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The Minimum Work Principle in the Universe
Nov 1, 2014

Gravity is usually accepted as the reason behind the fall of every object we drop. Physicists, however, associate this fall with the trend of an object to reach the lowest potential energy level. Yes, even though in terms of causation, it is not incorrect to say that the objects fall under the effect of gravitational forces as we see, this provides an incomplete picture. The fact that an object is guided to the ground because this will be the location of its lowest potential energy is often ignored. Let's put it this way: objects fall because of gravity, and gravity has been wisely designed as a force to help objects reach their lowest energy state.

The minimum work principle is the force used on deeper levels (the maximum economy principle in other words). According to this, every action in the book of the universe is completed in a fashion to cause minimal energy consumption in the present binding conditions. The term binding condition refers to conditions that are mandatory (forced) for the system here. For instance, the total energy of a gas in a container that is perfectly insulated from the external environment is constant and therefore when we are investigating this gas, we should not overlook the conservation of total energy as a binding condition. Therefore, even for tiny actions, from the swing of a tree leaf with the wind to the flight of a dust particle in the air, the lowest energy consumption is essential in terms of present binding conditions.

We can make the topic easier to understand via short cut events of circuit boards. The reason behind a short cut is the conduction of electrical charges by the route with the least consumed energy. If even multiple short cuts are designed to attract electrical charges in an electrical circuitry, these charges are conducted via the route that requires the lowest energy.

It is all right, but how do electrical charges know this route? It is possible to ask a similar question about the orbit a ball follows when we throw it forward in a horizontal direction. The thrown ball continues on the orbit with the lowest amount of energy consumption depending on the present binding conditions (such as wind direction, strength, and the ball's geometry). This is all well and good, but how does the ball know it will exert more energy on another trajectory?

Light follows the path where it moves fastest in the environment. In physics, "Fermat's principle" states that when light is passing from one environment to another, it will be refracted not in the shortest path, but in the fastest direction of travel in the new environment (Figure 2). Therefore Fermat's principle is the projection of the minimum energy principle on optics. In other words, the least amount of energy is spent by light on the path in which it will move fastest. However, for light to determine the direction that will be fastest, does it not have to first display refraction in all angles to identify the fastest path?

For science historian James Gleick it is impossible for physicists to discuss the minimum energy principle without giving the ball some type of willpower; the ball seems to choose its own orbit, as if it has knowledge of all the possibilities ahead of time.

A nice example in the living world for the minimum work principle is the similarity of ant behavior to the maximum economy principle. When some groups of the ant colony set out to forage, they communicate with pheromone hormones amongst each other. An ant that has found food leaves pheromones on the ground - indicating the quantity and quality of food - to guide others.

Another ant that follows this pheromone trace reaches the food, and marks the surface on the path back to nest with the pheromone by assessing the amount and quantity. Pheromones in spots that are not renewed by the ants within a certain time frame evaporate. Upon investigation of the ant routes, they are always found to follow the shortest path in between the food and nest, and leave pheromone tracks accordingly. For instance, when an asymmetric obstacle is positioned on the ant route (Figure 1), ants after a certain time are able to locate the shortest route again.

However, a more interesting case is the movement of the ant species named Wasmannia auropunctata when they are passing from one environment to another (Figure 3). It's based on Fermat's principle.

Not only ants, but also humans display trends that follow Fermat's principle. For example, an emergency worker trying to rescue a drowning swimmer adheres to the most suitable strategy to reach the person at sea: When the beach and sea are considered as two different environments, first the rescuer runs to the nearest point to the swimmer on the beach, then reaches swimmer by entering the sea. Since humans move at different speeds on sand and at sea, if rescuer tried to reach the swimmer by entering directly into sea, it would take longer to reach the swimmer.

As seen in the above principle, the natural order of the world is created with incredible wisdom, without wasting any energy. Each truth has different projections on each existence and event. However, this distance in between the events or existences feels very far to us, therefore it is necessary to look more carefully to notice this relation among different projections.

There are also projections of this minimum work principle in our personal lives too. During the position of prostration in prayer, which can be considered as the humblest state of being when one feels closest to the Divine, the head, the highest point of body, is brought down to the level of the feet to compose a potentially lower energy status. This, in terms of the physical sciences, is the situation with the lowest work achievement capability, and can be seen as a status in which human deficiency and weakness as opposed to the infinite power of the Almighty are declared.

The minimal work principle can also be adopted in shaping the methods and style of providing services to other people, especially in the service of faith. Humans are the sons of their ages. Each age can be defined as a different environment. Therefore, when humans interpret their experiences, the socio-cultural environment where one is born and the specifics of their period must be considered. The shortest cut to people's hearts and minds with minimal work principle is possible when the conditions of the time are taken into consideration. Said Nursi once said if he were to live in the time of Rumi (13th century), he would have written the Mathnawi, rather than his magnum opus the Risale-i Nur, and Rumi would do the same if he lived during his time. The Mathnawi eight centuries ago was and the Risale-i Nur today is the safest, shortest, and widest public avenue of faith and reflected the zeitgeist of their respective periods in history, Nursi argued.


  1. James Gleick, Genius, Richard Feynman and Modern Physics, Abacus, London, 1993.
  2. Jan Oettler, Volker S. Schmid, Niko Zankl, Olivier Rey, Andreas Dress, Jurgen Heinze, Fermat's Principle of Least Time Predicts Refraction of Ant Trails at Substrate Borders, PLoS ONE 8(3): e59739. doi:10.1371/journal.pone.0059739