A natural force enabling unity, coordination, and cooperation at all levels, from physical to complex human systems.

 Ariel Daliot

Abstract: Synchronization is defined as the concerted operation or activity of several elements. I.e these elements communicate and operate in unison. Synchronization is an observed phenomenon from the physical, through biological and to the human sociological world. In physics it is sometimes termed as spontaneous order as it seems to contradict the laws of thermodynamics that dictate the opposite, that nature should inexorably degenerate towards a state of greater disorder, greater entropy. Yet all around us we see magnificent structures – galaxies, cells, ecosystems, human beings – that all have somehow managed to assemble themselves.

We may speculate that cooperation and consensus make sense to complex systems with higher conscience such as human interactions. The pervasiveness of this phenomenon at all levels though may indicate that there is something more fundamental to unity, coordination and cooperation, hinting towards more of a “law of nature” despite the possible contradiction to thermodynamics and statistical physics. The common features of synchronization phenomena from physics through biology to sociology is the distributed nature of the synchronizing elements, their means of influencing each other or being influenced by some common central element. Essentially, they must also have a common advantage from synchronizing with each other. This may perhaps be easier to explain in physical systems (e.g. due to energetic advantages) but may be more difficult to model in human sociological interactions. In this work we will suggest that cooperation and consensus are part of our nature even down to the lowest physical levels. We may speculate that we perhaps are supposed to strive to overcome the second law of thermodynamics and aim to organize and synchronize on the common good.

Introduction

As humans we take for granted that we wish and are able to coordinate our actions and beliefs with other humans. We take for granted that we find pleasure in for example dancing with another person and that we are even able to align and harmonize our common steps. We implicitly attribute the ability and motivation to psychological factors and to some level of consciousness. It is less obvious that animals display synchronous behavior and even less so molecular biological and physical systems. Why would these groups, networks and systems with little to no consciousness have any cause or advantage in investing in maintaining coordinated, orderly actions, despite the fundamental laws predicting that they should disengage and deteriorate over time.

Entropy is traditionally related to as the measure of disorder in the universe and of the availability of the energy in a system to do work ^[1] D. J. Amit, Y. Verbin, “Statistical Physics: An Introductory Course”, World Scientific Publishing, 1999. There are many equivalent mathematical formulations and definitions of entropy, depending within what discipline it is described: thermodynamics, statistical physics, mechanics, machine engineering, ecology, information theory, computer science, chemical engineering, sociology, etc.  All of course essentially describe the same statistical physical notion stated in the second law of thermodynamics: the total entropy of any system does not decrease other than by increasing the entropy of some other system. The second law of thermodynamics is a statistical law, not a fundamental one like, say, conservation of energy. The entropy of an isolated system, could, in principle, “magically” decrease due to a random fluctuation, but the bigger the system, the less likely this is. The total entropy of the universe is hence widely believed to increase monotonically and constantly.

The second law of thermodynamics also places a limit on a system’s ability to do useful work as a correlation to the increase in entropy, i.e. the ability of a system to transfer energy to another system decreases as entropy increases.

This has led to the current hypothesis of the heat death of the universe which suggests the universe will evolve to a state of no thermodynamic free energy and would therefore be unable to sustain processes that increase entropy. This is when the universe reaches thermodynamic equilibrium in which all possible physical work ceases. This is the ultimate death of the universe and it is inevitable according to the laws of physics as we know them today.

Our basic physical intuition settles with that of ever-increasing entropy. We can all relate to the notion that any structure deteriorates and becomes more disordered over time. As a matter of fact, that any material inevitably crumbles and deteriorates over time, if not maintained.

It is possible for a system to decrease its entropy, i.e. increasing the order but that requires investing energy from outside of the system. Nothing in thermodynamics or statistical physics relates as to why a system would invest external energy in order to decrease its entropy at the expense of increasing entropy at another system. The term “spontaneous order” may even imply that it is believed that systems do not have a reason for decreasing the entropy through organization.

At a first glance it may seem that creating order emerges from some conscious will but as we will see this is not solely related to the level of conscious. In this work we will elucidate the subject through the notion of synchrony as expressed in a wide variety of the aspects of the cosmos.

