“A Person Might Drown While Attempting To Cross a Stream With an Average Depth of Six Inches”
Numbers often lie. We frequently rely on statistics to make important decisions. However, blind faith in these figures can lead to disaster. The quote above perfectly illustrates this danger. It serves as a stark warning about the deceptive nature of averages. While an average provides a general overview, it often hides critical details. Specifically, it obscures the extremes that exist within a dataset. Those extremes—the peaks and valleys—are often where the real risks hide.
This article explores the fascinating history of this cautionary tale. We will trace its origins from ancient proverbs to modern textbooks. Additionally, we will examine why this simple sentence remains so relevant today. You might think you understand the math. Yet, the lesson goes deeper than simple arithmetic. It challenges how we perceive risk and safety in an uncertain world.
The Deceptive Logic of Averages
At first glance, the quote seems paradoxical. How can someone drown in six inches of water? The answer lies in the definition of an “average.” An average flattens out variations. It takes high numbers and low numbers and mixes them into a single, middle figure. Consequently, this process erases the specific details of the landscape.
Imagine a river that is ten feet wide. For nine feet of its width, the water is only one inch deep. However, the final foot of width contains a sudden drop-off. This hole plunges down to ten feet. If you calculate the average depth across the entire width, the number remains quite low. Mathematically, the stream appears safe.
The Fatal Flaw in the Math
Nevertheless, the reality is quite different. A traveler walking across this stream faces a binary outcome. They are either perfectly safe, or they are in mortal danger. The average depth does not matter to the person in the deep hole. They cannot breathe an “average” amount of air. They encounter the specific depth at their specific location. Thus, the statistic creates a false sense of security. It suggests uniformity where none exists. This is the “flaw of averages.” It is a trap that has caught many unwary travelers, investors, and planners throughout history.
Tracing the Origins: The Indian Connection
Many people attribute this witty observation to modern writers. Source However, the roots of this story go back much further. Research reveals that the tale likely originated in India. . This early version sets the template for all future iterations.
In this original telling, the characters are a father and his son. They belong to the Kayasth caste, known for their clerical skills. They reach a river of unknown depth. The father decides to apply his mathematical knowledge. He measures the depth at various points. Then, he calculates the mean.
A Tragic Miscalculation
The father determines the average depth is safe for his son. Confidently, he orders the boy to cross. Sadly, the river contains deep pockets that the average ignores. The boy drowns. The father is left with his correct calculations but a dead son. This grim story served as a warning against relying solely on book learning. It highlighted the difference between theoretical knowledge and practical reality. Over time, this specific cultural context faded. Yet, the core mathematical lesson remained intact.
The Evolution of the Tale in the 1900s
As the story traveled, it evolved. Different cultures adapted the details to fit their needs. By the turn of the 20th century, the story appeared in various Western publications. In 1899, Reverend Edward Latham used a variation in his writing. His version featured a tall man attempting to ford a river. The man stood six feet tall. The river averaged only four feet deep.
Despite his height advantage, the man drowned. Latham used this to illustrate a theological point. He argued that general safety does not protect against specific perils. This version shifted the focus from a father’s authority to individual hubris. It suggested that even strong, capable people can fall victim to statistical anomalies.
The Bureaucratic Twist
Soon after, another variation emerged. This one targeted government officials. In 1900, Major-General Fendall Currie published a book titled “Below the Surface.” He recounted a story about a village accountant in India. This official, proud of his education, calculated the river’s average depth. He assured a traveler that the crossing was safe.
The traveler trusted the official’s expertise. Unfortunately, the traveler drowned in a deep section. Critics used this story to attack British colonial administration. They argued that tax assessments relied on “averages” that ignored local famines. Just as the river drowned the traveler, average tax rates drowned the poor during bad harvest years.
Animals and Statisticians: New Victims
The story continued to mutate throughout the early 1900s. Writers began substituting different victims into the narrative. In 1903, R.H. Halsey presented a paper to the National Education Association. He cited an “old Hindoo proverb.” However, in his version, the victim was an ox.
The ox attempted to cross a stream. The average depth would have only covered its hoof. Yet, the beast perished. This version emphasizes the absurdity of the situation. An ox is a strong, sturdy animal. If an average can kill an ox, it can certainly kill a human.
The Statistician’s Hubris
Eventually, the story turned on the mathematicians themselves. In 1907, Henry S. Wilcox published “Frailties of the Jury.” He included a version where statisticians became the victims. In this telling, a group of statisticians measures a stream. They check the banks and the middle. They calculate an average depth less than their own height.
Convinced by their own data, they attempt to cross. They all drown. Wilcox used this to make a philosophical point. He noted that quantities cannot change qualities. You cannot calculate your way out of a physical reality. This version adds a layer of irony. The very people who should understand the numbers best are the ones who die by them.
The Mystery of W.I.E. Gates
In modern times, you often see this quote attributed to W.I.E. Gates. Many quote books from the late 20th century cite him as the author. Specifically, a 1977 collection connects his name to the famous phrasing. However, our historical review proves this is incorrect.
As we have seen, the story existed long before 1977. It appeared in print nearly a century earlier. Therefore, Gates did not invent the concept. He likely repeated a well-known saying. Over time, the attribution stuck to him. This is a common phenomenon in the world of quotations. Famous or recent speakers often get credit for ancient wisdom.
Why the Attribution Matters
Correcting this record is important. It shows that this is not a modern observation. Rather, it is a piece of folk wisdom. People have understood the danger of averages for generations. Long before modern data science, farmers and travelers knew better than to trust the mean. They understood that survival depends on handling the worst-case scenario, not the average one.
Why This Lesson Matters Today
We live in an age of big data. Algorithms drive our lives. Consequently, the lesson of the six-inch stream is more relevant than ever. We often look at average returns in the stock market. We look at average temperatures in climate models. We look at average life expectancy.
However, we do not live our lives in the average. We live in the specifics. An investor can go bankrupt during a market crash, even if the “average” return is positive over ten years. A homeowner can lose their house in a flood, even if the “average” rainfall is low.
Avoiding the Trap
To survive, we must look at the distribution. We must ask about the extremes. What is the deepest part of the stream? What is the worst possible market crash? By asking these questions, we avoid the fate of the traveler. We acknowledge that the average is just a tool. It is a map, not the territory.
Conclusion
The quote about the stream and the six-inch depth is timeless. It has survived for over a century because it speaks a fundamental truth. Statistics are useful tools for understanding large groups. However, they fail when applied to individual survival.
Whether the victim is a traveler, an ox, or a statistician, the message remains the same. Do not trust the average blindly. Always check for the deep water. The average might look safe on paper. But in the real world, the extremes are what define our fate.