The Energy Physics of Continuity in Change

The implications of the unifying the conservation laws in A General Law of Emergence and Continuity [i] are diverse, but seem to for the first time to allow natural complex systems to be defined by their location, independent of theories of how they work, so that the varying sciences can refer to them as the subjects they have in common.   That finding is carefully described in Systems Energy Assessment along with showing how too construct a rigorously defined boundary for businesses as environmental systems that work as units of animate and inanimate parts. 

Over the years the work of exploring the meaning of it, and developing applications has taken precedence over concisely describing what was being found.   So that remains to be done really, with the following an accumulation of short descriptions that need work.   They are four approaches to describing the implications, collected at various stages of thinking about how to explain it.    One way to say the problem is that both theory and observation strongly indicate that it makes a great deal of sense to nature to connect all her “lawful” behaviors with “lawless” ones.  That comes from the logical and observed necessity of systems developing by accumulation, starting from something else, and maintain energy continuity in the process.    The instrumental mechanisms by which energy using processes develop, are not the equations that will describe them after they have developed is one catch.   What takes place is an organizational "learning" process of building on seeds of conserved order either left by other things, occurring circumstantially, or discovered as systems wander their environments experimenting with connecting things in new ways, like weather systems or economies, resulting in explosions of complex design as transient regular systems.  jlh ed. 1/7/11 2/11

Ó Jessie Henshaw

§1.   Preface

ed. 10/22/09 - Unifying the conservation laws of physics (Henshaw 2009) does something unexpected things.   It effectively changes the story of physics from one about the rules that controlled events follow in nature to how uncontrolled processes develop and work by themselves.   Uncontrolled processes as they take care of themselves sometimes predictably appear to follow abstract rules, and sometimes not.   If you study individual physical processes as for how they individually transpire, it’s very obvious that in reaching their ends they employ complications in the details than make them individually impossible to explain.   Average behavior never seems to occur, and even if validating the general abstractions of science, individual physical processes apparently never following them.    

Maybe the easiest way to understand the deeper issue, is through the missing variable in thermodynamics exposed by the question of how things work by themselves.    The issue is not with the general principle of thermodynamics that energy is lost whenever you use energy.    Any energy transfer process appears to generate energy losses.    The curiously missing variable in that equation has to do with how that energy transfers get started, not what they do as a steady state.   The riddle is that is seems necessary for energy to have been used to build the energy transfer process itself.   That self-investment of energy in building the energy use system, or ‘syntropy’, is an energy flow.   It necessarily precedes the assortment of entropies and work outputs of degrading the gradient.   

What this reveals is the need for development prior to the release of energy from the gradient!    That is to say, we often just don’t know where that energy source that builds the energy use process comes from, or have any information about what organizational process it energizes.   Yet, to this time, it has been represented as part of the energy released from gradient at some later time, but it may have come from somewhere else entirely.  

This is not actually mysterious at all except in physics, as “seed resources”, or
“venture capital” are very commonly understood as essential energy sources for kick starting the self-investment cycles for developing larger scale energy use processes.   Physics has been lumping that preceding energy flow in with the following energy use process as it was one of the energy loss products of depleting the gradient rather than the spark which initiated it.    That oversight means that science did not notice that this central principle of business models is also what all of nature uses to get its individual energy use systems going, and to initiate the construction of systems that take care of themselves…   My response on noticing that was to say “oops..” and choose to just carry on.   It’s a very good way to be responsive to things when you’re completely unprepared and not quite sure what response to make.

Even after being initiated by the energy from a seed resource an energy transfer process has not yet developed to the point of depleting the gradient.  A sprouting seedling has yet to begin photosynthesis, for example, and a business that opens its doors has yet to make a sale.   From that point the energy for building an energy transfer process mostly then comes from self-investment of the process in itself.   Like the ionization cascade that opens a channel for a spark discharge, self-investment from the initial current leak serves to open the channel, using a portion of the energy output of the process to expand the process.  That second source of syntropy, the fraction of the energy transfer product self-invested for building the processes, is also represented by physics as part of the entropy of the system of energy transfer.  

