UNDERSTANDING SUSTAINABILITY. BIO-ECONOMIC,ENTROPIC-EXERGIC, SELF-ORGANIZING EMERGENCE OF

LIFE

A. SenguptaInstitute for Complex Holism Kolkata, INDIA.

E-Mail: osegu@iitk.ac.in

Abstract

Bio-economics, a hetrodox integration of economic demand-supply philosophy and thermodynamic entropy-exergyprinciples, provides a fruitful representation for emergent, self-organizing systems. Darwin’s natural selection in mod-ern synthesis with mutation, gene flow, and genetic drift presents a biological framework of the thermodynamic conflictbetweeen entropic dispersion and exergic concentration. In conjunction with the dynamics of the logistic map, Part Idemonstrates that nonlinear Hardy-Weinberg-like product interaction of these opposites can induce complex homeosta-sis in the spirit of competitive cooperation that neither of the adversaries, acting in disregard of the other, can emulate.Sustainability emerges as a specialized measure of complexity characterized by a full Cause � Effect causal feed-backs, that “supply” of symmetry-breaking genetic and epigenetic variation in conflict with the symmetry-inducing“demand” of natural selection define as antagonistic direct and inverse arrows of the real and its negative world. Ourgoal in this Part is to interpret neo-darwinism in the light of nonlinearity to account for the acknowledged complexinteractions between the environment, phenotype and DNA-genotype.

Part II exploring this interaction in relation to the dynamics of the logistic difference equation λx(1− x) withits effect-supply of the present feeding as cause-demand of its immediate successor, establishes that under extremeconditions of disequilibria with the direct and inverse feedbacks vigourously exploiting each other for their combinedand enduring well-being scripted by the give-and-take of mutual trade-off, the thermodynamics of Second Law ofentropy can be integrated with complex-chaotic dynamics of the logistic to uniquely define the parameter λ in termsof thermodynamic temperatures alone. This dynamic-thermodynamic handshake defines (Defn. 2, Sec. 7.2) holisticsustainability as “the art of healthy enduring living from the past into the future, choreographed by the competition-cooperation-adaptation of self-organizing, emergent present” of limit cycles and periodic points. Beyond the reduc-tionist confines of the incomplete and partial feedbacks of fixed and nascent periodic points — neo-classical economicsand Gaia Daisyworld of weak and strong sustainability serving as examples of Brundtland sustainable “developmentthat meets the needs of the present without compromising the ability of future generations to meet their own needs”— holistic sustainability of self-organizing emergence defines the essence of life and living in a delicately balancedvulnerable fragility.

Keywords: Complexity; holism; biological sustainability; competition-cooperation-adaptation; holistic sustainability.

Prologue: Chaos, Complexity, Holism

Biological systems are complex holistic systems — thermodynamically open, self-organizing emergent, and out-of-equilibrium. The normal tools of Newtonian analysis of linear reductionism fail to address these issues, just as classicalNewtonianism was unable to embrace the microscopic, necessitating the quantum revolution more than 100 years ago.The inadequacy of reductionism of a composite whole as an assemblage of its parts, works so long as its foundational“normal”, isolated, near-equilibrium — as opposed to “extreme”, open, out-of-equilibrium, stressed — conditions aresatisfied. Increasingly, it is being realized however, that most of the significant manifestations of nature and life displayholistic tendency wherein the component parts of a whole cannot exist and be understood outside of the entierity: wholesgenerate interdependent, interacting effects that are qualitatively different from what may be induced by the componentson their own. Complex self-organizing systems evolve on emergent feedback mechanisms and processes that “interactwith themselves and produce themselves from themselves” as “more than the sum of these parts” — complex systemscannot dismantle into their components without destroying themselves. The cybernetic system is involved in a closedloop where action by the system causes some change in its surroundings which is then fed back to the system that causes it

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to adapt to these new conditions — the system monitors its own behaviour. This circular causal relationship is necessaryand sufficient for the cybernetic perspective of competitive-cooperation that constitutes the basis of sustainability inNature.

Micro-evolution defined as change in allele frequency is a two-step mutually interdepedent process of genetic changessmall or big in a population, inherited through Darwinian selection over several generations. For an event to be evolu-tionary, changes at the genetic level of a population have to be transmitted through generations so that changes in thegenes — now understood as “inherited distributed cause” of DNA sequence information-carriers over biological net-works of the environment-phenotype-DNA (gene) [Kohl et al., 2010] — more precisely in the alleles of the population,are propagated in the phenotypes. The first stage of symmetry breaking, random, infinitely small, heritable mutationsof genetic variations, is followed by symmetry generating natural selection of fixation of beneficial changes as its prin-cipal motive force. As elaborated in the “systems biology” approach [Kohl et al., 2010], current realization supportsthe view that each phenotype characteristic additionally depends on cellular inheritance and epigenetic1 environmentaleffects, mediated by the biological network: “the logic of these conditional effects may be very complex” necessitatingan “integral view of genetics”. The system “an entity that maintains its existence through mutual interaction of its parts”consciously combines the reductionist top-down gene/DNA ← system/phenotype analysis and bottom-up gene/DNA→ system/phenotype synthesis to a middle-out stasis, resulting in multi-dimensionality of the multitude of complexnetworks of interaction in biological systems.

Can the Darwinian paradigm of linearly smooth, gradual continuous variation-selection-retention explain complexityand holism? Symmetry-inducing “demand” institutes a symmetry-breaking “supply” which in turn fuels the “demand”in a demand � supply loop of emergence and self-organization, essential for complex holism [Sengupta, 2010b,c]with evolutionary pressures acting on whole organisms rather than on single genes. A particular gene being invisible tonatural selection, is always in the context of other genes and their mutual interactions that determine its relative selectivity[Mayr, 2001], implying that the product of the antagonistic mutation and selection progress in time to complex, emergenthomeostasis. Somatic mutation, sexual genetic recombination, gene flow and horizontal gene transfer increase variationwhile natural selection and random genetic drift decrease available free-energy (exergy) that accounts for the price/costof maintaining the bi-directional feedback of complexity and life. Charles Darwin’s natural selection without the geneticmachinery of inheritance and quantitative traits available only sunsequently, lacked the necessary target to act upon.

At the heart of neo-Darwinian Modern Synthesis2 [Rose and Oakley, 2007] — a synthesis of Darwin’s natural selec-tion, Gregor Mendel’s particulate genetics, and August Weismann’s germ plasm theory of heredity — was the questionof whether Mendelian genetics, with the contribution of each parent guarding its own integrity rather than cooperatingwith the other, could be reconciled with the gradual evolution of natural selection. Since genetic characteristics are notentirely identical among individuals in a population, the feature of genes that reproduce successfully surviving at theexpense of genes that fail with subsequent consequences at the organism or phenotype level, is unlikely to be a ran-dom process. Gene flow of movement of genes from one population to another and sexual recombination leading toindependent assortment of new combinations are additional contributors for genetic variation.

In this paper we generalize the contention that complex nonlinear networks encompassing DNA-Environment-Phenotype of biological systems with evolution of DNA sequences that might actually lower fitness, can attain a measureof genomic complexity beyond that of molecular and cell biologic reductionism of modern synthesis, limited to its indi-vidual genes without interaction among others. Nonetheless, with “interactions between particular DNA sequences andparticular phenotype characters mediated by biological networks, there is no reason to assume direct causal relationsbetween particular DNA sequences and particular phenotype characters in biological systems”, the causation betweena DNA sequence and a character “changing as it is transmitted through, and modified by, the biological interactionnetworks. Strictly speaking, not only do the causal arrows change, they interact with the network” [Kohl et al., 2010].

Emergence, self-organization, holism and sustainability are, we suggest, determinants of the biological network ofthis new science that require inter-disciplinary tools and techniques for its study, analysis and interpretation. “While awidespread international consensus now exists on the need for more socially-inclusive models of growth and develop-

1Epigenetics describing anything other than DNA sequence that influences the development of an organism is “the study of mitotically and/ormeiotically heritable changes in the gene function that cannot be explained by changes in the DNA sequence”. Cellular differentiation in eukarytoticbiology in which stem cells become pluripotent cell lines of the embryo transforming into the fully differentiat cells provides a prominent illustration— as the simgle fertilized zygote divides, the resulting daughters metamorphose into the different cell type of the organism through activation ofthe expression of some genes while deactivating others.

2Modern Evolutionary Synthesis is a 20th century integration of ideas from genetics, paleontology, systematics that provided a widelyaccepted view of evolution. Apart from the pre-eminence of natural selection as the defining force, modern synthesis recognizes the significanceof genetic mutation and epigenetic gene flow and genetic drift, to integrate them with natural selection into a new inclusive framework.

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ment, little in the way of concrete policy guidance has emerged. There is a growing need for analytical frameworks andevidence-based solutions suited to this purpose. From this practical, evidence-based perspective, the current debate oninequality and social inclusion is unduly narrow and unnecessarily polemicized. It is possible, indeed essential, to bepro-labor and pro-business, to advocate a strengthening of both social inclusion and the efficiency of markets”3. “Therealization among business and political leaders that economic growth is only sustainable if it is inclusive, and not re-stricted to a small elite, may have taken too long, but at last the message is being received loud and clear: you can bepro-growth and pro-equity -– and you must be pro-equity to be pro-growth. Decades have been lost, for one thing througha stubborn adherence to the belief that focusing on market efficiencies alone would allow wealth to trickle down. Flawedthinking has led to a polemicization of the political debate. But the age-old orthodoxies of the left or right are not goingto get us anywhere; they will just deprive the world of collaborative spirit when it is so badly needed to find a creativeand more durable solution”4.

It is the intent of this work to define an analytic framework of this competitively-cooperative endeavour by surmount-ing the orthodoxies — neither the left nor the right were wrong, neither the right nor the left are right.

Part I

Reductionism and Modern Evolutionary Synthesis1 Pump-Engine Realism of the Participatory Universe

1.1 The logistic nonlinear qubit: cooperative-adversity of supply and demand

The logistic difference equation xt+1 = λxt(1− xt) of interaction between individualistic supply x and cooperative de-mand 1− x as the starting point in our consideration of complexity and holism [Sengupta, 2006-Sengupta, 2010c] withλ an environmental parameter, can serve as a simple model for the gametic5 lifecycle of sexually reproducing organismswith differential survival and reproduction of genotypes leading to selection, it being assumed that in the absence oflimiting factors, λx the population in a succeeding generation is the positive supply feedback in effective regulation bythe negative demand of depletions 1− x.

The adversaries individualistic supply and collectivist demand cooperate nonlinearly to generate life in a win-wingame where no participant wins and none lose. The self-organizing, emergent system working on a positive� negativefeedback mode adjusts to the environment it finds itself in leading to a homestasis6 of “inevitable limitations, com-promises and tradeoffs” that neither of the participants working alone and independently can possibly achieve. Bothadversaries have equal stake in the complexity of holistic life and participate as equal partners, each competing with theother for its own cooperative welfare. In this capital-culture contest [Sengupta, 2010a] of self-organization and emer-gence, one of the contestants assumes a dispersive passive role of an “offerer” that elicits an active “confirmation” froma concentrating opponent leading to a handshake transaction [Cramer, 1986] of an explicitly non-local character withthe cause and effect entangling and intermingling in a new two-phase complex synthesis. The concentrator uses theofferer as a “vehicular tool by which levers itself into the next generation” [Dawkins, 2006]; it needs the vehicle as anecessary physical impediment in inhibiting the cancerous growth of uncontrolled replication. Non-reductionist graphi-cal convergence in an extended multifunction space is almost a natural consequence of this view of the phenotype of the

3World Economic Forum Insight Report, The Inclusive Growth and Development Report (2015).4Gemma Corrigan, Economist, WEF, You Must be Pro-Equity to be Pro-Growth (2015)5Gametes are reproductive haploid sex cells. The male sperm fuses with the female egg to form a fertilized diploid zygote which then undergoes

mitosis to develop into a new organism within the female environment.6Homeostasis. Any self-regulating process by which biological systems tend to maintain stability while adjusting to conditions that are optimal

for survival. If homeostasis is successful, life continues; if not disaster, disease or death results. The stability attained is a dynamic feedbackequilibrium when continuous changes occur yet relatively uniform conditions prevail.

The human body manages a multitude of highly complex interactions to maintain balance or return systems to functioning within a normal range.These interactions within the body facilitate compensatory changes supportive of physical and psychological functioning essential to survival. Theliver, kidney and brain help maintain homeostasis — the liver in metabolizing toxic substances and maintaining carbohydrate assimilation, thekidney in regulating blood water levels, reabsorption of substances, maintenance of salt and iron levels in the blood, regulation of blood pH, andexcretion of urea and other wastes.

Heart failure, for instance, may occur when negative feedbacks are overwhelmed by positive feedbacks; diabetes, dehydration, hypoglycemia,hyperglycemia, gout and toxins in the blood is an incomplete call-list of homeostasis imbalance.

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replicator-vehicular antagonistic cooperation embracing the unconventionality of HGT. The classical notion of order innear-equilibrium compared to out-of-equilibrium homeostasis can be rather different.

While biologic life is supply regulated depending principally on the resources available, an individualistic supplyeconomy can lead to severe collective stresses. Working within the dual structure of of individualism (↓) and collectivism(↑) of increasing positive and negative slopes of the rising and falling branches of the logistic map, the� feedback ofemergence and self-organization achieve in one nonlinear step the dual functions of inducing the resource of scarce orderin an universal background of pervasive disorder. Thus if deaths were absent with only ordering component x available,there would be no cutoff to the explosive growth of fitness; likewise with only 1−x present, the vanishing unfit, steadilyeroded through selection, would lead to the eventual collapse of the species.

The logistic map through its nonlinear Hardy-Weinberg7 like handshake of the opposites achieves the remarkabletransaction of inclusive holism that we now consider.

1.2 Alleles and genotypes. Confrontation of opposites: a generalization

To establish the perspective of our consideration that follows, consider the iconic Mendel pea-plant experiments. Themonohybrid case is summarized in Punnett diagram of Fig. 13: the alleles8 R (phenotype “smooth” seeds) and r(phenotype “wrinkled” seeds) formally correspond to the “spin” strategies (↓) and (↑). Of the two alleles for everytrait, the chromosome contributed by the female (R) in her ova is taken to be dominant, with the male allele (r) inhis sperm recessive. Joined together in fertilization, there are three possible genotypes for each trait: RR homozygousdominant, rR/Rr heterozygous dominant and rr homozygous recessive. Compared to Mendel’s use of the dominantallele completely masking the phenotypic effect of the recessive in heterozygous combinations when the phenotypeproduced is identical to that by the dominant partner, in nonlinear holistic evolution regulated by interactive “demand”�“supply” feedbacks, symmetry breaking gravity9 induced order of the supply pump moderates the Second Law demandengine of symmetry inducing dispersion, with dominance representing overriding exergic modulation on the entropicW+ by the negative world W−, as expressed in the ordered structures of Nature.

The value of Mendel’s pea-plant experiments of particulate inheritance abstracted in the Punnett diagrams of Fig. 13lies in their generalization from the simplicity of matrix algebra to the complex homeostasis of self-organized emergencedynamically induced by the logistic map. Unlike the stationary world of Newton, perfectly knowable and completelypredictable, for Darwin history matters; the future depends on the past. It is not enough for effect to simply depend oncause, reciprocally cause is simultaneously influenced by the effect it produces. In what follows, we explore this theme.

2 Yang-Yinism of Darwinian Evolution

In the unified framework for evolutionary dynamics of Nature of which the linear characterizations of quantum non-locality, biological Punnett squares, and economic payoffs and equilibria are simple manifestations, complexity resides inthe interactive cooperative adversity of the compopnent parts, with the individual units retaining their defining attributes,contributing to the whole in its own characteristic fashion within a framework of dynamically emerging inclusive glob-ality. Although the whole emerges from the parts, the parts acting independently on their own fail to account for thecollectivity of the total.

2.1 Direct and inverse systems

Inverse and direct limits [Dugundji, 1966] denoted lim←− and lim−→ constitute a rationale for the simultaneous existence ofopposing directional arrows from very general considerations, Fig. 1.

DIRECT LIMIT X−→. Let {(Xα ,Uα)}α∈D be a family of spaces and let {ηαβ : Xα→ Xβ}α�β∈D be forward continuousmaps connecting the present to the future satisfying (i) ηαα(x) = x, ∀x ∈ Xα , (ii) ηαγ = ηβγ ◦ηαβ , ∀α � β � γ ∈D. The

7Hardy-Weinberg Principle. Gene frequencies and genotype ratios in a randomly-breeding population remain invariant between generations inthe absence of mutation, gene flow, genetic drift, natural selection and non-random mating. Under Hardy-Weinberg product interaction (p+q)2 = 1for p+q = 1.

8Alleles are the alternate forms of the two genes of an organism located on chromosomes that control each heritable characteristic/trait onecontributed by the female, the other by the male. When gametes develop during meiosis (a process of cell division that produces sex cells) eachgamete receives only one of these alleles.

9Gravity is the thermodynamic legacy of the negative world on the real world, generating the dispersion-concentration, two-phase signature ofcompexity and holism.

4

.

Xα

Xβ

Xβ Xγ

Xγ Xα

X−→X←− X←→

Cause←Effect

⊎Xκ

INVERSE

{System {Xβ ,πβα}Limit X←− : Engine

ζα

ζ

ξ

ξ β

Cause→ Effect

πγβ

pα

Q

ηβγ

∏Xκ

πα

πβηα

ηβ

ηα

β

πβ

α ζ βξ

α

ηα

γ =η

βγ ◦

ηα

β

ηkn ,

η(n−

m)η(m−

k)η(k), n≥

m≥

k

πγα=

πβ

α ◦π

γβ

DIRECTED SET: α � β ∈ (D,�)

η(k) ≡ f (k)λ

, π(k) ≡ η−(k)

pγ

pβ

Demand� SupplyBidirectional feedback:

“M A R K E T”

are the direct and inverse iterates of fλ

DIRECT

{System {Xα ,ηαβ }Limit X−→ : Pump

πnl ,

π (m−k)

π (n−m)π (n), k ≤

m≤

n

Figure 1: Direct and Inverse limits (X−→,FT{Uκ ;ηκ}), (X←−, IT{πκ ;Uκ ;}) of a family of spaces {(Xκ ,Uκ)} with respect to a family

of continuous connecting maps oriented respectively along and in opposition to the directed set. In our usage, Xn consists of thedistincr, non-equivalent, fixed points of the nthiterate f (n) of the logistic map fλ = λx(1− x).

direct system {Xα ,ηαβ} generating equivalence classes

[xα ]∼−→={

xγ ∈ Xγ : ∃γ � β � α s.t.ηαγ(xα) = ηβγ(ηαβ (xα))≡ ηβγ(xβ )}

(1a)

is distinguished by the common successors

xν = ηµν(· · ·(ηβγ(ηαβ (xα ∈ Xα)))) ∈ Xν , ∀α � β � γ � ·· · � µ � ν ∈ D (1b)

If⊎

Xα is the disjoint union10 of the spaces, the quotient set⊎

Xα/∼−→ equipped with the largest final topology inducedby the quotient map Q :

⊎Xα →

⊎Xα/∼−→ is the direct limit of equivalence classes [xα ]

X−→=⊎κ

Xκ/∼−→ (2a)

of the direct system with ηκ : Xκ → X−→, the continuous restrictions of Q to Xκ such that V ⊆ X−→ is open if and only if(ηα)−(V )∈Uα for all α mapping each element of Xα to its equivalence class ηκ(xκ)∈ [xκ ]. Qualitatively, two elementsof a disjoint union are equivalent iff they eventually become equal in the direct system; an element of the union beingequivalent to all its images under the maps of the system.

The pair (X−→,ηκ) must be universal in the sense that if there exists any other such pair ( X←→,ζ κ) there is a uniquehomorphism ζ : X−→→ X←→ induced by {ζ κ} with the respectice sub-diagrams commuting for all α � β ∈ D such that

X−→=⋃κ

ηκ(Xκ) (2b)

the algebraic operation on X−→ being defined vis these maps in an obvious manner. Clearly, ηκ = ηλ ◦ηκλ .Example. 1. Let {Xi}i=1,2,··· be a nested increasing family of subspaces of a space X partially ordered by inclusion, withηm≤n the inclusion map. Then

X−→=∞⋃

i=1

Xi

is the prototype of a direct limit.2. The forward iterates η(k) = η(· · ·(η(η)))︸ ︷︷ ︸

k times

of a non-injective continuous map with increasing number of injective

branches on a common domain X uniquely expressed by its fixed points η(k)(x) = x, satisfy for k ≤ m≤ n

ηkn , η(n−k)

η(k) = η

(n−m)η(m−k)

η(k)︸ ︷︷ ︸

η(m)

= ηmn ◦ηkm : Xk→ Xn

10The disjoint union(⊎

Xα ,U ) = {⋃

α (α×Xα ) : U ∈U iffU ∩Xα ∈Uα}of topological spaces (Xα ,Uα ) with U open in the union iff U ∩Xα is open in Xα . The disjoint union is the final topology with respect to thefamily of canonical injections. If Xα = X for each α , the disjoint union is the cartesian product X×D.

5

qualifying thereby as connecting maps of a direct system.Let { fλ}λ∈[3,λ∗=3.5699456) on [0,1] be the family of logistic maps λx(1− x) indexed by the real parameter λ . Under the

equivalence relation ∼−→ of Eq. (1a), let

X1 = {Fixed points of fλ}

X2 ={

Fixed points of η12( fλ ) := f (2)λ

}X3 =

{Fixed points of η23( f (2)

λ) := f (3)

λ

}(3)

...

Xn ={

Fixed points of ηmn( f (m)λ

) := f (n)λ

}for some λ ∈ [3,λ∗ = 3.5699456), all (red) unstable fixed points { f ( j)

λ(x(i)) = x(i)} j>i of the forward images being

equivalent, see Fig. 5a, f (1)λ

(x(1)) = x(1) = 1− λ−1 defining the fixed point of f . In each case the blue stable pointsbecome (red) unstable as λ increases, and bifurcates into two stable additions. The union

X−→=∞⋃

k=1

ηk(Xk)

=∞⋃

k=1

[f (k)λ

]with ηk : Xk → X−→ mapping each element of Xk to its equivalence class [ f (k)

λ] consisting of the red unstable, and blue

singleton stable points without equivalent-partners ; alternatively ηk can be viewed to choose a representative from theequivalent elements [ f (k)

λ] that constitute Xk; hence X−→ comprises all distinct fixed points of the largest superset of {Xk}.

