© Springer Nature Switzerland AG 2020
A. BejanFreedom and Evolutionhttps://doi.org/10.1007/978-3-030-34009-4_3

3. Hierarchy

Adrian Bejan1  
(1)
Duke University, Durham, NC, USA
 
 
Adrian Bejan

Keywords

HierarchyNonuniformityInequalitySocietySizesNumbersCitiesForestsAcademiaRankings

Hierarchy is everywhere we see flow, movement, and vestiges of things that were once flowing. This phenomenon consists of few large and many small, flowing together, in stasis. When its physics origin is not questioned, hierarchy is often described as complexity, networks, turbulence, inequality, and diversity.

Hierarchy is the visible manifestation of freedom, economies of scale, and the configuration “choices” that flow systems seem to make to enhance the access to the finite space that is available to them. Hierarchical systems cover a hugely diverse territory in science. In this chapter, I sketch the backbone of that body of knowledge with just two strokes of the idea pen:

The first is that the diversity of hierarchical flow covers the broadest spectrum accessible to human observation: all size, scales, animate, inanimate, human made and not human made, and steady and time-dependent. Here are a few examples, and note that they come from overtly dissimilar domains of knowledge.

Under the falling rain, the ground surprises us with rivulets that arrange themselves into an all familiar “tree” configuration. The tree flows and morphs, freely. It is alive. It keeps rearranging itself to flow more easily, to evacuate the water faster down the slope. Scientists call this evolutionary flow architecture by many names such as diversity, multi-scale, dendritic, fractal, and many more. They should take courage and call it hierarchy.

The streams fill, bathe, and define a living whole, a live flow system that is continuous and thriving hand in glove with its environment. This natural tendency is obvious, undeniable, and it repeats itself. The streams arrange themselves hierarchically so that a larger stream flows because of its tributaries. The reverse is also true, as the flow of tributaries is possible only because the larger stream is draining them, bundling them and flowing as one. Harmony of movement is hierarchy, and it happens naturally. Hierarchy is good for the life and performance of the whole.

Hierarchy is a good word for expressing what we see, which is that a few large flow together with many small. Compared with hierarchy, the word complex, or complicated, does not say much because complex means twisted together. Inappropriate are also the words multi-scale and diversity, which suggest segments of many sizes in a stick drawing, or balls of many sizes dumped into a sack. Even Aristotle’s line “the many and the few” does not capture the physics, because in reality the many are always small and moving slow and short, and the few are always big and moving fast and long.

We do not need to imagine rivers and river basins to see the natural origin of hierarchy. Players on a team know and use hierarchy every second. When I was a player, I observed that hierarchy happens as soon as the basketball coach puts a fresh group of players on the court. Every player knows it and uses it for the good of the team. After the first game, all the players know which player should receive the ball more often, because that player is a better shooter, and because this other player stands like a tower under the basket. Hierarchy is good for the access of the ball from the area (the court) to the point (the basket). Because of the same physics, hierarchy is good for the access of rainwater from the area (the river basin) to the point (the river mouth).

During my academic career, I observed that a newly formed committee organizes itself hierarchically the same way, naturally and spontaneously. After the first argument, every committee member knows who is the vision generator, the discussion leader, and with whom to associate to benefit from being on that committee. Advice to the revolutionary: if you have a different vision, do not join a committee, form your own.

In my own department at Duke, hierarchy and “diversity” emerged naturally, unnoticed. Those were the proverbial good old days. They were not the result of commands from above, although commands kept coming. They happened because of freedom in the pursuit of new ideas and forming and empowering the students’ lives. We resembled a top sports team where origin, skin color, and passports did not count. The new player who knew how to play, played. Along with diversity came a hierarchy of talent and ability, which is good for the whole. This is the design of the great university of the good old days.

