Current Market: Mathematic perfection

You've seen my struggle with finding the elusive "point E;" the top of the market since the 2000 top.  I believe it is determinable but I cannot discern the laws of math that make it so.

If point E is determinable, then there must be math.  It doesn't start with proving point E.  We already have completed two dimensional formations that can be evaluated mathematically to see if they follow the mathematic laws of the 1X1 square and the two adjacent 1X1 squares.  We have those formations in the current market; square ABCD and twin squares forming the rectangle ABGH:

ABCD doesn't look like a square and ABGH doesn't look like a rectangle comprised of two such squares.  That's because the proposition is the structures are four dimensional solids being viewed on a two dimensional chart.  Or, that's how the story goes.  Supposedly, the math will tell us the truth where our vision is unable to sort out the truth.

A very limited objective of this essay; is ABCD a square and is ABGH a rectangle comprise of twin adjacent squares.  If the diagonals of ABCD is not root 2 (1.4142) of the side and/or if the diagonals of ABGH is not root 5 (2.2361) of the side, then further inquiry is, likely, unwarranted.

The above insert is drawn using software that computes the Pythagorean Price Time Vector ("PTV") value as described in previous essays.  Its calculations are dependent on how closely a visual fit of the vectors can be made.  We need more accurate measurements.  Following are the measurements:

The black bolded solid lines are "real vectors"  On either end, they have points of price and time that have occurred.  The grey lines have at least one end point that has not occurred in price and time; they are imagined and not a subject of this essay.  

Seeming hit or miss mathematic relationships.  Analysts tout their great insights by pointing out, "aha, PTV CD divided by PTV AB is within two one hundredths of the root of Phi."  Or "AC divided by AB is within two one-hundredths of the number 2 and WD Gann had a thing about doubling and halving time or price."  That does it, a couple isolated observations and we all think its magic...and we buy that book or course.  Not that they aren't mathematically related, but they hardly create mathematic structure.  On the other hand, I believe each of the ten PTVs are related to every one of the other ten.  Its just that we have to go very deep into the several steps that comprise the relationships.  I've done a lot of that and found several three deep relationships.  Three deep where say three mathematic metrics such as root 3, root 5, Phi are required to explain the difference between two PTVs.  Pass on that for now.  Just realize you may see PTVs that are apparently related by a known math metric.

Root 2 and the square ABCD.  I've overviewed this before with PTV values that were created by the charting software as opposed to rigorously determined PTV values.  The above table removes any doubt:

The diagonals of the 1X1 square are 1.4142 (root 2) times a side of 1.  That's law.  If you add the four PTVs that comprise the ABCD square take their average side value and divided it by the average diagonal the result is 1.407536 or .47% less than ideal root 2.  

If you divide the sum of the four side of ABCD by the sum of its diagonals the result is .47% greater than ideal root 2.

And the two calculations averaged are within .001% of of ideal root 2.   

I've asked before, can that be coincidence?  But it doesn't end there.  There is a second real configuration that we can evaluate; the double square.

Root 5, root 3 and the twin adjacent cubes.  The "law" is that the diagonal of adjacent 1X1 squares sharing a common side will have diagonals that are root 5 times the square of one side.  As the contemporary thought goes, "but its complicated."  

We can do this lots of ways.  Above we find the ave side of 1448.72 divided by the ave diagonal/root 5 is 1.315420.  Or we can divide the average side by the ave diagonal to yield .5882739 and multiply by root 5 to again arrive at 1.315420.

But 1.315420 is not the root what we expected.  We'd already buried the root 5.  We should have gotten the number 1, not 1.315420.

No, that's where it is complicated.  We have the fourth root of 3.  Recall the primer essay on geometric solids; 3 is the center diagonal of the three dimensional 1X1X1 cube.  Square 1.315420 and square it again and you have the number 3.  If you leave the calculation at root 3, you find that it is within .001% of ideal root 3.

Is that coincidence?

Morphing two dimensions into an allusion of three dimensions.  With all this in mind, take another look at the market chart.  We have a two-dimensional square near to and facing but it does not "look" like a square.  Nevertheless, the math demonstrates the hallmark mathematic property of the square; its root 2 diagonals.  Not just close...but to 5 decimals.

Now look at how the visibly appearing further away, twisting and receding rectangle ABGH morphs from vertical side AB to vertical side GH that now appears far away from us.  Over that distance, both the two dimensional metric root 5 and the three dimensional root 3 have interceded to create the vector GH; a vastly diminished reflection of its opposing edge AB.

 Evolving mathematic metrics.  Its very unsatisfying that vector AC divided by AB is 2.02132.  We want it to be a perfect 2.00000 to demonstrate the doubling and halving of time, the innermost working of the root 2 growth spiral.  But it isn't.  Probably every one of the vector relations is imperfect even to the point we doubt they are what they are.

But when we aggregate them and look for the expected value, the metric we seek becomes more accurate.  To wit, the ave side of ABCD divided by the ave diagonal, we get close to ideal root 2.  Then, if we reverse the process with the gross sides divided by the gross diagonals, we get another measurement that's close to root 2 but in the opposite direction.  Still further, when we average the two measurements, we are off from root 2 by less than 4 significant digits.  

Yet one step further.  The 4 significant digit error in the root 2 measurement of the ABCD square seems to be offsetting to the 4 significant digit error of the twin adjacent squares of ABGH.

