E.The Battle of Tours in the year 732, Charles Martel against the Arabs, the latter commanded by the brave Abderraman. It was a warlike action of the second aggressive process of the French Empire against the Arabs. The French Empire developed its first aggressive process from the year 250 to 561 (a duration of 311 years), its great depression from 561 to 688 (a duration of 125 years), the second period of great strategic victories from 688 to 815 (a duration of 129 years) and disintegration from 815 to 879 (64 years), resulting in a total of 629 years. The Arabs, owners of Spain and after one century of victories, attack Gaulin the year 732. After the defeat of Tours, they retreat to Spain for eight centuries until they return to their continent due to Hispanic weapons.F.The Battle of Saratoga (October 7, 1778). This battle decides the independence of the United States of America. Great Britain was practically at the beginning of its great depression when it faced its then colony in this decisive battle.G.The Battle of Lepanto(October 7, 1571). In the historical process of Europe and adjacent areas, where it concerns the first mathematical-historical cycle, in chronological order, the Persian, Carthaginian, Macedonian, Roman, Visigoth,French,and Teutonic Empires developed. It was the mathematical substitution of the supremacy of some for others respectively. The second mathematical-historical cycle begins with the TurkishEmpire, then the Spanish, French, English Empires and the Federal Republic of Germany. The Turkish Empire is followed by the Spanish, so that the Battle of Lepanto, a warlike decisive event in this process, expresses the phase of decadence and disintegration of the Turkish Empire and the first period of great victories of the Spanish Empire. This is the reason for the result of this battle.“Great strategic victories belong to the phases corresponding to two great aggressive processes. Victory is a constant and it is the conclusion of every attack. That is the phase of great offensives”. This was the phase of the Spanish Empire.“Decadence and disintegration is the phase in which strategic offensives are useless to back up the continental or intercontinental empire. Effective strategic potentiality is effective for the imperial body or nation, but it is always useless for the second empire of the mathematical-historical cycle, that is, when the nation is about to go through the era of great demographic fractionation”.The Turkish Empire had gone through the phases of the first period of great victories (1250-1392), the great depression (1392-1422), second period of great victories (1432-1572) and was about to develop the phase of decadence and disintegration with a brief duration of the conservation phase. Although Lepanto was at the end of 1571 is it considered as the beginning of the phase of decadence.H.The Battle of Valmy(September 28, 1792). The ethnic group of the Germanic area was undergoing the Great Demographic Fractionation era. France was ending its phase of Great Depression (1697-1793), in which, generally, the Empire is invalid in order to afterwards be able to expel the invaders. At the end of this phase, begins the second period of great victories in 1793. “Victory in the defense is a characteristic of the era of great demographic fractionation. Strategic victories are reserved for the defensive. Successful offensive is only achieved in order to enforce the defense of the region. It is the defense and counter-offense phase”.According to this mathematical-historical principle, the Germanic ethnic group did not have an offensive strategic ability. On the other hand, France was about to end its second period of Great Strategic Victories.I.The Battle of Bailen (July 15, 1808). The result of this battle was due to the independent value that territories in the historical process of the corresponding ethnic group have. An empire is developed, it expands towards its neighbors, when they are undergoing the depressive phase, but when they recover they expel the invader. There is no permanent occupation but it is rather temporary. Thus, there exists a historical force that provides unity and sovereignty to each geographical area, with its corresponding ethnic group. To the expansion of the French Empire in its second period of Great Victories, there follows a setback that is known as the Military Disaster, which was the Battle of Waterloo in the year 1815. Likewise, as in the French retreat from Spain, essentially marked by the Battle of Bailen.“Conservation is a phase of Empire maintenance. Any strategic operation in this phase should be closely analyzed, including the human means factor. Victories and defeats alternate with each other. It is more a phase of the defensive in the maintenance of conquered geographical regions of the imperial body”. This mathematical-historical principle was influential in the victory of Bailen.J.The Battle of Bleinheim(August 15, 1704). This Battle that is called, Hochstedby the French and Belinheim,by the Germans, gather a series of European Countries, among which was the British Empire, in the phase of the first period of Great Strategic Victories (1609-1783).K.The Battle of Orleans (May 7, 1942). At this time, the English and French were undergoing an era of Great Demographic Fractionation, and, according the mathematical-strategic concept, England did not have a strategic offensive capacity and, as we have