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The basis condition of the ecosphere from which all life evolves is the existence of Earth and the Sun. Earth and the Sun form because of the conservative gravitational and nuclear strong forces that are universal laws described by physics theory. They are conservative in that the energy contained by the interaction between properties of matter and the fields of these forces is conserved. No irreversible entropy is generated by the interaction of conservative force fields and matter. The gravitational force results in particles of matter being pulled together through inelastic collisions into collections of greater density to form Earth and the Sun. The nuclear strong force results in atoms of hydrogen being pulled together through inelastic collisions to fuse into helium within the Sun as it collapses under the gravitational force. Calculations of the changes in entropy of the matter that collapses from a cloud of hydrogen to form the Sun and the matter that collapses from a debris field of heavier elements to form Earth reveal that the collapsing matter has a net negative change in entropy. ² As the matter collapses, the heat that is generated and expelled from Earth and the Sun spreads into space and results in a larger net positive change in entropy in the surrounding space than the net negative change in entropy of the matter that forms Earth and the Sun into relative islands of order, thus not violating the second law of thermodynamics (Wallace, 2010; de Souza et al., 2015; Greene, 2021, page 63 and footnote 14).

The generation of heat and the net positive change in entropy correlates with the conservation of momentum theorem that dictates that when inelastic collisions occur, mechanical energy that is typically conserved in the interactions between matter and the conservative gravitational and nuclear strong force fields is lost to heat-generating mechanisms in a proportion that conserves the momentum of matter (see Supplementary Presentation 1 : Pancosmorio Theory Classical Mechanics Clarifications for discussion of Conservation of Momentum and Entropy). If the process ends here, the result is the Sun at a high temperature, the Earth at a lower temperature, and surrounding space at an even lower temperature, with heat passing from the Sun to Earth and space and from Earth to space. This simplest form of the movement of energy in the form of heat from a high temperature source to a low temperature sink produces maximum specific entropy ³ (Figure 1A).

However, the process does not end there. The result of the formation of Earth is a gravity well. This gravity well has a spherical rock lithosphere and core at its center with a hydrosphere of water and an atmosphere of gases pulled against it. The force of gravity pulling against the water and gases results in normal forces of the lithosphere pushing back against the hydrosphere and atmosphere; these normal forces fundamentally exist because of the conservative electrical force of repulsion between atoms that exceeds the force of the gravitational field packing the atoms together. It is the pull of gravity and the push of such normal forces that result in the phenomenon of the apparent force known as weight (see Supplementary Presentation 1: Pancosmorio Theory Classical Mechanics Clarifications for discussion of The Apparent Force of Weight).

Weight resulting from the combination of gravity and normal forces produces an important effect. The weight of layers of water and atmosphere piled from the lithosphere to the top of the hydrosphere and atmosphere result in a gradient of depth pressures, with depths closer to the lithosphere having greater pressures. These material spheres, their depth pressures, and the solar insolation falling on the interfaces between the material spheres result in convective forces driven by temperature differences and in the latent heat of evaporation of water from the hydrosphere. Solar power is used to overcome gravity through the gravitationally driven conservative buoyancy force lifting masses of air and evaporated water through the pressure gradient and higher into the atmosphere (see Supplementary Presentation 1: Pancosmorio Theory Classical Mechanics Clarifications for discussion of Buoyancy as a Conservative Force). Gravitational potential energy of the rising air and water vapor increase, such that when the air and water vapor expel heat in the upper atmosphere (and positive specific entropy) into space, the gravitational potential energy generates the power to return each unit of mass to its elevation of origin.

