Lucretius: Atomism, the Swerve & Holism

Synopsis

On the Nature of Things, a poem by Lucretius, reintroduced the philosophy of atomism to Western civilization. Atomism is the theory that the universe consists of tiny particles that obey absolute laws of nature. Returned to circulation during the Renaissance, the book initiated and catalyzed the scientific mentality that eventually resulted in the discovery of the atom. The theory could easily have provided inspiration to forward looking thinkers such as Galileo, Jefferson, Darwin and Freud.

According to atomism, the material world behaves mechanistically. However, Lucretius believed that humans and other life forms exhibit free will. At any moment, Life can initiate a swerve that changes the predetermined course of these tiny atoms. In this way, Lucretius’ perspective differs significantly from scientific determinism. However, it is totally in line with my Theory of Attention.

Lucretius’ poem introduced atomism to the scientific community. Under this perspective, the immutable nature of the parts determines the nature of the whole. Scientists applied this reductionist way of thinking to the material world to generate our technological wonderland. Their fabulous successes led them to the misconception that our Universe is entirely atomistic.

Rather than atomistic, an abundance of evidence indicates that living systems are holistic. Contextual relationships are more important than absolute content for holistic systems. This fundamental difference between living and material systems translates into differing mathematical systems. While Matter’s equations are closed, set-based, and definitive, Life requires equations that are open, reflexive, and probabilistic. The Living Algorithm both fulfills these requirements and reveals the patterns of Attention.

 

Section Headings

• History: Poggio’s rediscovery of Lucretius’ poem
• Discovery of Lucretius revives Atomism
• Materialism of Atomism: Alternative to Religious Superstition
• The Swerve: Alternative to Scientific Determinism
• The Logical Possibility of Choice
• Holism vs. Atomism
• The Sphere, Mobius Strip & Yin-Yang Symbol
• Mathematics: Inert Atomism vs. Living Holism

History: Poggio’s rediscovery of Lucretius’ poem

More than one scholar has written about the highly significant historical impact of On the Nature of Things upon the development of Western civilization. In his book, The Swerve, Stephen Greenblatt, Humanities Professor at Harvard and the author of many books on the Renaissance, claims:

“Its return to circulation changed the course of history. The poem’s vision would shape the thought of Galileo and Freud, Darwin and Einstein, and –in the hands of Thomas Jefferson– leave its trace on the Declaration of Independence.” ¹

Who wrote this pivotal work? Why and when did the book fall out of circulation? Who rediscovered the poem? What is the context of both the culture that produced this significant piece of literature and the culture that was receptive to its message? How did it ‘change the course of history’?

A Roman by the name of Lucretius (94-50 BCE) was the author of On the Nature of Things. He composed the book in poem form in the first century before the Common Era. Lucretius “argues that the world is made of atoms and that fear of death is foolish.”² According to St. Jerome (340-420 CE), Lucretius went crazy on love potions and committed suicide at the age of 44. This highly skewed account is unfortunately the only biographical information we have about him.

On the Nature of Things disappeared from circulation for over a millennium. The Italian Poggio Bracciolini (1380-1459) rediscovered Lucretius’ great poem in the 15th century. It launched all kinds of radical intellectual inquiry that eventually spawned our modern mentality.

Why did the book disappear? What factors led to its rediscovery? Why did it have such a large impact? Let us connect some dots.

Poggio Bracciolini was part of the emerging humanist movement in Italy. The humanists redirected their attention to Greco-Roman times. More specifically, they were interested in pagan antiquity, i.e. pre-Christian culture. To this end, they began collecting anything that came from this long lost era. This included statuary and literature.

One of Poggio’s colleagues, a wealthy aristocrat, was instrumental in transforming ‘old junk’ into ‘valuable collectibles’. Initially, the citizenry was happy to provide the ‘ancient debris’ for a nominal charge. Seeing how valuable it was to him and his circle, the peasantry eventually, perhaps inevitably, began charging ever higher prices for these collectibles from antiquity.

As a scribe who was famous for his handwriting, Poggio’s specialty was literature. He was not just any old scribe, Poggio was the head scribe of the Pope. Poggio’s boss was also exceptional in that he was perhaps the most corrupt Pope in the history of the Catholic Church. The Pope’s abuses of power were so extensive that he was forcibly removed from his exalted position – an extraction without precedent.

