Cambridge University Press, 2002

David Creese. The Monochord in Ancient Greek Harmonic Science. Cambridge University Press, 2010.

Leon Crickmore. A Re-Valuation of the Ancient Science of Harmonics. Psychology of Music, 31, 2003, 4 [text]

Antonio de Nicolas:

Marcus du Sautoy:

Kenneth Eggert. Musica Universalis: From the Lambdoma of Pythagoras to the Tonality Diamond of Harry Partch. Montclair State University, 2013 [text]

Douglas Hofstadter:

Douglas Hofstadter and Emmanuel Sander. Surfaces and Essences: analogy as the fuel and fire of thinking. Basic Books, 2011

Jamie James. The Music of the Spheres: Music, Science, and the Natural Order of the Universe. Springer, 1995

Robert Kanige. The Man Who Knew Infinity: a life of the genius Ramanujan. Charles Scribner, 1991

Jay Kappraff:

Johannes Kepler. Harmonies of the World.

Taliya Khafizova. Pythagoras Musica Universalis Theory in Global and Human Perspective [text]

George Lakoff:

George Lakoff and Mark Johnson.  Philosophy in the Flesh: the embodied mind and its challenge to western thought, Basic Books, 1999

George Lakoff and Rafael Nuñez.  Where Mathematics Comes From: how the embodied mind brings mathematics into being. Basic Books, 2001

Flora R. Levin., The Manual of Harmonics of Nicomachus the Pythagorean. Phanes Press, 1994

Ernest G. McClain:

Guy Murchie. Music of the Spheres. Houghton Mifflin, 1961

Athanase Papadopoulos. Mathematics and Music Theory: from Pythagoras to Rameau. 2002 [text]

Jordan B. L. Smith, Elaine Chew and Gérard Assayag (Eds). Mathemusical Conversations: mathematics and computation in music performance and composition. World Scientific Publishing, 2016 [review]

René Thom:

William Irwin Thompson:

Dmitri Tymoczko:

Ralph Waldo Trine. In Tune with the Infinite. Crowell, 1897 [text]

Anthony Peter Westbrook. The Divine Vina and the World Monochord: musical cosmology from the Rg Veda to Robert Fludd. Faculty of the Graduate School of the University of Maryland, 2001

F. Leighton Wingate. The Published Writings of Ernest McClain through Spring 1976. North Texas State University, 1977 [text]

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