Robert Gordon's 7 days - Pythagoras Theorem and Gurdjieff''s Diatonic Scale

With yet further minor corrections and with all 'pivots' in RG's trip (all 21 locations with NYC counted twice as beginning and end), here is the further evolved version which I believe Gann intended to convey:

To understand the derivation of the above requires understanding of Pythagoras' Theorem, Pythagoras' diatonic scale and dynamics of the octave as taught by Gurdjieff and explained by Russell Smith and spherical distance computation according to Great Circle methods.

The yellow highlighted fields indicates the actual miles traveled reconciled, or 'squared,' to distance computed by the Pythagoras Theorem on the very last leg of RG's trip.  Theretofore, those distances did not 'square.'  The blue highlighted fields indicate the trip that began at DO-DO-Do-do 7 days earlier had arrived at the highest level of the nothing to all (0 - 2^15) diatonic scale at SI-SI-Si-si (in blue).  Both Pythagoras Theorem and the final position registered on the diatonic scale suggest the cycle that began on July 20, 1932 completed 7 days later.

[As a side note, the green highlighted field indicates the sum of the East/West mileages closely equals the sum of the absolute value of the North/South mileages and thus two sides of a square were complete.  Further, the sum of the East/West mileage roughly equaled the circumference of the Earth at the 40.7127 latitude.  The difference is believed the result of the approximation method of the haversine formula.  The red highlighted fields indicate 'oscillating do's' according to the teachings of Gurdjieff.]

In my opinion, there are greater insights to be had than those illustrated above.  The above is only a beginning.

Jim