Dynamic Complex Systems and Emergence

When dynamic elements in a system interact with other dynamic elements, they generate positive feedback loops. Qualitatively different and often surprising new phenomena emerge as a result.

Unexpected behavior emerges by the continued action of positive feedback in adaptive complex systems. This sort of phenomenon is ever present in nature (see some examples here). They are also common in systems created by humans. Consider microphone feedback squeals. We all have heard a loud squeal from a speaker when the microphone gets too close to the speaker or the amplifier gain is too high. The positive feedback occurs because the initial sound picked up by the microphone is amplified, sent out through the speaker and returns to the microphone louder than the original sound. A few cycles of this feedback loop generates a loud squeal. Once you understand the mechanism, it seems unremarkable and controllable. To kill the squeal, simply move the microphone farther from the speaker or turn down the amplifier gain, thereby reducing the intensity of the amplified sound that reaches the microphone.

As a thought experiment, consider a large open space, say a football field, on which a hundred speakers, amplifiers and microphones are placed randomly. Add connections (wires), one at a time, between a randomly chosen microphone and amplifier or randomly chosen amplifier and speaker[1]. Sooner or later, a squeal will arise because a speaker happens to be close enough to the microphone that feeds it. Let us call that microphone-amplifier-speaker trio an autocatalytic set, i.e., a self-reinforcing set of elements that produce an emergent property of the system (the squeal). Adding more wires will create a second squeal, and a third, and so on. There tends to be a threshold beyond which new feedback loops are created very rapidly and shortly thereafter nearly all the speakers will be emitting squeals. Since the output of any given speaker reaches more than one microphone, some of the autocatalytic sets (i.e., feedback loops) may involve multiple microphones, amplifiers, or-speakers. Likewise, a given speaker or microphone may be participating in more than one autocatalytic set, i.e., emitting multiple squeals at various pitches (because the pitch depends upon the distance between the participating speaker and microphone).

In 1965, Stuart Kauffman did computer simulation experiments analogous to the speakers on the football field using random Boolean nets. The simulations showed, to his surprise, that autocatalytic sets (called state cycles in these Boolean nets) inevitably emerge quickly. The number of autocatalytic sets that emerge is roughly the square root of the number of elements in the Boolean network [2]. Mutually reinforcing feedback loops form in all sorts of complex systems. The probability that at least one autocatalytic set will emerge increases as more elements are added to the system, more interconnections are added, or the elements themselves become more complex and therefore can interact with others in more complex ways. In other words, any change to the system that increases the number of possible positive feedback loops increases the probability that an autocatalytic set will emerge. How big does a system have to be before feedback loops become nearly inevitable? It tuns out that it depends upon how complex their interactions are and how many other elements each interacts with. In general, the simpler the elements and their interactions, the more of them are needed to give a high probability of emergence.

Consider two familiar examples of emergent systems in human affairs:

iron age coins Money -- Cattle, wheat, chunks of metal or cowrie shells were used as tokens of trade at least as early as 3000 BC and perhaps as early as 9000 BC. But such tokens became far more useful once they were visibly distinct, had agreed upon values, and were under the imprimatur of an authority.  Coins of different values -- due to different metal composition, e.g., gold and silver, emerged between 650BC and 550BC in Lydia. As the benefits of money were recognized by more people, more coins were minted which, in turn, allowed those benefits to be experienced by more and more traders. Within two hundred years, the idea of using coins with specific values had been adopted throughout the Mediterranean region. China had developed coins as well. Coins changed commerce forever. Counterfeiting and debasement of the metals in the coins soon emerged. Increases in the rate at which coins were minted (or counterfeited) created early cases of inflation. When there are more coins than needed to purchase goods in a given economy, the price of the goods rises. Thus there emerges a metalevel dynamic relationship between the total money supply and the total demand for goods.  In hindsight, however, the bigger effect of coinage was to generate the notion of price. A price is a numeric quantity -- a number --  that can be printed on paper currency, added and subtracted, and entered in accounting books. Eventually, when accounting became computerized, prices became just the bits that describe the number.  Bits can move at electronic speeds in world-wide financial markets that change in milliseconds due to the positive feedback of greed or fear generated by the price moves themselves. Many financial instruments have become no more than abstract "baskets" of abstract "bets" such as "futures" and other more arcane "derivatives" that can bankrupt organizations and markets in a flash: witness the "Flash Crash" that occurred at 2:45pm, May 6, 2010.  So emergent metalevel upon emergent metalevel, human commerce grew from cowrie shells to Synthetic Collateralized Debt Obligations and "Swaps".  My oh my!

The Internet The Internet -- In computing, TCP/IP and HTTP protocols create new sorts of interactions between computers. The Internet emerged from TCP/IP protocols and the Web emerged from HTTP protocols. The communication infrastructure of these sorts of systems grows because of positive feedback known as the “network effect.” That is, as the network grows it becomes more attractive for others to join the network. Telephones and fax machines are the usual example of prototypical positive feedback network effects. On top of the base communication networks, content and usage models proliferate easily because when bits are "free" both in the sense of "free beer" and "free speech," innovative startups have very low costs of entry.  Google and Facebook could start in dorm rooms. Blogs and Twitter communities appear out of nowhere.  Less welcome but just as much emergent phenomena are the myriads of viruses, worms and other malware that exploit email, blogs, and Web content to support all sorts of scams and cyber-crime.

I tis important to note that complex dynamic feedback gives rise to emergent entities that are qualitatively different from those of the underlying elements. A marketplace based upon money is qualitatively different from one based upon barter because easily communicable prices create relationships between all goods and services and anything can be given a price. More specialized goods and services can participate on an equal footing with everyday commodities. So too, the emergent behavior called the Web is dramatically different from communities that swap files by FTP even though the low-level technical differences between FTP and HTTP are relatively minor.

[1] Note: since this is an abstract thought experiment, we allow multiple microphones to feed the same amplifier, a microphone to feed multiple amplifiers, and an amplifier to feed multiple speakers. We also ignore the likelihood that, in real life, amplifiers may blow fuses and speakers may shred themselves.

[2] See Chapter two of Complexity: Life at the edge of chaos, by Roger Lewin, 1992l, Macmillan Publishing Co. For an informal discussion. Stephen Kauffman has developed the formal theory, known as NK Systems. See S. A. Kauffman. The Origins of Order: Self-Organization and Selection in Evolution, Oxford University Press, New York, 1993.

Contact: sburbeck at mindspring.com
Last revised 8/6/2013