An essay on the mathematics of life

Raymond E. Gangarosa, MD, MPH, MSEE

June 5, 2020

Abstract

This draft of a blog introduces what I believe to be a new perspective of the mathematics of life, based on first principles of how the dynamics of chemical reactions unfold over all timescales and organizational levels. Two mathematical induction proofs, proceeding in both directions — top-down looking upward to all higher levels, and bottom-up looking at the same level and downward to all lower levels — generalize the mathematics of life to all levels of existence. The existence of power laws, inheritance relationships, and memory over many timescales suggests fractal and percolation processes. This analytical framework, confirmed by our own intuitions, explains how the remarkably cooperative physiological states, structures, and functions inside the human body have served as an evolutionary platform at higher levels for the emergence of thought and civilization.

Considering civilization as the highest level of human life over the longest timescales — which also confers analytical tools and spiritual insights that never have been available to life, its evolution, or its development — the mathematics of life can serve as a design foundation for the advancement of human civilization. As described elsewhere, this perspective is entirely compatible with the most important aspects to which human civilization can aspire and is consistent with timeless theological doctrine, setting a foundation for a new kind of theological discourse and dismissing objections to “social engineering” that has always been directed by narrow ideological agendas at piecemeal problem-solving.

This perspective of the mathematics of life explains a great deal about how our bodies work, how they established evolutionary and embryological platforms for thought, how we think, and how we are able to create a civilization. It explains the advantages of multicellular existence and civilizational life over all other modes of existence currently on earth, the different optimization modes that life employs, the rationale for development that all things undergo — from species to embryos to children to education to technologies to computer bootups to networks — and it weighs in heavily to explain the meaning and purpose of life. The mathematics of life suggests that human civilization is making a universal unicellular-to-multicellular embryonic transition, around the developmental stage of a 16- to 18-day-old human embryo. It establishes a basis by which human civilization might transition toward fluent civilizational transformation with purpose and meaning, corresponding to a mature, wise, and compassionate adult. Those comparisons date human civilization as a maturation process and suggest how humanity might establish ourselves as a responsible, good citizen within the fragile biosphere of our planet and exert wise stewardship over the course of life on earth.

Introduction

Mathematics provides powerful tools for conceptualizing and developing design of a single civilization that encompasses all of humanity’s development over all time. The timelessness of just that one civilization on earth can be represented in relation to 1. past | 2. present | 3. future | and (optionally) 4. irreversible transformation — as the basis for connecting with deep theological truths (e.g., the Trinity), relating the theory to the physics of chemical reactions, and engaging engineering design principles. Abstract mathematics might expand the design space to search through the full range of civilizational possibilities and potentials to optimize civilizational design | avoid design flaws | and attain maximum futurability.

The first principles on which the mathematics of life work relate to the five kinds of “moieties” in the universe that have been articulated by the contemporary physicist and computer scientist John Letcher: charges | masses || photons | spins || neutrinos. Neutrinos don’t interact, so the four remaining moieties only and always interact in a characteristic order: the two static moieties, [1. past:] charges | and [2. present:] masses, which establish the basis for nature’s, life’s, and civilization’s “hardware”, followed by the two (near-)relativistic moieties, [3. future:] photons | and [4. irreversibility:] spins, which establish the corresponding basis for “software”.

In our sedate corner of the universe, that order of interaction influences the unfolding of chemical reactions, either in coherent form (a generalized Schrödinger equation that considers quantum potential as an integral over the system’s past over all previous time, consistent with the memory inherent in multicellular life and civilization) or mass action (similarly generalized reaction-diffusion processes). Life renders those daunting equations solvable by translating time into space or vice versa through some developmental process, starting during embryogenesis with the traveling waves of chemical signaling via Turing morphogenesis that set up body segments. That process turns an intractable inhomogeneous partial differential equation in space and time into a second order homogeneous ordinary differential equation in either space (“hardware”) or time (“software”) (but not both), which, at least in principle, might be solved with a Laplace transform and the quadratic formula!

However, the nonlinearities and approximations involved in setting up developmental traveling waves further modify the Schrödinger equation with fractional calculus that manifests as fractal structures, fractional dimensions, and another source of memory embedded in network structures. Life incorporates these features into many aspects of its designs (most often as essential features but sometimes as bugs that make it vulnerable to attack or senescence) and uses more sophisticated fractal methods for solving the resultant equations. Life further modifies the nonlinear and potential terms of the Schrödinger equation into pairwise interactions between consecutive levels of Maslow’s hierarchy of needs, which sets up its multilevel developmental structure.

The price that multicellular life pays for solving the memory-enhanced Schrödinger equation is the fragmentation of step-by-step and level-by-level development, compelling it to make continual progress developing structures and processes to stay alive. That point is well illustrated by how different chemotherapies and chemical warfare agents can disrupt cellular metabolism. I also think humanity is experiencing the same disruptive fragmentation effects from with dictatorial rulers | adverse side effects of social media in an undisciplined society | and a proliferation of conspiracy theories and false realities | many of which are deliberately intended to obfuscate the truth and avoid accountability. By extension, I think this period of a unicellular-to-multicellular transition is fraught with peril, as illustrated by the high miscarriage rate at the corresponding period of embryogenesis.

However, multicellular life parlays that potential disadvantage and vulnerability relative to unicellular organisms with a host of advantages that arise from designs that ensure the required progress — starting with the two-stage memory inherent in embryogenesis recapitulating evolution and then, for example, proceeding to fractal structures in organs (e.g., lungs and brain) that spectacularly enhance performance, emergence of a platform for development during adulthood of novel capabilities (most notably, thought), and ultimately, civilization, which allows creative design of hardware and software tools. Interaction between levels begins as a burden (e.g., manifesting dominance and slavery) | progresses to responsibility (to live up to the principles of democracy) | advances to potential (where the least developed subpopulations become the best future investments) | and introduces new possibilities (where interdependence leads to civilizational resilience || cohesiveness || and strength). Thus, obligate interactions and developmental processes force multicellular organisms and humanity as a whole first to develop civilization and then to keep transforming it with new capabilities.

Multicellular organisms, human civilization, and their coexistence and coevolution with microbial life further instill into the course of life on earth purposiveness, whether we consider it scientifically in terms of teleonomy (e.g., forces that sustain nature | life | and civilization) or theologically in terms of teleology (the hand of God). All of life has too much invested in its development to let the whole structure collapse, and also depends on human civilization to maintain the existing structure and transform it to something that works much better. Our own bodies give a good first approximation of the best that life can attain, but then also science and theology, working together, can identify combinations of biology and technology that can work even better in specific designs. Regardless of how each person prefers to think about life’s purpose and meaning, this conceptual framework establishes the basis for a public theological discourse about the most important aspects of human existence and civilization, augmented by the science of theology and the theology of science.

Such a theological discourse could break the toxic logjam that currently exists between progressive and conservative viewpoints that is blocking the transition of human civilization from unicellular-like thinking (“Greed is good”) to multicellular-like collective action (in Christian terms, designing and building “the body of Christ” as all of human civilization). The mathematics of life suggests that human civilization is making a universal unicellular-to-multicellular embryonic transition, around the developmental stage of a 16- to 18-day-old human embryo. Minorities | progressives | and conservatives are taking on the dynamics of 1. past | 2. present | 3. future, respectively, aspiring to the roles of embryonic mesoderm | endoderm | and ectoderm that are fated to become musculoskeletal system and internal organs | digestive tract | and nervous system and skin; that is, aspiring to 1. taking on useful and valued functions within society by which future generations might no longer experience discrimination | 2. nourishing generations who are currently alive | and 3. steering (but not navigating) society. The process of navigating civilization is one of democratic and international consensus, attained through citizenship and goodwill, democratic institutions and diplomacy, and sincere, nondenominational, theological-like discourse about what is really important at the highest levels of life, as they influence all lower levels.

As humanity makes this transition from unicellular-mode operation to multicellular development, conservatives’ monopoly on dominance and control is challenged by exposing their duplicitous efforts to navigate human civilization by undemocratic means, culminating in the autocratic rule of Donald Trump. When never-Trump Republicans take over after his defeat in the 2020 election as the electorate recognizes his profound and poorly-hidden civilizational sins of ignorance | stupidity | corruption | exploitation || duplicity | treachery | and existential threat to democracy ||| planetary health ||| and the future of life on earth, a congenial sociopolitical environment can be restored that will expose dictators and dictator wannabes | hold them to personal account for the harm they do in office | and discourage those with authoritarian inclinations from “serving” in government leadership roles. With this perspective of current events as an embryonic-like unicellular-to-multicellular transition, we might envision the coronavirus pandemic as playing the role of catalyst (exposing the supreme incompetence of unicellular-mode operation | making any future unicellular-like economy nonviable due to crushing debt and insufficient potential capabilities | and forcing development of multicellular-like structures and functions) and bringing the civilizational reaction from mass action to coherence at the individual level (forcing each person to adapt to changing collective conditions | making awareness of common interests and a sense of shared fate universal and very real | pooling collective creativity | and applying it at the individual level using flexible personal technologies like cell phones and 3D printers). The unicellular-to-multicellular transition that recognizes civilization to be in an embryonic state exposes preexisting ideas favoring indiscriminate economic growth to be a prescription for embryonic tumors, like teratomas, and instead redirects growth along specific structural and functional lines that attain needed capabilities and prepare for future demands. Whereas multicellular life improves over unicellular designs with two passes through structured development, civilizational design adds two more passes to complete a quartet, consisting of evolution | embryogenesis | mathematics | and technology.

This mathematical perspective of life leads both to very specific conclusions about the nature of multicellular organisms and multicellular-like civilization and extremely far-reaching visions of the possibilities and potentialities of human civilization. The developmental sequence at each structural/organizational level translates into the processes of [1. past] anticipatory modeling of a linear system (characterized by dominance and control) | [2. present] bilinear contact inhibition of bilateral interactions through sigmoidal tradeoff functions (the give-and-take of human equality) | [3. future] multilinear digitization that rectangularizes the gradual tradeoff curves into sharp transitions to avoid timing errors (most likely manifesting as fluent and unambiguous tradeoff relationships) | and [4. irreversibility] development of a digital toolbox, comparable to thought, to computers, or to networks (perhaps through coherent vectoring of human activity via smart phones), that can perform linear analysis that anticipates the next level of development (e.g., from life to hardware or from hardware to software). Although this sequence was derived from mathematical and biological considerations, we can recognize from historical and engineering standpoints how technology has followed exactly the same pattern. This sequence extends indefinitely to ever-higher manifestations of life’s plan — in our case, to ever-higher levels of human civilization — successively resolving counterfactual conspiracy theories through theological discourse and purging dictatorships through development of accountability mechanisms and laws.

The role of abstract mathematics

Analogous to considering all life forms instead of just one species, abstract mathematics offers a framework for expanding consideration of civilizational design space to cover the entire span of life forces driven by chemical affinities, and not just the specific equations used to simulate the behavior of one particular example. Gauge transformations, applied to the memory-expanded Schrödinger equation, would generalize the solution to all combinations of scalar and vector potentials that solve it. Graph theory and/or some other topological manipulation could “boot up” a constructive cooperative coevolution algorithm so initial conditions are preset to optimize the trajectories for all the interacting agents, including those (like natural ecosystems and other species) that can’t assert their own interests. Pilot-wave theory provides an analytic framework for quantum interactions and/or computing under Schrödinger’s equation that allow consideration of trajectories, consistent with optimization processes and contrary to the soon-to-be-fully-discredited Copenhagen interpretation of quantum mechanics. Current optimization technologies and algorithms find least-squares error algorithms easiest to compute, but it’s conceivable that life or civilization might favor designs that respond to the absolute magnitude of errors on some kind of sliding scale, which might be analyzed in Banach space. Abstract algebra could help analyze multidimensional convolution operations of linear, bilinear, and multilinear systems that emerge under this developmental framework.

Since the solution of the Schrödinger equation is one of the foundations of quantum mechanics, it’s important for me to identify how I imagine quantum science applying mechanistically to social phenomena, aside from mere statistical evidence to that effect under Bell’s test. Some of the earliest models of quantum behavior, by Madelung (1928) and de Broglie (1927), dating to before the Copenhagen interpretation (1928), now find surprising macroscopic empirical confirmation in the hydrodynamic experiments of Couder et al. (2005). Oil droplets bouncing on a sonicated water tank clearly demonstrate phenomena that the Copenhagen interpretation rejected: trajectories, pilot-waves, and physics that does not require observers. The visible experiments in Couder’s water tanks disprove the Copenhagen interpretation of quantum physics and invalidate all its pseudo-philosophical trappings, leaving a scaffold of mathematics and physics with clear physical meaning. On that basis, we adopt Bohmian mechanics, which was rejected too long by preconceived notions, persistent self-righteous group-think, outright bullying behavior, and rigid social structures that suppressed reasonable dissent within its ranks and tainted all of scientific discourse.

The most charitable interpretation I can venture for the scientific establishment adopting such nonsensical, self-contradictory, and timid application of quantum principles tainted is that the pioneers in the field were unwilling to apply them to human affairs. Looking at human civilization as an inseparable, interdependent wave embedded in planetary dynamics was more than they were willing and able to take on, so they put all kinds of barriers in the way of scientific progress that might proceed in that direction. We see the same kinds of cultural smokescreens in the historical course of systemic racism that are just now coming to light.

With de Broglie-Bohm quantum physics, we not only can explain explicit trajectories but also the blurring, oscillating, defocusing effects of pilot-waves. We can abandon classical objectivity and understand the quantum-like smearing of interdependence effects, which allow us to see humanity as part of a whole that cannot be separated through reductionism as an isolated part separate from the whole. To attempt to separate human civilization from planetary dynamics is to perform the equivalent of removing an organ from a body, thereby kill it, and only observe, through reductionistic methods, its static characteristics. What’s really important is our dynamic interactions with the rest of life, especially given our impact on its future.

With this new perspective, we can imagine humans, humanity, and human civilization as comparable to cells in our body relative to higher levels and longer timescales. This is a difficult concept to accept, given pride, heritage, religious teachings, and anthropocentrism. It is a huge scientific hurdle to overcome because knowledge is configured to advance incrementally in academia, and huge barriers exist to considering the whole picture at once.

An even larger hurdle is taking on the responsibility of applying such principles to issues of civilizational design. However, in giving up all the crazy philosophical predictions of Copenhagen interpretation quantum mechanics (e.g., observer-dependent physics and Schrödinger’s cat), the much purer mathematics of Bohmian physics also connects with deep theological insights (as I explain elsewhere).

Mathematical methods and models for civilizational design — a first-pass analysis

I can think of four mathematical models that might characterize multicellular-like systems comparable to civilizations, during and after their embryogenic period. They are mutually compatible and sequentially ordered from general to specific. The series may have been inspired by the 4-step developmental sequence described above but is not strictly related to it. I think, but cannot yet prove, that the set of models may instead represent successive influences exerted as embryogenesis proceeds. For the four ordered, successively nested, models that emerge from the processes of civilizational embryogenesis. I envision applying a goodness of fit test to each model, so the whole set of tests would determine which permutation of these models is influencing the system at any given time. Both as a reduced model control and as a basis for modeling pathogenic or symbiotic interactions, the theory allows for consideration of unicellular-like behavior by leaving out memory and all downstream capabilities that multicellular-like behavior could attain.

[I want to develop a notation for pointing out where other mathematical disciplines, of which I have only passing knowledge, might further contribute to design potential | possibilities | capabilities | and transformation.]

model 1. the basic effects of chemical reactions on lifelike systems.

overview.

Generally speaking, model 1 considers life as driven at all levels by its chemical necessities, inheriting previous dependencies at ever-higher levels. Memory is the main distinguishing feature of multicellular life that sets it apart from unicellular existence; this model considers memory as a (conventional) integral over time. Many filtering, percolating, and/or reverberating structures (e.g., mitochondria, endoplasmic reticulum, and macroscopic neuronal circuits, respectively) could contain memory over fairly long timescales, perhaps as long as an organism’s lifespan, suggesting likely fractal and percolation nature of this memory, as discussed in model 2. Obviously, civilization takes memory to another level over biology, and conversely, the cumulative nature of culture and technology transcending mortal lifespans are the basis for civilization. Scale invariance would allow us to apply insights from one familiar level to another where intuition is lacking, but it would also force us to confront our arrogance, where we have expected ourselves to receive special treatment from nature and would allow us to see how mathematics has been used as a smokescreen to avoid applying natural laws to ourselves (e.g., the 1928 Copenhagen interpretation of quantum physics as an obfuscating barrier to insight, which remained hidden until Couder et al.’s hydrodynamic experiments in 2005 demonstrating quantum phenomena on a macroscopic scale). In our era, we can now see clearly that Lyapunov exponents and chaos imply sensitivity to initial conditions, putting great pressure on humanity to accept responsibility and curtail multifaceted risks of collapse. We are the only known species that manifests collective memory as well-developed civilization, and this capability carries enormous responsibility for the future course of life on earth.

mathematical development.

In model 1, we start with Schrödinger’s equation for a single nonrelativistic spinless particle

and then add memory by making the quantum potential an integral of its history over all time,

…

As we’ll see, memory turns out to be the basis for all other capabilities that multicellular-like systems have over unicellular-like operation.

That substitution yields the central equation for model 1, the memory-augmented Schrödinger equation that applies for multicellular-like life at all levels, from biochemistry to civilization:

…

We recognize this partial differential equation to have the three terms with respect to time of a familiar PID (proportional-integral-derivative) controller, where the Ñ^{2} term, which is a function of structure but not of time, is the “proportional” term. We further note that a sentient being or analytical civilization could apply some kind of model of the controlled system’s expected behavior to apply feedforward anticipatory control.

…

We can relate Letcher’s four interacting moieties to corresponding terms in the equation in relation to the stepwise sequence of processes that occur during chemical reactions:

- Charges manifest chemical affinities in the ¶/¶
*t*term, which expresses how the reaction will proceed in relation to structural configuration, incident energy, and conservation of angular momentum. - Masses determine system structure in the Ñ
^{2}term, which is a partial derivative with respect to spatial coordinates. - Photons supply energy to the reaction via the quantum potential term
*V*, which I’ve further expressed in terms of the system’s memory of its entire past history. - Although not shown in the equation because spins are not modeled explicitly, they conserve angular momentum and ultimately determine how the chemical reaction goes to completion. At the end of this blog, I’ll discuss how spin behavior might be modeled with density matrices.

Because of intractable mathematics of a multi-body problem | sensitivity to initial conditions (chaotic dynamics) | and seemingly incoherent mass reactions of stochastic ensembles, it is not possible to anticipate irreversible spin interaction phenomena mathematically at the level of Schrödinger’s equation, so I’ve adopted a new approach (at least during this early period of development): don’t bother to try. More specifically, since interactions between the near-stationary moieties, charges and masses, can progress reversibly, we will consider that all irreversibility involves the (near-)relativistic moieties, photons and spins, by beginning with a context-dependent configuration of photon trajectories and ending with spin interactions that preserve angular momentum in all the (unpredictable) aspects of the chemical reaction.

Thus, for now, I will consider photon-initiated interactions between spins qualitatively, as an explanation for any dynamic and stochastic phenomena that occur irreversibly, whether they proceed to collapse or transition or transformation. Where that effect loses the phase coherence of the Schrödinger equation and progresses as a mass reaction, I will substitute the otherwise similar memory-enhanced reaction-diffusion equation

…

where

The memory-enhanced Schrödinger and reaction-diffusion equations are inhomogeneous partial differential equations in time and space that are not solvable without specifying the relationship between the system’s temporal dynamics and physical structure.

For multicellular organisms — and for an analytical civilization that consciously emulates them — that relationship is determined by traveling waves set up during embryogenesis to synchronize body segment sequencing with a developmental clock.

One possible solution, especially for complex multi-body problems, would be to use sonicated water bath experiments and hydrodynamic models of quantum phenomena in the manner of Couder et al. The system’s boundary conditions in space and time could be matched with ultrasonic arrays as the sonication stimulus.

…

We can also solve the equation analytically, especially for simpler configurations. Noting that Heaviside’s familiar form of Maxwell’s equations incorporates circular reasoning by not keeping track of the specific phases of electromagnetic waves — a mistake that would be disastrous in embryogenesis — we should further include Jefimenko’s correction for causal systems:

…

If this traveling wave established during embryogenesis were “perfect” and its effects persisted in perfect synchrony throughout life, in principle, we could substitute temporality for structure and thereby convert the inhomogeneous partial differential equation into a homogeneous ordinary differential equation. If the equation were linear, we could take a Laplace transform and solve it with the quadratic equation!

