A drop of water
The Law of Least Action

When we think of Nature what mostly comes to mind are mountains, trees, rivers, all the various creatures: the flying, the crawling, the running.

But we should first think of ourselves ... we are Nature. We are not apart!

It is clear that natural laws exist. We have the obvious physical laws: electromagnetism, Newtons laws, Quantum Mechanics and so on. Underlying all these laws is what is sometimes called the Law of Balance (1) in nature.

In Physics this law is called the Law of least action which is a restatement of the second law of thermodynamics (the law of balance the way physicists talk about it). This is the basic law from which all other physical laws derive. It is the basis of all action that we see on earth.

The second law of thermodynamics states that the energy in any given system will decrease and approach a minimum value at equilibrium in the most efficient way possible (the way of least action).

Nature demands balance! Think about a marble thrown into a mixing bowl. The marble will roll around in way that uses the least energy in order come to rest at the bottom of the bowl. This is the second law in action. Other examples include: "a line is the shortest distance between two points" and "light travels in the way that uses the least time".

We are subject to the law of least action too. We are, at least for most of us, not aware of it in our psychology, social behavior, and our politics. It is always present in full force!

The rest of this note posits how the "law of least action" shows up in our lives and illustrates some of the ways that it governs us more than we can imagine.

This law in a wider context: ethics, markets,politics,and international relations

Let's begin with something familiar - something in the ethical domain. We have all heard the golden rule: "Do unto others as you would have them do to you". This is the law of least action in the ethical domain. Clearly harmony (Balance) abounds when we treat others as if they were us, and when we don't trouble shows up. That trouble eventually leads to action (of some type) till harmony is restored. Sadly the principle of least action sometimes leads to great discord or even death. Harmony is always restored and quite quickly.

Next, Let's consider something in the economic domain. The stock market obeys the law of least action perfectly. The price of a stock goes up and down until buyers and sellers come to harmony over the value of a share of stock. It is worth noting that minimum effort is involved in the trade - doing the trade as quickly as possible is to everyone's advantage.

The law of least action for countries was stated by Isocrates ((2) - in the fifth century B.C.): "Deal with weaker states as you think it appropriate for stronger states to deal with you." We rarely notice incremental movements as the law of least action works. But today, as I write, we are are all aware the Law of Least Action being violated in the Ukraine. Because Russia and Ukraine have wildly different views on the idea of governance we have a huge imbalance. The situation has become violent because the law of least action requires that it be resolved with minimum action. Throughout history the "go to war" solution plays out over and over again. The marble in the mixing bowl will always come to rest with least action - sometimes that comes to war!

Modern airplanes are balanced toward straight and level flight. That is, if the pilot takes his hands and feet off of the controls, the airplane (after some least energy wiggles) flys wings level with a gradual descent to the ground. All pilots in early training learn about this and are told about PIO (pilot induced oscillation), which is overcorrecting when in a turn so as to throw the plane into an even steeper turn to the other side. This action, when repeated, can tear the wings off of the plane. All objects falling in air reach a state that minimizes least action. When we overcorrect violating the law of least action, we have problems.

I could easily write a five-hundred page book about the Law of Least Action and how it governs every thing we do, think, and are. In conclusion I might note that so much of what we do to 'improve' things only makes them worse. And we, without realizing it, (3)violate the law of least action (or balance if you prefer) at our peril. Least action is sometimes doing nothing.

Euler-Legrange Equation

REFENCES (some Math and Physics here)

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