Luck v Destiny: Episode 1.

The “scientific” world disagrees to accept luck as a parameter to analyse success or destiny. I hear the tone of disquietude from my friends a lot often  when I speak about luck being a strong influential force in destiny. Am I perturbed or is my hunch right? I have reasons. Let me state them here.

Consider every physical parameter such as luck, destiny, fate, etc. as an event. Now each event has a starting point and an ending point. The starting point can have any number of parameters to it.

If we consider the chaos theory, then for every event with different starting conditions can have different ending possibilities. If we tend to apply the same concept with luck, then an analogy can be drawn.

Any thing with a different set of input parameters can end up differently. A car with half a tank of petrol can travel half the distance only. The same car with full tank of petrol can travel further more. If a car with full tank of petrol is driven in the first gear then the distance one can travel varies. Numerous probabilities. This is what luck is! It is one of the destinations of in numerous possible out comes of an event. If we take any event and try to model it with a certain set of input parameters, we will get an attractor equation.

A system is a vector of real numbers which define its state. The main aim would be to provide a complete description of the system at some point in time, space or any physical dimension.The set of all possible states is the system’s phase space or state space. This space and a rule specifying its evolution over time defines a dynamical system. These rules often take the form of differential equations [1]. An ordered set of state values over time is called a trajectory. Depending on the system, different trajectories can evolve to a common subset of phase space called an attractor.

Let t represent time and let f(t, •) be a function which specifies the dynamics of the system. That is, if a is an n-dimensional point in the phase space, representing the initial state of the system, then f(0, a) = a and, for a positive value of t, f(t, a) is the result of the evolution of this state after t units of time. For example, if the system describes the evolution of a free particle in one dimension then the phase space is the plane R2 with coordinates (x,v), where x is the position of the particle, v is its velocity, a = (x,v), and the evolution is given by

Attracting period-3 cycle and its immediate basin of attraction for a certain parametrization of f(z) = z2 + c. The three darkest points are the points of the 3-cycle, which lead to each other in sequence, and iteration from any point in the basin of attraction leads to (usually asymptotic) convergence to this sequence of three points.

{\displaystyle f(t,(x,v))=(x+tv,v).\ } f(t,(x,v))=(x+tv,v).\

An attractor is a subset A of the phase space characterized by the following three conditions:

  • A is forward invariant under f: if a is an element of A then so is f(t,a), for all t > 0.
  • There exists a neighborhood of A, called the basin of attraction for A and denoted B(A), which consists of all points b that “enter A in the limit t → ∞”. More formally, B(A) is the set of all points b in the phase space with the following property:
For any open neighborhood N of A, there is a positive constant T such that f(t,b) ∈ N for all real t > T.
  • There is no proper (non-empty) subset of A having the first two properties.

Since the basin of attraction contains an open set containing A, every point that is sufficiently close to A is attracted to A. The definition of an attractor uses a metric on the phase space, but the resulting notion usually depends only on the topology of the phase space. In the case of Rn, the Euclidean norm is typically used.

Many other definitions of attractor occur in the literature. For example, some authors require that an attractor have positive measure (preventing a point from being an attractor), others relax the requirement that B(A) be a neighborhood [2]

Since luck has many inputs and many outputs, its attractor would be strange [Refer strange attaractor].

Now let us talk about destiny. Destiny is the final outcome of an event. Based upon the attractor equation that would be derived, destiny can be mathematically thought as one of the possible output.

It is possible that in coming days of A.I we succeed to model the attractor equation for luck and choose our own destiny.