already seen: “Victory in the defense if a characteristic of the era of great demographic fractionation. Strategic victories are reserved to the defensive. A successful offensive is only obtained to enforce the defense of the region”. It was thus impossible to detain the French mathematical-historical process.The destruction of the undefeatable Armada of Phillip II in the year 1558. The Spanish Empire was at that time in the first period of great strategic victories (1479-1643). However, England was in an era of Great Fractionation and soon to begin the year 1783, year in which that phase was to end. We already know by the mathematical-historical principles of the characteristics of nations during that era and, in this case, furthermore, the advance of the creative force, developing, in chronological order the Turkish, Spanish, BritishEmpires and the Federal Republic of Germany, and this second cycle of Europe and its adjacent area.This is then the mathematical-historical reason for the result of this Battle, the truth and its pure cause.L.The Battle of the Boyne(July 1, 1690). The BritishEmpire was in the phase of the first period of Great Victories (1609-1783) and so was the French Empire, but the phase was coming to an end, so that in 1697 the Great Depression ended. The reason for the result of this Battle is that the phase which the English were undergoing, has as a characteristic, the unification of the geographical area with ethnic groups, that is, Great Britain. In this manner, then, the mathematical-historical process of the era of Unification in its second cycle of 1,700 years, had begun in the year 1609 to end various centuries later, estimated to be five or five and one-half centuries later.M.The Battle of Syracuse (year 413 B.C.). In this Battle the Syracusans defeated the Athenians.The reason for this was that Athens was in the year of Great Demographic Fractionation, in its first mathematical-historical cycle, and by concept and principle, nations in this phase do not have a strategic offensive capacity to conquer, occupy and overcome. The Italiannations were also developing the era of great fractionation of the first mathematical-historical cycle of Europe.The term “decisive battles” is a very broad concept. It must be determined if they are decisive in a war between empires, nations in conquest, or liberty of a continent or geographical areas, that make up large or medium spaces.The battles in the 1stor 2ndperiod of Great Victories are, in their majority, decisive in the conquest of an empire or nation. Also in the phase of great depression, whether to occupy or to expel the enemy. Likewise in the military disaster, if it is one sole battle or the last one, if they are various from one or another part of the adversaries. In the phase of decadence or disintegration, the first battle that is fought indicates the beginning of the phase, and the last one, marks the end of the empire.Lastly, in the phase of relative independence, the last one is the decisive battle to begin the phase and that provides liberty to the country. Man is the expression of the historical phase, battles are historical events that express said phase and they form the whole of the nation’s process. Everything is continuity in time and in space. Everything is decisive in the thread of the historical process.In the field of Operational Strategy battles would be defined by the three Clausewitz rules: “The concentration of effort, the strong man’s actions and the decision for the battle in the principal theater of operations”.In the area of National Strategy, High or Grand Strategy, its definition is given with precision, the mathematical-historical concept, the mathematical-historical principle and the mathematics of history, as has been exposed and analyzed in this modest work.In the mathematical-historical concept, we could say that it is a mathematical and humanistic world, in which the first determines the general process of cultures and civilization, of the creations, development and duration of empires and nations, where man is the expression of historical phases. Man can change his destiny only by mental and spiritual excellence.Evolutions and revolutions follow each other without improvisation or delay, nothing is the work of chance. In cultures, civilizations and processes of man’s life in the planet, historical happenings and events occur as a chain reaction, as a great gear of a perfect machine, and an operation having a continuity and permanence in time and space. Everything is exactly fulfilled with an admirable precision. The process of a mathematical world framed within a humanistic field, of a man who oscillates from a maximum civilization to a minimum one.Dr. Deulofeu says: “Today we have discovered a law that arranges the evolution of nations in the same manner as we know the law that governs the evolution of the individual. Perhaps one day we may know the circumstances that have caused collective evolution, as we know the physiological circumstances that produce birth, but it is possible that man will never know what is the profound origin of life”. That is, that perhaps the cycle of life or evolutionary cycle may not be modified, neither from the individual or from the collective point of view. Be that as it may, at the present time, man has been smoothing out the individual process protecting himself more and more against the inclemency of weather and illnesses.In like manner, he can ensure as of now that the evolution of nations be done without bloody and violent struggles, without external or internal wars. What can man do to modify his destiny? “Man follows a defined evolution, he is born, he grows up, he reaches adulthood, enters decadence and finally dies. From the individual event, lets go on to the collective one. It has been shown that nations go through phases of winter inactivity, through phases of spring growth, through summer phases of complete creativity and finally through fall phases of decadence, to again enter into the winter phase and begin the cycle again”.