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Mathematical Creativity

By Roy D. Follendore III

Copyright (c) by RDFollendoreIII

June 17, 2005

Philosopher Scientists preestablished the idea that our universe consists of order and disorder. For mathematic this was probably an inevitable consequence. The concept of formal mathematical thinking begins with the notion that optimal order exists.  Mathematics must assume that order exists, because if it didn't, mathematical logic would have no place to begin. Logic builds upon itself because the application of logic is all about the acceptability of optimal order. Science had to choose the formality of logic because the inconsistency of disorder prevents repeatable solutions from taking place. Concepts that are repeatable are powerful because they are more believable and convincing. People like that because consensus is easier to reach. The thing to know is that the boundary between order and disorder seems to be exactly that space of reason where creativity can arise.

 

Creative thinking is dependent on certain expectations of disorder. It is easier if we imagine creative ideas as watercolors. Like the capillary action of watercolors running together as they are absorbed into paper, new potential images become available.  It is as though through the very act of reasoning through disorder that new and beneficial ideas are able to emerge. The creative watercolor artist must be careful to time the application of new colors as the paint flows and ultimately it is time that all creative artists must attempt to master.   

 

Time is that distilling factor that orders our natural physical world. Scientists interests in the questions of why things work the way that they do means that they have a compelling need to understand and be able to predict the arrangements of things. For instance, Geologists work to understand the arrangements of layering in rocks so that they can understand the patterns of events relative to time. The maze of chaotic events seems to somehow turn into these ordered geological layers of recorded change. Geological predictability arises from stochastic events, not in spite of them.

 

Nowhere in the any of the geological layers are numbers. They are not to be found within the sky on a starry night and they don't grow from trees. You can't find numbers in a microscope and you will not find a number inside a human brain. They have never bounded across an African savannah or migrated though the seas or the air.  Numbers simply do not exist in nature. Human minds are not numerical, they are symbolic. Our brains assign value to the things that it filters into our consciousness. We have to be symbolically creative because we have the requirement to remember the relationship of objects together.  Unique arrangements of memory to actions is far more economic when they happen in close proximity of a particular moment because it anchors our assignment of symbolic value.

 

This instantaneous ability to relate things and carry that relationship on as the starting point is the fundamental language for establishing value judgments within our minds. Unlike the axiomatic cardinality that takes place in judging the relevance of numbers, this does not require a transposition or a prequalified set of relationships. It is the starting point for creativity.  Because of its self defining nature there is little or no definable room for the language of the creative human mind to reside within that perfect world called mathematics.   

 

Mathematics is not capable of containing the creative language of the mind and yet it is the mind that can conceive and utilize mathematics as a creative process. Perhaps those elusive numbers that we do not see in the physical world is our metric that represents our creative boundaries. The number can never be a creative act because we have disembodied it from that very thing which would make it truly unique. Numbers are always unfinished ideas. We can say that a number represents, or that a number is, but we can never give a number its own true identity because the moment that we do the number becomes a symbol.

 

All of this leads to that ultimate fallacy that the manipulation of numbers is the creative act of mathematicians and scientists; that creativity arises from mathematical computation.  The root of creativity must have existed before mathematics was created. As such, mathematics may be the color of the paint but it is not the act of painting. The manipulation of numbers has always been cryptic and mysterious. It is therefore easy to assign larger creative physical values where no value is warranted. But from the perspective of the artist it is not the formulation of the metric of puzzles that is the creative process; rather it is the creation of the physical puzzle itself. Mathematics may be the tool, the paintbrush that applies the paint, the essence of the color palate that describes, or perhaps even the fabric of the canvas that holds the intellectual paint together, but it is not the masterpiece of creative inspiration.  

     

 

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