Which leads to the question previously posed...as the formation matures, do measurements increasingly approach their ideal expectations?  As if a larger vibration, set in motion, overshoots its mark but by decreasing margins until, ultimately, it is perfected.  

***

The only two geometric images of the three dimensional twin adjacent cubes are conclusively supported by the level of exact mathematic structure that, by law, we expect to manifest.  Its not exactly as we expect because the individual PTVs are wishy washy.  But their averages are not.  And we have the unexpected intrusion of the three-dimensional root 3 into the mix.

But what do you expect.  We are trying to explain a four dimensional phenomenon, namely price/time, using a two-dimensional chart.  

We do not know the structure of four dimensional price/time, or at least, I don't.  We can't see it or feel it or smell it.  We can only imagine it.  But that's what we have.  We have the clues to imagine it.

Socrates' allegory of the cave and the prisoners having never been in the light see images on the wall; two-dimensional images.  One prisoner leaves the cave to discover the images seemingly having only length and width have depth as well.

Painfully, C Howard Hinton in "The Fourth Dimension" (1906) develops how a being am to sense only the planar existence (length and width) can notice anomalies in his environment that leads him to conclude the existence and certain properties of the fourth dimension.  Bradley Cowan relates a similar scenario in which a planar being is confronted with a vertical wheel of five colors.  Of course, he can't see the tall wheel that is before him; all he can see is a color.  As the wheel turns he sees the colors flash in sequence before him.  After many turns of the wheel he realizes the sequence of colors repeats.  He has a clue.  He can't see the wheel but he knows the structure of sequence that presents itself time and again.  Exact time durations and exact sequence.  Its a clue.

So, its settled, at least in my mind.  The first and only two complete geometric structures in the price/time chart of DJIA from 2000 to 2017 articulate the most important properties of planar geometry to a precision that's impossible to claim as coincidence.  And they introduce the third dimension as well.  But most telling is their measurement is according to a yardstick comprised of both time and price according Pythagoras' 345 triangle and the Price Time Vector.

Now, back to evaluating point E.  Once point E and F are projected, the entirety of the cube will be known.  Perhaps point E has occurred or is yet in the imminent future.  Point F certainly lies ahead.

Jim Ross

Current Market: Indication of the loose thread

The previous essay indicated the math according the first formulation of twin cubes did not seem to work out as expected and that both cloned ellipses and an alternate formulation of the twin cubes suggests a final new all-time high in DJIA on about April 27, 2017 at above DJIA 22000.  The latter suggestion of a new all-time-high was based on a visual fitting of the 2000-09 square ABCD and has been updated by a more, but not entirely, mathematic triangulation of point E (the suggested final all-time-high) at DJIA 22300 on May 2, 2017.  Again, this revised calculation is a better "biangulation" of point E but remains not entirely mathematic in its derivation.  Here's the revised chart:

What early tip-offs did I have that March 1 was not the final top for the 2000-17 cube?  First and as previously noted, I should have recognized, by my own chart, the cloned cubes B and C axes did not form a perfect, overlapping straight line with their enveloping ellipse A:

Second, I should have noticed from my own chart of the period 2009-present, not previously shown, has some imperfect math:

Sectioning PTV's CE and DE according to the intersection of the 2007 price high and actual price results in components of those vectors that appear to be edging closer and closer to ideal root 3 and root 2:

But they have not reached root 3 and 2 ideals...yet.  Recall the mathematic significance of root 3, the center diagonal of the 1X1X1 cube (3 dimensions) and root 2, the diagonal of the 1X1 square (2 dimensions).  By establishing a new higher high in the not distant future, the subdivisions of CE and DE will inch closer to the Platonic ideals.

Isn't this intuitively attractive according to WD Gann commentaries on how we expect "vibration" to reach its mathematic extreme before some new shock or impulse or predetermined mathematic extreme reverses the market?

I should have known earlier, that a marginally new high is needed to perfect the math.  It was the loose thread at that moment that I did not follow.  Now, is the point E I seek, the newly identified point E at DJIA 22300 on May 2, 2017?   That's my best "biangulation" at the moment.

Still working on the math.  I expect a still finer point E projection and math that will support (or refute) the model of the market structure shown in the chart at the very top of the page.

And then the question will become, what is the correct point F...the next pivot bottom counterpart of point E top?

Jim Ross

Current Market: The math didn't work

As I'd asserted, the validity of the below market formulation of four market points (points A, B, C, D) in price/time supporting a fifth future point (point E) depends upon their mathematic and geometric interdependence.  The five points, forming vectors between each set of points, must demonstrate the mathematics of adjacent 1X1 cubes adjusted for growth.

If the mathematics worked out for every so formed vector of the many, then point E would be indicated as the final high of the 17 years since the DJIA January 2000 high.

After hours, days of working the math, many of the relationships among the many vectors formed by the four points and one prospective points do not work or work in a way that is contrary to the laws of the adjacent 1X1 cubes.  My conclusion is that point E or the DJIA March 1, 2017 high, is not the final high in DJIA.  Were I a bit more diligent I would have noted the closeness of the adjacent cloned ellipses featured in one of the first posts in the "Current Market" series:

I'd noticed it before.  The inscribed ellipses B and C axes (bold purple lines) do not adjoin to form a perfectly straight line.  The axis of the enclosing ellipse A (bold dashed lines) is be the adjoining of the inscribed eclipses axes.  A detail or loose thread.  I should have known.

The three ellipses' axes present configuration suggest to me another marginal high that will result in the inscribed, perfectly equal ellipses forming a perfectly straight line overlapping the axis of the axis of the greater ellipse A.  Think about it.  Point E moves up very slightly to yet a new all-time-high, large ellipse rotates up to point E and inscribed ellipse C rotates up to point E.  All three ellipses now have overlapping central axes that overlap and extend the axis of ellipse B.

That's visual and visual is perception and perception is subjective.  As a finite mathematician I rail against perception and subjectivity.  Failing with my mathematics, I'm using a subjective tool to prove myself wrong.  No, the math didn't prove my rendition of the cubes as correct.

When first I posted the twin cubes, a commenter, perhaps innocently or perhaps with greater insight that I then had, asked the question, "Where is the back side of the second cube formed?"  And I believe, in retrospect, he is right.  Here is the re-imagined formation of the adjacent cubes:

Concentrate on the bold black (real) and bod grey (imagined) lines that outline two cubes sharing a center side that twist from their side nearest us (square side ABCD) and rear side furthest from us (square side EFGH).  

I have tentative math that suggests point E, the higher high, will occur April 27 at just over DJIA 22,000.  The math is a visual fitting of the above vectors and the "camera obscura" projection of square ABCD and its component triangles to imagined square EFGH and its component triangles.

["Camera obscura" is a favored optical/geometric concept of the 17th century mathematician, scientist, physicist, alchemist, philosopher of the court of Queen Elizabeth I, John Dee.  Dee is a name that appears 45 times in the acrostic and telestic encoding of WD Gann's "The Tunnel Thru the Air," 44 times as the word "Dee" and once, perfectly between the first and second 22 occurrences as "007."  The James Bond of the 17th century was, indeed, John Dee and "007" was John Dee's signature to Queen Elizabeth I in their secret and coded correspondence.  See HERE.  John Dee's relation to "camera obscure" is well documented in Jim Egan's ebook on the geometry of the Monas Hieroglyphic found HERE.] 

The image of the twisted cubes can be modeled in mathematics.  If its a valid formulation, then the many vectors formed by real points ABCD and imagined point E will demonstrate the metrics of the two-Platonic 1X1 cubes augmented by growth.  And if it is a valid mathematic formulation, the triangulation of point E based on points G and H and the projected "camera obscura" image of square ABCD to square EFGH will give us a perfected price and time projection of exactly where the market will top.  

If I know myself, I'll first mathematically project point E.  Only after having the exciting answer as to whether and exactly where (price and time) the market tops, I'll test the many vectors to see if the math supports the above formulation.  This is otherwise known as "cart before the horse."

If it doesn't work, I'll continue to work.  If it does, I'll continue to work.

Jim Ross

Current Market: I hate it when "there is a loose thread in the world."

To put the subtitle of this essay in context, its from Mark Gattis' and the BBC's rendition of "Sherlock Holmes; The Six Thatchers," season 4 episode 1.  Further context, Sherlock, Dr. John Watson and Inspector Lestrade are visiting with the parents whose son was tragically lost when Sherlock rudely leaves the couple to stare at an inexplicable detail of the room; an apparent (to Sherlock) table dedicated to Margaret Thatcher with a gap in between pictures and an irregularity in dust patterns.  From the transcript that can be viewed in its entirety HERE:

[FYI, "By the pricking of my thumbs, Something wicked this way comes" is from "Macbeth" and linked to HERE.]

From the table, Sherlock deduces a bust of Margaret Thatcher had been positioned there but had been removed, most likely broken....but not broken next to the table because there was a thick area rug.  A loose thread, where had the bust been broken?  Why steal a bust not having substantial apparent value in a house (semi mansion) having, no doubt, many valuable and marketable items?

As the trio are leaving the home Sherlock stops on the porch to examine something he'd seen on the porch when they first arrived and this exchange occurs:

Noteworthy, Intuition; data processed too fast for the conscious mind to comprehend.  Loose threads, details without identified connections to the puzzle and solution that must exist.  Arthur Conan Doyle was a spiritualist and his Sherlock did not miss details even if their connections were not apparent.  Mark Gatiss' Sherlock is equally attendant to inexplicable details and ever more so the believer that something deeper than the mind is at work in each of us.

Details.  First, the market cube chart for convenience:

Now the 10 PTVs and values in tabular form:

Pythagoras' root 2.  The first "structural aha" was discussed in the previous essay; if ABCD were a square in perspective then I'd suspect it would relate to its diagonals....and it did.  In the table above the average side length is 948 and extended by root 2 becomes 1334 (within 6).  Perhaps the diagonals of any four-sided structure will demonstrate such a relation; at least, any two-dimensional, space measurement only structure.  But this is a price/time measurement structure.  Regardless, the math worked exactly as I expected.

Vindication of Leonardo de Pisa' Phi.  An early iteration of Fibonacci series is 3 and then 5 giving us an early and easily recognized iteration of Phi at 3 / 5 = .60 or its inverse of 1.666.  Look at the diagonals (of square ABCD and the two squares) and note how they subdivide:

The earliest iteration of Phi in the chart which occurs chronologically before the later versions emerge is a crude approximation.  It is the relation of the diagonals of square ABCD at 1.6790 or its reciprocal .5956.  I thought this was an "aha" moment but it just didn't seem close enough.