“Nations follow a cyclical process that is analogous to that of plants, but just as the cycle of plants lasts 365 days, that of nations is 1,700 years. If we compare the human process with that of irrational animals, we observe a fundamental difference where they do not know how to come out of their determinism, while man constantly breaks it. Cats and dogs have been defending themselves with their nails and fangs from time immemorial, man, on the other hand, constantly modifies his means of defense. Analogically, animals walk on their hoofs starting from their origin while man discovers other means of locomotion. With plants, the same or almost the same happens when collectively considered, they continue their vegetable cycle in an identical manner through the centuries, as long as the solar system is not modified. But man, at the same time as he has been discovering the laws of nature, has modified his way of life and has progressed as a result. Why should he not progress the day he discovers the laws that govern the life of collectivities? Human progress has been evidenced in the extinction and management of great epidemics with the discoveries of bacteriology. The same progress should be expected in the political, social and cultural arena, with the discovery of the mathematical law that has been governing the life of nations up to the present time”.“While it was not known it was not possible to do anything in this sense. All societies or nations that have been built through time in order to avoid war, have resulted to be inoperative. But knowing said law, knowing before hand what will happen, it is absurd to think that men would voluntarily launch themselves into a precipice being able to modify the trajectory. Today we know where we are and where we are going. Is it in the hands of man to deviate the helm and change the course? The transcendental operation of turning the destiny of the world, advises us to study the process and system to be followed to execute this change of course”.“At once a fundamentalneed arises: to tone down the convulsions that entail the foreseen process; once this has been accomplished, the possibilities of totally modifying it can be considered. When he develops from infancy to old age, man does not follow a smooth and easy course, on the contrary, he, in fact, has to sustain a constant struggle in order to defend himself in the environment that surrounds him (climate, illnesses, survival). He has been improving in this struggle, that is, modifying his natural condition of life and greatly reducing natural difficulties. Housing and hygiene conditions to a great extent have lessened mortality and human suffering; medical progress tends to diminish pain. And if it has been this way, capable of eliminating collective calamities such as cholera and yellow fever, it is possible to conceive that the day will come when all illness will be eliminated and man will be able to go on with his life without these perturbances”.“Nations, when they begin their evolutional cycle, follow a road of progress and creation, but this road is not smooth, on the contrary, in order to progress they need to sustain a constant struggle against themselves. Extinct institutions do not disappear if it were not for violence. Exhausted regimes do not resign themselves to be voluntarily substituted and fight to the death to persist. Nations in full growth, if they want to extend themselves, have to forcibly drown decadent empires. Decrepit institutions, due to their instinct of conservation and because they think that by fighting they can lengthen their time, resist disappearing”.“But institutions and their men, if they knew the fate that awaited them in the struggle before hand, would stop fighting if they knew they were going to be defeated. As soon as they knew of the catastrophes that would be produced and their results, the nations of the world should suppress wars. Will men abolish calamities in the same manner as violence has been abolished from individual combat and taking justice by one’s own hand be replaced by the creation of courts of justice?”So man improves mentally and spiritually in order to have a better life, is our greatest desire when we pose bellicosesubjects.THE MATHEMATICS OF HISTORYThe universality of the law of History.The law of History governs the process in all domains of human activity. Nations evolve, progress, decline and rise again, following some perfect cycles in the political, social, artistic, philosophical and scientific arenas. Nothing is the work of chance. The appearance and disappearance of great empires, the creation of architectural styles, the great discoveries, the great philosophical conceptions, obey a mechanism that is as precise as a clock. Up to now men have ignored it. Some have suspected it but