“We humans are such limited creatures — how is it that there are so few limits when it comes to human suffering?”
— Pierre Marivaux, La Vie de Marianne[1]
Must we suffer? If so, why? Is the qualitative experience of suffering essential to embodied consciousness, or might it be transcended without consequence? Such questions permeate the world’s religious writings, forming a metaphysical through-line that spans humanity’s existential struggles. Beyond written artifacts, the oral traditions that birthed our religious inscriptions extend humanity’s reflections upon suffering by some unknown thousands of years. That these reflections both penetrate so deeply in time and span the breadth of human cultures suggests a developmental hypothesis. Namely, that embodied suffering provides a phenomenological foundation upon which humanity erected its otherwise multifaceted edifices of religion and philosophy. From Marduk’s Ordeal to Buddha’s Sutras, from the Upanishads of Hindu Rishis to Christ’s Sermons, the question of suffering animates humanity’s religious inquiries. Buddha’s first Sutra succinctly captures the concept’s centrality within the phenomenology of religious thought:
Now this, bhikkhus, is the noble truth of suffering: birth is suffering, aging is suffering, illness is suffering, death is suffering; union with what is displeasing is suffering; separation from what is pleasing is suffering; not to get what one wants is suffering; in brief, the five aggregates subject to clinging are suffering.[2]
Jesus’s disciples were equally interested in the topic:
For it is commendable if someone bears up under the pain of unjust suffering because they are conscious of God. But how is it to your credit if you receive a beating for doing wrong and endure it? But if you suffer for doing good and you endure it, this is commendable before God. To this you were called, because Christ suffered for you, leaving you an example, that you should follow in his steps.[3]
Thus across the millennia, as humanity organized itself into social assemblages of increasing complexity, we held the question of suffering — perhaps the deepest of religious questions — close at hand. Yet only three centuries ago, amidst the rise of Enlightenment thought and its methodology of scientific empiricism, the epistemic pendulum swung rapidly away from ontologies predicated upon shared qualities of subjective human experience, and toward those centered on aspects of experience amenable to formalization via objective measure. After all, if something could not in theory be measured, it could not in practice be modeled. And if one could not model a phenomenon in practice, how might a free-thinking scientist of the Enlightenment form a hypothesis concerning its analytic behavior? This belief-system reached its 20th century apotheosis in the form of Logical Positivism, of which Heisenberg once said:
The positivists have a simple solution: the world must be divided into that which we can say clearly and the rest, which we had better pass over in silence. But can any one conceive of a more pointless philosophy, seeing that what we can say clearly amounts to next to nothing? If we omitted all that is unclear we would probably be left with completely uninteresting and trivial tautologies.[4]
In this spirit of fertile ambiguity, we will herein seek new common ground between the religious and empirical perspectives so typically framed as opposites. With the concept of suffering as our speculative blueprint, we will begin to bridge ontologies erected separately upon the axiomatic shorelines of subjective experience and objective analysis.
In service of this aim, we will formulate and attempt to make tractable the problem of suffering through a process-focused, rather than a substance-focused, empirical framework. I hope to demonstrate that such a synthesis need not undermine the phenomenological wisdom of the past, encoded time and again within our species’ many religious traditions. To the contrary, it appears this novel definition of suffering — one that draws upon both recent and well-worn concepts in mathematics, physics, neuroscience, and philosophy — returns us to the religious axiom of suffering as the existential ground from which the experiential figure itself emerges. Or, as translated into the language of physics: I will argue that processes typical of evolved biological consciousness demonstrate functional symmetries that fundamentally conserve the experiential quality we call suffering. In so doing, I aim to clarify the relationship between emergent symmetries of process and the subjective experience of human suffering, and to demonstrate why attempts to reduce suffering in any absolute sense will likely undermine the capacity for conscious experience itself.
Symmetry and Conservation: A Fractal Application of Noether’s Theorem
“Felicity is a continual progress of the desire, from one object to another; the attaining of the former being still but the way to the latter.”
— Thomas Hobbes, Leviathan[5]
Before we map the relationship between symmetries exhibited and properties conserved within simple physical systems onto biological cognition and the concept of suffering, we must first discuss the fundamental connection between mathematical symmetries and conserved physical properties. In 1918, with World War I coming to a close, German mathematician Emmy Noether published one of the most transformational theorems of the 20th century. Her theorem demonstrated that for all symmetries within a system — given said system meets certain mathematical constraints[6]— there exist corresponding conserved quantities. It is difficult to overstate the impression her discovery left upon the field of physics; suffice it to say a great deal of modern physics rests upon this relationship between mathematical symmetries and conserved physical properties.