And then I applied the Phi subdivision to the combined values of the two diagonals of the cube and found them to be much close to a Fibonacci 5 / 3 arrangement; 1.6662 and its reciprocal .6002.  Within  mere 10 thousandths of perfection.

What might be gleaned?  Obviously Phi is at work.  But more comforting, just as the Fibonacci series iterates closer and closer to theoretic Phi, so perhaps the market's early iterations of the mathematic goal to which it strives becomes more refined as the structure is formed.

More details.  Phi, root 2 and 2, Pi, root 3 and 3.... all over the place.  Here are just a few:

The square ABCD and Root 2 revisited.  Recall the early "aha" in discovering the sum of the four sides of ABCD divided by the sum of its two diagonals provided 1.  To be honest, I was a bit disappointed that average diagonals divided by average sides was 1.4068 compared to ideal root 2, that being 1.4142.  But there may yet be a happy ending.  Let's look at that same averaging number but let's also look at the reciprocal of the gross PTV values of sides and diagonals:

The sides of that twisted, supposed square ABCD in perspective relate to its diagonals by the ideal root 2 to the 4th significant digit.  Perfection.

Is that a coincidence?

***

I'm sure there are "details" above that are invalid, though seemingly close.  In those law does not require that they work out as they did; we have true coincidence.  The above represents but maybe a half day of searching.  A more disciplined and instinctive searcher than myself would find many more relations than did I.; many more "loose threads" I suspect.

Some "intuitive" thoughts:

Does the development of and 'end game' in the current market correspond the perfection of Phi or other metric among PTVs?  Take Fibonacci 3/5 or .60.  The diagonals of the sides of square ABCD, AD and BC are sectioned in to imperfect but recognizable .4044 and .5956.  Those vectors are complete early on in the current market, point D having completed in March 2009.  Much later on, vectors AE and DE complete (prospectively) in March 2017 and relate to one another again by Phi.  At this latter endpoint, a more accurate reflection of Fibonacci 3/5, that being .3998 (DE /(AE+DE)) and .6002, has developed.

Does the market, as it vibrates, exceed the Phi mark on an early swing and with each successive swing miss the mark by less and less until the Phi mark is substantially perfected?  Can a new marginal high create yet greater perfection of Phi between diagonal PTVs AD and BC or the Phi relation between two side PTV CE relative to center of cube diagonal BE (2734/(2734+1681)=.6193)?

Did March 1, 2017 print the final high of the structure that began in January 2000?  What happens to all these market measurements, which seem to have found perfection in their four PTVs AE, CE, BE and DE, if point E makes a higher high?

Which are the more sensitive PTVs in seeking Phi perfection; the pair of AE and DE face diagonals or the pair of the two sides vector CE and cube center diagonal BE.  The former are very close to perfection of the Fibonacci 5 / 3 iteration of Phi (presently at .6002) while the latter are far less perfected of the ideal Phi at .618 (presently at .6193).

Another all-time-high, only if marginal, or is it close enough to structural perfection?  A loose thread that perhaps some sensitivity analysis might answer but which will surely be answered in time.

Jim Ross

Current Market: Adding to the mathematic "aha's" and hints of mathematic market structure

"Every market high and low is caused by another point in the market."  Or at least, that's the belief that WD Gann expressed dozens of times.  That there is a cause and effect in everything and markets are not exempt.

And that's what I'm increasingly finding in the current DJIA from the 2000 top.  Beginning with the 2000 top and ending with the present all-time-high of only a week ago, there are 5 market market pivots.  Those points are each related to the other by the market metrics which were presented HERE.  No, ladies and gentlemen, we aren't talking about a "Gann fan" or Phi spaced support and resistance levels...stuff that shows there are rhythms and approximate cycles but which are woefully short in saying "this is the one price and the one time."  We are talking about structured mathematics between each of those 5 in price/time; the one and only price at the one and only one time.

And lest we forget; the stock market was only Mr. Gann's laboratory of spacetime in my humble opinion.  This time I'll give you the exact quotation:

In my suspicion, Mr. Gann had, by the time of that quote, already worked out the four-dimensional structure of the market and had, as well, applied that mathematics to personal and world events using the Law of Vibration and Luo Clements' (imo, WD Gann) methodology.  Remember also from the Ticker Interview that stocks are like the elements of the Periodic Table; they can be classified by their "number" and those within a class of similarity behave similarly.  Didn't Luo classify names by number and specify that those of the same class (3,6,9 or 2,5,7, etc) react and behave similarly?  So, if I or someone am ever able to specify the mathematical structure of the market with Mssrs. Gann and Cowan's instruction, that's only a minute beginning.  The market is the "simple" case.  Its the amoeba in the petrie.

Now, back to the "aha's" of the current market.  There are so many "aha's" in the 17 years of the current market I'm overwhelmed.  Of the 5 real price/time points (A, B, C, D and prospective E), each  is the original for at least 4 Price Time Vectors (PTV).  Those vectors from each point are mathematically related to one another.  And because those PTVs joint at other real price/time points, every PTV must be related to every other PTV.  It is just a matter of taking the time to figure out the math.

