When observing singular links, you see one thing joining to another thing to create some new thing. Sperm joining egg creates a zygote. A spark joining gunpowder creates ignition. A hot poker from the fireplace joining water creates steam. In each of these cases, the joining process suddenly creates something new.
Take a moment to consider the fact that sudden changes such as these are relatively unusual. Sudden change is far less common in the world than gradual change. Most changes that you witness unfold in sequential steps, from A to B to C to D, not from A to D in a single step. The sun gradually rises and sets. Winter gradually turns to spring, which gradually turns to summer. You are born, gradually grow up, and mature, and you can look at the photos of yourself at various stages (remember that haircut?). Geological erosion, evolution by natural selection, succession in ecosystems, urbanization, and most everywhere you look, when things change, they pass through a series of intermediary steps in the process.
However, some of the most interesting changes, and many of those associated with singular links, happen very rapidly or in a single jump step, rather than through gradual, iterative processes. Let’s look at some of them.
Volcanic eruptions and earthquakes are geological examples of rapid change. Hurricanes, while not instantaneous, create extensive damage and change in a matter of hours. Tornadoes can do the same in a matter of minutes. A tectonic shift at the bottom of the ocean can happen rapidly, resulting in tsunamis that crash on shores hundreds of miles away. Lightning strikes can be measured in millionths of a second.
What do all these have in common? They all involve the release of pent up energy. For volcanoes, molten magma rises to encounter resistance from the earth’s surface, building pressure until it suddenly erupts. For earthquakes, there is an immediate release of stress along faults in the earth’s crust. Tornadoes spring from a significant buildup of energy stored in the earth’s atmosphere. Lightning erupts from static energy in thunderclouds.
Many mechanical devices also deploy the release of stored energy to initiate rapid change. Think of a mousetrap, a jack-in-the-box, firearms, automobile airbags, electric circuit breakers, or electric speakers whose diaphragms react to changes in electrical energy, moving rapidly to produce mechanical energy in the form of sound waves.
A catalyst that releases pent up energy can create singular links.
Another type of rapid change happens in the form of exponential growth. For instance, if you plotted the growth of the human population over 100,000 years, from roughly 98,000 BC to 2,000 AD, the line would look more or less flat as you moved from left to right, with a sudden spike at the end. For the first 99,600 years until the year 1,600, the human population had grown to an estimated 550 million people. Then it took a little over 200 years for that number to double to around 1 billion. By the time the next 200 years had elapsed, the human population had rocketed to a whopping 7 billion.
In what would be considered a blink of the eye in planetary terms, the human population leapt from insignificant to highly significant.
If you could somehow have set a time-lapse camera in space pointed at the earth for the same 100,000 years, you would have seen a planet that was pitch black at night for a long long time. It would have been a very boring movie. However, eventually, just a moment after you noticed some faint flickers of light in New York, London, and Paris around the late 19th century, the time-lapse movie earth would suddenly light up like the giant incandescent bulb it is today.
This is exponential growth.
To be clear, the term “exponential growth” is often used to mean, simply, rapid growth, but their meanings are different. Exponential growth and rapid growth are two different forms of growth. Not all rapid growth is exponential and not all exponential growth is rapid. Rapid growth just refers to something growing at a fast pace. For instance, if a town of 1,000 people grows by 1,000 people per year, that may be rapid, but not exponential. By contrast, exponential growth refers to something whose growth is proportional to its population. So, the larger the population, the more it grows. Eventually, as the population of a town becomes sufficiently large, if it continues to grow exponentially, its population will jump by huge amounts from one year to the next. It might add hundreds of thousands or even millions of people in any given year. Meanwhile, the other town that continues growing by a fixed number, rapid as it may be, will add just 1,000 new people each year.
Children’s ability to acquire language follows a similar exponential growth curve. When a child first learns to mimic the words “mama” or “dada,” the growth of her language skill is modest as she picks up a few new words here and there. Eventually, she starts using more words, stringing them together in phrases, then sentences, and then suddenly – boom – she becomes a chatterbox. Her language increases exponentially.
Exponential change exists in the world all around. Think of epidemiology, bacterial colonies, technological advancements, compound interest, social networks or, in the case of exponential decay, radioactive decay and carbon dating.
Here’s the key point: even if something changes exponentially, it changes modestly for long periods and changes dramatically for a short period. In the case of the human population, for most of the past 100,000 years, growth was modest, until it wasn’t. In the case of a bacterial infection, symptoms may be so slight as to be undetectable for long periods, until the exponential growth forces the patient to the emergency room. Then, after she receives antibiotics resulting in exponential decay of the infection, the bacterial population declines exponentially at the beginning, followed by long periods of modest reduction thereafter.
So, while something may appear to change all of a sudden, its changing process may have been underway for a long time before it suddenly appeared to jump. It may look instantaneous, but it’s really just following an orderly, continuous growth curve.
In the next post we’ll explore examples of sudden changes in different domains.