In real-life where increasing n in the periodic doubling sequence {2n}n∈Z+ leads to increasing λ , the emergence of anever-increasing number of (blue) nodes of unrestricted neg-entropic growth follows as a consequence. To moderate thissusceptibility of unbounded growth through a matching redistribution to homeostasis in the choice of a compatible λ ,the adversity of inverse limits is needed.INVERSE LIMIT. For spaces {(Xα ,πβα)}, let the backward contituous maps {πβα : Xβ → Xa}α�β∈D connecting thepresent to the past with (i) παα(x) = x ∀x∈ Xα , (ii) πγα = πβα ◦πγβ , ∀α � β � γ ∈D. Then the inverse system {Xβ ,πβα}over D — with the image of xβ ∈ Xβ under the connecting map πβα as a predecessor of xβ , and pα : ∏κ Xκ → Xα

projections of the Tychonoff space with coordinates xα = pα(x) — generates the inverse limit of {Xβ ,πβα}

X←−,{

x ∈∏κ

Xκ : ∃γ � β � α s.t.πγα(xγ) = πβα(πγβ (xγ))≡ xα

}(4a)

of smallest topology that makes each pα continuous as a subspace of ∏Xκ . Two points of X←− are considered identical iffthe continuous restrictions πα : X←−→ Xα of pα have their images coincident for all α . Qualitatively, x = (xκ) ∈ Xκ is inX←− iff its coordinates match in the sense of common predecessor

xα = πβα

(· · ·(πµλ

(πνµ (xν ∈ Xν)

)))∈ Xα , ∀α � β � ·· · � λ � µ � ν ∈ D (4b)

As in direct limits, the pair (X←−,πκ) must be universal in the sense that existence of any other pair ( X←→,ξ κ) implies the

existence of a unique homomorphism ξ : X←→,→ X←− induced by {ξ κ} with the respective sub-diagrams commuting forall α � β ∈ D. The sets (πα)−1(Uα), Uα ⊆ Xα open is a topological basis of

X←−=⋂κ

(πκ)−1(Xκ)

and a,b ∈ X←− are identical if and only if πα(a) = πα(b), ∀α .Example. 1. Let {Xi}i=1,2,··· be a nested decreasing family of subspaces of a space X partially ordered by inclusion, withπn≥m the inclusion map. Then

X←−=∞⋂

i=1

Xi

6

is the prototype of a inverse limit.2. On a common domain X , the inverse iterates η−(k) = η

−(η−(· · ·(η−)))︸ ︷︷ ︸, π(k)

k times

, π := η−, of the non-injective

continuous map η defined by ηη−η = η and η−ηη− = η−, with the inverses π of decreasing branches satisfying fork ≤ m≤ n

πnk , π(n−k)(η(n)) = π

(m−k)π(n−m)

η(n)︸ ︷︷ ︸

η(m)

= πmk ◦πnm : Xn→ Xk

With Xk the sets of Eq. (1a), X←− consists of the fixed points of f (k)λ

for some k, embedded in [0,1], each inverse iterationcoalescing two stable points of Xm into an unstable point, stable in Xm−1 as λ decreases. Together with the adversity ofdirect limit, inverse limits select a definite value of λ ∈ [3,λ∗) appropriate to the prevailing environment τ = 1−λ−1.

For a particular λ , the inverse X←− and direct X−→ limits acting in cooperative opposition to each other, represententropic disorder confronting exergic concentrative order leading to the dynamical homeostasis X←→. This is the essenceof entropy production in the universe at the expense of free-energy that in simple terms represents the opposition of acold stable system to the urge of a hot unstable constituent to stabilize at its expense. The entropic second law representsthe straightforward stipulation that a part of the useful exergy of an isolated system must necessarily be dispersed asentropic heat, entropy being a quantitative measure of the amount of thermal energy not available for useful work, of thetendency of all matter and energy in the universe to evolve toward a dead state of inert uniformity. In the absence of thedirect limit, however, the inverse lim←− would proceed to its logical destination X←− leading to the maximum-entropy frozencold death which translated to practical terms requires the whole system to acquire the degrowth properties of the infinitecold reservoir. Direct limits with their connecting opposing maps manifests through the forward direction of lim−→, whichacting on its own would likewise lead to the minimum entropy roasted “heat death” in X−→. In partnership with each other,X←→ shares properties of both with homeostasis representing a mutual resolution of the contestants.

One of the noteworthy features not immediately apparent is the increasing/decreasing values of λ of the forward/backwarditerates: each distinct Xn corresponds to a distinct λn, λm < λn, m < n see Fig. 7. Accordingly λ1 = 3.0000 < λ2 =3.2361 < λ4 = 3.4986 < λ8 < λ16 < · · · < λ∗ = 3.5699 generate {X2n}n=0,1,··· for the corresponding value of λ2n , andthe trade-off between the forward and backward iterates seeks a value of λ , and hence of τ = Tc/Th (Eq. 21a), the envi-ronment in which the economy-society operates, with a larger value of λ indicating increased development and growth.Having decided on τ , the homeostatic T for this λ corresponds to the multifunctionally converged limits of Fig. 10. Theforward and backward iterates of f collectively define graphical convergence of limitations, compromises and trade-offs,Fig. 2(ii).

2.2 Handshake of opposites

Figure 2 summarizes our current understanding of complex holism. The fundamental issue is the existence of a negativeworld W− ,multi(X)

W− , {w : {w}⊕{w}= /0, ∀w ∈W+}; (5a)

for every real world W+ , map(X) as the negative, or exclusion, set of W+. Here, the usual topological treatmentof pointwise convergence in function space is generalized to generate the boundary multiBdy(X) between map(X) andmulti(X) where map(X) and multi(X) are respectively proper functional and non-functional subsets of all correspon-dences Multi(X) on X

Multi(X) = map(X)⋃

multiBdy(X)⋃

multi(X) (5b)

This generalization defines neighbourhoods of f ∈map(X) as those functional relations g in Multi(X) whose images atany point x ∈ X lies not only arbitrarily close to f (x) but whose inverse images at y = f (x) contain points arbitrarilyclose to x: the graph of f lies not only close to f (x) at x, but must additionally be such that g−(y) has at least branchin U about x, with g constrained to cling to f as the number of points on its graph increases with convergence. Unlikefor simple pointwise convergence, no gaps in the graph of the limit is permitted not only on the domain of f but inits range too; this topological extension of the function space map(X) to Multi(X) is fundamental in our treatment thatallows non-functional limits as possibilities. Hence for all A ⊆W+ there exists a neg(ative) set A ⊆W− associated with(generated by) A satisfying A

⊕G=A−G and A

⊕A= /0. The pair (A,A) act to control and stabilize each other inducing

a state of dynamic homeostasis in W+ of limitations, compromises and tradeoffs that permits out-of-equilibrium complexcomposites of a system and its environment to coexist despite the privileged Second Law, the homeostasis of W+ and its

7

antithesis W− balancing each other, with W− being the gravitational source of all creativity in W+ that natively supportsonly consumptive dispersion.

.

TcTh qcQhT

q =( 1−ι

ι

)Q

W = (1− ι)Wrev = (1− ι)(

1− TcTh

)Qh

(i)≡ H (enthalpy)−A(exergy)

Q =(

TTh

)Qh

PE

T S (Profit) = ιWrev =Wrev (Value/Price)−W (Cost)

.

TTcDirect lim−→:

Explosive HEAT DEATH0

Limits to Growth

W−: FIRM, GENE

Implosive COLD DEATH

W+: HOUSEHOLD, ORGANISMInverse lim←−:Dispersion ConcentrationENTROPIC EQUITY EXERGIC GROWTH1

COMPLEX LIFE

E: Household Expense Th←−P: Firm Product

BOTH ADVERSARIES WIN, BOTH LOSE

Win-win transaction and handshakeSELF-ORGANIZATION Virial Engine EMERGENCE Virial Pump

Q: Demand, OfferNATURAL SELECTION: Choice

Symmetry, Entropy ↑

Function. Friction, Culture

iq: Supply, ConfirmationAsymmetry, Entropy ↓

Science, Technology, InnovationGenetic drift, Epigenetics

Glucagon SUPPLY Insulin DEMAND

ι(T ) =T −Tc

Th−T:

Fitness/Gini (1− ι)→

Tragedy of Commons

VARIATION: Genetic Mutation, Gene flowselection coefficient

(ii)

INSULIN AND GLUCAGON CONSTITUTE A� FEEDBACK THAT REGULATES HOMEOSTATIC STABILITY OF BLOOD GLUCOSE

Economics should be the study of the social relations and processes governing production, distribution and exchange of therequisites of life [Hodgson, 2005] on the push-pull boundary T by “taking the product to the customer” while “getting him to

come to you”, rather than the persuit of material wealth of unlimited wants by scarce means. The “productive base” of the pumpconfronts the “consumptive demand” of the engine [Dasgupta, 2007] ensuring the cooperative and sustainably enduring

dialectics encoded in ιq = (1− ι)Q.

Figure 2: A Blueprint for Complexity. Reduction of the dynamics of opposites to an equivalent Pump-Engine thermodynamicsystem; Wrev = ηEQh, W (T ) = ηQh = ηE/(1−ηE)Q = (Th/T )ηEQ, where ηE = 1− (Tc/Th), η = 1− (T/Th) are thermodynamicefficiencies of the respective engines. The cooperative confrontation of Q(T ), Qh−W (T ) = Qh− [1− ι(T )]Wrev = (T/Th)Qh andq(T ) = [(1− ι(T ))/ι(T )]Q, permits the interpretation of Q as “demand” that is met by the “supply” ιq in a bidirectional feedbackgive-and-take, sustained by each other in the context of the whole.

This W+-W− dualism is formalized in the Engine(W+)-Pump(W−) bidirectionality of Fig. 2 that is noteworthy forthe implied unconventionality of the

2.2.1 Virial theorem: decreasing entropy with increasing temperature

The unconventional concentrative growth in W+ — despite the entropic implication of the Second Law — is a conse-quence of gravitational attraction induced in W+ by the inverted causality of W− regulated by constructive emergenceas opposed to the destructive allocative dispersion of W+, that we understand to be the sole source of creativity in W+;gravitational concentration is at the heart of structure formation in the universe. The dynamics of gravitational attractionoperates through the average long-range attractive potential V ∼ −1/r and its virially induced average kinetic energyT ∼ 1/2r of the virial theorem 2T +V = 0 that applies to any system of particles with pair interactions when theparticle distribution does not vary with time. Thus even though the temperature of the compressed gas increases as rdecreases, the entropy instead of increasing11, actually decreases with r, the specific heat being negative so that en-ergy extraction leads to increased temperature. This unusual and contradictory behaviour arises from the momentum

11In a spring-loaded piston-cylinder device with a gas on the left L of the piston, removing the constrain causes the piston to compress the gasby volume V = Aδ to the left (i) decreasing position uncertainty of the gas molecules, and (ii) increasing momentum uncertainity and temperatureby conversion of spring potential energy V = kδ 2/2 to molecular kinetic energyT . With δ = L− x, the piston compression increasing to theleft, dV/dx ∝ −1, and dT /dx ∝ −kδ , where k > 0 is the spring constant. Hence dE /dx ∝ −(kδ + 1) < 0, and total uncertainty, entropy, andtemperature increases with compression.

8

uncertainty dT /dr = −1/2r2 < 0 under virial expansion increasing slower than the decrease in position uncertaintydV /dr = 1/r2 > 0 of virial contraction, for an overall decrease of energy E = −T uncertainty dE /dr = 1/2r2 > 0.With T ∼ T , V ∼−T , it follows from

T (r)∼ 1r

that the gas warms up as it collapses, the entropy actually decreasing with creative emergence of new structures andpatterns. This apparent violation of the Second Law by the virial pump is more than compensated by the increase inentropy of the virial engine despite its attendent decrease in temperature. Two immediate contradictory consequencesare the negativity of specific heat C = dE /dT ∼−1/2, and entropy S(r) =

´dE /T = lnr < 0 as r→ 0.

An engine E needs fuel to deliver; this is its “demand” in exchange for an “offer” of non-entropic, useful exergicwork. Complex systems achieve this by establishing an auto-catalytic positive feedback pump P that counters the sym-metrization of E though symmetry breaking inducement of structures, thereby realizing an induced homeostasis of theentropy and free energy adversaries, in the context of a given available enthalpy of maximum Carnot work Wrev. Formacroscopic processes, the entropy E-increase must eventually dominate its P-decrease of increasing exergy, simplybecause W+ is administered by the law of increasing entropy.

Figure 3 illustrates the spaces of multi-functions A = multi(X) ⊆Multi(X) and functions B = map(X) ⊆Multi(X),Eq. (5b). in the topology of pointwise biconvergence [Sengupta, 2003] of Multi(X). The adversity of these componentsof Multi induces a common boundary multiBdy(X) of the constant function/multifunction as indicated in the figure.Relative to the derived set, the subsets A, B can be classified into the three types

1. Selfish: Der(A)⊆ A. Pure individualism: a convergent sequence of multifunctions eventually in A, is a multifunc-tion. ι = 0: heat death.

2. Altruist: Der(A)⊆ B. A consists of isolated points only. Pure collectivism: a convergent sequence of multifunc-tions eventually in A is a function. Altruists engage in pro-social behaviour benefiting their partner at a cost tothemselves; individualistic self-seekers are entitled to no such luxury. ι = 1: cold death.

Between the two extremes of selfishness and altruism, lies the second law entropic reality of nature: 0 < ι < 1.

Cooperative: Der(A)Der(B)

} ⋂{A 66= /0B 66= /0

of handshake of opposites and homeostasis of creative destruction distin-

guished from (A, A) by the derived sets of A and B extending beyond BdyB(A), BdyA(B) to the respective sets. ForA = multi(X), B = map(X), Der(B) consists of functions that are limits of proper sequences of functions with BdyA(B)the one to many chain-dotted a ∈ multi(X) which although not a function is arbitrarily close to being one; Der(A) aremultifunctions to which proper sequence of multifunctions converge with the function b ∈ BdyB(A) arbitrarily close tosome multifunction obtained by unfolding the overlapping arms of the one-to-two multi. Note that a, b “belong” to bothA and B being arbitrarily close to either; the tie “payoff” T then is an eminently appropriate attribute of the simultaneousappearance of a boundary as in 11.

In this sense the solutionx = f−(y), f : (X ,U )→ (Y,V ) (6)

of the ill-posed problem f (x) = y for f− f (U ∈ U ) := sat(U) the saturation of U and f f−(V ∈ V ) = f (X)∩V :=comp(V ) the component of V on the range of f — reflecting the ill-posedness of Eq. (6) neither being identities ontheir respective spaces — as a bidirectional dynamical system with y determining x which in turn defines y, captures the� homeostasy of the nonlinear evolution. With both x ∈ X and y ∈ Y unknown, the operator f initiates a participatoryplatform between X and Y prevailing on the adversity to a creatively-destructive adaptive trade-off between the inversex = f−(y) compatible with y ∈ Y that in turn is compatible with the x ∈ X direct y = f (x) arrow for a handshakehomeostasis. The tools of initial and final topologies are specifically suited for situations like this, the coarsest initialtopology on the domain and finest final topology on the range defining pre-image and image continuity of f , AppendixA.1.

While growth is essential for development, unrestrained growth of “intrinsic vulnerability to cancer must be counter-intuitive to anyone who views our bodies as the product of purposeful design or engineering. Darwinian medicineprovides the opposite view: the blind process through which we have emerged carries with it inevitable limitations,compromises and tradeoffs. The reality is that for accidental or biologically sound adaptive reasons, we have historicallyprogrammed falliability. Covert tumours arise constantly, reflecting our intrinsic vulnerability, with mutant clones with

9

Selfish(0)DILEMMA

PRISONER

Altr

uist

(1)

A♀ A♀

A♀

B♂

Selfi

sh(0

)

B♂ B♂

L0

L0 W0

C1 T1

= Bdy(B)

b ∈ Der(B)/BdyB(A)

C < L < T < W

B♂

A♀

Bdy(A) = BdyB(A)∪BdyA(B)

PAYOFF/UTILITY

A(♀≡W−);

mul

ti(X)

B(♂≡W+); map(X)

a ∈ Der(A)/BdyA(B)

Coo

pera

tive

Multi(X) = map(X)⋃

multiBdy(X)⋃

multi(X)

A♀

BdyB(A)

Der(A)

BdyA(B)

Der(B)

A = multi(X)

b ∈map(X)

a∈

mul

ti)X)

B = map(X)

a

bB♂

C1

T1

Altruist(1)

W0

.Der(A) = {x ∈ X : (∀N ∈ Nx)(N∩ (A− x) 6= /0)}

= {x ∈ X : ((∃asequenceζ inA− x)(ζ → x))}Bdy(A) = {x ∈ X : (∀N ∈ Nx)((N∩A 6= /0)∧ (N∩ (X−A) 6= /0))}

Figure 3: Classification of A,B ⊆Multi(X). The derived set Der(A) of A may be wholly in B (altruist) or wholly in itself (selfish,closed). The payoff L < T indicates that mutual cooperation 11 is superior to mutual defection 00, although T < W and C < Lstipulate that 00 is the only Nash equilibrium from which each can only lose by unilaterally deviating. The dilemma: irrational 11at the individual level yields a better outcome than rational defection; each player pursuing his own interest leads both to be worseoff, the choice to cooperate at the individual level being irrational from a self-interested point of view. In a 01 pair the selfish partnerdoes better — he benefits from his partner’s altruism without incurring any cost. However 11 is better than other possibilities: theboundaryless 00, for example, lacks the cooperative possibilities of the other three.. Real-life examples of game theory, the mathematical study of strategic decision making of conflict and cooperation betweenintelligent and rational decision-makers, exemplified for example in the inherent dilemmas of tragedy of commons, climate change,and arms race. In the former cooperation emerges spontaneously, groups communicate and manage the commons among themselvesfor their mutual benefit enforcing social norms to preserve the resource and achieve the maximum good for the group, in the lastalthough the ’best’ overall outcome is for both sides to disarm, the rational course for both is to arm, and in the case of climatechange while all realize the benefits of a stable climate, any individual country is often hesitant to curb CO2 emissions. Ratherthan a “dilemma”, a more pragmatic view that suggests itself is that purely selfish individualism is not Nature’s preferred mode ofexpression as collective reality is scarcely an aggregate of individualism.

malignant potential. Clinical cancer rates would be worse were it not for the fact that cancer clone emergence is relativelyinefficient evolutionary process, subject to many constraints or bottlenecks. Perhaps only one percent of the covert pre-malignant clone ever acquire the necessary additional or complimentary mutations required for graduation” [Greaves,2007]. Needless to say, the biologically sound natural entropic adversity of the self-organizing engine keeps this exergiccancerous emergence caused by unrestrained P in holistic check. Nevertheless, with the passage of time the cosmicdeterminism of second law asserts itself, the inhibiting influence of P diminishes and eventually stops. Coupled withpossible lifestyle extravaganza, this may leave holistic organisms like homo sapiens with unpaired excess of accumulatedW− emergence of broken symmetry, no longer amenable to the failed entropic self-organization of W+ — leading toa genetic predisposition and intrinsic vulnerability to malignancy. Benign tumor growth appears as a natural corollary,subvertible under normal circumstances through the much more effortless entropic dispersive failure of normal organs.

10

2.2.2 Competitive-cooperation homeostasis

Let η and ζ be the efficiency and coefficient of performance (COP) of a reversible engine and a reversible pump operatingbetween temperatures (Th,T ) and (T,Tc) respectively, for an unknown (equilibrium) temperature T . Define for θ = T/Th,τ = Tc/Th [Sengupta, 2010a],

α(T ), ηζ =

(Th−T

Th

)(T

T −Tc

)=

(qQ

)θ =

(1− ι

ι

)θ =

θ(1−θ)

θ − τ(7a)

ι =T −Tc

Th−Tc=

θ − τ

1− τ(7b)

with the revealing insight that these purely thermodynamic quantities interact in a dynamic logistic fashion

ια =θ(1−θ)

1− τ(7c)

for the dimensionless homeostatic temperature θ . Then

θ±(α) =12

[1−α±

√(1−α)2 +4ατ

](8a)

=

{((1−α),0) = (0,0)α=1, τ = 0(1,−α) = (1,1)α=−1 τ = 1

(8b)

for an adaptation α . The homeostatic balancing condition

ι(T ) = cα(T ), c ∈ R+ (9)

defines the most appropriate equilibrium complexity conditions

θc± =c+(2− c)τ± (1− τ)

√c(c+4τ)

2(1+ c(1− τ))(10a)

ιc± =c(1−2τ)±

√c(c+4τ)

2(1+ c(1− τ))(10b)

with an inverse

c =ι2

τ− (1− τ)ι2 +(1−2τ)ι(10c)

In this paper the analysis centers mostly around c = 1 that appears to be of special relevance to biological systems, but wealso offer some insight on the value of c > 1 necessary for sustainable economic and social systems from experimentalvalue of World Bank ι and theoretical sustainable τ .

For c = 1 then,

θ± =1+ τ± (1− τ)

√1+4τ

2(2− τ)=

{(43 ,±∞

)τ = 2∓

(∞,−∞) τ → ∞(10d)

ι± =1−2τ±

√1+4τ

2(2− τ)=

(1,1) τ →−∞(2

3 ,∓∞)

τ = 2∓(1,1) τ → ∞

(10e)

and as Fig. 4a demonstrates12

θ ∈ (0.5τ=0,1τ=1)ι ∈ (0.5τ=0,0.6180τ=1)

}⇒ Collectice Equity ⊕ Individualistic Growth (11)

12Interestingly, (ι+)τ=1 the conjugate golden ratio Φ = 0.61803398875 root of Φ2 +Φ−1 = 0 bears with the golden ratio ϕ = 1.61803398875of ϕ2−ϕ−1 = 0 the relation Φ = ϕ−1−1 = ϕ−1.

11

Biologically, irreversibility ι corresponds to the selection coefficient of the fraction of a transformed resource (differencein temperature, specific volume) in terms of the available quantity: ι represents entropic dispersal and 1− ι exergicgrowth of life’s cooperative antagonism which accordingly represents the increase in fitness. The quasi-static value ι = 0at no loss signifies the maximum theoretical capacity/potential of the organism; of this, life’s inevitable wear-and-tear instaying alive entails the cost of a resulting fitness. Complexity is a holistic expression of individual selfish concentrationand collective altruist dispersion, recall our earlier altruist, cooperative, selfish classification. It is significant that theW+-entropic irreversibility of Eq. (11) exceeds 50% by definition but is not so high as to render the neg-entropic growthcontribution from W− irrelevant. Given a (Tc,Th) i.e. the environment, the holistic homeostasis (T+, ι+) of Eqs. (10d, b)defines complex holism.

2.3 Two-phase synthesis of individualism and cooperatism

Combining Eqs. (10d, b) with the inverse τ = ι(2ι−1)/(1− ι)2 leads to the revealing

θ± = ι±+ τ(1− ι±) (12a)

that will be recognized as the fundamentalvvg

= x+v f

vg(1− x) (12b)

equation in the thermodynamics of two-phase mixtures, with v, v f , vg the specific volumes of the mixture of qualityx := (v− v f )/(vg− v f ), and of the fluid and vapour states respectively. What Eqs. (12a,b), represented in Fig. 4a, haveachieved beyond this is to obtain explicit expressions for the specific volume and quality that identifies two types ofregions

(a) (I) T := T+ ∈ (Tc,Th) and (IV) T := T− ∈ (0,Tc), both characterized by ια > 0 together constitute the realfunctional world W+. Denote (IV) by w− =−τ/(1−τ) of induced negative irreversibility −Tc/(Th−Tc), the (negative)COP of a reversible refrigerator operating in (Tc,Th); hence (IV) can be viewed as a repository of fixed assests ρ− ofnature and public assests ι− of the state, available to W+ through (I) of productive “labour” ρ of reversibility 1− ι , in asecond-law world of entropic dispersal ι .

Figure 4a verifies that (i) ρ + ι −w− = (1− τ)−1 = Qh/Wrev, (ii) |w−|Wrev = τQh is the fraction of Qh usefullyaccessible to (I) through (IV), and (iii) (ρ + |w−|)Wrev = [(1− ι)+τι ]Qh. Moreover, (iv) W = ρWrev and (v) T S = ιWrev,where Wrev = ηQh, η = 1− τ the thermodynamic efficiency of a reversible engine between (Tc,Th), are the (exergic)labour and (entropic) profit outputs of W+ (I). The composite irreveversibility curve ι± of Fig. 4b(iii) demonstrates howthe real world W+ is born with its two components branching off at the negative Tc of τ =−0.25 from the complex rootsof τ <−0.25 chatacteristic of W− in (III).

(b) (II) T > Th, and (III) T < 0 of ια < 0 define the negative multifunctional world W−. T and ι can be multi-valuedor complex valued.

