EROS AND LOGOS

Abstract

For the ancient Greeks, the world was both Eros, the god of chaos and creativity, and Logos, the regularity of the heavens as law. From chaos the world came forth. The world was home to ultimate creativity. Two thousand years later Kepler, Galileo, and then mighty Newton created deterministic classical physics in which all that happens in the universe is determined by the laws of motion, initial and boundary conditions. The Theistic God who worked miracles became the Deistic God who set up the universe and let Newton’s laws take over. Eros, raw creativity, is dead, all is Logos.

Quantum mechanics replaced the determinism of classical physics with fundamental indeterminism. This was a major crisis in physics, but remained entirely within the Newtonian paradigm of laws, here the Schrödinger equation, initial and boundary conditions. The Schrödinger equation entails the deterministic propagation of a probability distribution. The probabilities concern the indeterminate outcomes of quantum measurement events.

The central issue of this article is to show that no laws at all determine or entail the becoming of our biosphere or any other among the 10²² solar systems in the universe. This claim is radical. If no laws determine or entail the becoming of biospheres, and biospheres are part of the universe, the Pythagorean dream that All is Number, All is Logos, is dead. There is no Final Theory that entails all that become in the universe. Eros is again, and always was, rambunctiously alive in the raw creativity of the becoming of life anywhere in the universe. The becoming of life is based on physics, on Logos, but beyond it, emerging from Eros.

The reasons Eros is at play in the evolution of biospheres are fourfold.

First, the universe will not make all possible complex things. That is, the universe is vastly non-ergodic. Yet complex things such as the human heart exist.

Second, the reason human hearts exist is that organisms are Kantian Wholes in which the parts exist for and by means of the whole. Hearts exist because they fulfill the function of pumping the blood that keeps the whole organism alive. Such organisms propagate progeny that carry with them the hearts that keep them alive.

Third, adaptations like hearts, the flagellar motor, the loop of Henle in kidneys that concentrates urine, and flight feathers, are tinkered-together contraptions stumbled upon in evolution. Parts and processes that arise in evolution are jury-rigged for unprestatable new functions that help keep the entire Kantian Whole organism alive and propagating in the evolving biosphere. There is no deductive theory of jury rigging. We cannot deduce the emergence of such novel functions.

Fourth, the functions of parts of organisms emerge in unprestatable ways and form the unprestatable and ever-changing phase space of evolution. Since we cannot prestate the ever-changing phase space of evolution, we can write no laws of motion in differential equation form, so cannot integrate the equations we do not have. Thus, no laws entail the becoming of any biosphere.

Evolving biospheres are everywhere creative. This is Eros, the chaos from which the world emerges. This profound creative emergence is the stuff of story, of narrative. Evolving biospheres always were and always will be both Eros and Logos, the stuff of story and the stuff of law. We always live in a world of Art and Science.

Keywords:

• Eros
• god of creativity
• Logos as law
• Newtonian Paradigm
• Kantian Whole
• non-ergodic
• no entailing law
• narrative
• story

1 introduction

I wish to show that the becoming of the world is both entailed by the natural laws of physics and is also a becoming beyond any law at all. Three hundred and thirty years after Newton in 1687 published his Principia, in which the world is an entailed becoming, my statement that the world is a becoming beyond any law at all is revolutionary. In fact, we live in a world that is both: law and story, entailed becoming and narrative. We have come to know that C.P. Snow’s “Two Cultures,” Art and Science, are in fact, one world.

We inhabit and make that world with the rest of life on the planet, but at the same time, we are destroying that planet. We face a crisis our species has not seen in our 300,000 years of existence. Our $100 trillion global economy is growing at 4 percent a year. It will be tenfold larger in ad 2100. Our economy lifts millions from poverty, reduces childhood death rates, increases literacy, links our nations in trade, and is the means by which we earn our livings and find much of our meaning. But the same global economy is driving climate change with sea level rise, flooding, severe weather, and ocean acidification, as we have come to know in 2020. The same growing global economy is driving a mass extinction event. By 2050, thirty years from now, 1,000,000 species, 20 percent of the standing diversity, will be extinct. As we speak, wildlife populations dwindle. Humanity uses about 40 percent of the planet’s land surface to grow our food. Over 50 percent of the terrestrial biomass of the planet is humans and our domestic products, cows, pigs, chickens, wheat, rice, sorghum. We are almost ten billion in abundance. For mammalian species, a population of a million is vast. We are 10,000-fold more abundant than each single member of such a species.

Our issues are global in both scale and existential magnitude. We are badly out of balance with the biosphere. Our species, for the first time in its history, will either come together and piece together a way forward to survive sustainably on our finite planet, or, driven by our growing juggernaut global economy, we will fail. If we fail, we fail the evolving life that spawned us: the rest of life on this planet. The story we need is a new narrative of our becoming on our planet, a new origin myth, and from it a transnational mythic structure by which we can orient ourselves anew. It is our story to construct.

2 the ancient greeks

We mirror the ancient Greeks in their appreciation of Eros and Logos, creative chaos and the law. For the ancient Greeks, Eros was the god of creativity from whom the world emerged from primal chaos. The events on earth consisted of chaos mixed with fate and the intervention of man and the gods. Ancient Greece is the Bronze Age, some 40,000 years after our ancestors in Indonesia painted the hunt with half mythical beasts, 20,000 years after Cro-Magnon painted the walls of Lascaux with aurochs killed with the atlatl, and seven thousand years after the onset of agriculture in the Near East. Early animistic gods of the volcano, lake, stream, dancing stone, and the hunt, gave way to the Greek Pantheon – Zeus, Athena, Diana, Mercury – who, having killed the Titans, ruled heaven and earth, played tricks on one another, fought, were jealous of one another, loved, laughed with and at humanity below, and arranged the world as they would.