Those two “little twists” that reverse the time sequence of essential energy transfers almost seem implicitly to have been intentional.   Perhaps they served some purpose in history that is no longer apparent or necessary.   It certainly changes everything to realize the error, though.    How local systems use self-investment to produce energy transfer processes, employing an outside source of energy to begin, was disguised.    Also hidden by lumping all the “lost energy” of natural energy transfer processes into “entropy” was the energy flow responsible for allowing some energy use systems to stabilize rather than simply deplete their gradient and exhaust themselves.   Self-investment systems that grow by diverting some of their energy product to build their process can also stabilize.   They do so by divesting the same source of energy, stopping the accretion and stabilizing their development by doing so.  

Fortunately for people various kinds of energy using systems in nature ignore our failure to understand how, and take care of us by not exhausting themselves.  They both successfully initiate and then stabilize themselves, on their own, as if for our benefit, despite our theoretical construct of the universe not telling us to do so as well.   In theorizing about the universe we somehow arranged a couple critical aspects of cause and effect out of sequence. 

Over the past few centuries as science was applied to business and economics (the energy processes creating wealth), our misunderstanding kept us from seeing that the energy source used for business self-investment needed to be divested.  Otherwise business exhausts its resources and can’t stabilize.   It has monumental consequences for the future of the earth and our comfort on it.   Being unaware of local causation, or you might call it “self-determinant” causation, leaves us with no reason to end what seemed to work before, and no qualms about continuing our multiplying self-investment in creating wealth to a point of exhaustion and collapse.   The notion of divesting the same energy source as used to multiply the process just doesn’t come up.   Since human access to energy for any purpose is by purchasing it, that energy source for the self-investment growth of wealth and consuming the energy gradients of the earth, is money.

So, the theorem unifying the conservation laws is fairly simple, as theorems go.  It’s that using calculus the law of energy conservation can be differentiated, to create an infinite sequence of conservation laws for all the higher derivatives of energy flow.   When you then integrate that sequence of laws you get a polynomial expansion representing how energy flows begin or end.   What you get is in the form of an exponential, implying the presence of physical processes to develop that way.    

What it demonstrates is that the conservation of energy implies that local developmental processes are a necessary mode of causation.   By looking for and studying them you find confirmation of that and many other particulars about them.   Traditional physics and the other sciences that inherited its approach, which represent physical processes as controlled by operators between numbers,  overlook the questions about the intrinsic processes of physical developmental that are instrumental to change.   It’s the same error, it seems, as Plato and Ptolemy made, of representing nature as following our own ideals, that we invent to help us organize our thoughts for our own purposes.    

What the theorem does, in effect, is to turn all those answers into questions.  It points to where other scales of organization, beyond our information and ability to idealize, play crucial roles in the continuous chains of events.    That’s the place of complex systems.   Some of the characteristic gaps in our explanations for things point beyond our information to where these physical processes are filling the gaps, and we can look to find them.    It implies that science is just information, and that the subject of science is not how our information refers to itself.   The real subject of science is how our information refers to the realities beyond our information, pointers to the non-information world of real physical things and processes, and how they are inherently different from information  in kind.

The following Abstract and introduction to the theorem approach the subject from the readily observed features of how energy transfer systems begin and end in nature.   It’s with energy flows that start from an energy and organization seed than initiates a boom of complex system development .    It’s a surprise at first, but doesn’t take too much digging to discover that growth phenomena like a spark discharge, an organism, a culture or organisms, a group or personal work project, a business enterprise and a personal family, as well as plants, are all examples of that.   That much of the process necessarily occurs beyond the limits of our information proves that physical systems exist (odd that we should wonder about that, of course) and why getting anything started and completed is so complex.

§2.   Abstract

ed  5/12/09 - The form of physical processes needed to satisfy the boundary conditions for the conservation laws is considered, along with the form of mathematics needed to explore the emergent phenomena in nature.   Asking what needs to occur for natural events to begin and end yields important new insight into both.    The constraints of conservation for energy, momentum and reaction forces combine into a single law of continuity in rates of change, and so for transitional processes that allow change without discontinuity. 