Without a patron, Poggio was able to pursue his other passion – collecting ancient manuscripts. Poggio headed north to the monasteries of France, Switzerland, and Germany. He was in search of Greek and Roman documents. Poggio, however, was not looking for just any old manuscript. He was looking for On the Nature of Things by Lucretius.

How did he know that it even existed? By this time, the humanists had uncovered many documents. The existent literature from Greco-Roman times had referenced many works that had not yet been discovered. Evidently Lucretius’ lost poem had been mentioned enough times that it had piqued the curiosity of the humanists.

Why did Poggio’s search lead him to monasteries? Catholic monks had been meticulously transcribing ancient documents for over a millennium. Most of the works were Christian in nature, e.g. the Bible, St. Thomas Aquinas, and St. Augustine. They also copied pagan literature. This included Greek and Roman histories, plays and philosophy.

There was, however, an entire class of literature that was neglected, ignored, or outright avoided by the monks. This category included any compositions that were deemed heretical in nature. The Church’s followers had burned some of these books. The monks censored the heretical documents that survived the conflagration by simply refusing to copy them.

Some of these censored works were Christian in nature, but from the branch that lost, i.e. didn’t follow the official Church dogma closely enough. Intriguingly, many pagan documents survived via repeated transcriptions that concerned philosophy, e.g. Plato and Aristotle, science, e.g. Ptolemy and Euclid, and ancient religions. As these works didn’t directly attack the rigid beliefs of the Church, they weren’t considered heresy and could presumably be read without the fear of corruption and rebellion from the fold.

The philosophical tradition that spawned On the Nature of Things emerged long before Christianity’s ascendancy, which began in the 4th century of the Common Era with Constantine the Great. As such, literature from this school of thought never directly attacked Church dogma. However, censors considered any documents from this tradition as heretical. The content was perceived as heresy. The works were either burned or neglected by the transcribing monks for over a millennium. Why? The intellectual content was an indirect challenge to the precepts of Catholicism.

If the rest of the writing from this school was lost, why was Lucretius’ poem copied? As there is no existent evidence one way or the other, no one really knows. The best guess is that the poetry is so compelling that monks continued copying the document despite its heretical content. Perhaps the poem’s beauty was so distracting that they ignored the content.

Further, the book was only available to the monks in a particular monastery, not the general public. The monks could be exposed to radical ideas for two reasons. As they were insulated from the general society, the beliefs could not infect a greater population and spread. As True Believers, the monks were more immune to the heresy.

After an arduous search through many monasteries, Poggio finally came upon the sought after document. Perhaps because of the beauty of the poetry, Poggio was able to escape the watchful eyes of the censors and return Lucretius’ poem to more general circulation. Then perhaps due to the greater curiosity of the Renaissance philosophers, the right people read and became inspired by the poem to perceive the natural world from a fresh perspective. As these curious and questioning people accumulated, traditional superstitions faded in significance and the scientific mentality took hold. This general trend eventually resulted in our modern world.

Discovery of Lucretius revives Atomism

Why was the content of Lucretius’ poem so inflammatory that it was first banned and then transformed human culture? Whatphilosophical school did Lucretius belong to? And why did the Church censor their literature?

According to Greenblatt’s well-researched analysis, Lucretius was following the intellectual tradition of the Greek Epicurus (c341-270 BCE).

“With Epicurus, we close the circle back to Lucretius, for Lucretius was Epicurus’ most passionate, intelligent, and creative disciple.” ³

Epicurus was an Athenian philosopher, whose philosophy, Epicureanism, had a significant impact on the intelligentsia of both Greece and Rome for over half a millennium.

“[Epicureanism] regarded the purpose of life to be the pursuit of pleasure, by which was meant contentment and peace of mind in a frugal life.” ⁴

A prodigious writer, Epicurus wrote some 37 books, all of which have been lost to the ravages of time and presumably Christian censorship. According to Diogenes Laerties, a contemporary Greek philosopher, Epicurus didn’t cite other authors, but spoke for himself. ⁵ His philosophy was based on the notion of epilogismos, ‘reasoning based upon empirical data’. This was an everyday procedure for assessment and appraisal’ – “not reserved for mathematicians and dialecticians.” ⁶

The philosophy expounded by Epicurus, in turn, revived the atomism of Democritus.

