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Finger signs and finger notation

Handing Over: Handy metaphors for the communication of intent (Part #14)

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The relation between numbers and finger signs in many cultures is helpfully summarized by Claudia Zaslavsky (Excerpts from World Cultures in the Mathematics Class, International Study Group on Ethnomathematics (ISGEm) Newsletter, 6, 1, November 1990). Finger signs were necessarily vital to arithmetical calculation in antiquity -- from which the term "digits" derived (Eva Matthews Sanford, De Loquela Digitorum, The Classical Journal, 23, 8, May 1928, pp. 588-593) as well as finger notation (J. Hilton Turner, Roman Elementary Mathematics, The Classical Journal, 47, 2, Dec. 1951, pp. 63-74 and 106-108).

The transition to modern notation, the introduction to Europe of the Hindu Arabic positional decimal system for writing and manipulating numbers, as articulated in 1202 by Fibonacci (Laurence E Sigler, Fibonacci's Liber Abaci: a translation into modern English of Leonardo Pisano's Book of Calculations, 2002) and reviewed by Serafino Cuomo notes that:

Multiplication, and later division, require the "keeping in hand" of numbers (today's "carrying"); both come across as very physical operations involve memory, writing, and the fingers (which function as an extension of memory).... At the beginning Fibonacci refers to the subject at hand as a scientia, yet throughout the book he talks of ars. The scientia in question is in effect profoundly practical because it has to be achieved through exercise... "for science by practice turns into habit ; memory and even perception correlate with hands and figures, which as an impulse and breath in one and the same instant, almost the same, go naturally together for all; and thus will make a student of habit."

Given the possibility of extending the pattern language methodology of Christopher Alexander (A Pattern Language,1977) to psychosocial patterns (cf 5-fold Pattern Language, 1984), the set of mudras is worth considering as a pattern language with the particular advantage of having been successfully adapted to popular dance and theatre -- itself associated with the dramatized martial art of Kalaripayattu in Kerala. Also of relevance is the two-person Pushing Hands variant of T'ai Chi Ch'uan and Pa Kua Chang, through which practitioners become acquainted with the principles of what are known as the "Eight Gates and Five Steps," enabling them to handle the variety of problematic situations involving an other. In the metaphysical vision of ancient Japanese esoteric Buddhism, mudras constitute the patterns of change, whereas mandalas define the essential structure (Thomas Kasulis, Japanese philosophy, 1998 Routledge Encyclopedia of Philosophy). In the rituals of Hinduism mudras are part of a system which employs both body and mind, and makes the former express and emphasize the intentions of the latter [more].

Also of potential interest is the relationship of mudras to "five-element theory" and practice (in China and Japan), as fundamental to an enhancing cycle, an exhaustive cycle, and a destroying cycle in feng shui, qi gong, medicine, acupuncture and the martial arts (cf The Book of Five Rings). It would be ironic if such five-foldness proved to be a cultural bridge between both seemingly disparate disciplines and between the seeming differences between East and West -- notably in the light of isomorphism between the hand, Leonardo da Vinci's Vitruvium Man, and the problematic significance attached to the pentagram in esoteric traditions.

A number of these issues are brought together in an exploration by Dennis Goldwater (Evolution through the Dimensions of Time and Space, 1998-2005):

Our species understands the stages in the cycle of evolution as dimensions. Our species, with its 5 senses and its 5 fingers per hand, has evolved to the awareness of 5 dimensions of time and space.... The existence of each of the dimensions of time and space can be comprehended by the mind only in relation to a simultaneous awareness of the existence of a corresponding dimension of space or time. In other words, space and time are understood by the mind in terms of 5 dimensions, each of which is a dimension not of space alone or of time alone, but of space-time: We live in a world of awareness of 5 dimensions of space-time.

Because everything in nature follows the same cycle that is evolution, if we could discover any one avenue by which to better understand the stages in the cycle of evolution, we would better understand all manifestations of the cycle. I have developed an extremely simple, yet extremely powerful model of space and time, wherein I explore in detail two such avenues of understanding, the evolution of finger signs and the evolution of the languages of our species.

Finger signs are relationships among the fingers that mankind progressively recognized that enabled our species to become aware of and to symbolize the dimensions of space-time on the body. [emphasis added]

In his complementary exploration of language, Goldwater notes:

The grammar of Chinese guides its speakers to develop a single, unified model of nature, known as the Dao. The Dao is the Chinese model of the 5 stage cycle of evolution. Each of the stages of the Dao is explored in great detail, and is compared with the corresponding stage for the speakers of English. This includes the Chinese symbolism on the fingers of their awareness of space on the earth and time in the heavens (day, month, year) as their ancestors successively evolved to the awareness of each of the 5 dimensions in the cycle of evolution. The symbolism behind the concepts of the Dao, Yin and Yang, the Ba Gua, and the 5 Elements is discussed in great detail. [see also finger representation of Tao]

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