What brought the storms, the whirlpools that come and go, sinking ships, the failure of rain and crops, the blights, but at the same time the olives and olive oil to trade around the Aegean? Could humans avoid their Fate or shape it? Oedipus did not as Athenians were told. The Iliad and Odyssey were founding civilizational myths of sword, love, loyalty, and war – epic tales of this struggle. The heavens with the ordered patterns of the stars in their constellations, the sun and moon, were the abode of order, and the first hint of natural law, of order and perfection, of Logos.

Aristotle taught that the circle was the perfect form, hence that the universe was a set of concentric spheres. The sun, moon, and the fixed stars were on these spheres rotating about the earth. The irregular motions of the five planets, the “wanderers,” worried the Greeks, particularly Plato. Two thousand years later, Kepler, knowing the circle was the proper orbit for a planet, surrendered that conviction to find the ellipse later predicted by Newton.

The first real steps toward science itself arose in Ionia with Thales of Miletus, a city in Asia near the island of Samos. Thales, about 540 bc, was the first to seek a common “principle” underneath all things that might explain the world without invoking the gods. What we now say of quarks and gluons, electrons and photons, he said of water. Anaximander, friend of Thales, determined the length of the year and made the first sundial. Empedocles, holding closed the openings to a clepsydra filled with water, showed that no water flowed out, so the clepsydra must be filled with an invisible stuff, air, made of invisible particles (Sagan 175–85). The single substance of Water slowly became earth, air, fire, and water. In 430 bc, Democritus argued that, rather than earth, air, fire, and water, the world was made of uncuttable units, atoms, moving and colliding randomly in the void of empty space. All atoms were of different shapes and all complex things made by combining atoms of different shapes. Centuries later, Lucretius, 94 bc in De Rerum Natura, introduced the random “swerve” to avoid the determinism in the universe of Democritus. Democritus and Lucretius 2,000 years ago presage the determinism of classical physics and the indeterminism of quantum physics of today.

So, for ancient Greece, the world was one of Eros and Logos, Creativity and Law, the Muse and the Ruler with its ordered line.

Foundational to the Ruler was number. Pythagoras, 570–495 bc, and his school of mathematics, discovered that for a right triangle, the length of the hypotenuse could not be a ratio of whole numbers such as 23/17. This discovery shattered the certainty in the Greek world that all numbers could be expressed as ratios of whole numbers, hence “rational numbers.” The length of the hypotenuse is not a rational number, nor is the famous “pi,” the ratio of the circumference to the diameter of a circle. The Greeks discovered irrational numbers.

An even more compelling result due to Pythagoras was his discovery that the different musical notes of a plucked string were different stable patterns of vibration of the string: Fundamentals, Thirds, Fifths, Octaves. Quantitative physics grows from this to this day.

“All is Number” proclaimed Pythagoras. This view, the Pythagorean dream, underlies most of contemporary physics, both in classical and quantum physics. It is the “Dream of a Final Theory” down there, voiced by Steven Weinberg some years ago, that entails and explains by such deduction from a fundamental law all that arises in the evolution of the universe. This dream is Reductionism, the “Dream of a Final Theory.”

The world of physics is the world of Logos. All is Logos. Eros is dead.

What a brave brilliant Age was Ancient Greece.

3 the origin and evolution of life: the rebirth of eros

We now turn to the origin and evolution of life here on earth – and perhaps more widely in the universe. There are 100 billion galaxies, each with 100 billion stars. Most stars have solar systems, so there are some 10²² solar systems. If life arises easily, as I will suggest, the universe is rife with life. Stunningly, the evolution of life on our, or any, planet, the evolution of biospheres, is entirely beyond entailing law. Evolution beyond Law, beyond Logos, is Eros. Our planet and the universe are rife with Eros and Logos. The Greeks were right.

My statement that no law entails the becoming of our, or any, biosphere is indeed revolutionary. Such a bold claim needs careful presentation, and careful criticism. I believe the claim is correct (Kauffman, Reinventing 120–49; Humanity 64–81; A World 115–28). If so, it transforms our understanding of science, of reality, and our place in the cosmos. It bounds the Pythagorean dream. Caveat lector, I may be wrong.

4 the universe is non-ergodic above the level of atoms

Our first step beyond entailing law will seem odd: can the universe in its 13.7-billion-year history create all possible proteins 200 amino acids in length? Recall that a protein is a linear string of twenty different kinds of amino acids strung together by peptide bonds. A typical protein in us is about 300 amino acids long. How many possible proteins are there of length 200 amino acids? Well, at each position there are twenty choices, so the total number of possible proteins length 200 is 20 raised to the 200th power. Twenty to the 200th power is 10 raised to the 260th power. This is a hyper-astronomical number.

Can the universe have made all 10 to the 260th possible proteins length 200? There are 10 to the 80th power particles in the known universe. The shortest timescale is 10 to the −43 seconds, the Planck timescale. So if all 10 to the 80th particles were operating in parallel for each 10 to the −43 seconds to make proteins length 200, and the universe is 13.7 billion years old, which is about 10 to the 17th seconds, it would take the age of the universe raised to 10 to the 37th power to make all possible proteins length 200 just once.

This fact is fundamental. Since the Big Bang 13.7 billion years ago, the universe has made all 102 stable atoms: hydrogen, helium, carbon, to uranium and beyond. But the universe can have made only an infinitesimal fraction of the possible complex molecules, each with many atoms. A protein length 200 amino acids, for example, has about 4,000 atoms. The physicist’s phrase, “ergodic,” means, rather roughly, that the system does all that is possible in the time available. For example, if a drop of milk is placed at the center of a cup of coffee, rather shortly thereafter the drop will have diffused all throughout the cup of coffee to a homogeneous distribution. This is the well-studied subject of equilibrium statistical mechanics, invented by L. Boltzmann in 1884. (This is the famous “Second Law of Thermodynamics” that C.P. Snow said too few people in the world of literature understood.)