Synchronization is a complex phenomenon being defined as the concerted activity of several elements. I.e these elements not only communicate, interact and influence each other but they also achieve to operate in unison ,at the same time or at a similar rate, or display the same behavior as a result of mutual or a common influence.

Synchronization in nature

In physics there are many examples of seemingly disparate elements that should apparently have no reason for working in unison or for even having a mechanism for interacting and influencing each other, but they still do ^[2] S. Strogatz, “SYNC, The Emerging Science of Spontaneous Order”, (2003), ISBN 0-7868-6844-9. Huygens discovered that pendulum clocks for instance that are attached to the same wall will eventually synchronize their ticks even if they were initially completely or partially out of synchronization. This happens by minor vibrations that each pendulum exerts on the common matter that they hang on, the wall.

Synchronous rotation of objects is when an object takes just as long to rotate around its own axis as it does to revolve around its partner, such as the moon and the earth. This causes the same side of the moon to always face earth. They interact through their gravitational forces. They will stay so indefinitely unless external energy is introduced into the system.

Synchrony of gravitational waves can cause an ejection of huge boulders out of the asteroid belt and towards earth; the cataclysmic impact of one such meteor is thought to have wiped out the dinosaurs.

Synchronization gives some sort of physical advantage to the collection of synchronizing elements. It can be useful. Lasers are an example where engineering is cleverly utilizing the phenomenon of quantum phase coherence (a term for synchronization at the quantum level) of Bose-Einstein condensate matter in order to get an extremely concentrated beam of perfectly synchronized photons or light. This would not have been possible without the inherent synchronization tendencies of Bosons in the quantum realm. It’s an example where synchronization enables the principle of the whole being greater than the sum of its parts. Lasers are invaluable in medical applications, manufacturing, CDs and optical discs, scanning, printing, communication etc.

Electricity generators produce power by harnessing some form of natural energy source, for example burning gas or coal in order to create enough heat to boil water into steam, and then use the steam to rotate a turbine, or use the fall of water for that sake. The rotating turbine rotates magnets that in turn induce electrical power. This power is then drawn into the electrical grid by elements that consume the power such as light bulbs. In order to supply all the electricity demand of the modern world there must be many such generators with turbines in the grid that are all interconnected. A fundamental technical difficulty with interconnecting all the generators is that they must be synchronized to spin at exactly the same rate, even if they are separated by hundreds or thousands of kilometers. Without this synchrony power would go uncontrolled back and forth through the grid causing tremendous current surges and generators and cables would explode. Part of the solution came from the laws of physics. Electrical engineers found that generators connected in parallel had inherent tendencies to synchronize their rates of rotation. In other words, a parallel grid tends to be self-synchronizing: a beautiful instance of spontaneous sync, in the spirit of Huygens’s sympathy of clocks. The effect is easiest to understand for the case of two generators connected in parallel. If they ever happen to rotate at different speeds, the slower generator automatically draws power from the faster one, so the slower one speeds up and the faster one slows down, which corrects the discrepancy. In more physical terms, any disturbance that causes one generator to pull away from the other is opposed by corrective electrical currents that immediately begin circulating. Thus, the pair of generators tends to synchronize spontaneously.

The phenomenon of synchronization is displayed by many biological systems, and it plays an important role in these systems. For example, the heart of most living organisms is regularly activated by the synchronized firing of neurons in the cardiac pacemaker network ^[3] A. Daliot, D. Dolev and H. Parnas, “Self-stabilizing Pulse Synchronization Inspired by Biological Pacemaker Networks”, arXiv:0803.0241v2, 4 Mar 2008. The circadian pacemaker neurons that determine the day-night rhythm of humans and animals.

In macrobiology, individual animals routinely face decisions that are crucial to their survival. In social species, however, many of these decisions need to be made jointly with other group members because the group will split apart unless a consensus is reached. Consensus decision making is common in non-human animals, and cooperation between group members in the decision-making process is likely to be the norm, even when the decision involves significant conflict of interest^[4] L. Conradt, T. J. Roper, “Consensus decision making in animals”, Trends in Ecology & Evolution, Volume 20, Issue 8, Pages 449-456. 2005. ^[5] I. Eshel, D. Weinshall, U. Motro, “On the evolution of altruistic cooperation”, Biomathematics and Related Computational Problems. Kluwer Academic Publishers, pp 279–282. 1988.

Examples of synchronization in the animal world include:

• The malaccae fireflies in Southeast Asia where thousands of male fireflies congregate in mangrove trees, flashing in synchrony in order to attract females. The synchronous flashing can be detected by females many kilometers away and apparently increases the probability of mating ^[6]S. Strogatz, “SYNC, The Emerging Science of Spontaneous Order”, (2003), ISBN 0-7868-6844-9..
• Crickets that chirp in unison, for apparently similar reasons as the fireflies ^[7] S. Strogatz, “SYNC, The Emerging Science of Spontaneous Order”, (2003), ISBN 0-7868-6844-9.
• Male fiddler crabs who court females by waving their gargantuan claws in unison.
• Coordinated mass spawning in corals. The coordination increases the probability of successful reproduction.
• A recent article ^[8] A. J. Dibnah, J. E. Herbert-Read, N. J. Boogert, G. E. McIvor, J. W. Jolles, A. Thornton. Vocally mediated consensus decisions govern mass departures from jackdaw roosts. Current Biology, Vol. 32 … Continue reading describes how in the early morning, large groups of up to hundreds or even thousands of roosting jackdaws, often take off together in sudden, almost instant, mass departures. These departures commonly occur in low-light conditions and structurally complex habitats where access to visual cues is likely to be restricted. Roosting birds are often highly vocal, suggesting that vocalizations, which can propagate over large distances, could provide a means of enabling individuals to agree on when to depart – that is to establish consensus – and thus coordinate – the timing of the unified mass flight movement.
• Synchronization does not necessarily have to mean in unison, it can also mean consensus on a leader such as when birds migrate in a synchronous formation. The formation is in a hierarchy with a leading bird where each leads in turn. The leader does not benefit from the decreased air friction as the other birds but yet they relentlessly take their turns.
• Vigilance in birds is a phenomenon where a group of birds congregate together to forage and the birds take their turn to stop eating in order to watch for predators ^[9] G. Beauchamp,  “A comparative analysis of vigilance in birds”. Evolutionary Ecology 24(5):1267-1276, 2010). (( U. Motro, D. Cohen, “Selfish cooperation in social roles: the vigilance game in … Continue reading. ^[10]U. Motro, D. Cohen. “A note on vigilance behavior and stability against recognizable social parasites”. Journal of Theoretical Biology, 136:21–25. 1989. Each bird interferes its eating way less when in a group as it’s enough for one bird to ring the alarm.

Synchronization in these systems is typically attained despite the inherent variations among the participating elements, or the presence of noise from external sources or from participating elements ^[11] A. Daliot, D. Dolev and H. Parnas, “Self-stabilizing Pulse Synchronization Inspired byBiological Pacemaker Networks”, arXiv:0803.0241v2, 4 Mar 2008.

• In human beings synchrony operates at three different levels. First cells within an organ are mutually synchronized (heart beat ^[12] A. Daliot, D. Dolev and H. Parnas, “Self-stabilizing Pulse Synchronization Inspired by Biological Pacemaker Networks”, arXiv:0803.0241v2, 4 Mar 2008; gastrovascular system; within neural networks; the circadian clock, i.e. the sleep wake cycle; synchronization in-between different neural networks such as that involved in associative learning etc.). Second, synchrony occurs between individuals, but the method of interaction is still chemical/biological. E.g. synchronization of feminine menstrual cycles in close physical contact, is apparently enabled by chemical communication between the women. The third level of synchrony is between our body and mind and the world around us and is elaborated on in the next chapter ^[13] S. Strogatz, “SYNC, The Emerging Science of Spontaneous Order”, (2003), ISBN 0-7868-6844-9.The exhibition of synchronization in inanimate objects as well as biological system and in living organisms hints that there is an apparent advantage for separate elements to communicate and work in unison although according to the laws of thermodynamics they are required “to invest energy” in order to attain this, something that is not explained by entropy^[14]  [12]. There is also evidence that gives rise to the postulation that life itself could not have formed on earth if RNA molecules would not “cooperate”, this theory is coined “the cooperative … Continue reading. ^[15] Z. Néda, E. Ravasz, Y. Brechet, A. L. Barabasi. “The sound of many hands clapping”. Nature 403, 849–850 2000.

  The human side of synchronization is significantly more complex and harder to model and understand than the physical and biological examples of the previous chapter. Theses former examples though may emphasize simple principles, which may in turn give insights into human behavior. As an example, consider the synchronization of cardiac neurons whose concerted firing determines the cardiac rhythm. In ^[16] A. Daliot, D. Dolev and H. Parnas, “Self-stabilizing Pulse Synchronization Inspired by Biological Pacemaker Networks”, arXiv:0803.0241v2, 4 Mar 2008 it is shown that the more a certain neuron senses other neurons firing in synch the more it is itself prone to join them in the firing, enhancing the collective synchronous behavior of the whole network. There is some element to this neuronal principle that can, to some extent, elucidate collective human behavior, as brought forward in the following paragraph and next chapter.

  What is behind the herd mentality of stock traders and the resultant boom and crashes in the market; the brutal mentality of mobs; how riots can emerge all of a sudden; what facilitates sudden unforeseen political shifts; the seemingly unpredictable sudden rise and fall of fashions, trends and crazes. Typically, the motivation for trying to decipher these phenomena in humans has often been for the vast political and economic implications this has. There has been no to very little mention of how to learn and control these phenomena in order to make a better and more just world.

  There is reason to believe that human nature will just as much, if not more, want to follow someone that does a good deed; to lean on someone that represents some ideal and to synchronize with other humans around universal values. As an example, there is proof that Neanderthals 70,000 years ago cared for the elderly and sick, even though these where a burden on the group, and they even buried them after death ^[17] W. Rendu, C. Beauval, I. Crevecoeur, P. Bayle, A. Balzeau, T. Bismuth, L. Bourguignon, G. Delfour, J.P. Faivre, F. Lacrampe-Cuyaubère, C. Tavormina, D. Todisco, A. Turq, B. Maureille, “Evidence … Continue reading. ^[18] A. Gómez-Olivencia, R. Quam, N. Sala, M. Bardey, J. C. Ohman, A. Balzeau, “La Ferrassie 1: New perspectives on a “classic” Neandertal”, Journal of Human Evolution, Volume 117, 13-32, 2018.

  As philosophers, we may propose that in humans, synchronization is expressed in all three spheres: physical, like the synchronization of menstruation; psychological, as in the mobilization of mobs or fashions; spiritual, as when following a universal axis or something that is greater than the individual.

  Underlying mechanisms for synchronization

  Although accurately modelling human behavior is an extraordinarily difficult task, extremely simplified models may shed light on underlying mechanisms. The sociologist Mark Granovetter suggested in 1970 a model for illustrating what can cause a hypothetical mob to riot ^[19] J. Lumsden, L. K. Miles, C. N. Macrae, “Sync or sink? Interpersonal synchrony impacts self-esteem”, Front. Psychol., 19 September 2014.