The main finding is that divergent eruptions of development are needed to do it, with higher accelerations necessarily coming  from eruptions of change on a smaller scale in .  These implied “little bangs” that initiate divergent processes of system development are observable at the beginning of most energy transfer processes as seed events of nucleation that germinate a larger “run-away boom” of organizational development that systemizes any new energy flow process.      The reasoning appears to be similar to why a period of inflationary change needed to be hypothesized to start the “big bang” of the universe, a kick start to conform the basic laws of physics.    What would also be implied is some distinct ‘nucleation’ or ‘seed’ event to initiate the boom of developmental process that may result in a an environmental response to stabilize or destabilize the system of energy flows so initiated. 

§3.   Continuity; Nucleation, Divergence & Response

gr00.jpgThis theorem relates to physical mechanisms by which local systems may emerge to break and make local ‘laws of nature’ that arise as local systems of conserved change develop.    It also relates to the mystery of why so much persistent heterogeneity of complex form is observed in nature to accumulate and be preserved, when the statistical laws imply it should always be decaying.   The implied answer is that it comes from local individual developments, not general probabilities, or more simply “it’s local”.     If what we observe is energy flows locally beginning and ending, what is implied by continuity is a local cascade of complex processes of conserved addition to do it, emerging from their environment.     When you look for these start-up sequences of conserved addition you often easily find them.   They operate within the laws of probability, as the physical mechanisms by which energy is transferred, and necessitating the development of the complex systems to do it.    If the forms of systems develop locally, it suggests that time is an accumulative process in general, and not a location on a scale.  As such, energy transfer by physical systems seems to involve transient steps of local organizational development and extinction not entirely unlike how both individual organisms and whole species also do in evolution.  

Direct observation of the beginning and end of emergent phenomena such as organisms, storms, sparks, eruptions, cultures etc., all display that their primary ‘non-linear’ behavior is simply beginning and ending.   Those beginnings and endings all involve the development of conserved systems of energy flow and other kinds of conserved change, definite in that they occur but indeterminate as to how.    The math that fits that mix of definite but indeterminate processes along with the basic laws of physics is what follows.    Those transitional periods of change, to the limits of our observation, generally reveal explorable complex processes that temporarily diverge developmentally and organizationally from anything else around them, not displaying an equal cause & effect but emerging order from local gradients that diverges from the prior state and leads to an environmental response.     Because they are hard to describe they’re mostly just omitted from our catalogs of  things we can describe, and glossed over.   We don’t know how to connect divergent mathematical sequences with convergent ones.   We don’t know how to represent or define an environment.  These problems have often been considered impossible or unscientific to address.   

What seems to correct the problem is to switch to using our models as questions, leaving things out, rather than representing complex systems with simple rules because simple rules is all we can define.   The problem with environmental processes is that they develop independently until they run into something else, i.e. have a form of connection without prior determinism.     While all these “missing parts” does foil any attempt to obtain definitive answers based on data alone, having a model of what’s missing does serve to raise new high quality questions, pointing to issues beyond the present evidence, in a way to facilitate new hypothesis and ways to discover information to confirm them or raise other questions.   

The general mathematical questions of describing nature with divergent mathematical series may have been most thoroughly studied by Robert Rosen.   His short 1995 essay[ii] describes how a mathematics of predictable convergent sequences, excluding the study of improper’ divergent sequences fails to match the variety of behaviors of nature.     In his observation, both emergence in complex systems and in life are subjects only seen in divergent processes which science would need to use divergent sequences to study.  

The present theorem demonstrates that the beginnings and endings of energy flows require divergent sequences to be described mathematically.  That identifies a key feature of life and emergence that a study of divergent sequences is needed for, substantiating Rosen’s complaint.     Because defining true environments for equations is more than difficult, and because the divergent processes of most interest already have their own environments… is a further reason for a switch of method from representational to exploratory mathematics seems called for.   Instead of using math in isolation, a way to use it to raise questions open system environments seems required.   One general way to do that, for example, might be to replace environmental parameters with strategic queries.   A mathematically assisted study of ‘divergence and response’[iii] is then an interactive discovery process using conventional scientific tools and a map of local information gaps within developmental processes, a work I started in the 1970’s that led to the present analysis of the problems of mathematical physics that would need to be solved that way.  

