Towards a periodic table of ways of knowing -- in the light of metaphors of mathematics

Periodic Pattern of Human Knowing (Part #10)

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In the spirit of Gregory Bateson (Angels Fear: towards an epistemology of the sacred, 1988), this theme is explored (in Annex 1) as an exercise based on assumptions detailed there in relation to:

• Towards a periodic organization of the Mathematics Subject Classification: use of the Mathematics Subject Classification (MSC) as implying a form of periodic table of mathematial ways of knowing, suggesting the possibility of "groups" and "periods". In contrast with the (above-mentioned) preoccupations of mathematical knowledge management regarding access, the emphasis is placed on employing the insights of mathematics into order and relationship so as better to configure the map as a whole -- if only to enable neophytes to navigate the terrain and discover territory they find meaningful..
• Mathematics and metaphor: cognitive understanding of mathematics, as indicated above (Origin of mathematics and the periodic table -- in human cognition?), The topic has been variously explored but it is useful to distinguish some possible "flavours", since some may be far from implying others. Annex 1 therefore cites authors distinguishing: Mathematics as metaphor, Metaphors of mathematics, Mathematical metaphors
• Associating metaphor with formal representation: the I Ching of Chinese culture: the mathematically interesting pattern of hexagrams of the I Ching of Chinese culture. The specific relevance here being the fact that metaphors are associated with the elements of the pattern to facilitate understanding of each and of the pattern as a whole
• Comprehensive set of ways of knowing: the All-Embracing Net of Buddhist culture: Of great relevance to explorations of any ordering of ways of knowing is that formulated in the Brahmajala Sutta. This is considered to be one of the Buddha's most important and profound discourses, weaving a net of sixty-two cases capturing all the philosophical, speculative views on the self and the world (Bhikku Bodhi (Tr). The Discourse on the All-Embracing Net of Views; the Brahmajala Sutta and its commentarial exegesis. Kandy, Buddhist Publications, 1978).

The emphasis on the cognitive dimension, and the processes and modes of learning, also suggests that in effect such a periodic table (informed by mathematical insight) could be understood as a "periodic table of metaphors". This has a notable justification in that the originating insight for many mathematical innovations typically takes metaphorical form. Such a table therefore provides a vital link to the process of "doing" mathematics in contrast with focusing on the use of what has been formed by others in the past. The "elements" of any such table are then to be understood as generative metaphors "through", or "out of", which ways of knowing are framed.

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