How many times have we uttered this phrase when troubles, problems, pains, fears, uncertainties and curiosity creep into our lives and those of our beloved?

We are like stranded survivors of the Titanic, faced with the vast oceanic horizon, feeling lost and wandering where to go on in body and mind. In what directions should we head my lifeboats towards and how do we carry on from here without our loved ones?

The human heart yearns for security, peace, love, hope, happiness, comfort and predictability. Unfortunately in Truth, the world in which we live in contradicts our wishes. Wars, battles, disputes, lawsuits, misery and crises are just some examples of recurring worldly events that are disturbing. Anger, fear and ill faith seems to be encompassing all of us. Extremism trends are plentiful whether in the past or the present.

For our want of the absolute, the world operates in the relative. Wars maybe senseless and brutal in the eyes of the peaceful, but rightful and honourable in the eyes of the warring parties. An event presents the opportunity for a counter-event that negates or counteracts the original event as well as for a forward-event that enhances or amplifies the effects of the original event, both in linear and non-linear manners.

In an argument, debate or dispute, there are multiple-sides or dimensions to the event that have varying effects. The party that "wins", for example wins a lawsuit, achieves a gold medal or has the "last laugh" may well be due to the still academically unverifiable chance. The chance that a crucial piece of evidence has been preserved and uncovered, that the sports athlete flexes a muscle group just at the right moment and conditions to edge past the adversary, or that a series of unanticipated events that dilute the other party’s circumstances. Can chance be subjected to scientific investigation?

Exploration, investigation and analysis of worldly and virtual phenomena that is so fundamental and striking at the roots of the phenomena that yield a certain degree of predictability and understanding of the phenomena forms the basis of science. Whether the Mens Rea or intention is one of faith, curiosity, need or want does not matter, the fact of the matter is that the operational principle of worldly events is the doctrine of relativity. Any results, conclusions, findings, theories and laws of science should be publicly accessible and depending on the unpredictable individual, group or society, be of use or misuse for "good" or "bad".

The fact of the matter regarding life, social behaviour, economics, politics or any event whatsoever is the inherent complexity yet partial predictability and pseudo-infinite relationships with expressed patterns mirrored by fractals. The intention, purpose, use, need or want to interpret "useful" meaning of these recurrent events is the true question. In quantum mechanics, the experimenter through the act of experimental observation & testing has already altered the original sequence of events.

The essential nature or Truth of events may or may not matter to the inquirer depending on surrounding circumstances. For example, the captain of a ship trapped in a storm will find it useless to question why the storm came about, but he surely needs the means, skill, crew and luck to survive.

The concept of the participant vs the observer perspectives are the intrinsic factors influencing the conduct, relationship and chain of events that produce the eventual results.

The participant being involved in the activity or event is absorbed and becomes integrated along with other participants. Although its views are limited in scope to the events that the participant engages in, the depth to which that participant has analyzed and perceived would be very detailed. The observer, on the other hand, would be have views in broad scope across the entire spectrum and beyond, but the details perceived would be of lower quality. There is level of compromise, tradeoff or economics due to worldly nature of limited abilities /powers.

Let level of tradeoff be e.

e = [0,1]

where

e = 0 represents perspectives either complete in scope or detail, but not both

e = 1 represents perspectives that fully encompass both scope and details

0 < e < 1 represents perspectives with a variable mix of scope and detail, but incomplete in either.

Both e = 0 and e = 1 are extremes that do not exist in this world, as such they are considered ideal cases. However they can serve as useful benchmarks to evaluate, analyze and compare various perspectives. This is similar to the price / earnings ratio used in shares evaluation in economics.

In nature, the ratio of e depends on the complex circumstances faced within and without the perception-making unit, individual, group, society or species. As e should ideally tend towards 1 (unity) for perfect completeness in perception, means of increasing e should be encouraged. By the principle of superposition, the level of perception of an individual (whether participant or observer) can be enhanced, deepened or widened by that of another in either linear or non-linear manner.

