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Mayasite World View
Meta Stage Emerging
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sme001
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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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sme002
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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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sme003
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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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sme004
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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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sme005
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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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em006
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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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sme007
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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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sme008
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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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sme009
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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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sme010
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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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sme011
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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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sme012
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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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sme013
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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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sme014
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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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sme015
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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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sme016
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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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sme017
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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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sme018
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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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sme019
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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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sme020
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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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sme021
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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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sme022
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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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sme023
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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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sme024
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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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sme025
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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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sme026
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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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sme027
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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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sme028
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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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sme029
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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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sme030
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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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sme031
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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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