Region (I) directly linked to (II) through T+ and ι+ is the active complex world we inhabit; region (IV) linked to (III)via T− and ι− is a passive component of W+, not immediately accessible from (I) because of its negative irreversibiltythat possibly represents, due to its refrigerator characteristic, natural resources like climate, minerals, land, and water —the so-called “free goods” of economics — over which (I) has no direct authority except through the holistic mediationof W−. (II) and (IV) cooperate to generate the two-phase individual-collective integration (I).

For ι = α , the relative magnitudes of the components of (I) and (IV) take definite values, that however can be upsetby infringement of the fragility of the induced homeostasis. Under such conditions of decoupling of ι and α , the relativeratios can show non-holistic behaviour arising from changes in the environment Tc leading to modfications of the regions.

The World Bank in its search [World Bank, 2014] for a more realistic indicator of wealth than the “market” based

GDP =(Gross value of output+Taxes

)−(Cost of material, supplies and services to

produce final goods or services+Subsidies) (13)

proposes the multidimensional comprehensive wealth

CW = Produced capital (machinery, structures, equipment) + Natural capital (agriculturalland, protected areas, forests, minerals, energy) + Intangible capital (labour, human,

social, institutional, governance, health care, education)(14)

as a composite “present value of future consumption” measure of total national wealth, Fig. 4a suggesting the correspon-dences

12

−1.5

θ+

θ−

4

1

2.5

θ , Eq. (8a)

−4

W+(IV), ια > 0

W+(I), ια > 0

(a)

0

3

Th = 480

Tc = 300

1

W−(II), ια < 0

α

W−(III), ια < 0 0

4↑ λ

3.57

(i)

.

4

1

4

W+(IV), ια > 0

−4

ι , Eq. (7b)

w− =− τ

1− τ

ιWrev

W+(I), ια > 0

ι−

ι+

ι = αcomplex holism

0

ι+ι−

Qh

α

W−(III), ια < 0

ι−

W−(II), ια < 0

ρ = 1− ι ⇒Wι=

cα, c=

1

(b)T = 0, ι =−1.67

ρ− =− θ−1− τ

Eq. (10d)

T = Tc = 300

T = Th = 480

(ii)Bio-Economic correspondence of the four Regions (Table 1b/Fig. 11): (I): Mitosis (Life)/Household,

(II): Meiosis (Gonad: Gamete)/Factor Market, (III): Fertilization (Fallopian tube: Zygote)/Firm,(IV): Implantation (Uterus)/Product Market

Figure 4a: Plot of Eqs. (8a, 7b) demarcates the four regions that define the universe. Decomposition of the real world W+ inaccordance with the Second Law T S = Wrev−W suggested as in (ii), is composed of two disjoint regions: the complex holisticworld of primary production and consumption (I) defined by the + solution supported and dependent on (IV) from the − solutionof the tools of gravitational growth in W−.

SUMMARY ι± =1−2τ±

√1+4τ

4−2τ

τ→∞= 1 [Eq. 10e]. τ ,

Tc

Th=

ι(2ι−1)(1− ι)2

1. Wrev = ηQh, η = 1− τ: Efficiency of areversible engine between (Tc,Th).

.

(ι− ι−)/Qh

λ = (1− τ)−1, Eq. (20c)

ι− ι−ρ−ρ−

λ∗ = 3.57

0.330.17−0.25

ι/(1− ι)

θ+

ι+

τθ−

0.621.00

1.62

−1.62

−1.00

1

−2

4

0.5

(I)(IV)(III) (II)0.67 0.720

λ = 3.00

ρ/Qh

ρ−/Qhι±

θ±

(iii)

ι−

2. (i) −w−Wrev = τQh: Fraction of naturalresources available to (I) through (IV).

(ii) ρWrev ≡ (1− ι)Wrev =W . Productiveoutput in (I)

(iii) ιWrev = T S =Wrev−W . Entropicallocation in (I)

3. (ρ−w−)Wrev = [(1− ι)+ τι ]Qh

4. (ι−w−)Wrev = [ι + τ(1− ι)]Qh

5. (ρ + ι−w−)Wrev = Qh, (ρ + ι)Wrev =Wrev

6. −w− =τ

1− τ, ρ + ι−w− =

11− τ

(iv)

Qh: Comprehensive wealth, ρ: Produced capital, |ρ−| : Natural capital, ι + |ι−| : Intangiblelabour (ι), human, institutional, social capital (|ι−|). Wrev: enthalpic capital, w−: neg-

enthalpic capital,Intangiblecapital

Producedcapital+Naturalcapital=

ι + |ι−|ρ + |ρ−|

=(1− τ)

√1+4τ

2− τ− (1− τ)√

1+4τ

Figure 4b: The particular values of τ in (iii) result from the dynamic-thermodynamic synthesis introduced in Sec. 7.2, Fig.9(iv), which identifies the Wrev-normalized Qh = (1− τ)−1 as the logistic parameter λ . Significantly, although the ratio of hu-man to produced capital ι/ρ monotonically increases with τ always exceeding 1, taken in conjunction with the alternate measureintangible capital/(produced+ natural) capital (ι − ι−)/(ρ −ρ−) that initially increases with τ decreasing thereafter, constitutes awarming against indiscrimanate exploitation of nature in the confrontation of production and utilization.

Comprehensive wealth , Qh, Exergic produced capital , ρ ,Natural capital , |ρ−|, Entropic intangible capital , ι + |ι−|,

permitting the thermodynamic decomposition

CW = (Gibbs) Enthalpic capital Wrev + Neg(ative) Enthalpic capital |w−|

13

The entropic contribution of labour ι of (I) together with the neg-entropic social and institutional share ι− from (IV) isresponsible for holistic self-organization of the emerged wealth induced by ρ and ρ−. The fraction of ι not contributingto human capital comprises profit, a necessary component of the antagonism of competitive-cooperation. It is significantthat the relative magnitudes of each of the components of total wealth Qh are completely determined by the environmentparameter τ , the holistic � interaction integrating the different components into an all-inclusive global totality, future“well-being” being linked to the present and past through changes in τ , restricted by the bounds of Fig. 9(iv). Sustain-ability, we believe, is primarily a manifestation of the multi-valued self-organization of emergent structures from intensenon-linear interactions of multiple adversarial partners, endeavouring a homeostatic trade-off mutually beneficial andacceptable to all.

As Fig. 4b(iii) indicates, although the entropic fraction relative to neg-entropic growth ι/ρ increases as Tc→ Th, theoverwhelming influence of the accompanying increase of |w−| and its components masks this increase in (ι + |ι−|)/(ρ +|ρ−|), tilting the balance in favour of ρ . The value τ = 0.6392 at which produced and natural wealths collectively surpassthe share of intrinsic wealth heralds the onset of sustainability in 0.6777≤ τ ≤ 0.7199 the interaction of the subregions ofW+, with (I) representing the thermodynamic system and (IV) its surrounding, generating the homeostasis of competitivecooperation.

The correspondence between dynamics of the engine-pump system and the logistic map λx(1− x), with the com-petitive forward-direct iterates f (i) corresponding to the “pump” W− and the cooperative, backward-inverse iteratesf−(i) representing the “engine” W+ constitutes the basis of our analysis. The two-phase complex region (I) λ ∈ (3,λ∗),T ∈ (Tc,Th), ι ∈ (0,1) is the outward manifestation of the tension between (I), (IV), ια > 0, on the one hand and (II),(III), ια < 0, on the other: at the two extremes Tc = 0 and Tc = Th the two worlds merge at α = ±1 bifurcating asindividual components in 0 < Tc < Th.

2.4 Mitosis: Life (I)

The labeling of the interdependent, interacting, stable points in Fig. 5a follows the following convention. The interval[0,1] is divided into two parts at 1/2 with “0” corresponding to female ♀(↓) and “1” the male ♂(↑); the rationale inassigning ♀ to W− and ♂ to W+ being that emergence of new structures is founded in ♀ in cooperative-adversity withself-organization of ♂ through genetic variation, sexual reshuffling and natural selection in the case of biological life,and consumer culture selection and technological innovation for economy-society. At any stage of the iterative hierarchyof the open unstable points, the filled stable points are labeled left to right along the positively sloped female “supply”curve supplemented by the negative slope of male “demand”. The dispersive second-law W+-engine operates as longas its demand for evolutionary fuel is met by the induced concentrative anti-second law W−-pump supply of requiredvariation for selection to work on, in a causal� anticausal feedback loop.

Hence the symbolic representation, in a notation of homologous bonds13 of forward h1 7→ h2 arrow complementedby a backward loop-arrow h2 to h3, h2# h3, takes the form

N = 1 (2− cycle) 0 7→ 1# 0 (15a)

N = 2 (4− cycle) 00 7→ 10# 01 7→ 11# 00 (Fig. 5a(ii), Fig. 13(ii)). (15b)

N = 4 (16− cycle) 0000 7→ 1000# 0111 7→ 1100# 0011 7→ 1011# 0100 7→ 1110# 0001 7→1001# 0110 7→ 1101# 0010 7→ 1010# 0101 7→ 1111# 0000 (Fig. 13(iii)) (15c)

The homologous units correspond to respective female-male contributions; thus 01 7→ 11 and 0000 7→ 1000, 0010 7→ 1010are examples of homologous couplings, while 00 ◦ 01, 1010 ◦ 1011 illustrate sisters. The N = 1,2,3 cycles of Fig. 5arepresent stable states; segregation of homologues corresponding to sex, meiosis, unstable gametes, and progeny zygotesis considered in Sec. 2.5. Observe that the homologous components ♀,♂ lie on either side of the fixed point xfp = 1−λ−1

that yield these components through bifurcation, and because of the � feedback at every stage of the process, genesreplicate in the common background of the other genes and their interactions, not in isolation. “However independent

13Homologous chromosomes are chromosome pairs carrying the same type of information with genes for the same characteristics at corre-sponding loci, one of the pair being inherited from the organism’s mother the other from the organism’s father — in diploid organisms the genomeis composed of homologous chromosomes involved in meiosis when they cross over. Homologous chromosomes are similar but not identical.Each carries the same genes in the same order, but the alleles for each trait may not be the same. In garden peas, for example, the gene for podcolour on the maternal chromosome might be the yellow allele while the gene on the paternal chromosome is the green allele.

14

Unstable FP x(1) of f (1),(2)

0.3 0.5 0.9

23♂(1)

10

1

0.5

0

(i) 2-cycle: λ2 = 3.2361Iterations: 1−2,101−102

1110 1

1

0.5

4 stable FPs x(4)00,01,10,11 of f (4)Iterations 1−4,101−104(ii) 22 cycle: λ4 = 3.4986

00

01

10

1

0� 1

0.5

0.5

f12

0.5

f13

f15f37

f48

f24

f26

0.9

0.3

10.50

(iiia) 23 cycle: λ8 = 3.5546Iterations: 1−8,101−108

23♀(0)

λ2→ λ4

10 ◦ 11

00 7→ 10 01 7→ 11

DIPLOID CELL

chromosomes46 homologous

chromosomes

Replicated 92

00 ◦ 01

Sisters assortindependently

Sister chromatids

0 7→ 1

Dominant Female ♀(↓)recessive male ♂(↑)

111

2 stable FPs x(2)0,1 of f (2)

Unstable FPs x(1),x(2)0,1 of f (1),(2),(4)

Homologues are denoted by h1 7→ h2, sisters by s1 ◦ s2

CHROMOSOME SHAPE S : Smooth R(0) wrinkled r(1) alleles

100

101

010

(iiib) 8 stable FPs x(8)i jk of f (8)i, j,k = 0/1

Unstable FPs x(1), x(2)i , x(4)i jof f (1),(2),(4),(8)

000

011

001

110

In (iv)

{Homologues 000 7→ 100, 001 7→ 101, 010 7→ 111, 011 7→ 110Sisters 000◦001, 010◦011, 100◦101, 110◦111

Figure 5a: Logistics of mitosis. The effective nonlinearity 0 ≤ χ ≤ 1 of the logistic nonlinear qubit fλ (x) = λx(1− x) in therepresentation fλ (x) = x1−χ increases with λ , as the system becomes more holistic with a larger number of interacting parts ofunstable fixed points shown red, the blue stable filled points being the interacting, interdependent, components of the evolvedpattern. The resulting green holistic patterns are entangled manifestations of these observables, none of which can be independentlymanipulated outside the cooperative whole. Cooperation of the direct iterates f (i)

λ(x) of individualism and the inverse iterates f−(i)

λ(x)

of collectivism leads to homeostasis of the graphically converged multifunctions of dynamic equilibrium. xfp = (λ − 1)/λ is thefixed point of fλ .

and free genes may be in their journey through generations, they are very much not free and independent agents in theircontrol of embrionic development. They cooperate and interact in inextricably complex ways, both with each other, andwith their external environment. · · · The whole set of genes in a body constitutes a kind of genetic climate or background,modifying and influencing the effects of any particular gene” [Dawkins, 2006].

The transactional interpretation embodies — through the “offer” and “confirmation” waves handshaking to com-plete an explicitly nonlocal “transaction” — the philosophy of the Pump-Engine dualism. In this necessary antagonismbetween “capital” and “culture” representing bottom-up individualistic competition, entropy decreasing order and con-centrative emergence, and top-down collective cooperation, entropy increasing disorder, and dispersive self-organization,complex holism emerges as a dynamical homeostasis of the win-win game in which neither adversary wins and neitherloses.

2.5 Meiosis: The Negative World (II)

In this Section we fill in the gaps in the Female-Male rivalrous partnership responsible for the cooperative adversityof holism. The bottom-up synthesis of characteristics of the whole that cannot be accounted for by the parts does notnegate the top-down analysis of components which behave differently when incorporated into the whole than it does

15

in isolation suggesting a different process operating at a higher level, beyond that of reductionism — this is holism.Among the most remarkable features of the appearance of higher forms of life in W+ involving sexual reproduction isthe incredible multi-valued self-organization of emergent structures appearing from the innocuous fertilized egg, withoutany “intelligent design”, except for residence in the female uterus: although the zygote can be fertilized outside the bodyin a “test-tube”, it is constrained to be transferred back to the uterus to induce successful pregnancy. This generationof the order of life assumes especial significance in our setting because order in the entropic W+ occurs only throughgravitational coalescence originating in W− , through the intermediary of an induced virial pump. The female uterusassumes a significant character in biological order in W+ — it is among the most definitive expressions of W− in W+.

0

00 01 10 11

23 pairs ofhomologous

chromosomes

MEIOSIS I

homologoes segregate

Alleles on sistersassort independently

(1)

(3)(2)

HAPLOID GAMETES

(5)

Replicated 92

0 7→ 1

chromosomes

MEIOSIS II

Alleles for genes on

(4)

1

1

(ii) 5-cycle; λ5 = 3.7382

1

10

(iv) 9-cycle; λ9 = 3.6872

00

01

1011

0

1

1

(i) 3-cycle; λ3 = 3.8284

0 1

1

(iii) 7-cycle; λ7 = 3.7016

chaisma

0

1

⇒ Genetic diversity

Chaisma, site forhomologous crossover

λ3→ λ5

DIPLOID

Figure 5b: Logistics of meiosis. This complement of Fig. 5a for cycles of the type 2N +1, appears in the chaotic region λ∗ < λ <λ3 = 1+

√8, for odd 2N + 1 cycles. Odd cycles are especially significant as the 3- and 5- cycles correspond to the generation of

the haploid gametes. Left to right 00, 01, 10, 11 are the gametes produced in the 5-cycle of (ii), see Fig. 13(ii) on the union ofheterozygous smooth Rr parents.

Period doubling 2N , N = 1,2, · · · , bifurcations of Fig. 5a introduced stable, self organizing, emergent, diploid homol-ogous states of ♀−♂ origin. Fig. 5b its meiotic counterpart, illustrates the formation of gametes in self-organization ofnatural evolution. The 3, 5, 9, · · · odd cycles differ from 2, 4, 8, · · · even cycles in having the homologous combinationsseparated by the chiasma “fulcrum” leading to modification of Eqs. (15a, b) in the inception of gametes 00, 01, 10,11; the symbolic representations of Fig. 5b defines the formation of the unstable gametes whereas the units of Fig. 5arepresent subsequent evolved complex organisms. This shuffling of the genetic deck is responsible for daughters that aredistinct from each other as also from the parents.

The meiotic cycles f (i) : i = 2N + 1 (Fig. 5b) for λ > λ∗ = 3.5699457 in the fully chaotic region depends on λ ;observe in comparison, that the 2N cycles of Fig. 5a are all in the complex-holistic region 3 ≤ λ ≤ λ∗. Hence the timeevolution of a natural system is decomposable to the interactive dialogue between two disjoint domains, the real-worldmanifestation (IV) λ ∈ (1,3) of W− (III) in rivalrous-partnership with the chaotic region (II) W−, λ ∈ (λ∗,4). Nature’slegacy ρ− in W+ (IV) is utilized by the “labour” ι of W+ (I) derived from (II), to generate the complexity of “life”through holistic entropic allocation ι of W+ (I), Fig. 4a. This supply of individualistic capital “gravity” of W− is thelogical corollary of the dispersive entropic arrow of the negative world [Sengupta, 2010a] as experienced in W+.

The value λ∗ of λ is of decisive significance. As observed in [Sengupta, 2006], numerical results suggest that

limN→∞ χN3≤λ→λ∗−→ 1 at λ∗ = 3.5699456. Since χ = 0 gives the simplest linear relation in the effective power law x1−χ ,

16

where

χ = 1− ln〈 f (x)〉ln〈x〉

, with

〈x〉= 2N λ→λ∗−→ ∞ and

〈 f (x)〉= 2 f1 +N

∑j=1

2 j−1

∑i=1

fi,i+2 j−1 , N = 1,2,3, · · ·

= {[(2 f1 + f12)+ f13 + f24]+ f15 + f26 + f37 + f48}

provides a measure of complexity, the value χ = 1 indicating largest non-linearly emergent complexity so that the logisticinteraction is maximally complex at the transition to the fully chaotic region. It is only in (I), 3 < λ < λ∗ that a globalsynthesis of stability inspired self-organization and instability driven emergence lead to the appearance of complexstructures.

Sarkovskii ordering of positive integers Evolutionary implication

3≺ 5≺ ·· · ≺ (2n+1)20 ≺ ·· ·(II): MEIOSIS, λ > λ∗W−: λ ∈ (λ∗,4), λ2n+1→ λ∗+Gonads: Ovary, Testicle, GameteCycles ≥ 7 not of type 2n are unstable

3 ·2≺ 5 ·2≺ ·· · ≺ (2n+1) ·21 ≺ ·· ·...

3 ·2m ≺ 5 ·2m ≺ ·· · ≺ (2n+1) ·2m ≺ ·· ·(Competition)

... λ = λ∗

(I): MITOSIS

· · · ≺ 2N ≺ ·· · ≺ 23 ≺ 22 ≺ 2≺ W+: λ ∈ (3,λ∗), λ2n → λ∗−(Adaptation) Limit cycles, self-organization,

emergence. Life(III): FERTILIZATION W−: λ ∈ (0,1)Fallopian tube: Gamete→ Zygote

≺ 1 (IV): IMPLANTATION W+: λ ∈ (1,3)(Cooperation) Zygote travels up fallopian tube,

enbeds in uterus. Picks a λ ∈ (3,λ∗)Emergence, self-organization, birth

Table 1a: Sarkovskii order of the natural numbers — if f : I → R is a continuous function on an interval with a n-periodic pointf n(x) = x, then f has a m-periodic point for every m succeeding n — and meiosis-mitosis. The period doubling limN→∞ 2N cyclesconverge at the chaotic limit λ = λ∗ = 3.5699456 from below as the limn,m→∞(2n+ 1)2m cycles do from above. Adaptation is a2-phase mixture of Competition and Cooperation, Fig. 10.

In the fully chaotic region λ > λ∗ where emergence persists for all times with no self-organization, the systemabruptly transforms to effective linear simplicity on crossing the chaotic edge. This emergent but non-organizing region(II) competes cooperatively with (IV), λ ∈ (1,3) where irreversibility generates self-organizing useful changes in thesystem in order to attain the levels of complexity needed in the evolution. While eventual evolutionary homeostasyappears only in (I), λ ∈ (3,λ∗), the effective linear simplicity of λ > λ∗ conceals the resulting self-organizing thrust ofthe higher periodic windows in this region, with the smallest period 3 appearing at λ = 1+

√8 = 3.828427.

By the Sarkovskii ordering of natural numbers, there is embedded in the fully chaotic region a backward arrowthat induces connectivity to lower periodic stability eventually terminating in the doubling sequence in 3 ≤ λ ≤ λ∗.According to this Theorem [Sharkovskii, 1964], if f : R→ R is a continuous function with a n-periodic point, and ifn≺ m in the Sharkovskii order of positive integers (Table 1a), then f also has a m periodic point. Sarkovskii order startswith the odd number 3 in increasing order, then 2 times the odds, 4 times the odds, and ends with the powers of 2 indecreasing order with 1 the largest, every positive integer appearing only once in the list. Sarkovskii’s theorem does notinsist on the stability of these cycles, only their existence. Hence there is embedded in the chaotic region a backwardarrow that induces chaotic tunnelling to lower periodic stability, eventually terminating with the doubling sequence in

17

3≤ λ < λ∗; this reciprocal connectivity between order and disorder induces subsequent appearance of life in W+ — thehomeostasis is a consequence of the cooperation between the backward arrow of increasing inverse iterates f−(i) dictatedby the second law of increasing entropy and symmetry in W+ and the forward arrow f (i) of increasing direct iterates f (i)

dictated by the reciprocal law of decreasing entropy and symmetry.

(IV) Implant (Uterus) MITOSIS (Life) Generation (t +1)

Generation (t) Emergence Self-(I)Diploid FETUS organization

(III) ZYGOTE Viability−−−−−→

ADULTFertilization↑ Sex

(Fallopian tube)

NATURAL

SELECTION(II) (t)

Haploid ←−−−−−−Fecundity Parents

GAMETE MEIOSIS (Gonads)

Table 1b: Gametic life-cycle of organisms. The basic characteristic that distinguishes meiosis from mitosis is the cross-over ofhomologous chromosomes resulting in meiotic production of gamete sperm and egg cells in the gonads. The cycle can be broadlysequenced into four stages as shown.

The basic property distinguishing meiosis from mitosis is the crossover of homologous chromosomes in the formerresulting in the production of sperm and egg in the male and female gonads. The gametic life cycle of organisms in Table1b can be summarized in four steps following the scheme of Fig. 4a

MITOSIS, Life (I): Emergence of new structures. The emerged structures undergo extensive self organizationfollowing prolonged mitosis, leading to the complexity of adult human existence.

MEIOSIS, Gametes (II): Sperm and egg haploids form in the male and female gonads. A diploid somatic cellreplicates, undergoes cross-over and segregation of the homologous and sister units in sequence to generate the haploidgametes. The sequence of division is important as mitosis is the segregation replicated sister units with homologousbonds in tact, to form two diploid cells.

FERTILIZATION, Gametes → Zygotes (III): In the female fallopian tube the male and female haploid gametesfuse to form diploid zygote.

IMPLANTATION, Embedding of zygote in uterus (IV). The eggs are born to be fertilized which the sperms arehunting for — this is the natural outcome of the coexistence of the predator-prey relationship following the second law.

3 The Bottomline: Central Dogma. Systems Biology, Limit Cycles, Periodic Points.

DNA contains the codes for manufacturing various proteins. According to the central dogma of molecular biology, theone-way flow of information DNA→ RNA→ Protein is the basis of all life: “once information has passed into protein,it cannot get out again” [Crick, 1970], back to the nucleic acid. The 3 major classes of biopolymers — DNA, RNA andprotein — allow the 9 possible reductionist linear information transfers of Table 2: normal general transfers 2� that canoccur in all cells, restricted special transfers 1 do not occur in most cells but may occur in special circumstances as invirus-infected cells and in the laboratory, and forbidden unknown transfers 4 [Crick, 1970].