Our simple example shows that, above the level of atoms, the universe is vastly non-ergodic. This has physical meaning. History enters when the space of what can possibly happen is vastly larger than what does happen. History is child of the non-ergodicity of the universe. The enormous non-ergodicity of the universe means that most complex things will never exist. This fact raises a profound puzzle. Every human reading this article has a human heart. Human hearts are very complex things. Then, why do hearts exist in the non-ergodic universe above the level of atoms?

We know the outline of the answer. Human hearts pump blood, whose circulation in the body helps keep the human alive. Humans have children, so our species propagates in the biosphere. As this happens, surviving humans carry along the hearts that sustain their lives, and heritably pass the heart to their offspring down the generations.

The central conclusion is that hearts exist in the non-ergodic universe above the level of atoms by virtue of the fact that by pumping blood the heart keeps the organism alive and propagating descendant organisms that carry with them their hearts.

The biological function of the human heart is to pump blood. But the heart also makes heart sounds and jiggles water in the pericardial sac. These latter causal consequences of the heart are NOT the function of the heart. Thus, the function of an organ is typically a subset of its causal consequences. Here the function of the heart is its causal pumping of blood, not its making heart sounds or jiggling water in the pericardial sac.

In sum, hearts exist in the universe in virtue of their function in sustaining the whole organism of which the heart is a part. The whole organism propagates offspring that bring with them the hearts by which the whole organism is sustained (Kauffman, A World 13–16).

5 kantian wholes

A foundational concept is that of a “Kantian Whole.” The amazing philosopher, Immanuel Kant, in about 1790 wrote, “In an organized being, parts exist for and by means of the whole.” This is a Kantian Whole (Kant; Kauffman, Humanity 67–69; A World 8). Given such a system, the function of a part is its causal consequence that sustains the whole. If this is true, then already biology cannot be reduced to physics. Functions pick out subsets of the causal consequences of parts. Physics talks about all the causal consequences of a “thing” but cannot pick out any preferred subset of these.

The origin of life is the origin of Kantian Wholes.

I now introduce the fifty-year-old concept of “collectively autocatalytic sets” (Kauffman, A World; “Cellular”; “Autocatalytic”; Farmer, Kauffman, and Packard 50–67). Consider a set of three small proteins: peptides, say thirty amino acids in length. Catalysts speed up chemical reactions in their approach to chemical equilibrium. Let peptide 1 catalyze the formation of peptide 2 by ligating (gluing) two fragments of peptide 2 together to create a second copy of peptide 2. Let peptide 2 catalyze the formation of a second copy of peptide 3 by ligating two fragments of peptide 3 to create that second copy of peptide 3. Let peptide 3 catalyze the formation of peptide 1 by gluing two fragments of peptide 1 to create a second copy of peptide 1. This is a “collectively autocatalytic set” of three peptides. Note that no peptide catalyzes its own formation. The set as a WHOLE collectively catalyzes the formation of all three peptides.

This three-peptide collectively autocatalytic set is a very simple example of a Kantian Whole. Each peptide exists for and by means of the whole set of three peptides. The function of each peptide is to catalyze the formation of the next peptide in the set. Each peptide also jiggles water in the Petri dish. Jiggling water is not the function of each peptide. So again, the function of a part is a subset of its causal consequences.

Such collectively autocatalytic sets of peptides have been created experimentally. Gonen Ashkenasy at the Ben Gurion University in Israel has a nine-peptide collectively autocatalytic set reproducing in his laboratory (Wagner and Ashkenasy). His set is a Kantian Whole where, indeed, the function of each peptide is to catalyze the formation of the next peptide around the cycle of nine peptides. A powerful implication of this set of nine reproducing peptides is that molecular reproduction does not depend upon nucleic acid polymers such as DNA or RNA, as described further below. Life need not be based on nucleotide polymer replication as commonly held.

6 living cells are collectively autocatalytic sets, hence kantian wholes

The cell is the minimal unit of life. Already in Newton’s time, Joseph Hooke studied a thin slice of wood under an early microscope and noted what he called “cells.” Cells are bounded by a membrane which is a bilipid structure with pores that control what molecules enter and leave the cell, and receptors on the membrane recognize such molecules. Trans-membrane pumps control influx and efflux. Inside the cell are the chromosomes housing the famous DNA double helix. The genes of a cell are encoded in the specific sequences of the four bases: A, T, C, and G, along the DNA strand. Triplets of these bases – for example, CCA – code for specific amino acids in the famous “genetic code.” The DNA encoded genes are copied, or transcribed, into a sister molecule, RNA. The triplets along the RNA specify sequences of amino acids that are linked together by peptide bonds to form the newly synthesized protein. The ribosome, a structure of peptides and RNA, creates these peptide bonds.

Thousands of different small molecules are linked in the metabolism, where the reactions among these molecules are catalyzed by protein enzymes encoded by genes. Among the thousands of protein products, some form linear structures, or fibrils. Molecular motors hold and transport other molecules, like cargo across the cell, to defined destinations.

Genes turn one another on and off. The protein specified by one gene can transcribe another gene into its RNA or help or block that transcription into RNA. Bacterial cells have some 3,000 genes. Humans have about 23,000 genes coding for proteins. Thus, the human cell links about 23,000 genes into a network in which genes turn one another on and off, rather like twinkling Christmas tree lights. Humans have about 300 distinct cell types: nerve, liver, muscle, and so on. We know that each cell type is a different stable pattern of the genes blinking on and off, or in different patterns of steady on or off activity (Kauffman, Origins 441–522; Huang, Emberg, and Kauffman). Living cells are Kantian Wholes. No molecule alone creates a second copy of itself. In dividing cells, thousands of metabolic and other “tasks” are collectively achieved, hence are Kantian Wholes. The function of each such process is the causal consequence that sustains the whole living reproducing cell. Functions are real in the universe.

7 the origin and evolution of life

Life on earth started about 3.7 billion years ago. The Hadean earth had an ocean and volcanoes that created land masses above the ocean, rather like Hawaii today. On land, rainfall led to shallow pools near volcanoes, draining to the ocean. Such environments were rich in a high diversity of many thousands of small organic molecules, metals, and so forth. The atmosphere was largely nitrogen, with no oxygen (Deamer).

No one knows how life started. A first favorite theory is that life started with long double stranded RNA molecules that could copy themselves by template replication. This is the RNA World hypothesis (Gilbert). A second hypothesis (Kauffman, “Autocatalytic”; Farmer, Kauffman, and Packard; Hordijk and Steel) is that life started with the spontaneous formation of collectively autocatalytic sets of small organic molecules, then peptides and RNA, followed by the emergence of long double stranded RNA or DNA that could template-replicate. Plausible sites for life’s origin are deep water hydrothermal vents, rich in organic matter, or volcanic hydro-fields with freshwater pools subject to repeated evaporation and refilling. Such wet–dry cycles add energy to the system that can drive the linking of amino acids together to form peptides, or nucleotides to form long RNA polymers. Such polymers, housed in hollow lipid vesicles called “liposomes” which can grow and bud, may be the origin of early protocells. Experiments on all these fronts are underway (Deamer).

This 3.7-billion-year process of evolution has created on earth the most complex system of which we know. If life is abundant among the 10 to the 22 solar systems, life is a major feature in the evolution of the universe. Life may well be abundant. By five billion years ago, the universe had “cooked up” a high diversity of organic molecules, perhaps 60,000 or perhaps millions of molecular species of the organic atoms, CHNOPS: carbon, hydrogen, nitrogen, oxygen, phosphorus, sulfur. Such diversity is found on a meteorite, the Murchison, which fell in Australia. The Murchison was formed five billion years ago as the solar system formed. Today, on Enseladus, a moon of Jupiter, a similar diversity is found.

If small-molecule, collectively autocatalytic sets form easily in such rich mixtures, the universe was everywhere ripe for life five billion years ago. A group led by Joana Xavier and Bill Martin (Xavier et al.), have recently reported finding small-molecule, collectively autocatalytic sets in bacteria and archaea from more than two billion years ago, before oxygen was in the atmosphere. Each set has no polymers, no DNA, RNA or proteins, yet it reproduces.

Each set has about 1,500 types of molecular diversity and 1,500 reactions. The two sets, bacteria and archaea, overlap in a collectively autocatalytic metabolic set of about 800 molecular species. This suggests that this group of about 800 autocatalytic sets precedes the divergence of bacteria and archaea billions of years ago, and that highly diverse soups of small molecules can indeed form self-reproducing collectively autocatalytic sets. The universe may indeed have everywhere cooked up molecular reproduction eight billion years after the Big Bang. The universe may be rife with life.

We can imagine, then, how early life on earth propagated and organized itself through a process involving non-equilibrium living cells. This created the three great branches of life: bacteria, archaea, and eukaryotes – cells with nuclei. For the first two billion years, life consisted of single-celled bacteria, archaea, and more complex eukaryotic cells with nuclei housing their chromosomes. Among these, stentor are amazing. A single-celled organism, it lives attached to rocks as a filter feeder. If confronted by toxic molecules, it averts its “mouth” area. Confronted a second time, it averts its “mouth” more rapidly. If still confronted with toxins, it “vomits” by turning its insides out. Yet more toxin, and the stentor inverts its “stomach” and crawls off to a new safer location. As Peil points out, the stentor samples its world, evaluates it “good or bad for me,” and acts. Such evaluation – good or bad for me – is the onset of value in the universe. The stentor has values. So do all living things. Acting in the world is “agency.” All living things are agents: self-reproducing, non-equilibrium systems doing thermodynamic work cycles, able to choose and act on their own behalf in their worlds: “yuck” vs. “yum” (Kauffman, Investigations; A World). This is how we begin to move from “matter to mattering.” Sensing the world, evaluating “good or bad for me,” and acting is, Peil suggests, the first sense, which is emotion. Later, as life evolves, more fully developed emotions evolve, and with it, eventually, our ethics.

Multicellular life arose six times, about 1.4 billion years ago. In sexual multi-celled organisms, most cells give up propagating progeny forever, and die with the organism. Only sperm and egg pass on down the generations. With multicellularity, about 650 million years ago in the Ediacaran, rather complex worm-like organisms, among others, arose. The stunning Cambrian Explosion was 550 million years ago, well studied from the Burgess Shale (Gould). Almost all later phyla arose in the Cambrian. Vertebrates arose in the next, Ordovician period. This plethora of multi-celled life branched into the phyla and lower taxonomic groups. Today, there are millions of species, many dying in the mass extinction our growing global economy is causing.

Organisms create niches for one another. The trunk of a tree has a hole that houses a woodpecker. Life’s branching organisms create new niches faster than new organisms arise to live in those new niches. The biosphere explodes in diversity. Organisms “make a living” with one another: my refuse is your food. My solid surface affords a place on which you can crawl or run. Reindeer run on the permafrost. The permafrost now melts, the reindeer stagger, the Lapps lose their herds after thousands of years of a stable lifestyle. We all make our livings with one another.

Evolution is not all increasing diversity. Small and large extinction events have dotted the past 550 million years. There have been five large extinction events. The largest, the Permian, some 255 million years ago, wiped out 94 percent of all species. It is thought that this extinction was caused by increased atmospheric CO₂ which increased over several hundred thousand years. Current climate change is increasing CO₂ dramatically by the decade. If one million species will be extinct by 2050, how large will this mass extinction be, quantitatively speaking? Qualitatively, we are in the process of destroying the collective knowhow, hard-won, of millions of species that have come into existence over 3.7 billion years, creating niches for and making their livings with one another. In destroying accumulated life on this planet, we know not what we do – and, so far, we seem not to care.

8 no laws entail the becoming of the biosphere: logos bounded, eros unbounded

I turn now to my major claim: no entailing law governs the becoming of our, or any, biosphere in the universe – a universe of perhaps 10 to the 22nd in size, flowering in abundance. The context of this claim and its prospective importance reaches all the way back to Pythagoras and his dream. Aristotle said that scientific explanation is deduction. All men are mortals. Socrates is a man. Therefore, Socrates is a mortal. This basic model, in which the logical force of the premise, if true, entails the conclusion, later becomes classical and then quantum physics.