The solar insolation and gravity power sources, the air pressure gradient, and the conservative gravitational and buoyant forces result in a gravitational heat engine (Figure 1C) that drives the rising and falling actions to produce the orderly gravitational dissipative structures of the water cycle and barometric weather cells. Forming the material trapped in the gravity well of Earth into the orderly structures of heat engines results in the material having another net negative specific entropy change. This moves Earth further away from thermodynamic equilibrium. However, the orderly structures are also dissipative structures in that they move heat through the Earth ecosphere and out into space. If the gravitational heat engines only involved an ideal gas atmosphere as a working medium, then the net change in the entropy of the heat captured from solar insolation and then expelled to the space heat sink would be zero, as with a Carnot cycle (Figure 1E). However, considering the atmosphere is not an ideal gas, there are inelastic collisions (i.e., friction) occurring between particles as gravitational potential energy converts to kinetic energy, and kinetic energy is subsequently lost to heat through the conservation of momentum in inelastic collisions. This inefficiency steals some of the heat input from solar insolation away from performing useful work, resulting in the generation of extra heat that is lost to space. It is this extra heat loss that results in a net positive entropy change for the heat transfer of solar heat passing through the material of Earth and out into space that adds up over time and exceeds the net negative change of entropy for the material formed into orderly dissipative structures on Earth. There is a total positive change in entropy for the overall Sun-Earth-space system.

We conceive that the conservative gravitational field acts as an ideal pump (Figure 2A) that neither depletes an external energy source nor generates entropy with its pumping action that uses a conservative force. We postulate that the action of the ideal pump of the gravitational heat engine results in a semi-reversible cycle. In effect, this means that the gravitational heat engine is self-restoring even as the working medium used by the heat engine loses kinetic energy to heat during non-conservative inelastic collisions between the non-ideal-gas particles of the atmosphere.

As time passes, Earth becomes dominated by geophysical and biogeochemical cycles capturing available resources into gravitational and electrochemical dissipative structures that are more orderly and result in a net negative specific entropy change for Earth, moving it further from thermodynamic equilibrium. Electrochemical interactions require proximity of constituents and availability of heat, so the development of electrochemical heat engines proceeds and grows as the right combinations of elements and molecules are brought together by the geophysical cycles involving gravity, water, weather, and heat from solar and geothermal power. We postulate that electrochemical heat engines are pairs of irreversible endothermic and exothermic chemical reactions that sustain each other in a semi-reversible cycle (Figure 1D) with the conservative electrical force acting as an ideal pump. The irreversibility of the chemical reactions is referring to the heat that is required to initiate the reactions and the mechanical energy that is lost to inelastic collisions when atoms are kinetically pulled together (i.e., chemically bonded) or kinetically separated (i.e., bond breaking). Whereas an endothermic chemical reaction combines various atoms and molecules into a larger molecule, an exothermic chemical reaction breaks that larger molecule back down into the original atoms and molecules, thus making that material re-available for the recurrence of the endothermic chemical reaction and the semi-reversible cycle. The electric field is conserved in this cycle, with its full energy continuing to be available to govern the cycle, just as with the gravitational field.

Defining gravitational heat engine cycles and electrochemical heat engine cycles as being semi-reversible is to differentiate them from both a completely reversible ideal Carnot cycle (Figure 1E) and a completely irreversible heat engine cycle in which all applied forces are non-conservative (Figure 1B). The implication of the first and second laws of thermodynamics is that naturally occurring self-restoring heat engines are more efficient than irreversible forced heat engines, resulting in a semi-reversible cycle that generates the entropy of heat transfer at a lower rate than an irreversible cycle relative to equivalent useful work performance. Self-restoring heat engines utilize ideal pumps, described earlier. They do not require an external heat engine to drive them as is required by the pump of an irreversible heat engine cycle (Figure 2B). They also do not require maintenance due to wear, nor do they suffer from ultimate failure. The irreversible heat engine’s pumping force, the pump external power source, and the pump’s wear and failure are more entropic than the semi-reversible cycles of self-restoring heat engines.

The transition away from thermodynamic equilibrium is explained in Table 1 as an exergy-building process of the Universe. As entropy generation rate of the solar heat transfer through the material of Earth and out into space drops with the capture of Earth material into gravitational and electrochemical dissipative structures, the additional energy available for work results in more exergy captured in the building of more dissipative structures. The exergy captured as useful work in upstream dissipative structures is utilized as available work energy to build the heat engines of new downstream dissipative structures. The buildup of lengthening networks of self-restoring heat engines as more Earth materials are captured into cycles results in an increase in the net negative change in specific entropy of Earth as it transitions further away from thermodynamic equilibrium. This forms the basis of sustainable growth of an ecosphere on Earth.