The DNA → RNA → Phenotype reductionism suffers the same individualistic limitations considered earlier: theentropy decreasing free-energy utilization of genetic information leading to the forward DNA→ RNA→ Protein pro-cess does not forbid, it infact seeks, the antagosistic dispersion-concentration cooperation. According to this view allthe components of Table 2 participate collectively and competitively in enabling the forward generation of proteins,in a forward-backward limit-cycle type ambience, as suggested in (b). Without them the information content of theDNA might not have been there in the first place, the observed forward arrow being the consequence of mutual an-tagonism of entropy and exergy. This bidirectional information flow in complex biological systems — rather than theuni-directionality of classical dogma — appear to support the recent finding of widespread differences between DNAsequences and their corresponding RNA transcripts in human cells [Li et al., 2011] demonstrating that these differencesresult in proteins that do not precisely match the genes that encode them, and that mRNA and proteins — not simplythe DNA — might hold the key to understanding the genetic basis of molecular biology. The “mad cow disease” (BSE)

18

(a) DNA RNA Protein

DNA 2� 2� 1

RNA 1 1 2�

Protein 4 4 4

(b) !RNA

↗↙ Homeo-Stasis

↖↘

DNA!

−→←−

Protein!

Table 2: (a) The Central Dogma of molecular biology asserts that mRNA is transcribed from DNA and translated into protein:

DNAreplication−→ DNA

transcription−→ mRNA translation→ Protein → Phenotype, as deterministic copy-paste, one-to-one, faithful transfers.(b) Current molecular epigenetic discoveries “are likely to lead us to a significant reformulation of our basic assumptions aboutthe organization and role of the genome in phenotypic expressions, heredity, and evolution” in out-of-equilibrium “middle-out”homeostasis of evolving systems. This emerging “systems biology” modeling complex biological systems “focuses on complexinteractions within biological systems, using a holistic approach instead of the traditional reductionism. One of the outreachingaims of systems biology is to model and discover emergent properties [of] organisms functioning as a system whose theoreticaldescription is only possible using techniques which fall under the remit of systems biology. · · · Systems biology is about puttingtogether rather than taking apart, integration rather than reduction. It requires that we develop ways of thinking about integrationthat are as rigorous as our reductionist programmes, but different. It means changing our philosophy, in the full sense of the term.”[http://en.wikipedia.org/wiki/Systems_biology]

for example, have been recorded to be transmitted even after the infectious media was treated by means that normallydestroy genetic material. When the medium was treated by agents that only destroy proteins and leave nucleic acids in-tact the infection was however blocked, indicating that BSE is actually transmitted by proteins. In the ultimate analysis,a paradigm shift from the fixed-point equilibria of death to periodic-point, limit-cycle, homeostasis of emergence andmulti-valued self-organization is clearly indicated as the operative dialogue of Nature.

Molecular geneticists studying the genetic material have over the last few decades been turning up evidence thatincreasingly contradicts the Central Dogma. There is an immense amount of necessary cross talk between genes andthe environment, that not only changes the function of the genes but also the structure of the genes and genomes. ThusShapiro [Shapiro, 2009] believes that the following lessons from current molecular discoveries “are likely to lead usto a significant reformulation of our basic assumptions about the organization and role of the genome in phenotypicexpressions, heredity, and evolution”.

• There is no unidirectional flow of information from one class of biological molecule to another. Many types ofmolecules participate in information transfer from one molecule to any other. In particular, genomic functions areinherently interactive because isolated DNA is virtually inert and probably never exists in that state in a cellularcontext. DNA cannot replicate or segregate to daughter cells by itself.

• Classical atomistic-reductionist concepts are no longer tenable. Every element of the genome has multiple com-ponents and interacts either directly or indirectly with many other genomic elements as it functions in coding,expression, replication, and inheritance; each process involves multiple molecular components and one region ofthe genome may be important for more than one process. Heredity thus has to reflect the inherently systemic anddistributed nature of genome organization.

• The post central dogma discoveries relate to the importance of multivalent and combinatorial techniques. Themobility and interaction of different submolecular domains are increasingly apparent. It is of great biologicalsignificance that multivalent operations provide the potential for feedback, regulation, and robustness that simplemechanical devices lack.

• Genomic change arises from natural genetic engineering, not from accidents. Realization that DNA change is abiochemical process opens up new ways of thinking about the role of natural genetic engineering in normal lifecycles and the potential for nonrandom processes in evolution.

• Informatic-entropic rather than mechanistic processes control cell-functions.

• Feedback signals play a central role in cell operations. The use of signals is critical for basic functions likehomeostatic regulation, adaption to changing conditions, cellular differentiation, and multicellular morphogenesis.

19

Unpredictable signals in biological processes generates an inescapable indeterminacy that contradicts the centraldogma and other reductionist statements of genetic determinism.

• DNA + Protein + RNA + signals + other molecules� Genome structures and phenotype

• To abandon the outmoded atomistic vocabulary of 20th-century genetics, a new lexicon of terms based on a viewof the cell as an active and sentient entity, particularly as it deals with its genome, needs to be introduced. Theemphasis has to be on what the cell does with and to its genome, not what the genome directs the cell to execute.In some ways, the change in thinking reverses the instructional relationship postulated by the central dogma. Thetwo basic ideas here are: (1) Sensing, computation, and decision-making are central features of cellular functions,and (2) The cell is an active agent utilizing and modifying the information stored in its genome.

The general correspondence of the above with our foundational principles are all too evident to require further elabora-tion, all of which goes against the basic tenets of central dogma of linear, mechanistic control. To reflect this new realism,our use of the term “variation” includes sexual genetic recombination, gene flow, HGT, and “selection” admits randomgenetic drift available on demand in extreme circumstances: while an organism’s phenotype is obviously determinedby its genotype and the environment, the new dialectics requires higher forms of homeostasis to be an expression of awin-win game between the two that itself generates and sustains each other.

4 Irreducible Complexity

The new world of complex holism calls for a renovation of the way science is done: “We are in a revolutionary periodbut are using the inadequate tools of normal science” [Smolin, 2007]. The new science has a distinctive mathematics ofnonlinearity, multiplicity, non-smoothness and equivalence classes leading to a new physics of stand-off between selfishindividualism and altruist collectivism, and an interpretative philosophy where both the adversaries participate, win, andlose. Of course, “this doesn’t mean that atomism or reductionism are wrong, but it means that they must be understoodin a more subtle and beautiful way than before”. Just as the advent of quantum mechanics did not signal the demiseof Newton, complexity and holism simply ventures beyond the linear pathway of reductionism in exploring the themethat “the geometry of spacetime is a beautiful expression of the idea that the properties of any one part of the worldare determined by its relationships and entanglement with the rest of the world”. Indeed, “the real blow to the idea thatthe choice of which laws govern nature is determined only by mechanisms acting at the smallest scales came from thedramatic failure of string theory”. The peer sentiments expressed above, lends credence to the possibility of a quest fora roadmap of adventure beyond reductionism.

The canvas beyond reductionism is synthetic rather that analytic distinguished by bumps, blockades, multi-valuedfunctions and jumps, that contrast with the ubiquitous uniqueness, smoothness, and continuity of Newton. Negativetemperature and specific heat and decreasing symmetry generators of structure, run counter to the established wisdomof increasing symmetry and entropy of the real world W+. The cooperative manifesto of ♀W−�♂W+ is through theentropy reducing effect of “gravity” as the source of Schroedinger’s neg-entropy and W− �W+ homeostasis of life:gravitational contraction is at the heart of structure formation in the universe.

Although the New Science does not negate reductionism, its paradigmatic shift in methodology calls for a freshbeginning to proceed beyond its rich analytical legacy. This is easier said than done: the multifaceted inertia is likelyto be not only academic but social, cultural, economic and political.14 The central issue is likely to be the fundamentalnotion of competitive-cooperation. That collectiveness is not a mere by-product of selfish individualism15 is reallyat the centre of the controversy: selfish individualism and altruist collectivism share a common platform for mutual

14“In the West, those who hold to a view of a theistic God, including the Christian fundamentalists of such power in the United States, findthemselves in a cultural war with those who do not believe in a transcendent God, whether agnostic or atheistic. This war is evidenced by thefierce battle over Intelligent Design being waged politically and in the court systems of the United States. While the battleground is Darwinism,the deeply emotional issues are more fundamental. These include the belief of many religious people that without God’s authority, morality hasno basis. Literally, for those in the West who hold to these views, part of the passion underlying religious conviction is the fear that the veryfoundations of Western society will tumble if faith in a transcendent God is not upheld” [Kauffman, 2007].

15“The supposed omniscience and perfect efficacy of a free market with hindsight looks more like propaganda against communism than plausiblescience. In reality, markets are not efficient, humans tend to be over-focused in the short-term and blind in the long-term, and errors get amplified,ultimately leading to collective irrationality, panic and crashes. Free markets are wild markets. Surprisingly, classical economics has no frameworkto understand ’wild’ markets. · · · The recent financial collapse was a systemic meltdown, in which interwined breakdowns · · · conspired todestabilize the system as a whole. We have had a massive failure of the dominant economic model” [Bouchaud, 2008].

20

benefit with neither superseding the other — if Male and Female failed to cooperate, the family would be dysfunctional.Female Capital with their unlimited resources would indulge to death without the cushion of Male Culture which, inits turn, would starve without the supply of essentials by the former. In this world of mutualism, profit as the sourceof unavailable surplus economic energy does not in itself represent stored exergy. The reciprocal feedback of collectiveculture is indispensible for transformation of unavailable entropic profit/benefit to exergic information. This antagonismof individualistic selfishness and collective altruism are necessary components of this contract.

What is Life? The abstract and non-specific vision presented here emphasises the multi-valued emergent and self-organizing character of evolving open systems. Availability of exergy embodied in the W−-pump generated by a dissi-pating W+-engine as a defense against its eventual second-law entropic death comprises the sustaining immunity of life:the evolving two-phase composite of collective cooperating (engine) and individualistic competing (pump) induces thetop-down-bottom-up homeostasy of the “living”.

Part II

Beyond Modern Synthesis: Sustainability, Life5 Survey and Review

Mainstream neoclassical economics, founded on the premise that people have rational preferences among possible out-comes that can be identified and associated with values, act independently on full and relevant information, with income-constrained individuals maximizing utility and cost-constrained firms maximizing profits, is a maximization equilibriummathematical abstraction of the real world of allocation of scarce resources among alternate competing ends; institutionsthat might be considered as prior to and conditioning individual behavior being de-emphasized. The Invisible Handmetaphor of Adam Smith describing the self-regulating character of the free market where individuals’ efforts to max-imize their own selfish gains indirectly benefits social well-being, automatically channeling the self-interest to sociallyoptimal ends: every individual, acting solely in the pursuit of private gain, is “led by an invisible hand to promote anend which was no part of his intention”. In fact a central justification for the laissez-faire economic philosophy is theperception that competition between buyers and sellers channels the profit motive on both sides of the transaction towardproduction of improved products at lower costs — “the invisible hand is a sort of system of social pressure that persuadesthe wealthy to do, of their own volition, what the society around them requires” [Wikipedia, 2013]. Adam Smith believedthat an invisible hand guided society and would ultimately reconcile the pursuit of private interests through market ex-change with the general interest of society; if each consumer is allowed to choose freely what to buy and each producercan choose what to sell and how to produce it, the market will settle on a product distribution and prices that are beneficialto all of the community as a whole.16 Efficient methods of production are adopted to maximize profits, and low pricesare charged to maximize revenue in market share. Investors invest in those industries most urgently needed to maximizereturns, and withdraw capital from those less efficient in creating value. All these effects take place dynamically andautomatically.

Global actualities however, tend to suggest otherwise: unrestrained growth has been shown to be more effectivein expanding social inequality, concentrating wealth in the hands of a few, than in actually generating more wealthand increasing living standards, with the financial crisis having spurred a debate about the proper balance betweenmarkets and government and prompted questions on whether the conditions of neoliberalism are meaningful. Indeedunderstanding such allocation is often considered definitive of (neoclassical) economics, the philosophical approach of

16This is the essential import of the competitive-cooperative stand-off between adversaries. Where neo-classical economics fails is in its explicitdistaste and denial of society and environment: demand and supply in real life are intertwined in reciprocal feedbacks in a connected universeof economic agents, who are more non-rational humans with concerns beyond self-interest maximization, than rational mindless preprogrammedrobots. The economy does not operate in vacuum, it depends on the social environment — in an isolated neo-classical universe of economics andthe economy alone, predisposition of Pareto optimality to selfish individualism rather than altruist distributive collectivism is to be expected.

The market is much more than a linear price-seeking mechanism; it is a (nonlinear) social institution where cooperative demand-supply antag-onists explore a handshake, win-win resolution of their contradictions in the homeostasis of limit cycles and attractors. Genomic functions, it isworth recalling, are inherently interactive because isolated DNA is virtually inert and probably never exists in that state in a cellular context. Genescannot replicate to daughters in isolation but require the common background of other genes and their interactions.

Recent events worldwide — economic, social, environmental — spanning approximately the last 30 years provide adequate evidence for theinference with a fair degree of confidence that neither bottom-up synthesis nor top-down analysis is sufficient on their own for welfare in any, orall, of the three dimensions: they are necessary but not sufficient stand-alones.

21

methodological individualism17 of collective behaviour as an aggregate expression of individual agents without regard toany possible cooperative global manifestations that might emerge beyond the reductionist regime — a group is simply acollection of individuals co-existing — holds that social phenomena can only be understood through the motivations andpurposeful rational utility-maximizing behaviour of individual agents; social goods are necessarily decomposable. Theextraordinary explanatory impact of emergence and self-organization in the social sciences being yet to be acknowledgedfollowing the neglect of the second law of thermodynamics, the theory of microeconomics is based on the assumptionof atomistic behaviour of agents. Social irreducibility and social animalism are of little concern to methodologicalindividualists.

As will be seen, some of the phenomena crucial to the interpretation of the multidimensional crisis of the present de-rive from the specific properties of the aggregates which, once certain thresholds are crossed, emerge as the consequenceof the specific ways of interaction among agents. This mathematization of “the science that studies human behavior as arelationship between ends and scarce means that have alternative uses” without regard to whether they describe observedreality, relies on subjective preferences for determining prices in a competition of individual rival interests, rather thanany objectivism that values goods with reference to some basic commodity or the labour input required to produce it.This patently unrealistic distortion bestows on mainstream economics a static, non-evolving character in which each in-dividual does the best he can given what the others are doing; “if our models of the complex organism called an economyare insufficient to predict the effect of this policy or that, then we cannot expect those models to explain what did in facthappen”. After all, in contrast to the rational economic man, real humans are subject to all sorts of foibles during thedecision-making processes.

This disregard and denial of the role of an absolute benchmark is endemic to neoclassicalism. Classical economists,in particular Adam Smith and Karl Marx, on the other hand understood very well that this circular, recursive process ofincrease in profit, new investments and new profits is the fundamental trait of the modern capitalist economic system.The neo-classical interpretation while focusing on the (presumed) self-regulatory nature of markets, has little to offeron the evolutionary attribute of the process of accumulation, supporting a view of general equilibrium that is basicallyahistorical. Obviously efficiency and growth are indispensable but, in neoclassical models of the Solow-Stiglitz type,it is essentially attributed to increases in productivity, innovation, and technological progress, their theory is based onan aggregate production function in which resources do not appear at all, and which takes production to be a functiononly of capital and labour, “a mathematically clear way of saying that the world can, in effect, get along without natu-ral resources” [Daly, 1997]. Properly functioning markets allocate resources Pareto-efficiently; they cannot determinesustainable fairness that can be achieved only in a broader extra-economic framework.

As an example of the destructive potential of the stabilize, privatize, liberalize mantra of “capital” sans “culture”,the debate appears to have shifted from whether the broader interpretation of a neoliberal manifesto of the WashingtonConsensus [Williamson, 2002] as a shift from the state to market policies with focus on GDP growth “is dead or alive,but over what will replace” this “damaged brand”. The many areas conspicuous by their absence in the WashingtonConsensus revolve around significant market failures that cannot repair themselves but require active interventionistpolicies. They were not part of Consensus-style agenda because the Consensus relies on well-functioning markets tosolve the development challenges and “viewed any state interference in the economy with suspicion”, being “essentiallycontemptuous of equity concerns” [Birdsall et al., 2010]. Reducing poverty is impossible without growth, but growthon its own is not enough and governments need to adopt policies that made growth more inclusive (as) “the evidence isoverwhelming that if you pursue gross domestic product without inclusion you are building instability into your system.Growth has to be inclusive and there is much evidence to support that view” [Elliot, 2013].

Drawing on natural phenomena, discernable patterns of financial markets turning to the infinite intricacies of naturein biological economics for inspiration is now beginning to be considered as a respectable alternative. Biology and thenatural world are helping economists build new models to understand the dynamics of the financial sector and why theUS sub-prime loan crisis caused so much global damage with the crash threatening to bring down whole economies.“This was not something that our conventional models could make sense of” opines one executive director of a bank,“activity in every country around the world fell off a cliff”. Comparisons are being drawn between biological systemswith their complicated webs of interactions between different species, with attention on the system, rather than thereductionist assembly of parts, atom by atom, node by node. “We didn’t differentiate between the big and the small,

17Methodological individualism is the view that collective social phenomena can only be understood through the motivations and actions ofindividual agents — groups or “collectives” it is premised cannot act except through the actions of individual members — which in turn must beexplained by reference to the intentional states motivating the individual actors on the basis of whatever knowledge they have or believe to haveand whatever expectations they entertain regarding external developments and especially the consequences of their own intended actions.

22

we didn’t really think hard about the joins between them”: until now, system-wide data collection in banking has beenvirtually non-existent. Looking at economics through a biologic-system standpoint might lead to realization on why thefinancial world became so vulnerable.

Paradoxically, as the system grew, it ended up being more homogeneous holistically. The quest for diversificationand globalization leads to lack of diversity, with the multi-cellular structure being unwittingly bartered for uni-cellularity.In biological terms, lack of diversity in a population leads to lack of robustness that can trigger the spread of diseasesby a “superbug”, who through its contact with large number of others is responsible for the spread of an infection. Theinterdependent interactions between institutions should be so managed that when there is trouble, everything does not gowrong simultaneously: streamlining interconnections that maintain diversity.

The present work seeks to focus on the theoretical contours of these goals of holistic sustainability18 by generalizingthe profile of sustainable existence of a healthy adult human, outside the periods of generic troubles of growth at less than∼ 12 years of age and the entropic tragedy of dispersive decay beyond∼ 60 years. A severe critique of neoliberalism hasbeen advanced in degrowth [Georgescu-Roegen, 1971] based on the observation that neoclassical economics disregardsthe second law of thermodynamics of the increase of entropy accompanying every activity, and in steady-state economy[Daly, 2005] of constant stocks of people and artifacts, maintained at some desired sufficient levels, by the lowestfeasible throughput of matter and energy from the first stage of production to the last stage of consumption. Theseprescriptions in downscaling economic production and consumption for increasing human well-being and enhancing theecological conditions and equity on the planet calls for a future where societies live within their ecological means, withopen localized economies and resources, more fairly distributed through new forms of democratic institutions. Suchsocieties do not depend on the perpetual “grow or die” neoliberal rancour, unlimited material accumulation no longeroccupying the defining attribute in an individual’s cultural iconography. Degrowth not only challenges the centralityof GDP as an overarching policy objective but proposes a framework for transformation to a lower level of productionand consumption, a shrinking of the economic system to leave more space for human cooperation and co-evolution withNature, and acknowledgement of the ecosystem. Degrowth advocates downscaling of production and consumption —the contraction of economies — arguing that overconsumption lies at the root of long term environmental issues andsocial inequalities.

In support of this distinctive counter-offensive, it has been argued that although economists seem to be aware ofthe first law of thermodynamics and its consequences with production functions often incorporating a material-balanceconstraint, Limits to Growth [Ayres, 1996] stemming from the entropic constraints of second law of thermodynamics arenot yet understood or appreciated. Degrowth views sustainable development as an oxymoron as any development basedon neg-entropic growth in a finite and environmentally stressed world is potentially unsustainable. In what follows, wedistinguish between a complex holistic system that need not necessarily be sustainable and one that is — the formeris purely a thermodynamic issue of coupled real (as opposed to reversible) heat engine and real heat pump, the laterqualifying this thermodynamics with the logistic dynamics of emergent neg-entropic (pump) growth and self-organized(engine) distribution and allocation.

6 Reductionist Sustainability: Weak and Strong

Complex holistic systems provide a foundation on which the edifice of sustainable development — and the emergingnew science of sustainability — should be built. Since these are nonlinear systems with the bi-directional

Cause� Effect (16a)

feedback implying a reciprocalDemand� Supply (16b)

manifestation of limit cycles and periodic points, complex holistic systems can be expected to display marked departuresfrom the near equilibrium, linear, reductionist counterparts we are familiar with. As a significant example of a complexsustainable system, the human mind-body system when external medical support is generally not required to keep the

18Sustainable development is a pattern of growth in which resource utilization aims to match human needs while saving the environment so thatthese needs can be met not only in the present but also for generations to come, in satisfying “the needs of the present without compromising theability of future generations to meet their own needs. · · · Growth by itself is not enough. High productive activity and widwspread poverty cancoexist, and endanger the environment. Sustainable development requires that societies meet human needs by increasing productive potential andensuring equitable opportunities for all” [WCED, 1987]

23

complex phenotype appropriately functional will serve as our prototypical metaphor of holistic sustainability. Surely,perturbations in the form of deceases do occur (and Darwinian medicine seeks to understand why the human body shouldbe as vulnerable as it indeed is) but equilibrium is generally restored through exogenous support that may be withdrawnonce the original state is revived. In contrast, the age groups ≤∼ 12 yrs and ≥∼ 60 yrs, when continuous exogenoussupport is needed in maintaining homeostasis, constitute an excellent example of non-sustainable complex system.

Standard economic science does not consider feedbacks because it tends to explain phenomena mechanically bylinear chains based on the Cause→ Effect principle. However, it is essential to consider the circular relationships aboveif we are to interpret the evolutionary long-term dynamics between socio-economic system and the biosphere, and aboveall to recognise the potentially self-destructive outcome of unchanneled efficiency and growth. It has been observed[Daly, 1987] that the forces propelling economic growth are simultaneously eroding the moral foundations of the verysocial order providing purpose and direction to that growth. Glorification of self-interest and the pursuit of “infinitewants” leads to a weakening of distinction between luxury and necessity while the unrestrained power of science-basedtechnology is erroneously believed to be capable of overcoming all biophysical limits. In fact sustainability requiresmaintaining intact the moral knowledge or ethical capital inherited from the past “sufficient to offset, insofar as possible,the inevitable degradation of our physical world” [Daly, 1987].

That sustainable life emerges from a single fertilized egg entirely on its own through self organization, without anyexternal guidance or intervention, is the marvel of complex-holism that needs to be captured in any acceptable formu-lation of sustainability. Repeated mitotic bifurcations of the fertilized egg must be maintained within the strict boundsof sustainability through proper homeostasis of emergent neg-entropic growth and entropic self-organized dispersion ofthe ensuing non-linear dynamics, failure resulting in either hyperglycemic exergic heat death from limits to growth orits complimentary hypoglycemic entropic cold death of equity in the Tragedy of Commons [Hardin, 1968]. What is thesource of this entropic dispersion and what plays the role of partners in entropic cooperation in the win-win game of lifeagainst the rivals of exergic competition, yet avoiding the entropic implosive collapse of cold death?

