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Four dimensional Fractal Equation


Butters

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I like the idea that the universe could be described as a four dimensional fractal equation. A fractal is similar at all magnifications, and at first glance it would appear that our universe is not. But what we describe as the universe probably does not encompass the entirety of existence. It could be that our universe is one of many, and that the reason we can't see it is that we are not able to look at things from far enough away. Or close enough. Quantum particles popping into existence briefly could be far more than they seem when considering the smaller scale of the equation.

 

I realise that analogies between the orbits of subatomic particles and interstellar objects don't hold up to scrutiny in terms of this, but perhaps as residents of our universe, the most we can see is our snapshot of the infinitely complex. It does seem to suggest that we can zoom in or out in either direction and continue to find complexity.

 

This would also imply of course that everything is deterministic. Some people would dispute that, but I have no problem with that being the case. I am my brain, and my brain structure was determined without my input or consent. Therefore everything I think and do is a result of something that I did not consciously 'choose'. I may feel like I have free will, but do I really have the free will to be a different person. I can make a conscious effort to alter my behaviour, but even that effort is a pre-programmed part of who I am. The outside influences that may lead to such a change are also no more than predictable patterns.

 

 

There's a very good reason I put this in speculations, but what do people think?

Edited by Butters
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According to some, if you look hard enough you will see that the universe has self-similarity (a fractal property). The DNA, neuron, brain, societies and Universe have been described using fractal laws and believed to be self-similar in progressively larger (or smaller) scales.

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For a start, search Medline for DNA/fractals, brain/fractals, neuron/fractals etc.

Rather technical papers are

 

http://www.ncbi.nlm.nih.gov/pubmed/20365626

 

http://www.ncbi.nlm.nih.gov/pubmed/20954409

 

http://iopscience.iop.org/1009-1963/11/12/318

 

Also, below is an extract of my draft paper on the matter:…

 

 

[b]Interconnectivity and relationship between progressively higher levels of complexity with reference to humans

1. DNA

 

2. Neuron

 

3. Brain

 

4. Society

 

5. Global Integration

(Trans-humanism)

 

 

Fractal geometry

The complex and dynamical nature of the individual components of the model (1-4, and perhaps 5) is manifested in the underlying sophisticated geometry with power- law properties, which can be described in terms of objects with fractal dimension.

 

The fractal dimension of the DNA has been described (for example, Cattani C. Fractals and Hidden Symmetries in DNA. Mathematical Problems in Engineering Volume 2010) who have discussed the geometrical rules that describe the distribution of nucleotides along the DNA molecule and described that the DNA is characterized by DNA walks with fractal shape. With regards to the neuron it has been proposed that Euclidean geometry is not suitable for a geometrical interpretation of its structural and functional properties, at least in humans (Pellionisz AJ. Neural geometry: towards a fractal model of neurons. Cambridge University Press, 1989), and neural fractal properties are widely manifest. In addition, the fractal properties of the brain as a whole have been described by several researchers. See for example, a full discussion here: http://www.dhushara.com/book/paps/chaos/bchaos1.htm. Finally, one level up from the level of individual brain, is the level of society integration. The dynamic, continual processes that characterise societal interactions operate within an integrating field and have properties that are describable by fractal geometry (Harle R. Chaos, archetypes, and the all-integrating field. Nonlinear Dynamics Psychol Life Sci. 2010;14(1):101-15). [/b]

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