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Mathematical theology enabling the quest for a meta-pattern?
Meta-pattern via Engendering and Navigating Pantheons of Belief? (Part #5)
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Role of number: In the desperate quest for global coherence and harmony, it is strange to note the manner in which number seems to play a central role in seemingly unrelated modes:
- in the constraints of human comprehension and the memorability of articulations of fundamental principles and strategic initiatives
- in the preference for patterns or pantheons of meaning of particular size, with no explanation as to the choice made
- in the role of music as the primary discipline in ordering patterns meaningfully, memorably and attractively for many
- in the mathematical disciplines assiduous in their study of highly complex patterns of relationships, irrespective of whether their insights can be rendered meaningful to many or to the governance challenges of the times
- in the enthusiasm of many for particular patterns of numbers, deprecated as pseudoscience and superstition by the relevant disciplines, despite determining seating arrangements in important negotiations or in the design of buildings
- in the importance attached to number, proportion and symmetry in architecture, design and symbolism, whether or not framed in terms of sacred geometry
- in the importance to the theology of different religions of particular patterns of numbers -- as they may indeed govern the sacredness of geometry
With respect to the challenges of governance, and to any understanding of the global unity to which reference is so frequently and glibly made, it is then appropriate to ask: how is "unity" to be understood? This is especially the case within a global civilization in which there is also considerable preoccupation with the respect for diversity and its implications for individual and collective identity.
Unfortunately it is only too easy to recognize that appeals for unity are simply and naively a disguise for exhortation to agree with "my plan", or "our plan". (Rebekah Koffler, The Words that Undermine Biden's Call for Unity, White House Dossier, 21 January 2021; Exhortation to We the Peoples from the Club of Rome, 2018; Adhering to God's Plan in a Global Society: serious problems framed by the Pope from a transfinite perspective, 2014). It is however remarkable how global consensus has been achieved in response to the pandemic with respect to social distancing (Humanity's Magic Number as 1.5? Dimensionless constant governing civilization and its potential collapse, 2020).
The interrelationship between the distinct modalities of appreciation of number (as listed above) could indeed be explored. The challenge is of course that as distinct modalities they could be held to constitute a pantheon governed by an elusive meta-pattern -- one potentially perceived as alien by each. Those identified with each mode would readily tend to promote their particular relevance to eliciting such a meta-pattern -- to the extent that they recognize the possibility of its existence.
Mathematical theology: Given the primary association of pantheons with religious belief, and despite the secularisation of belief systems, there is a case for exploring the challenge of emergent "unity" (and the nature of any "meta-pattern") through the seemingly improbable discipline of mathematical theology. The possibility is discussed separately in terms of self-reflexive global reframing to enable faith-based governance (Mathematical Theology: future science of confidence in belief, 2011; Bibliography of Relevance to Mathematical Theology, 2011). Relevant commentaries include;
- James Bradley: Theology and Mathematics: an introduction (Theology and Science, 9, 1, 2011)
- Philip J. Davis: A Brief Look at Mathematics and Theology (The Humanistic Mathematics Network Journal Online, 27, 2004)
- Hitoshi Ochiai: Mathematical Theology (Sekaishisosha, November 2009)
- W. J. Eckerslyke: Theological Mathematics (WikiInfo, 11 January 2009)
- Rebecca Newberger Goldstein: Mathematics as Theology (Dialog -- Philoctetes Center), 1 December 2009)
- Sarah Voss: Mathematical Theology (Spiritual Information: 100 Perspectives, 2005)
- Edward A. Maziarz: Meta-mathematics and Meta-theology: an inquiry (Philosophia Mathematica, 1975, 2)
- J. R. Lucas: Mathematical Theology (Oxford Scholarship, 1970)
As implied by the above argument, any initiative in quest of a meta-pattern would be expected to engender a pantheon of contrasting modalities and mutually challenging dynamics. Its method, however institutionalised, would indeed be a metaphor of its own preoccupation, as envisaged separately (International Institute of Advanced Studies in Mathematical Theology Enabling Proposal for Faith-based Governance, 2011):
Self-referential quest? With respect to such a grail-like collective quest for transformative, integrative insight, the initiative might be provocatively enriched by the symbolism of the traditional Sufi tale of The Conference of the Birds (Mantiq al-tair) by Farid al-Din Attar. In their collective pursuit of that transformative understanding -- a transcendent theory of everything -- each of the 30 birds in that tale has a special significance, and a corresponding didactic fault. In reaching the expected goal -- the land of the mythical Simurgh -- all they see there are each other and their collective reflection in a lake. "Simurgh" actually means "30 birds" in Persian -- potentially to be understood as a dynamic form of pantheon.
It might then be asked whether the Sustainable Development Goals of the UN would have been of greater global significance had they taken the form of a 30-fold pattern -- corresponding to the 30-fold articulation of the Universal Declaration of Human Rights.