  He illustrated his results with a story about a hypothetical mob involving 100 people, possibly on the brink of rioting. Granovetter assumed that each person’s decision whether to riot or not is dependent on what everyone else is doing. Instigators will begin rioting even if no one else is. Other people need to see a critical number of others causing mayhem before they’ll join in. That critical person’s threshold is assumed to be distributed across the population according to some probability distribution. Granovetter’s most famous example concerns the case of a mob with a uniform distribution of thresholds ranging from 0 to 99. In other words, one person has threshold 0, another has threshold 1, and so on. It’s easy to predict what will happen in a crowd like this. The person with threshold 0 is ready to begin rioting even if no one else is. He is the instigator. Then the person with threshold 1 becomes activated, since he sees one person (the instigator) breaking windows. Now that two people are rioting, the person with a threshold of 2 joins in. Like the burning of a fuse, or the toppling of a row of dominoes, the riot recruits more and more people until everyone is involved. That much is obvious, but here’s the twist. Suppose, said Granovetter, that we alter the initial composition of the crowd in the slightest way. Suppose the person with threshold 1 is replaced by someone with threshold 2. Now when the instigator starts looting, no one else joins him, since everyone’s threshold is greater than 1. In other words, no riot. The surprise here is that the two hypothetical situations are almost indistinguishable, at least by the usual sociological measures. The average makeup of the crowd has changed in the smallest way possible, and the overall distributions of thresholds are almost identical. Yet the outcomes are as divergent as they could be: an all-out riot in one case, a lone maniac on a rampage in the other. An onlooker might describe the first crowd as a bunch of thugs and the second as a peaceful demonstration marred by one lunatic, when in fact the two crowds are near replicas of each other. The lesson is that the collective dynamics of a crowd can be exquisitely sensitive to its composition, which may be one reason why mobs are so unpredictable. This emphasizes the complexity and hierarchical structure of the network. The right network structure and hierarchy can be tremendously effective for the good or for the bad. In marketing language, the instigator would be called “innovator” and the other ones from “early adapters” to “late majority”.

  All these phenomena involve herd behavior, where each person relies on the decision of others to guide his or her own actions. More abstractly let’s imagine a network of nodes – companies, people, governments, decision makers – and supposed each node is facing the same binary choice: adopt a new technology or not; to buy or not; to give or not; to riot or not; sign the Kyoto treaty or Glasgow agreements or not; to adopt progressive legislation as seen in another country or not.

  In practice these network models are significantly more complicated than Granovetter’s model. Nodes are mainly influenced by (and they influence) neighboring nodes; the actions or decisions are not necessarily binary; there is an inherent variability in the extent to which nodes are influenced by and influence other nodes; some nodes influence many neighbors while other influence very few. This extension of the network model is what lies behind complex networks in general and small-world complex networks in particular^[20]  D. Watts, S. Strogatz, “Collective dynamics of ‘small-world’ networks”. Nature 393, 440–442 1998.

  What characterizes small-world complex networks is the:

  • Short degree of separation (e.g. all living humans today are separated by at most six degrees of acquaintances),
  • Extraordinarily high effectiveness (e.g. a random network node will have access to more or easier access to resources than if part of a non-small-world-network)
  • Very high robustness (e.g. a healthy community is resilient to the dysfunctionality of a random member).

  In small-world complex networks there are necessarily hubs which are nodes with vastly greater connectivity and influence than that of the exponentially more numerous regular nodes. This implies a hierarchical and heterogenous structure of complex networks.

   Why synchronize?

   Synchronization is ubiquitous in nature at all levels and it’s a fundamental driving force behind the formation of complex networks when nodes are not identical to each other. Explaining why stuff or nodes have a motivation for synchronization on the other hand is a formidable task. At the physical level it may possibly be explained by having energetical advantages if they synchronize. In the chemical/molecular biological network context it may additionally be explained that synchronization yields resiliency and robustness (e.g. having many neurons fire synchronously makes the network robust to failures of individual neurons). Neurons synchronizing their firing is also explained as the basis for learning, i.e. “neurons that fire together wire together“ and learning means survivability. The synchronization of biological neural networks is also suggested as the molecular basis for how the brain supports the mind. It is well documented that synchronized neural activity can be recorded within the brain when an individual recognizes being aware of something in contrast as when not being aware of it ^[21]S. Strogatz, “SYNC, The Emerging Science of Spontaneous Order”, (2003), ISBN 0-7868-6844-9.

  In the macrobiological context, synchronization between individuals can give evolutionary advantages from energy preservation up to increased survivability (jackdaws, bird vigilance) or other advantages such as increased chance of successful breeding (fireflies, fiddler crabs, crickets).