Without hierarchy, humanity would not have evolved to have language, religion, science, books, army, government, university, library shelves, and grocery shelves. The word hierarchy comes from the Greek word for chief priest, who by all accounts is a good person. Unfortunately, hierarchy acquired a negative interpretation following the French revolution, when the lack of social mobility and the nonuniform distribution of wealth in the old order (feudalism) was equated with inequality and immortalized in the slogan Liberté, égalité, fraternité!

The égalité was institutionalized overnight by similar revolutions, and, as if by magic, the next morning a new hierarchy emerged in place of the old. It happened this way with Wikipedia, which in the beginning was a wall on which any volunteer could affix new posters and correct old ones. Overnight, this writing activity was organized under an anonymous hierarchy of few editors and many trolls who write with “authority,” delete what new volunteers write, and cite publications that surprisingly come from the same few sources. This is how we begin to guess who the anonymous members of that hierarchy are.

In the next chapter, we will see that nonuniformity in movement does not mean inequality. It means the absence of a single size in the flowing architecture that evolves naturally because it has freedom. The single size is absent because it is not part of nature. Look at the lung, the river basin, the city traffic, and the rest. They all have few large and many small streams flowing together, which is why they look the same even though one is animal design, another is geophysical flow architecture, and the third is the fabric of human social organization.

Given the liberté, the flowing whole equips itself with a hierarchical nonuniformity that enables every organ of the whole to flow (to live) as well and as easily and economically as possible. With liberty, each organ has égalité—equal access to change, to collaborate, to contribute, and to associate to pursue an easier, longer, and safer life.

Hierarchy is an integral part of the natural design of the flowing landscape and living world. The flows of nature evolve in time such that they flow more and more easily, for greater access. They attain this ever improving quality through the generation of flow design, that is, by acquiring configurations that evolve freely. Existing designs (drawings, literally) are replaced by new designs that flow more easily. In this mental viewing, we fit all the evolutionary scenarios of biology, the emergence of river basins and climate, and the evolution of technologies toward greater efficiency of human movement.

The flows that connect us as a society exhibit the same natural tendency to generate hierarchical flow configurations. Commerce and knowledge (science, education, news) flow in one direction: from those who have them to those who seek them because they are empowered by them. Those who receive them are set in motion, new territories open up for them, and they become freer and wealthier. When both ends of each such river basin have them and know them, the flow stops. What is not new does not travel.

Flowing leads to easier flowing. In this mental image reside the hierarchies that are visible in all the flow systems that cover the world map. These architectures form a multi-scale weave of point-area and area-point tree flows, all superimposed, all sustaining everything that flows and sweeps the earth. One example is the hierarchy of channel sizes and numbers in all the river basins that have been catalogued. With the constructal law, we deduced that the number of tributaries that feed a larger channel should be approximately four [1]. This prediction is in agreement with Horton’s empirical correlation of river numbers, which states that the observed number of tributaries falls in the range between three and five [2].

Another obvious hierarchy is in the numbers of cities of the same size on large areas such as a continent (Fig. 3.1). The distribution turns out to be almost linear when plotting logarithmically the size of the settlement versus its rank. This line with slope in the range between −1/2 and −1 is known as a Zipf distribution, and it is found empirically (i.e., by observation) in virtually all the natural flow systems that connect discrete points with finite areas or volumes. The descending line in Fig. 3.1 has been predicted [3] by recognizing the flow access between two populations that live on each area construct (small and large) that covers the landscape. On every area construct (shown in white in Fig. 3.2), there are two groups that exchange flows: the people who live on the land and those who live in a settlement (village, town, city), which is shown as a splat of black ink. We return to Fig. 3.2 later in this chapter.
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Fig. 3.1

The ranking of European cities according to size throughout modern history

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Fig. 3.2

The landscape of multi-rank cities and universities as a tapestry of hierarchically assembled areas

Predicted is also the fact that the straight line will shift upward in time while remaining parallel to itself. This is a consequence of innovation, ideas, and technology evolution, which empower those who live on the land to achieve flow exchanges (e.g., production, trade) with larger and larger numbers of people living in the settlement. This too is in agreement with the history of the size-rank distribution over the past four centuries (cf., Fig. 3.1).