Pantheon of mathematics? Of peculiar relevance to this argument is the degree to which mathematics can be understood as an extreme form of detachment from personal belief -- in contrast to the preoccupation of theology as the extreme identification with belief. Both extremes pose a challenge with respect to the organization of meaning.
Paradoxically, despite vigorous assertions of impersonal objectivity, many mathematical innovations are named after their discoverers -- who have become the icons of that discipline. That seeming contradiction is exemplified in the so-called "folklore" of mathematics by recognition of the Erdos number, namely the "collaborative distance" between mathematician Paul Erdös and another mathematician, as measured by authorship of mathematical papers.
The "icons" of mathematics are readily recognized and may even be said to belong to the "pantheon of mathematics" in any non-mathematical description of the psychosocial system of mathematicians -- however irrelevant this may be held to be from a mathemaical perspective. From that perspective it is appropriate to note the existence of an online database named Pantheon. This project uses biographical data to expose patterns of human collective memory.
Pantheon has one dataset -- effectively a Pantheon of Mathematicians -- profiling 828 people classified as mathematicians born between 500 BC and 1988. Thr focus of the dataset is on the geographical associations of the mathematicians (birth, death). Together with the period they were alive, this is the only concern with how they might be considered to be related as a social system. There is no indication of how their mathematical preoccupations might be related in defining mathematics as a system.
Citations as framing an emergent meta-pattern? It might be assumed that the relations between mathematical papers -- through the vast network of citations -- would offer a more systematic understanding of mathematics as a whole. The major difficulty is that there are multiple citations databases with problematic coverage of the literature as a whole (Best citations database, MathOverflow).
A major complicating factor for any systemic comprehension is the manner in which ranking of journals and papers is taken into account (Citations of Mathematical Journals). This is most evident with respect to any notion of an impact factor, namely a measure of how many times an academic journal article or book or author is cited by other articles, books or authors -- but potentially biased by the coverage of that citation index and its selection of journals.
Perhaps remarkably, rather than endeavouring to recognize mathematics in systemic terms, the American Mathematical Society frames the practice of mathematics in non-mathematical terms as a "culture" (The Culture of Research and Scholarship in Mathematics: citation and impact in mathematical publications, American Mathematical Society: Committee on the Profession). In that valuable clarification is noted:
A scientist's publication record is the basic "statistic"' on which promotion, salary and funding decisions are made. In many fields the number of citations to a work, the order of authorship, and impact factor of the journal, are used as proxies for expert evaluation. For a variety of reasons, mathematicians have not embraced the impact factor as a reliable indicator of a journal's quality. Indeed, there are documented cases where unscrupulous editors have dramatically inflated the impact factors of entirely undistinguished journals...
Several issues combine to require careful consideration of publication cultures before understanding and using citation statistics in Mathematics... Citations tend to be focused and targeted to specific required results rather than being used as a broad survey of the field.... These citation practices may contribute to the relatively low impact factors of even the most prestigious mathematical journals, as compared to those in other fields.
The degree to which current practice is dissociated from any systemic understanding of mathematics is further clarified by the report of a Joint Committee on Quantitative Assessment of Research from the International Mathematical Union (IMU) in cooperation with the International Council of Industrial and Applied Mathematics (ICIAM) and the Institute of Mathematical Statistics (IMS): Citation Statistics (2008).
The situation is also complicated by differences within subdisciplines of mathematics:
Variation of citation counts by subdisciplines within a particular discipline is known but rarely systematically studied. This paper compares citation counts for award-winning mathematicians in different subdisciplines of mathematics.... We find a pattern in which mathematicians working in some subdisciplines have fewer citations than others who won the same award, and this pattern is consistent for all awards. (Lawrence Smolinsky and Aaron Lercher, Citation rates in mathematics: a study of variation by subdiscipline, Scientometrics. 91, 2012)
Further insights are offered by Keith R. Leatham (Observations on Citation Practices in Mathematics Education Research, Journal for Research in Mathematics Education. 46, 2015, 3). One notable factor is the often extreme delays in publication in "high impact" journals compared to the rapidity of publication in other media which may not be covered by citation indexing. Somewhat ironically the coverage by Google Scholar may be deemed more comprehensive than other facilities -- although deprecated as "tainted" by the absence of effective peer review.
Notably missing from a systemic perspective, no distinction is made between citations implying a development of what is cited -- namely supportive of the earlier articulation to some degee -- in contrast with any implication that that articulation is obsolete, misleading, or even dangerously incorrect. Such an omission precludes recognition of how contrasting perspectivess might complement each other in enabling the emergence of a more inclusive perspective . This is especially the case if citations of relevant studies are ignored or omitted for reasons which will prove to be historically questionable. Myths highlight the dynamics of support and opposition between the deities of any pantheon understood in systemic terms.
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