Modern physics begins with Copernicus and his advocacy of a heliocentric world view, in 1543. Kepler, using the data of Tycho Brahe, showed that planetary orbits are ellipses, not circles, with his three mathematical laws. In 1621, Galileo watched swinging chandeliers in church and saw that the period of the oscillation was independent of the amplitude. The same Galileo, around 1630, diluted gravity using shallow incline planes and found that by rolling balls down the plane, the distance covered increased as the square of the time elapsed. Pythagoras had claimed “All is Number.” Here was the Pythagorean dream 2,000 years later. The motions in the heavens and on earth were governed by mathematical laws.

Then the claw of the lion: Newton, with his three laws of motion, universal gravitation, and his invention of the calculus, differential and integral, soon after reading Euclid. Newton is probably the greatest scientist in history, surely in physics. From him comes the foundation of classical physics. In 1684, he united the motions of heaven and earth and indeed, those of the entire universe. Newton’s laws are entirely deterministic. Given initial and boundary conditions, integration of his differential equations yield the deduced, hence entailed, future behavior of the system. That behavior, the trajectory of the system, is fixed forever. The universe is a clockwork. With Newton, the struggle between science and religion increased because on this view, God could cause no miracles. By the Enlightenment, the Theistic God had disappeared in learned Europe, replaced by a Deistic God. God set up the universe and stepped aside for Newton’s laws to govern what would happen, forever. God became the God of the Gaps where science had not yet reached.

Even more importantly, perhaps, Newton taught us how to think within the Newtonian Paradigm: (1) Write down laws of motion for your system in differential equation form. (2) State the initial conditions. For billiard balls on a table, these are the positions and momenta of all the balls on the table. (3) State the boundary conditions. For billiard balls, the boundary conditions are the shape of the edges of the table. These boundary conditions specify the “phase space” of the system. For the billiard balls, the phase space is the set of all positions and momenta of the balls on the table. In the physics of the Newtonian Paradigm, it is always essential to state ahead of time the phase space of the system. The behavior of the system in time is a flow, or trajectory, in that state space. (4) Integrate the differential equations to yield the logically deduced, hence entailed, trajectory of the system in its state space. For billiard balls, this entailed trajectory is the motion of the balls for all time, ignoring friction – and also, their motion backward in time, for Newton’s laws are time reversible.

The Newtonian Paradigm stands astride all of physics. Between Planck’s discovery of the quantum of action in 1900, and the formulation of the Schrödinger linear wave equation in 1927, physics confronted a major crisis. The moment when a radioactive decay occurs is entirely random. Thus, there can be no determinate cause in the Newtonian sense. Similarly, in quantum mechanics, it is extremely well confirmed that randomness cannot be eliminated from events. That randomness is not epistemological uncertainty, as in classical physics, but ontological. If this is true, the becoming of the world, even at the level of physics, is not deterministic. This was a major crisis for science. Determinism had to be abandoned. Einstein never accepted this. As he famously quipped, “God does not play dice with the universe.”

For all of that, however, quantum mechanics remains entirely within the Newtonian Paradigm. The Schrödinger linear wave equation is entirely deterministic. However, instead of determining the trajectories of balls in a phase space, the Schrödinger differential equation, upon integration, yields a determined trajectory of a probability distribution. The probability distribution is the probability that a given quantum event happens at some time and place in the universe.

In fact, all of contemporary physics and chemistry are within the Newtonian Paradigm. Weinberg’s “Dream of a Final Theory” is within the Newtonian Paradigm. The dream is to unite the four fundamental forces – gravity, electromagnetism, the Weak Force and the Strong Force – in a single theory. Much has been done. Weinberg himself played a major role in uniting the electromagnetic and the Weak Force. Gell-Mann and Zweig discovered quarks and gluons binding quarks in atomic nuclei. Quantum Chromo Dynamics describes this Strong Force. The current standard model of particle physics unites all three quantum forces and is amazingly confirmed by work at CERN and elsewhere. The Higgs particle has recently been discovered, bringing the standard model to completion. All are within the Newtonian Paradigm. So too is Einstein’s magnificent Theory of General Relativity. But the search for a means to unite the classical physics of General Relativity with quantum mechanics, the twin pillars of twentieth-century physics, has so far met with no success. This union would be Weinberg’s fulfilled “Dream of a Final Theory”: Pythagoras redux.

I am about to tell you that the evolution of our, or any, biosphere in the universe is entailed by no law at all. We can now say, probably for the first time in science since Pythagoras and Newton, that the becoming of biospheres falls entirely outside the Newtonian Paradigm. The reason, as we shall see, is that the very phase space of biological evolution – which includes biological functions – persistently evolves in ways that we cannot even prestate, let alone predict. Without a prestated phase space, we can write no law of motion in the form of differential equations, hence we cannot integrate the equations we do not have. Thus, no laws at all entail the stunning unfolding of our, or any, biosphere in the universe. But our biosphere is the most complex system we know. So, no law is required for the amazing, ever-creative becoming of biospheres. Reality is not what we have thought – quite the contrary. Moreover, Weinberg’s “Dream of a Final Theory” is dead. Biospheres are part of the universe, of course, and if no law entails the becoming of biospheres, then no final theory entails all that unfolds in the universe. There is and can be no Final Theory. With this realization, Logos is bounded, and Eros unleashed. As did the ancient Greeks, we live with the creativity of Eros, seen in the ever-creative becoming, beyond any entailing law, of biospheres. The world of Eros is embedded in the laws of physics, but it is also a world beyond physics. The third crisis for physics, then, beyond the indeterminism of quantum mechanics that remains firmly in the Newtonian Paradigm, is that no law “governs” the ebullient unfolding of a biosphere.

