Soulful Sundays: Stochasticity

“The existence of life depends on a delicate balance between order and chaos.” — Ilya Prigogine

On January 17, 1995, a magnitude 6.9–7.3 earthquake struck Kobe, Japan. The quake killed over 6,400 people and caused an estimated $100–200 billion in damage. Anyone who has been affected by a natural disaster (or any disaster) knows how devastating and unfair the circumstances can seem. We are left questioning: Why did it happen? How were we left vulnerable? What are the chances it will ever happen again? Conversely, extreme positive outcomes follow the same stochastic principles. Investing $1,000 in Bitcoin in 2010 would have grown into more than $1 billion today. Both positive and negative extremes follow the same underlying principle. They both obey power laws.

Stochasticity means the presence of randomness or probabilistic outcomes in a system. Most of us are familiar with the normal distribution, or bell curve. This describes most biological systems that have evolutionary pressures constraining the characteristics of individuals. Height, hemoglobin, number of offspring, and IQ all follow a normal (Gaussian) distribution, meaning outliers are extremely uncommon and self-limiting. The rare few on the tails are reassimilated into the middle after only a few generations, so the probability of normality is very high and the influence of abnormalities is naturally bound.

Power-law distributions follow a different pattern altogether. Instead of being bell-shaped, they resemble a side-lying hockey stick. The highest frequency of outcomes are small in impact (like the daily change of the stock market), but a few examples carry astronomical weight (like Bitcoin). And in power laws, the tail is essentially unbounded.

In 1896, Vilfredo Pareto, an Italian economist, studied wealth distribution throughout the developed world. Again and again, he found that 20 percent of the population controlled 80 percent of each country's resources. (This became known as the 80/20 principle.) The concentration of wealth follows a power law. Natural disasters also follow power laws, with the majority of events being insignificant, and a select few earthquakes, hurricanes, and wildfires causing the majority of the damage.

Power laws emerge in areas that thrive on chaos. The more unstable the system becomes, the closer it gets to windfall events—like the buildup of fuel right before a forest fire, or the erratic actions of panicked investors right before a market crash. The same principles can be used for benefit, too. Making many small bets might eventually lead to one of them really taking off. All that is needed is one golden goose to completely transform the gander. But we must not confuse noise with signal. Not all choices should be considered equal.

In the buildup to the Kobe earthquake, an English trader with Barings Bank named Nick Leeson was playing a dangerous game. Early in his career he placed a few winning bets in the Japanese stock market and realized outsized gains, totaling over 50% of the bank’s profits in 1994. Thinking he could strike big again, Leeson doubled down but lost heavily when the Japanese market began to decline. He hid his losses from his superiors in a secret account and continued to spin the roulette wheel, thinking his old strategy would eventually yield again. It never did, and after the Kobe earthquake, his position became hopeless. When everything was said and done, he had lost the bank £827 million (about $1.3–1.4 billion), and it was declared insolvent.

We can all become better tuned to the power of randomness. Both negative—a major traffic collision, a life-changing diagnosis, an unexpected loss—and positive—a lucrative investment, a key relationship, a crucial discovery—outcomes obey the law of power amplification. A surprisingly small number of decisions define our reality. Terrifyingly, we are simultaneously just one small step away from either catastrophe or flourishing. To avoid the former involves capping our downsides and not becoming over-leveraged, where we must keep relying on the break that comes too late. To ensure the latter involves running many small experiments and repeating the ones that are successful. We use leverage when we find it, but as soon as the advantage disappears, we must let it go.

The final hexagram of the I Ching, is called Before Completion and says "the fox crosses the river, its tail not yet wet.” It speaks to the moment just before something becomes real—before success, before collapse, before transformation. It is a state of fragile imbalance, where the smallest misstep carries enormous consequence. This hexagram teaches that the world is always on the verge of change, poised on an edge where order and chaos mingle. Progress is possible, even likely, but never guaranteed. One must move carefully, deliberately, with sensitivity to timing and circumstance.

Do not assume completion just because you are close to it. Do not assume disaster just because the current is strong. Attend to the smallest details, for they carry the weight of the whole.

In a stochastic world where outcomes follow power laws, this hexagram becomes a quiet compass. It reminds us that everything important happens at the margins, where slight changes invite vast consequences. To live wisely is to remain alert at these thresholds—stepping lightly, adjusting course, and allowing completion to arise without forcing it.

When we act with care in moments of instability, we cross the river without wetting the tail. When we act with arrogance or haste, we invite the flood.