§4.   Balancing the budgets for the ‘business’ of nature

ed 8/10/10 – from Henshaw (2011b draft) If moving energy is the ‘business’ of nature, where one draws an accounting boundary defines what you are accounting for.    Any boundary can be considered as a question of what’s available outside, what’s crossing the boundary, or what happens inside.    Sustaining the energy resources inside a boundary is the same arithmetic for either your home or the global economy.   It’s universal, because energy is not created or destroyed, and takes costly processes to get it or use it.     As affordable environmental resources become scarce you could either improve ways to bring energy in, or to reduce what you use.   If the boundary is a growth system then neither of those solutions work, except momentarily perhaps.   Increasing use of resources that are increasingly costly as you use them becomes absolutely unaffordable with abrupt natural limits as the cost exceeds returns.    For complex environmental systems one has no equations but if you can measure the total you can watch to see how nature integrates the behavior of the whole, and read a great deal from that.    If you can’t add up everything crossing the boundary “total” is undefined, and so are “change”, “direction of change” or “acceleration”, or even the ability to use the measure to scientifically refer to the system as a physical subject of discussion.    

Because energy flow requires first building an energy flow process (Henshaw,  2009) the general narrative of change for energy systems is development from small beginnings leading to small ends, involving assembly and disassembly of the process.  In time series data that appears as growth and decay, generally found confined within a definite boundary as a network “cell” of complex processes.   Narrative is a necessity for complex systems science, as an aid to exploratory investigation, requiring care in collecting “just the facts” as a precedent to studying how to fit them together (Allen et. all. 2001), which is presented here as “just the facts” about the subject of an identified individual physical system.    To trace their energy flows is like “follow the money” for detective work, locating the coordination of energy and self-organization animating the process.   

Life cycle of development and decline

Net energy uses in individual system

Figure 1 Simplified Development Cycle and Process Succession diagrams of typical complex systems.

One can outline a rudimentary energy budget (Equation 3,4) to satisfy the conservation of energy and internal needs of system development, products and losses.   The system needs to maintain positive net energy, beginning with a seed resource, used in starting the system for investing and returning net energy from the environment as it uses its seed or net returns to develop itself and operate to produce internal products while maintain net energy throughout, all of which results in losses and discards.    These energy uses are implied for all energy using systems, needing to add up and operate, and so provide a start for exploring how  any individual complex energy using processes begins, operates and ends.    These questions about energy use over time observably apply to most systems and serve as things you  know about any individual system before knowing how any part works.   They are largely necessities for changing scale in working processes implied by energy conservation (Henshaw,  2010b).  

                       Ein =   Eseed +Einv+ Eret+ Edev + Eop + Enet + Eloss+ Edisc                     (1)

                                                         Enet > 0                                                          (2)

It does take effort to account for a whole system’s energy budget, which starts as just a map of missing information about it, once you locate its boundary so you can define the task of coming to an estimate of the total energy uses.      The simple kind of powerful conclusion that gives you immediately is that not every part can rely on energy use far below average, like what you see.     Further exploration both fills in some gaps and creates better questions.    Going back and forth between the subject and different perspectives of it is the methodology that maintains the focus of attention on the complex system as an individual physical object, making this physical rather than statistical science, about physical subjects that remain beyond one’s own full imagining.

It sounds rough but it does help frame inclusive questions needed reach conclusive answers.      For asking inclusive questions about the world economy, for example, one can see in the total energy budget (Figure 1)  how the relation between money and energy changes in remarkably regular fashion.     That translates to a steady average rate of energy use for every dollar of GDP.    “Average” is certain to be a better estimate than zero for any estimate of personal or business energy use assessment.   Any product or service does actually require and support highly diverse business services throughout the world economy, and markets do select products to use the least energy possible.   If some service supplier was an inefficient energy user a business would stop using them because it would reflect in their price.  

All combined, average global energy use per dollar is not a farfetched initial estimate, at least.   One important direct result is readily apparent.   If you account for your own impacts on the earth as being “about average” for every dollar spent, it matters much more what your income is than what you spend on.   Add it up and see.    That illustrates another way a whole system view starkly contrasts with the popular use of persuasive arguments and symbolic values.    It puts the arguments and symbolic values in context, grounding them in the practicalities of living in a physical world in which nature adds everything up using the conservation of energy.