…

…

…

However, we might expect that any deviations from a “perfect” traveling wave, a linear time-invariant system, and/or lockstep synchronization throughout life would probably manifest as some kind of fractal phenomena, which we’ll consider in model 2. Indeed, these observations could explain why many organs in the body (lungs, brain, liver, spleen, etc.) have fractal structure.

With the Schrödinger equation converted through embryonic development into an ordinary differential equation in time only, the terms correspond to the elements of a proportional-integral-derivative controller, with intelligence and foresight further allowing for anticipatory control as feedforward.

…

How might these memory-enhanced equations — a coherent Schrödinger version and a mass reaction-diffusion form — emulate the span of existence from biochemical reactions within microscopic multicellular organelles at the lowest structural level to human civilization over vast scales of structure and time?

Consider how life “processes” these chemical reactions simultaneously for two (or three) adjacent levels of Maslow’s hierarchy of needs: physiological, safety, love, esteem, and self-actualization.

box 1. Maslow’s hierarchy of needs (from website https://www.simplypsychology.org/maslow.html):

Humanity’s process of sleepwalking through history, dominated over the last few centuries primarily by laissez-faire capitalism, has dumped most of the world near the bottom two levels of that scale, in the economics of scarcity — despite the fact that life itself indicates an economics of abundance is possible. The security, nourishment, and quality of life that our own cells enjoy relative to those of single-celled organisms point out the tremendous advantages of the multicellular paradigm over unicellular existence.

However, the essential feature of multicellular life is not benefit to the cells, but dedication to the whole. Thus, cells must be willing to sacrifice their interests and even their lives if their continued existence seriously threatens the whole (e.g., apoptosis, or programmed cell death, of cells that become cancerous). And if the whole organism is starving, its cells must correspondingly cut back their demands on the system’s resources.

For both these reasons — humanity’s starting conditions and life’s demands that cells be willing to hover at the edge of survival, if necessary — we will consider operation at the two lowest levels of Maslow’s hierarchy. Then we will consider how successive transformations might allow a person or civilization to climb through Maslow’s hierarchy to higher and higher levels of operation, function, and capability.

The essence of developmental sequencing is that progress is reversible until stage 4, involving interactions between spins, where an irreversible step sets the system on a new path. One or two such cycles are not sufficient to develop fundamentally new capabilities in a civilizational design, because three such irreversible steps — that is, a full temporal cycle of past | present | future, | with nature deciding the irreversibility transformation, corresponding to all four explicit and implicit terms in the Schrödinger equation — are required for such transformations.

It’s a mixed blessing to complete a design in that way, because its 4-term, full-cycle irreversibility “locks in” any design flaws. The pitfall of embedded design flaws is just one aspect of why transition to conscious civilizational design involves so much commitment, especially at this early stage of development. I plan to make an exhaustive list here, but all the reasons center around laying down a foundation for the design of human civilization for the rest of all time.

…

Such a foundation would be reversible only after complete collapse. Thus, in establishing that foundation, our era would be taking responsibility for the welfare of all future generations || the health of planetary dynamics || and co-creative partnership with God in designing and building our civilization into the body of Christ. The immortal words of the spellcheck poem apply even more to setting up a permanent process that will continually purge human civilization of design flaws before they are “baked in” permanently: “And wee mussed dew the best wee can, sew flaws are *knot aloud*.” The “ratchets” embedded in the irreversibility steps are like knots in a very real way, and a foundation for civilizational design that looks like a giant hairball could permanently limit the ultimate capabilities of human civilization, the prospects of future generations, the course of life on earth, and the civilization that we leave God as a tool for vanquishing evil in the universe.

I will first consider the 4 ´ 2 pattern of interim, incremental developmental transitions, which involves pairs of adjacent levels of Maslow’s hierarchy and sets the stage for induction proofs of self-similarity across levels.

… [table or diagram]

As each developmental process successfully rounds stage 4 at each level, the irreversible nature of that step engages a kind of “ratchet” that puts the next level’s development on a firmer footing. Conversely, if a precipitous decline of resources at the higher level breaks the bulwarks at stage 4 of the next lower level, the collapse is accelerated.