up to now nobody had defined it. For this reason, men and nations have been following a road that, unknown to them, was traced beforehand.Declarations of the mathematical law that determine the evolution of nations: We can resume that law in the following paragraphs:1.All nations go through eras of Great Demographic Fractionation, alternating with other of Great Unification or imperialist eras.2.Eras of Great Fractionation have a duration of six and one-half centuries. Eras of Great Unification last ten and one-half centuries. The cycle of evolution is made up of seventeen centuries.3.During this process of evolution, nations go through perfectly established phases so that at the end of the cycle they occupy the same position it had at the beginning thereof.4.The cycle of evolution covers all areas of human activity, that is, in addition to the political cycle, we must consider the social, artistic, philosophical and scientific ones.5.All nations follow the same evolution, but it is ahead or behind, according to the geographical position of each country.6.The creative force is not the same for all nations.7.Imperialist nuclei that give way to eras of Great Political Unification, follow perfect biological processes that are identical to each other and with one same longevity that lasts from five to six centuries.8.The transformation of political-social regimes is not done according to a constant ascending or descending line, but through alternative advances or reversals, some more intense than others, that produce a broken line as a result. The result of this line is equivalent to an advance in a determined sense. This is given the name of “Law of two paces towards the front and one towards the back” or “Oscillating Law”.We are going to precisely determine and explain these paragraphs through a graphical representation of the evolutionary cycle. If in a system of Cartesian Coordinates we mark time over the X axis (horizontal axis) and the changes nations go through, from every point of view of human activity, over the Y axis (vertical axis), we can represent the evolutionary process thereof, as seen in Chart 1.Marked on the horizontal axis, we see seventeen divisions that correspond to the seventeen centuries, that is the total duration of the cycle. The first six and one-half centuries correspond to the era of great fractionation. During this one there are no great political units, that is, nations or empires, such as we know them in our day, but, in fact, each city, with the small region that surrounds it, constitutes a real Independent State. During this era and starting from its origin (A), nations follow a life of progress in all areas of human activity, until they reach a maximum (B). We represent the evolutionary process of this first era by the ascending line that goes from A to B, that coincides with the end of this era of great fractionation.Afterwards, an important political change occurs: nations lose their political liberty that reached up to a director nucleus. At the beginning, it will establish a military hegemony without intervening in the internal political organization of the cities, or in their particular governments. A broadly federal organization is then created. Gradually, the political regime changes and the hegemonic one accentuates its influence and intervention takes place in the local governments and, after a process of unification that lasts two centuries we see the particular governments disappearing.Local languages and laws are substituted by the laws and languages of the hegemonic nucleus, at least in written documents, by the government.We will call this first phase of the imperial era the Federal Phase, and is represented in the chart by the descending line B-C. Afterwards, we enter the unitary phase of great nations or empires.The cities that form part of the empire have completely lost the conscience of their own personality and they feel identified with the hegemonic nucleus. This phase represent a regime that is completely opposed to the era of great fractionation and, in the chart it is represented by the line that goes from C to D.From this moment on, that is, four centuries after the imperialist era began, the hegemonic nucleus starts its disintegration. The perfect unity achieved starts to deteriorate until it reaches total decomposition and substitution of the first imperial nucleus for a hegemonic one, which the unitary regime will maintain during a space of four and one-half centuries, that is, until the end of the cycle.The two imperial nuclei do not present the same characteristics. The second enters the scene in a fully unitarian or absolute phase. The first empire considers its subjects as citizens, whether they belong to the imperial nucleus or to the other nations that form part of the empire, only with the condition that they waive their own characteristics and adopt the imperial language and law.The disintegration of this first empire is manifested, as we have said, by a weakening of the central power, by the lack of discipline in the army, by civil war and by anarchy. Nations that make up part of the empire wish to make themselves independent and recover their own personality. Finally, disintegration of the empire is produced but the country immediately falls under the dominion of the new imperial nucleus. This one will act from the beginning as a true tyrant, will take power as well as wealth into its own