Hierarchical are also the sizes and numbers of trees in forest. In Fig. 3.3, the descending bands of size versus rank were deduced by arranging tree canopies of many sizes on the forest floor such that the entire floor facilitates the flow of water from the ground to the blowing wind. Two examples of arrangements (triangular and square) are shown in the upper right corner. The slope and intercept of the size-rank line are insensitive to the type of arrangement. Important is the hierarchy in the configuration of the multi-scale canopies that fill the forest floor so that the water flow rate upward, from the whole area, is facilitated. From this holistic view of free evolution came the prediction of the seemingly random and multiple scales of trees in the forest, and the alignment of the size versus rank data [4].
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Fig. 3.3

Distribution of tree canopy sizes versus rank in the constructal design of the forest floor. The distribution is insensitive to the pattern (say, triangular vs. square) in which the multi-scale tree canopies are arranged on the forest floor. Pattern is neither design nor evolution

Society is a “live” flow system, perhaps the most complex and puzzling we know. It is the superposition of flow systems—a vast multi-scale system of flow systems—with organization (design), hierarchies, and time direction of morphing. It is a laboratory with evolution on display. It is the most difficult to comprehend because we, the minds that try to make sense of it, are small and deep inside the flow system. Each of us is like an alveolus in the lung, an eddy in a turbulent river, or a vein on a leaf on a tree branch in the deep forest. From such a position of nothingness, which is identical in rank to the positions of enormous numbers of individuals, it is a formidable task to see and describe the big picture—the lung, the river basin, and the forest.

That’s the first idea. Hierarchies are everywhere, including where it matters to us the most, in society. We will discuss social organization in greater depth in the next two chapters.

The second stroke of the idea pen is that while all hierarchies are happening naturally, not all are accessible to the human eye. Some are invisible by design or out of reach and not on our minds.

In society, hierarchies are of both kinds, those that are in plain view and known to everyone, and those that are invisible to most, and known only to a few [5]. In the field of social dynamics, the latter are known as dark networks and mafias. These are scientific concepts, not pejorative terms. An example of the first kind is the distribution of cities—their sizes and numbers—on a finite territory such as Europe (Fig. 3.1). In France, there is one big city the size of Paris, and many other human settlements that are obviously more numerous as they are smaller. This has been true since records are kept. Here is how to use flow evolution to predict the descending trend visible in Fig. 3.1:

Imagine an area element A1 the inhabitants of which produce many streams (students, agricultural products, timber, game, minerals, and so on). The flow rates of such streams are proportional to A1. These flow rates sustain a human concentration (a dot) located on A1, where the number of inhabitants is N1 and the production streams are of a different sort (education, knowledge, services, devices). There is an equilibrium between what flows from the area A1 to the human concentration N1, and what flows from N1 to A1. Key is that both classes of flow rates (area-point and point-area) are proportional to A1, and this means that the size of the human concentration N1 must be proportional to the size of the area A1, which is allocated to the concentrated settlement.

The flows from the human settlement N1 to the individuals spread over A1 consist of goods and knowledgeable individuals, books, and science. The human concentration in this case is the city or the university campus [6], and the area A1 is the territory that the concentrated human settlement serves. The constellation of cities on the landscape is a reflection of the area constructs of land-city counterflows that sweep the globe.

The distribution of human movement on the earth’s surface is a natural construction of compounding area constructs, as shown at the top of Fig. 3.2. Like an area element in a river basin, which feeds the big stream that is discharged from the area, each area construct sustains the flows that reach a human concentration on the boundary of the construct. It follows that the human concentration on the boundary is proportional to the area size of the construct. If the human concentration is a university, then the size of the university (the generated flow of new ideas) is proportional to the size of the flow area that it serves. The landscape is covered by settlements ranked hierarchically because the area constructs have multiple sizes and are assembled hierarchically. The analogy between societal flow and the river basin is explored further in the next chapter.

