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A Three Dimensional Political Model

Everyone is familiar with the one dimensional political model. In this view, people fit somewhere along a line, oriented from left to right. If one is positioned to the left of the middle of the line, they are classified “liberal” in the modern parlance of what it means to be liberal . If one is positioned to the right of the middle of the line, they are classified as “conservative”. And if one is roughly near the middle of the line, they may be called “moderate”. In addition, others have proposed two-dimensional models. In particular, David Nolan has proposed what I believe is the most compelling two-dimensional model, with personal freedom plotted on a vertical axis and economic freedom plotted on a horizontal axis. The defining element of his model is the degree of state control over human action which is advocated.  I propose that the one dimensional model is far too simplistic to identify someone’s true political orientation, and that even the two dimensional models which have been proposed have no value in explaining the dynamics of political change. I will propose and outline a three-dimensional political model that I believe is vastly superior to the conventional view of the one dimensional  left-right spectrum, and also superior to any two dimensional model. I believe that this new model can: 1. more accurately identify a persons true political orientation; 2. explain the dynamics involved in political change; and 3. predict the political outcomes of an engaged populace, or a government intervening in the politics of another country. The model that I am proposing is to some extent an elaboration of a synthesis of Nolan’s model and the Cyclical Theory Model proposed by Arthur Schlesinger. Schlesinger intuitively embraced the metaphor of the “political pendulum” to explain the fluctuations seen in politics throughout American history.  Before elaborating on the design of the 3-D model, certain definitions and terminology must be clarified. The model I am proposing is an idealized system, and certain types of political systems must be seen as opposites to one another. The labels I will use to identify a particular form of government may not be exactly synonymous with the existing vernacular, but I must use them for convenience. The model also excludes theocratic  systems of government. So, to clarify:

  • Democracy – representative government directly elected by the people in which the supreme power resides with the people.
  • Capitalism – economic system characterized by private ownership of goods and services and in which prices, production, and distribution are determined by competition in a free market.
  • Liberal – within the constraints of democratic capitalism tend to advocate expansion of personal liberties, coupled with restraints or regulations on private enterprise.
  • Conservative – within the constraints of democratic capitalism tend to advocate expansion of unrestrained capitalism coupled with restrictions on personal liberty.
  • Libertarian – within the constraints of democratic capitalism tend to advocate both a maximized expansion of personal liberties and unrestrained capitalism.
  • Statist – within the constraints of democratic capitalism tend to advocate restrictions or regulations on both personal liberties and capitalism.
  • Fascism – a centralized, dictatorial and autocratic  form of government that ultimately serves the few at the expense of the many. In this system, personal freedoms are very limited or non-existent, while capitalism persists.
  • Totalitarianism –  advocating a political regime based on the subordination of the individual to the state and strict control of all  aspects of daily life. In this system both personal freedoms and private enterprise are very limited or non-existent
  • Anarchy – a social structure without government or law. The complete, or nearly complete absence of government. Law of the Jungle. Vigilante justice. Absolute freedom in all arenas, but no accountability.
  • Communism (Small “c”) –  a social structure advocating common ownership of the means of production and a distribution of the products of industry based on need. One party, non-democratic, de-centralized government with state or local (commune) ownership of the means of production. No for profit free enterprise, but many personal freedoms are retained. Not to be confused with Marxism or Bolshevism which in practice are Totalitarian. Synonymous with Socialism.

With the above list, certain parings must be considered opposites for convenience and simplicity even if they don’t mesh entirely with conventional wisdom and definitions. They are:

  • Liberal and conservative
  • Statist and Libertarian
  • Fascist and communist(small “c”)
  • Anarchist and Totalitarian

One should note that the first two contrasting pairs are still democratic, while the last two contrasting pairs are not democratic.  One should also recognize that a common perception is that liberalism carried too far becomes communism; conservatism carried too far becomes fascism; libertarianism carried too far becomes anarchy, and statism carried too far becomes totalitarianism.  This understanding now leads to the first alteration in the well understood one-dimensional model, with a two-dimensional model with a left-right axis and a top to bottom axis. It is similar to Nolan’s Model rotated 45 degrees and elaborated upon to include non democratic systems.  See figure 1 below. The dashed line in the figure has significance, but we will return to that later.


