February 2016
Ivan Obolensky

On January 29, 1886, Karl Benz patented the Motorwagen. It was an automobile fueled entirely by gasoline. Less known is that Bertha Benz, his wife and business partner, also played a significant part. After all, it was Bertha who created one of life’s finest diversions: the road trip.

In 1888, Bertha Benz, unbeknownst to her husband, travelled from Mannheim to Pforzheim and back again in his invention. She was accompanied by her two teenage sons, who may, or may not, have had something to do with it. Ostensibly, she wanted to visit her mother, but what she really wanted to do was generate publicity for her husband’s recently patented automobile. She was wildly successful. The family business evolved into the Mercedes-Benz of today, illustrating once again that behind many a successful man is an equally successful woman (who can also act as a mechanic when needed).

Benz’s invention has had an extraordinary impact, yet its success was not particularly envisioned by the population of the late 19^th century.

In the Chicago World’s Columbian Exposition of 1893, various leading lights attempted to predict life one hundred years in the future—in 1993. Although they correctly anticipated much more powerful weapons and the proliferation of global communication, none of them anticipated the extraordinary rise of mass transportation that the automobile would eventually bring about. Like most things, the growth of the car began slowly at first before it exploded upward.¹

For example, in 1895, there were exactly four passenger vehicles in the United States, but by 1900 that number had increased to 8,000. By 1929, the number of passenger cars had rocketed to 29 million. In 1990, this figure topped 133 million. ²

If the growth of the number of passenger vehicles in the United States were plotted on a graph, it would look like an S, with the top of the S flattening since the year 2000.

This leads to an interesting question: can automobile growth be sustained? Will the number of vehicles collapse, or will it stay flat going forward?

To examine this question, we need to go back some forty years before Karl Benz received his patent.

In 1798, Thomas Malthus published An Essay on the Principle of Population. In it he stated,

“The power of population is so superior to the power of the earth to produce subsistence for man, that premature death must in some shape or other visit the human race.”

Malthus gave birth to the Malthusian Controversy: the idea that population growth is geometric while resource growth is linear. Visually, a graph of the human population over time looks similar to the graph of the number of cars on American roads through 1929. It starts slowly and grows faster and faster. Imagine available resources as a straight line with a fixed upward slope placed higher up the graph. When the two lines cross, which eventually they must, the result is a cataclysm: the collapse of the human race due to famine.³

So far this has not happened, but the possibility continues to haunt the human psyche as a dark possibility that manifests in various films and stories of a dystopian future where human existence has devolved to a dirty hand-to-mouth scramble, set against a dark landscape of a once-proud civilization that has crumbled into dust. Was Malthus wrong in his concept of growth?

Perhaps.

Partly in response to this controversy, a Belgian mathematician by the name of Pierre Verhulst came up with another solution called the logistic equation,* which underlies the logistics growth model. Rather than a collapse of the population, the model calls for eventual slower growth in the form of a plateau.

The model incorporates the exponential rise of a population in its initial phase where resource availability is not a factor. Over time, available resources start to act as a constraint causing a slow-down. The result is a graph that looks like an S.⁴

Population growth studies, whether of humans, companies, bacteria, or otherwise, seem to invariably follow this S pattern.**

The plateauing of the S curve illustrates the problem confronting all countries, corporations, species and life forms: how is it possible to move beyond the eventual limits of resources as reflected at the top of the S curve?

To illustrate this, imagine you are in an airport and step onto a moving walkway. Now imagine you only notice the walkway is moving in the opposite direction because a poster to your right seems to be keeping pace with your progress in spite of your steady walking. Realizing you are on the wrong walkway, you have a choice. You either stop moving, let the walkway bring you back to the beginning, and get on the one going in your direction, or you increase your speed to make it to the other end. ⁵

This analogy illustrates many parts of the S curve dilemma. The walkway moves in the opposite direction at a constant speed similar to the straight line constraint of available resources. We can imagine accelerating to a higher speed so we progress faster than the walkway. We can decide to run. But if the walkway is infinitely long, we will make progress until we tire, and once again we are just keeping pace. Welcome to the S curve.

How do we get off this treadmill?

Analyzing this predicament leads to several interesting and useful observations.

1. If an organization, or an individual, can transform itself internally faster than the environment can change, it is possible to create a new S curve on top of the existing S curve and reach a new higher level of performance.
2. Even if we succeed in creating a new S curve on top of the existing one, new resource constraints will once again show up to create a new plateau.
3. Most people and organizations find themselves at a fixed level of performance where they have to run just to stand still. The solution is to create resources that will do the running for them.
4. Transitioning to a higher plateau is rarely a function of the environment decreasing its pressure, or new resources appearing out of nowhere. We must create them, or at least recognize an opportunity when we encounter it.
5. Growth as defined by following a new higher S curve is ultimately the result of internal transformation rather than external factors, although sometimes life gives us a pass in the form of additional resources. Winning the lottery might fall under this category, but the chances of winning are slim and unreliable.
6. Resources are always scarce and the walkway never stops. If we are lucky, it might slow down, but that is all.
7. We can recognize and utilize new resources to create a new higher S curve, but only if we change how we view the world so we can recognize opportunities as opportunities and new resources as resources when we meet them.
8. We do have the option to give up, go back to the beginning, and attempt to get on the right walkway, but the laws of the universe militate against ever finding one that constantly provides for us. Resources in the form of free energy are scarce, or soon will be. Regardless, we will once again visit the limits of growth but in a different guise. Such pockets of respite eventually die or dry up.
9. If we cannot change and internally transform, the environment will intercede, and not necessarily in a way we would like.
10. Requiring fewer resources, or creating resources that continually provide for us, still requires seizing the opportunity once presented.

Life is a constant process of renewal, observation, awareness, and choices. It can be likened to a treadmill, but none of us would miss it for the world. Life is full of opportunities. We just have to recognize them as such.

Road trip?

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*For those mathematically inclined. The Logistic equation (also called the Verhulst model or logistics growth curve) is a differential equation with a solution sometimes known as the sigmoid function, better known as the S curve.⁶

**The environment can always intercede in the S Curve growth pattern. For instance, one can drop the petri dish and the bacteria is spilled all over the floor. It’s either a disaster for the bacteria… or an opportunity.

1. Tenner, E. (1996) Why Things Bite Back. New York, NY: Vintage Books.
2. A. (N.D.) Bureau of Transportation Statistics Publications, Bureau of Transportation Statistics, Table 1-11: Number of U. S. Aircraft, Vehicles, Vessels, and Other Conveyances. Retrieved February 2, 2016 from http://www.rita.dot.gov/bts/sites/rita.dot.gov.bts/files/publications/national_transportation_statistics/html/table_01_11.html.
3. JOC/EFR (January, 2014) Pierre François Verhulst. Retrieved February 2, 2016 from http://www-history.mcs.st-andrews.ac.uk/Biographies/Verhulst.html.
4. Administrator (July, 2013) Malthusian Controversy. Retrieved February 2, 2016 from http://www.blisstap.com/en/poems/item/161-malthusian-controversy.html.
5. Obeng, E. (February, 2013) Advice from the Red Queen. Edie Obeng’s Blog. Retrieved February 2, 2016 from http://imagineafish.blogspot.com/2013/02/advice-from-red-queen.html.
6. Wolfram Research (2016) Logistic Equation. Retrieved February 2, 2016 from http://mathworld.wolfram.com/LogisticEquation.html

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© 2016 Ivan Obolensky. All rights reserved. No part of this publication can be reproduced without the written permission from the author.