31 Mar Asymmetrical Balance, True Love and Chaos
Inequality is the Pattern
Unequal distributions characterize everything in the universe from subatomic particles to galaxies. In fact the whole idea of “equality” in the physical universe seems at least a tiny bit sketchy. At the extreme end of unequal distributions is chaos. On the near end are things that approximate equality: balance, parity, equal opportunity, symmetry and pattern-level matching. Near equality is useful in lots of places. In art, the concept of balance is often a sign of quality in a piece. Often it is an asymmetrical balance, and often the combination of asymmetry and balance is that makes a piece so irresistible.
Consider St. John the Baptist Catholic Church. It’s across the Mississippi from where I live. While researching my roots, I recently learned that many of my family line were baptized and married here so I went over to take some pictures. The different sizes of cathedral style windows, the different heights of the towers and spires, even the differences in the roof style and slope add to the beauty of this architecture. Now, add to that, my knowledge that many of my people began their lives and their married lives here, the beauty is greater still.
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There is beauty and understanding in both symmetry and its absence. When we are talking about human thought and human language, understanding and interpretation, equality, and even symmetry, may be hard to come by. It is a hopeless goal to expect two humans to understand each other “completely”. When I experience approximations of mutual understanding, I tend to gravitate toward the person who can really understand me. I married one of them. and over the past 30 years of being together, Ann and I have developed even closer affinity and ability to understand one another. But it’s never really complete. There is always something in the way I understand something Ann says that differs from what she intended and vice-versa. It’s usually infinitesimal and has no impact on our ability to cooperate, but the closer we get to mutual understanding, the more successful our mutual operations become.
Forgive me for a slight detour here, but consider Miracle Max and his wife in “The Princess Bride”. We witness between them a dialog in which she has to remind her husband that she is not a witch but his wife. There are a few lines of dialog showing how well they know each other, a little collaborative action, then a closing scene with them smiling arm in arm discussing the likely outcome of their efforts. This is true love. How truly this shows how we all communicate!
Ovid described the chaos that existed before God or nature calmed the elements as “the rounded body of all things in one”. The idea of “rounded” embodies some structure. I believe that before, during and after the big bang, a set of immutable laws governed everything and that the big bang (or whatever happened) and everything that followed occurred within the framework of those laws. I believe that before, during and after communication, a set of immutable laws exist, and despite our weakness in knowing and applying those laws, understanding is an inescapable consequence. Among other things, the contexts in which we all find ourselves make this so.
Despite the chaotic organization of the image at right, it exhibits structure both at the micro and macro levels. Olav Kallenberg describes three basic symmetries of probability theory – contractability, exchangeability, and rotatability, exhibiting invariance in distribution under contractions, permutations, and rotations (Kallenberg, 2010). My approach makes use of each, but mostly exchangeability in a frame-based model of heating up fillers in semantically defined slots.
The model I have been proposing for a language understanding system uses a knowledge base that is ontological, distributed and symmetrical in structure, but asymmetrical in content. The hundreds of thousands of elements, eventually growing to millions, form a chaotic network of connections. They are bound together by context and meaning, but they are differentiated by human experience and symbolic logic. With such a knowledge base, how does one tame the chaos? This is a very important question and the subject of large amounts of research and experimentation. The laws of physics are what we use to describe the basis of order in the universe. What laws or rules govern understanding? In the section on Language I will discuss the different language strata and the rules that operate within each stratum and between the strata. My intent in this section of the blog is to introduce the model for replicating cognitive tasks and and explain why context is so important.
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