The article Emergence: A unifying theme for 21st century science in a Santa Fe Institute journal, by David Pines, Co-Founder in Residence, is on how physics needs to confront a stubborn problem, that the emergent properties of the systems of nature we find all around us have been exceedingly difficult for physics to study… The article below reports on my approach to that. (images from the original article)
Emergence is what we see from cosmic events to the flocking of birds…
David Pines makes a very intelligent assessment, saying in part “The central task of theoretical physics in our time is no longer to write down the ultimate equations, but rather to catalogue and understand emergent behavior in its many guises, including potentially life itself.”
I was one of those who figured out why that would become necessary back in the 1970’s. The behavior of complex systems of equations that permit true emergence will not be knowable from the equations. It’s not just their complexity, but that their emergent properties are emergent and dependent of histories of development rather than being formulaic.
I have also been writing papers and corresponding on the problem very widely since then, and really wondering why I was so unable to get systems thinkers, from any established research community to join me, in studying the commonalities of individual emergent systems. I started with air currents, that generally develop quite complex organization quickly with no apparent organizational input, behave very surprisingly, and seem individually unique.
I actually developed a fairly efficient scheme for studying any kind or scale of emergent system, using the simple device of starting with the question: “How did it begin”. What starting with that question does is immediately shift the focus of interest to considering systems as “energy events”, that you consider as a whole in looking for how they developed. That approach also directs you to look for the event’s naturally defined spatial and duration boundaries, which are highly useful too.
In addition to being fairly productive as research approach, it also made it easy to skirt lots of spurious questions, like “how to define the system”. With that approach your task is finding how the subject defines itself, still looking for a pattern language of structural and design elements to work with, within and around the system, confirming what you think you find.
What I finally arrived at in the 90’s was that the equations of energy conservation implied a series of special requirements as natural bounds for any emerging use of energy. I was thinking that the issue was how nature uses discontinuous parts to design continuous uses of energy, and in working with the equations noticed that the notation for the conservation laws were either integrals or derivatives of each other.
Then one afternoon I just extrapolated an infinite series of conservation laws to define a general law of continuity, and integrated it to find the polynomial expansion describing the boundary conditions for any energy use to begin. It was a regular non-convergent expression, a surprising confirmation of Robert Rosen’s interest in non-converging expressions for describing life, and became very useful as what to look for in locating emergent processes to understand how they worked. I circulated the proof for discussion many times, submitted it for publication a few times and wrote numerous introductions, the following the most recent: