The Universal Law of Change

Change is variation, impermanence, acceleration, flux.  Heraclitus, an ancient Greek philosopher, said:  “Change, the state of flux, is a permanent feature of nature”.  Greeks philosophers were fond of paradoxes.  Another ancient Greek philosopher, Parmenides disagreed: “Change is ephemeral and things truly staid the same”.  Greek philosophers were fond of disagreement.  The dictionary says it’s the process of becoming different.  Men have lamented the constancy of Change and decried the lack of Change.  Barack Obama won a presidency promising Change.

The interesting thing about Change is that many, if not all, equations describing change look about the same.    Let’s say Change is C, some driving force prompting the change is DF, and resistance to change is R.  Then the generic form for most equations describing change is:

           C = DF * 1/R

If this Universal Law of Change applies to many different Changes, perhaps it also applies to the economic and social Changes?  For example:

  • Influx of Mexican immigrants to the United States, driven by the difference in hourly wages, and resisted by the high “coyote fees”, border patrol and vast deserts.
  • A flood of Central American children to the Texas border, driven by fear of death or injury from the local gangsters and resisted by the distance, and other resistances mentioned above.
  • Implementation of green energy generation driven by the fears of climate change, but resisted by the high cost of the green energy.
  • Etc., etc.

As mentioned, there are many laws describing change is physical systems that look about the same.  For example, here’s Newton’s famous law as it is commonly written:

               F = m  a

Or force is mass times acceleration.  In this case, acceleration, “a”, represents change.  Acceleration occurs when something is at rest or traveling at a constant speed, and then it accelerates (positive acceleration) or decelerates (negative acceleration).  Rearranging the equation:

               a = F * 1/ m

So change, a, is equal to a force F driving for a change, acting on the object with the mass m.  A heavy bowling ball has more mass, so it’s harder to make it accelerate than, let’s say a tennis ball.  So m is resistance to change.  Given the same driving force, the bigger m, the less change there is.  Broadly interpreted, Newton’s law is a mathematical representation of change:

Change = (Driving Force) * (1/Resistance to Change)

In fluid dynamics, a science describing fluid flow, there’s a famous equation called the Bernoulli’s equation:

            V12/2g + P1/ρg + Z1 = V22/2g + P2/ρg + Z2

Looks complicated, but rearranged into the Change = (Driving Force) * (1/Resistance to Change) it looks like:

            (V22 – V12) = (P1 – P2)* (2/ρ) + 2g(Z1 – Z2)

Where (V22 – V12) represents the change of velocity in this case, the differentials in pressure and height are the driving force and density ρ is the resistance.  Density is mass per unit volume, so it’s very much related to the mass in Newton’s equation.   If you are not interested in details, skip to the next paragraph, but V1 and V2 are velocities of a fluid at two points 1 and 2.  P1 and P2 are intrinsic pressure of the fluid at the two points.  Z1 and Z2 are the respective heights of the fluid.  ρ (Greek letter Rho) is the density of the fluid (mass/volume) and “g” is the gravitational constant.

Sometimes the driving force like F or (P1 – P2) is represented by a symbol Δ, as in ΔF or ΔP for shorthand.

Heating something up on an electrical stove or keeping warm on a cold day involves the following equation:

            Q = U A ΔT

Or transfer of heat from the stove to the pot, or from a body to the cold air, Q or change, is equal to the driving force ΔT, or the difference in temperatures between the two places multiplied by the inverse of resistance to change UA. So the colder the outside air, and the thinner the jacket, the faster you get cold.

Rearranged it looks like:

            Q        =         Δ T         *     (U A)

Or, once again

(Change) = (Driving Force) * (1/Resistance to Change)

Again, don’t care about details, skip to the next paragraph.  In this equation, Q is the flow of heat, rate of change of heat energy from one object to another.  U is the so-called “overall heat transfer coefficient” a measure how a particular material or series of material transfers heat.  For example, wool is known to be a very good insulator, primarily because the hair filaments making up the wool are hollow and contain air, which itself is a very good insulator.  Down and some synthetic fibers are also excellent insulators.  So, wool and down-filled clothing would have a low U, thus not allowing heat to escape the body on a cold winter day.  A is the area across the heat is transferred.  For example, it could be the surface area of a person.  A person’s hands have a very high surface area as compared to their volume and the blood vessels which carry the heat around the body are very close to the surface of the skin, without much of an insulating fat layer.  That is why it’s helpful to wear gloves or mittens when it’s cold: to keep the heat from escaping from a large surface area of the hands.  Δ T or more correctly Δ T lm is the temperature differential between the bodies.  Temperature is an indication of the internal energy of an object.  The differential in internal energy of the objects as measured by its temperature is the driving force which compels the heat to flow from one object to another.