Academia, like the population on a territory, is a laboratory to study the evolution of flow hierarchy in our lifetime. A few years ago, I documented the coexistence of the two kinds of flow hierarchies in society, the visible and the hidden, and for this I used the society I know best, which is academia [5]. For a hierarchy that is naked on the table, I used the world rankings according to the citations of scientific publications. For a hidden hierarchy, I used the rankings according to numbers of members of a national academy.

What the constructal law predicted for multi-scale river basins, demography, and forests also applies to the design of human flow on the same globe. Science and education flow naturally through a vascular body of student and professor paths to universities. Each university is connected to the entire globe, sustained, fed, and drained by the entire globe.

The older universities have dug the first channels, which are now the larger, immutable channels that irrigate the populated landscape. “Larger” does not mean a greater number of bodies moving in and out of classrooms. Larger are the streams of the more creative. The creative are the big channels that attract the special individuals who have the gift—the calling—to generate new ideas, and who develop disciples who produce and carry new ideas farther on the globe and into the future [7]. The swelling student population is served well by the memory built into the education flow architecture of the globe.

Out of one spring, say, Harvard, come lots of drops that fall on fertile ground. The history of the university system in America is that the drops from Harvard gave birth to Yale, and then there were two springs that gave birth to Princeton, Penn, and Columbia, all in a perfectly straight line on the map, from Boston to Philadelphia. That line is now the trunk of the big tree of university education in the U.S., which is the envy of the world. On that trunk, new and more specialized grafts took life, for example, universities with engineering and medicine orientations.

True is that in every house where the family is old, there are rules that have become rigid. Yet, if the family teaches the culture of free questioning, out of that home also emerges a stream of new thinkers who question the world and the status quo. That new stream wets the plain. This is the good news. It is what I have been observing, for example, in the growing immensity of publications these days. The highly cited authors are from everywhere, but a lot of them were educated on the trunk of the university flow system that holds, wets, and nourishes the world.

From this theoretical view followed the prediction that the hierarchy of universities should not change in significant ways [6]. The same rigidity and predictability characterize the hierarchy of the universities that win basketball championships [8]. This kind of hierarchy is as permanent as the hierarchy of channels in a river basin. It is in the open, above board. It is natural because it is demanded by the entire flow system—the globe—on which huge numbers of individuals pursue the same thing: physical changes in their lives, for easier and freer movement and living. The implementation of changes is what knowledge is [9].

The rigid ranking of universities is a reflection of the reality that university fame is essentially the same hierarchy as the hierarchy of the individuals who generate the ideas for which the universities are known. The highly cited authors have a natural hierarchy because theirs is the result of the efforts and choices of very large numbers of researchers and practitioners who do not talk to each other before deciding to cite their sources. Even greater numbers appropriate and use the good ideas and do not cite their sources (cf., Chap. 11). The hierarchy of the most cited authors is an indicator of the nodes and areas (elemental constructs) of the flow of ideas. The highly cited hierarchy is shown in the lower part of Fig. 3.4, where the nearly straight band represents the ranking of universities according to the number of authors that each university has on the highly cited list. Important to note is that the lower band of data is nearly straight and has the same slope as what we saw in Figs. 3.1 and 3.3.
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Fig. 3.4

In this figure, there are two descending bands of data because each university is represented by two points, which are aligned on the vertical. The abscissa shows the ranking of universities according to their number of highly cited authors: that number is indicated on the lower half of the ordinate scale. For example, the ranking begins in this order: Stanford, MIT, CalTech, etc. The upper half of the ordinate scale shows the number of academy members of each institution. The two bands of data are strikingly dissimilar

All flow structures are evolving and improving, yet some are hidden from view. The hidden are the channels where participation is based on personal connections, on who you know, and on who needs you for the safety and perpetuation of the dark network. Here is the difference between the clarity of the flow of ideas (Fig. 3.4, lower band) and the opacity of dark networks that permeate the same flow space. I took this example from engineering publishing [5], because this is the field I know best. Scientists from other fields can construct analogous examples by examining their own hierarchies of idea production and access to their national academy. Furthermore, the numbers fluctuate slightly from year to year, but the two patterns that emerge are so dissimilar that fluctuations do not matter.

