We all know the Fibonacci growth spiral that gives us Phi and most serious market students accept that it is a fabric of markets. But what about 2? We know WD Gann taught his students the heuristic of doubling and halving of time or price. He ascribed the importance of the 45* angle to its dividing time and price into equal parts. At the basest of levels of biology, the cell divides into equal parts. Back maybe a 2000 years a riddle of the ancients' was how to propagate the 1X1 square forward to create a square of twice the area of the first.
The ancients riddle of the growth spiral of 2. It is 1, 1.4142, 2, 2.8284, 4, 5.6568, 32.... Its the side of the square beginning with the 1X1 square having a side of one, followed by the grown square having a side length of the hypotenuse of the 1X1 (which is 1.4142, e.g. root 2), followed by the grown square having a side length of 2 (which is the hypotenuse of the 1.4142X1.4142 square e.g. sqrt(1.4141^2 + 1.4142^2).....
Two growth spirals from two well known numbers; 2, and Phi. Already knowing what I want to find for you because I had the "aha" moment this morning, take the two spirals and concoct a number we want to find in the twin cubes.
The PTV values on the above are approximate because one must visually fit the end points to tops and bottoms. Here are the perfect calculations the software makes according to the application of Pythagoras' theorem of the hypotenuse of the 1X1 square to time and to space (the PTV):
Now let's arrange certain of the vector values to comprise each of the two cubes. Hint, a cube has 12 unique edges or PTVs. [I underscore the word unique as a segue to a future 'aha' and essay.]
Perhaps one cube of spacetime PTVs ruled by 2 and the successive one by Phi? And their conjoin representing a hint of the structure of spacetime?
.26% difference. Coincidence? Remember, its all extrapolated based on two assumed future points, K and L. If I change point K from April 20, 2017 to April 20, 2019, the percentage difference becomes 5.04%. Get the drift? If the calculations were based on finer data (time to the minute - or four minutes to satisfy Mr. Gann's claim it being the smallest cycle - as opposed to the hour), might we find a more perfected set of dates and prices that would make the percentage difference even smaller. Simulation, optimization. A process of getting closer and closer to a perfect solution but never getting there. Hmmm, like Pi.
Imagine you find yourself instantly comprised at an age of say, 5, without and previous history, in the middle of a vast corn maze. You haven't a past to remember so as to compare your predicament to past happy or sad events, you haven't any frame of reference. No sense of sadness or happiness. Just 7 foot high corn stalks all around you and turning paths between them. There's nutritious berries and vegetables (and, of course, corn) on every path. All the base needs of which you are aware are met. But, each day at the same time as the previous day, when you look up at the sun, you know you're about where you've been before. You haven't made progress to where ever it is you intended to go.
You dream of what is beyond the maze as you wander its paths for years and decades of your life. At the corner of every turn where there are alternate paths, you notice signs with different color configurations that, over the years of seeing them and thinking about them, you decide they have some meaning in the scheme of the structure of the maze.
Then, one day, you get the idea that you'll follow one series of the several sets of signs at each junction. You'll concentrate on finding that same sign at the next junction and if is not there, then you'll back track to the previous junction and take the alternate path. On that alternate path you find the sign that you had decided to follow. You find the sign you for which are looking as if they were put there for you to find. By who?
Ultimately, you reach a dead end.
But its not a failure, you've eliminated a path. Now, with the time you have left in your life (however long that is), is there time to follow all the sequences of signs to get where you think you want to go?
And really, is it all so important that you get there? Or is the challenge more the end in itself? Thinking and knowing the small but not inconsequential part of the whole that you might represent if you simply go about doing what you feel you were intended to do.
Sadly, I doubt I'll ever see the structure of the maze as I believe Mr. Gann saw it. But, like the golfer whose terrible round is ended with a birdie that brings him back for another round, I have the "aha's."