  Trying to explain the motivation for synchronization in human behavior is as anticipated way more elusive and is difficult to formalize in scientific terms ^[22] O. Mayo, I. Gordon, “In and out of synchrony-Behavioral and physiological dynamics of dyadic interpersonal coordination”, Psychophysiology vol. 57,6, 2020.  ^[23] M. Granovetter, “Threshold models of collective behavior” American Journal of Sociology Vol 83. pp. 1420-1443. 1978.

  Intuitively:

  • We need the power of the group in order to motivate ourselves and to set us in motion. It’s easier to overcome obstacles together if we synchronize on the same goal or the timing of the goal. It’s easier to fulfill a personal goal using the power of the group, seeing others succeed, frequently helps us to overcome obstacles in spite of our initial disbelief. This requires interaction between the group members, something that also encourages group goals. This requires synchronizing and to reach consensus. Sometimes synchronizing our personal goals to be the one and same yields a higher probability of reaching the goal than if done completely individually or even enables us to overachieve the goal (e.g. synchronized clapping).
  • We have a tendency to imitate others and thus to synchronize with them as we are innately inclined to believe that if something is good for someone else then it probably is good for us as well.
  • Being in consensus with other people reduces the tension we feel.
  • Consciousness is understanding that meeting our personal goals also motivates other people and hence striving to meet our own goals in order to help others. It also means being aware that the group goal is higher than the sum of each individual goal (e.g. a symphony orchestra).
  • We are all a bit different, from the formative laws of complex small-world network we may learn that a hierarchical social structure significantly increases the contribution of synchronization to achieve personal as well as community goals when the nodes are heterogenous.

  All these examples of so-called spontaneous order are not necessarily a contradiction to the definition of entropy. The common argument used to explain this is that, locally, entropy can be lowered by external action, e.g. energy introduced from the sun. This local decrease in entropy is, however, only possible at the expense of an entropy increase in the surroundings; here more disorder must be created. The condition of this statement requires that living systems are open systems in which both heat, mass, and or work may transfer into or out of the system. The putative entropy of a living system would drastically change if the organism were thermodynamically isolated. If an organism was in this type of “isolated” situation, its entropy would increase markedly as the once-living components of the organism decayed to an unrecognizable mass. Were earth to be completely shut off from any external energy then entropy would inevitably maximize locally.

  Thermodynamics and statistical physics in general and entropy in particular do not explain or even relate to why there is a driving force towards local assemblies and greater order. If entropy is such a fundamental law why does nature incessantly try to utilize any available energy in order to work against the law of entropy?  

  Philosophical implications

  Among the possible philosophical implications and contributions brought forward in this monograph may lie some principles underlying the recruitment of masses of people. Imagine if instead of utilizing knowledge of how to spread and propagate a new product for economic gain and personal power we would know how to efficiently mobilize the people into groups helping each other for nothing material in return. Imagine if instead of many groups of good people doing volunteering work, we could instigate a mass movement of people where mutual help and the common good would be the norm.

  Another philosophical implication is surfaced by the vast amount of scientific evidence pointing out that there is an advantage in cooperating to the point of reaching consensus and even unity. I.e. this is not a game-theoretic case in which there is consensus on a strategy for reaching one winner and one loser. In the case of synchronization, if the one loses, the other loses. If the other wins, the one also wins. The whole is truly greater than the sum of its parts. We may view synchronization as such a fundamental natural driving-force for cooperation, order and formation of networks for maintaining this order that it makes it worth investing all energy available in order to overcome the other fundamental natural force pushing for disintegration and disorder. The fact that synchronization is traditionally termed in physics “spontaneous order”, and not, say, “organized order” or so, hints that this duality may yet have to be brought forward to popular awareness.

  As philosophers we should work with these insights by understanding that cooperation and consensus is part of our nature even down to the quantum level. We should thus invest all available energy in creating order, in cooperating, in understanding that the success of other is also our success and vice versa.

  We actually cannot really live without synchronization; without it we will disintegrate into a chaotic mass of disorder. That is the dualistic implication of the laws of nature.

  References

  [1] D. J. Amit, Y. Verbin, “Statistical Physics: An Introductory Course”, World Scientific Publishing, (1999).