The process of solar insolation power pouring down over a long period of time on all the material present in the gravity well of Earth results in five exergy-building phenomena that engage increasingly more material and energy in adding to available work energy, summarized in Table 2. We postulate the Earth ecosphere builds in a manner that maximizes three traits: self-restoring order characterized by dissipative structures conditions present in the prebiotic Earth, capacity characterized by solar power conditions pouring down on the surface area conditions of Earth, and organization characterized by network vitality conditions and functional diversity conditions of the resulting biotic ecosystem. These phenomena and the empirical data collected for real ecosystems have been proposed to be observational evidence for a central hypothesis of ecological thermodynamics theory. This hypothesis was first formulated at a workshop in Møn, Denmark, August 1993, by J. J. Kay, S. E. Jørgensen, H. F. Mejer, S. N. Nielsen, and E. D. Schneider as a proposal for a fourth law of thermodynamics (Jørgensen, 2002, p. 164). Jørgensen et al. (2016, p. 58) states the latest form of the hypothesis:

Jørgensen et al. (2016, p. 54) identifies three biological growth forms of ecosystem development under the ecological thermodynamics hypothesis, summarized in Table 3: increasing the amount of available work energy as stored biomass Eq. 4, stored genetic information (Eqs. 5 through 7), and total system throughflow in the growth of the network as whole (Eq. 8). We describe these as three basal growth forms that enable the increase in self-restoring order and capacity of a basal ecosystem through the natural selection of the organization that moves the entire ecosystem further from thermodynamic equilibrium. Basal human populations in the form of hunter-gatherers are a result of and are sustained by this basal ecosystem. The basal ecosystem provides the minimum human life support.

Humans capitalize on these types of growth forms to access basal exergy sources within the ecosphere to augment human society above what is basally produced by the ecosphere under basal dissipative structures conditions, power conditions, network vitality conditions, functional diversity conditions, and area conditions. By so doing, humans have utilized what we describe as three augmentational growth forms, a known and observed human activity, that are corollary to the basal growth forms described by Jørgensen et al. ⁴ This corollary is provided in Table 3. Using the basal ecosystem, humans have built their augmentational ecosystem under augmentational power conditions, network vitality conditions, functional diversity conditions, and area conditions. The self-restoring order, capacity, and organization of the basal ecosystem provides a fundamental basis for sustaining the capacity and organization of the human augmentational ecosystem.

If the current state of human civilization on Earth were to be placed in an ecosphere with lesser basal self-restoring order, capacity, and organization than present on Earth, then humans would have access to less exergy in an ecosphere that is closer than Earth to thermodynamic equilibrium. It would be like expecting your car to run with a cell phone battery. The consequences that can be drawn from the preceding discussion are that human civilization would decline to a level of basal ecosphere self-restoring order, capacity, and organization that is sustainable by the available exergy. The implication in terms of the three augmentational growth forms in Table 3 is that decay of exergy in the human augmentational ecosystem would result. Over time and in an uncontrollable and unpreventable way, supply chains would disappear, market resources would be depleted, advancement in human pursuits would be disrupted, social and governance systems would falter or collapse, human population numbers would decline, genetic diversity in the human genome would be lost, average human individual biomass would decrease, and human knowledge and understanding would be forgotten.

The answer to sustaining the human enterprise as it tries to expand into space has at its heart an understanding that such expansion cannot be in such a way that humans decline in the long term. In the short term, such a reversal of growth would appear as failed settlements. A failed settlement could be an outpost where the humans have lost Earth support, forced to survive on an insufficient production of basal ecosystem exergy. Over time, such an isolated settlement of humans could deteriorate in ways discussed in the previous paragraph. The answer of how to sustain humans in space requires an understanding of the basal ecosystem of Earth and an ability to duplicate the conditions of that basal ecosystem in space. This should be the objective of environmental control and life support (ECLS) systems used in space.