Let individual level of perception be e_i

& group level of perception be e_T.

e_T = ^NS _i=1 ( w_i.e_i) / ^NS _i=1 (w_i), the weighted product of each level of perception

where

w_i: ranges from (0,1)

Assuming that all individuals are "equal" (w_i=1), the group level of perception, e_T would be the average of those of the individuals. Therefore, to raise the group level of perception, members with "higher" levels of perception has to be identified and integrated with the existing group. Members with "lower" levels can be removed.

However this is nevertheless an extremely simplified model with intrinsic assumptions. The complex and variable nature of each "individual" guarantees that there is no fixed level of perception and as such "ranking" of individuals (like what have always been conducted in our society) and the subsequent addition or removal to the group according to these rankings may prove to be more of a detriment than an enhancement.

The same can be implied to science. Experimental verification to theoretical exposition often prove to be the holy grail of all theorists, as should be in order to conform to the order and nature of this world. But, as the saying goes:

What the present world’s nature may be a special case of a wider, extra-worldly nature. If our world’s nature can be considered as finite ( since scientists have shown it is even though the universe is still expanding ), there probably would be an infinite nature that encompasses ours. This is similar to statics (no time variations) being a special case of dynamics (time variations).

Is there a chaotic chance that our established laws are only theories and our present theories, extra-ordinary expositions or absurd jokes are in fact laws within the infinite natural extra-world? How perplexing this can be!

In fractals world, there is an intrinsic characteristic of self-similarity. Can we apply this self-similarity concept to the world at large by the method of induction? Where is our present state – exploring within the self-similar entity itself or already extending beyond one to other entities?

Assuming that the self-similarity nature extends multi-dimensionally without ends, there is no need for us to worry about our present state. Wherever and however we explore and investigate, we are always being encompassed in self-similarity with fractals being within and without. Thus events from the beginning, the process to the end are mirrors within and without themselves.

Extrapolating this to life, as self-similarity mirrors itself, there is the nature of complexity within simplicity and simplicity within complexity. The chain of events leading to any consequence may be complicated by the need for simplicity and simplified through the prevalence of complexity, as illustrated by bifurcation.

Life is self-similar in itself, possessing characteristics that mirror or reflect on themselves multi-dimensionally. By investigating and understanding this natural aspect, an individual dependent on its level of perception, should grasp the simplicity in one is the complexity in another. Yet there is the seed planted for the reverse or counter-event for every event, as in the saying:

Predictability may be regarded as an indicator of knowledge and is widely sought after, but the ability for insight of self-similar characteristic of event-within and event-without is a gem. Upon attainment, life itself is transformed, for after the war comes peace, after the sadness comes happiness, after the drought comes rain and after the panic comes rest. The fundamentals to life can thus be laid. Freedom of individual coupled with self-similarity understanding creates lasting harmony, whether in simplicity or complexity, whether in wealth or poverty and whether in health or sickness.

The process of change, formulation or evolution of life, or any event can be directly attributed to the environment, for within it contains the seeds of generation as well as destruction. The principle is the survival of the fittest with respect to the environment changes.

The circumstances surrounding life or the process culminating to an event are dynamic in nature with multi-dimensional variations. In order to survive, live and prosper, an organism requires either the desired optimal survival conditions or evolution or transformations to adapt to the dynamic surroundings.

Natural phenomenon provides inspirations on this front. The flies, rats and cockroaches are seen everywhere due to their excellent adaptability. The extinction of flora and fauna is the result of inadaptability. Like the captain of a ship caught in a storm out at sea, his ability to ride the waves and winds securely is the criteria to survival. The concept of chaotic adaptability is dependent on the circumstances within and without the decision-making individual.

Since 1960’s, the realm of artificial intelligence has been explored for understanding, implications and applications. The main branch of Artificial Intelligence research in the 1960s -1980s produced Expert Systems. These are based upon a high-level model of reasoning processes (specifically, the concept that our reasoning processes are built upon manipulation of symbols). Further studies based on natural phenomena yielded simulated annealing, genetic algorithms and neural networks.