“Democritus of Abdera (c460-370 BCE), Greek materialist philosopher. One of the earliest exponents of atomism, he maintained that all phenomena were explicable in terms of the nomic motion of atoms in the void.” ⁷

Democritus first formulated the theory of atomism in the 5th century BCE. Epicurus revived the theory 200 years later in the 3rd century BCE and then 2 centuries later Lucretius refocused attention upon atomism. And then after a millennia and a half, it provided a major impetus to modern scientific thought.

What is this atomism that philosophers passed on for centuries and then proved so influential to our modern world?

 “Atomism, the theory that all matter consists of atoms – minute indestructible particles, homogeneous in substance but varied in shape. Developed in the 5th century BCE by Leucipus and Democritus and adopted by Epicurus, it was expounded in detail by the Roman poet Lucretius.” ⁸

Materialism of Atomism: Alternative to Religious Superstition

The philosophy of atomism was a refreshing alternative to the religions of the time, especially for the intellectuals. Most, if not all, ancient cultures, including Romans, Jews, Egyptians and Greeks, attempted to propitiate their gods, goddesses or god through a variety of means, including sacrifices, rites, donations and/or rituals. These actions were intended to gain the favor of the gods and thereby change their behavior. For instance, women lit candles to the appropriate goddess in order to become pregnant; men sacrificed animals or erected temples to their gods to become successful in war; and humans practiced what they considered to be good behavior to further their chances in the after-life.

In contrast, Lucretius and the atomists held that even if there are gods, that human behavior does not influence their actions. Instead, the atomists maintained that the collisions of atoms, ‘minute indestructible particles’, determine the events of the world, both celestial and earthly. If all is matter, then spirits, afterlife and divine propitiation are all figments of the human imagination. This materialist approach stands in direct opposition to the fundamental beliefs of most religions. In fact, the Greek word religio is translated as superstition.

It is easy to see why the Catholic Church would have suppressed any document associated with the atomist way of thinking as heretical. It is probably no accident that none of the 37 books written by Epicurus survive. Curiously, the reason that Lucretius’ book, On the Way of Things, might have endured despite religious suppression was due to its poetic nature. Even after Poggio unearthed the work and had it translated, many Catholic intellectuals read the book for its poetry, simultaneously warning of its subversive content.

It is equally easy to see how the atomist philosophy espoused by Lucretius may have liberated forward thinking individuals from medieval views towards science. Lucretius’ notion that intractable laws govern the behavior of the atoms that make up the entire universe, i.e. both the heavens and the earth, certainly may have inspired Galileo’s search for absolute laws of motion. Recent documents unearthed in the Vatican suggest that Galileo was persecuted by the Catholic Church for his heretical views on both heliocentric view of the universe and atomism.

It is certainly striking how the beliefs of the atomists anticipated Newton’s discovery that both the earthly and celestial realms obey the same law of gravity. This leap in understanding could have easily been catalyzed by the atomist way of thinking that began to spread through Europe like wild fire after the return of On the Way of Things to circulation. It is equally amazing how the atomist perspective mirrors the modern perspective of the intellectual community. Our technological miracles stand as mute testimony to the scientific view that all is made of atoms. Indeed even the word ‘atom’ derives from the atomists of ancient Greece.

The Swerve: Alternative to Scientific Determinism

Despite his materialist perspective, Lucretius didn’t adopt the strict scientific determinism of the modern world. He believed that humans and in fact all of life has the ability to choose. Presumably, his belief was based in observation and direct experience. It is readily apparent that most life forms are constantly making choices, on the most basic level what to eat and how to procure it.

Lucretius was acutely aware of the conflict between a rigid atomist perspective and free will. He begins with the question of where choice comes from if we live in a world that is determined by logical necessity.

“If all movements are invariably interlinked, if new movement arises from the old in unalterable succession, if there is no atomic swerve [declinado … primordial motus] to initiate movement that can annul the decrees of destiny and prevent the existence of an endless chain of causation, what is the source of this free will possessed by living creatures all over the earth? What, I ask, is the source of this power of will wrested from destiny, which enables each of us to advance where pleasure leads us …?” ⁹

How is one to reconcile free will with atomic necessity? Lucretius goes on to state that unpredictable and minute swerves of these tiny particles enable the possibility of choice.

