Boylai and Guardjieff weigh in on Robert Gordon's 7 days

One might subtitle this, “Why there are no straight lines in nature.”  This is going to take a long time to get to the punch line.  For me, this component of the RG story became a personal epiphany which I do not here overstate.  For others who endure it to the end will find it a yawn, maybe someone will 'consume' it.  I don’t care because this is my journey.

Recall the Robert Gordon spreadsheet which tracks RG’s 22 stops in “7 days” and 20 intervals of distance in between.  Obviously, the number of notes and intervals, respectively, in the second scale of octaves according to Russell Smith.  In that spreadsheet RG travels 33,543 crow fly miles from east to west circumnavigating the Earth. I segregate the 33543 mile between the east to west miles and the north to south miles by both Haversine formula and by referencing distances according to popular distance calculators.  The E/W miles were 18213 miles and the N/S miles were 0 miles, net.  Here is the spreadsheet for convenience:

Let’s simplify the numbers with some rationale.  Gann intended that we find the E/W miles were 18842, not 18213 miles and N/S miles were 18842 miles, not 0.  Why?  Because at the latitude of the NYSE (the misspelled ‘Mammouth’ Building) is 40.7069* and the circumference of the Earth at that latitude is given by cos(radians(40.7069))*3956*3.14159.  [The E/W distance calculated on the spreadsheet differs from the theoretic value of 18842 likely because Haversine doesn’t perfectly compute spherical distance, nor does any method since the value of pi indeterminate.]  

Now, why is N/S distance 18842 versus 0 on the spreadsheet.  If you add the absolute values of the N/S miles you find 18495 miles, not 0.  The 0 is net miles.  And, once again, I propose that Gann wanted us to find the circumference of the Earth at the 40.7069* latitude since he devised RG’s trip to be so close to that magic number, 18842.  Both E/W and N/S were very close to the magic number…not a coincidence IMO.  Contrived for a point.

So, we have 2 revised distances.  That questions the third distance, the total trip miles of 33543 crow fly miles.  The spreadsheet found that, at only one point in the entire trip did the total miles equal the application of the Pythagorean theorem to the X and Y legs of the mileages….when RG arrived home.  At that point, the then used X and Y legs plugged into the theorem gave us a 33630 mile trip.  That’s pretty darn close to the actual miles of 33543.  Again, Impossible for me to conclude that Gann did not intend for us to find that Pythagorus did not contrive RG’s trip with this in mind.  Let’s refine that hypotenuse with Gann’s intended value of the total crow fly miles.  It is:

OMGosh, that didn’t work.  We needed to find something close to 33630 miles as the hypotenuse.  Need to remember, Gann gave us a ‘key’ on TTTA pages 400 and 401 of 100 / 60 = 1.6666.  When we found that hypotenuse of 33630 miles (that was validated by the actual miles of 33543) we had to measure N/S distance from the equator, not from the 40.7069 latitude.  And eemember, the 40.7069 latitude provided a net N/S 0 miles so that would wreak havoc on the Pythagogrean squaring.  So, we calc’d the total distances from the equator to the various stops as 47117 miles and backed that down to 28271 mile via Gann’s ‘key’ 100 / 60 or 1.666.  With X and Y legs of 18213 and 28271 miles (47117 'equator' miles / 1.666) the theorem gave us 33630 miles.  Try it.  Again, Gann contrived with a purpose.  That 100 / 60 key wasn’t just an accident IMO.

So, since Gann had to fake the N/S mileage by expanding it to the equator, how do we relate it to the true N/S miles.  Let’s see if there’s a bread crumb by dividing the 28271 by the theoretic N/S absolute miles (the circumference of the Earth) or 28217 / 18842 = 1.5004.  Can exactly 1.5 be a coincidence?  Don’t think so.

So here’s the final theoretic length of the trip according to Mr. P’s theorem:

All is now simplified.  We now have 2 legs of 18842 (one extended by a key of 1.500) and a hypotenuse of 33968.  [We also have a sphere of 18842 miles in circumference but that's for another day.  Hint, cube the sphere as opposed to square the circle.]  From this point forward, those are the values I’ll use for N/S mileage, E/W mileage and the crow fly mileage (18842, 18842 and 33968, respectively).  I hope I remember that.  A beautiful and perfect isosceles right triangle.  Gosh, that seems so very very wrong because RG’s trip zig zaged all over the map.  Nothing right about that!!!! 