In pragmatic terms, what does Noether’s theorem tell us?
Consider an object moving through space. While observing the object, one might ask whether the regularities of its movement depend upon its position within the system. For example, let us consider a 2-dimensional Cartesian plane with coordinate system (x, y). Given our simple system consisting of a single moving particle, we observe the particle travel from point (0,0) to point (0,1). Next, we shift the experiment up by one unit in the y-dimension and observe that the particle travels from (1,0) to (1, 1). If our particle exhibits no change in its behavior, we say that its dynamics are symmetric under transformation. We may also conceptualize this symmetric transformation as formalizing our inability to specify an absolute frame of reference for our system with respect to linear transformations, given that all objects within it behave identically despite shifting the coordinate system. The above describes the symmetry of space under translation, and Noether’s theorem tells us that this particular symmetry conserves linear momentum within the system. In other words, if this symmetry holds, momentum is conserved; if momentum is conserved, this symmetry holds.
The relationship between symmetry and conservation accurately describes observed dynamics at multiple scales and across a wide variety of physical systems: the translational symmetry of space conserves momentum; the translational symmetry of time conserves energy; the rotational symmetry of space conserves angular momentum; the quantum mechanical symmetry of phase conserves charge. But the theorem’s application does possess limits. As mentioned earlier, certain criteria must apply if we wish to leverage Noether’s theorem. Foremost among these is the requirement that the system under consideration remain continuously differentiable.
Let’s unpack this concept using our 2-dimensional example. For our one-particle system to remain continuously differentiable, we must at any point upon a curve tracing its movement through space and time retain the capacity to find a line tangent to said curve. In other words, the theorem only holds for physical systems that we may approximate using smooth mathematical structures. Yet a vast majority of natural systems, including biological systems, exhibit distinctively rough — or fractal—structure. It appears that if we wish to connect this abstract mathematical theorem to the domain of biology, let alone to the subjective experience of human suffering, we must refine it such that the implication of conservation via symmetry holds even for supposedly non-differentiable fractal systems.
Is such a refinement of Noether’s theorem possible? Might we apply its elegance and power to the fractal systems so prevalent in nature?
Given recent research into the matter, it appears likely. Within the field of fractional dynamics, researchers have developed the capacity to apply calculus to a growing array of natural systems that exhibit fractal characteristics.[7] In fact, earlier this year a group of mathematicians published a paper proposing an analog of Noether’s theorem within fractal calculus.[8] Therein they describe a kind of symmetry that holds across the self-similar scales of a fractal process, coining the corresponding term fractal momentum to describe the conserved property in question. For the moment let us suspend analytic scrutiny, and instead raise the question as to how we might conceptualize this systemic property of fractal momentum. Insofar as it’s possible to communicate abstract mathematical concepts using language, one might describe fractal momentum as a process’s tendency to generate a specific pattern of recurrence as it unfolds — governed by its own internal dynamics — across time. This unfolding symmetry characterizes fractal animations in which one zooms into a complex shape exhibiting apparently unique structure, only to observe familiar structures reappear at novel scales. Such visualizations trace the eternally recurrent fingerprint of a generative process responsible for a specific fractal pattern.
Using this definition, nature conserves fractal momentum by building upon processes that demonstrate the capacity to re-create stable symmetries across scales, a capacity I would like to call recursively generative symmetry. We see such recursively generative symmetries throughout nature’s varied domains and across its many scales, though we should remain careful not to confuse the substantive symmetries produced by these processes for the symmetries of the processes themselves. For example, the self-similar patterns of a fern’s branching leaves display static symmetries of substance, precipitated in the present by ancient dynamic processes whose fractal momentum recursively generates the fern’s momentary physical structure. Such a process, informed by its prior states, must generate outputs that facilitate its developmental trajectory. These outputs in turn become the inputs of the next recursively generative cycle. That this process retains its integrity across time, that it does not simply disintegrate into random mutations or chaotic non-patterns, is well-captured by the relationship between its recursively generative symmetries and their conservation of fractal momentum.
To see why, we shall return to our one-particle system and its momentum-conserving translational symmetry. If we introduce a massive object at one edge of this system, is the system’s momentum still conserved? No, it is not. We may no longer arbitrarily translate our coordinate system without observing changes in the behavior of the particle; we have broken its translational symmetry and may no longer rely upon the conservation of the system’s momentum. Analogously, let us consider the implications of symmetry breakage within recursively generative processes. Breaking such a symmetry interrupts its capacity to re-generate itself across time. Given that recursively generative symmetries may at any moment incarnate their potential for continuation within a large number of actualized organisms, breaking a generative symmetry requires nullifying the entirety of its generative potential by terminating all organisms capable of conserving its fractal momentum. Thus, the breakage of recursively generative symmetries and the corresponding loss of fractal momentum appears indistinguishable from extinction.