“Both willing oneself to go forward and willing oneself to remain stationary are only possible because everything is not strictly determined, that is, because of the subtle unpredictable, free movements of matter. What keeps the mind from being crushed by inner necessity is the ‘minute swerve of the atoms at unpredictable places and times’.” ¹⁰

Lucretius consciously rejects absolute determinism without ambiguity. According to his reasoning, there is no Prime Mover, no predestination, no Big Bang, no initial conditions from which all else follows by logical necessity. He believed in what Greenblatt translates as the ‘swerve’.

Greenblatt paraphrases Lucretius on this topic:

“The swerve is the source of free will. In the lives of all sentient creatures, human and animal alike, the random swerve of elementary particles is responsible for the existence of free will. For if all motion were one long predetermined chain, there would be no possibility of freedom. Cause would follow cause from eternity, as the fates decreed. Instead we wrest free will from the fates.” ¹¹

Notice that in Greenblatt’s summary he employs the word ‘random’ to describe the swerve. While the word ‘random’ is in line with current scientific thinking, it is slightly, yet significantly, different from the Lucretian translation of ‘unpredictable, free movements of matter’. ‘Unpredictable and free’ imply the possibility of intentionality, while ‘random’, although still unpredictable, has the connotation of unordered, i.e. unintentional. ‘Random’ shifts the meaning from free will to scientific determinism. Lucretius definitely believed in free will. In fact, he suggested that humans should consciously choose pleasure over pain, peace over war, sex over abstinence.

Greenblatt continues with his overview of the Lucretian philosophy.

“But what is the evidence that the will exists? Why should we not simply think that the matter in living creatures moves because of the same blows that propel dust motes? Lucretius’ image is the split second on the race track after the starting gate is opened, before the straining horses, frantically eager to move, can actually propel their bodies forward. That split second is the thrilling spectacle of a mental act bidding a mass of matter into motion. And because this image did not quite answer to his whole purpose – because, after all, race horse are precisely driven to move by blows of the riders – Lucretius went on to observe that though an outside force may strike against a man, that man may deliberately hold himself back.” ¹²

With this example, Lucretius might be suggesting that our only real choice is to resist acting, i.e. ‘deliberately hold himself back’. In other words, logical necessity in the form of cultural conditioning and material laws pushes us forward. While we have the free will to resist this external pressure, it might be less possible, if not impossible, to initiate action upon our own.

To aid retention and set the stage, let’s review what we’ve learned. Historical evidence indicates that Lucretius’ book, On the Way of Things may have opened the door to the atomist way of thinking, first articulated by the ancient Greek, Democritus and then expanded by Epicurus. The materialist perspective of atomism could in turn have easily catalyzed the discoveries of both Galileo and then Newton, which eventually led to the technological miracles of modern science.

In contrast to the modern perspective, Lucretius attempted to reconcile free will with the theory of scientific determinism that derives from a strict interpretation of atomism. He stated that minute and unpredictable, not necessarily random, swerves of minute particles at different times and places could account for the apparent and omnipresent existence of free will. Lucretius goes on to suggest that choice may have more to do with resisting the decrees of logical necessity than actually initiating behavior.

The Logical Possibility of Choice

As mentioned, the philosophy of Epicurus, and by extension his disciple Lucretius, was based upon the notion of epilogismos, ‘reasoning based upon empirical data’. In other words, Epicurus advocated the employment of reason tempered by what could be observed or experienced. Logic doesn’t stand alone, i.e. independent of facts. This is the heart of the scientific method. However, epilogismos was not reserved for the philosopher, scientist or mathematician, but is a type of pragmatic common sense based upon what is.

This type of reasoning is why Lucretius wrestled with the problem of how to reconcile free will and the automatic behavior of atoms. Reason led him to the necessity of material behavior and yet observation suggested that living systems have the ability to choose between alternatives. Even this article is an attempt to persuade the Reader to choose one belief system over another.

The swerve, ‘unpredictable, free movements of matter’, was the solution that he presented for this apparently irresolvable conflict between material and living systems. Presciently, Lucretius anticipated the difference between the atomic and subatomic worlds. The behavior of each individual atom can be precisely predicted, i.e. atoms obey the laws of logical necessity. In contrast, the behavior of individual electrons and protons is entirely unpredictable. It is their collective behavior that is predictable.

