Indeed; the end of the impulse (1) of the rising tendency, coincides with the positioning of the graph in the upper left corner of Hamilton’s Diagram. From here the correcting impulse (2) is produced which will bring the positioning of the graph to the lower left corner of the Diagram, due to the set back of demand, but as supply does not show up, demand increases again and an impulse (3) to rise is produced, which will bring the graph again to the upper left corner.

From here, History repeats, during the new correcting impulse (4) demand decreases, until the graph is positioned again in the lower left corner. But as supply does not appear, demand goes up again, impulse (5) is produced and we go back again to upper left corner.
Yet, now, after all this rising process, prices are much higher than the first time it reached this corner, and a decrease of demand, which will bring a fall of the graph, can here induce a withdrawal of supply, which did not happen in the previous cases.

In the case of the falling tendency, which we have sketched beside the other, reasoning is similar, but on the right hand side of the Diagram of Hamilton. Here, the end of impulse (1) to fall, coincides with the positioning of the graph over the lower right corner and the contrary reaction to the rise or impulse (2) which follows ends in the right upper corner, to fall again by impulse (3) to reach again the lower corner of this same stretch.
Again, by reactive impulse (4) the curve goes back to the upper right corner to finally and through Pulling down impulse (5) arrive again to the other corner, the lower, on the same side, but now prices have fallen sharply and a decrease of supply now, which would mean a rise of the graph, can induce here the appearance of demand, which did not occur in the previous cases.

We realize that reasoning based on impulses which generate setbacks of an stock graph or CHART is part and parcel with Hamilton’s vector deployment or, in other words, whoever knowing the vector impulses of Hamilton and seeking its verification in the behaviour of charts detects the existence of characteristic waves in them, and given that he’ll be conscious of the importance of the subject, he will be ready to make prolonged efforts of study and observation which the cataloguing of those waves demands.

Naturally Hamilton who, remember, constructed the Dow Theory and named it after and in honour of Charles Dow, did not know, nor could he, the Elliott waves. But Elliott did know the works of Hamilton.

On the other hand, it is known that without the active concourse of A. Hamilton Bolton, (another Hamilton) we would not have known Elliott’s Theory of Waves, and probably this method of analysis would never have been examined in serious circles, given Elliott’s unrefrainable tendency to the esoteric, which brought him to write, in his last days and against all who wished him well, a very odd book titled "The Law of Nature" in which he tries to unveil the universal principle or in his own words the "secret of the universe" based in magic and Fibonacci numbers.

There is ground to believe that either Elliot or A. Hamilton Bolton, who was the true driving force, systematiser, clarifier and ultimate promoter of the Principle of the Elliott Wave (Elliott wrote confusedly and without method), were inspired by Hamilton’s vector impulses, to later develop the most advanced part of the Theory, or they had access to his papers or, everything is possible, developed an astonishing affinity which stretched beyond name coincidence, so dear and fascinating to the last Hamilton.

The validity of Elliott’s Theory is undisputable in what refers to his verifications on chart behavioural patterns, but this is not so with the exuberant sociological literature generated to explain the reason of the appearance of these patterns.

We also know today in the FRACTAL method that Fibonacci’s famous 0,618 is not so, but 0.6110154705, 0.611 in practical terms, and we have the scientific demonstration of it and why this number so constantly appears in fractal formations (it is the most probable elongation).

This definitively clears the controversy arisen around the 0,618 factor which seems brought by force into the system and which is included by Elliott because 0,618 is the only singular number found in his magic – esoteric universe (0,618 is no less than the golden proportion to where Fibonacci’s series tend) to explain these elongations of a little bit more than 61 % which he finds everywhere in the graphs.

And then delirium happens, as Elliott sees in this number a universal principle (golden number, Fibonacci’s succession) which links up with the module he has found in his studies of the Stock Exchange and which makes his work transcendent, converting the Wave of the Elliott’s principle, in a module of universal application on any phenomena.

The best prove of the supremacy of the 0,636 number, which come up from the fractal rational- conception of the Elliot’s waves and modules, against the 0.618 number which emerges from the classical conception on the feelings of the mass of investors, - emotional- , is that the classical conception, after years of tests, accepts that the stripe of "minimum setback" is situated between 33 and 38% and that the stripe of "maximum setback" between 61 and 66%.

If we make a simple arithmetic average we obtain:

33 + 38                                                                                                      
---------- = 35,5 % = 0,355 (average level of minimum setback)
2                                                                                                       

61 + 66                                                                                                       
---------- = 63,5 % = 0,635 (average level of maximum setback)
2                                                                                                       

With that above it is demonstrated that even in the tests done with the classical emotional theory of Elliot, the average point (0,635), in which the popular wisdom says where the truth is, is closer to 0,636 than the classic 0,618, and the same happens with the complementary because (1- 0,636) = 0,364, is closer to 0,355 than to the classic complementary (1 - 0,618) = 0,382.