  The two dimensional model above can adequately identify a person’s true political orientation, but it is still useless in explaining the dynamics of political change, or how systems of government can change over time; change that may be small, or revolutionary in scope. Only a three-dimensional political model can explain political change, and if properly understood, has predictive value. Before introducing the 3-D model, I will discuss the metaphor of the pendulum which is so often used to explain observed change within democratic systems, and even to predict future change. Arthur Schlesinger certainly understood the political pendulum when he proposed his Cyclical Theory. This concept of the “political pendulum” will become an important component in the 3-D model that I will propose.

Most people familiar with the left-right political spectrum, are also familiar with the metaphor of the pendulum. This metaphor is often used to identify where the existing system of government is located, and to predict what may happen next. In recent decades the American democracy has been observed by some, to have shifted to the right. Those who adhere to, or subscribe to the metaphor of the pendulum would say that “the pendulum has swung to the right”, and they would next expect a natural “self-correction” with the pendulum eventually swinging back to the left, as a real pendulum would do. I believe that the metaphor of the pendulum is apt.

Let’s consider a pendulum for a moment. As it swings back and forth it has energy. It has both kinetic energy and potential energy. It has maximum kinetic energy when it’s velocity is fastest, which occurs when it passes through the bottom of it’s swing. The pendulum’s potential energy is all gravitational and dependent upon height above some reference level. Therefore the pendulum has no potential energy at the bottom of it’s arc, but will have it’s maximum potential energy at the top of it’s arc when it’s velocity has fallen to zero. Therefore maximum PE correlates with minimum KE.  A pendulum also has acceleration, and according to Newton’s second law of motion (F=ma), acceleration is directly proportional to force. The pendulum’s acceleration will be greatest at the highest point in it’s arc, when it’s velocity is zero, and will fall to zero at the bottom of it’s arc when it’s velocity reaches it’s maximum. Since acceleration is a vector quantity it has direction. The acceleration vector always points toward the bottom of the arc, but tangent to that point where the tail of the vector touches the curve of the pendulum’s arc. Therefore as the pendulum moves downward through it’s arc, the acceleration vector gradually gets smaller, reaches zero at the bottom, then reverses direction and gets longer as it continues. The length of the vector represents the magnitude of the acceleration, and since acceleration requires an unbalanced force in the same direction, the force vector also points in the same direction as the acceleration vector. Therefore, one can see that in order for a pendulum to swing back and forth a “restoring force” must exist that will cause an acceleration toward the midpoint or bottom of the arc .  See Figure 2 below. Untitled2 In Figure 2 above notice that the potential energy (PE), acceleration, and force have their maximum values at the top of the arc of the pendulum, at Position A. Notice that the acceleration and force vector can be drawn as a single vector tangent to the point swept out by the pendulum. It really represents the two vectors superimposed atop one another. Notice that the slope of the tangent line, representing the acceleration and force vectors at Position A is very steep, with the vector being very long. Notice at Position B that the force and acceleration vectors are shorter because the tangent line to a point swept out by the pendulum is not as steep.  At Position C all the stored PE from Position A has been converted to Kinetic Energy (KE). With the slope of a tangent to a point on the line swept out by the pendulum now being zero, the acceleration and force vectors are also zero. Finally, notice at Point D how the acceleration, and superimposed force vector have reversed direction. One can see that the force vector represents a restoring force since it is always directed toward the midpoint of the swing. Remember from above that people who acknowledge the metaphor of the pendulum to explain political change intuitively recognize a natural “self-correction” when the system veers too far toward one extreme or another. This is analogous to the “restoring force” of the pendulum which always directs the pendulum toward the center. But what is the “restoring force” or “self-correcting force” in democratic political systems? With the pendulum we saw that energy, force and acceleration are all proportional to one another. Likewise, it is the energy and force of an engaged electorate which permits the change one observes in democratic political systems.  Now let us re-draw the pendulum and insert familiar political labels.  See Figure 3 below. Untitled3 The above figure shows the conventional left-right or liberal-conservative dichotomy. High on each side, where “very liberal” and “very conservative” are located, the electorate would need to be very energized to drive the system to such extremes, because the self-correcting restoring force is trying to drive the system back toward the center. One can also ask the question: Does the slope of a tangent line to a point continue to become steeper the further toward the extremes one proceeds, or will it perhaps reach an inflection point?  Also, remember there exists a perpendicular axis which represents the less familiar libertarian-statist dichotomy. Let us now re-draw the pendulum, swinging back and forth perpendicular to it’s original orientation. See Figure 4 below. Untitled4 One can ask again if the slope of a tangent line to a point along this curve will continue to become steeper as one approaches the extreme ends. Also with just a little imagination, we can see that if we combine the two mutually perpendicular political spectra, we get a “bowl-shaped” structure. Our model  now has three dimensions, though still nowhere near complete. See Figure 5 below. I’m not an artist, but hopefully you can make out what I’m trying to illustrate.   Untitled5

From the model above one can see that not only does the political pendulum swing back and forth left to right, but it swings “forward” and “backward” as well.  We also now  recognize that energy represents the third dimension, or height of the bowl-shaped model. The  energy of the system is a product of the activism or engagement of the electorate. Should the people become utterly apathetic and disengaged, the model would lose it’s three dimensional character and become a flat two-dimensional plane. In the absence of the naturally stabilizing restoring force of the 3-D political landscape, democracy is gravely threatened and will not endure. So at this point we have a bowl-shaped structure with ever steepening slopes toward the margins, or rim of the bowl. Does the slope at any particular point have any meaning?  From algebra we learn that the slope of a line is the rise over the run, or  Δy/Δx. What is Δy? It is the change in energy. What is Δx? It is the change in the political system. Therefore Δy/Δx equals the amount of energy required per unit of political change. In other words, the amount of energy that needs to be expended by an engaged electorate to affect a particular “unit” of change within the existing political system. As you see, the slope has great explanatory  significance  and predictive value. See Figure 6 below.   Untitled6     Looking at Figure 6 above, we see that when the political system is at Position B, the slope of the line is very gentle, and only a small amount of energy, ΔY, can have a substantial affect on the change in the political system, Δx. But when the political system is at Position A, the slope of the line is far steeper than at Position B, and far greater energy, ΔY, is needed to affect a far smaller change in the system, Δx. I am now in  a position to dispense with the metaphor of the pendulum and replace it with a “ball” moving within the bowl-shaped structure. We will find that the ball is far more utilitarian as my proposed 3D model becomes more fully developed. We can think of the contact point between the ball and inside surface of the “bowl” as representing the location of a particular political system at any point in time. The contact point can move depending upon the interplay of both internal and external forces. The internal forces are those resulting from the aforementioned “engaged electorate”, or constituencies contesting one another. The external force is the natural, center-seeking, restoring force, so vital in stabilizing democratic systems. I can now introduce a fundamental postulate in this discussion: All systems, whether natural or man-made seek their lowest, most stable energy configurations. This postulate may seem intuitively obvious, but I suspect that it is rarely introduced in discussions of political dynamics.

Figure 7 below shows the interplay of forces that can “move” a political system. In this hypothetical scenario, we have an existing political system that is considerably right of center as determined by the contact point between the “ball” and the line. Vector A represents the “force” or energy of constituency A in pushing the system rightward. Vector B represents the force or energy of Constituency B pushing the system leftward. Vector C represents the natural Restoring Force based on the slope of the contact point, which in turn is based on the PE of the system. You should see that in this scenario, the political system can be driven rightward only if the magnitude of Vector A is greater than the sum of Vectors B and C. See  Figure 7 below. Untitled7 I will now re-draw figure 7 and provide a more detailed explanation of each force acting on the system. See Figure 8 below.


