What is Ergodicity, an abstract mathematical process associated with Probability, doing hanging out with the likes of ‘Natural Justice’ and ‘Divine Karma’? Ergodicity is an impersonal, objective, number-based property of random numbers. Justice and Karma are about as subjectively human as it comes. How could these disparate characters possibly approximate (≈) each other?
Justice subjective? It is ‘we’ that impart meaning to events. To determine criterion for justice, we evaluate actions as good or bad – positive or negative. Our evaluations are not inherent to the underlying material substance. Matter just reacts. Molecules and protons certainly don’t care about justice.
Humans, actually all life forms, evaluate some data streams as good or bad; positive or negative. Edible or poisonous; friend or foe; repulsive-attractive; and on the most basic level, too much – too little. These are just a few of the many criteria that we employ to evaluate environmental signals. These determinations enable us to decide whether to approach as in food or retreat as in enemy.
We must make these judgments in order to survive and pass on our gene pool. Matter is qualitatively different. While persisting, it doesn’t replicate with the intention of continuation.
‘Justice’ and ‘karma’ are terms that humans employ to distinguish good from bad actions. These determinations facilitate group survival by encouraging cooperation. The criteria we choose enable us to distinguish between actions that society wants to encourage or discourage. According to both justice and karma, positive deeds should ideally have positive consequences and bad deeds should have negative consequences. Both terms are employed to keep the members of the family/tribe/country in line.
Sometimes society administers justice, as in when the legal system punishes lawbreakers for infractions. Some hold that a divine force, such as the God of the Old Testament, can directly intervene, say with a lightening bolt, to punish sinners for violating the divine law. The final way, which concerns us here, is when events play out over time to administer inevitable consequences.
Evil is punished and Good is rewarded, but over time. The robber is eventually caught or racism/sexism is eventually exposed.
Sometimes this process is called natural justice. Other times it is called divine karma. Some attribute these rewards and punishments to a higher power, others not. The ultimate result is frequently the same.
Ergodicity could easily be a factor in these sentiments. Ergodicity is the inevitable mathematical tendency of certain stochastic processes (a sequence of random events) to end up in the same place. Even though the result is equivalent, the variety of courses can be radically different. This is an objective, mathematical truth.
The inevitable consequences of the law of averages is one way of thinking about this unusual term. No gambler can throw lucky 7’s forever. Eventually, probably sooner than later, his luck will inevitably run out.
To provide further clarification, let us provide a real-life example from Nicholas Taleb’s quadrilogy, which includes The Black Swan. He tells multiple stories of unusually lucky stock traders, who become fabulously wealthy in the short term, maybe a year or even a decade. But then when their luck turns (an unexpected, but inevitable downturn), they blow up (lose all or a substantial amount of their wealth).
This is ergodicity at work. This probabilistic process is a type of ‘natural justice’. The law of averages dicates that there will be an inevitable leveling of fortune. Some traders will be lucky and others unlucky, just by probability, not necessarily skill. If given enough time, this type of luck will eventually reverse itself ‘naturally’.
Most, if not all, ancient cultures believed in this type of natural justice in human affairs. There is balancing of the ledger. Good is rewarded and bad is punished – eventually.
The leveling of fortune is frequently attributed to a higher power. But it could just be ergodicity. Humans could easily be reading Divine Intent into Probabilistic events. The Law of Karma could have a mathematical basis.
How do we differentiate between divine and random? Intentional from ‘natural’? Is there some easy criterion that reveals the difference? Not really. Just a matter of personal preference/affinity – the belief that fits our personality. I might credit Providence for what my intellectual friends attribute to random events.
As evidence of the influence of ergodicity in human affairs, most, if not all, ancient cultures recognized the phenomena. However, they generally attributed ‘natural justice’ to divine factors. Could the Divine be shaping the random sequence to teach us a lesson or provide assistance? Or is the Random teaching us instead?
It doesn’t really matter as long as we learn the two lessons of Patience and Humility. Patience that virtue eventually pays off. And Humility that luck always plays a part in our success.
Let’s look at some specific historical examples of natural justice.
The Mahabharata, a Biblical-level Indian novel, provides a good example of ‘divine karma’. Two sides of the ruling family vie for control of an ancient Indian kingdom – Bharata. One of the competing sides consists of five Pandava brothers. Led by Yudhishthira and Arjuna, they attempt to be virtuous – fair in dealing with others and respecting their elders and customs. To avoid the destructive consequences of armed conflict, they offer to split the large kingdom – even to taking the less fertile and prosperous half. By almost any standard of virtue, they are the indisputable good half of the family.
In contrast, their cousins, the Kurus, are led by Duryodhana, who epitomizes lack of virtue. He regularly attempts to cheat his cousins out of their birthright by any means at his disposal– murder by poison or fire, cheating at cards, and breaking a contract. Most people in almost any time and place would consider his behavior to be despicable, dishonorable, and downright bad or evil. Refusing to share, he and his family drive the greater clan into a destructive war. They are the bad half of the family.
