Some Notes for the First Segment of the Course.  These may be useful as a guide to the readings, and as review for the first exam.  The material in blue provides some transition between different readings.  The notes cover primarily "What is Chaos" and "The Essence of Mind and How to Program It."  These readings will be covered most thoroughly on the exam.

We start with some discussion of the "Global Brain."  This is a metaphor or an analogy - what does it mean to say that the global computer network is a "brain".  It means that the brain and the global computer network have organizational traits in common, that they are organized in similar ways.

•  Peter Russell's book The Global Brain introduced this term.  Part of a long historical trend, including steps such as the invention of language, writing, printing telecommunications and now computers and the internet
•    argues that we are developing into a global community, with information as the key resource - a point that many have made
•   the development of the societal nervous system is analogous to the development  of the human nervous system - increasing number of connections between cells resulting in a "brain"

Theories of Chaos and Complexity

• General Systems Theory Developed in the 1940-1960 period, limited by the lack of computers to do simulations
• Chaos theory is the study of deterministic, rule-based systems that nevertheless appear to be acting completely unpredictably, even at random - An example is the "logistic equation" which can be modeled in a spreadsheet program.  It is possible to produce the graph at right with the logistic equation, Xn+1 = AXn(1 - Xn)
• This is most striking in the physical sciences, where measurement is precise and theory would lead us to expect things to be predictable.  Meteorology is a common example.
• The What is Chaos lecture provides a good outline
• contrasts chaos theory to deterministic science
• refers to Newton's Three Laws of Motion as an example of deterministic science
• chaos theory deals with situations which are highly sensitive to initial conditions
• no measurements can be perfectly precise, which means that systems which are highly dependent on initial conditions are unstable
• Chaos is not just due to errors in measurement,  but can be shown in pure mathematics, generating "strange attractors" out of fairly simple formulas.
• Complexity is not the same as chaos, it refers to systems where a large number of variables interact with each other.  Complex systems may or may not lead to chaotic behavior.
• We are interested in studying complexity  - in general - because we may find similar patterns emerging in diverse systems.  Otherwise, we can study each complex system independently.  Thus, we believe that systems as different as the brain, families, the climate, auto traffic, earthquakes and financial markets may have things in common.

• fixed point - constant, not changing
• limit cycle -  changing within a fixed pattern, periodic, e.g., motion of the planets.  These can be studied with mathematics, e.g., Newton's laws, calculus...
• Strange Attractors are patterns which have irregular, nonlinear shapes and which emerge out of repeated iterations of a system.  They must be studied with computer simulation.  They often make beautiful graphics.
• There is evidence that strange attractors exist in the brain, e.g., in the olfactory lobes of rabbits

• evolution requires a large number of competing entities, which can survive or not survive depending on circumstances in their environment
• these entities must also have the ability to mutate or combine to form new entities

• entities which maintain their structure despite environmental pressure to change
• if part of the structure is destroyed, the other parts act to replace or compensate for it

the ability to create new components which serve to strengthen and maintain the existing system

Why look at metaphysics?

• previous efforts at AI have oversimplified "mind"
• the metaphysicians have been examining how we think for centuries, and they have reached some interesting conclusions
• many of the metaphysicians have anticipated ideas that scientists have discovered only much later:  atoms, quantum indeterminacy, digital logic, for example
• it is likely that our brains evolved as they did because that is the best way to think, other intelligent beings would probably think in much the same way - including ones we might create
• we need a vision of the big picture, as well as detailed computer code
• The work of Pythagoras of Samos is particularly prescient of digital philosophies.

• 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
• The economist Kenneth Boulding wrote, in his old age, sonnets to the small integers.
• Alan Manning's novel Suppositon Error is based on Peircian theory.

• 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

• 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

• 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

• 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 Threes"

• 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

The Mind and the Brain
• philosophers have long debated the question of the relationship between the "mind" and the brain.  Descarte in particular is associated with the idea that the mind is something quite distinct from the brain.  Not all peoples believed that the mind was in the brain;  I've heard that the ancient Egyptians did not bother to preserve the brain in mummies because they didn't see any use for it.
• in Descartes' view the rational soul was an entity distinct from the body which made contact with the body at the pineal gland.  The mind could influence the body, as well as the body influencing the mind.  He was interested in the brain and nervous system, as well as in the logic of thought, did a lot of research on reflexes and physiological psychology.
• today, complex systems theory gives us an understanding of how something as complex as the mind can emerge from the interaction of comparatively simple components.
• we will look first at some basic information about the brain and how it works, then at a model of how the mind works which is rooted in complexity theory.
How the Mind Works - (according to Ben Goertzel's model)
• this is a model of "Mind" in the abstract, not just of the human mind.  The fundamental assumption is that the mind is a set of attractors of a complex system - that it results from the interaction of a large number of autonomous parts over time
• these parts can be called "agents".  They have the capacity to transform, create & destroy other agents.  Mind

consists of structures that emerge from systems of intertransforming agents.
• many of these agents act by recognizing patterns in the world, or in other agents
• thoughts, feelings and other mental entities are self-reinforcing, self-producing systems of agents
• these self-producing mental subsystems build up into a complex network of attractors and meta-attractors
• this network of subsystems & associated attractors is a "dual network" in structure; it is structured according to at least  two principles: heterarchy (associations based on similarity) and hierarchy (relationships of control between categories).
• agents pass attention ("active force") to other agents to which they are related
• because of finite memory capacity, mind must contain agents able to deal with "ungrounded" patterns, i.e. agents which were formed from now forgotten agents, or which were learned from other minds rather than at first hand -- this is    called "reasoning"
• a mind possesses agents whose goal is to recognize the mind as a whole as a pattern -- these are "self"
• the structure of the mind - the way it would look if you could take a snapshot of it at one instant, is organized according to two interacting structural archetypes - hierarchy and heterarchy
• the dynamics of the mind - the way it would look if we could see it in action in a video - follows two interacting process archetypes - evolution and autopoiesis.
• this model is too complex to "prove" mathematically, and cannot be fully tested with data about the brain.