We're talking about a lot of time to work out all the math.  If we have 10 real vectors and every one is related to the other then there are a lot of combinations and a lot of relationships to work out.  Perhaps 10 factorial or 10X9X8X7X6X5X4X3X2X1 = 3.63M relationships?  No, that's not right because order is not a factor.  Maybe its 10! less 9!  Still, 90 relationships is a lot to assess.  Regrettably, I do not recall from that statistics class from 40 years ago in combinations, permutations and probability the model that needs to be applied here but its only a confirmation of what I intuitively know; there are a lot of "aha's" that can be worked out from this exercise.  I will only rigorously and completely work out one of the PTVs that are associated with one point and a couple more of interest and of necessity.   To start, let's reprise the current market chart:

You'll see in red text the relationships I teased you with in the previous essay.  A couple are "duh aha's" that any semi mathematic observer can ferret out.  For example, the first red "aha" is CE divided by CD is equal to two.  Well, not so much because it is equal to 2.07 to be more accurate.  I give that a teaser "aha."  A little closer is AC / AB = 1.98.  

What's the big deal about PTVs having a relationship in magnitude of 2?  Its the root 2 growth spiral in nature.  A biologic cell at it base level divides itself into exactly two parts.  A 1X1 square divides itself by replicating its 1.414 hypotenuse to form a square with sides of 1.414 and exactly twice the area of the 1X1 square; that being 2.  That 1.414X1.414 square; what's its hypotenuse?  It is sqrt(1.414^2 + 1.414^2) =....you got it...it 2.  Finding vectors relationships to one another of 2 implies the root 2 growth spiral is as Mr. Gann might say "at work in the market."

Now lets use some averaging to sniff out some structural relations.  Its very disappointing that the supposed square ABCD has sides, none of which are equal.  And the diagonals aren't equal nor doe either of them extrapolate from any given side that would indicate squareness of the sides.  Go to the fourth of the four red "aha's" above.  You are summing the diagonals of BC and AD and dividing by the sum of the four sides.  The math:

That's one of the first "aha's" that told me I was on the right track towards confirming the market struct that Mr. Cowan asserted must be present.  The average of the two diagonals divided by the four sides is 1.4068, comfortably close to the relation of the hypotenuse of the 1X1 square to one side or 1.414 (root 2).  It worked kinda like I thought it must work according to the perhaps the grandfather of all laws; the Pythagorean 345 triangle and the calculation of it hypotenuse.

Do you understand the importance of the above?  Its not like, "wow, price hit the Phi retrace and reverse" when it happens 1 out of 10 times or 1 out of five or its hits one of the several Phi levels.  The proposition was, if ABCD is actually a square in a tangled, twisted perspective view that defies the limitations of what we can visually interpret, then its diagonals must relate to the sides by 1.414.  It couldn't be otherwise...and was not.

So why are the sides not equal?  Well, we know they never (well, pretty much never) are in the market.  Having already worked out many of the 90, or whatever, unique vectorial relations, I know the difference is the many growth spirals that are simultaneously occurring.  I've seen enough to know, those four sides of the supposed ABCD square are mathematically related, by some permutation of a growth spiral or market metric, to each other and every one of the other 9 real vectors.  It's law.

***

Do you see where I am going?  If the four points and associated vectors of square ABCD are mathematically related to those four vectors that connect them to hypothetical point E (e.g. PTVs AE, CE, BE and DE), well, point E is mathematically determined.... it is determinable.

If you caught the "*" notation of the previous essay, point E in three dimensional space can be predicted from three fixed points.  You know, all the action movies have the detective asking the cellular folks to "triangulate" the bad guys cell phone.  In two dimensions, you only need two points and a vector of fixed magnitude.  With those givens, point E can be determined from PTV AE and AD or from PTV BE and AD or from PTV CE and AE.....  And all of those PTVs' magnitude are mathematically determinable from points ABC and D.

Once the low of March 2009 occurred, the die was cast for Point E; both time and price.

No, I have not worked them all out nor have I codified how the growth spirals will work to create a model of the structure.  There's a lot of work yet to done in this laboratory.

Next up, I'll go over some simple "aha's" and implication.  Further down the road, I'll take point A and look at the mathematic relations between the four vectors that radiate from it; AE, AC, AD and AB.  That's where I suspect we will first begin to codify the structure of price/time.

What is the cause and what is the mathematically consequent effect?

Jim Ross

Current market: The mathematic landscape

If you saw the next previous essay on the symmetry of the current market a natural reaction by many of us to the presentation of ellipses might be... "something has ended"... at the March 1 all time high.  We like symmetry, its human nature.  But its subjective.  Likewise, when we see a sophisticated application of Phi support and resistance, we are blown away by the apparent knowledge of the author.  What an "aha" moment when you see the market reacting to Phi for the first time!  I plead immensely guilty.  It speaks to our nature that when a researcher finds similarities of tops and bottoms along with a magical number that we are persuaded.  But those coincidences, conflated to systems and methods, are not according to natural law.  They're according to an accumulation of coincidence; scant accumulations at that.  They might repeat somewhat better than 50%...which is good.  Don't get me wrong, if systems of coincidence tilt the odds favorably, its good.

But a web of coincidence is not mathematic, geometric natural law.  That makes anything other than natural law largely subjective....hunch.  Law, on the other hand, means it is inerrantly objective and predictive.  Its cause and effect.