     3D Model-3

In Figure 8 above, Letter “E” is a line perpendicular to the slope of the contact point, which runs through the center of the circle (ball). Letter “D” represents the potential energy of the system. Notice that it’s magnitude will fall to zero when the slope falls to zero. Letter “C” is the natural restoring force of the system, whose magnitude is entirely dependent upon θ, which equals the slope of the contact point. Don’t be confused by where I have drawn “theta” in Figure 8 above. This  “Θ” has the same value as the slope of the contact point.  Also, by examining the geometry of the configuration one should see that the restoring force is equal to the potential energy times the cosine of theta, or RF = PE(cos Θ ).  Letter “A” is the force of engaged constituencies pushing the system rightward, while letter “B” is the countering force of constituencies pushing the system leftward. And as I said before, the political system can be driven rightward only if the magnitude of Vector A is greater than the sum of Vectors B and C.

Issues not as yet discussed with regard to the model are the concepts of momentum and inertia. Momentum equals mass times velocity, or (P = mv). It could be represented in the model by changing the size of the ball; a larger ball representing a larger population of voters and therefore a larger momentum. With a system already in a state of change it could be argued that the “momentum of the system” might by itself drive the system to change. However, a greater population (mass) also has greater inertia, and inertia is a resistance to a change in motion. So inertia of the greater mass completely counters any inherent momentum a political system has, and therefore momentum has no net impact on change. This is analogous to why all objects near the surface of the Earth accelerate downward at 9.8m/s² in a vacuum, regardless of mass or density. The more massive object may be attracted to the Earth with a greater force, but it also has more inertia “due” to it’s greater mass. Remember again, according to Newton’s second Law of Motion, acceleration is directly proportional to force, but inversely proportional to mass.

One could argue that momentum and inertia do become important should the forces both pushing and resisting political change simply vanish. In this case one might expect the “ball” to simply roll to it’s lowest stable configuration and stop. But remember, this scenario implies that engagement (energy) of the electorate is lost, and as such the third dimension of the model collapses to a two dimensional plain.

I am now in a position to return to a question I posed much earlier: Does the slope of the line within the bowl-shaped political model perpetually increase, or is an inflection point eventually reached? Answer: an inflection point is reached. Not only that, eventually the slope becomes negative in every direction. Why is this? Remember earlier when I outlined what is perceived to happen when different political systems go too far in any one direction? They become non-democratic systems: communism, fascism, totalitarianism, or anarchy. How does this happen? As the democratic political system is driven further and further to an extreme position due to the spectacular, passionate ardor of very engaged and activated constituencies, a revolutionary crest is reached, what I call “the revolutionary rim“, after which the institutions of democracy can no longer be maintained. The system then cascades inexorably and remorselessly  toward non-democratic forms. If for example, in contemporary America the forces of the political right can successfully drive the system further and further rightward with their spirit of revolutionary ardor (think Tea Party), then the risk of reaching the Revolutionary Rim and collapsing remorselessly toward a fascist state become realistic. See figure 9 below. The drawing is not great; the rim is too sharp. But I think it makes it’s point.


Notice that it has the shape of a volcano.  We can now elaborate on the “bowl-shaped” model with a “volcano-shaped” model. The dashed line represents the inside surface of the volcano’s crater, what I now call “The Well of Democracy“. Notice how the potential energy of the systems falls to zero in all directions outside The Well of Democracy. But didn’t I say earlier that the PE at the bottom of the “bowl” was zero? It is clearly higher than the energies of the non-democratic forms. Remember PE is always measured “relative” to some reference level. I simply took the bottom of the bowl as my reference point. As long as the pendulum of political change is swinging back and forth within the well of democracy, the bottom of the swing  IS the zero reference point.   So we can see from Figure 9 that at the bottom of the Well of Democracy there is still potential energy as measured relative to non-democratic forms of government. Again, democracy requires participation of the electorate. Should the people become utterly apathetic and uninvolved, energy fall to zero, and the model becomes a two-dimensional plane.