9 eros anew

The universe, then, is truly non-ergodic above the level of atoms. Most complex things will never get to exist. One way to get to exist as a complex entity in the non-ergodic universe is to be a living evolving “Kantian Whole.” As Kant said, “In organized beings, the parts exist for and by means of the whole.” Vertebrates with hearts, for example, are Kantian Wholes. And as we saw earlier, the function of the heart is a subset of its causal consequences: pumping the blood that helps keep the whole organism alive. The essential issue, however, is that hearts only get to exist in the non-ergodic universe by virtue of their causal role in sustaining the whole organism of which they are parts. The evolving vertebrate lineage since the Ordovician some 500 million years ago propagated Kantian Wholes, and with them their evolving hearts, in all their complexity.

Or, think of cells and organisms. Hearts exist in the universe by virtue of their functional role in sustaining the organism. But so too, do the fibrils traversing cells and the molecular motors that do thermodynamic work to crawl back and forth along these fibrils carrying their needed freight around the non-equilibrium reproducing cell. So too, do the flagellar electric motors with a rotor and a stator, rotating the flagellum clockwise or counterclockwise to move up a sugar gradient for food. The stripes of the zebra, the eye of the octopus, the loop of Henle in vertebrate kidneys that concentrates urine: all exist in the non-ergodic universe by virtue of their functional causal roles in sustaining the Kantian Whole, the living, evolving organisms of which they are parts. The issue, then, is this: can we have a deductive theory that, like those of Newton and Schrödinger, entails the becoming of these adaptations since the origin of life 3.7 billion years ago? The answer is NO. And the reason is what I call “Tinkering.”

Nobel Laureate François Jacob wrote about evolution as a process of ongoing tinkering, or “bricolage” in French. Evolution stumbles upon new uses for structures and processes that already exist and grafts these new uses into the organisms in which they arise. The amazing flagellar motor in bacteria arose precisely in this way. This motor is a jury-rigged, tinkered-together contraption of the unused causal features of the several initial molecules that came together to form a new combination and found a new function. And from their new combination, the new stator–rotor electric motor system emerged.

Evolution is rife, of course, with Jacob’s tinkering, in which unused causal features of parts of organisms come to be used for novel functions. Such new uses arise due to what are called Darwinian “pre-adaptations,” or by Stephen Gould, “exaptations.” Consider again the heart. Darwin would tell us that the heart evolved, hence exists in the non-ergodic universe, by virtue of its function of pumping blood. But again, the heart makes heart sounds and jiggles water in the pericardial sac. Darwin brilliantly pointed out that such “unused” causal features of an organ might, in some different environment, come to be of selective value. Darwin did not mean by “pre-adaptation” that evolution had foresight, but rather that some causal feature of no selective and functional use for an organism in a first environment, might, by chance, have selective value in another environment.

A favorite example of a pre-adaptation is the swim bladder. Some fish have a swim bladder where the ratio of air and water in the bladder tunes neutral buoyancy in the water column. Paleontologists think the swim bladder evolved from fish with lungs. Water got into a fish’s lung, which was now partially filled with air and water. Such a lung was poised, in turn, to evolve into a swim bladder. Once the swim bladder evolved as a new causal consequence of a sac filled with air and water, a new function (detecting neutral buoyancy) came to exist in the evolving biosphere. The swim bladder is a complex structure that gets to exist in the non-ergodic universe by virtue of the function it performs in the Kantian Whole: the fish with a swim bladder that lives and propagates over generations.

Something stunning is happening here. Once the swim bladder exists, it affords what I will call a new “Adjacent Possible” empty niche. A worm or a bacterium could evolve to live only in swim bladders. Now let’s ask: did natural selection play a role in crafting a functioning swim bladder? Of course, natural selection played a role (crafting) such that functioning swim bladders evolved. But did natural selection craft the swim bladder so that it could constitute an Adjacent Possible empty niche into which a worm or bacterium could evolve? NO. This means that evolution is creating its own future opportunities without selection (in the Darwinian sense) determining them. Without selection achieving it, evolution creates its own future pathways of becoming. Evolution, due to variation and natural selection, is then “sucked into” the very opportunities it creates, only to create yet more opportunities (Kauffman, Humanity 64–98; A World 115–38). This is a kind of magic.

Let’s now ask whether we could anticipate, or prestate, all possible Darwinian pre-adaptations for all organisms – or even merely humans in the next three million years. How would we do this? What new environments might arise, calling for new uses tinkered together to “solve” some adaptive problem? What are these uses, or tasks? How might they be met by the particular, and changing, features of existing organisms? We cannot answer these questions exhaustively. We cannot “prestate” all possible Darwinian pre-adaptations.

To make the impossibility of “prestating” all such pre-adaptations clearer, I now present what I call “The Screwdriver Argument” (Kauffman, Humanity 64–82; A World 115–22). I hand you a screwdriver, say in New York, in 2020. You tell me all the things you can do with a screwdriver, by itself or together with other things. Well, you can screw in a screw, open a can of paint, stab someone, scrape putty off a window, wedge a door open, wedge a door closed, smash a window, tie the screwdriver to a stick and spear a fish, rent the spear to the locals for 5 percent of the catch, and so on. My favorite use of a screwdriver is to lean it against a wall, prop up a plywood board on the end of the screwdriver and place a wet oil painting beneath the plywood board to keep the painting dry in case of rain.

So, is the number of uses of a screwdriver in New York in 2020, by itself or in conjunction with other things, a specific finite number like 16? Is the number infinite? Is the number “indefinite?” In fact, the number of uses of a screwdriver is not a specific finite number, but neither is it infinite, for there is no iterative process of counting its possible uses, like N and N + 1 to infinity. The number of uses of a screwdriver is, in fact, indefinite.