The mainstream routes to sustainability, expressed through weak and strong sustainability, are essentially optimizedstatic fixed points of intersection in three-element Venn diagrams of Fig. 6(a), (b), without dynamic interdependenceand interaction of the components, that however constitute the distinguishing features of the out-of-equilibrium, stronglyinteracting systems of present relevance.

6.1 Weak sustainability

The approach to sustainability in the industrialized world, places efficiency and growth ahead of development and distri-bution. Sustainable development is considered synonymous with sustained growth — technological progress can meetevery demand on Nature, man-made capital can replace natural capital and technology can be improved upon or replacedby innovation — there is a substitute for any and all scarce material through optimization of fixed points, the essencebeing to consider the natural world in terms of its economic worth under the tacit assumption that the nonhuman worldis fully expressible by its economic or instrumental value.

Whereas mainstream (neoclassical) economists tend to be technological optimists, ecological economists reason-ing that the natural world has a limited carrying capacity and that its resources are likely to run out under uninhibiteduse, are inclined to be technological pessimists. Since destruction of important environmental resources could be irre-versible and catastrophic, ecological economists justify cautionary measures, resulting for example, in the “degrowth”and “steady-state” alternatives. Degrowth has been criticised for its failure to address the underlying problems of neo-classical economics of growth and market capitalism. Solow and Stiglitz, for example, hold that capital and labourcan substitute natural resources in production either directly or indirectly, ensuring sustained growth and sustainabledevelopment.

Weak Hartwick-Solow sustainability is seen as a problem of managing a portfolio of capital, including natural capital,at a constant level allowing virtually unlimited substitution between man-made and natural capital: taking consumptionas a measure of utility the aim is to ensure constant capital stock. Hicksian sustainability on the other hand requiringnon-decreasing consumption — including consumption of environmental goods and services — is “virtually equivalent”to Hartwick-Solow sustainability; thus the Hartwick-Solow weak sustainability in terms of genuine saving

Γ = (Gross National Saving+ Investment in Human Capital)− (Consumption ofFixed Capital+Natural Resource Depletion+Environmental Degradation)

(17a)

24

ENVIRONMENT

SOCIETY

(c) HOLISTIC: Dynamic Nonlinear

Full Cause� Effect limit cycle

ECONOMIC GROWTH

SOCIETALEQUITY

Complex Life

ENVIRONMENT

Emergence, Self-organization

Sustainable

Viable

Bearable

Cause→ Effect fixed point

ECONOMY

(a) WEAK: Static Linear

ENVIRONMENT

SOCIETY

ECONOMY

Partial Cause� Effect limit cycle

(b) STRONG: Nonlinear

Daisyw

orld

Susta

inable

310

300

290

T

280

1.4 1.61.21.00.6 0.8

Whi

te,Eq.

(28d

)

Bla

ck, E

q.(2

8c)

Bare

, Eq.

(26)

Homeostasis, Eq. (??)

L

Equitable

Figure 6: Sustainability. (a) Weak (b) Strong: Optimized static fixed points of intersection in three-set Venn diagrams. (c) Holistic:Dynamic complexity of self-organized and emergent non-chaotic fractal attractors of limit cycles and periodic points. The full linesof the graph representing the Daisyworld of Lovelock [Watson and Lovelock, 1983] comprises an example of strong sustainabilitywith non-linear bidirectional feedback. In the absence of emergence and self-organization, homeostasis determines the proper ratioof black and white in the population of daisies, not the emergence of new colours consistent with this mean, that would be the normin (c). This marked difference with holism is interpreted to be due to incomplete entropic redistribution, see Fig. 7 and discussionstherein.

can be formalized asσ =

Γ

G(17b)

with σ the index of sustainability, G the GNP, the economy being weakly sustainable of unbounded consumption if Γ≥ 0,the policy expression of which has been to focus on providing equal opportunities for present and future generations,see footnote 21(c). Neoclassical models fit this perspective, by using the standard methodology of dynamic optimizationto generate utility patterns over time with gross economic output or gross consumption accepted as proxies for welfare;how preferences are formed or whether they correspond to biological or physical reality is considered outside the scopeof economics. Weak sustainability requires that all profits earned from exhaustible resources currently extracted bereinvested in produced and human capital rather than consumed, and that the latter are perfect substitutes for naturalcapital.

Examples. (a) A hot ball mass mh, specific heat sh at temperature Th dropped in cold oil mass mc specific heat sc, atTc. Then weak sustainability is defined by

θW =1+µγτ

1+µγ, θ =

TTh

, µ =mc

mh, γ =

sc

sh, τ =

Tc

Th(18)

The simple weighted average corresponds to the intersection — man-made capital can replace all types of natural capitaland every technology can be improved upon or replaced by innovation; thus for Th = 700K, mh = 30kg, sh = 0.5kJ-(kg-K)and Tc = 300K, mc = 150kg, sc = 2.5kJ-(kg-K)−1, µγ = 25, τ = 0.4286 gives T = 315.4K.

(b) Neo-claassical economics that do not incorporate any information about ecosystem structure.

6.2 Strong sustainability

Fig. 6(b) in contrast, advocates “a decentralized way of life based upon greater self-reliance in order to create a socialand economic system less destructive of nature.” Strong sustainability does not allow substitution of human-generated

25

capital for natural capital — man-made products cannot replace natural capital. The stock of natural resources andecological functions are irreplaceable and some minimum level of natural assets is required for human and non-humanlife support. Non-substitutability of the eco- and bio-system, and the importance of ethical considerations, distinguishstrong from weak sustainability with the implication that sustainability requires preservation of the natural world inkind, not just in its economic barometer — for strong sustainability minimum amounts of a number of different types ofcapital (economic, environmental, social) should be independently maintained, in real physical and biological terms —“the biosphere is finite, nongrowing, closed (except for the constant input of solar energy), and constrained by the laws ofthermodynamics. Any subsystem, such as the economy, must at some point cease growing and adapt itself to a dynamicequilibrium, something like a steady state. Birth rates must equal death rates, and production rates of commodities mustequal depreciation rates” [Daly, 2005].

In order to deal with stability and uncertainty in a way consistent with ecological theory, integration of economic andecological models is necessary. Integrated models specially (co)evolutionary models, seem the obvious tools for dealingwith this linkage problem. Unless externalities cover dynamic impacts — including evolutionary effects of activities anddecisions made now — “internalization” or “optimization” of such externalities is inadequate to realize environmentalsustainability. This perspective has been linked [Ayres, 1998] to strong sustainability by recognizing that maintenanceof natural capital does require a precautionary approach which takes safety margins into account, as stability is notguaranteed by operating at the margin of optimal levels of capital.

Examples. Lovelock’s Gaia Daisyworld with two types of life (Appendix A.3), the black daises collectively rep-resented by Th = 313K the temperature above which no life survives and white daisies responsible for Tc = 278K thetemperature below which daisies are likewise extinct, with T the equilibrium temperature under both types. With L asluminosity of daisyworld’s sun Appendix A.3 explicitly derives the temperatures involved.

Static aggregate growth models of optimal allocation are inconsistent with scientific findings of living evolutionarysystems. Apart from the patently suspicious assumption of substitutability between natural and manufactured capital,economic growth cannot be the proxy of human well-being. If this were so then the argument about substitutabilityreduces to a purely economic debate about elasticities of substitution, technological advance and so on. If, on the otherhand, substituting financial capital for natural resources is incompatible with maintaining a suitable physical environmentfor life, then strong sustainability implies that we must broaden conventional market framework to promote conditionsfor human happiness [Ayres, 1998]. Increased wealth and growth does not guarantee increased happiness, welfare, andequity. Far from it, “when the struggle to gain further wealth becomes too intense, there are likely to be major personaland social costs. Family life is disrupted, children are neglected, health suffers. Urbanization has destroyed much thatwas attractive and satisfying, without replacing it with anything comparable” [Ayres, 1996], social inequality more likelythan not increases with GDP, and economic growth does not guarantee welfare and quality of life. Income and growthare of course necessary, but the post-2008 global economic reality casts doubt on whether economy-wide income-growthis also sufficient to further health, education and distributive justice. The economics of growth and its relationship withdevelopment requires a radical rethink. A vast theoretical and empirical literature almost uniformly equates economicgrowth with economic development under the assumption that people care only about consumption, and maximizationof growth under equilibrium should be the policy-maker’s objective.

From a conventional marketing perspective, consumer behaviour focuses largely on the purchase stage of the totalconsumption process, as it is the actual point at which a contract is made between the buyer and seller, ownership ofproducts transferring to the consumer. Yet from a social and environmental viewpoint, consumer behaviour needs to beunderstood as a whole since a product affects all stages of a consumption process: Is the increasing competitiveness ofthe market, by the market, and for the market the enduring philosophy of human existential well-being?

This is what the holistic sustainability of competitive-cooperation based on the complexity of self-organization andemergence of strongly interacting non-linear systems of many interdependent components seeks to explore and formulate.

6.3 Mendel peas, Lovelock daisies

That a gene may have two homologous copies of each chromosome as alleles, puts the growth and development ofdiploidy in a formal one-to-one, binary {0,1} correspondence with the supply-growth, demand-dispersion frameworkof complex holism thereby opening up the possibility of a general approach to holistic sustainability. The three MendelLaws of traits that are passed inter-generationally through discrete genetic units retaining their ability to be expressed,not necessarily in every generation, is characterized by the remarkable independence of the different traits from eachanother and in allelic dispensation to the future, in marked contrast to the foundations of interactive interdependence of

26

collective sustainability.In Appendix A.3 we trace the exact solution [Saunders, 1994] of the Daisyworld equations to appreciate our catego-

rization of Daisyworld as “strong”, Fig. 6(b). The temperature of Daisyworld depends on the solar luminosity and on theplanet’s albedo. As black daisies have a smaller albedo, it renders the planet warmer than without them; in the oppositeextreme a planet with only white daisies will be cooler than the bare planet. With only black daisies present, a warmplanet will grow warmer increasing their growth rate so that black daisies cover more of the planet reducing the albedofurther with the planet getting warmer still. This positive feedback cannot continue indefinitely however “because thereis progressively less space for the daisies to expand into and this [negative feedback] tends to slow their growth rate.Eventually the two effects balance and the population stabilizes. The combination of the two leads to regulation: oncethe two processes exist and interact they produce regulation”.

Without all the� feedbacks of Fig. 7 for example, weak and strong sustainability are not outgrowths of complexity— complete limit cycles are required for complexity. Holistic homeostasis under multi-valued convergence of emergenceand self-organization generates positive solutions of Eqs. (10d) and (10e), with

θW(Eq. 18) = θ ⇒ µγ =3−√

1+4τ

1−2τ +√

1+4τ

=1− ι

ι

which for µγ = 25 has no meaningful solution for either τ or ι , a reflection of the serious compromise that fixedpoint dynamics of weak sustainability entail over holistic emergence and self-organization involving Cause � Effectbi-directionality. In comparison, the strong sustainability of Daisyworld with Th = 313 produces

θS(Eq. 30) = θ ⇒ 0.911(

LL−0.127

)0.25

=1+ τ +(1− τ)

√1+4τ

2(2− τ)

⇒ τ ∈ (0.9445,0.8713)

for the relevant values of L from Fig. 6(b), illustrating the significance of holistic� feedback. However absence of theentropic allocation # in this case results in too high values of τ that, as will be seen in what follows, is far removedfrom the sustainability of Fig. 6(c). Infact, precisely this mutual compromise and tradeoff of selfish-malignancy andaltruistic-equitability opposites of biological multicellularity, generates the higher sustainablity of human life.

7 Holistic Sustainability

It is undeniable, nonetheless, that since the industrial revolution, the middle class has progressed almost everywhere,which raises the inevitable question of whether economic growth is indeed indispensable for these fundamentally sci-entific and technologically fueled developments in human society. Science and technology are the mutational inducersof variation on which economic growth is rooted: neg-entropic growth results from demand generated by innovations,and conversely. Entropic redistribution of the benefits of growth does not occur on its own in a trickle down from theinvisible hand as increasing inequality cogently testify, it needs to be induced by proper collectivist measures and pro-grammes. Growth and equity are unsustainable on their own from heat and cold deaths respectively, only through theircircularly� causal rivalry in competition supported by the partnership of cooperation and co-evolution can the adversityof individualistic profit and collective utility attain sustainable mutually beneficial interdependence.

Alternative ways of co-existing with the goal of maximizing happiness and well-being through non-consumptivemeans involve the relocalization of economic activities in order to end humanity’s dependence on fossil fuels and reduceits ecological imprint. Despite improvements in the ecological efficiency of the production and consumption of goodsand services, global economic growth has led to increased extraction of natural resources and waste emissions. Moreover,unequal exchange in trade and financial markets has increased inequality between countries; degrowth proponents aimto reduce the global ecological footprint to a sustainable level. Whether this can be achieved through individual, localor networked activities remains an open question, as does how institutions could or should be transformed to supportsustainable degrowth, leading in due course to a steady-state economy: GDP is a partial incomplete measure of wealth,and if we wish to include the whole range of possibilities, we must stop using it as the compass.

Holistic Sustainability, Fig. 6(c), is generated by a

27

Cause (Demand Engine)� Effect (Supply Pump)

homeostasis of complex, self-organized, emergent structures. Unlike its static counterparts, holistic sustainability in-volves the bi-directional causation of a generalized Engine-Demand � Pump-Supply closed loop where action by the(engine) system causes changes in its (pump) surroundings that is fed back to the system causing it to adapt to the newconditions — the system’s changes affect its own behaviour. This necessary and sufficient “circular causal” relationshipof set-valued self-organized, emergent fractal attractors of limit cycles and periodic points of the cybernetic perspectiveof competitive-cooperation, comprises the basis of sustainability in Nature. In neoclassical economics, however, socialand economic systems are characterized by exclusively competitive behaviour expressed through optimizing-maximizingfixed points, the reductionist interpretation of evolution has led to a representation of the living universe dominated bythe “struggle for survival” that has been extended to social and economic systems. However, it is now acknowledged thatin ecosystems competitive and cooperative behaviour coexist and that both are essential for the preservation of species;likewise, relationships of a competitive and cooperative nature coexist among economic subjects, the latter being essen-tial to compensate some self-destructive spirals that characterize pure competition. Biological organizations teach us thatpursuing efficiency through competitiveness as the sole objective of economic activity is not only the consequence of areductive concept of the human being, but also easily leads to deleterious aftermath.

In living organisms growth is always constrained by limitations. In complex organisms it is generally self-regulated:they reach a certain size, after which internally generated chemical signals restrict its growth. In general too high, ortoo low, values of any variable is dangerous: too much oxygen involves the combustion of the tissues, too little leads toasphyxia. In the biological world there are thresholds everywhere which cannot be bypassed. This gravely conflicts withthe assumptions of standard microeconomic theory, according to which the behaviours of economic agents are exclusivelyof a optimizing-maximizing type: a larger quantity is always preferable to a smaller one. On a macroeconomic level,nothing opposes a continual growth of income and consumption; indeed it is held to be the first and essential objectiveof every economic policy.

Thus the opposites of firm-profit and household-utility maximizations need not hold simultaneously — increasesin GDP coexist with increasing inequality, and “everywhere despite social safety nets, the youngest, poorest and leasteducated are significantly worse off than their counterparts twenty years ago”; “the fierceness of the competitive gamefor ’growth’ and ’market share’ has been extremely traumatic for many of the workers who are lower in the corporatehierarchy. In short, contrary to theory, ’free trade’ as currently practiced is not good for everybody. Rather, an equity� growth bi-directional feedback, each provoked stimulated and sustained by the other, is capable of seeking a distincttwo-phase, individualistic-collective, competitively-cooperative, destructively-creative homeostatic handshake of the op-posites. Increasing competitiveness symbolized by unbridled growth without matching utility is inherently explosive,susceptible to malignancy. The Great Recession (2007/2008) is a specific case in point — the vigorous promotion ofhouse ownership by the U.S. government affordable housing policy in conformity with its supply-side economic policywas primarily instrumental in switching on the cancerous growth gene. With little or no moderating disciplining asa result of widespread financial irregularities, breakdown in corporate governance including too many financial firmsacting too recklessly and taking on too much risk, an explosive mix of excessive borrowing by households and risk byWall Street, supported by key policy makers ill-equipped for the crisis and lacking full understanding of the financialsystem they oversaw19 resulted in a near total evaporation of all exogenous entropic filtering that might well have savedthe bubble from combative antagonism of the discredited neo-liberal Washington Consensus, to cooperative benignancy.Recall footnote 16.

Example. Figures 5a, 7 and 10 are significant illustrations of the Cause� Effect duality leading to higher levels ofstructure and patterns induced by the nonlinearity of emergent self-organization. Fig. 5a(i) illustrates the basic 0� 1two-way cycle representing this advanced-retarded interdependence of cause and effect. The 4- and 16- cycles likewiseare shown in Figs. 5a(ii) and 7, with ♀ 7→ ♂ symbolizing the direct arrow of exergy and ♂# ♀ the inverse arrow ofentropy. In conjunction with Fig. 10, this constitutes our view of sustainability, weak, strong, holistic, based on the Cause� Effect duality of limit cycles of the logistic map λx(1− x), the evolved holistic composite of each node is served byincoming and outgoing feedback arrows.

With reference to the (A) 7→ (C)# (B) 7→ (D)# (A) scheme and Fig. 10, call the cycles

19Majority report of the U.S. Financial Crisis Inquiry Commission, as quoted in Wikipedia Great Recession, May 2014. Of the two separatedissents one found that “there were multiple causes, of which government affordable housing policies was one” while the other “primarily blamedU.S. housing policy” for the crisis — limits to growth could not have been more explicitly expressed.

28

0.60.3

0.6

(A)

0.8EXERGIC SUPPLY 7→

(iii) 16-cy

cle

(B)

ENTROPIC DEMAND#

(C)# (B)

(1,2)

(B) 7→ (D)(5,6)

(7,8)

(3,4)

(ii) 4-cycle

(1)00 (A)↓ ↓(B) (2)01(3)10 (C)↗ [↖](D) (4)11

00 7→ 10# 01 7→ 11[#]00(A) 7→ (C)# (B) 7→ (D) [# ](A)

1λ 16

=3.5

667(C)

(D)

(9,10)

(11,12)

(15,16)

0.9

(13,14)

(A) 7→ (C)

1

fp

(A) (B)

00

01

10

11(D)(C)

0

DEMAND#

(ii) 4-cycle: λ4 = 3.4986. Fig. 5a(ii)

ENTROPIC

EXERGIC SUPPLY 7→

(D)# (A)

(i) 2-cycle

0� 1

0.9

(iii) 16-cycle

(1)0000 (2)0001 (A) (B) (5)0100 (6)0101(3)0010 (4)0011 ↓ ↓ (7)0110 (8)0111(9)1000 (10)1001 (C) (D) (13)1100 (14)1101(11)1010 (12)1011 ↗ [↖] (15)1110 (16)1111

(1) 7→ (9)# (8) 7→ (13)[#](4) 7→ (12)# (5) 7→ (15)[#](2) 7→ (10)# (7) 7→ (14)[#](3) 7→ (11)# (6) 7→ (16)[#](1)

Figure 7: Fixed points of 4th and 16th iterates of the logistic map λx(1− x). While all [#] feedbacks might not be establishedin strong sustainability, holistic sustainability is defined by the full set of positive-negative feedbacks of emergent-self-regulatedassemblies. See Fig. 5a.

(a) WEAK: Fixed point dynamics, no limit cycles and periodic points. A non-complex, reductionist system.(b) STRONG: Exergic supply (A) 7→ (C), (B) 7→ (D) backward entropic demand (C)# (B) and/or (D)# (A) absent.(c) HOLISTIC: All forward and backward links present and active. A holistic system of the economy-society-

environment complex.In the absence of matching allocative demand of self-organization, the unrestrained supply (A) 7→ (C), (B) 7→ (D)

is prone to runaway overgrowth. Thus in Lovelock’s Daisyworld of “strong” sustainability, as the sun’s luminosityincreases, warming black daisies appear with temperature, followed by the cooling whites as the temperature overshootstolerability of the blacks. At the confluence of the warming blacks and cooling whites, lies a considerable range ofluminosities at habitable temperatures (Fig. 6(b)) which would be impossible without the coupled positive and negativefeedbacks. As argued in Sec. A.3, this feedback is not generated dynamically, being the solution of coupled algebraicequations, hence not holistically coupled through limit cycles. Without full Cause� Effect operationally active, whitedaisies do not survive the full onslaught of increasing luminosity, and the equilibrium is a discrete mixture of the twodistinct types, not the synthesis of new colours and hues that could arise from their fusion.

29

7.1 The sustainable world of complex holism

The Demand-Cause� Supply-Effect dualism is formalized in the Engine Pump, positive� negative feedback of Fig.8.20 Complexity, holism, and the derivative holistic sustainability, are distinguished by nonlinearity and positive �negative feedback leading to new features of multi-valued emergence, self-organization and general equilibria of periodicpoints, limit cycles, and fractal attractors. These vastly richer manifestations of homeostasis of competitive-cooperationadd new dimensions and features to out-of-equilibrium systems that linear optimization of opposing antagonism cannotgenerate. Holistic sustainability as an expression of this new dialectic seeks to explore and formulate the intricacies ofthe whole being beyond the sum of its parts that none of the constituents on their own, can emulate.

F

eP

t

sa

r

u

tu

Present T

Holistic homeostasis

Top-down analysis

Tc

Reductionist

ThExergic growth

Entropic allocation

Bottom-up synthesis

0

1

Homeostatic T

Tc: Collectivism

Bottom-up P

Top-down E

Th Individualism

White Daisies

Black Daisies

(i)

←−

T,E

ntro

py

W− Growth

(1−

ι)−→

W+ Equity

aB

Ab

.

Ab

glucosedeficient

aBneighbouring

surplusglucose

neighbouring

β ∼ 65%α ∼ 35%

}in humans

Tc Th

GABA

PANCREASTATIN

Exergic emergentgrowth. Black daisyorganizing equity.

Entropic self-

White daisy

β -cell: Insulinand pancreastatinsecreting Pump

(ii)

(1− ι)−→

and GABAsecreting Engine

ι =β

α +β

α-cell: Glucagon

Figure 8: Insulin-Glucagon Homeostasis. (i), a more graphic representation of the blueprint for sustainable holism presented in Fig.2 Part I, forms the basis of (ii) adapted from Koeslag, Saunders and Wessels [Koselag et al., 1997], for possibly the only naturallyoccurring holistically sustainable system of nature: the adult, healthy, mind-body system. Top-down analysis← of E and bottom-upsynthesis→ of P are both reductionist, their product competitively-cooperating interaction " of give-and-take defines complexity,holism, sustainability. .

The opposites of “creation” and “destruction” takes the form of exergic concentration and entropic dispersion. Thereal entropic world W+ — the entropy of an isolated system never decreases; isolated systems spontaneously evolvetowards thermodynamic equilibrium of maximum entropy — does not natively support exergic creativity. Creativitydoes not reside within isolated systems as nothing can be produced or generated for free — an engine needs fuel tooperate. The available output of an engine is utilized by the pump to generate and produce, entropic dispersion beingan inevitable second-law consequence of total available energy. This purely thermodynamic framework integrated withthe dynamics of an interactive nonlinear supply� demand process completes the foundation of holistic sustainability.Thermodynamically, the entire system can be taken as an (isolated) universe; alternatively the real-world engine Econstitutes the system and its complement the environment. In the former, invariance of internal energy allows theuniverse many more degrees of freedom than is available to the system E in the later, leading to possible catastrophicdisequilibria.

