Numbers as Archetypes of Thought

Charles Saunders Peirce

• an interesting thinker because he was both a philosopher and a scientist
• he anticipated many key findings simply by thinking about how he and others thought - his assumption was that the rest of the world would function much as his brain did
• spontaneity rather than determinism
• random swerving of microscopic particles
• the brain has no central cell
• small integers as fundamental units of organization in the universe - numbers as "archetypes"

Numbers as Archetypes

• many philosophers have seen numbers  - particularly the small integers - as "archetypal", as a fundamental organizing principle for reality.  The Pythagoreans were especially strong on this idea.
• Peirce was particularly taken with first, second and third as archetypes.  But he also thought about zero, and about combinations of the first three, e.g., firstness of second, secondness of third, etc.
• Carl Jung also thought numbers were archetypal, but he placed much more emphasis on the number four which he saw as the archetype of synergy, or self-sustaining order.  Ben and I agree with Jung on this.  Higher numbers can also be seen as archetypal
• this may seem like foolish speculation, but it is remarkable that the same imagery occurs both in classical creation myths and in the latest astronomical theories of the origins of the universe

Naught, the Formless Void

• the original state of the universe - some physicists believe that a "zero-point field" or quantum vacuum underlies all apparent mass and energy in the universe.
• scientific astronomy has reached the same conclusion
• not the same as the integer "0" - this is something before arithmetic existed, before order of any kind existed
• also found in many religious traditions, e.g., the Buddhist concept of the "Formless Void" - meditation seeks to bring the worshipper into this state
• perhaps this concept is captured by The Really Big Button That Doesn't Do Anything.
• complex systems theory also shows that order can emerge out of chaos

First, Raw Being

• the conception of being or existing independent of anything else
• the first step in the emergence of order out of chaos
• in human psychology, firstness comprises feelings that are immediately present, such as pain, blue, cheerfulness, the feeling that arises when we contemplate a consistent theory, when we contemplate God.
• in physics, it is the quantum indeterminacy of matter, behavior which does not follow any law
• in philosophy, it is usually equated with idealism, the position that ideas just emerge on their own rather than being determined by physical realities

Secondness, The Reacting Object

• for Peirce, secondness is the conception of being relative to, the conception of reaction with, something else
• in psychology, sensations of reaction
• in physics, laws of relationship between variables
• in mathematics, a vector - a line with an arrow at the end, having both position and direction
• in complex systems theory, the movement from one state to another

Thirdness, The Evolving Interpretation

• for Peirce, this is habit, abstract thought, the process whereby two things are understood to be in a relationshp
• these feelings and thoughts about relationships come to have a existence of their own
• in the physical sciences, thirdness is general theories or principles such as the Theory of Evolution, Quantum Theory, Newtonian Mechanics
• in mathematics, thirdness is a pattern or equation which explains how systems are related.  Geometrically it is represented by a triangle
• in general, it is a pattern that emerges from a series of numbers
• example:  "The Rule of Three"

Fourthness, The Unity of Consciousness

• Peirce did not think in terms of fourthness, which led him into a lot of confusing terminology such as Firstness of Second.  Some people like these complex theories, others do not
• Carl Jung stressed the quaternity, seeing it as the  minimal number for representing a unified system: a collection of overlapping, synergetic relationships.
• fourthness is a pattern which emerges from a web of relationships which support and sustain each other so that the whole is greater than the sum of the parts
• this concept is often captured by the word "synergy"
• geometrically, fourthness is the tetrahedron
• Buckminster Fuller was a creative exponent of the tetrahedron
• fourthness can also be represented as a dual network, combining hierarchy and heterarchy - this is how we think of it in Webmind
• this kind of emergence of thought is the essence of what we call "thinking" in the brain
• truly intelligent AI systems will have to be able to do this, not just follow instructions

Friedrich Nietszche

• a philosopher that many people have found profoundly inspiring
• often thought of as a nihilist, a person preoccupied with nothingness
• he saw the "will to power" as the force which enabled people to overcome nothingness
• Neitzsche's "will to power" is equivalent to Peirce's "one law of mind".  Order emerges out of chaos because it just does.
• the universe is a huge pool of entities, struggling with each other, leading to an emerging reality

Archetypal Patterns Can Be Observed in Many other systems of metaphysics, e.g.,  Tarot cards