Let's look at the mathematics of the current market, use Bradley Cowan's adjacent cubes structure of the market and his Price Time Vector (PTV) measurement given the proper squaring (see the previous essay).  Let's see if there is a preponderance of the "great numbers;" not just Phi, but root 2, root 3, root 5, Pi....  Here's the chart:

Let me describe it.  First, its two adjacent cubes and it is a perspective drawing that reflects the "moving location of the observer" or, alternately, the "moving location of market points relative to the stationary observer."  Solid black lines connect 5 specific market tops and bottoms (January 2000 top, October 2002 bottom, October 2007 top, March 2009 bottom March 2017...err something).  I call the 5 solid black lines "real" because each connects two real price/time points.  The remainder of the black lines are dashed and I call them "imagined" lines.  They help us (me) in visualizing the mathematics, the structure of law, that must be taking place, if the market has formed adjacent cubes as Bradley theorizes.

In addition to the apparently differing lengths of the solid black lines are colored dashed lines; two blue dashed lines representing the two diagonals of the square, two red dashed lines representing two of the four face diagonals that span two cubes in length, and one purple dashed line that traverses the center diagonal of the two cubes.

So how many "real" lines do we have?  We have 10 since the colored diagonals all have market endpoints.  There are 5 real points in price/time named A, B, C, D and E and there are 10 real vectors that are created by those 5 points.

Now one last item for this introduction.  Look at vector AB; at near its midpoint is the number 648.27.  The software (Cycletimer) has computed the PTV value given points A and B and the squaring parameters that I have shown at the top left of the chart; the change in trading days X 6.5 hrs per day X .10 and the change in price X .10.  Those are the same squaring parameters I used in the previous essay to compute vector AB's PTV value.  Computed in the previous essay the value was 650.27 whereas the software computed 648.27.  Obviously the mathematic calculation is preferable.  The software works fine but the vectors are visually fitted to the high and low points and some small differences are introduced.  A small price to pay to be able to fit vectors and create scenarios visually.

I've added some teaser equations.  There are perhaps two dozen numerical "aha's" in the above chart I'm sure.  I've probably discovered two dozen at this point.  And I've added in red 5 of those discoveries.  I've added them to whet your taste for what's to come.

Its not the number of "aha's" that are important; its the structure.  Unless Bradley Cowan was deluded in his description of the importance the cube, the importance of the two adjacent cubes and the importance of root 5 (an aspect of two adjacent cubes, we should see mathematic structure in this chart.  We should see the measurements and metrics described in the previous essay unfold in order to one another.  Since the chart progresses left to right according to time, the mathematics unfold in that order.  If we see a certain configuration of math occur in the market today, then, according to the mathematic structure of the Platonic solid being formed by the market we should see the next dependent mathematic aspect unfold in the successive market movements.  Structure creates expectation...creates determination.

Work through the five teasers in red and see if we are not producing a variety of the mathematic metrics presented in the first essay.  Take any of the 10 PTV values showing on the chart or all of them and recalculate them to keep me honest; its the same calc that derived the 650.27 value of PTV AB in the previous essay.

***

Next up I'll develop more of the preponderance of "aha" metrics of the adjacent cubes and perhaps categorize them.  Two essays from now I expect to describe the structure of adjacent cubes using the metrics created and our expectations created by the math of the adjacent cubes.

I'm not sure I will take the analysis into a final essay using structure and metrics to predict, retrospectively compute point E in the current market.   Prediction will, at that point, be only a matter of triangulation.  Think about that.  

If points A, B, C and D and the structure of the adjacent cubes can derive our expectations of the values of PTVs AE, BE, CE and DE, is not determining future point E just a matter of triangulation*?  

Well, that's the plan.  Let's see how far I get.

Jim Ross

*Finding a point in three dimensions requires 3 points and three vector to find a fourth point and is called triangulation.  But market charts are two dimensions; we need only two points and two vectors to find a point.  When I use the word "triangulation" it is only to connote the mathematic fixation of an otherwise unknown price and time.  The "tri" would be more appropriately "duo" or "bi" and hence,"duoangulation" or "biangulation."

Current Market: A primer for understanding the current market since the 2009 bottom

The title overstates my competence to present the findings in the next several essays.  Anything I present is based upon the works of WD Gann and Bradley Cowan, his derivations from WD Gann and further discoveries of natural law.  None of the following essays is my work other than the application of what they instructed.  Lest you believe my insights are valid by associating my findings with the genius of these men, what follows is my continuing attempt to understand the structure of the market and, moreover, the structure of spacetime.  I've proven fallibility.  Despite the proof of the structure of spacetime provided by WD Gann and the 'abc' s of the four-dimensional structure of spacetime reduced to two and three-dimensional geometry, my work cannot be relied to be valid at this point.  On the other hand, if you are a mathematician, you've got to go "hmmm."   Remember, I'm a finite mathematician, an accountant...just a wannabe.  Be gentle with me.

Because many (most) readers are even less savvy with geometry than I, this post is a primer for essays on the geometry of the current market.  It will cover relevant metrics of two and three-dimensional structure.  I will be brief so you need to refer to high school level and freshmen geometry texts (believe me, I had to retrain myself).