7.1.1 Insulin-Glucagon Homeostasis

Figure 8 generalizes the implications of the Engine� Pump homeostasis of Fig. 2 in terms of the glucose concentrationof a healthy human, considered here as the supreme convention of sustainability. The hormones insulin and glucagonare produced in the pancreas and are involved in the uptake of glucose by the organs of the body. After a meal, whenblood-glucose levels are high, insulin encourages the liver and muscles to absorb glucose and to convert it into theinsoluble carbohydrate glycogen. When the blood-sugar level falls, glucagon is released by the pancreas to help convertthe glycogen back into glucose and release it from the liver and muscles into the blood, thereby maintaining homeostasisof blood-sugar levels by the cooperating glucagon-secreting α cell and the insulin-secreting β cell antagonists. With theα−β units operating as flip-flop devices [Koselag et al., 1997] that secretes either insulin (in the aB mode) or glucagon

20Note the decreasing-entropy, increasing-temperature behaviour of the pump coupled with increasing-entropy, decreasing-temperature characterof the engine. This “anti-second-law” disposition follows from the long-range nature of the only tool of concentrative creativity available to Nature— gravity — in the world of spontaneously destructive dispersion. This virial effect is considered in Part I, Sec. 2.2.1.

30

(in the Ab mode), spontaneously flipping between insulin and glucagon states, the glucagon-Ab mode promote aB→Abtransitions among their immediate neighbours, while insulin-aB units promote Ab → aB transitions. A fall in glucoseconcentration (increased ι) increases the probability of aB→ Ab flips thereby progressively increasing the proportion ofAb units leading to increasing glucagon:insulin ratio of the blood with time; likewise, an increase of the blood glucoseconcentration (increased 1−ι) has the opposite bias of Ab→ aB transitions. Only when normoglycaemia is fully restoredby the feeddback will the biases dissapear resulting in glucose homeostasis. Fig. 8 illustrates how this actual mechanismof sustainability can be synthesized to general complex systems by the irreversibility parameter ι = (Wrev−W )/Wrevthrough the correspondences Wrev := α +β , W := α , so that ι = β/(α +β ) represents the fraction of insulin secretingβ -cells relative to the total α +β cells.

A relative reduction in glucose concentration in the fall of (1− ι)/ι = (Th−T )/(T −Tc) ratio as T → Th is counteredby exergic-growth in Fig. 8 that inhibits the degradation of Th to match the initiation of aB → Ab flips. Conversely,increase in glucose concentration as T → Tc is challenged by the insulin-induced entropic-dispersion that helps to main-tain the relative stability of Tc through with the Ab→ aB transitions. It now follows that the homeostatic pancreatic cellparameters are related by the insulin-glucagon ratio (Fig. 4b(iii))

β

α=

ι

1− ι=

1−2τ +√

1+4τ

3−√

1+4τ

=

1 τ = 0.01.4574 τ = 0.67771.4848 τ = 0.7199√

5−13−√

5= 1.6180 τ = 1

(19)

obtained from the + solutions of Eqs. (10d,b), with T the homeostatic condition for a given τ . The remarkablyoutstanding feature of (19) is of course the primacy that complex holistic homeostasis assigns to equity over growth —without redistribution of the concentrative individualism of exergic, neg-entropic growth to dispersive utilization andcollectivism of entropic welfare, growth is potentially self-destructive. Generally, ι0 = 0.5 and ι1 = 0.6180 [(Eq. 10e(b)]the bounds shrinking dramatically for sustainability as summarized in Fig. 9(iv). A summary of this � blueprint isdisplayed in Table 3.

WHITE DAISIES due to their higher BLACK DAISIES due to their loweralbedo, decrease the temperature albedo, increase the temperature

of Daisyworld of Daisyworld

BACKWARD INVERSE ARROW←−−−−−−−−−−−−−−−−−−−−− FORWARD DIRECT ARROW−−−−−−−−−−−−−−−−−−−→W+ : Natural Selection W− : Mutation

Top-down analytic engine E Bottom-up synthetic pump P

Disorder; Increasing entropy Order; Decreasing entropy

Dispersive self-organization Concentrative emergence

Collective: Cooperation Individualistic: Competition

ALTRUISTCULTURE: Phenotype←−−−−−−−−−−−−−−−−−−−−−−−

SELFISHCAPITAL: Genotype−−−−−−−−−−−−−−−−−−−−→

Demand offer Supply confirmation“MIDDLE OUT” holistic handshake of opposites, T

Table 3: Complexity and holism. Observe the virial effect: changes in entropy and temperature are inversely related

7.2 Generalized demand, supply, logistic

The purely thermodynamic basis of Fig. 8 would fail in its purpose of providing a foundational framework of sustainableholism if it did not link with the dynamics of non-equilibrium systems. In Fig. 10 the logistic map λx(1− x), λ ∈[0,4], x ∈ [0,1] representing a multiplicative interaction of top-down, dispersive utilizing demand/collectivism/culture

31

1− x and bottom-up, concentrative supply/individualism/capital x, symbolizes the antagonistic tension between exergicgrowth-efficiency and entropic equity-dispersion: neg-entropic growth is the manifestation of P while entropy and equityrepresent E. Of course without growth there can be no redistributive justice as there would be little to distribute; likewisegrowth would be meaningless without consumers interested in the produce. Concentration and dispersion are two sidesof the same coin expressed in the thermodynamic law of total enthalpy being the sum of entropic dispersion and exergicavailability, with irreversibility of entropic dispersion defined as the ratio of unavailable energy to the total endowment.The “engine” E is the consumer of the produce generated by the “pump” firm P, their antagonistic collaboration E� Pgeneralized in Fig. 2(ii) implying that selfish efficiency is as inevitably malignant in boom-growth-heat-bust death fromlimits to growth as its altruist adversity of redistributive implosive cold demise from tragedy of equitable commons, Fig.8(ii).

Here we establish the significant result that (holistic) sustainable systems are necessarily complex though complexsystems need not be sustainable: the “triple bottom line” of long-term social equity and justice, economic prosperity,and environmental conservation in the sense of weak sustainability is inadequate. To establish the comprehensiveness ofthe thermodynamic, positive� negative confrontational feedback, general characterizations of demand sink and supplysource is needed to look beyond the prevalent mechanistic models, the economic problem being “how to reconcile thetension between scarcity and unsatiated wants”.

Reversibility ρ , 1− ι −→0 1

1.5

1.0

(ii) EQUITABLE GROWTH

Demand Q, Eq. (20a) Qh = 1

τ = 0.0

τ = 0.5

Logistic ιqQ, Eq. (20c)Supply ιQ, Eq. (20b)

1.0

0 1

1.5

(i) MALIGNANT GROWTH

QqInteraction qQ

Qh = 1

τ = 1.0

τ = 0.5

τ = 0.0

Reversibility ρ , 1− ι −→

1.0

10

λ

1.5

(II): W−

Reversibility ρ , 1− ι −→0 1 43 λ = 3.5699Tc Th

ιS, (10e)

τS, (21b) −∞

θS, (10d)

0 0.7500

0.5 0.8644 0.8873 0.9000

0.5 0.5976 0.6000

0.6667 0.7199

0.5931

→ ∞0

θ =TTh

Demand Q = [1− (1− τ)ρ]1/2

Supply ιq = ρQSustainability ιqQ = ρQ2

(iii) SUSTAINABLE GROWTH

The fitness/gini 1− ι ' 0.4 demonstrates

Eq. (19) — the message of ιqQ equitabilityover qQ malignancy.

primacy of cooperation over competition,

τ = 0.0

τ = 1.0τ = 0.5

Qh = [1− (1− τ)ρ]−1/2

↑1

2-phase: (II)+(IV)

X

(I): W+, LIFE

T −∞

(iv) HOLISTIC SUSTAINABILITY

τ := 1−λ−1

(III

):W−

(IV

):W

+

τ = 1.0

Figure 9: Supply is ιq, rather than q because q→ ∞ as ι → 0, the condition of hot explosive death. ιq = Q iff ι = 0, at noevolution. This thermodynamic-dynamic synthesis modifies the purely thermodynamic interpretation of Wrev-normalized Qh of Fig.2 as required for sustainability.

From the definitions of irreversibility ι and adaptibility α , the thermodynamic quantities (see Fig. 2(i))

Q =

(TTh

)Qh = Qh [ι(T )+ τ(1− ι(T ))] (20a)

iq = (1− ι(T ))Q = Qh(1− ι(T )) [ι(T )+ τ(1− ι(T ))] (20b)

for a comprehensive wealth Qh and adaptibility α of the engine� pump system qualify as generalized “demand” and

32

“supply” respectively. Then the non-linear Hardy-Weinberg interaction for ι = (θ − τ)/(1− τ), reduces to

ιqQ =(Q2

hθ)[(1− τ)−1

θ(1−θ)]

(20c)

defining a general supply-demand cubic logistic for demand Q, supply ιq, and an environmental factor 0≤ τ := Tc/Th <1. For a given τ the complexity condition ι =α constrains a system to the narrow range of permissible values of Eq. (11);protection from the both the extremes ι = 1 of heat death and ι = 0 cold death ensures homeostacy of equity-growth.With Eqs. (10d, 10e), set

λS ,1

1− τS∈ (3,3.5699) (21a)

⇒ τS = xfp ∈(

23,0.7199

)(21b)

QhS =

√Th

T=

[4−2τS

1+ τS +(1− τS)√

1+4τS

]1/2

∈(

1,√

2)

(21c)

in (20c) to define sustainability as a subclass of complexity with the logistic parameter λ := (1−τ)−1 now assuming therole of Qh of Fig. 4a, the bounds of Eq. (21b) following from allowed region of periodic doubling bifurcations, withxfp the fixed point. These relations indicate that reduction of heat extracted Qh with increasing homeostatic temperatureT resulting in increased ι , impedes the growth of T through attendant increased entropic dispersion; see Fig. 4b(iii).It is remarkable that τ , a thermodynamic parameter, uniquely defines λ a dynamic parameter with the environment τ

representing the fixed point of the dynamic map. It follows that λ is a dynamic synonymy of magnitude (1−τ)−1 of thethermodynamic real world W+: (I) + (IV).

For sustainability then, from Eqs. (20c), (7c)

αS = qSQS, Qh =1√θS

(21d)

compared to the general (7a), the sustainable logistic taking the explicit form

ι(qQ)S =1+2τ2± (1−2τ)

√1+4τ

2(2− τ)2 , (22)

+/− relating to Regions (I) and (IV) respectively. The singularities of ι at τ = 2 and the complex roots for τ <−0.25,indicate the extreme caution needed in dealing with dynamical processes involving a system-surrounding strategy, assevere deformative disequilibria from ill-posedness is likely as Tc→ Th leading to a breakdown of the system-surroundingpartition in (22). Puncturing the Tc diaphragm separating System(I) and Surrounding(IV) by the forward-backward ι �

τ := ι(2ι−1)/(1− ι)2, 12 < ι <

(√5−1/2 = 0.6180

)dynamics (Fig. 4b(iii)) eliminates the ι± and θ± choices that no

longer explicitly depends on the environment τ , the System and Surrounding having merged into an all-inclusive isolatedglobal system W+ that might occur either as Tc→−0.25Th (physically unrealizable global cooling, θ− = θ+ = 0.1667)or as Tc→ Th (global warming, θ− = θ+ = 1). This, we suggest, is the mechanism underlying climate change.

The standard thermodynamic prescription of invariant Th > Tc representing environmental sources and sinks fromwhich finite amounts of energy can be extracted or supplied without altering the respective temperatures is usually madein the system-surrounding formulation. In the complex thermodynamic case the surroundings remain as such largelyunaffected; sustainability however requires the full bidirectional consequence of Cause � Effect achieved through thecomplete integration of dynamics with thermodynamics as in Eqs. (21a,b,c). While the thermodynamic prescriptionfor complexity is defining under normal circumstances, situations can arise where this division is stressed, with thesystem encroaching on the surroundings and appropriating to itself the role of an (isolated) universe. This highly stressedsituation broadly corresponds to invariance of internal energy U(T ) of the integrated enlarged system, assumed to dependon temperature T only. Removing the partition between two halves of a rigid and insulated container containing differentgases at Th and Tc represents such a situation; taken as the universe, the total sum of all forms of (internal) energy intrinsicto an isolated thermodynamic system remain constant and is of non-decreasing entropy.

Changes in enthalpy H = U + pV of reversible work Wrev = (1− τ)Qh ∈ [0τ=1,√

2τ=0] with environment τ can beincorporated in the expression for entropy S = ιWrev/T that yields for the competitively� cooperative homeostasy ofQh = 1/

√θ the entropy expression of Table 4 with the correspondence of the four components of Fig. 4a as shown.

33

ThS =(1− τ)

√4−2τ

(1−2τ +

√1+4τ

)(1+ τ +(1− τ)

√1+4τ

)3/2

Region Value,

3

5

7

0−0.4 1 2

1

-1

ThS

τ

(III)s1

τ→−∞

→−∞±is2, τ <−0.256.1237, τ =−0.25√

2+, τ = 0−

(IV)√

2, τ = 00.2460+, τ = 0.67−

(I)0.2460, τ = 0.670.2003+, τ = 0.72−

(II)

0.2003, τ = 0.720.1757, τ = 0.750, τ = 1−0.4330, τ = 2

s3τ→∞

→−∞±is4, τ > 2(i) (ii)

Table 4: Monotically decreasing entropy with increasing T (virial effect, Sec. 2.2.1), −0.25 ≤ τ ≤ 2, according to ThS = ι(1−τ)/θ 3/2, Qh = 1/

√θ . W− regions (II) and (III) are clearly the sources of negative entropy, the basis of all creativity in W+. See

Fig. 9(iv).

The negative-entropy [Schroedinger, 1992] region 1 < τ < ∞, Tc > Th, is an equal partner in the creative� destructivemanifestation of complexity, holism, and sustainability, the real (complex) roots ι± (Eq. (7b)) coalescing at 1

3/1.00 asτ →−0.25+/∞ (τ →−0.25−/−∞). The potential of the positive and negative branches of θ± and ι± acting simul-taneously is the basis of climate change; system sustainability in comparison, due to the constraint of an effectivelyunchanging environment, Eq. (22), leads to the less catastrophic disequilibrium of global warming. Ability to reducethe dynamics of any living system to a confrontation between a generalized demand (eg. growing population and con-sumerism) and a generalized supply (eg. limited resources of the earth and its biosphere) and their nonlinear encounteris the basis of a successful win-win negotiation between the antagonists that makes “life” possible. Note that both (II)and (III) of W− support positive and negative entropies but are predominantly neg-entropic.

While the supply correspondence of ιq(T ) in this positive negative, auto-feedback loop is fairly obvious, the demandanalogy with Q(T ) follows as the confrontation of Q with ιq bestows on the former the character of a collective demandthat is met by individualistic supply ιq in a feedback loop that sustains, and is sustained by the other in an overall contextof the whole. This collective and cooperative consumer demand induces, preserves, and nourishes the individualisticcompetitive supply that constitutes the capitalist base of the firm.

The interactive factor adaptation (21d) suggests

Definition 1. (Technical) Sustainability is the science of the art of prevailing on the adversity of tragedy of commons andlimits to growth a holistic Cause� Effect participatory set-valued platform of creatively destructive, out-of-equilibrium,“middle-out”, homeostatic adaptive tradeoff between allocative dispersion Q and malignant growth q, reined by a Qh-disciplined utilization of Nature.

Recalling that sustainable systems are necessarily complex although complexity does not imply sustainability, provokesthe

Proposition. Life is the out-of-equilibrium, homeostatic, complex holistic, superbase of sustainability.

Hence we conclude that

Definition 2. (Operational) Sustainability is the art of healthy, enduring living from the past into the future, chore-ographed by the competition-cooperation-adaptation of self-organizing, emergent present.21

21Compare: (a) A state in which society does not systematically undermine natural or social systems within the biosphere.http://www.naturalstep.ca/glossary

(b) A development path is sustainable if utility does not decline at any point in the path [Pezzey, 1989].(c) A development path is sustainable if social welfare does not decline at any point along the path [Dasgupta, 2001], where social welfare

34

Remarks. 1. Note that “life” being a complex, middle-out expression of Nature need not be sustainable: without birthand death nature would not evolve.2. The Demand = Supply benchmark applied to Eqs. (20a, b ) leads to the revealing ι = 0, no-equity, Pareto optimal,unrestrained growth assigning all to one and nothing to everybody else.3. Since ι determines dispersive demand, the condition ι =α specifies demand through nonlinear interaction of allocationand production of an adaptive negotiating platform α .4. Although Limits to Growth is undoubtedly an expression of unlimited desires conflicting limited resources, a basicfeature of living organisms is its finite, mediated intake of low-entropy exergy for healthy and enduring living. Unfetteredappreciation is a malignancy-prone biological anachronism, irrespective of the availability of resources.

7.3 Thermodynamic-Dynamic Overview of Holism

Figure 10 presents a survey of our current understanding of the dialectics of complexity, holism, and by extension, of sus-tainability. Between the extremes of collective tragedy of commons representing self-organizing cold death of maximumdispersive and re-distributive equity, and the catastrophic limits to growth symbolizing emergent heat death of uncon-trolled malignancy of development and productivity, lies the severely restricted region of sustainability characterized byτ = 1− λ−1 ∈ (0.6667,0.7199)λ∈(3,λ∗) which is infact the fixed point of the logistic λx(1− x). Whereas complexityand holism are purely thermodynamic concepts, sustainability is a special dynamical subspace in the restricted of theenvironment τ . The product of irreversibility ι and adaptability α , ια = (1− τ)−1θ(1− θ), defines and demarcatesthe negative exergic world W− of spontaneously decreasing entropy, decreasing symmetry, increasing structures andpatterns for ια < 0 and the real entropic world W+ of spontaneously increasing entropy and symmetry and decreasingstructures and patterns, ια > 0. Any constructive activity in the naturally dispersive world W+ is to be understood asthe signature of W− through the medium of attractive gravitation, which as Table 4 indicates dominates the eventualityof Second Law, providing a possible rationale for the apparently contradictory appearance of life in W+.

The two-phase thermodynamic composite that defines life is apparent from the forward photosynthesis, backwardcellular respiration equation

6CO2 +6H2Osunlight�ATP

C6H12O6 +6O2

in which glucose C6H12O6 is oxidized to carbon dioxide and water, with release of ATP energy. In addition to maintainingnormal levels of oxygen in the atmosphere, photosynthesis is the primary source of energy for nearly all life on earth,either directly or indirectly, as food. In Fig. 11, we view this production of glucose from carbon dioxide, free electrons,and ATP in the economic Firm� Household stand-off, and identify the two-phase mixture as the composite of glucoseand oxygen.

The forward iterates of ια induces emergence of new structures, as Figs. 5a(ii, iii), 10(iii) demonstrate, through thefixed points of f and of higher f (n)’s, the backward iterates f−(n) inducing self-organized allocation of symmetrization.Variation of λ in the demand-supply interaction λx(1−x) is expected to represent a generalization of the simple demand-supply equality criterion of neo-classical economics so as to include out-of-equilibrium situations that depend not only onthe fixed point of f but also on those of the evolved states of f (n): complex holism in the extended, graphically converged,set-valued, limit space determine homeostasy of the evolving dynamical system. Altruist collectivism reciprocates selfishindividualism that in turn is sustained by the generosity of entropic dispersion — meaningful only under the exergicconcentration of W−- individualism — in W+, individualism being necessary to sustain it and be motivated by thereciprocal demands of collectivism.

the present value of utility along the development path, is a measure of inter-generational well-being; it is an economic programme along whichaverage well-being of present and future generations, taken together, does not decline over time.

Formally [Arrow et al., 2012], if δ is the discount rate of well-being and V (t),´

∞

t U(C(s),K(s),A(s))e−δ (s−t)ds, an aggregate of consumptionservices C, capital stocks K, and activities A people enjoy, human inter-generational well-being at time t taken to be equivalent to the comprehensivewealth of sll capital assets and institutions of the economy, development is considered sustained at t if dV/dt ≥ 0. Clearly, our holistic sustainabilityis quite different from this weak economic variety.

35

1(i) λ = 0.9 ∈ (III)

Maximum entropy of self-organization,Fertilization: Fallopian tube,

Cooperative cold death at Tc

Gamete→ Zygote

xfp = 1− 1λ

Iterations 1−10

0

TRAGEDY OF COMMANS: Inverse lim←−

1No emergence or self-organization

(ii) λ = 2.9 ∈ (IV)Zygote travels up fallopian tube,

= τ

101

LIMITS TO GROWTH: Direct lim−→

1

1

(III), (IV): C O O P E R A T I O N

Mitosis: Limit cycle, LifeEmergence and self-organization

Chaos, minimum entropy of emergence

(iv) λ = 3.82 ∈ (II)

Competitive heat death at Th

Meiosis: Gonads, Gamete(iii) λ16 = 3.5667 ∈ (I)

Iterations 101−10510(II): COMPETITION

0

1

(I): ADAPTATION

fixed point implantation in uterus

Figure 10: Domineering productive growth or consumptive equity are roadmaps to disaster. (i) defines W− Region (III) of λ ∈ (0,1),(ii) W+ Region (IV) of λ ∈ (1,3), (iii) and Fig. 5a(ii)-(iiib), of holistic competitive cooperation of these adversaries defines holismand sustainability. of W+ Region (I), λ ∈ (3,λ∗), and (iv) corresponds to W− Region (II) of λ > λ∗. Note from Table 4 that theentropy decreases monotonically from (i) to (iv) (recall the virial theorem), with the negative entropy domains closing on each otherthrough equivalence at τ =±∞ of entropy −∞.

8 Holistic Sustainability and Complexity: Sustainable Systems are Complex

8.1 Economic circular flow

In economics, basic circular flow is a simple model that describes the reciprocal circulation of income between producerfirms and consumer households providing each other with factors to facilitate the opposing flows of income and produce.Firms provide consumers with goods and services in exchange for consumer expenditure and households provide firmswith factors of production of land, labour, capital and enterprise in return of wages, rent, profits and interest, Fig. 11. Thusexpenditure of one sector is the income of the other and supply of goods and services by one section of the communitycomprises demand of the other, typical of the reciprocal Demand � Supply interaction. This simple model presumesthat households spend all their income on goods and services or consumption — there is no saving, and all output offirms is purchased directly by households with no intervening banks and governments. It is a closed economy with noexports or imports, a text-book example of the thermodynamic system-surrounding.

Inclusion of government and financial sectors in the cycle representing a more realistic economy does not change thisbalance of the adversaries of clockwise money-flow demand and counterclockwise material-flow supply. In the broaderopen perspective, households save part of their income in financial markets that generate investment funds for firms andgovernments interact with the financial sector, in addition to taxation of households and firms, to induce further moneyflow. The four components of Fig. 11 broadly associates with those of Fig. 4a as follows. (a) Household conformsto W+ (I) of biological mitotic life, (b) Factor Market represents gonad generation (II) of labour and capital gametes,(c) Firm represents fallopian tube fusion (III) of gametes to develop zygote good, and (d) Product Market uterus (IV) iswhere the zygote matures to provide utility and sustenance to households, thereby allowing a view of the market as asocial institution where the adversity of productive growth and dispersive consumption seeks a cooperative homeostasisin limit cycles and periodic points.22 While the simple fixed-point route of equality of domestic income and domestic

22“Economists know how markets work, and they can say with some confidence how a mature market economy will respond to their policy

36

PRODUCT SUPPLY ιqPRODUCT DEMAND Q

(II): FACTORMARKET

MARKET(IV): PRODUCT

O2: Domestic ProductConsumer demand

H2O: Domestic Expenditure

Factors of Production→

Domestic Product = Domestic Income

(III): FIRM

Firm Supply

HOUSEHOLD

CO2: FACTOR SUPPLYLabour, Capital

Enterprise, Land

Money Income flow! : ι Material Product flow" : 1− ι

C6H12O6:FACTOR DEMANDWage, Salary, BonusProfit, Dividend, Rent

6CO2 +6H2Osunlight�ATP

C6H12O6 +6O2(I):

← DOMESTIC INCOME

“Market” is a social institution where the adversity of firm productive growth and householdutility dispersion seek a cooperative homeostasis in limit cycles and fractal attractors.