Despite their virtue and favor with the gods, the Pandava brothers and their wife go through many misfortunes. Their travails include exile in the forest. They must leave the pleasures of the court – no servants, bark for clothes, and danger. At one point, the Pandavas are even required to be servants with Arjuna, their hero, disguising himself as a woman to prevent detection.
To comfort them in their difficulties throughout the long novel, many gods, wise men and women counsel them to be patient. “The gods will eventually reward your virtuous behavior and punish your cousins for lacking virtue. Not to worry. No matter what adversity you must endure, divine karma will take care of this imbalance.”
Indeed after their excruciating ordeals, justice is finally meted out. Forced into a destructive war, the Pandava brothers prevail. Almost all the military heroes on both sides of the conflict are killed in battle. But in the end, Yudhishthira becomes the benevolent, virtuous king of the entire empire. The country then enters a golden age of peace and prosperity. The story’s authors give this justice a divine twist, but it could easily be attributed to ergodicity.
The ancient Greeks have a sense of the same process, which is revealed in their lush mythology. A fortunate king attempts to enter into an alliance with another king. But the second king turns him down because he has been too lucky for too long. The lucky king throws his ring into the river to change his luck. A fisherman catches the fish that consumed the ring and it is inadvertently served for dinner as the two kings are about to sign the pact. The second king immediately breaks the deal. He is afraid that the good fortune of the lucky king has run its course. Sure enough, there is a soldier rebellion and the previously fortunate king is killed. The Fates or random events?
And from China: The Chinese believe(d) that the ancient, almost prehistorical, Shang dynasty was overthrown and replaced by the Chou dynasty because their rulers acted against virtue. One of their last kings was cruel and greedy. More importantly, he neglected his kingly duties. Rather than attempting to rule the kingdom, he lost himself in the pursuit of pleasure. Due to this non-virtuous behavior, Heaven withdrew its Mandate from the Shang and gave it to the Chou. Divine justice at work, at least according to Chinese culture.
Is this justice due to divine intervention or just ergodicity, i.e. random probability? It doesn’t really matter. Justice is served either way. A Balancing of the Scales; Excess is pruned back.
Sometimes this balancing process is discontinuous. Disruptions like earthquakes, another type of balancing, can be abrupt and sudden – resulting in long, permanent changes. Witness the Covid pandemic.
We’ve presented ancient examples of ‘natural justice’ from Greece, India and China. In each case, events are allowed to play themselves out over time with no real overt divine intervention. Relying upon duration, the participants expect the law of karma to work its magic – balance the scales. We could easily interpret this natural law as ergodicity, where a sequence of random events can lead to an inevitable result, whether the overthrow of an inept dynasty, the reversal of a king’s fortunes, or the triumph of virtue over corruption.
The Biblical God of the Israelites is different. Rather than plausible, his retribution frequently contradicts/violates the ‘natural order’. For instance, he parts the waters of the Red Sea to allow the 12 tribes of Israel to pass. Then just as abruptly he reverses his divine intent and allows the waves to crash back down and kill all the Egyptian forces.
This was his revenge for the Pharaoh’s obstinacy. First, the Pharaoh wouldn’t allow the Israelites to perform a collective sacrifice to him and then he attempted to prevent them from leaving Egypt. Ironically, God put it into the Pharoah’s mind to be obstinate and treacherous. He took this devious course so that he could exhibit his wrath and power to ancient world.
While the other cultures relied upon the natural order to right the wrongs, the Biblical God of Moses violated the natural order to show his power – nothing random here. Ergodicity is not a factor in unnatural events, just in random sequences.
These are all mythical examples from the ancient world. Let us apply this ergodicity to slavery and human rights.
Ergodicity requires sufficient time and events to perform his magic. A single lifetime is frequently not long enough to stabilize human affairs. However, when a culture persists for generations, for millennia, when life forms have been around for billions of years, ergodicity always performs his leveling act.
Evolutionary time is certainly long enough for ergodicity to generate stable biological systems. History’s cultural time has been long enough to generate stable political systems that provide for human rights. Sometimes, ergodicity is even able to bring down pride and arrogance in a single lifetime.
In this context, ergodicity could be called the probabilistic law of karma. Our out-of balance actions eventually catch up with us. We can only be lucky or unlucky for just so long. A risk taker will eventually have an accident. Injustice will eventually be righted.
After gaining his freedom from American slavery in the early 1800s, Frederick Douglass went to become one of the foremost writers and orators of his time. In his writings and oratory, the former Negro slave inadvertently applied ergodicity to the slave owning culture of the South specifically and to American racism as a whole. He preached: There will be repercussions for slavery, natural or divine, for this imbalance. Ergodicity takes justice out of the hands of Providence and places the cosmic balancing act in the realm of mathematics, specifically probability. Random events over time provide the ultimate justice against the wicked.
In recent times, endemic racism has ignited peaceful protests and destructive riots. Ergodicity ensured that there would eventually be a spark. A balanced society does not stoke the fire of anger. An uprising is unnecessary if there is nothing to balance. Ergodicity only rights the scale. He doesn’t grant boons.
