Chinese articulation of magic square insight

Salvation Enabled by Systemic Comprehension (Part #5)

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Histories of development of magic squares make repeated reference to their first recognition in China as the Lo Shu square (Schuyler Cammann, The Magic Square of Three in Old Chinese Philosophy and Religion, History of Religions, 1, 1961, pp. 37-80; Frank J. Swetz, Legacy of the Luoshu: the 4,000 year search for the meaning of the magic square of order three. A K Peters, 2008).

Juxtaposition of Lo Shu square with conventional 3x3 magic square (images from Wikipedia)

Their representation within that culture necessarily transcends the conventional Western distinction between numbers and letters, given the nature of the script. Of particular interest is the transformation of the Lo Shu square into the long-valued Ba Gua pattern of 8 trigrams, with its extensive metaphorical associations typically expressed in poetic form, elaborated further within the I Ching of 64 hexagrams.

The following correspondences feature in an extensive discussion by Quincy Robinson and Paul Martyn-Smith (Evidence of Modern Physical Knowledge from Asiatic Antiquity: Re-integration: Nine Realms of Middle Earth, 2015).

Correspondences between Lo Shu, Ba Gua and 3x3 magic square patterns

In considering the relevance of Chinese cultural insights, there is a strong case for recognizing the associated subtlety, as helpfully articulated in texts regarding the Literati Tradition (The Origins of Chinese Philosophical Thinking; Analogical Understanding and Translation; The Conceptual Scheme of Chinese Philosophical Thinking).

With respect to analogical understanding, the concluding argument made is:

Beyond the good intentions of missionaries and sinologists, and the increasing awareness of divesting interpretations of Chinese philosophy of Western preconceptions, the recent archaeological findings challenge the authority of existing translations on Chinese philosophical thinking. To the extent the newly unearthed texts written on silk scrolls and bamboo strips now provide us with a compelling clarity to the over all Chinese cosmology, and thus enable us to understand Chinese philosophical thinking in a way that has not been possible before. Frederick Mote notices that Chinese history, culture, and people's conceptions of their ideal roles all must be explained in terms of Chinese cosmology, and not -- if we really want to understand Chinese civilization -- by implicit analogy to ours... hence, the records of Chinese culture must be interpreted, and the texts translated and retranslated until our inadvertent uses of historical and cultural analogy are detected, weighed, and if necessary, corrected....

However, one cannot divest the Western interpretations of Chinese culture of Western cultural analogies simply by translating and retranslating the texts, nor can one do so by using the more abstract and specializing -- no less culturally biased -- language of the professional philosopher. Sarah Allan suggests that one must begin by exposing the metaphors that underlies the Chinese terminology and imbue it with meaning.... In other words, one begins to understand the conceptual scheme of Chinese philosophical thinking more accurately by recognizing the conceptual scheme of Chinese thought, or "the root metaphors" within the socio-cultural contexts from the viewpoints of not only historical and epistemological but also anthropological perspectives, and aesthetic and literary criticism.

Of some relevance to these points are the arguments of Martin Svensson Ekstroem (Illusion, Lie, and Metaphor: the paradox of divergence in early Chinese poetics, Poetics Today, 23, 2002, 2, pp. 251-289).

As discussed separately, the term "correlative thinking" was a characterization of Chinese thinking by Joseph Needham (History of Scientific Thought, 1956). It referred to a general propensity to organize natural, political/social, and cosmological information in highly ordered arrays or systems of correspondences. His characterization was very influential as a subsequent focus of sinological studies. (A C Graham. Yin-Yang and the Nature of Correlative Thinking, Singapore Institute of East Asian Philosophies, 1986). A degree of equivalence is now to be found in the Western expression "joined-up thinking", as articulated by Stevyn Colgan (Joined-Up Thinking, 2008).

Related arguments have been developed by Susantha Goonatilake (Toward a Global Science: mining civilizational knowledge, 1999), as discussed separately (Enhancing the Quality of Knowing through Integration of East-West metaphors, 2000).

To what extent are the UN Sustainable Development Goals a reflection of correlative thinking -- any more than the pattern articulated in Agenda 21 (1992)?

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