These observations, both good and bad, define the all-or-none nature of multicellular life. Cells in a multicellular organism are committed to its health or they will die with it.

We can look at this strong mutual interdependence from both bottom-up and top-down perspectives with mathematical induction proofs, which apply over all structural levels for which the system retains multicellular-like memory. From a bottom-up perspective, looking at the same and higher levels, the process of advancing between consecutive levels of Maslow’s hierarchy depends the same way on the irreversible ratchet of stage 4 of the lower level, no matter how high or low we are considering on that hierarchy. By that token, if we consider civilization to be a higher manifestation of Maslow’s original hierarchy, as it generalizes to multicellular-like operation, then this observation becomes a mathematical induction proof showing how the development of higher-level capabilities depends on the work of agents operating within the (super-)organism at lower levels. This proof speaks to our responsibilities to civilization, planetary health, and the future of life on earth.

Conversely, the same proof applies top-down, looking down at lower levels — e.g., how we see the cells in our bodies as protecting our lives, how future generations will evaluate our actions at this critical inflection point in human civilization, and how God also must judge us. Gaining capabilities and preventing collapse both depend on the lower stage 4 in each pair of levels under development. The extent to which we design our civilization wisely at this early conscious phase and make its bulwarks strong and resilient is the extent to which the multicellular-like superorganism that we are creating of our civilization is capable and resistant to collapse.

We can thus think of multicellular life in terms of a generalization of the Golden Rule to the interactions between higher and lower levels. Multicellular architectures must regard these interactions in terms of pervasive interdependency, like team play that must bolster its weakest links. Those criteria stand in strong contrast to the standards for unicellular life and laissez-faire capitalism, namely, bilateral reciprocity that the strong can exploit.

These bidirectional induction proofs establish a basis for cross-level inference, wherein insights at one level can be applied to all others, within reasonable limits established by system parameters and operational dynamics. For example, I have already alluded to comparisons between embryogenesis and civilizational development, which I’ll describe further below. Since vastly different levels have different windows and blind spots for empirical observation, this powerful theoretical tool allows combining their observational strengths and weaknesses to fill in gaps and get a picture of what happens in common at all levels.

Next consider the 4 ´ 3 pattern of full-scale transformations (or collapses), which involve progression (or regression) of development through triads of levels until qualitatively unique capabilities are gained (or lost).

… [table or diagram]

Multicellular life covers these three levels in three passes:

past. (lowest) level 1. embryogenesis: using timing to generate structure |

present. (intermediate) level 2. hardware: using that structure to generate timing capabilities |

future. (highest) level 3. software: using those timing capabilities to generate transformational capabilities at yet higher levels

We can apply this conceptual framework to different narratives, for example,

- the human life cycle: 1. embryogenesis | 2. the “hardware” level of childhood physical development | and 3. the “software” level of adult maturation to wisdom
- technological “progress”: 1. ad hoc development of primitive tools | 2. the design of advanced, e.g., electronic, “hardware” | and 3. the maturation of “software” tools
- civilizational biomimicry (after multicellular life): 1. the “embryogenesis” of sleepwalking through history | 2. the design of more advanced social structures, like the “hardware” of a circulatory system | and 3. the “software” of interaction processes within civilizational “organ systems” and networks
- civilizational design: 1. life’s design | 2. the “hardware” of social structures emulating technological designs | 3. applications emulating human software engineering

In this blog, I will concentrate primarily on civilizational design, which follows this stepwise sequence:

level | stage → | 1 | 2 | 3 | 4 |

1 | life’s development | physics | chemistry | embryogenesis | childhood |

2 | “hardware” of social structures | linear PID controller with anticipatory feedforward modeling | bilateral, bilinear interactionscontact inhibition → bilateral tradeoff curves | universal multilateral, multilinear interactions“digitization”: “rectangularization” of tradeoffs to eliminate timing errors → digital hardware | a digital-like “toolbox”, analogous to electronic computers and networks |

3 | “software” of civilizational applications | optimization algorithms | applications | fluency | gateway | invitation | commitment to higher-level capabilities |

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