The approach to date that has been used for providing ECLS for humans in space has been completely augmentational. The volume of spacecraft containing humans is minimized to reduce the size of the space that must be controlled. Technology generates the resources that humans need. Such technology is also necessarily limited in size and uses irreversible forced heat engines designed by humans that have high power densities resulting from the concentrated consumption of energy and a concentration of non-conservative forces that are added to drive cycles (e.g., real pumps). Compared to the basal self-restoring heat engines on Earth that provide the basal human life support, the use of technology for life support results in a greater entropy generated per unit of energy consumed to drive the cycles. It also results in the need for maintenance against wear, as well as the eventual failure of the technology due to entropy. Augmentational human technology is ultimately non-self-restoring. Such augmentational means of life support are inherently unsustainable by themselves. A basal ecosystem must be actively producing exergy that an augmentational ecosystem needs to operate. An augmentational ecosystem in space requires the exergy production of Earth—or someplace like Earth.

To better comprehend the difference between augmentational systems and basal systems beyond the theoretical discussion of conservative versus non-conservative forces, entropy, and exergy, consider everything on Earth that does not require human work or input. As an example, breathing is a passive activity for humans. The production of oxygen by the Earth ecosphere is performed without active human involvement. Basal life support on Earth requires no effort by humans for it to be available to humans. Now consider the amount of human effort required to make a technological (i.e., augmentational) system operable and indefinitely available off planet Earth, where humans would not have a basal ecosphere from which to passively draw oxygen. Generating air to breath becomes an active working effort to operate and maintain the augmentational systems required to create the oxygen and scrub the air of the exhaled carbon dioxide. The maintenance of such systems includes a support infrastructure of industry and knowledgeable humans on Earth to continue to provide repair parts and handle issues of malfunction, part and technology obsolescence, and supplier market changes as they occur. The operation also requires power technology and possibly fuel, both of which come with their own support infrastructures. All the oxygen generation technology, power technology, human societal effort, and industry that would be needed to just breath in space would be new in our lives as such. How much extra, non-passive support would be required?

And that is only the oxygen.

The nature of non-self-restoring augmentational systems that utilize irreversible cycles is that they require self-restoring basal systems that utilize semi-reversible cycles to be sustained. This is known as strong sustainability (Pelenc et al., 2015; Maiwald, 2023). The International Space Station would not be able to function without ground support from Earth and the basal ecosystems of Earth to support all of it. Moving further out into space, ground support from Earth becomes more difficult, more costly, riskier. This suggests that the weak sustainability of technofixes (Huesemann and Huesemann, 2011) as has been the to-date approach for deep-space missions is risky for human life. However, solutions that maximize self-restoring elements in a basal ecosystem approach, even if they do not have all that are present on Earth, might reduce the risk of failure.

These considerations suggest what Pirni (2016) calls an “anthropology of limit” to the human endeavor of migration into and habitation of space. Holy-Luczaj and Blok (2019) recognize the need of human life to be conative to the natural environment and the natural environment to be responsive to human life to sustain the integrity of human function on Earth. They raise the question of whether technology, biomimetic technology, or hybrids can be used to improve such conativity and responsiveness. Nielsen (2006) posits that eco-mimetic technology rather than biomimetic technology is needed to achieve sustainable production in human society, but that more studies are needed to understand how to use the basal properties of ecosystems in societal systems. The attempt to move life into space, effectively presenting life with a more extreme environment than on Earth, extends these ontic and ontological questions to space. The evidence suggests that the ability of humans and Earth-life to adapt to space is problematic, with the use of technology to simulate basal Earth life support also having challenges. The trade-off of trying to establish a basal life support system in space is that it would effectively need to be like Earth. The question is whether that is possible? Before we consider the possibility, we need to understand what it means to have a location in space outside of Earth be “like Earth.” The ideas presented in this paper extend the science of ecological thermodynamics theory into space.