Through exploring, understanding and formulating natural and artificial (real or virtual) activities in terms of mathematical and computational forms, technological advances have pushed the human limits of perception and will be of great assistance to scientific investigation in the present and future.

Evolution of life, process of social behaviour and change, state of the economy and political reforms are just some examples of dynamic, chaotic results that continually influence future events in relation to the prevailing circumstances. Even though these systems are not completely boundless in terms of future events, the order and underlying mechanisms, if any, of these systems are near impossible to be investigated and known explicitly.

In the light of this, modeling with cause-effect approach can be applied under certain assumptions. For good approximation to reality, the assumptions would be best inspired from reality itself. Through identifying critical or significant natural or artificial factors of the real event, computation and simulation based on these factors would yield the particular aspect of reality. This is in fact the basis of science itself.

However for simulated scenarios to tend towards reality, more and less significant factors must be considered. Thus therein lies the economics of modeling research, a compromise or tradeoff between high detail, low approximation as well as low detail, high approximation subjected to constraints such as technology, skills, talents, etc.

The following is a short write-up on optimization simulation based on natural phenomenon of evolution of genetic species.

Genetic algorithm was proposed by Holland (1975) as a computational process based on chance to attain or approximate towards a mathematical optima of a modeled event domain using certain criteria set. The criteria set can be regarded as objective properties of any event within the domain that are desired, useful or successful in the context of the environment.

As of present knowledge, genetic algorithm possesses high versatility and robustness to a wide range of reality events or problems from scheduling, time-tabling, the travelling salesman problem to portfolio selection, agriculture, fisheries etc. Its fundamental basis is evolutionary chance. This has been observed as the single most critical factor leading to life and perhaps other chaotic events. Chaotic chance may simply be all-encompassing factor that includes all unknown, unquantifiable and unqualitative order and mechanisms in relation to the particular worldly events we are facing.

Genetic algorithm can then be considered a probabilistic search approach, which is founded on the ideas of evolutionary processes. The evolutionary chance itself is based on the Darwinian principle of survival of the fittest. The algorithm is as follows:

• An initial population is created randomly containing a predefined number of individuals (or solutions), each represented by a genetic string (incorporating the variable information) or chromosome.
• Each individual has an associated fitness measure, typically representing an objective value derived from objective function set that contains criteria crucial to its survival within the system or simulated world.
• The concept that fittest (or best) individuals in a population will produce fitter offspring is then implemented in order to reproduce the next population.
• At each generation, selected individuals are chosen as parents for reproduction.
• Just as in real life, computational exchange of parents’ chromosomes (or crossover) is carried out.
• An appropriate mutation factor to randomly modify the genes of an individual, in order to develop the new population.
• Iteration of the above with the new population.

The results are sets of individuals based on the original subjects leading to subsequent populations with better (min. or max.) individual fitness. Therefore, the algorithm identifies the individuals with the optimizing fitness values, and those with lower fitness will naturally get discarded from the population.

Concept of fitness is the key to understanding the internal workings of the genetic algorithm, charismatically called GA in short. Without fitness, the GA is no different from a random simulation or search for a desired or required ending, solution or result. Fitness relates the individual chromosome directly to the simulated system through the objective function set. Its chance of survival within the system is evaluated in numerical form from the objective function set and subsequently influences the GA results.

Another key component is the chromosome representation, which can be in binary or non-binary form depending on the situation at hand. Both chromosome and objective function set are the only components within GA that need to be altered to cater to the system, event or problem. The other processes are universal, thus explains the versatility of GA.

However evolution itself may not give rise to the best, optimal result as the process is continually being molded in chaotic chance. GA can provide excellent approximations towards reality, but it will not produce reality itself. Neither can reality repeat itself if it restarts itself from some arbitrary initial point in the multi-dimensional spectrum. Chaos is an inherent, intrinsic property of the world. By bravely and wisely investigating, experimenting, simulating and learning from the worlds within and without, it is hoped that humanity may understand the lessons within.