Indeed the discovery of subatomics was resisted due to its erosion of the then prevalent notion that atoms are the building blocks of matter, which automatically obey the mathematical laws of science. Due to the many discoveries supporting this viewpoint, atomism had become a standard belief in the intellectual community by the end of the 19th century. Even an intellect as great as Albert Einstein could not accept the unpredictability of individual subatomics and spent his remaining years attempting to disprove the theory. Richard Feynman, a Nobel Laureate for his work on subatomics, stated in no uncertain terms that the Atomic Realm is easily comprehensible for most, while the Subatomic Realm is beyond human understanding. Could it be that ‘minute swerves’ on the subatomic level enable choice?

Let’s now jump off the bridge of conventional thinking. The scientific method is based upon the marriage of empirical data and reason, which Epicurus called epilogismos. Logic independent of data is like the headless chicken in reverse – a body-less Head. Indeed incontrovertible empirical evidence has frequently proven impeccable logic to be wrong.

The brilliant Einstein with regards to the unpredictability of individual subatomics is a case in point. However there are many more. For instance the discovery of plate tectonics was delayed for decades because of the supposed ‘logical impossibility’ of moveable continents. In other words, the best logic is frequently wrong, if unsupported by empirical data. Indeed, a favorite maxim of my Uncle Gene, a professor of biology at North Carolina State, is: “The further away from the facts, the more likely the reasoning is wrong.”

The scientific determinism that derives from atomism is another example of reasoning divorced from evidence. Logic is the only process supporting the notion that all actions in the universe are determined by the mindless collisions of tiny particles. In contrast, the evidence, not incontrovertible of course, suggests that choice is omnipresent in the Realm of Attention. Religion, advertising, and political campaigns are all based upon the premise that individuals are not automatons, but actually choose what to buy, what to believe in, and who to vote for. On the personal level as a writer, I consciously make multiple choices every time I attempt to translate my thoughts into print. In fact, the only evidence for scientific determinism is on the atomic level or exclusively material level. Living systems seem to be ultimately unpredictable on the individual level, presumably because of the ability to choose. Even Lucretius, the purveyor of atomism, claims that free will pervades the living world. As logic provides the only support, scientific determinism remains a questionable intellectual construct that both lacks supportive empirical data and provides little explanatory power.

Holism vs. Atomism

Predictable Matter atomistic: Unpredictable Life different system?

Why is choice so elusive? Material behavior falls completely under the deterministic sway of the atomist mindset. Why is living behavior so unpredictable? Could it be that atomism, while logically consistent, is incomplete? Is it possible that life forms require a different type of logical system to characterize their behavior? If so, what would that system be?

Lucretius’ atomism: nature of parts determines whole

Lucretius and the Epicureans introduced a way of thinking to the scientific community that has proved incredibly productive in terms of understanding material behavior. The method is based upon first breaking things into their smallest constituent parts, i.e. ‘atoms’ in their case, and then using an understanding of the absolute nature of these parts (tiny atoms) to understand the nature of the whole of which they are a part. Building from small to large, the atomist perspective is sometimes called the building block mentality.

Ziporyn’s Definition of Atomism: Removed from Relationships

Following is Brook Ziporyn’s definition of the word ‘atomism’ from his book¹³ that delves into the topic.

“‘Atomism’ is the view that the real nature of a thing is what it is in itself, removed from relations, and the best to way to understand something is to analyze the nature of its constituent parts rather than how they are related or how it behaves as a whole in its relation with other things. If we know the nature of the parts, in this view, we know that nature of the compound they form. Holistic views, on the contrary, hold that the nature of the compound, or whole, must be understood in terms of its relation to other things and of the relation among whatever component it comprises.” P. 28

Living Systems: Holistic, Not Atomistic,

Rather than the atomism of Lucretius et al, it seems to be more instructive to view living systems through the lens of holism. What is holism and why is it different than atomism?

Ziporyn’s Definition of Holism: Dependent upon Relationships

In his same book, Ziporyn provides a contrasting definition of holism.