The list of highly cited authors in the entire “engineering” domain (all disciplines, all countries, living and deceased, in February 2009) contained 253 names worldwide. The membership in the National Academy of Engineering (US alone) contained 2440 names. The 1:10 ratio between the two lists means that most of the members of the academy are not highly cited.

The contrast is even sharper. I placed this comparison on a common basis by removing from the 253 highly cited the 80 names of researchers who work in countries other than the US. I also removed the two names of highly cited authors whom I knew to be deceased (the academy deletes immediately the names of its deceased members). After these subtractions, which are conservative, the highly cited list shrank to 171 names. From the list of academicians, I removed the 197 who work in foreign institutions, and I kept the remaining 2243. The resulting comparison is between 171 highly cited and 2243 academicians, which form the ratio 1:13. Furthermore, only one-third of the highly cited authors (namely, 60) are also in the national academy, and they represent a shockingly small 2.7% of the 2243 members of the academy.

The contrast between the two bands in Fig. 3.4 is a reflexion of the fact that unlike on the highly cited list, which lies naked on the table, the path to the national academy is not visible. The vast numbers of researchers who vote for one highly cited author every day by using and citing ideas in the literature are not inside the academy, they cannot nominate, and they cannot vote for an idea generator.

The applicability of these findings is general. All steps of promotion, honors, and peer review in the science profession, all the way to the difficulty to publish in Nature and Science, can be analyzed in the way that the flow into the national academy was unveiled here. Peer review is not the culprit: the peer review system crumbled two decades ago because of the deluge of electronic publishing and the opacity that comes with that. It crumbled along with the old-fashioned ways of publishing, which meant respecting and protecting the original author’s ownership of the original idea (cf., Chap. 11).

In complete accord with the constructal law, when one hierarchical flow structure crumbles it is replaced by another. Always. That’s evolution. Instead of honest reviewing, today we see a global competition for citations and clever ways to game the citations system [1017], which in an increasing number of cases is driven by nationalism encouraged by the government [18, 19]. This has led to the natural formation of forests of dark networks: the citations cartels [1921] of invisible groups of authors (not co-authors) who cite each other’s articles at every turn, gratuitously.

In the face of this physics, the challenge is to protect the precious and noble features of the western tradition of science, and to defend fiercely the merit system and the paternity of ideas. What is to be done then? Nothing, except a little advice to the young: the aspiring scientist should make a choice early in his or her career, and stick with it. If the scientist is creative, then the “highly cited” is the stadium in which to play. Take a hint from Ludwig Boltzmann, who wrote “I see myself better at integrals than at intrigue” (“ich verstehe mich aufs integrieren besser, als aufs intrigieren,” Letter to Henriette von Aigentler, 1876).

In summary, the hierarchy in the knowledge “industry” today is a manifestation of the universal urge to live a better and easier life, which in modern society is measured as wealth: money or fuel spent with purpose is the physical measure of how good life is, while being lived. The hierarchy of universities is good for the lives and wealth of the professors and students who flock to the best universities. This is natural, and is why the university hierarchy happens, why it is rigid, not changing much. Hidden in the university hierarchy are the dark networks of researchers who pursue similar topics: science here, medicine there, engineering somewhere else. These are the national academies, known by those who are on the inside, good for those who are inside.

Hierarchy in academia flows the same as in a team sport. On the soccer field and the basketball court, the best are few and the near best are many. In sports, as in academia, the “near best” commit more of the fouls and more of the cheating. Some are very good at masking it, and are rewarded for it even though fouling, cheating, and plagiarizing threaten the life and career of the victim. In academia, the many who believe they should also be in the elite are the ones who cheat more and also write more of the vicious anonymous reviews of their peers’ manuscripts. They come out of the closet when one of them, a critic, writes a book review that savages a truly original work.