The flow of electricity, change of electrical energy from one point to another is estimated by the Ohm’s law:

           I = ΔV / R

I is the electrical current; ΔV is the voltage differential between two points of an electrical grid or two end of the wire.  R is the resistance of the wire or the elements of the electric grid.  Typically, there are a number of resistances in an electrical network:

This equation, too, follows the general pattern of a generic equation for change:

           I       =           ΔV           *      1/ R

(Change) = (Driving Force) * (1/Resistance)

Basic equation for change in concentration of one component in a physical mixture is

         J = – D * Δ C

Where J is mass flux or a change in concentration of a component from one point to another point of a system.  D is the diffusion coefficient.  It is a measure of resistance of the system to change.  Δ C is the concentration gradient from one part of a mixture to another and the force that drives the diffusion.  For example, if a spoon of sugar is poured into a cup of tea, the sugar will settle to the bottom initially, and then slowly dissolve.  If the tea is not stirred, a few minutes after introducing sugar the tea will be noticeably sweeter at the bottom than at the top.  After several hours, provided the tea is kept at the same temperature, the cup of tea will be uniformly sweet as the sugar would have diffused throughout the cup.  The high concentration at the bottom of the cup and the low concentration elsewhere drive the sugar to be dispersed.  So, once again:

           J      =          Δ C        *     – D

(Change) = (Driving Force) * (1/Resistance)

To summarize, the most generic form of the Universal Law of Change is:

(Change)   =   (Driving Force)  *  (1/Resistance)

Let’s substitute letters for words for the purposes of shorthand:

           C = DF * 1/R

C is the change occurring in a system, DF is the driving force, R is a resistance to change.  The greater the driving force DF the greater the change.  The greater resistance to change R the less the change.

This equation is the most generic representation of all the laws of change.  It applies across all physical, electrical, chemical, biological and botanical systems.  Perhaps it also applies to economic and social systems?

The driving force to a migration of a herd of buffalo maybe the relative abundance of food at the winter pasture, and the resistance to the change maybe physical barriers between the present location and the destination.

The driving force for the presence of millions of undocumented Mexican workers in the United States is clearly the great differential in their potential earnings in the United States and Mexico.  The impedance to their migration is clearly the distance to the new place of work, the fence or the river at the border, the border patrol, and the swathes or desert on both sides of the border.

The driving force for the appearance of thousands of Central American children at the US borders is the likely death or injury at the hands of local gangs, and certain poverty vs. at least a few years of good food, education and perhaps permanent residence in the United States.  The resistances also appear awesome, the lawless expense of Mexico, the praying coyotes, the price of transport, and once again, the border patrol, the deserts and the praying human traffickers in Houston or Los Angeles.

The driving force for the election of Barack Obama was the dissatisfaction of the majority of the American electorate with jobs, social safety nets, illegal wars and dominance of old white guys in the leadership of the country.  The resistance is obviously the other party.

The driving force for green energy is concern for the climate change and the government subsidies.  The resistance, for the most part, is the high cost of green energy which has a hard time competing against fossil fuels and the inconsistency of the aforementioned subsidies.

The driving force for a company to do well is clearly the financial benefit of the shareholders, the management and, for the most part, continuing employment for the rank and file employees.  The resistance maybe many, including perhaps high cost of production, declining markets, old equipment, complacency of management or employees, fraud, etc., etc.

Let’s suppose one can assign sets of driving forces and resistances to various changes in human society.  The challenge would be how to quantify the driving forces and the resistance to understand if the resulting change is large, small or nil.

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10 thoughts on “The Universal Law of Change

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