Review Lecture. These are some notes for a review lecture I plan to give on Tuesday night. Given the shortness of our summer term, I thought I would send them out to the mlist so you could think about them in advance. If you can integrate one (or possibly even more) of the general themes here into your presentation, so much the better. If you have questions, bring them to class on Tuesday.  In addition to this review lecture, you will find it useful  to review the  Notes for First Half of the Course and Notes for Second Half of the Course.  The exam will cover the entire course and will emphasize the Assigned Reading as well as material covered in class.

• We started with the concept of the "Global Brain." A metaphor, drawing attention to increased interconnectedness among a very large number of units leading to intelligence. This is how the brain works, the individual neurons are not "intelligent" but almost mechanical. But with enough of them linking together in the right way, we have a system that is able to cope in creative ways with the unexpected. Will the earth as a whole develop this capacity? Do we want it to? Individual humans are more intelligent and more independent than neurons, perhaps we do not want to be part of such a global intelligence, or at least we want to be able to opt out of it. We certainly are becoming dependent on Internet access for information necessary to our lives, we may depend on software that is not on our PC's, etc. The analogy between the human brain and the "global" brain is something to think about, they are clearly not the same in every respect.
• The emergence of intelligence is part of a larger question of how order emerges out of chaos. And how chaos emerges out of order, because a key feature of intelligent systems is that they do not just respond mechanically to stimuli but display creativity. This is an old philosophical issue, often framed as "free will vs determinism." Charles Saunders Peirce and the early American Pragmatists resolved this by postulating a fundamental spontaneity to even the smallest particles of matter - a metaphysical speculation that has later been confirmed by physicists who have probed the "quantum" nature of sub-atomic particles. Mathematical studies show that chaos can emerge out of order in the sense that deterministic equations can lead to chaotic results when the results are recycled over a number of iterations - as we saw in the spreadsheet demonstration of the logistic equation.
• Pythagoras and Peirce drew attention to the fundamentally digital nature of the universe. Phenomena tend to be segmented into discrete units that can be counted, e.g., the chemical elements. The small integers, the counting numbers, have unique characteristics - especially Zero and One - or Being and Nothingness as J.P. Sartre called them. We can see these as the fundamental nature of reality, or just use them as guide in understanding how complexity emerges.
• An example of the emergence of complexity is the computer industry. In the beginning, computing was done in the mind or with mechanical instruments such as the abacus. With the invention of the algorithm - a set of sequential mathematical instructions - it became more complex and more able to model more aspects of the physical world. Turing developed the idea of a machine that could carry out algorithms, and showed that a sequence of zeroes and ones, if it was long enough, could solve any logical problem.
• The computer industry developed out of the need for machines to do massive numbers of computations, primarily for military purposes such as breaking codes and calculating trajectories for artillery. This personal computer industry grew because of hobbyists who found this fascinated and wanted to be able to play with it at home. Its growth is a case study in the emergence of order out of chaos. This happened as part of the market economy, another classic example of the emergence of order from chaos. As is typical in markets, we see a large number of competitors at the beginning, with a winnowing out of all but the strongest as the process develops. The same process can be seen with the Internet, with search engines competing for our attention and the system coming to be dominated by a few. The lawsuit against Microsoft is an attempt to use governmental authority - the rational mind of "society" - to control this process. These matters are still in flux today, and your investigations for your Presentations may give us some up-to-date information about what is happening.
• There are several themes we should be looking for in these contemporary developments, and in speculations about the near future. These include:
• Increased Complexity. Each of the topics we look at: arts, sciences, business, education, etc, develops from ideas or concepts to mechanical systems to cybernetic systems to autopoietic systems - or from firstness to secondness to thirdness to fourthness in Peirce's quaint metaphysics. We can see this in every realm of life, e.g., in education we start with a thinker who has an idea, we have a dialog between him or her and others, then we have a systematic set of ideas that can be written in a textbook or presented in a series of lectures. Finally, we have a self-sustaining network of scholars and teachers who respond to threats to their ideas by developing and refining them. Finally, these systems become stale and are challenged by a thinker with a new idea and the cycle begins again. With computer networks, these networks need not be local, nor need they be based on an institution such as a university. In economic life we see this as new product ideas become huge industries with vested interests, only to collapse when a new product is invented. In the arts, we have successive schools or musical genres that begin with a freshness, develop into fairly predictable patterns, then are replaced by something new and exciting. We should be able to detect elements of this pattern in everything we examine.
• Attractors Emerging Out of Chaos. Out of all the chaotic interaction we observe when there are thousands of competitors, certain patterns succeed and become typical. We can think of these as attractors. For example, internet-assisted home schooling, charter schools, online enrichment courses, etc. In the business world, certain business models succeed - online bookstores, encyclopedias, pornography sites, etc. - while others fail. A big part of success in any field is being attentive to which attractors are emerging successfully. Those that are most successful become self-maintaining systems. Which ones are emerging in your field of interest? What will the major players ten years from now look like?
• Hierarchy and Heterarchy or Networking. These two organizational principles are found in all complex systems, but some emphasize one more than the other. Often they go through phases with early dominance by an innovator being succeeded by a chaotic, heterarchical period, followed by dominance by market leaders. In the computer industry, IBM's early dominance was broken by the PC industry and Microsoft's policy of licensing its operating system to multiple manufacturers. Now Microsoft's own dominance is imposing hierarchical order, which is challenged by Linux and other competing movements. Recently, Microsoft has actually been the main source of new software for Apples, which is often more advanced than the Windows software - perhaps because Microsoft recognizes the need for heterarchy in the system, or only because they have been able to make a lot of money by bailing out a competitor that looked like it was going under.