It should therefore prove possible to use impending measures of fractal momentum within complex adaptive systems , above posited as a proxy for the integrity of underlying processual symmetries , to assess the stability of evolutionary processes. Of course, the process of interest in this essay — upon which our phenomenological speculations rest — is the evolution of our own subjective experience. Empowered with a generalized Noether’s theorem and aware of its implications, we may discuss how recursively generative symmetries shaped the emergence of humanity’s own sense-making capacities and explain the centrality of said symmetries to the subjective experience of suffering.
Emergent Attractors Upon the Neurobehavioral Landscape
“The ladder’s the same. I’m at the bottom step, and you’re above, somewhere about the thirteenth. That’s how I see it. But it’s all the same. Absolutely the same in kind. Anyone on the bottom step is bound to go up to the top one.”
“Then one ought not to step on at all.”
“Anyone who can help it had better not.”
“But can you?”
“I think not.”
— Fyodor Dostoyevsky, The Brothers Karamazov[9]
Given our desire to map the concept of a recursively generated symmetry onto the domain of cognition, we must posit properties that the simplest such symmetry might possess. Conceptually, what is the simplest such process that if observed we might consider aware of its own context? Given our generalized Noether theorem, we may flip this question on its head and instead ask: what is the simplest process that conserves its own fractal momentum? Such behavior would demonstrate an organism’s capacity to alter its own survival probability, and for a process to alter its own probability of survival it must increase the likelihood of future events that maintain its processual symmetries while decreasing the likelihood of events that break them. That is, such a process must avoid certain death and seek opportunities for continuity. Furthermore, it must demonstrate this capacity at a level beyond what one would expect of a random, undirected process. As an aside, we should clarify that when speaking of death or continuity, we are speaking in the abstract. Formally, we are concerned with any behaviors that impact the continuation or cessation of a recursively generative process beyond a random baseline. Such a process dynamically conserves its own fractal momentum across time via the maintenance of its own processual symmetries.
Are we aware of such processes? As it turns out we are, both in abstract mathematical and concrete biological terms. Beginning with the latter, biologists call an organism’s capacity to respond behaviorally to a molecularly relevant environmental gradient chemotaxis. Many single-celled organisms can detect the presence of molecules either disruptive or conducive to their metabolic coherence. Not only can these ancient lifeforms detect such gradients, they can move toward that which is conducive and away from that which is disruptive to their own continuation. In this way behavioral characteristics emerge — early in the evolutionary process of life itself — that meet our criteria of conceptually simple mechanisms capable of facilitating the conservation of an organism’s own fractal momentum. This shift from a largely stochastic process in which fortune alone selected winners and losers, to a process in which an organism’s survival correlates with its capacity to behave in a context-dependent manner, traces the closure of an emergent processual symmetry, and therefore the establishment of a conserved property of some kind. We will below more adequately explore what this symmetry conserves, but first we must clarify the abstract concept of processual closure itself.
Processual closures establish stable cycles. To understand why such cycles emerge, we must introduce the concept of a cellular automata (CA). CAs are computer programs that encapsulate the relations between entities in simple rules governing local interactions, then allow these rules to guide the system’s behavior across time. For example, a one-dimensional string of binary cells (0|1) three units in length possesses 2³ possible system states. To begin we choose an initial state at random, then assign rules that each cell uses to generate its next state. Consider the following simple rule, applied for each of our three cells at each step in our simulation: if at least one of my neighbors is 1, invert my own state, else do nothing. We then iterate this one-dimensional rule-based system some number of times. In our one-dimensional example, as well as within higher dimensional CAs, most rules yield uninteresting interactions, converging rapidly to fixed states that no longer evolve in time.[10] However, a small proportion of exceptional cases demonstrate remarkable behaviors. Famous among these exceptions is Conway’s Game of Life, in which a finite set of rules governs the behavior of binary cells upon a two-dimensional plane.[11] From the game’s deterministic rules emerges a complex behavioral ecology consisting of higher-order processual species. These emergent species sustain coherent multi-cellular behaviors as a byproduct of locally deterministic interactions between cells. They can move, eat, and even reproduce. Critically, the underlying rules define none of these behaviors.