Then the consequence is that the current fractal foundation, obtained by rigorous and rational scientific methods overcomes the classic emotional reasoning based on the feelings of the mass which, empirically elaborated in around the 29 crack and based on never checked suppositions , is transmitted mimetically since 1934 until today’s fractal present where it happens the paradox:

The average of results obtained by the classic theory when it uses the scientific method (that is, when it checks) is much closer to what the fractal theory predicts than to what the classic theory itself predicts within its own framework.

In the XVIII century the naturalist Count Buffon, found something very similar to what is demonstrated by fractals, in his famous "experiment of the needle", which consisted in taking a flat surface and tracing on it 7 equidistant straight lines, hence dividing the surface in 8 stripes of the same width. Then he took a needle of the same length as this width and let it drop on the surface.

Buffon considered it a favourable fall when the needle was crossing one of the seven lines and non favourable when it fell between lines without crossing any.
His astonishing discovery was that if he multiplied the number of trials by two and divided by the number of favourable throws, the result approached Pi number as much as the number of throws increased.

Consequently if:

then:  Pi x  Favourable = 2 x Possible

                     Favourable           2
then: Probability =    ---------------------- = ---------- = 0,636
                       Possible              Pi

Later, in 1901 the Italian mathematician Lazzerini repeated the experiment, letting the needle drop 3.408 times and got for Pi a value equal to 3.1415929, with an error of less than 0.0000003.

The experiment of Buffon is independent of the number of lines used in order that the needle cuts any of them, as far as the needle has the same length as the distance between lines. If so the probability will be 0,636 and hence the frequency of elongations of the order of magnitude of the 60% of the scale of the graph will be maximum, whatever this scales is, and then this is what we’ll observe more frequently.

Furthermore, the fact that the fractal number were 0,636 instead of the golden 0,618 does not mean that we are getting far from phenomena related with the reestablishing of the balance of the non linear mathematics, that as it’s known, is established through spiral type patterns.
On the contrary, as we pass from a pattern restricted only to the golden spiral to a generalized pattern which affects any type of spiral. Indeed:

A fundamental feature of the non linear mathematics is the existence of limit cycles. An spiral tends to approach to the stability condition and the limit circle of stability has a ratio between the arch made of a fourth of the circumference formed by the spiral and its respective radiuses , Pi / 2 or 1,57. This is the inverse of the probability found by Buffon: 2/Pi.

Then, all seems to state that when a fractal of the equity quotation random walk type is destabilized, finding elongations within the range of 60% is the most probable. When the inverse situation occurs, that is, when the graph tends to destabilize, reaches the limit cycle getting back in elongations of 50% because:

           2          Favourable                   Favourable
Probability =  -------  =  -------------------  =   ---------------------------------------------
                        Pi           Possible            Favourable + Unfavourable

or, dividing the expression by the Favourable:

Unfavourable         Pi
and hence: ------------------------ = --------- - 1 =  0,57
  Favourable            2

This seems to indicate that if in a fractal graph we measured the consolidation elongations (setbacks to keep the same tendency) those most likely setbacks would be of the range of 50% of the fractal pattern, whatever the scales is, even though the most probable "pulls" we observed would be of 60% in favour of this tendency. This is also pointed out by Elliot’s theory but without justify the reason of this 50% in full.

Probability = 1 / (1 + (Unfavourable / Favourable )) = 1 / (1 + 0.618) = 0.618

This is so because this is the only number which keeps this relation.

The golden proportion is the only number which the relation between non favourable cases divided by favourable cases is equal to the relation between favourable cases divided by all possible cases, that is the probability. Should this happen it would not be any tendency as the pulls would be the same as the setbacks.

If Buffon and Lazzerini had detected that the ratio non favourable / favourable was 0.618 (the golden proportion) instead of 2 / Pi then the setbacks within a tendency would have been of the order of 60% because in this case the ratio Unfavourable / Favourable would also be the golden number 0,61803398, but tendencies could not be possible (the graph would not go ahead as the elongations would be the same as the contractions).
This is so, because the golden proportion is the only one which has the singularity that Unfavourable / Favourable equals Favourable / Possible.

Probability = 1 / (1+(Unfavourable / favourable)) = 1 / (1 + 0.618) = 0.618

If rises are the same order than falls, tendencies can not be formed.
If instead of taking the golden proportion we take 2/Pi as a base of Elliott’s module, even though the difference seems insignificant (0,61 against 0,63) the setbacks are not of the order of 60% but rather of the 50% and then graphs are possible, even though these graphs are fractals of Random Walk type which, so being, show the 2/Pi probability.