The question arises: Where is ergodicity’s natural balance point - the natural equilibrium – the strange attractor that inescapably draws social events – despite human obstinacy? What is the natural justice that ergodicity enforces – the place that the random unfolding of historical events inevitably aims?
Frederick Douglass said that enslaving another human being, even worse another race, against his or their will is against the natural order of human equality. Ergodicity will eventually balance the slate naturally. Unfortunately, this balancing process might take lifetimes, even centuries or millennia, for completion.
The sequence of events that culminated with America’s Civil War provides support for F. Douglass’ conviction that human equality before the law is an innate feature of the natural order. The United States paid a terrible price for this transgression. Subsequent events, i.e. the right to vote for blacks, women, and Native Americans, provided further validation for the notion that human equality under the law is history’s balance point – ergodicity’s ultimate destination.
Unfortunately, the race riots and protests of 2020 associated with the ‘Black Lives Matter’ movement indicate that ergodicity’s battle against injustice is ongoing rather than at an end. This indisputable complex of events is a good example of the inevitable movement towards justice in human affairs. There was no international or even local groups that sponsored and organized the protests. Rather the imbalance spilled out in spontaneous anger on a global level due to the filmed strangulation of a black man by white police. There had been many other racially charged murders of a similar caliber, which didn’t evoke the same rage. However combined with the frustrations due to state-imposed coronavirus quarantine, this outrage ignited a global conflagration.
Where does our sense of justice arise?
Ergodicity is a mathematical property of probability whereby certain stochastic processes, i.e. a sequence of random events, will produce similar results with enough time. Another way of putting it: Luck, good or bad, will inevitably reverse itself given enough events. Humans frequently live long enough to be humbled by ergodicity – natural mathematical justice – nothing divine.
As the natural result of a random sequence, ergodicity aims at a balance point. Random excess is eventually moderated. But excess from what mean? What is the location of this natural mean? Why not some other location? Where exactly is ergodicity headed? What are its parameters when it comes to natural human justice?
To better understand the relevance of this line of questioning, let us look at the evolutionary forces that could have given rise to our belief in fairness.
Humans have an innate sense of justice. A little imbalance is acceptable, but when the ratio becomes more than two to one (2:1), there is trouble. The violated become angry and will act recklessly against their own interest and that of the species.
This innate human tendency, shared by both monkeys and dogs, probably arose to ensure that all members of the group, e.g. pack or tribe, were fed properly. Dogs and monkeys will actually starve themselves, i.e. stop eating in protest, if they believe that others in their pack are getting an unfair share of the available food.
Evolutionary forces could easily have chosen this inborn trait to protect the weaker members of the pack from exploitation by the powerful. If the stronger consumed an inordinate amount of the kill, then the weak might perish along with the pack. Conversely, those packs whose members had a sense of justice would survive and thrive because even the weakest members would have an adequate amount to eat. Compassion for the weak could be an emergent feature of this natural justice.
Justice for all -> Tribe Survival
No Justice (Extreme Disparity) -> Tribe Extinction
One response to this injustice could have been withdrawal. Another response could have been anger. One consequence of anger and rage is fearlessness – the willingness to risk everything, including our very life, to right the perceived wrongs. We see this extreme rage erupting from time to time due to extreme poverty, labor exploitation, and slavery. Let us return to the sense of injustice that led to America’s Civil War.
In the decades leading up to the Civil War, Frederick Douglass prophesized the downfall of slavery as it was against the natural order. Random events had allowed this brutal American institution to flourish especially in the Southern States for centuries. Now random events were going to wash it away.
Due to random luck, i.e. birthplace and skin color, American whites enslaved black Africans. Random (unpredictable) explosions of rage against this unjust treatment, eventually led to emancipation and the defunding of the police. White supremacy, although kicking and screaming, is now unacceptable, at least publicly.
Justice for the entire pack is the natural order in this case – equality before the law. Slavery violates this principle and is gradually eliminated by the stressors of time. All the random events that put slave owners on top of the heap suddenly reversed and put them on the bottom, for a while a least.
Justice for all Humans = Natural Order
In this sense, Ergodicity can be likened to the natural justice of a higher power – or even the guiding power of Providence or Destiny. Cheaters are eventually caught; Sexual predators are eventually exposed; Racist practices are eventually condemned. Random events might place corrupt individuals on top of the heap for a time. However, ergodicity ensures that the random will eventually reverse itself and bring the offenders to justice.
America’s Donald Trump was able to take advantage of a unique confluence/conflagration of natural events to rise to the Presidency. Yet these same random events, in this case the Covid pandemic, conspired to take down this unbalanced, dissonant, non-virtuous man. Hooray for Ergodicity!
Random events are sometimes kind and other times mean. Bemoaning our fate corrupts the process and entices us to change course. Better to hold onto virtue, the center. Rely on ergodicity. Justice is served – eventually.