Newly found Mayan hieroglyphics (at Dos Pilas, Guatemala) that describe a series of wars between Mayan "superpowers" Tikal and Calakmul appear to support a new mathematical theory of civilizations. Major events in the history of Teotihuacan (near Mexico City) in Mayan times also are consistent with the predictions of this theory

Blaha, S

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1October 7, 2002New Mayan Hieroglyphics Support ForA Mathematical Theory of CivilizationsByStephen Blaha*ABSTRACTNewly found Mayan hieroglyphics (at Dos Pilas, Guatemala) that describe aseries of wars between Mayan “superpowers” Tikal and Calakmul appear tosupport a new mathematical theory of civilizations.  Major events in the historyof Teotihuacan (near Mexico City) in Mayan times also are consistent with thepredictions of this theory.                                                * Telephone: 603-626-1566, 702-442-5401 (FAX), baliltd@compuserve.comEXT-2002-07207/10/20022IntroductionRecently new Mayan hieroglyphics were accidentally found in Dos Pilas, Guatemala thatdescribe a series of events and wars between the Mayan “superpowers” Tikal andCalakmul [1]. These historical findings appear to support a new mathematical theory ofcivilizations [2]. Previously Mayan history was viewed as a collection of random warsbetween city-states that ended around 900 AD in a mass exodus from the cities. It nowappears that Mayan civilization was undergoing a pattern of development that is similarto the pattern of development of Eurasian civilizations. The pattern of Eurasiancivilizations is described in Reference 2.Summary of the Theory of CivilizationsThere have been numerous attempts to develop a theory of history that would make somesense of the seemingly random events of history.  Toynbee [3] and others [4] haveexamined 6,000 years of history and concluded that the course of history should beviewed in terms of civilizations. Civilizations appear to have a common structure ofgrowth and decline that Toynbee characterized as a “three and a half beat pattern.” Thisroughly 1,000 year pattern consists of a growth phase that ends in a breakdown (usually amajor conflict). The breakdown begins a disintegration phase with peaks and valleys(“rallies” and “routs”) following a regular pattern with 400 years spent in a time oftroubles phase followed by 400 years in a universal state. The rallies of a civilizationprogressively decrease in amplitude as it disintegrates.Based on the work of Toynbee and others, we [2] have developed a mathematical theoryof civilizations that appears to match historical events in detail for all civilizations. Thetheory is formulated within a Newtonian dynamical framework. Its approach is similar inspirit to that of Lewis F. Richardson’s theory of arms races and wars [5].We assume that a civilization can be described by two variables: its societal level S andthe change in its societal level C. The definition of the societal level of a civilization isnecessarily imprecise. We will define the societal level S to be the “health” or strength ofa civilization in terms of its political and social institutions, social cohesion, ability tosolve problems, capacity for technological innovation, flexibility in finding solutions, andenterprise in meeting challenges. The societal level is also a measure of the innerdevelopment and inner state of mind (the psyche) of the people of a civilization. It can3also be viewed as a measure of the “sentiment” of the civilization’s members about thefuture. In a sense Rome fell because the sentiment of the Roman Empire turned negative– people had very negative expectations about the future. The phrase “cosmicsenescence” summarized that view – the universe, and Rome, was winding down. AsRome expected to fail it did and the barbarians easily overcame a dispirited populace.The societal level can be viewed as a civilization’s equivalent to “consumer sentiment” ineconomics. Consumer sentiment indicates the consumer’s view of the future and thus theconsumer’s likelihood to spend. Societal level indicates the populace’s view of the futureand the health of its civilization.The variable C is the time rate of change of the societal level:C = dS/dt (1)As a result the societal level is:t   S  =   ∫ dt' C(t') (2)            0When we discuss civilizations we often speak of the forces affecting a civilization:internal  forces (primarily social), and external forces (barbarians, environment, and soon). These forces “move” a civilization in one direction or another. With this thought inmind we have constructed a preliminary theory of civilizations using Newton’s law:F = mA (3)where F is the total force on a civilization, m is its “mass”, and A is its “acceleration”(which is related to its societal growth). We assume the acceleration A = C′′, the secondtime derivative of C.For most of Mankind’s existence societies have been static with S = C = 0. Civilizationsare dynamic societies that first appeared about 6,000 years ago. They grow and change,and have been observed to have a 3.5 beat pattern of disintegration. It is reasonable toassume that this pattern is inherent in civilizations and not the result of external forces.4Toynbee suggests this point when he refers to the ‘Laws of Nature’. So we separate theforce on a civilization into an internal force Fint and an external force Fext, and assume thata 3.5 beat pattern is generated by internal forces.F  =  Fint  +  Fext (4)When we consider change in society we notice that there is often resistance to change.Resistance takes two forms: a resistance to the increasing rate of change, and a resistanceto the total change. We express these socio-psychological concepts as forces:Fint  = F0 =  – rC′  – sC (5)(F0 is introduced for later use.) In the absence of external forces Newton’s law (eqn. (3))becomes the equation of a damped harmonic oscillator:mC′′ + rC′ + sC =0 (6)The solution can be taken to beC = c1e–atsin(bt) (7)with the societal level:     S(t, r) =  c1[b – e–at(a sin(bt) + b cos(bt))]/(a2 + b2) (8)where a, b, c1, and c2 are constants, t is the time since the civilization’s beginning, anda = r/(2m) (9)b = √s/m  – r2/(4m2) (10)Both C and S are zero at the beginning of the civilization. S approaches a constant valuerepresenting the cumulative effects of the civilization as t gets large:S(t, r) →  c1b/(a2 + b2) (11)5Although a civilization may disintegrate, parts