Thanks for visiting us. We'll show you market moves perfect to the exact day. Some moves are over forty years long. Our principles apply to all freely traded markets; financials, Forex, agriculturals, metals, etc. "We hold these truths to be self evident," basis empirical evidence within the markets. "Perfect" is a bold claim. Therefore we'll prove it for you right now with a few examples. Two of them show perfection from the June 25, 1962 low to the October 10, 2002 low.
Galileo, The Sidereal Messenger (1610)
“Philosophy (nature) is written in that great book which ever lies before our eyes. I mean the universe, but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. The book is written in the mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is humanly impossible to comprehend a single word of it, and without which one wanders in vain through a dark labyrinth.”
We'll show you that recurring and predictable movements do occur in all freely traded markets. Examples on this site use only the S&P 500 Index and Dow Jones Industrial Average. We are confident you'll be eager to explore every page of this web site after you see the three examples below. We strongly urge you to go directly to the Examples section when you finish this Home page.
First example: The geometry illustrates the relationship between the 1962 low - 1973 high, and 1973 - 2002 low moves. This forty year span is “perfect” to the day. We have other examples illustrating this degree of accuracy for periods over seventy years. This particular example, showing the evolution of a market move from the side of a square into the diagonal of a square four times larger, is not unusual.
There are 2656 trading* days between the June 25, 1962 bottom and the January 11, 1973 nominal price top. There are 7512 days between the 1973 top and the October 10, 2002 bottom. 2656 x 2.8284 ( 2 x 1.4142, sq. rt. of 2)= 7512
The following chart shows this relationship geometrically in three different examples:
- When the diagonal of a square ABCD = 2656, the perimeter of the same square ABCD = 7512
- The diagonal of a square BFEG with sides of 5312 (2 x 2656) = 7512
- When the hypotenuse of an isosceles right triangle BGE = 7512, one-half of one leg of the triangle = 2656
Click the chart below to see it full-sized:
Second example: This example also shows perfect timing, 1962 - 2002: From the low day in 1962, to the DJIA high day on January 14, 2000, to the low day in 2002. We chose this example among hundreds because it illustrates several different principles at work.
There are 9482 trading days* from June 25, 1962 to January 14, 2000, and 686 trading days between January 14, 2000 and October 10, 2002.
Click the chart below to see it full-sized.
9482 x .07236 = 686.12 You might be thinking "So what? What's the ratio 0.07236?"
0.07236 is 0.7236 scaled down by 10. 0.7236 is the inverse of the ratio 1.382. Although perhaps not immediately apparent, 1.382 and its inverse are important Golden Mean (Fibonacci, Golden Section, etc.) ratios. You probably recognize 0.382 as 0.618 squared.
There are hundreds of long range examples using more familiar Golden Mean ratios. We chose this one to introduce three important principles:
Principle 1: There are many permutations, and layers of Golden mean ratios active in the markets.
Here is an another example using 0.7236/1.382:
There are 5436 trading days between the 1966** DJIA top and the 1987 top. 5436 x 1.382 = 7512.5.
You've already seen 7512, the 1973-2002 move. It is not important that the 5436 and 7512 day moves are not contiguous on the plane. We consider market timing to be spherical and multi-dimensional in character.
Principle 2: Use multiples of basic Golden Mean ratios and mathematical constants.
3 x 1.618 = 4.854 There are 1620 days between the 1962 low and the December 2, 1968** top. 4.854 x 1620 = 7863
7863 + 1620 = 9483 This is one day longer than the 9482 day move, 1962 low to the 2000 top.
Principle 3: All mathematical constants and ratios may be scaled, up or down.
The most obvious example of this is the 3141 day move from the 10/20/87 crash low to the current historic S&P high, 03/24/00. 3141 is 3.1416 (Pi) scaled up by 1000.
Third Example: Here the product of two mathematical constants, Pi and the Golden Mean 1.618, is shown scaled up by 1000. It also illustrates the BalancePoint Principle. The resulting value leads precisely to the August 25, 1987 top.
3.1416 x 1.618 = 5.083. Scaled up by 1000: 5083. The exact number of days between the 1967 top BalancePoint and the 08/25/87 top is 5083. A BalancePoint is the midpoint between two pivotal days when DJIA and S&P reach their extreme intraday prices on different days.
In inflation adjusted or constant dollar prices the highest prices reached, from 1932, were in 1966, DJIA and 1968, S&P. Prices declined from there until 1982 and did not exceed the 1966 and 1968 prices until the 1990's.
Click the chart below to see it full-sized for derivation of the 1967 Top BalancePoint:
*A Note Regarding the Proprietary Ermanometry Trading Day Count and Determining Pivotal Days
Intraday extremes are used to determine high/low pivotal days. Closes are not considered.
** On a constant dollar/inflation adjusted basis, the DJIA made its highest price on February 9, 1966; the S&P on December 2, 1968. Prices declined until August 1982, and the 1966 and 1968 prices were not reached until the 1990's.