Mayasite World View
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.
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.
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, preoperational stage, a concrete operations stage, and a formal
operations stage.
In Piaget’s description, cognitive
development culminates in the achievement of formal
operations.
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.
Before exploring the existence and implications of a postformal-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.
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.
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.
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.
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.
I’ll apologize in advance as we begin to try to identify the
existence of this next stage. Next-stage thinking poses a mindwrenching challenge to most of us.
Even the most
compassioinate presentation of next-stage achievements can
be difficult to digest.
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).
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.
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.
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.
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 twostatement version takes the form “The next statement is true.
The previous statement is false.” Again, the truth of either
statement is undecidable.
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.
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.
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.
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).
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.
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.
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.
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.
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.
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.
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 selfreference: 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.
In his book The Structure of Scientific Revolutions, by 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. Godel
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.
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 selfreference.
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.
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.
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.