Scott Carney's "Deep Crab" & the Fields Medal in MathematicsQ: What does the former have to do with the later?
A: The intuition in the former (S. Carney) is born out by the later (A. Avila; Fields Medal - 2014)
From Scott Carney's website;
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"Harmonic Trading: Volume One Page 136
The Deep Crab Pattern™, is a Harmonic pattern™ discovered by Scott Carney in 2001.
The critical aspect of this pattern is the tight Potential Reversal Zone created by the 1.618 of the XA leg and an extreme (2.24, 2.618, 3.14, 3.618) projection of the BC leg but employs an 0.886 retracement at the B point unlike the regular version that utilizes a 0.382-0.618 at the mid-point. The pattern requires a very small stop loss and usually volatile price action in the Potential Reversal Zone."
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From Artur Avila's Fields Medal Citation;
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"Artur Avila is awarded a Fields Medal for his profound contributions to dynamical systems theory, which have changed the face of the field, using the powerful idea of renormalization as a unifying principle.
Description in a few paragraphs:
Avila leads and shapes the field of dynamical systems. With his collaborators, he has made essential progress in many areas, including real and complex one-dimensional dynamics, spectral theory of the one-frequency Schrödinger operator, flat billiards and partially hyperbolic dynamics.
Avila’s work on real one-dimensional dynamics brought completion to the subject, with full understanding of the probabilistic point of view, accompanied by a complete renormalization theory. His work in complex dynamics led to a thorough understanding of the fractal geometry of Feigenbaum Julia sets.
In the spectral theory of one-frequency difference Schrödinger operators, Avila came up with a global description of the phase transitions between discrete and absolutely continuous spectra, establishing surprising stratified analyticity of the Lyapunov exponent."
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The connection here, as it is related to the specific "Deep Crab" harmonic pattern in trading, between intuition and general, analytical result, is illustrated somewhat simplified (but without distortion).
In essence, Avila has shown that in dynamical systems, in the neighborhood of phase-transitions in the case of one-dimensional (such as: Price) unimodal distributions, after the onset of chaos, there are islands of stability surrounded nearly entirely by parameters that give rise to stochastic behavior where transitions are Cantor Maps - i.e., fractal.
From that point it is an obvious next step to generalize to other self-affine fractal curves , such as the blancmange curve , which is a special case of w=1/2 of the general form: the Takagi–Landsberg curve. The "Hurst exponent"(H) = -log2(w) , which is the measure of the long-term-memory of a time series .
Putting it all together, it is not pure coincidence that a reliable pattern (representation) emerges from intuition (observation) which proves to be a highly stable (reliable) pattern that is most often the hallmark of a near-term, violent transition.