of its social structure and culture generallysurvive.The constants a and b have been determined by earlier studies [2] of Eurasiancivilizations to have the values a =  0.00281 and b = .0235. Since we are unable toexperimentally measure the absolute value of S we set c1 equal to 1. The relative valuesof S during the history of a civilization can be compared to historical events and thusprovide copious “experimental” tests of the theory.We will call the S curve with these parameter values the Standard S curve. The equationfor the Standard S curve is approximately:S(t) =  [1 – e–.00281t (.12sin(.0235t) + cos(.0235t))]/.0235   (12)with time measured in years.Theory Compared to Mayan HistoryWe have compared the standard solution (eqn. (12)) of the theory (and the extendedtheory) with various civilizations and found a close match with the history of all knownEurasian civilizations [2]. If we now apply the Standard S Curve to Mayan civilizationwe need to set only one parameter – the point where the civilization began its rise. InReference [2] we set the beginning of Mayan civilization to 223 BC with the result:  SMayan(t) = S(t + 223) (13)where SMayan(t) is the curve for Mayan civilization. (t = -223 or t = 223 BC is thebeginning year of the civilization; prior to that year we view the Mayan society as largelystatic.) BC years are specified as negative numbers. The Figure shows the plot of SMayan(t)as a red line. Some events of Mayan history (including the new hieroglyphic data) areidentified in the Figure and show good agreement with the ups and downs of SMayan(t).6Comments on Mayan CivilizationA series of major wars between Tikal and Calakmul, Mayan superpowers, in the fifththrough seventh centuries appears to have brought Mayan civilization to its knees.Recently unearthed hieroglyphics [1] describe phases of this war such as the founding ofan important military outpost (stronghold) Dos Pilas by Tikal in 629, its conquest byCalakmul around 650, its emergence as a powerful state that conquered its founder Tikalaround 660, and its eventual abandonment in 760. Thus a sequence of what originallyappeared to be local conflicts between 600 and 700 were, in reality, a continuation of a“world war” between Tikal and Calakmul that culminated in the conquest of Calakmul in695 by Tikal.The roughly 250 years of warfare between Tikal and Calakmul lasting from the fifththrough seventh centuries corresponds to the 267 year cycle found in Western civilizationand Middle Eastern and Asian civilizations found by Blaha [2], and Arnold Toynbee [3]and others [4], in studies of 6,000 years of human civilizations.Mayan civilization began with a roughly 134 year period of major growth starting around223 BC. Great cities were built such as El Mirador. Teotihuacan was also founded in thefirst century BC. Mayan civilization then went through three and a half cycles of ups anddowns just like Eurasian civilizations. The last cycle was dominated by constant warsbetween Tikal and Calakmul that culminated in the decline of Mayan civilization. Tikal’sconquest of Calakmul around 700 AD started the last stage of decline that ended in thecomplete abandonment of the Mayan cities around 900 AD. The last stages of the declineof the Mayans can be compared to the last stages of the decline of Rome: constantwarfare with Barbarian invaders culminating in the conquest of Rome and the reductionof Rome to a small agricultural village among splendid ruins.Thus the spectacle afforded by Mayan history compares with that of European and Asiancivilizations, and confirms the evolution of civilizations is based on our common humannature.The Figure shows a chart of the ups and downs of the history of Mayan civilization fromits beginning around 223 BC until its end around 900 AD according to the Theory ofCivilizations. The red line is a plot of the “societal level” – the inherent strength (health)7of the overall civilization. The graph is superimposed on a photograph of an impressiveMayan Temple.As can be seen in the period from 445 – 575 AD, overwhelming fratricidal warfarebetween states weakened the strength of the civilization. The period between 580 and 700shows an upturn in the civilization that is probably due to a lower level of conflict thatallowed the civilization to begin growing again. The settlement at Dos Pilas in 629 and itsgrowth into a major power support the notion that the Seventh Century was a period ofgrowth.The emergence of a “winner” – Tikal – in 695 with the conquest and destruction ofCalakmul roughly marks the high point of the period as shown in the Figure.The period denoted “Time of Troubles” [2] was probably a period of fierce conflictbetween the city-states. In Eurasian civilizations it is normally a period of ruinousconflict.The period denoted “Universal State” in the Figure normally [2] is a time in the life of acivilization where the civilization is dominated by an empire. In the case of Mayancivilization this time may actually have been a time dominated by a confederation ofstates that often had internal wars. It may have been analogous to the Parthian Empire,which consisted of loosely united, more or less independent provinces.Teotihuacan appears to follow the pattern of Mayan civilization. Based on trade and otherdata it appears Teotihuacan was part of the greater Mayan civilization. Note that it wasfounded during the period of great initial growth, reached its peak shortly after a peak inMayan civilization and collapsed at roughly the same time as Calakmul was conquered.ConclusionIt appears that new data on Mayan history supports the mathematical Theory ofCivilizations as applied to Mayan civilization.8REFERENCES1.  Williams, A. R., “A New Chapter in Maya History: All-out War, Shifting Alliances,Bloody Sacrifices”, National Geographic Magazine 202, no. 4 (October, 2002).2. Blaha, S., The Rhythms of History: A Universal Theory of Civilizations (Pingree-HillPublishing, 2002).3. Toynbee, A. J., A Study of History (in twelve volumes, Oxford University Press,Oxford, UK, 1934-61).4. See references in Melko, M. and Scott, L. R. (eds), The Boundaries of Civilizations inSpace and Time (University Press of America, Lantham, MD, 1987).5. Richardson, L. F., Arms and Insecurity (Quadrangle Books, Chicago, IL, 1960).

New Mayan Hieroglyphics Support For A Mathematical Theory of Civilizations

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