“Art critic! Is that a profession? When I think we are stupid enough, we painters, to solicit those people’s compliments and to put ourselves into their hands! What shame!
Should we even accept that they talk about our work?” (Edgar Degas).

So, that was the second idea. Hierarchies happen if the flow system is morphing with freedom over its area or volume, but many hierarchies are so big, distant, and obscure that they do not cross our minds.

Recent progress on the physics basis of hierarchy in nature continues to bring together phenomena that were previously not noticed. To the well-known animate and inanimate examples (animal locomotion, river basins, turbulence) covered by the constructal law, we now see examples that belonged traditionally to solid mechanics. The natural occurrence of hexagonal basalt columns is attributed to a principle of maximum “energy” release [22]. The occurrence of cracks in solids is based on the same principle [2325]. Soil cracking under the drying wind is the constructal phenomenon of evolutionary design that enhances mass flow and accelerates drying [26]. The aggregation of dust particles into clusters and dendrites was shown to be the result of the same principle, and its effect is to relieve electrostatic forces of attraction faster, through the evolutionary design of configuration [27].

Added to this growing list of evolutionary hierarchies is the example of bodies suspended in outer space [28]. Hierarchy emerges in two ways, through accretion (coalescence) and fragmentation resulting from collisions. Viewed from thermodynamics, the bodies in space form a system in a state of internal tension because of gravitational attraction between neighboring bodies. This system evolves freely by moving and changing its internal configuration. Bodies coalesce into larger bodies, and their collision (with fragmentation) dissipates the tension and the resulting kinetic energy, en route to reduced body–body attraction throughout the system. This phenomenon has been studied in celestial mechanics under several scenarios and is recognized as the basis for the formation process of planets and the asteroid belt [29].

Sizes increase over all scales through accretion. Yet, the natural phenomenon is not only the growth of the body sizes but also the emerging hierarchy. The fundamental question is why hierarchy happens in the first place, and why a uniform distribution of bodies of the same (growing) size must not happen. What causes the hierarchy? The gravitational effect alone does not explain the hierarchy of sizes of bodies in space. The additional effect is the natural evolution of the whole flow configuration during accretion, such that the flow and evolution of the system toward less tension are facilitated.

Consider a system of identical masses suspended uniformly in space (Fig. 3.5). Forces of mutual attraction keep the system in a state of internal tension. In time, the tension is relieved through the creation of aggregates. Two bodies attract each other with a force that is proportional to the product of the two masses and inversely proportional to their mutual separation distance squared. The shape and relative motion of the bodies are not considered. Assume that a space is filled initially with masses of one size (m) that are motionless and distributed uniformly. The spacing between two neighboring masses (r) is the same everywhere. This suspension is in a state of uniform volumetric and isotropic tension.
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Fig. 3.5

Bodies of equal size (left side) are suspended equidistantly in a plane in outer space, and constitute a system with uniformly distributed internal tension. Only the quadrant of the system with the center in the lower left corner is shown. The forces on the body in the corner are the resultants of all the forces integrated along the radial directions viewed from that body. The bodies attract each other, larger bodies emerge, and the internal tension of the system decreases. This takes time. If bodies coalesce nonuniformly, with few large interspaced with many small (as on the right side), the internal tension decreases faster than if the original system (left side) is followed by bigger bodies of one size suspended equidistantly

The coalescence of small masses into larger masses is driven by internal tension, which becomes smaller as a result. No movement (i.e., death) would be characterized by zero tension and complete coalescence, with all the individual bodies collapsed into one large body. In thermodynamic terms, the system is isolated and exhibits internal changes (mass flows) that take it from an initial state of internal tension toward a final state of no tension and no movement.

The phenomenon is not the death of the system. Nobody will be around to observe that. The phenomenon is the life of the system en route to that end. Should the system evolve as equidistant masses of a single size that increases through coalescence, or should the evolving design be hierarchical, heterogeneous, with few large masses and many small masses that feed the large masses? With high school mathematics, we showed [28] that masses in a suspension have greater access to their neighbors and coalesce faster when they coalesce nonuniformly, hierarchically (cf., Fig. 3.5, right).