hands, and will reduce the former citizens of the empire into the condition servants and slaves.The new imperial nucleus will fulfill its evolutionary process and will enter into a phase of disintegration and decomposition. The weakening of the central power will result in turning over power into the hands of governors and sub-governments of the regions and cities until reaching the complete disintegration of the empire and to a regime known as “Feudal or Over imposedPowers”. With this one, we enter in the new era of Great Demographic Fractionation. We then begin a new cycle.In the fourth paragraph of the law, this political cycle that we have just presented, is completed in the social, artistic, philosophical and scientific aspect, that is, that parallel to the first, we should consider a social, artistic, philosophical and scientific cycle.The last phase of the cycle, as we have just seen, is that of the imperial and feudal aristocracy, that is, that of governors and sub-governors who have declared themselves independent from the imperial nucleus. These personalities conserve a certain vassalagewith respect to their immediate superior, and he, at the same time, considers himself the vassal of the one above him. Under this type of aristocracy, the nation is subject to a regime of servants or slaves, without any material or spiritual power.From the cultural point of view, we find ourselves without any spiritual activity. On one hand, there is a corrupt and degenerate aristocracy, which doesn’t have any other worry or desire but to satisfy its appetite for material things. On the side of the subjected class we find ourselves with a nation that does not have any possibility of instruction and who lives under submission.We are about to enter the fifth paragraph of the law. If its fulfillment were as simple as we exposed and there were no other complications, this law would have already been discovered many years ago. But the case is given that, although said law is fulfilled with all precision in all the nations of the Earth, cycles are not simultaneous for all of them, but are advanced or delayed in some with respect to the others.This advance or delay is determined as a function of the geographical position. As a consequence, as long as there are nations that are in the fractionation era, others are in the imperial era, and while some are going through the phase of democracy, other live in the absolutist or priestly phase, or in the regime of servitude.This mixture is what gives the sensation of chaos that history presents, a purely apparent chaos, since it is enough to know the law that governs the evolution of nations, so that chaos may be transformed into an order for which nations are developed obeying a perfect clock movement.BIOLOGICAL PROCESSES ARE MATHEMATICAL PROCESSESIt is an undeniable fact that, up to now, little importance has been given to the precise regularity with which biological processes are unfolded and, on the other hand, it is an absolute evidence that said processes are true mathematical processes. Starting from cariokinesisup to the movement of great collectivities, mathematics govern the evolution of living beings.If we were to study cellular reproduction, we would always see how, starting from the fertilization of the egg up to the division of the fertilized cell, it goes through precise phases, perfectly defined, using for each one of them the same space of time. If from the fertilization of the egg we follow the process of multicellular beings until a new being appears, we observe how each animal specie always repeats the same phases and for this it uses the same space in time. It is well known that in the human being, the gestation period lasts exactly nine months and that for each specie there is an equally fixed and determined period. This gestation process of living beings is then, mathematical.If we go on from gestationto the evolution of living beings, from their birth to their death we see has all go through the same phases of growth, completeness, decadence and death.In man, for example, we know that children born today will continue a generation that will follow a process through precise stages of infancy, youth, completeness and death, that permits us to predict that in 20 years they will be youths like today’s 20-year-old individuals, that when they reach between 40 and 50 years old they will have reached completeness and that in a quite fixed age, determined by the arithmetic medium of the life of today’s man on the earth, his death will take place. With this, it is evidenced that human generations also obey a mathematical process. We are going to study this process that is not isolated but global, through the centuries of history.As in the physiological and functional aspect, all generations obey the indicated rhythm, if we study them in the order of their intellectual activities (artistic, philosophical and scientific), we will observe remarkable differences. We would see that in one same region of earth there have been generations where some have manifested great creative activity while others have remained inactive and impenetrable to all intellectual activity.However, these differences are not arbitrary but obey a precise rhythm to an exact mathematics. In a society, in a given moment, an awakening is initiated, that awakening is transmitted to successive generations, a creative breath begins to manifest itself and the