So far I have discussed energy only in terms of “the people” or “engaged constituencies”. Is there a “negative energy”, or an “energy of the state” that must be considered? And does this imply a further refinement in the model I have proposed? Answer: Yes and yes. Consider the energetic state of anarchy. Anarchy is the absence of government, and as such there is no effective energy of the people or the state. The “energy state” of anarchy is a true zero.  We know that nature abhors a vacuum, and anarchy represents a vacuum of power. Anarchy is inherently unstable, a two-dimensional flat political landscape, and ultimately someone grabs the reins of power and sends the country spiraling toward either communism or fascism, either of which can quickly become totalitarianism. Why? Remember the postulate I stated earlier: all systems whether natural or man-made seek their lowest stable energy configuration?   Anarchy so often quickly turns into communism, fascism, or totalitarianism because these are even lower energy states than anarchy. Anarchy may be zero energy, but  these others are negative energy states in terms of the people, or positive energy states in terms of the state. We can now re-define and refine the vertical or third dimension of the model; it is not so much an “absolute” potential energy, as it is a ratio of the potential energy of the people to the potential energy of the state. See Figure 10 below.

3D Model-2     We are looking at a cross-section of the right side of the model and hypothesizing what would happen in the event of a scenario in which highly energized constituencies drive the government rightward beyond the Revolutionary Rim. Newly introduced in this figure is the “Zero Line“, where the ratio of the PE of the people equals the PE of the state. As we examine this scenario the dangers of moving beyond the Revolutionary Rim will become obvious.  Examining this scenario will illustrate the primary means by which a democratic system of government is lost. Also, this scenario imagines democracy being lost as a result of an excessive push to the right, but it would work in precisely the same way in any other direction. Starting at Position 1 we can visualize highly engaged constituencies driving the system rightward. Their success is dependent upon the magnitude of the force of their engagement (Vector A), being greater than the sum of the forces of countering constituencies (Vector B) and the inherent restoring force (Vector C). As long as this is the case the government keeps being driven rightward, though still within the Well of Democracy. At Position 2 we reach the Revolutionary Rim. Reaching this crest puts a democratic government in a very precarious position. At this point, with the slope of the contact point falling to zero, the restoring force has likewise fallen to zero. The only way now to prevent a virtually unstoppable decent toward fascism is for the countering constituencies (Vector B) to have as much or more force as those forces driving the system inexorably rightward (Vector A). At Position 3 the government is now cascading remorselessly toward fascism. The slope of the contact point is now negative, meaning that rather than having a restoring force with inherent stabilizing attributes, we now have an “amplifying force“, (Vector C), that acts in conjunction with the forces driving the system rightward (Vector A).  This then accelerates the collapse toward fascism. Only the most monumental effort by those original “countering constituencies” I referred to can prevent a non-democratic result. Also, during this time the ratio of the energy of the people to the state may still be greater than one to one, but it is decreasing rapidly and about to go negative, where the PE of the state will now be greater than the PE of the people. At Position 4 we essentially have a fascist state in the process of stabilizing. The PE of the state is now far greater than the PE of the people. The amplifying force (Vector C), still drives the system rightward but with a smaller magnitude as stabilization occurs.

I can now introduce the completed Three-Dimensional Political Model. To gain the most comprehensive understanding of the model we will examine the model from four perspectives: 1. from above, 2. left-right cross-section, 3. front -back cross-section, and 4. a three dimensional perspective view. I am not an artist, so the three-dimensional perspective view will be hard for me to draw. Hopefully, the reader will be able to construct the 3-d model in their mind from the other illustrations should my artistry prove inadequate.

