Fourth dimension; we might presume, as did Sir Arthur Eddington in his first translation and explanation of Einstein's works, that time is the "fourth dimension." And that natural laws and principles of math and its dependent brother, geometry, rule all four dimensions..... that all things are mathematic, not just in the three dimensions we can see and feel, but in that dynamically related fourth dimension of time we can intuit.
How else would it be possible to predict the future, if that is indeed possible, if all things are random and related only by will and effort? How could the claim be made that "The thing that hath been, it is that which shall be; and that which is done is that which shall be done: and there is no new thing under the sun." [Eccl 1:9] if not that all is predetermined?
He proved it. Use your informed statistical intuition to satisfy yourself. Per "The Ticker Interview" 286 trades in 25 trading days with only 22 losses witnessed by an independent party. I've written essays on the vastly unlikely possibility of such an occurrence. If the market is a 'random walk,' can anyone undertake 286 trades and incur only 22 losses? I've even offered the 22 losses were purposefully taken for to demonstrate some properties of mathematics. Either Richard D Wyckoff and his independent party viewing the 286 trades was in on "the fix" or....Mr. Gann could "do it."
The market was just the simplest case in which experiments were easily undertaken and one that is subject to the undeniable proof of mathematics. It was Mr. Gann's laboratory. There is only time and money, both things that can be easily described in mathematic terms. Its not like viewing the future of a person who we have difficulty reducing to mathematics (although Luo Clement, err, WD Gann did) of judging whether the results support the predicted result. The market was the simple case from which to conflate larger and more elaborate definitions of natural law in other venues.
So if its so simple, why can't we see it in the market? You wouldn't be reading this essay if you had not seen the tracks of natural law in the market. You see Phi, cyclic periods, waves... But they don't occur with discernible mathematic regularity. Well, I think they do but its far too elaborate for us to place in a methodology that does more than bend the curve slightly in favor of the trader (resistance levels, Elliot Waves, etc). Math is perfect, not a bending. Today's trader, speaking only of the probability of a successful trade as opposed to "money management," is far from the perfection of mathematics.
At least, can we see rudimentary evidence of natural law in Mr. Gann's laboratory? I think so. Let's do it visually first and from that, then see some math. Recall for a moment the first two rows of the tetractys and images that we see in WD Gann's "The Magic Word:"
[Interesting, the third triangle above has 22 letters in it just as Mr. Gann took 22 losses in the 286 trades. It always bothered me that the sixth row had 7 letters instead of 6. Did he have to fudge it? Nah....]
Reflect on the nature of the triangle. The fewest number of lines (3) which, when connected, define a stable two-dimensional structure. The square, even with four lines, is unstable unless you add a fifth diagonal. And when you add the fifth diagonal line, well, you have two triangles to comprise the square. Richard Buckminster "Bucky" Fuller, architect, author, mathematician spent a lifetime developing his theories of natural law based upon the smallest component, the triangle and tetrahedron.
The simplicity and strength of the triangle is a similar property of the tetrahedron relative to other Platonic and Archimedean solids. Nature's smallest and strongest of two-dimensional structures found to be the smallest and strongest of three dimensional structures. Nature filling space with the fewest vectors arranged in the strongest manner.
What would be more logical than to extrapolate nature's triangle to the fourth dimension?
Consider the 1921 to 1937 Dow Jones Industrial Average and the supposed fourth dimension:
The two triangles (ABC and BCD) comprising the above quadrilateral is, apparently, a rotated tetrahedron. Each component triangle is, similar to the first two rows of the tetracty, subdivided into 4 component and equal triangles.
A nice thought to entertain; we unite space and time symbolized in the three dimensional tetrahedron by rotating the three dimensional tetrahedron. Don't, for a moment, think I think this is new. Many far smarter people than myself have proposed the fourth dimension is the addition of 'motion' to the third dimension.
Is there math coincidence to support the idea that future point "D" above can be predicted from past points A, B and C (the capital letters)? Connect the medials (small letters a, b, c, d, e) of the five visible edges of the tetrahedron to form two inscribed triangles abc and cde. Are there coincidental mathematic relations between them? Yes. But there is value in the observation that the outer perimeters are twice their medial subdivided triangles. Its a law in two-dimensional geometry I concede. But the mathematic measurement tool is one that uses both space and time measurements as will be explained in the next paragraph. That observation is not insignificant. Think about it.
The math tool necessary to measure space and time vectors is that of Pythagoras' 345 triangle as implemented in Bradley Cowan's "Price Time Vector" or PTV. [Yes, I know the Cowan / Baumring controversy, but the former published the PTV and copyrighted it regardless.] Simply, the square root of the sum of time squared plus price squared. I've used Cycletimer software and the numbers are approximate because you visually fit the beginning and end of a PTV.
I have not counted the many amazing properties of the above vector value relationships. Start with the perimeter of medial triangle abc (738.2) is half the perimeter of the larger ABC triangle in which it is inscribed (1469.2). The perimeter of cde is half the perimeter of the larger BCD in which it is inscribed. Well, that's mathematics...subdividing any triangle at the medials of its three edges will produce that proportion of one half. So, the more important challenge is to find out if there are relations between the triangles on the left (ABC and abc) and the ones on the right (BCD and cde).
A first observation.... vector ab at 189 which is substantially the value of vector de at 183 (allowing for visual charting inaccuracy on my part). Vector cd at 147.76 is roughly one half of the value of vector ac at 289.32 and side CD at 285.01. Perhaps that's the doubling and halving of which Mr. Gann often spoke.
Let's get a little more personal. Try vector bc at 261.06 versus vector ce at 212.17 or a ratio of 1.51. That would be 1.50 if vector ce were 213. Now divide 261.06 by the root of 2 (the diagonal of Pythagoras 1X1 square) and you get 184.6. That's frighteningly close to the vector values of ab and de.
Try just one more. This last item makes it most apparent to me the structure of the fourth dimension is the tetrahedron in motion; vector AC of the left triangle is substantially double the vector value of vector CD of the right triangle. I've reduced this last observation to a spreadsheet; AC is 567.8 and CD is 288.89 based upon the extreme values as opposed to closing prices. Very close to double.
I venture to say every point and vector from 1921 to 1937 are mathematically interrelated. Space and time are not causally separate; movement in one determines compensating movement in the other. And every point in the future...or in the past...can be derived. Determined.
The Dow from 1921 to 1937 is the easy case, visually and mathematically compelling...at least to me. The 1929 to 1942 period is equally or more compelling in even simpler and vastly more perfected math. It would seem the relationships and dependencies that might be derived from these simple cases can be applied to the more complicated time periods. Can point D of the future be derived from points A, B and C of the past? Can we prove the structure and nature of space and time in the Dow?
Back to the laboratory.
Note: A tetrahedron is often described as a three-sided pyramid. Medial points a, b, c, d and e appear as if an inscribed four-sided pyramid. And if you connect the medial of the sixth edge (vector AD which cannot be seen but we know must be there) to the four perimeter edges then you have two component four-sided pyramids. This after having recently read Peter Tompkins book on the Great Pyramid of Giza. One of the pyramids Robert Gordon did not destroy because he believed they were placed on earth for a divine purpose.