Figure 11: Basic Circular Flow in a Simple Economy. Universal Darwinism is a generalization of classical Darwinism that applieswith “essential and auxiliary explanations specific to each scientific domain” to all open evolving systems sharing the commonattribute of variation-inheritance-selection. Hodgson and Knudsen [Hodgson and Knudsen, 2004] uses this as the defining attributeof universal, generalized Darwinism, distinguished by self-replication. Households sell factors of production in factor markets andbuy products in product markets, firms buy factors of production in factor markets and sell products in product markets.

product can be appropriate under normal circumstances, out-of-equilibrium turmoils of the type that the sustainabilitydebate has generated in recent times, calls for the holism of emergence and self-organization.

In the next section, a thermodynamic basis of this expanded view is presented.

8.1.1 Thermodynamic Reversibility, Gini Index, Insulin-Glucagon Ratio

The notable feature of Fig. 9(iv) that defines the restricted window of sustainability, is the pre-eminent significance ofaltruist entropic collectivism over selfish egoistic individualism. τ — interpreted as the ratio of the income of the bottomx% of the population representing the sink temperature Tc to that of the top x% of the source temperature Th — shouldbe at least 2/3 but not much beyond. Sustainability clearly demands of the antagonists, mutually defining each other inthe homeostasis of complex holism, the dominant concentrative component to yield to its dispersive recessive partner —quite unlike to the invisible hand of passive welfarism. The Gini index G measuring twice the area enclosed between theLorenz curve and the equality diagonal, or its entropic variant T based on the Shanon entropy SSh = −∑

Ni=1 pi log2 pi,

records the deviation of distribution of income or consumption from perfectly uniformity, 0 representing the maximumentropic dispersive state of absolute utilitarian equality, and 1 of absolute inequality in the maximum exergic state ofmalignant-boom-growth, heat-bust-death optimality when one person gets everything at the exclusion of all others whoget nothing. The Theil index T of economic inequality, with entropy S based on SSh, pi = xi/Nx the normalized incomeof a population of N individual incomes xi of an average x = 1

N ∑Ni=1 xi given by

T , Smax−S

= log2 N +1N

N

∑i=1

xi

x̄

(log2

xi

x− log2 N

)is normalized as

TN =1

Nx̄ log2 N

N

∑i=1

xi log2xi

x=

{0, xi = x̄, everyone of equal income1, {xi}N−1

i=1 = 0, xN = Nx̄, individual N has it all

prescriptions. But mature markets rely on deep institutional underpinnings, institutions that define property rights, enforce contracts, conveyprices, and bridge informational gaps between buyers and sellers. Indeed, an important part of development is precisely the creation of theseinstitutionalized capabilities”. World Bank, The Growth Report: Strategies for Sustained Growth and Inclusive Development (2008)

37

suggesting a formal correlation with thermodynamic entropy T S = ιWrev = Wrev−W corresponding to S ; hence Trepresenting W = 1− ι in units of Wrev is a “negative entropy” in the sense that it decreases with increasing disorder,hence a measure of creation rather than dispersion, with Smax =S +T = log2 N, the theoretical maximum entropy whenall incomes are equal. Fig. 12(i) illustrates Lorenz curves for (a) quintile income distribution and (b) the thermodynamicbenchmark Lorenz L (x) = x(2−ι)/ι with inequality index G = 1−2

´ 10 L (x)dx = 1− ι for a trapezoidal approximation

G = 1−∑ni=1 (xi− xi−1)(yi + yi−1) for discrete data.

.

10.80.60.4

1

0.20

IndiaU.S.A.

Swedenι = 0.6, [Fig. 9(iv)]Lorenz L (x) = x(2−ι)/ι

Cumulative population fraction xi→

Cum

ulat

ive

inco

me

frac

tion

y i→

Country Normalized Theil TN

Sweden 0.0597

Germany 0.0822

India 0.1008

Canada 0.1000

China 0.1607

UK 0.1282

USA 0.1511

Data of Table 5

Figure 12: Lorenz curves L (x) = x(2−ι)/ι , Gini index G = 1− 2´ 1

0 L (x)dx = 1− ι . A selection of the World Bank income data[World Bank, 2015] of Table 5 is plotted here; the graphs of Norway and Denmark effectively reproduce that of Sweden. The LorenzL (x) for the sustainable value ι = 0.6 is more faithfull to the U.S.A., China data with a relatively higher value of G than those ofSweden, Norway, Denmark. This apparent discrepancy is addressed in (b) below. Note that two populations can have the same Giniyet different inequaliies as the respective Lorenz profiles may be of the same area with different shapes.. Clearly, the normalized Theil is far too equitable compared to the Gini benchmark of Table 5.

Figure 9(iv) is a summary of the correspondence between the dynamic parameter λ and relevant thermodynamicquantities. Thus temperature T is fully determined by definite absolute markers Th and Tc required for a thermodynamicformulation in terms of system and surrounding. In contrast simultaneous integration with the antagonistic dynamicsEqs. (21a,b,c) of the logistic map introduces well-defined narrow limits for the various sustainable quantities shown inthe figure, with Qh determining the permissible bounds for utilization of natural resources.

The Gini index in the form G = 1− ι for fitness and growth (Fig. 8), permits the inference that(a) For the human biologic system with a fraction 65−80% β -cells and 33−46% α-cells in islets of Langerhans,

the ratio β/α = ι/(1− ι) in the approximate range (1.4130, 2.4242), shows the theoretical estimate of Eq. (19)/Fig.4b(iii) as eminently pragmatic. Let Tc correspond to the normal fasting blood glucose level 70− 100 mg/dL. ThenTh ∈ (101,145) for an assumed average τ = 0.69 (Fig. 9(iv)) in the sustainable range compares favourably with thenormal postprandial glucose limit of 90−140 mg/dL, predicting a normally healthy glucose temperature T ∼ 90−130mg/dL.

This encouraging corroborative endorsement of our blueprint arising from the insulin-glucagon homeostasis of thesupreme example of a naturally occurring sustainable system of the healthy human represents our benchmark for sus-tainability. With the caveat that the DNA� RNA� Protein network of the current understanding of complex biologicalsystems replacing the uni-directional simplicity of central dogma — a crucial factor in the genetic blueprint of biologicalorganisms — appears to be further corroborated by the c > 1 requirement of non-biologic systems that we explore below.

(b) For the world economic system, let Tc correspond to the average income of the bottom 20% of a populationand Th of the top 20%. If the economy is to sustain itself, their ratio τ should be restricted to the narrow bounds in Fig.9(iv), i.e., the lowest income should be approximately 69% of the highest. Table 5 summarizes a selection of some ofthe relevant Development Research Group data of World Bank [World Bank, 2015] and compares it with the predictionsof Fig. 9(iv), the parenthetical values of the first row being the income of the bottom 20% that would be necessary forachieving economic sustainability — clearly the value of τ is far outside that required. If we take the encouraginglypositive indicators of (a) of arguably the most complex sustainable system in nature, holistic economic sustainabilityappears infeasible under the present economic dispensation, the invisible hand being far too biased in favour of (Pareto)

38

efficient individualism to distributive collective justice.23

World Bank data [World Bank, 2015]Sweden Germany India Canada China UK USA

Qui

ntile

Inco

me 1 (Tc) 9.5 (25) 8.3 (27) 8.5 (30) 7.1 (28) 4.7 (32) 5.8 (30) 4.7 (32)

2 14.3 13.1 12.1 12.4 9.7 11.4 10.43 17.8 17.1 15.7 16.8 15.3 16.2 15.84 22.7 22.4 20.8 22.7 23.2 22.6 23.1

5 (Th) 35.7 39.1 42.8 41.0 47.1 44.1 46.0

Gin

iG

G 0.261 0.306 0.336 0.337 0.370 0.380 0.411ι = 1−G 0.739 0.694 0.664 0.663 0.630 0.620 0.589

τ , Fig. 9(iv) 0.690, sustainable for c = 1. (ι = 0.595, θ = 0.874)c [Eq. (10c)] 2.277 1.739 1.465 1.457 1.212 1.147 0.967θc Eq. (10a) 0.919 0.905 0.896 0.896 0.885 0.882 0.873

c=

1

τ = Tc/Th 0.266 0.212 0.199 0.173 0.100 0.132 0.102θ [Eq. (10d)] 0.669 0.637 0.631 0.616 0.570 0.590 0.571ι [Eq. (10e)] 0.549 0.541 0.539 0.535 0.522 0.528 0.522

G = 1− ι 0.451 0.459 0.461 0.465 0.478 0.472 0.478

Table 5: World Bank quintile income data [World Bank, 2015]. Sweden, Norway, Denmark as the most equitable nations arefunctionally indistinguishable from each other, as are the most unequal nations U.S.A., U.K., China. The values in parenthesis ofrow 1 indicate the c = 1 lowest quintile for a sustainable τ = 0.690. “Income inequality has become so extreme that it could inflictmajor economic damage if we don’t take action. The gap between rich and poor in many countries, most notably the U.S., has beenwidening for decades”, Footnote 4.

Nonetheless, the objective reality of countries such as Sweden, Norway, Denmark, Germany suggests the possibilityof an unexplored route to sustainable reliability — the biologically positive template of the human genetic prescriptionneed not be the sole gateway. A value of c 6= 1, Eq. (10c), can offer a less restrictive track that unlike the c = 1 caseconsidered so far allows greater flexibility in socially engineering intermediate values between Tc and Th, the c-valuesof the national income distributions being shown in the Table. With this adjustable ι−α slope, the relative magnitudesof the parameters in Fig. 4a can be fine-tuned more representatively than possible under c = 1 in the obviously non-biologic-genetic human society. Thus examination of Fig. 4a(ii) reveals that c > 1 leads to a simultaneous increase ofι+ and |ι−|, which from graph 4b(iii) implies an increase of τ and hence in the income of the lowest 20% in terms of thetop 20%, as compared to c = 1. The effective

c =100ι2

(1− ι)(31ι +69)(23)

in Table 5 for sustainable τ = 0.69 and the “experimental” Gini ι provides an indication of the correction of the bio-logical standard necessary for environment-social-economic sustainability; of noteworthy significance to governmentsand policy planners is the unambiguous increased relative weight accorded to intangible human and institutional wealthcompared to produced and natural, as c exceeds 1.

23“We are all keenly aware that income inequality has been rising in most countries. Seven out of ten people in the world today live in countrieswhere inequality has increased over the past three decades.

“Some of the numbers are stunning — the richest 85 people in the world own the same amount of wealth as the bottom half of the world’spopulation. In the US, inequality is back to where it was before the Great Depression, and the richest 1 percent captured 95 percent of all incomegains since 2009, while the bottom 90 percent got poorer. In India, the net worth of the billionaire community increased twelvefold in 15 years,enough to eliminate absolute poverty in this country twice over.

“Let me be frank: in the past, economists have underestimated the importance of inequality. They have focused on economic growth, on the sizeof the pie rather than its distribution. Today, we are more keenly aware of the damage done by inequality. Put simply, a severely skewed incomedistribution harms the pace and sustainability of growth over the longer term. It leads to an economy of exclusion, and a wasteland of discardedpotential.

“It is easy to diagnose the problem, but far more difficult to solve it. Nevertheless, we need to get to grips with it, and make sure that ’inclusion’is given as much weight as ’growth’ in the design of policies. Yes, we need inclusive growth”. In A New Multilateralism for the 21st Century: TheRichard Dimbleby Lecture, Christine Lagarde, Managing Director IMF, London February 3, 2014.

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The homeostatic holistic temperature T of Eq. (10d) representing the inclusive holistic income of the population,lower bounded by 0.5Th [Eq. (11), Fig 4b(iii)] at Tc = 0, is a remarkable statement of the holism of entropic equityand neg-entropic growth as it guarantees redistribution of at least half the earnings from the able to the needy, for thecontinued well-being of both, inevitably interlinked as they are by the mutual Equity� Growth association. This boundappears to be upheld by the insulin-glucagon onset of hypoglycemic breakdown at∼ 50 mg/dL that roughly correspondsto this limit. The flat profile of Qh in the range of interest of Fig. 9(iv). is a clear indication of the severe restrictionsimposed by nature on “illegal mining” of its resources and thereby on the theme of weak sustainability of supposedlyinfinite substitutability through technological innovations and human ingenuity.

(c) Distinguished from global warming involving increase in surface temperature, breakdown of the system-surroundingpartitioning (Sec. 7.2) of climate change “in the statistical properties of the climate system considered over long peri-ods of time, regardless of cause” embraces this warming and all else that increasing greenhouse gas levels might giverise to. While the greenhouse effect has a definite contribution to the emergence and sustenance of life — without itsinsulating envelop, deep-freezing temperatures of approximately −20C would lead to cold destruction and obliteration— in the true spirit of competitive cooperation, the opposite extreme of heat malignancy from unreciprocated growth hasemerged as a main concern of the present times. Taking an average earth’s surface temperature of 288 K (15C), and a(Tc,Th) = (−46C,56C) corresponding to θ = 0.8750 and τ = 0.69 in the sustainability range, the greenhouse effect canbe understood to apply to a “surface” in the troposphere (of average height ∼ 15 km.), coupled to the surface of the earthby an environmental lapse rate dT/dz = −6.5◦C− km−1. With temperatures of the troposphere-stratosphere interfacebeing about −45C at the poles, −55C at mid-latitudes, and −75C at the equator, the sustainability value of Tc = −46Cis adequately well represented. Although the higher temperature Th = 56C is scarcely attained on earth, without lifeforms earth’s surface temperature would be in the range 50C−70C that embraces the theoretical estimate of 56C, thecorrection embodied in c > 1 on real, socio-economic-environment sustainability (Eqs. 10a, b, c) can be considered tobe convincingly demonstrated here. Complemented by a carbon-rich atmosphere, the∼ 25% increase in solar luminosityover the past 3.8×109 years would have warmed Earth’s surface by ∼ 30C [Lenton, 2002] otherwise.

While it is possible for the socio-economic system to achieve sustainability with respect to the limits of Fig. 9(iv),changes in (Tc,Th) and their ratio τ introduce altered boundary conditions for an altered environment that the system mustreadjust to. Environment is different from society and economy — the three “pillars” of sustainability — as it providesthe basis and infrastructure for them to communicate with each other. The greenhouse cycle with respect to Tc, makesthe environment-society-economy triad particularly well-suited to the strict and well-defined demands of Fig. 9(iv),provided the unattainably high value of Th is taken to reflect, through the regulation embodied in c > 1, the contention ofLovelock [Watson and Lovelock, 1983] that life-forms alter the environment to suit its own convenience and continuedexistence — organisms co-evolve with Nature and the environment by influencing their abiotic ecosystem which in turninfluences the biota by Darwinian process. Thus Th = 56C being too high, is reduced by living organisms, through theinducement of an effective c > 1, as they interact with their inorganic surroundings to form a self-regulating complexthat contributes to maintaining the conditions for life on the planet to a supportive thermodynamic state of disequilibriumof an effectively reduced Th.

(d) The Natural Step (TNS) pioneered by Karl-Henrik Robert [Robert et al., 2002] in the late 1980’s, providesan interesting comparation for our methodological philosophy. The Framework for Strategic Sustainable Development(FSSD) that TNS employs for the ecological-social biosphere regulated by Daisyworld-type incident-reflected solarradiation where the surface temperature of Daisyworld remains almost constant over a broad range of solar output, isbased on four sustainability principles (SPs) each of which can be interpreted formally in the comprehensive Demand� Supply perspective of entropic household-consumption interacting with gravitationally exergic, neg-entropic firm-production, to be associated with one of the four components ρ±, ι± of Fig. 4a. Specifically, FSSD advocates

(i) In a sustainable society Nature is not subject to: (SPI) systematic increasing concentrations of substances extractedfrom the Earth’s crust and (SPIII) systematic physical degradation of systems and processes for example, over harvestingforests, destroying habitat and overfishing, together corresponding to ρ−, (SPII) increasing concentrations of substancesproduced by society, corresponding to ρ , and (SPIV) undermining people’s capacity to meet their basic human needs(example: abuse of power structures leading to unsafe working conditions and inadequate pay to live on), correspondingto ι+ and |ι−| the intangible components of comprehensive wealth. Measures restricting exergic increasing growth inphysical production and attendant exploitation of natural resources (SPI, SPII, SPIII: decreasing entropy of gravitation-ally induced emergent structures and patterns) on the one hand, and uninhibited decreasing availability of means andmeasures of sustenance, endurance, and promotion of fair unbiased and equitable distribution for all (SPIV: increasingentropy of self-organization of emerged structures) on the other, acknowledges the respective roles of limits to growth

40

and tragedy of commons in determining an out-of-equilibrium, sustainable, barometer of competitive-cooperation,(ii) A Present ← Future backcasting initiative from the desired sustainable outcome to considered collective fore-

casting so as to enable these effects and complete the overall Forecasting � Backcasting circular affirmation " of“brain-storming”,

(iii) The funnel metaphor of increasing economic, social and environmental pressures on society from free un-hindered exergic growth (SPI, SPII, SPIII) resulting in decreased maneuverability, partially captures the competitive-cooperative dynamics of Fig. 8(i), calling for the intervention of equitable redistribution (SPIV) to relieve the pressure,and

(iv) Dematerialization and substitution including not only leaner production and degrowth but also recycling, newbusiness models and new innovations, primarily defining the nature of productive growth (SPI, SPII, SPIII) in meetinghuman needs. The antagonist consumptive entropic redistribution (SPIV) being tightly interlinked and interacting with(SPI, SPII, SPIII), is simultaneously under the comprehensive influence of dematerialization and substitution, in thespirit of strong sustainability, Figs. 6, 7. Although all the four principles can be managed in this approximation ofrelatively restrained complexity (plant life, for example) by a combination of dematerialization and substitution of metals,chemicals, and natural resources for the first three principles and saving of resources, coupled with “changes related to ahumanization of society” for the fourth, in the case of holistic sustainability of human society governed by intricate non-decomposable economic, cultural, environmental nonlinearities, keeping both malignant-boom-growth-heat-bust-deathof deleterious growth and dispersive, redistributive utilization and equity in check and homeostatic balance throughtheir competitive partnership should be the objective. While substitution and dematerialization are acknowledgedly thedriver of reductionist sustainability (Sec. 6), emergence of new features and their integration with entangled economic,environmental, and cultural dimensions constitute the basis of the more advanced complex holistic sustainability (Sec.7). With strong sustainability of incomplete and missing feedbacks inheriting characteristics of both, daisyworld forexample supports only a mixture of the black and white types in the complex sustainable state (Fig. 6(b)), not grey orany other emerging new colour. Indeed, emergence of new features that sets holism apart from reductionism is the basisof the vulnerability of (holistic) sustainability.24

It is significant that two disparately unrelated approaches, separated as they have been in time, culture, and objective,should in (i)-(iv) arrive independently, without materially conflicting each other, at a rather remarkable confluence of anemergent profile of which a great deal is perceived and precious little quantified. Growing out of distinctive goals andobjectives that are in apparent opposition to each other, one seeks holism and non-linearity as instruments for an evo-lutionary blueprint of the multiplicity, non-uniqueness, discontinuity and non-smoothness of emergent, self-organizing,periodic-point-limit-cycle, out-of-equilibrium systems, as the antithesis of neat and predictable fixed-point equilibria thatno longer apply. The distinctive character of positive � negative feedback responsible for the distinctive homeostasisof holism compared to the familiar reductionist equilibria, necessitates a process of relearning beyond Newtonianism —a paradigmatic shift from fixed-point equilibria of death to limit-cycle homeostasis of emergence, self-organization andlife, clearly indicated as the out-of equilibrium dynamic of Nature.

The almost opposite focus of TNS has been “to create a clear and robust manual for action that would respect thenon-linear holism that is already there — not necessarily trying to copy it as guidance for actions. Which tells peoplethat action-programs need not be overly sophisticated and built on very deep science, just because the system they aredesigned to protect is characterized by those things”, being demonstrably adequate for such ecological systems, theprimary focus being to “deduce robust and easy-to-understand principles for sustainability to respect the holism andnon-linearity that is already there”25.

The two approaches should be viewed as complementing each other, the theoretical backbone enshrined in self-organized emergence of the nonlinearity of Cause � Effect that updates the initial condition at each time step to the

24As non-trivial significant, illustration of the homeostatic stand-off between neg-entropic exergic growth and entropic utilization involvingapparent violation of the second law, the examples of protein folding and oil-water mixtures may be mentioned. Protein folding is the physicalprocess by which a polypeptide folds into its characteristic and functional 3-dimensional form from a random coil. Folded proteins have ahydrophobic core in which side-chain packing stabilizes the folded state, and the hydrophylic charged polar or side-chains occupy the solvent-exposed surface where they interact with surrounding water. Minimizing the number of hydrophobic side-chains exposed to water is an importantdriving force behind the folding process. For hydrophobic collapse, the free-energy increases with decrease of entropy toward the interior, whilein the hydrophylic surface exterior the opposite happens preventing total collapse. The folded protein represents homeostasy of the entropy andfree-energy adversaries: while this may not be the best option for either, under the joint influence of tragedy of commons and limits to growth,neither would be better-off otherwise: a misfolded protein may be a serious liability rather than an asset, the correct three-dimensional form beingessential.

25K. H. Robert, Private communication.

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output of the preceding, being ultimately responsible for the robust interlinking of the various constituents of the rules ofthe complexity-sustainability game that practice must necessarily play by — “the whole endeavour has been to organize a’bridge’ between science on the one hand, and concrete envisioning, analyses, planning, monitoring in business and pol-icy on the other to ensure that their modelling and simulation really occur in context of the non-linear world they want torespect”. Failure to understand, appreciate, and act by the paradigm shift that this entails from the smoothness-continuityof differential equations will hardly be conducive for an effective prescription of the malady afflicting the current state ofsociety-economy-environment. Regulated by the creatively-destructive, birth-life-death workbench of Nature, set-valuedcomplex homeostasis of self-organizing emergence can be very different and unexpected from “business-as-usual”, asworldwide events of the recent past cogently testify.

(e) Here we reproduce some significant observations of the Organisation for Economic Co-operation and Develop-ment (OECD), a forum of 34 countries “committed to democracy and market economy” to “stimulate economic progressand world trade”, that supports and corroborates the findings of this paper. All on Board: Making Inclusive Growth Hap-pen [OECD, 2014] observes that “Inclusive Growth, which is a new approach to economic growth that aims to improveliving standards and share the benefits of increased prosperity more evenly across social groups, has become a majorchallenge for many countries around the world. This objective is particularly relevant in high-income countries andemerging market economies, where income inequality has reached levels unprecedented in the post-war period. Inequal-ities in other non-income outcomes, including educational attainment, health conditions and employment opportunities,have become important determinants of growth and well-being. Inequality of income and opportunity undermines growthprospects in the long term. Addressing the multidimensional nature of inequality and its impacts on different segmentsof the population matters for sustainable economic growth. Therefore, fostering Inclusive Growth is an important partof a pro-growth agenda” is the advocacy of [OECD, 2014] that elucidates: “the distribution of disposable incomes (aftertaxes and social benefits) has been rising in most OECD countries over the past 30 years, including in countries whereincomes were previously comparatively evenly distributed. The average income of the richest 10% is now about 9.5times that of the poorest 10% on average in OECD countries, up from 7 times 25 years ago. In Germany, Norway andSweden, the gap between rich and poor has expanded from less than 5 to 1 in the 1980s, to more than 6 to 1 today: in1980, in no OECD country did the richest 1% of the population enjoy more than 8% of total pre-tax incomes; by 2010,they enjoyed 10% or more in 9 of the 18 countries for which data exist, and as much as 20% in the US. The gap betweenrich and poor has risen even faster since the global financial crisis than it did in the previous decade. This contrasts withthe post-war period of fast economic growth until the 1970s, when income distribution tended to become more equal inthose OECD countries for which reliable estimates can be made”.