 “Holism thus defines ‘parts’ and ‘wholes’ in such a way that the parts in a whole obtain their meaning from their contextualization in that whole and are altered, in all aspects of their being, by their relationship with the other parts. The context in which a part appears changes its meaning, significance, and character. The nature of each part is modified by the whole of which it is a part, which means also, inter alia, by all the other items, or parts, to which it bears a relationship.” P. 28

Holism: Context-dependent; Atomism: Content-based

In holism, context is of utmost importance. The contextual relationship between the whole and the parts determines meaning. This is the complete opposite of atomism. Content, rather than context and relationships, is of utmost importance to the atomist perspective. The nature of the parts determines the nature of the whole.  

Examples: Material & Living Systems

Material and living systems provide great examples of the difference between atomistic and holistic systems. As mentioned, material systems are generally atomistic, as the content of the parts (i.e. atoms, electrons and photons) reveals the nature of the whole (the Universe). Living systems have both a material and a non-material component. Both components are generally holistic, in that they are context dependent. Paradoxically, inert matter participates in atomistic systems, while living matter participates in holistic systems, as exhibited in the following diagram.

Living Systems: Holistic system, context–dependent

Let’s examine some details. Life’s material component, i.e. cells, organs, and organisms, tends to belong to holistic systems. Although composed of individual atoms, all parts of a life form are continually adapting to internal and external context. The very existence of the whole is context dependent. The specific atoms and molecules of which they are composed provide very little, if any, knowledge regarding the organism’s ultimate survival.

Context, not content, determines Living Meaning

Life’s non-material component, i.e. Attention, meaning and imagery, also tends to belong to holistic systems. Living meaning is generally determined by context not content. For instance, language, paintings, and sports are dependent upon time duration in order to experience their very existence. Their moment-to-moment content reveals very little knowledge regarding the whole. The ‘meaning, significance, and character’ of a word, color, or goal is dependent upon its relationship to the entire event. The content is superficial. A great actor, through his intonation and expression, can transform a single sound into a transformative experience. Devoid of context, this same sound is relatively meaningless.

Musical meaning: Example of Context dependency

Music provides another good example context-dependency. The meaning of an individual note is determined by the context in which it appears, not its content. The same C sharp can be dissonant, consonant, dramatic, surprising or even humorous depending on the surrounding notes, what went before and what follows. Analyzing the physical content of the note, i.e. frequency, amplitude, etc., provides very little, if any, explanatory power regarding the sound’s meaning for the listener.

Life’s material component requires the immaterial component for survival

Life’s material component requires the immaterial component for survival as a unit. This is due to a simple fact. A primary function of the immaterial component is to provide the contextual meaning that enables the holistic organism to survive. In contrast to the holistic systems of living matter, context is of minimal importance to the atomistic systems of inert matter.

The Sphere, Mobius Strip & Yin-Yang Symbol

It is evident there are at least two realms of existence: one atomistic, the other holistic. Even though atomistic material systems behave mechanistically, holistic living systems have the ability to choose. Closed equations that adhere to traditional either-or set theory accurately characterize material behavior, while an open, reflexive equation accurately characterizes living behavior regarding Attention. Further these mutually exclusive systems interact. How do we comprehend this seemingly paradoxical situation?

Visualization for understanding

To foster better understanding, we offer a visualization of these alternate, yet complementary, views of reality. Due to logical similarities, we associate atomism with the sphere, holism with the Mobius Strip, and their interaction with the Yin-yang symbol.

Objectification of a Sphere for Matter’s atomistic systems

The scientific community has employed the ideal sphere, an object, as a model for atomistic systems for millennia. The Pythagoreans (circa 500 BCE) were probably the first to employ the sphere in their speculations regarding the nature of the firmament.. Using the Sun and Moon as examples, they hypothesized that the macro world of stars and planets consisted entirely of perfect spheres. The atomists, Lucretius et al, applied the same visualization to the micro world of atoms. Modern scientists eventually employed the same spherical model for subatomic electrons and photons. In such a way, the scientific community ultimately objectified the entire material Universe as composed of tiny spheres.

Spheres are homogeneous & exist independent of movement

These spheres have a few notable characteristics in terms of atomistic systems. They are homogeneous objects that have a distinct mass and size. Although they move through space, heir existence is independent of movement. In such a way, the sphere is the ideal object.

Mobius Strip’s process as model for Life’s Holistic systems

While the objectification works perfectly for the Material Realm's atomistic systems, it is inadequate for Life’s reflexive, holistic systems. Based upon dynamic contextual processes, rather than static objects, living systems require a different model. The Mobius Strip fits the bill. It is easy to construct this unusual object. Simply twist one end of a paper strip halfway and then attach the ends.

