Mathematics
BTC;Criticality &Phase Transition; Thermodynamics of SpeculationThis is just a quick take on how markets , and more specifically Speculation - in it's most general, universal sense -, is informed by similar critical dynamics as those found underlying other social interactions. (The math is hidden. You're welcome.) What this is Not , is a ready-to-use model since the specific parameters or the full model description are not part of the proceeding.
The following "As is ..." ;
This statistical–mechanical model is based on the Boltzmann–Lotka–Volterra (BLV) method.
BLV models involve two components: a fast equilibration, Boltzmann , component and a slow dynamic, Lotka–Volterra , component. The Boltzmann component applies maximum entropy principle to derive the static flow patterns of instruments (or their utility , as is the case). The Lotka–Volterra component evolves the spatial distribution (Price & Time; i.e.the chart) and the flow pattern of a information according to generalized Lotka–Volterra equations for distributed information.
The resultant dynamics exhibit critical regimes, interpreted as phase transitions , where a small variation in suitably chosen (control) parameters changes the global outcomes measured via specific aggregated quantities (order parameters).
The main take-away here is that this is in line with the idea that, despite the complexity of such a system (as depicted) only few parameters may be necessary to understand drastic macroscopic changes.
The maximum entropy method has been applied to a variety of collective phenomena (E.g., Speculation; Yours Truly) suggesting a formal analogy between complex, socio-economic systems and thermodynamic systems.
We use a clear thermodynamic interpretation of the Fisher information as the second derivative of free entropy. Specifically, we investigate the minimum work required to vary a control parameter and trace configuration entropy and internal energy, according with the first law of thermodynamics. The thermodynamic work is defined via Fisher information and thus can be computed solely based on probability distributions estimated from available data.
Once we introduce the concept of thermodynamic efficiency as the ratio of the order gained during a change to the required work (information transmission), it can be rather easily demonstrated that it is maximized at criticality .
Note; The above further illustrates the common observation that Technical Analysis fails, in most cases, to capture (forecast) Finite-time Singularities - i.e the sudden appearance of exponential price increases or price collapses ( crashes ).
Geometric Brownian Motion in playAs you can see, price is brownian. As soon as price moved over the first standard deviation, it was riding it, then got above second standard deviation, and tested it, now testing a third standard deviation of Cones projection.
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Candlestick Math Candlestick Math - V1.0
Sometimes , you need to do some candlestick math to drown out the noise between the candles . This helps in better decision making overall by understanding the effect of the last few candles.
Candlestick Math creates a new blended candle which can be interpreted as a summary of the defined period . The indicator uses Lookback period as an option to define the period.
For those who are not familiar with the Candlestick math , please google it and you will see many references. Please do note that this is a very short code and future versions will contain Multi frame capabilities as well as candle recognition.
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Cheers ,
Bitfanatic