That systems following simple local rules generate coherent cycles of complex behavior presents a clue concerning the structure of the underlying evolutionary landscape. Research into this structure shows that such cycles act as attractors for states lying outside the primary cycle.[12] Consider a CA in state X. Given some set of rules, it moves from state X, to Y, to Z, then back to X. This forms a cycle of states, or limit-cycle attractor. It is an attractor because we may demonstrate that many states exist such that they eventually land upon states X, Y, or Z. And once within the closed loop of the X-Y-Z attractor, absent external interruptions, the state cycle continues ad infinitum. For this reason, we call such cycles basins of attraction, evoking imagery of water flowing down from widely distributed mountain peaks into something like a behavioral whirlpool. These dynamics possess deep parallels with the emergence of stable metabolic networks,[13] and it is therefore tempting to imagine self-aware cognition — no less consciousness — as a sensation that internally reflects the integrity of such a cycle’s recursively generative symmetries. Jumping from the emergence of metabolic networks to concepts such as cognition and consciousness might arouse suspicion, given many specialized fields each lay claim to territories along this spectrum. But it is this tendency to balkanize research within specific scales that has for so long rendered invisible features of complex systems that hold true across scales. If we flip this path-dependent paradigm and instead consider most real those behavioral tendencies that emerge regardless of scale or material substrate, it is natural to consider concepts such as consciousness as higher-order extensions of older phenomena at smaller scales, such as coherent metabolic networks. However, in order to satisfy our earlier litmus test for cognition, we must also posit the capacity of such a metabolic basin of attraction to process information concerning its own fractal momentum. What might that look like?
As it turns out, information-processing mechanisms capable of detecting environmental gradients appear to generate higher-order sensitivities to, and preferences for, symmetries of various kinds.[14] This tendency implicates the neural processes responsible for approach and avoidance behaviors as the origin of an organism’s capacity to detect environmental symmetries, and perhaps also the capacity of an organism to detect symmetries within its own internal state. If such speculations hold, we may re-frame the evolutionary path toward increasingly complex information-processing systems as the selection of those adaptations that allow organisms to detect and respond to increasingly complex symmetries, both without and within, substantive and processual. Thus, we see that stable basins of behavioral attraction — particularly those responsible for behavior relative to meaningful gradients—enable the emergence of new processual symmetries sensitive to increasingly differentiated phenomenological states. In this manner a system that conserves its fractal momentum may increase both the scope of potentiated and diversity of actualized subjective experiences. It is to the nature of such states, the most fundamental of which we call suffering, that we now turn.
States of Consciousness as Fractal Symmetry Sensitivities
I leave Sisyphus at the foot of the mountain. One always finds one’s burden again. But Sisyphus teaches the higher fidelity that negates the gods and raises rocks. He too concludes that all is well. This universe henceforth without a master seems to him neither sterile nor futile. Each atom of that stone, each mineral flake of that night-filled mountain, in itself, forms a world. The struggle itself toward the heights is enough to fill a man’s heart. One must imagine Sisyphus happy.
— Albert Camus, The Myth of Sisyphus[15]
This line of reasoning re-frames subjective experiences, or emotional states, as nested processes of increasingly differentiated, self-preserving symmetries. In this process-oriented model, the sensation we call consciousness emerges naturally out of the capacity of a metabolic cycle to process information pertaining to the environment’s impact upon internal symmetries responsible for its own continuation. Therefore, perturbing or breaking symmetries equates to a decrease in fractal momentum, and because decreasing fractal momentum eventually leads to death, a sensitivity to entropy’s constant asymmetric perturbations generates constant existential anxiety. It is in this sense that suffering forms the phenomenological ground from which a more nuanced conscious figure arises. Such a phenomenological backdrop fundamentally constrains the subjective experience of complex life forms: if our most fundamental processual symmetries emerge out of the capacity to direct behavior relative to gradients, the entirety of our subjective cognition nests within a fundamental symmetry whose maintenance generates existential suffering.
We should also note that the tension between symmetry-maintenance and entropy appears at once fundamental and irreconcilable. That is, at each step in a recursive process an organism may die, in effect paying the ultimate price and losing all opportunity for continuation. Yet there exists no move capable of attaining an upside of equally infinite magnitude; the best possible outcome is that an organism preserves its present internal symmetries such that it conserves the potential to maintain its symmetry in the face of future entropy. This is, at its most fundamental level, the Game of Life: the potential for infinite downside at any possible moment, balanced against hard-won upside that ever only amounts to the next round’s ante. We therefore observe the Sisyphean struggle baked into the foundations of consciousness itself.