Paradox: 3-D Mobius Strip is one sided

Viewed as a whole, this object represents a seemingly paradoxical process. Tracing a finger along one surface, one eventually touches both surfaces of the twisted shape. As it is impossible to make a definitive identification of top, bottom, inside or outside, the 3-dimensional Mobius Strip is one-sided – a paradoxical situation.

Mobius Strip: Set Theory applies to parts, not to the whole

Due to this unusual property, the Mobius Strip as a whole doesn’t adhere to set theory. However if we take slices from the whole, these individual parts do adhere to set theory, as each part has two sides with a top and bottom. In other words, set theory applies to the parts, but not to the whole. Rather than absolute content, the contextual process determines the attributes of the Mobius Strip.

How to visualize interaction between Matter’s atomism & Life’s holism

As an idealized object, the sphere is a good visualization of Matter’s atomistic systems. As an idealized process, the Mobius Strip is a good visualization of Life’s holistic systems. Yet how do we visualize the interaction between these two mutually exclusive systems?

Yin-yang symbol to visualize the interaction of the two systems

The Yin-yang symbol is an ideal candidate for the task. Two fish, one black and one white, swim around each other. The dynamic nature of the model indicates a process. The opposing colors symbolize the polar nature of the two systems. Further the white fish has a black eye and the black fish has a white eye, which symbolizes the subtle interaction between the two systems.

Application of Yin-Yang symbol: Interactive Duality

Let us see how this symbol could represent the interaction between atomistic and holistic systems. The Material Realm is atomistic, as Lucretius suggested, while the Living Realm of Choice and Attention is holistic. Although polar opposites, the two realms of existence coexist and interact. As such, they represent an Interactive Duality.

Mathematics: Inert Atomism vs. Living Holism

As mentioned, context is of utmost importance to both the material and immaterial component of living systems. These holistic systems require an understanding of contextual meaning in order to establish value that is the basis of survival. In contrast, the atomistic systems of inert matter are content-based. What are the mathematical ramifications?

Sustained Awareness: a necessary component for establishing meaning

In order to experience the context that is the source of meaning, living systems must have awareness of both the internal and external environment. For instance, an amoeba must have the capability of both being aware of internal hunger and external food sources. Yet sheer awareness is not sufficient. The organism must be able to sustain attention in order to experience both the appetite and the source of gratification.

Attention: Iterative Reflexivity between internal & external environment

Finally, this attention must also have the ability to iterate back and forth between internal and external to assess both significance and meaning. For instance our amoeba must assess the context of the internal state, e.g. sated or starving, to determine the desirability of a tasty morsel that he might sense. This process is reflexive in the sense that it regularly refers back to the internal sensor.

Matter’s Atomism can’t encompass Life’s Reflexivity

This reflexivity is an essential component in the determination of the meaning complex. Yet atomism can’t encompass this reflexive component that is inherent to the awareness of living systems. Purely atomistic systems and the equations that describe them are not reflexive in any way.

Immutable relationships of Atomistic systems are deterministic

The relationship-independent parts of Matter’s atomistic system have some permanent features that are true in each and every circumstance. Context does not exert any influence upon these immutable characteristics. On the assumption that our world, indeed Universe, is composed entirely of tiny deterministic atoms, the Epicureans and eventually modern scientists could accurately deduce that the whole should also behave deterministically. This understanding of the deterministic nature of his supposedly atomistic world threw Lucretius into a quandary because it came into direct conflict with the seemingly obvious existence of choice. To resolve the conflict, Lucretius proposed the Swerve.

Polyverse, both atomistic & holistic

A major flaw in the thinking of Lucretius et al is that the entire Universe is an enormous atomistic system. The evidence suggests otherwise. While Matter is incontrovertibly atomistic, Life seems to be holistic – context-dependent. While these two types of systems are mutually exclusive, they interact. Rather than a one-truth atomistic Universe, we live in a multi-truth Polyverse that contains both atomistic systems (the Material Realm) and holistic systems (the Living Realm).