   

  [2] G. Beauchamp,  “A comparative analysis of vigilance in birds”. Evolutionary Ecology 24(5):1267-1276, (2010).

  [3] L. Conradt, T. J. Roper, “Consensus decision making in animals”, Trends in Ecology & Evolution, Volume 20, Issue 8, Pages 449-456. (2005).

  [4] A. Daliot, D. Dolev and H. Parnas, “Self-stabilizing Pulse Synchronization Inspired by

  Biological Pacemaker Networks”, arXiv:0803.0241v2, (4 Mar 2008).

   

  [5] A. J. Dibnah, J. E. Herbert-Read, N. J. Boogert, G. E. McIvor, J. W. Jolles, A. Thornton. Vocally mediated consensus decisions govern mass departures from jackdaw roosts. Current Biology, Vol. 32 Issue 10 Pages R455-R456 (May 2022).

  [6] I. Eshel, D. Weinshall, U. Motro, “On the evolution of altruistic cooperation”, Biomathematics and Related Computational Problems. Kluwer Academic Publishers, pp 279–282. (1988).

   

  [7] S. Strogatz, “SYNC, The Emerging Science of Spontaneous Order”, (2003), ISBN 0-7868-6844-9.

   

  [8] O. Mayo, I. Gordon, “In and out of synchrony-Behavioral and physiological dynamics of dyadic interpersonal coordination”, Psychophysiology vol. 57,6 (2020).

   

  [9] U. Motro, D. Cohen, “Selfish cooperation in social roles: the vigilance game in continuous time”. Sociobiology and Conflict, Chapman and Hall, pp 55–61. (1990).

   

  [10] U. Motro, D. Cohen. “A note on vigilance behavior and stability against recognizable social parasites”. Journal of Theoretical Biology, 136:21–25. (1989).

   

  [11] Z. Néda, E. Ravasz, Y. Brechet, A. L. Barabasi. “The sound of many hands clapping”. Nature 403, 849–850 (2000).

  [12] D. Watts, S. Strogatz, “Collective dynamics of ‘small-world’ networks”. Nature 393, 440–442 (1998).

  [13] M. Granovetter, “Threshold models of collective behavior” American Journal of Sociology Vol 83. pp. 1420-1443. (1978).

  [13] J. Lumsden, L. K. Miles, C. N. Macrae, “Sync or sink? Interpersonal synchrony impacts self-esteem”, Front. Psychol., (19 September 2014).

  [14] J. Attwater, P. Holliger. “The cooperative gene”. Nature 491, 48–49 (2012).

  [15]  W. Rendu, C. Beauval, I. Crevecoeur, P. Bayle, A. Balzeau, T. Bismuth, L. Bourguignon, G. Delfour, J.P. Faivre, F. Lacrampe-Cuyaubère, C. Tavormina, D. Todisco, A. Turq, B. Maureille, “Evidence supporting an intentional Neandertal burial at La Chapelle-aux-Saints”, PNAS 111 (1) 81-86 (2013).

  [16] A. Gómez-Olivencia, R. Quam, N. Sala, M. Bardey, J. C. Ohman, A. Balzeau, “La Ferrassie 1: New perspectives on a “classic” Neandertal”, Journal of Human Evolution, Volume 117, 13-32, (2018).

   

   

   

  Notas[+]

