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Mayasite World View

Meta Stage Emerging

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The Mayasite World View is a knowledge framework being developed at this Mayasite website.  By “World View”, I mean a way of looking at ourselves and our environment.  “Mayasite” is not being used in a descriptive sense.  “Transcultural” is the descriptor I have been using for this world view, but I am using Mayasite now as a place holder in case a better descriptor emerges.

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What is the nature of a world view?  It is a form of knowledge.  My knowledge is something that is developing from reflexes and perceptions I had at birth through a succession of qualitatively distinct stages.

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Jean Piaget has described the developmental process by which knowledge develops in great detail.  While cognitive development is continuous, Piaget finds it can be divided into four qualitatively distinct stages: a sensori-motor stage, pre-operational stage, a concrete operations stage, and a formal operations stage.  In Piaget’s description, cognitive development culminates in the achievement of formal operations.

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The Mayasite World View extends Piaget’s description by asserting that formal operations is not a final stage, but that development continues to provide qualitatively distinct stages beyond formal operations.  More specifically, at least some people, including some with notable contributions to humanity’s knowledge, have reached a stage beyond formal operations.  Perhaps evidencing a lack of humility, the Mayasite World View considers itself a product of a stage beyond formal operations.

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Before exploring the existence and implications of a post-formal-operations stage, let us consider a time when there were no formal operations.   With apologies in advance to my cetacean friends, no species other than humans appears to have achieved formal operations.  Obviously, there were no formal operations at the dawn of life.     I believe further there were no formal operations at the dawn of humanity.  Human society predates formal operations.

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What allow later humans to achieve what early humans could not?  Better education.   Better education facilitates developmental progress so that adults on the average operate at higher developmental levels.  This allows them to form more advanced societies, which in turn can educate more effectively.  Thus, a positive feedback cycle is established between societal evolution and human development.  In the Mayasite World View, societies are continuing to evolve, education is becoming more effective, and individuals are achieving cognitive developmental levels beyond formal operations.

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Once again, we choose to go backwards before going forwards.  This time it is to an imaginary past at a time where formal operations were emerging, but not yet prevalent in humanity.  In this imaginary past, a proto-Piaget determined that there were three stages, sensori-motor, functional, and operational.  He did not use the phrase concrete operations, because there were no formal operations to contrast them with.  He used the term “functional” rather than “pre-operational” because he preferred a label that describes what is going on in the stage, rather than one that describes what is not.

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The next stage, i.e., formal operations, was not going to be a non-operational stage, it would be an advanced operational stage.   Likewise, the operational stage was not non-functional, and the functional stage did not lack sensori-motor activity.  Thus, for our next stage, we are not necessarily looking for something that does not involve formal operations, but rather something that extends formal operations to a point where something qualitatively new appears.

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Piaget’s description of the first four stages provides additional guidance for characterizing a next stage.  Each transition between stages involves organizing separate achievements of the previous stage into a system that is more than its parts.  The stage after formal operations should organize formal operational systems into a greater system that goes beyond the sum of its formal operational constituents.  In addition, one might expect that the resulting super-systems would resolve conflicts that were apparent in the formal operations stage.

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I’ll apologize in advance as we begin to try to identify the existence of this next stage.  Next-stage thinking poses a mind-wrenching challenge to most of us.  Even the most compassioinate presentation of next-stage achievements can be difficult to digest.

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In my opinion, the best book for facilitating the transition to the next stage is Godel, Escher and Bach:  The Eternal Golden Braid by Richard Hostadter.  This book is entertaining and inspiring at several levels.  It offers many mental exercises to provide the reader with some experience to help understand Godel’s theorem on the undecidability of certain formal propositions.  I consider Godel’s theorem to be the prototypical next- stage achievement (although I will not deny there are other good candidates).

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Most people get along just fine in their lives without ever considering the logical and mathematical fields concerned with Godel’s theorem.  Therefore, this theorem did not have a major impact on the general populace.  However, I think it is fair to say that Godel’s theorem changed the meanings of the lives of many who understood it.  Furthermore, the revolution that Godel’s theorem was a part of is affecting lives throughout the world today.

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Throughout history, humans have tried to develop an understanding of their world, just as we are doing on this website.  In the few hundred years leading up to Godel’s theorem, people’s theories seemed to be getting pretty good.  For example, the movements of distant planets could be predicted with great precision.   There was a general feeling that perhaps a scientific understanding of the world was within reach.

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Of course, there was a lot that still defied explanation.  However, it was recognized that reality was a complicated mess and its failure to conform to expectations was not always the fault of the theories that were applied to explain it.  At the very least, mathematical systems, which do not have to deal with the messy aspects of reality, seemed to be approaching some sort of completion.

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Godel’s theorem is, in a sense, an extension of well known semantic paradoxes.  Consider the statement “This statement is false.”  If it is false, then it must be true; if it is true, it must be false.  The truth of the statement is undecidable.  A two-statement version takes the form “The next statement is true.  The previous statement is false.”  Again, the truth of either statement is undecidable.

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What Godel proved was no formal system complex enough to include elementary logic could be completed without becoming inconsistent (a sin in logic).  In other words, to remain consistent, any logical system would have to include statements that could not be proved or disproved.   Of course, this was quite a blow to mathematicians and logicians who were trying to formulate complete self-consistent systems.