The results of research into the beforementioned questions are presented in Section 2 as a pancosmorio theory of human sustainability. The theory is developed based on the science of ecological thermodynamics theory using the methodology of abductive reasoning (Pfister, 2022). A description of the theory (Section 2.1) is provided that has as its factual consequent: i) there are conditions from which human life has evolved, ii) such conditions are required to sustain human life at its current level of growth, and iii) the availability of such conditions to humans defines the limit of their world. This is followed by two propositional antecedents and nine conditionals that can be abductively reasoned from this factual consequent in support of the propositional antecedents. Four analytical models of levels of sustainability in space (Section 2.2) and five testable pancosmorio hypotheses (Section 2.3) are provided. Section 3 contains a discussion of the elements of the theory, referring to the supporting body of research in the physical, ecological, and social sciences. It also contains a new quantitative method of human sustainability that is used in the theory. The methodology builds on and formalizes the proposals in the perspective presented by Irons and Irons (2021), presenting a method for quantifying the human sustainability of any context in which humans are a part, including on Earth or in space. Conclusions are drawn in Section 4 on the application to sustainable development and the potential for the use of a balanced sustainability approach to solve the challenges presented by the theory. Conclusions are also drawn regarding implications for the Fermi paradox.

The pancosmorio ⁵ theory of human sustainability, hereinafter referred to as the pancosmorio theory, has one factual consequent that comes from ecological thermodynamics theory. It is supported by two propositional antecedents and nine conditionals, described in Sections 2.1.2 and 2.1.3. Discussion of the supporting science for each element of the theory is presented in Section 3.1 through Section 3.4.

The conditionals of the theory are interpreted as conditions that an ecosphere separate from Earth must have for a human base or settlement to be sustainable. Any such ecosphere that has these conditions to a limited extent will have limited human sustainability. There are four levels of sustainability that are analytically modeled from the pancosmorio theory. Table 4 summarizes the application of the conditionals to the analytical models. Discussion of the supporting science for each model is presented in Section 3.5 and in Supplementary Presentation 3 : Pancosmorio Theory Sustainability Analytical Models.

Out of this theory, we provide five testable hypotheses. These hypotheses will be testable by the results of human missions, bases, and settlements as they migrate out into the Solar System and experience unplanned events of loss of productivity, blight, diversity loss, and cascade failure. Alternatively, failure mode tests can be designed and terraformed test platforms built in extreme environments on Earth or in space to test these hypotheses without putting life at risk. The tests for falsifiability of these hypotheses are summarized in Table 5. The tests use the quantitative method of human sustainability. Discussion of the supporting science for each hypothesis and this method are presented in Section 3.6.

The conditions required to sustain humans are empirically and factually associated with Earth where life evolved and can be determined in contrast to observable space where human life does not exist. Life on Earth is a factual consequence of the existence of these conditions. This is the fundamental basis of ecological thermodynamics theory. The pancosmorio theory expands upon the ecological thermodynamics theory by explaining what this means for human life and other Earth life to exist in any location in space.

The pancosmorio theory is developed using scientific philosophy and the theory of abduction (Pfister, 2022) (Figure 3). Abductive reasoning is necessary to infer a broader explanation of the existence of Earth and its ecosphere. When proven inductively by hypotheses and experiments, such a broader explanation can then be used deductively to apply to any location where humans attempt to establish an ecosphere outside of Earth. Risk to human life in the application of this theory is best mitigated by use of analog test platforms either on Earth or in space that do not involve human life or that have safety measures to protect humans. Such analogs could then be used as inductive experimental proofs of the pancosmorio hypotheses.

Research on Earth’s energy budget (Kiehl and Trenberth, 1997; Loeb et al., 2009; Trenberth et al., 2009) has determined that the average amount of power going into Earth’s atmosphere from solar insolation is 341 W/m². Of this amount, 102 W/m² is reflected from clouds, atmosphere, and snow and ice back into space. This means that 239 W/m² from solar insolation enters the ecosphere network and becomes exergy. Of the 239 W/m², 175 W/m² is converted into direct heating of the atmosphere, evaporation and entrainment of water in the atmosphere, convection, and turbulence. Except for the amount that is used for the latent heat of evaporation of water, 80 W/m², this power is used to overcome gravity, with gravitational potential energy stored in the gravitational field generating the power to return the air mass and water to its elevation of origin. Thus, the rate of gravitational energy input to the ecosphere through self-restoring gravitational heat engines is (175–80) W/m², or 95 W/m², equivalent to the amount of power from solar insolation that is required to lift the air and generate the gravitational potential energy. Thus, we arrive at an estimate of energy input rate per unit area of (239 + 95) W/m², or 334 W/m².

