A Christmas error, a gift and the final unwritten riddle of Robert Gordon

Last week I floated 25207 as the DJIA but dithered on a date, suggesting, perhaps "Tax Tuesday" as the day.  I had not proven the math and, at that point, I said that.  It was my perma bear speaking, my pathologic subjective poetic nature as opposed to the objective mathematic path I should follow.

Yesterday I promised a date based on perfected math, and the math was and continues to be beautiful.  But that math is not complete as I realized last night.

There remains an unresolved mathematic issue which, in "Robert Gordon's seven days," is a "riddle within a riddle."

The previously perceived perfect math:

Having believed I'd found the 'idealized circumference of spheroid Earth' at 24821, I stumbled into projecting a date for when that price interval would be achieved (note that the projected top is 25207 which differs from 24821 by the previous top of 386....24821 is the "distance projected to have been traveled since September 3, 1929).  Logically, the date is determined by the Kepler triangle, the only geometric structure that "squares the circle," approximately as it is.

How can one construct a Kepler triangle if we have only say, September 3, 1929 and some future date?  Isn't that how we so often try to reckon chart distances between an historic point a projected future point?  You can't do that.  Two points do not a triangle make.

So I created a Kepler triangle envisioning the endpoints of the Great Depression's highest high and lowest low.  One point for the price point of the highest high and one point for the time point of the lowest low.  For the price (space) I inserted what, in a previous essay, I back fitted to be the idealized circumference of spheroid Earth.  I then computed the product of 24821 by root Phi to create the second side representing the radius of time, that being 31573.  With two sides and the given 90* the final side is the Pythagorean calculation of the hypotenuse, computed to be 40161.

The "perfect math" date and time would be DJIA 25207 on December 17, 2018.  I say "perfect math" facetiously because it is a long way towards a solution, but it is not perfect.  It provides a different date for every different price (space) you insert in the above Kepler triangle.

Still, it is beautiful math; from the sides you can create virtually every one of the great geometric numbers.  You can create Phi, Euler's constant, root 2, root 3, root 5....  Your plate is full.

And Pi, where is Pi?  It is there.  Take the value of time or 31573 and divide by 10000.  You have 3.1573, Pi within .5% of Pi at 3.1416 (3.1573 / 3.1416 = 1.00497).

But today isn't without a mathematic gift.  Isn't that incredible, in plain sight on the insert above, we have the spatial displacement that is integral to our calculation of time (the equator of the earth at 24821) and the time factor that relates space to time.  We have both spheroid earth's equatorial circumference that defines the perimeter of the square of space and Pi that relates the radius (derived from the former by root Phi) to the circumference of the circle of time.  [As a note, the circumference of the circle and perimeter of the squares implied by the above Kepler triangle is 198378 and 198568, respectively, a minor difference in dealing with two transcendental numbers, those being root Phi and Pi.]

Such beautiful math...so where's the problem?  The problem leads to the final unwritten riddle of Robert Gordon.  The problem is the Kepler triangle gives us a set of paired values for space and time, not a single unique pair.  I can insert an equatorial value of 24822 instead of 24821 and behold, I have December 18, 2018 instead of December 17.  We have sloped line of paired values, not dissimilar in nature from say the 45* angle.  Which of the infinite pairs is the "one" solution of when and what price the DJIA tops?

The final riddle of Robert Gordon's seven days.  Robert completed a 360* circumnavigation of Earth, having departed from New York City, when he arrived in Montreal...exactly 7 days later.  He began at a certain longitude traveling east/west, and he exceeded that longitude (by a negligible degree) when he arrived in Montreal exactly 7 days later.

Robert's seven days were complete according to time on arrival at Montreal.

But the entirety of his journey was not complete; it would be 331 additional miles for Montreal until he arrived in New York City.  At 7 days plus 5 hours, his journey in distance was complete.  His trip was complete according to space when he arrived in New York.

In accounting, my life's career endeavor, there is always a final proof of the integrity of the accounting system of aggregation; a final balancing of debits and credits.  Nothing can be lost.  The solution is exact.

Similarly, there is only one answer to Robert Gordon's trip...when it ended the two-dimensional Pythagorean calculation (red arrow) of the hypotenuse of east/west and north/south values equalled actual crow fly (blue arrow) distance:

At any stop Robert made along his trip, that "Pythagorean equivalence" did not exist.  Only after time had ended (in Montreal) and space had ended (arrival in NYC) did the Pythagorean equivalence emerge.

That worked for Robert Gordon, but in the DJIA we still have an infinite supply of paired space and time points that all satisfy Pythagoras' formula in the Kepler triangle as applied.  We don't have a "crow fly" distance against which we can compare the third side of the Kepler triangle.

What then is our final proof?  The final balancing of the ledger's debits and credits?

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I have a date to watch, 25207 on December 17, 2018.  My initial inclination aforementioned as the perma bear and given the proximity of the current highest high of the DJIA of 24834 to the previously suggested 25207....well, how could we not reach that level post haste?  It's just gotta work that way, said facetiously.  That's the subjective me looking for the poetic ending, not the mathematically determinative perfect or correct ending.

The math, which, presently, is not perfect, suggests DJIA won't reach 25207 in the immediate future but not for almost a year from now.  If that date and time is the true, we have a year of chop, at best.  At worst we have a deeper decline and recovery to form a one-year double top.  But I remain unsatisfied with the math lacking a final proof.

What will be the final proof of the market?  I believe it will be found in the Biblical concept of Jubilee.  A concept that Mr. Gann discusses at length and far beyond my confusion point in "The Tunnel Thru the Air,"  Jubilee seems to begin when "time runs out" and, perhaps, without space having completed its journey.  An interim of "atonement," perhaps...or of "reconciliation" in the accountant's world.  Just as Robert ended his east/west journey and his seven days, he still had to travel in space another 331 miles to arrive at where he began; New York City.  That 331 miles is the as the 1 year of Jubilee to the previous 6 or the 1 year as to the previous 49.

That 5 hour, 331 mile final leg is the final riddle of Robert Gordon's seven days.  I believe Mr. Gann intended that we frame that final riddle without having to read it in the Foreword.

Have a Merry Christmas,

Jim Ross