Archive for September, 2016

158 – How Will History Judge Us? …

Thursday, September 15th, 2016

The most fatal enemies against the evolution of the Human mind are Greed – it makes us self-destructive – and Dogma – it chains the imagination.

As I visit other countries, other cultures, other peoples, I see the lasting effects of totalitarian domination … the trail of destructiveness; the deep scars, oftentimes fresh, from their unimaginable levels of cruelty. But as horrible as the effects of their domination have been and continue to be … Crusades, Inquisitions, Fascism, Communism, Colonialism, Kleptocracy … their impact is, for the most part, localized to specific regions. That is, until now, when under the harbingers of unabated Greed and blind Dogma, totalitarian domination has thrown our entire civilization, knowingly, into full-fledged Anthropocentrism (the fallacy that we have higher value than all other organisms and that Reality is to be assessed, exclusively, through human perspective). The consequences of this fallacy are already being felt in parts of the earth and will ultimately affect every single Human being.

The Human being, as far as we know, is the only creature conscious of its own capacity to self-reflect … to be able to look at its past and hope for its future, to imagine visions never before imagined … but Greed and Dogma have turned this capacity into a growing force of unsustainable and destructive consumerism with which we have already, irreversibly, altered the chemical balance of the environment that has allowed, and promoted, our evolution.

Greed and dogmatism, and the men who let their lives be enslaved by them, have condemned our Civilization to face its own decimation as Nature realigns the delicate equilibrium we have so thoughtlessly upset.

How will History judge those who, knowing the dire consequences of their irresponsibility, did not give a damn?

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157 – On Fractals & The Mandelbrot Set …

Thursday, September 1st, 2016

Fractal, from the Latin fractus meaning “broken” or “fractured”, is the recurrence of a pattern or shape which is replicated at decreasing or increasing scales and used to conceptualize fractional dimensions in Nature that look similar to the whole (small sections of clouds, mountain ranges, lightning bolts, blood vessels, snowflakes, cauliflowers). The recursive nature of fractals is also called Expanding Symmetry or Evolving Symmetry and is obvious, for instance, in a branch from a tree, which is a miniature replica of the whole, not identical, but similar in nature. If the replication of the pattern or shape is the same at every scale, it is called a Self-Similar Pattern and is best illustrated in the magnifications of the Mandelbrot set.

Mandelbrot Set

Mandelbrot Set

The elaborate boundary of the Mandelbrot set reveals ever-finer detail at increasing magnifications, with each magnification incorporating smaller repetitions of the set. So, the fractal property of self-similarity applies to the entire set and not just to its parts (the link at the bottom is a 2.14 Minutes YouTube video showing the recurrence of the set at increasing magnifications).

The Mandelbrot set has become popular outside mathematics, both for its aesthetic appeal and as an example of a complex structure arising from the application of simple rules. It is one of the best-known examples of mathematical visualization. [1]

Along with Holography (see post 154), the Mandelbrot set is one of the best analogies of Self-similarity I can find in the natural sciences: Everything in Nature, including you and I, is similar to everything else in the way we all unfold according to a common blueprint: Become, Self-organize, Bond, Self-generate, Self-regulate, Adapt, Self-perpetuate, Transform. This common blueprint endows every universal component – every one of us, every molecule, every galaxy – with the capacity to perpetuate the recursive cycle that begins with Becoming and always lead to Transformation. It is thus I believe that the perpetuation of this common blueprint is the universal foundation for building cohesive structures that can adapt to changing environments and engender hierarchical orders of complexity.

The Mandelbrot set is a computer-generated program in which we find the recurrence of identical repetitions, but ‘naturally evolving systems’ [2] are diverse, highly malleable, and completely reliant on a creative symbiosis with the evolutionary processes in which we exist; therefore, self-similarity in Nature is not identical as in the computer-generated Mandelbrot set, but is instead a supple and evolving symmetry towards greater and greater complexity.

Self-similarity in Nature can be ascending or descending, recurring from the whole Universe to atomic particles and vice-versa. Everything begins by becoming, then on to self-organizing, bonding, self-generating, self-regulating, adapting, self-perpetuating, and ultimately, transforming. This kind of cohesion can only be achieved with a level of communication we are not yet able to comprehend even though it is constantly occurring in us. How else can we communicate our own blueprint (DNA) to every cell we create in our bodies? How else can they in return, as a combined whole, communicate to us what we are, what we must do as the captain of our vessel, so we can follow primal instincts yet are able to choose?

It is obvious to me that the common knowledge of self-similarity in Nature can help us understand a bit better our intimate relationship with Nature, what is not obvious is why this knowledge is not in every curriculum of our educational systems?

https://youtu.be/9G6uO7ZHtK8

[1] The information above has been abstracted from Wikipedia

[2] By ‘natural evolving system’ I refer to ‘open systems’ which are generated by natural processes to interact freely with environments, as opposed to ‘closed systems’ which are man-made to fit specific expectations.

Revised September 2020   

Note: New posts are usually published on the 1st and 15th of the month. To subscribe to the Blog, click on the RSS feeder (orange icon) on the left column of the Home page, down below the Archives.