Applying Exponents & Sine Waves To TA

Now, mathematics and physics can apply to economics and geopolitics too, hence the connection with me and my site, subtitled 'A Sound Engineers Guide to Geonomics'. And before you pull me up, YES I DO know that there should be an apostrophe between the r and the s, but it looked wrong. And, in exponential quantum geonomics, if it looks wrong, it is wrong. Rule number 9. I just thought of it.

In sound engineering courses I teach, I make sure that we tackle exponents early on in the course, because they crop up everywhere in sound and music - from the dB scale to the audible frequency spectrum. Forgive me if the following explanation insults your intelligence, but order to make sure we are all singing from the same lyric sheet I am going to offer an explanation of exponents.

LINEAR SCALE LOG. SCALE

Musical Octave Frequency of sound (Hertz)

1 1

2 2

3 4

4 8

5 16

6 32

7 64

8 128

9 256

10 512

11 1024

12 2048

13 4096

14 8192

15 16384

16 32768

NOTES TO TABLE SHOWN LEFT

Each step represents a doubling of frequency. Each step also represents moving up one musical octave. The first 5 entries and the last entry are actually outside the range of human hearing, and could not be reproduced at all from a CD.

The left hand scale counts the OCTAVES, the right hand scale the FREQUENCY in cycles (vibrations) per second, AKA Hertz.

Going up the musical scale, every octave the frequency DOUBLES, while the size (wavelength) of the vibration HALVES.

The relationship between OCTAVE and FREQUENCY is not LINEAR, but LOGARITHMIC, or EXPONENTIAL.

We can express this as a formula

e(2) of N = 2^(N-1)

^{Where 'e' =
'exponent' and '(N)' = 'raised to the power of'}

Try it with any of the numbers in the table.

e.g. 5

e(5) of N = 2⁽⁴⁾= 2 x 2 x 2 x 2 = 16

Let's apply this 'doubling' exponential relationship to the price of shares. If shares double in value, they in effect go up by x 2. Each time they double in value they go up by another x 2. If they fall back to one half they are divided by two.

Now, if a stock has doubled in value, then that new value becomes its present value. The previous value no longer applies. It's history. We must reference any further movement from its NEW value. If it halves, it goes back to 50% of present value. If it doubles again it gains 100% of its present value. We have shown that ;

Charting (as every GOLD-EAGLE Forum member knows) is a way of predicting how stocks (and commodities) will move based on observed occurrences in the market. It is a black art, but it does seem to have some merit. However, many charts are drawn on a linear horizontal (price) scale. This can mislead as prices move exponentially, as I have shown. Therefore, only a chart with an EXPONENTIAL scale should reveal TRENDS as straight lines, especially over wide price movements.

The HUI bounce predicted in my March 2003 article "Exponential Quantum Geonomics" was later and from a lower level than expected. Why?

The original TA done in March 2003 was based on a support level shown by the blue dotted line. However, the rise in the HUI centered on Christmas 2002 (purple dotted ring) was almost certainly due to a war premium. This evaporated before 'hostilities' commenced. Buy the rumour, sell the fact. As such I now consider it to have been an aberration from the norm. The norm being a simple series of sinusoidal waves rising on an ascending base. However, the exponential scale used (lifted from the GOLD-EAGLE site, actually) is not extreme enough to engender parallel support and resistance lines - they diverge somewhat (dotted black and solid white lines). Compressing the log scale further would eventually force parallel support & resistance.

The original chart has been overlaid with a new white support line and flag tops, eliminating the peak caused by the POG of war. The horizontal* 'resistance' indicated by the upper dotted blue line of the second flag formation is probably an anomaly.

*Horizontal support and resistance lines are pretty meaningless anyway in a dynamic market. They takes no account of inflation, for one thing.

The previously expected up-thrust (yellow arrow) has now been replaced by a new blue arrow, indicating my current projection going forward. The HUI was rising when I posted the above graph (May 2003). And it still is now!

Vibrations in a guitar string are caused by a displacement away from an equilibrium position. The string is then released and allowed to return to rest. The bigger the displacement, the bigger the vibration. However, no matter how far the initial displacement, the equilibrium position remains the same.

A vibration over time forms a wave. These waves propagate through time for as long as the vibrations last.

Stock markets also exhibit wave-like behaviour. Look at the above chart again. A period of just over one year has been established for an oscillation between 'overbought' and 'under-bought' conditions of the market. Unless the trend changes, it is absolutely obvious that another up-leg to about 2-3 times the current level is imminent, to be completed sometime towards the autumn of 2003.

The next graph is my latest attempt to foretell the future of the HUI. I deliberately used only 2 curve points per cycle, to force all detail out of the picture. It seems the HUI may NOT have hit the natural support during the downwave centered on Christmas 2002, due to a war premium as explained earlier. I have therefore tried to interpolate a smooth curve through this period. This has the effect of further amplifying the increase in size of successive waves in the HUI. It may also lengthen the period of oscillation somewhat going forward. The pattern should only break if:

Barring unforeseen exogenous events, this pattern should continue until the market trend changes. In light the way the dollar is headed, this may be post-2004. At the time of the next Presidential election we might see a dip to HUI 200 - to be followed by an even more extreme up-leg. It could possibly even approach 4 figures.