  ↑1	D. J. Amit, Y. Verbin, “Statistical Physics: An Introductory Course”, World Scientific Publishing, 1999
  ↑2, ↑13	S. Strogatz, “SYNC, The Emerging Science of Spontaneous Order”, (2003), ISBN 0-7868-6844-9
  ↑3, ↑16	A. Daliot, D. Dolev and H. Parnas, “Self-stabilizing Pulse Synchronization Inspired by Biological Pacemaker Networks”, arXiv:0803.0241v2, 4 Mar 2008
  ↑4	L. Conradt, T. J. Roper, “Consensus decision making in animals”, Trends in Ecology & Evolution, Volume 20, Issue 8, Pages 449-456. 2005
  ↑5	I. Eshel, D. Weinshall, U. Motro, “On the evolution of altruistic cooperation”, Biomathematics and Related Computational Problems. Kluwer Academic Publishers, pp 279–282. 1988
  ↑6	S. Strogatz, “SYNC, The Emerging Science of Spontaneous Order”, (2003), ISBN 0-7868-6844-9.
  ↑7	S. Strogatz, “SYNC, The Emerging Science of Spontaneous Order”, (2003), ISBN 0-7868-6844-9
  ↑8	A. J. Dibnah, J. E. Herbert-Read, N. J. Boogert, G. E. McIvor, J. W. Jolles, A. Thornton. Vocally mediated consensus decisions govern mass departures from jackdaw roosts. Current Biology, Vol. 32 Issue 10 Pages R455-R456 May 2022
  ↑9	G. Beauchamp,  “A comparative analysis of vigilance in birds”. Evolutionary Ecology 24(5):1267-1276, 2010). (( U. Motro, D. Cohen, “Selfish cooperation in social roles: the vigilance game in continuous time”. Sociobiology and Conflict, Chapman and Hall, pp 55–61. 1990
  ↑10	U. Motro, D. Cohen. “A note on vigilance behavior and stability against recognizable social parasites”. Journal of Theoretical Biology, 136:21–25. 1989
  ↑11	A. Daliot, D. Dolev and H. Parnas, “Self-stabilizing Pulse Synchronization Inspired byBiological Pacemaker Networks”, arXiv:0803.0241v2, 4 Mar 2008
  ↑12	A. Daliot, D. Dolev and H. Parnas, “Self-stabilizing Pulse Synchronization Inspired by Biological Pacemaker Networks”, arXiv:0803.0241v2, 4 Mar 2008
  ↑14	[12]. There is also evidence that gives rise to the postulation that life itself could not have formed on earth if RNA molecules would not “cooperate”, this theory is coined “the cooperative gene” [14].   Synchronization in human social interactions A concert audience often expresses appreciation for a good performance by the strength and nature of its applause. The thunder of applause at the start often turns quite suddenly into synchronized clapping. The phenomenon is an expression of social self-organization that provides an example on a human scale of the synchronization processes that occur in numerous natural systems (( S. Strogatz, “SYNC, The Emerging Science of Spontaneous Order”, (2003), ISBN 0-7868-6844-9
  ↑15	Z. Néda, E. Ravasz, Y. Brechet, A. L. Barabasi. “The sound of many hands clapping”. Nature 403, 849–850 2000
  ↑17	W. Rendu, C. Beauval, I. Crevecoeur, P. Bayle, A. Balzeau, T. Bismuth, L. Bourguignon, G. Delfour, J.P. Faivre, F. Lacrampe-Cuyaubère, C. Tavormina, D. Todisco, A. Turq, B. Maureille, “Evidence supporting an intentional Neandertal burial at La Chapelle-aux-Saints”, PNAS 111 (1) 81-86, 2013
  ↑18	A. Gómez-Olivencia, R. Quam, N. Sala, M. Bardey, J. C. Ohman, A. Balzeau, “La Ferrassie 1: New perspectives on a “classic” Neandertal”, Journal of Human Evolution, Volume 117, 13-32, 2018
  ↑19	J. Lumsden, L. K. Miles, C. N. Macrae, “Sync or sink? Interpersonal synchrony impacts self-esteem”, Front. Psychol., 19 September 2014
  ↑20	D. Watts, S. Strogatz, “Collective dynamics of ‘small-world’ networks”. Nature 393, 440–442 1998
  ↑21	S. Strogatz, “SYNC, The Emerging Science of Spontaneous Order”, (2003), ISBN 0-7868-6844-9
  ↑22	O. Mayo, I. Gordon, “In and out of synchrony-Behavioral and physiological dynamics of dyadic interpersonal coordination”, Psychophysiology vol. 57,6, 2020
  ↑23	M. Granovetter, “Threshold models of collective behavior” American Journal of Sociology Vol 83. pp. 1420-1443. 1978