Plimpton 322 -- & U

Turning To The Wheel of Consciousness

To Resolve an academic dispute


by Sid Thomas, Ph.D.



A dispute has broken out in academiia over what is communicated as mathematical knowledge by the 1800 BC Babylonian tablet known as Plimpton 322. The interpretation of O. Neugebauer, exploded on the learned world in 1945 as proof the Sumerians knew the mathematics of Pythagorian triads, was challenged as incongruent with the background knowledge. The details can be found on-line.

Some historians have noticed that (1) each first column entry is the square of the cosecant of an angle of a right triangle, and (2) the associated angles are roughly one degree apart. So they have suggested that this is a trigonometric table of squares of cosecants for 45° down to 30°. This would be the earliest instance of cosecants by millennia, and the earliest instance of a trigonometric function by over a thousand years (the first trig function being the chord of an angle). It would also be the earliest instance of degree measurement by over a thousand years. In other words, that's a bold claim. A weaker claim is that the table was constructed to make the first column uniformly decreasing.

*****

One way of approaching the issue is by reconstructing a TokenSpace background common to both ancients, Pythagoreans -- and "us": those informed by the historical continuity of these fundamental and profound relationships.. Numbers (in cuneiform); in ennumerated vertical columns; each column extending left-wise in rows of number clusters; the heading of the three columns of rows as "width", "length" and "diagonal": That is what Plimpton 322 is.

This could also, abstracting these structural elements from the particular numerical values which are sometimes hard to follow, be taken as the schema of a succession of predicate-levels -- if the rows of individual dimensions of objects are successively contained (subsumed, as the points in one class include those of others, matching themselves, matched by in the container. This way of generating doubles (1-1 correspondences) from doubles (assuming a starting point of name-thing; consciousness-brainstate), through the series of containers (1-1) ->2 -> 3 -> 5 -> 8 -> 13, can be mapped onto the Fibonacci rectangles, yielding the expanding spiral line dividing each successively. This imaginary line may be arbitrarily terminated, and related back to the point of origin as "centre" after six steps, to the 7th square after 1. (set off-center, the spiral becomes a variant of the letter "G", matching its imagined reverse-fold (back-to-back) opposite in mirror TknSpc). This yields the schema of a line connecting the circumference of a circle through an accellerated rate of increase from its center, assuming all segments are traversed simultaneously (as concentcric rings of 7 similar equal stages)

These hypothetical simultaneously given concentric rings are orbits in Tokenspace Quadrants under seven levels of predicates, from lowest: 1 -the orbit of the neurophysiological world, passing over into the psychosemiotic level of dream consciousness; to 7 - the orbit-container of (the) God(s) of the sky and kingdom of heaven.. These are the antipodes of awareness spanned by Sign uses on the Wheel of Communication

http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html#spiral