Next point: there are four ordering relations in mathematics: a nominal scale in which there is no ordering; a partial ordering in which X is greater than Y and Y is greater than Z, so X is greater than Z; an interval scale, like a thermometer, in which 3°C is greater than 2°C by the same interval as 2°C is greater than 1°C; and a ratio scale where two meters is twice the length of one meter. The different possible uses of screwdrivers are merely on a nominal scale. There is no ordering relation between the different uses. These features of indefinite and unordered uses of things (e.g., screwdrivers) implies the following: no rule-following procedure – that is, no algorithm – can list all the uses of a screwdriver alone or with other things, nor compute the next new use of a screwdriver. Finding new uses of screwdrivers is not an algorithmic problem. Neither is evolution. The evolution of the biosphere is rich with jury-rigged pre-adaptations (new uses of the screwdriver). But as we have just seen, we cannot deduce that new use! We cannot logically or algorithmically derive all the new uses of things, or all the new functions, that come to exist in the evolving biosphere.

For example, all that has to happen in the evolution of some bacterium in a new environment is that some molecular screwdriver “find a use” that enhances the fitness of the bacterium in that new environment. Then, thanks to heritable variation and natural selection operating on the Kantian Whole of the bacterium, that new use, hence new function, may come to exist in the evolving biosphere. The molecular screwdriver and its new function – and the organism housing it – will get to exist for some period of time in the non-ergodic universe. But because we cannot list all the uses of screwdrivers, nor deduce the possible new uses of a screwdriver, we cannot PRESTATE what those uses will be. The issue here is vastly different from the difficulty of PREDICTING. Consider throwing a fair coin 100 times. We do not know if it will come up heads fifty-five times. But we can use the binomial theorem to calculate the probability it will come up fifty-five times. Critically, in the case of the coin flip, we know all possible outcomes of 100 flips of a coin. We know the “sample space” of the process, in which any particular outcome itself is a random process. But in the case of the evolution of the biosphere into the Adjacent Possible that it itself creates, we do not know the sample space of the process. We not only do not know what will happen, we do not even know what can happen. We cannot say what is “in” the Adjacent Possible of the evolution of the biosphere. Our incapacity to prestate possible future pre-adaptions is not a failure to predict; it is something far more profound. Because we do not know the sample space of the process of evolution, we cannot even define “random.” Such a definition requires that the space of possibilities can be specified first, and then a process can contain random outcomes in that space of possibilities. But here, we can form no probability calculus for the becoming of the biosphere into its unprestatable Adjacent Possible.

10 no law entails the becoming of a biosphere

In physics, we always prestate the phase space: for example, as we saw earlier, the phase space of the billiard balls on a specified table. But, as we just saw with our screwdriver example, we cannot prestate the ever-changing phase space of biological evolution – and for reasons that reach far beyond the “unpredictable” and the “random.” Because we cannot prestate the ever-changing phase space of the evolving biosphere, we can write no laws of motion for that evolution in the form of differential equations. Therefore, we cannot integrate the equations we do not have. And therefore, NO LAW entails the evolution of our, or any, biosphere (Longo, Montévil, and Kauffman). No Law. No deducing of all new uses of all things for all unprestatable tasks and functions. The rotation of flagella, molecular motors pulling cargo along fibrils, swim bladders, flight feathers, hearts that pump blood: all are part of the ever-changing phase space of evolution. Is it any wonder that no one could have predicted, three billion years ago, that the capacity of an elephant to spray water on itself via its trunk would help it survive three billion years later?

Kant said there would never be a Newton of a blade of grass, and he was right. We cannot “do Newton” for the evolution of biospheres. Three hundred and thirty years after his Principia, we are, with evolving life, beyond the Newtonian Paradigm. And we are beyond Pythagoras. It is not true that All is Number, and the dream of a “final theory” that will entail all that becomes is dead. Life is based on physics, Logos, but is a world beyond it. The becoming across time of biospheres is one of untellable creativity in which evolution creates and becomes into the opportunities that it itself, unprestatably, creates.

11 story

The becoming of life for 3.7 billion years is a Raphael tapestry richly interwoven, one that tells the story of millions of species and their populations that strut and fret their hour upon their stages and then, indeed, are heard no more. Shakespeare was right, as ever. The widely branching Tree of Life, entailed by no law, is the stuff of story, of narrative. If we cannot deduce what will happen, we can only tell the tale afterwards. We can reconstruct the history of life, as we have done with Darwin and paleontology. Story is needed where deduction fails us. So, here are the same facts, again, but a different story. From 3.7 billion years ago: protocells, single-celled prokaryotes and eukaryotes, multi-celled organisms, the Cambrian explosion, the Phanerozoic with thirteen phyla, the vertebrate lineage with fish, amphibians, reptiles, mammals. The hominid lineage branched from the broader Primate lineage about three million years ago with Australopithecus, followed by Homo erectus, Homo habilis, and us, Homo sapiens, with our cousin, Neanderthal.

We are social primates; our behaviors and ethics evolved with us. Franz de Waal did a wonderful experiment with two capuchin monkeys. The two were in adjacent cages and could see one another. For days, de Waal gave each monkey a slice of cucumber in the morning. One day he gave a grape to one monkey and a slice of cucumber to the second. Enraged, the second monkey spat out the cucumber, shook the cage door, and screamed out his anger: “It isn’t fair!” Thence our evolved sense of justice, or so de Waal surmised. From single-cell stentor to all organisms, emotion has evolved with the increasing complexity and diversity of the worlds we make with one another, our Umwelts (Hoffmeyer). As biosemiotics stresses, the bat lives in a “bat world,” the dog in a “dog world,” the trout in a “trout world,” and we, in a “human world.” Life has evolved from “approach or avoid” to the rich filigreed structure of our own legal systems.