Figure 11 below, shows the finished three-dimensional model from directly above. Think of it as an aerial view of the landscape of political dynamics. The terrain or landscape is complex. At the top center is Anarchy, or the Anarchic Plain. To the left is the Anarchic-Communist Escarpment, across which one falls from the zero energy state of anarchy to the negative energy state of communism. The Anarchic-Fascist Escarpment can be found to the right of the Anarchic Plain, where one falls to the negative energy state of fascism. On the lower part of the diagram can be found both the Communist-Totalitarian Watershed and the Totalitarian-Fascist Watershed. These regions have slightly elevated relative energies, indicating that at least some energy must be expended to transition from either communism or fascism in order for a system to become truly totalitarian. One can also see the Revolutionary Rim which encloses the Well of Democracy. Untitled11 Figure 12 below, represents a cross-sectional left to right view. One can easily see where liberal and conservative reside within the Well of Democracy. Remember, the vertical dimension is the ratio of energy of the people to energy of the state, with the Zero Line being that level where the ratio of the two falls to one-to-one. Highly engaged constituencies get the energy ratio very high at the Revolutionary Rim, with communism to the left and fascism to the right. Untitled12 Figure 13 is similar to figure 12 except that it is a cross-sectional view from front to back. One can see statism and libertarianism within the Well of democracy. As before, the vertical dimension is an energy ratio. This time, totalitarianism can be seen to the left, really front, and anarchy can be seen to the right, actually back.  On the right side, the energy of anarchy doesn’t slip below the zero line, since anarchy is the absence of a system and therefore zero energy. Figure 14 further below, is my attempt to provide a perspective view of the entire three-dimensional model.  It is not very good, and I hope to replace it before too long. Here are the labeled parts:3D Model-1

  • A – The Well of Democracy
  • B – The Revolutionary Rim
  • C – The Anarchic Plain
  • D – The Totalitarian-Communist Watershed
  • E – The Totalitarian-Fascist Watershed
  • F – Communism
  • G – Totalitarianism
  • H – Fascism
  • I – Anarchic-Communist Escarpment
  • J – Anarchic-Fascist Escarpment

Untitled14 Implications

This three-dimensional model of political dynamics I have proposed illustrates the strengths and vulnerabilities of democratic systems. It reveals how precious they are and how critical it is that they be nurtured in order to be maintained. A thorough understanding of the model illustrates that democratic systems have a natural self-correcting mechanism that helps prevent extremism and revolution, but doesn’t stop it entirely. We can clearly see the danger of extremism, because it leads to the Revolutionary Rim, and the loss of the institutions of democracy. An understanding of the model allows one to predict the outcome of certain events.

The model predicted that when the fascist government of Iraq was overthrown, that anarchy would prevail. It makes perfect sense. Destroying a government leads to the absence of government, anarchy, which is a zero energy system (or lack thereof). The institutions of democracy don’t simply materialize. To bring about democracy requires an engaged population, building and nurturing the systems of democracy carefully over time. This means that it requires climbing that energy hill until one passes over the Revolutionary Rim and descends into the Well of Democracy, at which time those institutions will become self-sustaining. Even George Bush himself implicitly understood this tenet belatedly when he said “We will stand down when they stand up”.

When the Soviet Union collapsed a similar situation unfolded; a communist government was replaced by anarchy for a time. The people avoided starvation through a combination of truck farming, urban gardening and animal husbandry. Everything becomes very local in anarchy, where people attempt to survive by having each others back. The hard work of building and nurturing the institutions of democracy never materialized in what became the Russian Republic, and many of the other ex-Soviet republics, so democracy never happened. Instead, it was easier, meaning it required less energy, to drift toward other low energy systems. The Russian Republic is now essentially a Fascist regime. There are Russian billionaires alongside people living in abject poverty. The government serves the few at the expense of the many. Remember, this was my definition of “true” fascism. This is also one of my fears for America. If the so-called “Tea Party” can successfully drive the agenda rightward with their intense activism, and with insufficient countering constituencies keeping them in their tracks, then we risk surmounting the Revolutionary Rim and cascading remorselessly toward fascism. We will be able to recognize that we have entered the danger zone when they can affect greater change while investing less energy. This would mean that we have passed the inflection point of the curve on the way to the Revolutionary Rim.

So there you have it; a new model for understanding the dynamics of political change.

P.S. I would like to get a huge amount of modeling clay and construct a physical model of my proposal, complete with labels, then photograph the result and incorporate into this blog.  Alternatively, I need to contact someone familiar with 3D computer animation for essentially the same purpose.