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Day forty-six -- about large and complex system

      From Tienzen:
      As soon as we organize a body of phenomena from a particular starting point (grammar in this case), the entire universe (linguistic universe in this case) will be polarized around this point, and the other concepts in this universe will be distorted.

      However different superficially for large and complex systems (such as, the physical universe, the life universe, the math universe or the linguistic universe) there are, they all share a set identical principles.
         1. Hierarchy principle -- every universe is built up from the bottom up, by its elementary members clinging or sticking together to from a higher globs. Such as:
               1. Physical universe: from elementary particles --> atoms --> elements --> molecules --> large objects (stars, lives, etc.)
               2. Life universe: from single cell life --> plants and animals --> human
               3. Human society: from individual --> family --> village --> country --> nation --> humanity
               4. Math universe: from numbers or geometrical points --> arithmetics and geometry --> ...
         2. Similarity principle -- whatever this clinging and entwining process (gravitation, food-chain, love, in sets, etc.) is, it repeats over and over in its hierarchy building.

      Therefore, a two point conclusion, at least, can be made:
         1. Thus, the theorems and laws of one universe "could" be also the theorems and laws of a different universe, although its clinging process could be different, such as, that the gravitation is replaced with love in the case of growing the human society.
         2. Every universe has a "natural and innate" hierarchy.

      Of course, each level of this hierarchy can be studied independently as a sub-domain without any distortion to this natural expansion. However, if a theory is trying to describe the entire universe without following its innate hierarchy by selecting a new beginning point as the center of this universe, then this universe will be polarized and distorted. And, many singularity points could be created by that theory. For example, the grammar is obviously a higher level object in the linguistic universe. If using the grammar as the "center point" for the linguistic universe, many singularities will appear.

      Are those singularities created or innate? This is a very important issue. Yet, it is a too big issue for our discussion. I will simply give my answer here; they are innate although they do not show up in its natural expansion of its hierarchy. Thus, these polarized theories are providing great information about that universe on its elasticity and plasticity, although those theories are partial theories in essence. In fact, as theory (or model) is almost always "hypothesis" centered, it is always polarized. That is, only the "Final Theory" can show the natural expansion of its hierarchy by de-polarizing it. In a sense, this polarization is difficult for layman to understand. Yet, there are some simple examples.
         1. Origami -- by different ways of folding the same piece of paper, different objects can be created.
         2. Jianzhi (the art of paper cutting) -- by different ways of folding the same piece of paper, the "same cut" on that paper will create different patten.

      Now, we can add third principle for any large and complex system (universe).

      The Singularity principle -- every universe has a number of singularities, from 0, 1 to 2.
      In Topology,
         1. a ball-shape-like universe has zero (0) singularity.
         2. a plane-shape-like universe has one (1) singularity.
         3. a donut-shape-like universe has two (2) singularities.

      That is, there are different types of universe. What kind of universe the linguistic universe is? What differences are there among these different universes? Without answering these questions, we cannot truly construct the Final Theory. Yet, there is a short-cut to this issue. Instead of construct a final theory, we can construct a virtue (linguistic) universe. These two approaches are dramatically different. Theory is always "hypothesis" centered. The constructed universe is built from the bottom up with some arbitrary definitions without any hypothesis. Of course, this constructed universe must be checked with the "real" universe, item by item (its theorems, laws, phenomena, etc.). And, this is what we can do in the near future.

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