... or hints on how to check brain power on members of the opposite sex

Entropy is simply a fancy word for “disorder”. It is a quantitative measure for this extremely common concept.
The spontaneous evolution of an isolated system can never lead to a decrease of its entropy (= disorder). The entropy is always increasing as long as the system evolves. If the system eventually reaches equilibrium and stops evolving, its entropy becomes constant.
In other words, a closed system, deprived of any help from the outside, is incapable of putting its own affairs in order. At best it can let the level of disorder creep up very slowly. At worst the disorder will worsen rapidly until it becomes total, which is the equilibrium state, the state of maximum entropy.

Order can also be regarded as information, so we can classify the complexity of a system by how much information we need to describe it. Chaos is a purely mathematical concept; it is an undeniable mathematical fact. Chaos is the rediscovery that calculus does not have infinite power.
Order from chaos demonstrates in mathematical terms that a system can only become more ordered when the system is acted on by energy more ordered than the system itself; further, that a system decreases in order when it is acted on by energy less ordered than the system itself.

What about Self-Organization..? Artificial Life studies emergent features that result from the interactions of multiple agents following their own local laws. The phenomenon of emergence could be called Extropy, the tendency of systems to create order from chaos - the opposite of Entropy. Generally the term Extropy isn't used, instead Self-Organization is the general term employed.

Fractals are shapes of infinite complexity. They are "self-similar," meaning that they are based on a motif, or pattern, that has been reflected onto itself again and again. Each little piece resembles in shape each big piece, since they are shaped after the same motif. Usually this motif is quite simple. The mathematical expressions used to generate fractal shapes are usually simple enough to be understood by someone with knowledge of high school algebra.

What makes the fractal infinitely complex is that, again, a recursive process is involved. The expression makes a small, predictable change to what it starts out with at the beginning of each turn -- but continued indefinitely, new patterns emerge that were unforeseen. The implications of this are astounding. This means that even the least little bit of matter in Universe knows how to generate complexity, when the conditions are right. The processes of creation are hard-wired into everything that exists.


Now interrelate all of the above.
Got it? easy peasy :-)

If still in doubt, please check with the next generation of "Alchemists and Magicians".

Tudo o mais são romancetes da treta que jamais constarão nos Anais do Conhecimento.