Mssrs. Boylai, Guardjieff, what say you?  

Ahh, Mr. Jonas “Boy genius” Boylai?  Mr. B was obsessed with proving Euclid’s #5 parallel postulate from his childhood until his demise.  His writings as a teenager were commented on by Carl Friederick Gauss saying Boylai’s ideas on the the parallel postulate were those he’d harbored for many years.  Whereupon a firestorm of controversy erupted over the authorship of the concept.  Whether it was Boylai, Gauss or Lobachevsky that came up with the seed of non-Euclidian geometry is unimportant.  But their collateral proof (story) is instructional for our Robert Gordon trip.  Pardon the CPA description as they don’t teach this on the finite, linear CPA exam.  The parallel postulate states that two vectors intersecting a third vector at the same angle on the same side of the third line will never meet.   As the story goes (recollection), the parallel postulate is invalid when one draws two lines perpendicular to the equator and extends them.  As do longitude lines, they meet at the north or south poles.  Two parallel lines that meet…invalidating Euclid's 5th postulate.  Hence, we have non Euclidian geometry.  The 5^th postulate is correct only in planar Euclidan geometry.

And Robert Gordon?  He was, no doubt intentionally IMO, confined to ‘vibrating’ between the poles.  Violating the poles would interfere with Gann’s demonstration of the E/W mileage being a proxy for time.  Ponder that for a while.  I’m pondering it and it’s my ‘solution’ de jour at the moment.  It might be a naive and unsophisticated solution but its the best I have at the moment.

Where might Mr. Guardjieff stand on all this?  We have a perfectly circular/spherical straight line (not really contradictory in non Euclidian space when you think about circumnavigating the sphere) which is E/W 18842 miles long at the 40.7069 latitude or X axis.  And we have a perfect 18842 N/S miles, but it doesn’t cross the north or south pole so it’s impossible that it be circular/spherical.  Or is it?  Just as perplexing, we have a solution for a perfect isosceles right triangle (isosceles and right are redundant but lets live with that) but the Y axis is anything but straight.  What say you G?

G speaks: “Jimmy Jimmy, fear not.  Take a look at page 128 " of “In Search of the Miraculous by P.D. Ouspensky (whose “Tertium Organum” was on Gann’s reading list).

[I must insert a note here to underscore my complete shock/astonishment.  I recalled the below development of the octave and ‘no straight lines’ in nature in Ouspensky.  But I wasn’t ready to find it on Ouspensky's page 128.  Why is page 128 important?  Well, 128 is twice the value of what Cousto calls “the primary tone c”.  But that provides me minor amusement.  Please recall my claim that Gann introduced the Pythagorean diatonic scale on page 128 of TTTA and confirmed it with John Clifford’s poem of the blacksmith’s anvil on page 129 (Clifford, whom I believe, at the moment, to be Sir John Herbert Clifford, a contemporary of Gann and, whom I believe, at the moment, to have been a master Mason).  Gann refers to the diatonic scale on page 128 of TTTA and G relates the diatonic scale to the circle on page 128 of Ouspensky’s work not published until several decades later.  Coincidence of Humbolt kosmos?  Without any evidence beyond coincidence, I nevertheless think not.] 

On Ouspensky's page 128 you find the linear Pythagorean diatonic scale forms a circle.   When one creates a linear reflection of the diatonic scale ((it is inherently linear) you get an irregular ‘vibrating’ jerky line.  But, when you invert the angle at each ‘retardation’ pivot, you find that it will create a circle.  And here is the circle that G was said to have created for students and as published by Ouspensky:

G would tell us that all activities are, in reality, a circle, even though they do not appear to be a circle?  RG’s trip E/W was an obvious, very ratable circle around the equator; a planar slice of a sphere.  But the 18842 mile N/S counterpart of his trip was not an apparent circle…..but for, that is, the fact that Gann conceived/contrived it to be the same distance of the N/S circle; 18842 miles.  Again, too coincidental.

And my personal amazement cannot stop there.  So as G might explain Gann’s N/S mileage as circular in the RG trip, so echoes Gann of G’s reflection (a chronologic improbability as Gann published first by decades) on the circular nature of all things (TTTA pg. 76):

Many meanings in that paragraph; geometric, metaphysical, spiritual.  Powerful.

At some point, I expect this journey of mine to relate the proxy E/W mileage to time and N/S mileage to price.  For now, I remain awestruck. Will Gann's promises in his Foreword to TTTA be realized?

Jim