The second dimension square has four sides any way you look at it. The third dimension cube is comprised of 6 square faces having 12 independent, unique edges. You dissemble the cube into 6 second dimension squares each having 4 edges then you have 6X4=24 edges.
12 unique edges of the assembled 1X1X1 cube divided into 24 less so independent edges of the dissembled cube gives us the metric of 2. And, as previously discussed, the growth spiral of the square of Pythagoras' hypotenuse of the 1X1 square is 1, 1.4142, 2, 2.8284..... 2 is a very very important geometric metric. And Phi, well, as expert market analysts we all know the Phi growth spiral (or as attorneys say "know or should have know").
What does the third dimension cube look like in the fourth dimension? We would want to see the metric 2 involved, wouldn't we? "As above, so below?" Let's take the question to the laboratory and examine data that has been accumulated on our lab rat name DJIA. We need data. Here are the ugly mated (sharing a common face) cubes of the period 2000-present:
In previous essay, Price Time Vector (PTV) values have been computed and presented. Both the approximate values in the chart above and the detailed mathematic values previously computed are based on the assumed points K and L. Points K and L were derived from the application of the "camera obscura" concept in a previous essay and from a yet to be described "coincidence." The above software calculations are approximate as they require visual fitting to points. The exact data has been computed and can be found HERE.
Will we find 2 when we assemble and dissemble each of the 2 cubes above?
Rearrange the previously computed PTVs to form the perimeters and average sides of each of the mated cubes, both for 12 unique sides of each cube and 24 sides of six squares of each cube:
Duh, it works. It had to work and I'm sure a mathematic notation and logic person could provide a proof in abstract logic. Me, I have to plod through numbers. Simply, 21319 / 10659 = 2 and 17595 / 8647 = 2.
Now that we have the numbers for such a seemingly inconsequential proof, let's see if there is something else. Let's check the relation of the perimeters:
.28%, a coincidence? What say ye, Randomites?
The '2' had to emerge from each cubes relation between of 12 unique sides of the cube to 24 redundant sides of the cube's component 6 squares. Had to happen; baring my computational errors. The laws of the second and third dimensions had to be respected in the fourth dimension.
Comparing the mated cubes; was there any two dimensional or three dimensional rule that required the relation of the perimeters of the mated cubes to be the quotient of 2 and Phi? No, I don't think so. Nature, at work in the DJIA, made it so. A "natural law" it would seem. Books have been written about how WD Gann used the phrase "natural law" as a code. If we knew more about the fourth dimension, would we have said "it had to happen?"
Does this suggest the hint of a law of fourth dimension systems of mathematic growth? I think so. Is it the same relation for every fourth dimensional system (markets, people, natural events...) or could there be other relations including the growth spirals of 5 or 3, etc? Of the effect of personal vibration (promoted by both WD Gann and his nom de plume, Luo Clement) on one's destiny? As well, I believe so. Like the consistency of math throughout its progression between the second, third and fourth dimension, it is intuitive (to me at least) that natural law will be consistent as between all natural phenomena; markets, physical geologic, atmospheric events, sociologic events... all the way down to personal destiny. But that's conflating
At a minimum, the experiment strongly suggests mathematic structure of spacetime. Not randomness. Exquisite mathematic structure; "geometric points of force." For every effect there is a cause. Everything is circular and responsive; for every action there is a reaction. Every point in the market is related to a previous point in the market. For every act in our lives, there is a response.
This experiment also suggests some level of integrity of the proposed and here above assumed values of points K and L. I do not believe K and L are exact, but increasingly, they seem to pretty close given the derivative appearance of these metrics. It will be interesting to see how DJIA plays out later this month.
Oh, there's so much more cooking in the DJIA laboratory.