There are other functional systems of note that generate power and provide vital functions to Earth life. The rotation and the resulting diurnal warming and cooling of the Earth, water, and air result in weather patterns that generally move west to east. An annual revolution of Earth around the Sun, a tilt of the Earth axis relative to its plane of revolution, and the revolution of the Moon around Earth also result in seasons and tidal forces. The lithosphere is heated by latent heat of the original gravitational collapse of Earth as well as ongoing energy input to the lithosphere from the tidal forces. Earth is protected by a magnetosphere from the solar wind that would otherwise generate high energy radiation on Earth and strip away water and gases from the atmosphere and hydrosphere. The magnetosphere is generated by an electromagnetic dynamo of circulating and electrically charged molten liquid matter in the core of Earth also formed out of the original gravitational collapse. Earth rotates on an axis, resulting in a diurnal variation of solar insolation. All of these dissipative structures are a result of the gravitational formation of Earth in orbit of the Sun. They are necessary to sustain life and must be provided for life when outside of Earth.

Gravity is also needed to sustain the biochemical and biophysiological function of humans and other biotic lifeforms. The mostly anecdotal and observational results of life-science research in gravitational orbit around Earth (e.g., see example reviews provided by Kandarpa et al., 2019; Kordyum and Hasenstein, 2021; Bijlani et al., 2021) provide evidence that living things do not function in the same way or at the same level of performance and efficiency in an inertial free-fall reference frame where there is gravity without apparent weight and centripetal force without apparent centrifugal force. Even with a space capsule pressurized to the same level of atmospheric pressure that exists at altitudes where humans live on Earth, the lack of weight and centrifugal force means that there is no fluid pressure gradient within the biotic organism body (see Supplementary Presentation 1: Pancosmorio Theory Classical Mechanics Clarifications for discussion of Forces on the Human Body in the Free-Fall of Space), which is a likely factor in the dysfunction of the human body and other organisms in space.

Our era of the Anthropocene is characterized by a contribution of humans to the total system throughflow of the Earth ecosphere in the burning of fossil fuels that are the stored exergy of past solar insolation being rerouted through the ecosphere. Based on the research of Syvitski et al. (2020), this augmentational power conditional is estimated to be 1900 W per capita of the human population on Earth. This is power that is in addition to the basal power conditional. Compared to the basal power required just to establish and maintain the natural part of the ecosphere, this might seem like a minor amount. However, it adds up quickly as the local population rises.

The objective of organization is a network that matches that of an equivalent Earth ecosystem in persistence and resilience to achieve human sustainability. As noted in Section 3.2, one element of persistence and resilience is an ongoing supply of sufficient power. That power must then be utilized by the ecosphere. The intuitive thinking has been that maximized biodiversity and maximized thermodynamic efficiency are requirements for sustainable power utilization. Solid theoretical justification is ambiguous at best for a positive relationship between biodiversity and sustainability (McCann, 2000; Loreau et al., 2001; Loreau and de Mazancourt, 2013). Ulanowicz (1997, Ulanowicz, 2002, Ulanowicz et al., 2008, Ulanowicz, 2009, Ulanowicz et al., 2014, Ulanowicz, 2018, Ulanowicz, 2020) has established by theoretical development and correlative, empirical evidence of Earth ecosystem network data that there is a network variety ( H ) comprised of a network constraint ( A ) and a network flexibility ( Φ ). In total capacity ( H ∙ T S T ; see Table 3 for definition of TST), the network provides ascendency ( A ∙ T S T ) and reserve ( Φ ∙ T S T ). Functionally, ascendency is a measure of the throughflow that is passing through the most stable of the network links and reserve is a measure of the throughflow passing through all the other links with a greater diversity of links resulting in a greater reserve. The relationship between ascendency and reserve is characterized by Eqs 10 through 13. H = − ∑ i = 0 N ∑ j = 1 N + 1 T i j T S T ∙ ln T i j T S T (10) A = ∑ i = 0 N ∑ j = 1 N + 1 T i j T S T ∙ ln T i j ∙ T S T ∑ j = 1 N + 1 T i j ∙ ∑ i = 0 N T i j (11) Φ = − ∑ i = 0 N ∑ j = 1 N + 1 T i j T S T ∙ ln T i j 2 ∑ j = 1 N + 1 T i j ∙ ∑ i = 0 N T i j (12) H = A + Φ (13)