Atomistic Equations of Matter can’t encompass Life’s reflexivity

These two types of systems require two different types of mathematics. For centuries, ever since Newton, the quest of the scientific community has been and is to determine the absolute relationships between the fundamental parts of atomistic systems. The equations that accurately (virtually perfectly) characterize the immutable relationships of exclusively material systems come in the form of Y = ƒ(X). Yet this type of equation can’t encompass the reflexivity that is inherent to the holistic context-dependent nature of living systems.

Reflexivity of Life’s holistic system requires reflexive equations

The innate reflexivity of Life’s holistic systems requires reflexive equations. Reflexive equations come in the form of X_N = ƒ (X_N-1). In other words, the current result is a function of what went before. Rather than immutable, the answer is dependent upon past context. Rather than a permanent relationship based upon content, this type of equation characterizes an ongoing iterative process.

Material Equations: Y = ƒ(X)

Living Equations: X_N = ƒ (X_N-1)

Closed Material Equations + Set theory = Definitive Statements

There is another major difference between the equations that describe Matter‘s atomistic systems and the equations that describe the Life’s holistic systems. Material equations are both closed to external input and adhere to traditional set theory. The closed nature of these equations combined with the either-or logic of set theory (inside or outside the box) enables scientists to make definitive statements regarding the behavior of Matter’s atomistic systems. For instance, hydrogen atoms exhibit identical behavior in identical circumstances.

Applying atomistic logic to holistic systems doomed to failure

Intoxicated with the possibility of absolute truth, scientists became obsessed with the reductionist logic of atomistic systems. Due to this intoxication, they attempted to analyze holistic systems from an atomistic perspective. The fundamental differences between the two types of systems doomed their collective endeavors to failure.

 Open, reflexive equations make Probabilistic statements re Holistic Systems

To accurately characterize the capacity for choice, living systems require reflexive equations that are open to external input. Reflexive equations do not obey either/or set-based logic and open equations cannot describe permanent relationships as conditions are ever-changing. As a result of these innate features, the statements that can be made about holistic systems with open reflexive equations are probabilistic rather than definitive. Rather than a liability, the lack of precision is an asset as it accurately reflects the probabilistic nature of contextual choice-based living behavior.

Material Equations of Atomistic Systems: Closed, Set-based & Definitive

Living Equations of Holistic Systems: Open, Reflexive & Probabilistic

Life’s open, reflexive equation?

We have suggested that Life requires an open, reflexive equation to characterize the dynamic, contextual nature of its holistic system. But does such an equation exist? How are we to evaluate its efficacy?

Living Algorithm from Theory of Attention fits description

Surprise, surprise! The Living Algorithm from Lehman’s Theory of Attention (that’s me) fits that description. Confirming its efficacy, the mathematical patterns of this open and reflexive equation accurately reflect the behavioral patterns of Attention. An abundance of experiential, observational, and experimental evidence supports the congruence between the mathematical model and living behavior.

Summary: Lucretius introduces deterministic atomism, which negates choice

In summary, the rediscovery of Lucretius’ On the Nature of Things could easily have introduced the scientific community to atomism. Atomism holds that the immutable nature of the smallest parts (atoms) determines the nature of the whole (the Universe). Atoms are deterministic therefore the Universe is deterministic – went their reasoning. However this necessary conclusion negates the possibility of choice.

Resolving the dilemma: Polyverse: 2 realms, one atomistic, the other holistic

To resolve the dilemma, we suggest that we exist in a paradoxical Polyverse, rather than a single logically consistent material Universe. Our Polyverse consists of both atomistic and holistic systems. Even though they possess contradictory features, the two systems interact.

Footnotes

¹ Inside cover, The Swerve, Stephen Greenblatt, WW Norton & Co., 2011

²Mary Beard, Professor of Classics, University of Cambridge, The Swerve, Back of book

³ Greenblatt, p. 274.

⁴ The New American Desk Encyclopedia, Signet Book, 1989, p. 419

⁵ Greenblatt, p. 278

⁶ Greenblatt, p. 273

⁷ Desktop Encyclopedia, p. 353

⁸ Desktop Encyclopedia, p. 99

⁹ Lucretius, On the Way of Things, 2.251-58, from The Swerve, p. 297

¹⁰ Lucretius, 2.293-94, from The Swerve, p. 297

¹¹ Greenblatt, p. 189

¹² Greenblatt, p. 189

¹² Brook Ziporyn, Evil and/or/as the Good: Omnicentrism, Intersubjectivity, and Value Paradox

 

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