Metrics of the square (two dimension) and cube (three dimension).  Derived by the 1X1 square ABCD, diagonal AC is the square root of the square of two sides each squared or 1.4142.  AC is the square root of 2.  Derived from the 1X1X1 cube, the center diagonal AE is the similar square root of one side and one diagonal or 1.7321.  AE is the square root of 3.  

Double squares and the root five growth expansion.  Two equal cubes sharing a common planar side have important interrelated metrics and demonstrate the relation of growth spirals of Phi (1.6180) and root five (2.2360).  The following is my rendition of Bradley Cowan's illustration found on page 51 of "Four Dimensional Stock Market Structures and Cycles" ("Four D" for short):

Phi and root five and mathematically and geometrically related.  In fact, Mr. Cowan refers to root five as more important than Phi in the market.  Moreover, analysts are frequently misled by the more readily identifiable footprints of Phi (square root of Phi, Phi squared, etc) when the more important growth spiral in the market is the root five spiral.

Adjacent cubes.  One last metric for now; the center diagonal of adjacent cubes or root six.  I expect this metric to occur in the 2009 to present market, but have not derived it as yet.  In the ideal world, here is one way you'd derive it:

And a tool; the measurement value of a spacetime vector.  As trademarked by Bradley Cowan as the "Price Time Vector" or "PTV, the PTV is an application of Pythagoras' formula for the hypotenuse of the 3-4-5 triangle.  Simply:

From two data points on a chart (typically one is a high and, the other, a comparable low) calculate the change in time and square it, calculate the change in price and square it and take the square root of the two after having added them.

Simple, right...except for "squaring."  That thing that WD Gann told us we needed to do to our chart paper and Brad Cowan says we need to read what WD Gann said about squaring.  From my studies, Pythagoras' formulation works only as long as both time and price have the ability to influence the value.  

To accomodate squaring I have two rules.  First I use natural units.  I use hours, days, weeks, months.  Of course the price side is simple to use the decimal to "balance" time and price.  Second, that "balance" word itself.  Over a long period of market time, time and price need to balance...  Neither should become the primary determinant in the Pythagorean calculation.  As well, I try to keep the ultimate output of the formula (the PTV value) to 3 digits by, whatever the price and time metric, reducing them by 10 to make the PTV value, ideally, 3 digits.  

The final comment on squaring; I cheat. Brad Cowan used a weekly calculation per dollar up to the late 1980's and thereafter, trading hours to the dollar.  I go one step further and reduce trading hours by 10 and dollars by 10 to make the value a 3 or 4-digit number.  The ultimate output of the Pythagorean formula is the same in either case differing by only one decimal.

Calculate the PTV value of the vector from the 2000 DJIA high versus the 2002 DJIA market bottom:

That's how its computed and, again, the squaring is trading days X 6.5 hours per day / 10 and price change in dollars /10.  

***

So what if we find all the above numbers in the DJIA from 2000 to present?  Gosh, we find Phi everyday.  There are resistance and support levels that we see hit all the time.  A big "so what?"

Its the structure.  If follows the structure of a Platonic solid.  Bradley Cowan indicates in Appendix G (hmm, does G stand for Gann) of Four D that the important growth spiral in DJIA is root five and, therefore, the Platonic solid would be the adjacent cubes.  

We find Phi all the time but can we predict every instance in which we are going to find it; exactly which day, exactly which price level in reaction to a previous price level?  Nope.  I defy anyone to assert the inerrant and predictable Phi structure.  

I'd say Brad's left something tucked away with only the remotest of hints.  I recall the first time I'd read anything about Bradley Cowan; it was in an interview in which he made the comment that every angle in the market is 60*.  Ultimately I came to understand we as observers see the 60* angeles differently because the market twists relative to our field of vision.  If you look face-on at a 10" X 10" piece of paper it looks square.  If we lay it on a table and look at it with our eyes level to the table, we see only the edge of the paper.  If its square to our vision, its a 10" long line without any height.  What we perceive about the third dimension, what we see, lies to us.  If our vision is subjective in the third dimension based on the location of the observer, how can it be otherwise in the fourth dimension?

That 60* hint; its the equilateral triangle in the second dimension and the tetrahedron in the third dimension.  The triangle and the tetrahedron is the most efficient of the Platonic solids in many regards.  In two dimensions, the triangle forms a solid structure with only 3 sides.  In two dimension, the four-sided square is not a solid structure until you add a diagonal to firm it up (which creates 2 triangles by the way).  Ditto those observations for the tetrahedron versus the cube.  Nature's smallest firm structure; the triangle and tetrahedron.

And what are the fewest number of tetrahedra that can be arranged to comprise a cube?  There is one and only one decomposition of a cube into five tetrahedra, the smallest number.  And there are twelve methods of decomposing the cube into six tetrahedra.  At least, that's what I read HERE.  Twelve and one.

Another "so what."  Perhaps the cubic structure of spacetime is most evident in the cube, but the cube is comprised of either 5 or 6 tetrahedra. One edge of a tetrahedra appearing on the face of the cube, perhaps two edges of each tetrahedra, forced into the cube provide the market's etching of its history on each cube.

What I believe we will see in the next essay is the PTV of the market creates minimal elements of the sides and edges on sequential faces of the two adjacent cubes.  The math confirms this as I hope I can demonstrate.