Functional diversity of the ecosystem is characterized by a normalized ascendency (a; a measure of the degree of organization of the network) between the values of 36% and 46% and a normalized reserve ( ϕ ; a measure of the degree of freedom of the network) between the values of 56% and 64%. This normalized reserve enables persistence that presents as a network reliability against external disturbances (Ulanowicz, 2009; Ulanowicz, 2020). Normalized ascendency and normalized reserve are provided by Eqs 14, 15. a = A / H (14) ϕ = Φ / H (15)

The normalized ascendency enables resilience that presents as a network robustness and is further characterized by a window of vitality (Ulanowicz, 2009; Ulanowicz, 2020). The window of vitality frames network effective connectivity (c), a measure of the weighted average number of links through which the throughflow is passing, between the values of one and three and the network effective number of roles (r), a measure of the weighted average number of trophic levels through which the throughflow is passing, between the values of 2 and 4.5 (Ulanowicz et al., 2014; Ulanowicz, 2020). The relationship between them is characterized by Eqs 16, 17. c = ∏ i = 0 N ∏ j = 1 N + 1 ∑ j = 1 N + 1 T i j ∙ ∑ i = 0 N T i j T i j T i j / T S T (16) r = ∏ i = 0 N ∏ j = 1 N + 1 T i j ∑ j = 1 N + 1 T i j ∙ ∑ i = 0 N T i j T i j / T S T (17)

The assumption is that there must be a diversity of abiotic and biotic resources equivalent to a matching Earth ecosystem. Modeling and comparison to real ecosystem networks provides key parameters to consider in building the network. The goal is to achieve a quantitative capacity ( H ∙ T S T ) that is equal to that of the equivalent Earth ecosystem with a 40%–60% balance of ascendency to reserve and the network within the window of vitality. The pancosmorio theory asserts that the establishment of the dissipative structures, power, and area conditionals provided for the basal system (see Section 3.4) ensures that sufficient self-restoring order and capacity can support the network. How the network is built utilizing functional diversity will determine whether it is within the window of vitality.

How network vitality and functional diversity are used to build an ecosystem matter. Experiments performed to-date of human-designed ecosystems that are closed to a complete or partial (quasi-closed) extent from the ecosphere of Earth result in local ecosystem dysfunction, even on Earth. Biosphere 2 (Allen et al., 2003; Gitelson et al., 2003, page 52) was an example of attempting to contain a high diversity within a closed system without proper network organization; biomes requiring different environmental conditions were juxtaposed in close proximity due to insufficient area, likely resulting in disturbances of proper throughflows of the biomes' networks. Biosphere 2 also failed to consider the impact of augmentational human systems and technology and their integration into the basal network.

The establishment of a local ecosystem in space likely requires the formulation of an ecosphere network in a managed stepwise fashion. Irons (2018) suggests a boot-strapping effort to establish three zones (i.e., a habitation zone, an agricultural zone, and an ecological buffer zone) using expedited primary succession, competitive redundancy, and ecological service reservoirs. This might be sufficient to get things started but would eventually have to proceed to a proportional fullness of network as exists in the Earth ecosphere. The key shown in Figure 4 is to aggradate the augmentational network with the basal network in a way that does not result in excessive contribution of the augmentational network to the effective connectivity and the effective number of roles. The augmentational network contribution to the combined network must also keep the combined normalized reserve between 56% and 64%.