It is the hierarchy that is natural, not the uniformity. This is in accord with the physics principle and all observations of freely evolving flow systems everywhere. The natural tendency toward nonuniform coalescence can be visualized in the kitchen (Fig. 3.6).
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Fig. 3.6

Drops of fish oil on water illustrate the phenomenon of hierarchical coalescence. Because of surface tension, the uppermost water layer is a two-dimensional system in tension. The freedom of the system is in its configuration of oil drops on water. The oil drops coalesce, the tension decreases, and hierarchy is the result. The hierarchy becomes more accentuated as time passes. The sequence of three photographs lasted approximately 20 min

Hierarchy also appears when compression is induced by a force at a point in a volume filled with a large number of granules that have freedom to shift and come in contact when compressed. This happens when a projectile impacts soil or sand. The volume is a flow system with untold freedom to morph, because the particles are free to rearrange themselves in practically an infinite number of configurations. Yet, the configuration that is born at impact is a tree of particles that are compressed the most, as if stuck together in solid columns, and their branches spread the point-impact force through the volume (Fig. 3.7).
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Fig. 3.7

The natural emergence of bones, skeletons, tree roots, and other solid members. When a force is applied suddenly on living tissue or soil, momentum is transmitted from the point to an entire volume by a spontaneous tree-shaped alignment of grains that transmit high stresses. The living system is a flow system for the flow of stresses. Its constructal-law tendency is to allocate mechanical strength (stronger and more material) along the channels with high stresses. These reinforcements become bones, tendons, skeletons, tree roots, and branches of roots (photograph courtesy of Prof. R. P. Behringer, Department of Physics, Duke University)

Earlier, I made the connection between this hierarchical alignment of solid and the origin of bones and skeleton [30, 31]. More recently, it occurred to me that the volume subjected to point impact is filled suddenly not only by a hierarchy of solid “bones,” but also by a hierarchy of forces.

The compressive forces along the trunk and big branches in Fig. 3.7 are bigger than along the smaller branches. Under impact, the volume fills with forces that are distributed hierarchically. The forces should be distributed this way because of the same physics principle as in Figs. 3.5 and 3.6. With hierarchy, the compressed volume reaches its new equilibrium faster.

Figure 3.7 is the clue to the puzzle regarding the mother force that serves as common origin of the hierarchy of multi-scale forces that fill the universe. The tree of forces that connects the point of impact with the volume is the answer to one of the darkest mysteries in physics. According to the Stanford physicist Helen Quinn [32, 33], there are four fundamental forces in the universe: gravity, which you can feel pulling you down into your chair, the electromagnetic force, which binds the atoms in your chair, the strong force, which holds the atom’s nucleus together, and the weak force, which is responsible for radioactive decay. Physicists have been trying to unify the forces for years.

The new idea is that the hierarchy of forces should have happened, and that the multi-scale hierarchy of forces should persist long after the beginning of creation. Just like the granules compacted in the canopy of its own tree of forces.

Another predictive idea that follows from this new connection is that the volume elements (soil, universe) inhabited by the smaller forces should be more numerous than the volume elements inhabited by bigger forces. The prediction of a hierarchy of numbers of multi-scale volume elements can be checked, although I think it is obvious. Important is the hierarchy of the tree-like architecture of the universe, which occurs naturally because freedom is a fundamental property that defines the universe.

By the way, one doesn’t have to use the language of the infinitesimal (particles and subparticles) to describe the flowing tree of hierarchical forces that fill continuously the outer space. One can look at telescope photographs to see the hierarchy of bodies flowing in space (which, not coincidentally, look similar to Fig. 3.7), and also their arrangements as trees of branching streams, from trunks to filaments. The whole universe is a flowing tree-shaped, interconnected and hierarchical architecture.