The first of the hominid lineage, Australopithecus, was the first to fashion stone tools, some dozen in number and crudely made. Hundreds of thousands of years passed, and tools improved at a glacial pace. Knife blades grew longer by a few centimeters over hundreds of thousands of years. Compound tools, such as knife blades grafted to a bone handle, emerged about 300,000 years ago, perhaps with the emergence of Homo sapiens. In many ways, we are the same species we were 300,000 years ago. Our technology evolved at the same glacial pace again for another 200,000 years, with a gradual increase in the number of tools and their gradual differentiation into more and more complex tools. Cro-Magnon inhabited the Périgord region in the south of France and the north coast of Spain some 30,000 to 15,000 years ago. The Cro-Magnon museum in Les Eyzies has a magnificent collection of superb pressure-flaked stone tools, arrow heads, needles, fishing hooks, spears, axe heads, bracelets, chisels, and polishing stone; the atlatl, the compound spear thrower that allowed Cro-Magnon to hurl spears at aurochs from meters away; and shallow stone hollows and shells to hold dried fern wicks for candlelight. The cave wall paintings at Lascaux, world famous, rival Picasso for line and form. What rites were held there? Neanderthal buried their dead and had needles and flutes 60,000 years ago.

With this evolution of simple to more complex and valuable tools, inequality also arose. Tim Kohler and his colleagues studied sixty-seven Neolithic sites from about 30,000 years ago and found clear evidence of inequality in the divergent distribution of living quarters (Kohler et al.). Another Neolithic site shows many graves, three with adolescents buried with complex necklaces comprised of thousands of beads brought from several hundred miles away. These bespeak inequality and inherited wealth. In The Great Leveler, Walter Scheidel pursues such clues in the larger context of 10,000 years of violence and collapse: a history of inequality.

The agricultural revolution was some 8,000 years ago. In the Near East, wild grasses were domesticated. Food diversity shrank, as did human stature, but food could be reliably stored. The plow transformed agriculture. The first empires arose: Egypt, Mesopotamia, in the Indus Valley, and China 5,000 to 4,000 years ago. Thus, about 7,000 years after hunter-gatherer Cro-Magnon, with its few hundred tools ranging from simple to more complex – we find in Mesopotamia perhaps 1,000 tools, ranging from the needle Neanderthal had 60,000 years ago to something as complex and laden with value as the chariot.

Ancient Greek culture flourished 2,500 years ago: Eros and Logos, the gods, the Fates, chance and contingency, Thales, Anaximander, Democritus, Socrates, Plato, Aristotle, Sophocles. From 4,000 years ago, the Jews and the monotheism of the Abrahamic Traditions arise. From 1,000 to 500 bc, the Axial age (Bellah and Jonas): Buddha, Confucius, Socrates, Plato, Jeramiah. Humanity seeking something beyond the god of the hunt. And then, the Roman Empire, from 300 bc to about ad 300: Lucretius and De Rerum Natura, and Emperor Constantine’s adoption of Christianity for the Empire in ad 313, Ptolemaic astronomy with its hypercycles to explain the wandering orbits of the planets.

St Augustine ad 400: The City of God, that founds much of Church Doctrine. And for almost 1,000 years in post-Rome Europe, people ignored this life, seeking their salvation in the next. Aristotle is lost in the West but survives in the Islamic world from ad 632 on, brought to Spain by Maimonides to Andalusia. With the reintroduction of Aristotle in the West, Aquinas, in Summa theologicae, argues in ad 1268 that both the Old and New Testaments (but also Nature) are God’s work. It becomes permissible to study this world. The Scholastics flourish, and universities are founded in Paris and Padua. Cervantes writes Don Quixote in 1615.

The earth is at the center of the universe, surrounded by the celestial spheres carrying the moon, the sun and the stars. God is above, below are the angels, below is Man, below Man are large animals, then worms, then the concentric levels of Hell. Humanity is the center of all things, enjoined by God, who commands Adam to name the animals and take dominion over all things. Then Copernicus, using the data of Tycho Brahe, proposes that the earth revolves around the sun, a heliocentric view last suggested by the ancient Greeks but lost. Galileo, using a simple telescope, sees the four moons of Jupiter. If the tiny moons revolve around giant Jupiter, why not tiny earth around the giant sun?

Consider the Church. Its cosmology for over 1,000 years was Ptolemaic, with the earth at the center of the universe, as Cervantes had written. All revolved around Man poised between God, heaven, and the deepest level of hell. If the views of Copernicus and Galileo held, the moral order of the Church and Western World would be lost. Galileo faces the Inquisition formed to block such moral insurrection; he faces house arrest and mutters “E pur si muove.” “And still it moves.” Galileo’s courage becomes the moral rallying cry of science: truth. Then Kepler, Newton, and Laplace and his demon, who, knowing the positions and momenta of all the particles, could compute the entire future and past of the universe. This is the birth of modern Reductionism. And Nobel Laureate Steven Weinberg dreams of a “Final Theory” in which Logos, law, is all. But this, as we have seen, is only half the story.

So where are we now? Our toolkit has grown exponentially, from a glacial pace over millennia to an explosion: hundreds of tools in the global economy ten millennia ago, billions today. For millennia, the needle Neanderthal had 60,000 years ago and its modest improvements; today, the Space Station. Our $100 trillion growing juggernaut global economy overwhelms the planetary biosphere that has flourished for 3.7 billion years. And here we are in the so-called Anthropocene, with global warming and a mass extinction event underway. Humanity has never faced such a crisis, either in scale or in existential terms.

What will the 7.7 billion of us do? What can our diverse civilizations weave together in the face of this crisis? We have, perhaps, a new origin myth: our becoming in the long flowering of our biosphere. We are of Nature, not above Nature. Life, our selves among it, is magical, is sacred. A transnational mythic structure is subtended by our membership and participation with all of life.

The Gospel of John begins:

In the Beginning was the Word.

The Word was with God

The Word was God

The Word became flesh and dwelt among us.

I prefer to read this passage with a different sense of the sacred. What more could we want from all the gods of our past 300,000 years – the gods of the stone, the stream, the willow, the volcano, the moon, the sun, Zeus, Athena, Diana, Mercury, Thor, Woden, the God of Abraham and the Axial Age – but that the gods afford us the opportunity to co-create our shared reality?

disclosure statement

I have no grants and am free to publish this work.