The effort required to set up the full set of basal and augmentational ecosystems with optimum network vitality and functional diversity will involve a detailed level of environmental management to establish patches and populations of biotic species and communities of biotic interactions within local, regional, and biome-wide ecosystem architectures of abiotic accumulations and flows. This must be done in a way that leverages the established dissipative structures. Once all abiotic and biotic resources are established in appropriate locations and quantities, the sufficient levels of temperature, atmospheric pressure gradient, apparent weight, and physical and biogeochemical cycles provided under the dissipative structures conditional will tend to naturally drive interactions between producers and consumers as evidenced by their function in the Earth ecosphere. These interactions create nodes and links of the network. And as more interactions engage, the network expands across the landscape and builds. Competition with sufficient management should drive the ecosystem into the window of vitality with the proper balance of the capacity between the ascendency and the reserve.

The area conditionals are at the crux of the relationship of all the conditionals. The power and area conditionals together determine the ecosphere capacity. The power conditional is in terms of power per unit area, therefore the total area condition of the ecosphere location in space will drive the total power condition. Diamond (1975) notes that when the area of an island or isolated ecosystem is not sufficiently large to support the diversity of biotic species, there will be local species extinctions that occur naturally. The body of work following Diamond’s 1975 paper has confirmed this phenomenon (e.g., Connor and McCoy, 1979; Saunders et al., 1991; Caughley, 1994; Debinski and Holt, 2000; Margules and Pressey, 2000; Sayer et al., 2013). Thus, the area conditional also impacts functional diversity and the ecosphere organization.

The lower limit for the basal area conditional of 60,500 m² per capita ensures the current basal evolutionary and adaptive state of humans can be supported by the capacity and organization of the ecosphere. It is based upon the surface area (including water) of Earth of 196.9 million mi² divided by the current population of Earth of 7.837 billion equaling 65,100 m² per capita, followed by subtracting the augmentational area conditional of 4,600 m² per capita.

The lower limit for the augmentational area conditional of 4,600 m² per capita is based upon the population of the United States of 331.9 million and the combined urban and agricultural area of the United States of 63,400 mi² and 530,400 mi², respectively (National Land Cover Database, 2016). Agricultural land is included with urban land in the augmentational area conditional considering that human agriculture is augmentational. Human hunting and gathering for food are basal and supported by the basal area conditionals, allowing for human survivability when augmentational systems fail.

The combined area required to support one person is the size of a square 255 m on a side. The per capita land area might seem excessive. It is assumed that the level of human augmentation at any point in the history of Earth is efficiently adapted to the available basal and augmentational surface area on Earth based upon that time’s human adaptation and technological advancement. Human civilization on Earth today utilizes the entire Earth to basally support human augmentational adaptation. A human settlement in space must be basally and augmentationally similar to a developed nation on Earth to be fully sustainable because that is what contemporary humans are adapted to.

The analytical models for levels of sustainability are based upon the way Earth evolved into an island of order. The steps that Earth proceeded through in its evolution of order are the building blocks of a functioning and sustainable ecosphere. Self-restoring order formed the early lithosphere, hydrosphere, and atmosphere using the gravitational dissipative structures. Power from the Sun poured down on the surface area of Earth to start the buildup of capacity with geophysical cycles and biogeochemical cycles. Ultimately life formed and, through patterns of growth of electrochemical dissipative structures, increased in capacity through the buildup of organization by way of network vitality and functional diversity. See Supplementary Presentation 3: Pancosmorio Theory Sustainability Analytical Models for further explanation of the levels of sustainability.

The first four pancosmorio hypotheses utilize four parameters: terraform threshold load consistence, terraform threshold disruption resistance, terraform threshold load persistence, and terraform threshold disruption resilience. These are based on an approach to measuring human sustainability derived from stability properties of an ecosystem as first proposed by Irons and Irons (2021). Section 3.6.1 provides a refinement of the original framework into a quantitative method of human sustainability. The first four hypotheses are then explained in Section 3.6.2 in the context of the refined quantitative method of human sustainability.

Section 3.6.3 explains the pancosmorio theorem hypothesis as a limit to the human sustainability of a terraformed ecosphere. The implications are that humans will be limited in how far away from their home Sun they can terraform their environment to an ecosphere of level 1 sustainability. Any attempt to terraform a human base or settlement beyond the distance calculated by the pancosmorio theorem will likely undergo the problems predicted by the cascade failure hypothesis due to not meeting the basal power conditional.