I expect the tetrahedron to be the basest structure of spacetime, five or six of which coalesce to form the cube.  But for now, we need to go about proving the structure in the market itself.  That will begin in the next essay related to which I've already identified most of the metrics presented above in a progression that demonstrates the higher level of structure, the cube.

In my current thinking, this is only a very early experiment in spacetime.  Ultimately, Mr. Gann was able to use the unique vibration of each person, place, thing (according to Luo Clement, aka WD Gann) to describe and predict its unique future according to the structure of time.  

Jim Ross

Current Market: Symmetry of the post 2009 bottom market

My studies of WD Gann's "The Tunnel Thru the Air" proved to me that Mr. Gann could identify future events.  So many of the events that are coded into The Tunnel are things that have come true or will come true.  For example, most researchers accept Mr. Gann predicted in 1927 the July 1932 bottom to within days/hours.  In my research I identified many, if not dozens, of events that have occurred.

And I was misled about events in our future.  Oh, not the nature of the events (the "what")...but the time (the "when").  As I step back from The Tunnel I know the "what" that will occur.  Everyone does.  Read today's news about the USGS declaring Los Angeles overdue for an earthquake.  Of course, the same is true of the Cascadia subduction and a San Francisco event.  We all know the "what."  How many people, even on the Pacific Coast, believe there will not be a great event?  Few I expect.  They're simply banking on it not occurring during their lifetime.  We all know the "what.  How often did Mr. Gann echo Mathew 16:3?  

The problem is the "when."  I imagined the "when" based on subjective clues I thought I saw in The Tunnel.  That's the big problem.  You can paint a scenario of the "what" with subjective language imagery; even if it is encoded.  Mr. Gann actually used the "Tao device," a mathematic spacing of acrostic/telestic words spaced a meaningful number of lines between the words, to confirm to us the "what."  Tao to WAR, equally spaced lines between the words Tao to WAR.  Meaningful mathematic spacing of "San Andreas" and a key phrase,  "Tip the hat," in that 2015 movie.  And that mathematic "Tao device" was appended to the date September 11, 2001 and the number of deaths that day; Mr. Gann predicted 9/11 and the movie that would lead me to discover the WD Gann map of time.  Yes, he could determine the "when."  Too many instances of subjective language supported by incredible mathematic symmetry encoded into The Tunnel to dismiss.

He knew the "when."  The most "in your face" example is the 286 trades in 25 days with only 22 transactions that lost money.  Is that statistically possible if the market.... and spacetime .... is a random walk?  Can any person do that without a computer and an observer stalking his every step on the floor of the NYSE?  

Mr. Gann often said, time is the most important factor.  Was he going to give away the "when" as easily as he gave away the "what" that we all have anyhow?  "When" is the perfectly accurate mathematic solution.  Having spent much of the last several months reworking my understanding of the mathematics which I believe is inherent in Mr. Gann's methods, I can see the signs of spacetime structure.  Again, we all can.  We see price and time reacting to Phi intervals.  If you look deeper you find sqrt(2), sqrt(5), pi, sqrt(3) and their roots and squares are in the market.  They are all hallmarks of two and three dimensional structure of structure if you study planar geometry and the geometry of Platonic solids.  What's missing is the integration of time with space.  Sir Arthur Eddington offered time as the fourth dimension.  If we didn't have our second eye we wouldn't "see" depth or the third dimension.  As Edington further offered, what if we had a third eye in our forehead, would we be able to to "see" the fourth dimension?

But we don't.  We can only intuit the existence of the fourth dimension.  One such feeling is when we see in our three dimensional realm things that fly in the face of randomness...when we see spacetime creating symmetry.  Symmetry, the arch enemy of randomness.

So what symmetry might we see in the stock market today?  

Price hugs the red ellipse for more than a year before diverging to rendezvous with the exact center of the ellipse.  And then price reaches the bottom of the ellipse for the last year of the prospective red ellipse' life.  

Now subdivide the red ellipse such that the purple ellipse A is inscribed in the left half of the larger red ellipse.  Price hugs the upper portion of that ellipse in its half life.  Clone smaller purple ellipse A and call it purple ellipse B.  Append ellipse B' left most point to the right endpoint of ellipse A and with only a little wiggling the end of ellipse B coincides with the right end point of red ellipse A.

But creating the ellipses is now what's intriguing.  Its price within the limits of the three ellipses.  Its confined if not conforming.

As if to put an exclamation point on the analysis, does not the midpoint of the red ellipse A occur at the price level of the top of the 2007 market?  That's indicated by the blue horizontal line.  

***

That's the visual, the subjective approach to intuiting the structure of spacetime....or, at least, in the market.  There is a mathematic level and I am beginning to see how the things we see occurring, the Phi's, the sqrt 2s, 3s and 5s.  I'm actually seeing more than just support and resistance popping in and out of the market at indiscernible intervals.  There is structure and the structure will predict the outcome.  The future outcome.  And its not just in the market.  

Its the solution to whether the Dow topped last week.  The solution to "when" the Hoover Dam will fall, "when" San Franciso and Los Angeles will be afflicted, "when" the Cascadia subduction will flood the Northwest....  

I don't have that mathematic structure and solution yet.  But I believe the math exists and there are a very few people who have components of that knowledge.  Certainly, not this duller knife in the drawer.  Not yet.

Jim Ross