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Two such mathematicians were Albert North Whitehead and Bertrand Russel, who together wrote “Principia Mathematica”, an attempt to provide a complete formalization of logic and mathematics.  They addressed the semantic paradoxes by introducing a theory of types.  The theory of types assigned each statement a hierarchical level.  The theory required every statement to refer to something in a lower level of the hierarchy.  Thus, the theory of types excluded the semantic paradoxes set forth above since they both involved references to statements at the same hierarchical level.

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I see the theory of types as a very advanced effort at the formal operations level.  It is advanced because it recognizes a formal operations conflict (the paradoxes), and suggests a plausible solution for them.   However, the effort was in vain because, as Godel indicates, none of the theories in which we are interested conform to the theory of types.

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Godel’s theorem not only impacted logicians and mathematicians.  It was also a blow to the scientists who were relying on such formal systems to explain reality.  It was no longer just reality that was messy, even the pure mathematical and logical systems used to understand reality were inherently messy (as they left loose-end propositions undecided).

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One could say that Godel’s theorem transformed scientists in search of understanding into engineers in search of more useful but admittedly imperfect models of reality.  Of course, only scientists that understood the theorem and its implications were transformed.  In practice, most scientists did not change much in response to this theorem.

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However, reality does not like to be ignored.  When you turn your back on reality, it tends to appear again in front you, perhaps in another guise.   In the same time frame, but somewhat later, the limits of formal operations confronted physics, the field of science most closely allied with mathematics.

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Physicists had been dealing with two conflicting theories of light:  particle theory and wave theory.  There were two inconsistent theories of the same thing.  One theory was better for some purposes and the other was better for other purposes.  But neither was adequate for all purposes.  Looking back we can say that it was not possible within the stage of formal operations to resolve the conflicting theories.

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Of course, we know there was a resolution of the conflicts and it was provided by quantum mechanics.  The development of quantum mechanics was a much more collaborative effort that Godel’s theorem.  Scientists argued and exchanged ideas step by step through the development of quantum mechanics.  The transition to quantum mechanics was a difficult one.  Many scientists could not make the transition.  Even Einstein, the foremost scientist of our time, could never accept quantum mechanics at face value.  Since quantum mechanics has stood the test of time better than its detractors, suggests a development transition is involved in understanding quantum mechanics.

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Rather than going into quantum mechanics in greater detail, let me recommend a book by one of the founders of quantum mechanics:  “Physics and Philosophy” by Werner Heisenberg.  It is his name that is given to the famous uncertainty principle of quantum mechanics.

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In one of its guises, the uncertainty principle states that one cannot know both the exact position and the exact velocity of a particle.  (More accurately, there is an inherent minimum to the product in the uncertainties in the measurement of a particles velocity and the particles position.)  One of the explanations for the limitations on our ability to observe certain combinations of parameters is that our observations affect what we are trying to measure.  For example, the light photons that we would bombard a particle with to determine its position would change its velocity

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We have just described two major scientific revolutions that occurred within a generation of each other.  Both of these revolutions addressed paradoxes:  quantum mechanics addressed the paradox between the particle and wave theories of light; Godel addressed self-referencing semantic paradoxes.  Both revolutions resolved the paradoxes, by embracing self-reference: self-referencing statements in Godel’s case, and the inextricability of the self, i.e., the observer, from that which is observed in quantum mechanics.  Both revolutions confronted us with the limits of our knowledge:  quantum mechanics with the uncertainty principle; Godel’s theorem with undecideability.

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In his book The Structure of Scientific Revolutions, Thomas Kuhn describes major and minor scientific revolutions in terms of paradigm shifts--which are shifts in world views--just like the one we are working on at the Mayasite website.  We are suggesting here that quantum mechanics and Godel’s theorem are not independent paradigm shifts, but rather two manifestations of a single major paradigm shift.

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The elements in common between the revolution represented by quantum mechanics and the revolution represented by Godel’s theory (and I am not suggesting that we have identified all such common elements) are characteristics of the major paradigm shift.  Further, we are suggesting that this major paradigm shift is a manifestation of the transition to a next, “Godel”, stage (pending a more descriptive label).  Finally, we are suggesting, because we are addresses core cognitive abilities, that this transition to the Godel stage has been, is being, and will be manifested in many more revolutions in diverse fields.

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In conclusion, in the Mayasite World View, there is a fifth stage beyond formal operations.  It resolves formal operational paradoxes by embracing self-reference and, concomitantly, explicit limits on knowledge.  At the Godel stage we formally accept the limits of formalization--another instance of self-reference.  And these limits are not simply due to the complexity of reality, but to the inherent limits of the tools we have to understand reality.

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In reaching this conclusion, we return to the beginning of this essay.  Just as quantum mechanics and Godel’s theorem force us to confront the limits of our knowledge, Piaget describes how it develops and point to what it can become.  We know ahead of time that the Mayasite World View will have its limits like any knowledge system

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Of course, one of the sources of “Mayasite” is the Hindu concept of Maya, which is that the reality that we perceive is illusion, which is not so far from the notion that the reality that we know is a product of our own development.  So the “Mayasite label is descriptive after all.  And, despite its limits, we trust some will find the Mayasite World View a useful one.

 

 

 

 

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