Sunday, July 18, 2010

The universe in one dimension - the one dimensional Harmony Set

The birth of structure in our world.

Trusting to the path of the modern Cartesian Meditator, a world evolves. It has interpretations in all dimensions, but the simplest to understand is the 1 dimensional Harmony Set, shown above. The graph shows successive iterations of the world. Because this world develops iteratively, the evolution provides a natural background metronome for the world (this may not be time as we think of it).

The universe begins as a pair of opposing vectors that lie in superposition, the strength of which is represented by the single bar (purple) at the front of the graph. Then this absorbed into the structure shown behind it (brown). This is then absorbed into the structure behind it, and so forth. Consequently the passed leads to the present. The future is not known until the next iteration arrives. Nevertheless, the form of growth can be considered with a level of certainty. But this is exactly what we find in our own world.

At first view it seems almost fractaline in appearance. Exploring it reveals many evolving numeric series that crowd ever closer to our most revered mathematical constants. The left edge exhibits exponential relations, and the whole structure is pervaded with variations of exponentiality. That such exponential relations are known to be at the heart of the equations that fuel quantum physics is relevant. That the peak of the evolving series grows with a rate that crowds in on the natural log of 2, one of the more important constants in physics, is again of interest. What is missing in this set is our treasured number Pi, but it is evident in higher dimensionalities. Is this not what one would expect?

That the model is a bar graph, rather than a continuum of change will bring many to dismiss it. But this difference is fundamental to allowing the world to work. Without this (which is inescapable if one begins with the implications of the General Principle of Equivalence) Zeno's paradox would bring the world to a sudden halt. Instead, here is a foundation for entropy, a proper foundation that ensures the world will evolve, a direction of time, and everything else.

How this world comes to be at all and comes to be as it is, will be the focus of future posts.

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