Furthermore, if suffering characterizes an emergent process whose sensitivity adapts to increasingly fine-grained disruptions, we should not expect to meaningfully reduce subjectively perceived human suffering without severely disrupting the fundamental symmetries that give rise to consciousness itself. Evidencing this pattern is the fact that despite exponential progress in absolute terms along numerous empirical dimensions used to measure material human progress, we possess no evidence that the average person experiences less psychological suffering. In fact, across many of humanity’s most materially developed cultures, we observe precisely the opposite: increasingly fine-grained psychological sensitivity to, and subjective suffering as a result of environmental factors that would appear quite desirable to our ancestors.
However, this is precisely what we would expect of an organism whose conscious awareness arises out of habituation to stable symmetries and sensitization to disruptions upon an ever-finer fractal boundary. In fact, it is in no way obvious that the processual symmetries discussed thus far could arise–much less stabilize–without the capacity to suffer in a manner that promotes self-preservation, given that our concept of suffering maps at its deepest level to the basic detection of symmetry breakage.
We should therefore meet with the greatest of skepticism the utopian notion that we may eradicate human suffering without severely compromising the very nature of consciousness itself. Such temptations metastasize during times of great uncertainty, and over the coming decades we will see no shortage of those who advocate for changing the fundamental dynamics of our neurological or genetic structure in service of reducing suffering, increasing bliss, or some such nice-sounding idea. Yet before walking naively down such paths it behooves us to think deeply about removing probable lodestones from the emergent tower of conscious experience. Our religious traditions have for millennia singled out suffering as one such lodestone, and I hope to have at least planted the seed in the reader’s mind that the vanguard of our empirical and theoretical lines of research appear to point, cyclically, back to truths once taken at face value as the foundation of the human condition: that life is suffering, and we must therefore embrace the probability that the capacity for consciousness itself rests upon suffering’s conservation.
Notes
[1] Pierre Marivaux, “La Vie de Marianne,” in John Gross ed., Oxford Book of Aphorisms (New York: Oxford University Press, 2003), 170.
[2] Buddha, Dhammacakkappavattana Sutta, translated by Bikkhu Bodhi, https://www.budsas.org/ebud/ebsut001.htm
[3] 1 Peter 2:19–21
[4] Werner Heisenberg, Physics and Beyond—Encounters and Conversations (New York, Harper & Row: 1972), 213.
[5] Thomas Hobbes, Leviathan (Harmondsworth, England: Penguin, 1986), Chapter XI, paragraph 1.
[6] Emmy Noether, “Invariant Variation Problems,” available in English translation at http://cwp.library.ucla.edu/articles/noether.trans/ english/mort186.html. Original Noether paper published as E. Noether (1918), “Invariante Variationsprobleme.” Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, 1918: 235–257.
[7] Carlo Cattani, Hari M. Srivastava, and Xiao-Jun Yang, eds., Fractional Dynamics (Berlin, Germany: De Gruyter, 2016), https://www.degruyter.com/view/product/469437
[8] Alireza Khalili Golmankhaneh and Cemil Tunc, “Analogues to Lie Method and Noether’s Theorem in Fractal Calculus,” Fractal and Fractional 3 No. 25: 1–15,
[9] Fyodor Dostoyevsky, The Brothers Karamazov (Ware, Hertfordshire: Wordsworth Editions Limited, 2010), 116.
[10] Stephen Wolfram, A New Kind of Science (Champaign, IL: Wolfram Media, 2002), 79.
[11] Martin Gardner, “Mathematical Games—The Fantastic Combinations of John Conway’s New Solitaire Game ‘Life,’” Scientific American, 223 No. 4 (October 1970): 120–123. doi:10.1038/scientificamerican1070-120.
[12] Andrew Wuensche and Mike Lesser, The Global Dynamics of Cellular Automata: An Atlas of Basin of Attraction Fields of One-Dimensional Cellular Automata (Reading, MA: Addison-Wesley, 1992), 9.
[13] Stuart A. Kauffman, The Origins of Order: Self-Organization and Selection in Evolution, (New York: Oxford University Press, 1993), 348.
[14] Magnus Enquist and Rufus A. Johnstone, “Generalization and the Evolution of Symmetry Preferences,” Proceedings of the Royal Society London, 264 (1997), 1345–1348, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1688578/pdf/6N2VRTWKHMQ43B5F_264_1345.pdf
[15] Albert Camus, The Myth of Sisyphus and Other Essays, translated by Justin O’Brien (New York: Vintage Books, 1991).