This provides a very effective way to go back and forth between measures of the whole and learning new meanings for the  behaviors of its parts.   Fairly accurate direct measures of the energy used by either business choices or whole business systems is possible using the System Energy Analysis (SEA) method of accounting for the energy required to deliver business products (Henshaw et. all., 2011b).    The study defines a new standard for measuring EROI (energy return on energy invested) for business choices.    When counting up the total energy a business uses the conventional approaches have nearly all been to add up what was visible.   The SEA method uses the global boundary to account for a business system by asking what energy uses were required for it to operate, and using “average” for the specific energy uses identifies that are unaccountable.     In the case study, which seems typical, the difference is a matter of about a 500% increase in the estimate of the embodied energy costs of operating the business.    These things will surely take some time to understand, but there’s little doubt that not every business can be using energy at a rate 80% below average per dollar either, but that is largely how our prior methods of accounting added it up.     Still, the facts may seem easier to establish than giving them meaning.   As with any other learning process it starts off wherever you start, and by going back and forth between different views you reach a point in your mind where it starts coming together.

Understanding how both the natural costs of energy and our societal energy overhead costs are rising and reducing our operating net energy is another way to look at the whole system energy budget.    It’s possible the energy available on earth will not continue to be cheap enough to run our world economy designed only for running on cheap energy, or large sectors of it.    Studies on that question were begun by Charles Hall with his work on EROI, the energy returned on energy invested, noting the drop in oil energy return on investment from 100:1 to 15:1 in the last century.   One of his interesting recent papers (Hall, C. A. S., et. al., 2009) introduces the idea that as our energy resources cost more energy to develop, and our society keeps accumulating more energy costs, there is a theoretical probability of a crossing point where our form of civilization could not physically operate.   

It is suspected by many observers that this kind of energy bankruptcy and failure of economic sectors unable to adapt to expensive sources of energy may have already started happening.    There was an exceptionally high demand for oil and a sharp rise in energy prices before the 2008 economic collapse, but with global oil supplies not responding as usual (Hamilton, J.D., 2009).     That’s exactly what the phenomenon discussed as “peak oil” would show, that with high prices, high demand, and plenty of warning, industry was unable to meet the demand and driving escalating  prices.    An net energy budget is like a financial budget with regard to needing a positive balance.   For some economic sectors, drifting over that line and becoming unable to maintain a positive energy balance might make investors pull out and bring about a financial bankruptcy.     That on present trends, maybe even in the next ten or twenty years, losing more sectors of our formerly healthy society for natural causes, in effect, or failing as a whole, is a bit of a shock.    This is a very young science, but based on the most well established principle of physics, so the questions seem rather pointed and appropriate, and should be followed up.

4.1    References

a)       Allen, T.F.H., Tainter, J.A., Pires, C., Hoekstra, T.W.,  (2001) Dragtnet Ecology – “Just the facts, Ma’am”: The Privilege of Science in a Postmodern World, Bio Science Jun 2006 61(6)

b)       Hall, C. A. S., Balogh, S. and Murphy, D. J. R., (2009). What is the Minimum EROI that a Sustainable Society Must Have? Energies, 2 25-47,

c)    Hamilton, J.D., (2009). Causes and Consequences of the Oil Shock of 2007‐08. Brookings Papers, Spring 2009

d)       Henshaw,  P.F. (2009). Law of Continuity, minor revision of 1995 theorem

e)       Henshaw,  P.F. (2010a). Models Learning Change, Cosmos and History, ISSN 1832-9101 6(1)

f)        Henshaw, P.F., King, C., Zarnikau, J.  (2011a). System Energy Assessment (SEA): Defining a Standard Measure of EROI for Energy Businesses as Whole Systems, special issue on EROI ed. C.A.S Hall, Sustainability, pending issue.

g)       Henshaw,  P.F. (2011b). The curious use of Stimulus for Constraint, Emergence: Complexity & Organization, in revision.

[i] Note:  The general Law of Continuity for energy processes was developed in 1993 and included in a circulated 1995 paper, excerpted as:

[ii] Robert Rosen 1996  “On the Limitations of Scientific Knowledge”  in On the Limits to Scientific Knowledge, John Casti & Anders Karlqvist eds, Perseus; collecting ten papers presented a 1995 Stockholm workshop of the same name sponsored by  the Swedish Academy of Sciences; link to scanned copy

[iii] Author’s archive of studies using various methods