Using fractals, topological and Hausdorff dimensions and novelty theory to estimate technological singularity and simulate
planetary intelligence; and an analysis of how such methods could be used to solve practical problems.
Introduction
Technological singularity is defined briefly as a point somewhere in the near future where an unprecedented explosion of technology and artificial and virtual life will take place, thus expanding civilization as we know it to a degree never seen before ; which will slowly be followed by gradual compression, both physical and mental. Civilization will, instead of colonizing outer planets, slowly start turning inwards, leading to near black hole-like instability. Singularity and MEST (Matter Energy Space Time) compression have become phenomena which a new era of ‘post-humanism’ or ‘transhumans’ will possess after significant advancement in technology.
A
fractal, very briefly , is a rough mathematical shape which is self-similar, that is, a magnification of an inner part of its shape will yield something very similar to the main fractal itself.
Among the many ways of measuring abstract quantities, the
topological and Hausdorff dimensions are the most commonly used methods. The dimension of a set is defined as the minimum number of parameters needed to
completely define that set. In a topological space, we define an open set which can be described in a minimum of n elements – here, n is the simple topological dimension. For more complex geometrical shapes whgich cannot be described this way, we define a set of minimum spheres of radius r which can cover it – if N(r) is the total no. of such spheres, and N( r ) varies as 1/rd as r approaches 0, then d becomes its Hausdorff dimension.
Novelty theory is a fascinating and elaborate study of numerical patterns reflected in random statistics of human behavior from around the world – traffic jams, customers in malls, passengers in a jet plane, etc. – it is a way of mapping the flow of events in human history. It is a very helpful way to estimate the rise and fall of ‘perceptible intelligence’ in a civilization, both for societies as well as individuals.
Main abstract
In this project, I will try to estimate a way of measuring human complexity and event complexity through a system of fractals, or, more correctly, through a series of self-
replicating and self-similar ideas and concepts, both physically tangible and abstract.
Barely a century ago, the world was in throes of finishing what is called the industrial age; by the 80s and 90s, the advent of computers suddenly ushered in a knowledge revolution, and today, in almost every particular aspect of technology, the ‘concept era’ is being talked about – a field where concepts and ideas are given top priority , which leads away to the accumulation of raw data, and then, at the lowest level, solving problems with manual labor. Barely ten years ago, the world used to flow through a barrage of information, now, it is the essence of human thought that counts more than anything. Naturally a question arises to a practitioner: what next?
Approaching human events and breakthroughs mathematically and experimenting with the possibility of measuring the flow of events has a wide scope of applications, beneficial not only now, but also for the quickly approaching future. The estimation of the intelligence of a planet is a fairly impossible task, but an understanding of human behavior with a possible construct of classifying them according to known mathematical behavior can have a wide variety of applications:
1. It is useful in understanding and solving the problems that are arising with technology and mental evolution – traffic jams, overpopulation, unbalanced economic growth etc.
2. It provides a fascinating insight to understanding the nature of self-replicating and self-similar systems – for example , seen from above, any human settlement would look like a cluster of habitats amidst areas of darkness – this observation is repeated throughout the planet, and it provides away of connecting practical examples to mathematical hypothesis.
3. It gives an excellent use of fractals and fractal dimensions – and extends their applications to subjects as diverse as pure
mathematics, population control, information systems, etc.
4. It provides a rigorous way of understanding technological singularity – thus helping us inhibit human behavior in machines – for example – the construction of a
semantic web which understands human language patterns just like humans themselves do.
5. It provides a way of understanding events going to happen in the future – it estimates the possibilities given our constraints of physical and natural laws.
6. It asks a very important question of Unification. Is the Unified Field Theory obtainable in the near future?
Using simulations and analyzing brief, small examples, I will try to connect the world of self-replicating systems to the applications mentioned above, and thus will examine their need and scope. Just like a field practitioner utilizes all the given methods and axioms at hand to study the problem and eventually solve it (thought-experimentation, trial-and-error, induction), I am going to examine fractal dimensions as a possible instrument in studying and solving problems of human evolution and behavior. The more instruments at hand – the more ways to solve any given problem – thus, I hope to create a system which can estimate practical problems with a minimum degree of error.