**1. Introduction**

#### **1.1 The multi-dimensional hierarchy of organisational levels in brain**

**Brains** are characterised by every property that engineers and computer scientists detest and avoid. They are **chaotic, unstable, nonlinear, non-stationary, non-Gaussian, asynchronous, noisy, and unpredictable in fine grain**, yet undeniably

they are among the most successful devices that a billion years of evolution has produced. **Brain systems** operate on many levels of organisation, *microscopic, mesoscopic and macroscopic*, each with its scales of time and space. **Dynamics**, the modelling of change, is applicable to every level, from the atomic to the molecular, and from macromolecular organelles to the neurones into which they are incorporated. In turn the **neurones** form populations, these form the sub-assemblies of brains, and so on up to embodied brains interacting purposively with the material, interpersonal, and politico-social environments.

Subsequently, the *mesoscopic* **level**, very aptly characterised by *nonlinear dynamical electroencephalographic (EEG) electrical activity* [1], seems to be the optimally suited substratum of interplay of neuronal discharge and its patterning, that seems to have been very beautifully and intelligently decrypted and decoded through the armamentarium of **digital biological signal processing across** *linear (relative and absolute power spectral densities, coherence and others)* **and** *non-linear classifiers (entropy, fractal dimensions and others)***.**

The varied discrete and quantal features of *Human Brain* working and co-opting, in tandem and in sync, across the dimensions and coordinates of space and time evolve into the *phase-space stochastic trajectory of* abstruse and arcane domain of *the Human Mind* observing the principles of *non-linear dynamics of Chaos [2]*. The human brain provides the scaffold and framework for the functional dynamics of human mind in real time [3] following the principles of *Chaos*, further documented by our centre in 2009 [4] (**Figure 1**).

*Carl Jung* has very aptly outlined the schema *as "In All Chaos There is A Cosmos, In All Disorder A Secret Order"*. The *Secret Order* as has been exemplified by Carl Jung forms the nidus to explore further the realms of *Chaos*.

*Hilbert transform of EEG lead pair across EEG lead pair for EEG frequency-waveform bands of δ, θ, α, β, γ representing the* stochastic trajectory of neural dynamics in real-time.