In the subsequent In It Together: Why Less Inequality Benefits All [OECD, 2015] explicates: “Over the past threedecades the Gini coefficient stands at an average of 0.315 in OECD countries, exceeding 0.4 in the United States andTurkey and approaching 0.5 in Chile and Mexico. In the advanced economies, much of the recent debate on inequalityfocuses on the richest 1% and, increasingly, the 0.1%, the groups that have enjoyed the lion’s share of income growth inrecent decades. In the United States, for example, average pre-tax income rose by 1% a year between the mid-1970s andup to the Great Recession. But when the growth that went to the top 1% of earners is excluded, the annual growth rate forthe remaining 99% was just 0.6%, about the same level as in France. The rise of the super-rich has led to warnings aboutthe risks of rent-seeking and political and economic capture by the economic elite”. Continuing [OECD, 2015] observesthat “while the flashy lifestyles and incomes of the top 1% are certainly eye-catching, focusing on them exclusively risksobscuring another area of growing concern in inequality — the declining situation of low-income households. In recentdecades, as much as 40% of the population at the lower end of the distribution has benefited little from economic growthin many countries. In some cases, low earners have even seen their incomes fall in real terms. Just as with the rise of the1%, the decline of the 40% raises social and political questions. When such a large group in the population gains so littlefrom economic growth, the social fabric frays and trust in institutions is weakened.”

Surely, something beyond cosmetic tinkering is indicated here in the “new approach to economic growth that aimsto improve living standards and share the benefits of increased prosperity more evenly across social groups” to meetthe formidable challenge to continued existence and well-being of the human race. “As long as all citizens have equalaccess to high-quality education, other public goods and services, finance and entrepreneurship, some level of inequalityof outcomes is both economically inevitable and politically acceptable. However, inequality of opportunity can beparticularly damaging when it locks in privilege and exclusion, which undermines intergenerational social mobility.Inequality is particularly likely to undermine growth if the income of the lower and middle-classes fall behind the rest —as it has in several OECD countries. Policies that aim to address inequality of outcomes will fail unless they ensure moreequal access to opportunity in the form of high-quality education, health care and infrastructure, which remain unevenly

42

spread both socially and geographically. This requires assessing the impact of policies on heterogeneous populationgroups, and calls for measures that go beyond the average individual or household when gauging the success of pro-growth policies. Taking account of income and non-income dimensions in the design of policies for Inclusive Growthcalls for new policy tools. Broadly defined economic and social policy choices should be made in the context of whatthey can do to foster both equity and growth objectives” is the unambiguous endorsement of All On Board [OECD,2014].

The basis of our thermodynamic considerations — confrontation of the dispersive engine E and its induced concen-trating pump P — is characterized by a significant defining attribute that needs to be noted explicitly: the unphysicalvirial effect of entropy reduction with increasing temperature (by the pump) coupled to the attendant increase in entropyfor decreasing temperature (by the engine) as elaborated in Part I. This second-law contradictory manifestation of “cre-ation” by the pump of gravitational contraction in competitive partnership with “destruction” of the engine endows thiscreative-destructivity with the unique property of forward backward linkage of the exergic, gravity-induced, neg-entropycreativity of W− and the real life entropic dispersion of W+

Epilogue. The Equity� Entropy Handshake of Opposites

The linear mathematics founded in calculus with maximization and contraint-based optimization seeking to maximizeutility for the consumer and profit for firms work with reasonable justification as long as its axioms of linearity ofpeople with rational preferences acting independently with full and relevant information make sense. This frameworkof rationality of economic agents of individuals or company working to maximize their own profits, of trickle-downeffect of the invisible hand of the market transforming the profit-seeking motive to collective societal benefaction, and ofmarket efficiency of prices faithfully reflecting all known information about assets, are relevant under severely restrictiveconditions: it is important to understand that fundamental tenet of capitalism — that human beings are rational, marketsare rational, and that markets assign prices the way it should be — are best taken with a liberal dose of salt.

In reality a careful analysis of the pathways toward the conclusion that the most preferred bundle for the consumerwould be guaranteed by competitive pressures of the “free reign of rational self-interest” demonstrates that the pictureof simultaneous maximization of utility and profit depends on demand that is reciprocally contingent on what is avail-able. The competitive-cooperation of the engine and its self-generated pump is identified as the tension between theconsumer with its dispersive collective utilization spending engine (cooperative “culture”) in conflict with the individ-ualistic resource generating pump (competitive “capital”) in mutual feedback cycles, attaining market homeostasis notthrough linear optimization and equilibrium of intersecting supply-demand profiles, but through nonlinear feedbacksthat generate entangled holistic structures — supply and demand in human societal metabolism are rarely independentof each other. To take this into account, the interactive feedback between the opposites of engine consumption andpump production can be modeled as a product of the supply and demand factors that, unlike in its static manifestation ofneo-classicalism, will evolve in time to induce dynamic equilibrium of periodic points and limit cycles.

The theoretical basis of the Invisible Hand, that individuals are led in the pursuit of their self interest by an invisiblehand to unconsciously promote public interest and this objective goal of self interest is more reliable than any other likestate involvement, for example, lies in the two Fundamental Theorems of Welfare Economics. The First Theorem statesthat under certain conditions, the competitive economy — where no individual can impact the welfare of others throughhis unilateral action although the action of a collection can — is always Pareto efficient in the sense that no one canbe made better off without penalizing somebody else to be worse off: capitalism, therefore, cannot be criticized for theaccumulation of too much wealth in the hands of too few. The Second Theorem of the “converse” requires every Paretoefficient allocation be attained through the market system. All that the government needs to do is engage in some initialtransfers of taxes and subsidies. The competitive market determines a Pareto efficient input-output equilibrium at theintersection of the decreasing-demand and increasing-supply curves because at this quantity-price, neither the buyer northe seller has an incentive to change his position, being the only point where the amount that demanders are willing topay for an extra unit of output matches the price at which suppliers are willing to supply that extra unit.

That Pareto efficiency scarcely ensures economic justice through equitable distribution is well-known, the SecondFundamental Theorem implying that economic efficiency is separate from social equity with the distribution of inequityand ill-being of assigning everything to a single individual being technically as Pareto efficient as any other among themany that might be admissible. Failure to account for the demand supply linkage amounts to linearized reductionism of anonlinear problem governed by self-organization and emergence. The considerable simplification that this entails in such

43

abnormal times as the post-2008 subprime crisis, together with the general failure of neoliberalism of the WashingtonConcensus, calls for serious introspection and re-evaluation of our inherited wisdom on the working of society, economy,and the real behaviour of humans in ways less “rational” than orthodox economists would rather have us subscribe to.26

Rarely guided exclusively by the gratification of unmitigated and limitless self-interested desires and wants that theelegant simplicity of neo-classicalism subscribes to, “markets [in general] are not efficient [and] there is an importantrole for government to play. Adam Smith’s invisible hand — the idea that free markets lead to efficiency as if guidedby unseen forces — is invisible, at least in part, because it is not there” [Stiglitz, 1991]. The pursuit of individualself-interest rarely benefits the common good; imagine the consequences of unpaired glucagon without its cooperative-adversary insulin or photosynthesis without the complementing cellular respiration.

“The fact that markets are not constrained Pareto optimal and the Invisible Hand does not work, rather than beingisolated and easily correctable by government intervention, appear to be all-pervasive” requires acknowledgment ofentropic human sociability — we are social animals who care about our relations with others — as a complement ofexergic efficiency and growth. Indeed “human beings engage in actions that are not in keeping with their narrow self-interests. Pressures that come from social norms, habits that make us not even consider actions, that if used, could yieldus benefits, and the pervasive power of culture can make us give away many individual advantages, and not even thinktwice about it”. Cautioning against the risk of “a mean, materialistic future”, Basu [Basu, 2010] feels that “the form ofcapitalism (based on the two myths that an industrialized nation’s markets are free, and that free markets are fair) that somuch of the world either relies on or aspires to · · · is a myth perpetrated, at times deliberately and at times unwittingly· · · that makes people feel that ’redistribution of wealth’ is wrong because the current distribution is somehow right”.

The actual policy transcription of the antagonistic debate of Nature in a thermodynamic-dynamic synthetic two-phase homeostasis of the material-spiritual adversity-in-cooperation, as suggested by the multi-valued emergent self-organization of holistic sustainability, ought to be the “focus of debate and discussion in democratic societies”. That thisis not an easy matter of simple cosmetic modifications and adaption of our present knowledge and understanding is abun-dantly clear. What is debatable, however, is whether this policy should be geared to the encouragement, promotion, andadvancement of effectively metamorphosising a supremely living multicellular organism of holistic complexity to hum-ble unicellularity, selfishly guided by the destructive malignancy of maximal efficiency and growth that transformationof the world into a globalized super-village would entail.

With this diagnostic workbench of Nature’s collective malignant legacy, we attempt

A prescription: ι = cα , c≥ 1?

If sustainability is indeed such a fragile, out-of-equilibrium, economic-social-environmental setup that understandably isdrawn to the attractor of exergy-less entropic death, the concern of complex life in temporarily evading this eventualitythrough the dialectics of sustainability should constitute the basis of our dialogue with Nature to enable the opposingparties to a homeostasis of competitive-cooperation. With the healthy adult human as the template of biological sustain-ability, three defining atttributes stand out unambiguously: the relative magnitudes of altruist dispersion to individualisticgrowth of approximately 65−70% : 35−30% is to be achieved by the same set of actors undertaking the required con-tradictory roles as required. Supported by the Shockley-Queisser limit of the efficiency of a single-junction solar cellunder unconcentrated sunlight of around 30%, this calls for a paradigmatic shift in our attitude to inclusive sustainabilityand relationship with Nature.

Under this natural limit of the efficiency of a thermodynamic system, the question of acknowledging this decidedly“non-economic” character of Nature for incorporation in the profile of a “market” assumes significance. The economywithout social and environmental integration being an empty rhetoric, the “market” as a (nonlinear) social institutionwhere cooperative demand-supply antagonists explore a win-win resolution of their contradictions, is much more than alinear price-seeking mechanism. To specifically integrate allocative redistribution in the corporate anatomy, the conceptof cooperative management of production and distribution has been suggested where labour “produces” for 5 days of the

26“A look around the globe makes it clear that the propaganda of the champions of neoliberalism is a myth. The advent of neoliberalism wasaccompanied by instabilities all around the globe. Starting with the Mexican peso crisis followed by a foreign exchange crisis of East Asiancountries and Russia, LTCM fiasco, bankruptcy of Enron and other large corporations accompanied by massive accounting frauds, Argentina’ssovereign bond crisis, and to top it all, the credit crunch destroying the future prospects of a whole generation, is a brief score card of the effects ofneoliberalism. Since its onset, the average growth in the industrialised world fell from 3.2 per cent to 2.1 per cent, accompanied by increased jobinsecurity and scaling down of social services. The share of national income of the top 1 per cent of the population in the United States increasedfrom 8 per cent to 18 per cent. In India, newspapers give perverse publicity to reports that we have more billionaires than Germany.” [Bagchi,2014]

44

week and “manages” on the remaining. Apart from questions of competence in an increasingly specializing environment,this 100:0 or 0:100 division — when both the antagonists are by definition never simultaneously present in the spirit ofcompetitive-cooperation — although perhaps adequate in small-to-medium scale operations is an unlikely candidate ofequitable social redistribution.

Based on this, a glucagon-insulin homeostatic society that suggests itself might run as follows. The public sector isthe guardian of the 60−70% beta share of national wealth; by its very nature the private cannot be expected to assumethis responsibility. To fulfill its obligation in this healthy-human context, the state needs to redefine its priorities andgoals; acting in the 30−40% growth role of a producer firm it is to play by the rules of the “market” of stock exchanges,selfishness, individualism and profit in this alpha incarnation — the present mechanism of raising state resources throughtax initiatives is to be replaced by corporate profit and earnings of the state, in competition with the private sector thatcontributes only 30− 40% of national wealth. This admitted sacrifice of efficiency in favour of redistributive equityis inevitable for playing by Nature’s rule to avoid malignancy, with the boards of the public sector having a 30− 40%participation from the private; reciprocally for the private sector. A 30− 40% fraction of the state’s market profits isobviously fed back to its corporate accounts, the remaining 60−70% going to the public exchequer of intangible human,social and institutional wealth, in lieu of taxes. The 30−40% national wealth private stake holder retains all its profits,without paying customary taxes (or perhaps only a token quantity, as shadow price of services received from the state).

Nonetheless, as observed following Eq. (10c), the environment-society-economy complex is decidedly not as au-thoritatively pre-programmed as are genetic biological systems; whereas specification of Tc and Th apparently sufficesfor the biological ι = α systems, the evidence of Sec. 8.1.1(b), (c), is indicative of their inadequacy when intermediatedata are called for. Social engineering in the framework of the societal market ι = cα , c ≥ 1, is clearly indicated insuch situations with decreasing Th or increasing Tc resulting in measurably significant changes ρ−, ι− (Region (IV))but only token, relatively imperceptible, perturbations in ρ and ι (Region (I)). Thus for given productive and intangiblecapitals ρ and ι , the c > 1 tool has a defining influence onthe relative magnitudes of intangible and natural wealths ι−,ρ−, effectively re-scripting the intermediate distribution of collective welfare without altering the bounds, unavailableunder the genetic c = 1 order. The undisputed relevance of re-distribution in human and institutional intangible welfareof education, health, and constitutional governance over self-seeking growth and GDP measures are all too evident forserious consideration.

A APPENDIX

A.1 Initial and Final topologies

Recall that (i) for f : X → (Y,V ) the preimage or initial topology of X generated by f and V is

IT{ f ;V }, {U ⊆ X : U = f−(V )∀V ∈ Vcomp︸ ︷︷ ︸Cause←Effect

} (24a)

(ii) for f : (X ,U)→ Y , the image or final topology of Y generated by U and f is

FT{U ; f}, {V ⊆ Y : U = f−(V )∀U ∈Usat︸ ︷︷ ︸}Cause→Effect

(24b)

where Usat, Vcomp are the saturations of open sets of X and the components of the open sets of Y when these are alsoopen in X and Y ; plainly, Usat ⊆ U and Vcomp ⊆ V . Hence the topology of (X , IT f ;V ) consists of, and only of, thef -saturations of all open sets of X , and the open sets of (Y,FTU ; f ) are the f -images in Y of the f -saturated open setsof X .

Combining Eqs. (24a), (24b), yields

IFT{U ; f ;V }, {U ⊆ X ,V ⊆ Y : U = f−(V )∀ (U ∈Usat)(V ∈ Vcomp

)︸ ︷︷ ︸}Cause�Effect

(24c)

that clearly reduces to a homeomorphism for bijective f : (X ,U )→ (Y,V ) with a well-defined inverse f−1. As shouldbe transparently evident from (24c), the initial-final problem is one of cooperative-adversity with the coarsest initial

45

topology U on X representing the increasing entropy of dispersive allocation initiated by the inverse problem, and thefinest final topology V of decreasing entropy, exergic gravitational growth on Y from the direct problem, Sec. 1. Thusin Fig. 5a, the fixed points of f 2N , N = 1,2,3 are equivalent (periodic points) in the sense that, in (ii) for example,00 ∼ 01 ∼ 10 ∼ 11 as they lie on the 22-periodic cycle. Taking the collection of these periodic points to represent amaximal saturated open set of X , the f -image f13 and f24 emergence of new structures from f12 is further textured intof15, f26, f37, f48 in (iv).

A.2 Mendel’s particulate dynamics

(i) Mendel’s Rule of Dominance

(♂ ↑) allele Sperm(♀ ↓) allele r↓ r↑

Egg R↓ R↓r↓ R↓r↑

R↑ R↓r↓ R↑r↑Homozygous parents RR/rr→ Hetero-

zygous Rr smooth dominance.

(ii) First Law of Segregation

(♂ ↑) allele Sperm(♀ ↓) allele R↓ r↑

Egg R↓ R↓R↓ R↓r↑

r↑ r↑R↓ r↑r↑Heterozygous smooth parents RR→

1 RR pure smooth : 2 Rr impure smooth :1 rr pure wrinkled genotypes in an overall

3 : 1 dominant : recessive ratio

S : R Smooth, r wrinkledR r

R RR Rrr rR rr

⊗

C : Y Yellow, y greenY y

Y YY Yyy yY yy

=

(iii) Second Law of Independent Assortment

Gamete RY Ry rY ry

RY RRYY RRYy RrYY RrYyRy RRyY RRyy RryY RryyrY rRYY rRYy rrYY rrYyry rRyY rRyy rryY rryy

(i) Rule of Dominance. In a pair of genes of diploid organisms, that which is expressed in the phenotype is the dominant gene,the other suppressed in the phenotype is recessive. The dominant “stronger” trait shows up when the dominant allele is present,

the “weaker” recessive trait is expressed only when the dominant is absent.(ii) First Law of Segregation. Independent segregation of alleles at a single locus. The two alleles of a gene pair for any traitsegregate separately into gametes so that half the gametes carry one allele and the other half the other allele — the offspring

receives only one allele from each parent.(iii) Second Law of Independent Assortment. Independent assortment of alleles at multiple loci. During gamete formation,segregation of alleles of the different genes is independent of each other — there is no mixing between the genes for different

traits, they remain separate entities.

Figure 13: Mendel’s Laws of Particulate Dynamics of dominant and recessive alleles that retain their identities through generationseven if phenotypically unexpressed in any one generation.

In the matrix linear setting of R “smooth” and r “wrinkled” parent alleles, R and r produce only Rr heterozygousgenotypes of smooth seeds which segregate into gametes with half carrying one of the alleles and the other half the otherallele which corresponds to the nonlinear entanglement of the logistic 22 cycle, Fig. 5a(ii). The three possible gametes— RR homozygous dominant, Rr/rR heterrozygous dominant, and rr homozygous recessive — in 3 : 1 ratio producesthe diploid cross of two independent traits as the tensor product ⊗ of the individual traits. Thus the (3 : 1)⊗ (3 : 1) crossS ⊗C of shape R and colour Y results in the degeneracy of the alleles into 4 groups. (a) at least one R, one Y dominant(RRYY,RRYy,RrYY,RrYy,RryY,rRYy,rRyY,rRYY,RRyY), (b) at least one R dominant (RRyy,Rryy,rRyy), (c)at least one Y dominant (rrYY,rrYy,rryY), (d) none dominant (rryy) for the classical 9 : 3 : 3 : 1 ratio of genotypesresulting from the independent 3 : 1 segregation of the two phenotypes. Clearly this reductionist expression has little tooffer by way of the integrationist manifestation of holism.

A.3 Daisyworld of black and white daisies

ONLY TWO TYPES OF DAISIES GROW IN PLANET DAISYWORLD.

46

Black Daisies on Ab fraction of available land of total area A = 1White Daisies on Aw fractionAg = 1−Ab−Aw fraction of bare groundGrowth rate of daisies, per unit area, per unit time:

βi(Ti) = 1−(

Tt −T+T−

)2

=

0, Ti < Tc = 278K1, Ti = T+; T± = 1

2(Th±Tc) = 295.5/17.5K0, Ti > Th = 313K

(25a)

γ = 0.3, death rate per unit timeTb,g,w : Local temperatures of black daisies, bare ground, white daisiesL : Variable luminosity of Daisyworld’s sunαb,g,w : Albedo, Reflected light/Incident light.α = αbAb +αgAg +αwAw = 0.5−0.25(Ab−Aw), average albedo of the planet, withαb = 0.25, αg = 0.5, αw = 0.75

Differential Equation. Popultion ecology model

dAi

dt= Ai (Agβ (Ti)− γ) , i = b,w (25b)

Effective Planet temperature. Radiation of the sun incident on the planet equals the total of radiation absorbed by theplanet and that re-radiated back to space

T 4 =SLσ

(1−α) , (25c)

where σ = 5.67×10−8 W-m−2-K−4 is the Stefan-Boltzmann constant, and S = 917 W-m−2.Local Temperature of Daisies. q = 2.06× 109 is a constant measure of the degree of redistribution of solar energy— q > SL/σ heat flowing from low to high temperature a physical impossibility, q = 0 local temperature of each areacovered by white daisies, black daisies and bare ground are all equal to the mean planetary temperature. For i = b,w, let

T 4i = T 4 +q(α−αi), for q = 2.06×109K

= T 4 +q(0.5−0.25(Ab−Aw)−αi) (25d)

that satisfies ∑i=b,g,w AiT 4i = T 4.

No Species, Bare Planet. Ab,Aw = 0, Eq. (25c) gives

Tg =4

√SL2σ

= 300L0.25 (26)

the planet heating up with increasing luminosity.Single Species. Aw = 0, Ab > 0 or Ab = 0, Aw > 0; i = b(+), w(−)

T 4 =SLσ(0.5±0.25Ai) [Eq. (25c)] (27a)

Ti = T+±T−

(A+ γ−1

A−1

)1/2

, Tb > Tw, [Eqs. (25a) steady state, (25b)] (27b)

T 4i =

SL2σ± q

4± Ai

4

(SLσ−q), i = b(+),w(−) [Eqs. (25d), (27a)] (27c)

The last two equations can now be solved for Ti with A = (8T 2−4728T +696847)/(8T 2−4728T +696112) to give

Lb =32sT 6−18912sT 5 +2784448sT 4 +735qs

24ST 2−14184ST +2089071S(28c)

Lw =32sT 6−18912sT 5 +2784448sT 4−735qs

8ST 2−4728ST +695377S(28d)

47

Both Species. Ab, Aw > 0, βb = βw = γ/Ag [Eq. (25b)]

Tb +Tw = 2T+ [Eq. (25a)] (29a)

T 4b +T 4

w = 0.5q [Eq. (25d)] (29b)

Considering one of the two solutions Tb = 300.5 of the pair as the cause and the other Tw = 290.5 as the effect, thesecoupled algebraic equations model Cause� Effect feedback that being non-dynamical, however, require exogenous datato complete the dynamics. This is provided by [Saunders, 1994]

β := βb = βw = 0.919; Ab +Aw = 0.673; α = 0.668−0.5Ab, Ab =0.902−0.664L

L−0.127

for the equilibrium temperature

T = 285.143 4

√L

L−0.127(30)

of the Daisyworld as a function of the luminosity. Lovelock’s Daisyworld is therefore is thus a static world of alge-braic cause � effect feedback without the characteristic dynamics that distinguishes the self-organizing emergence ofcomplexity and holism.

Acknowledgement. It is a pleasure to record the very constructive electronic dialogue with Dr Karl-Henrik Roberton the Framework for Strategic Sustainable Development (FSSD) that helped disentangle some of its finer points withrespect to this work. My appreciation also of the congenial and constructive atmosphere at the Department of MechanicalEngineering and Nuclear Engineering and Technology Programme at IIT Kanpur and to Dr Keshab Gangopadhyaya fortheir association during the initial stages of this work.

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