contributions accumulate themselves in forthcoming generations until a maximum creative power is accomplished that afterwards, begins a decrease of activity, diminishing the creative power and, after a very precise and determined decadence, as that in the individual being, there appears another society undergoing an ascending process that, through its generations, will repeat the same springtime growth, creative fullness and winter phases.After the winter phase a new creative cycle begins that will follow the same stages as the prior one, using, therefor, the same space in time, made up of seven centuries.This second cycle will give way to a new creative phase that is even more important than the first one. Once the second cycle ends, another one will begin, also creative and of a duration that is equal to the ones that came before, but with a marked decadent creative force. Once this third cycle ends, nations return to the state of primitive societies with the loss of not only the creative power, but absolutely forgetting the creative force of past generations. Within these 17 centuries, nations live a first era of Great Demographic Fractionation of six and one-half centuries and then, an era of Unification of ten and one-half centuries, for a total of the 17 centuries of a historical cycle.In the era of great fractionation, the geographical area of the ethnic group has a material and intellectual progress that keeps accentuating with certain characteristics and laws that govern this era of the nations.In the unification era, a city imposes itself over the other ones in the geographical area, forming the imperial power and the first unification nucleus of the era or first empire, in the true sense of the word. This first nucleus presents a first phase that is its first aggressive process, it then falls, this would be its phase of great depression, afterwards it rises again: second process. Now the military disaster follows so that the empire enters in its phase of conservation and afterwards in the phase of disintegration.All the great Captains have appeared in the second aggressive process: Hannibal, Alexander, Julius Caesar and Napoleon.Rome imposes and unifies dominating the whole ItalianPeninsula, thus forming the imperial body, afterwards the first aggressive process begins (the Roman Republic), afterwards it falls and great defeats take place. It rises again during the second period of great military victories (the Roman Empire), afterwards the military disaster takes place in the Battle of Teutoberg,while it tried to extend its empire in order to dominate the Germanic nations. Being that it was only a military disaster, it immediately recovers and enters into a phase of conservation and, then, disintegration.After finishing this period of unification or first empire, there is an independence phase at the end of which a second imperial nucleus begins, having the same phases as the prior one, but more or less weak in its development, depending on the nation’s geographical position within the historical cycle in which it is being developed.Analyzing the empires of this land since Egypt (4600 B.C.), those of Inner Asia(3700-3150 B.C.), China (2900 B.C.), Greece (2700 B.C.), Memphite (3150-2650), Sumerian (2900-2350 B.C.), Theban (2000-1450 B.C.) and Assyrius (1200-612 B.C.), all have followed the mathematical-Historical Process already mentioned in this strategic interpretation.I would like to indicate three points before continuing:1.Once again I would like to thank Dr. Deulofeu for making it easy for me to commit to his mathematical law, letting me have the files of his complete work, for without the summary of the published mathematics of history and the other books that cover the subject, it would not have been possible for me to make and present a complete Strategic Analysis, in such a broad domain.2.I have worked with this law since 1961, and as involved as I am with it, I affirm one more time that we have in front of us The Law of History, Dr. Deulofeu being worthy of all the honors when he discovered in the historical process a social, artistic, philosophical and scientific cycle, in this manner covering all aspects of the life and history of the population of our planet.3.Once the Mathematical Law has been read and comprehended, it should be directly verified in any history book, marking in the pages of text the phase that corresponds and thus obtain the desired historic curve and personally verify that we are before the true concept of history. The events of history cannot be discussed as such, at the margin of the process herein posed.In reference to the historical past that we referred to in this first part, it is convenient to retain that if wars and battles have had a determined result due to the phases each nation was undergoing, and that these were not real struggles but disputes between an empire or ethnic group against another one, each one in determined phases with characteristics and precise laws and not as it was thought and is still thought today, then, we can project the historical event to the future in a prospective field, with the phases of those nations and reason, in this plane of High Strategy, in order to take up the matter with truth as a principle.In the cold war or in the hot war, I have reasoned one section of the Army Staff of the National Defense, determining thus a second part or partial synthesis of the immediate and mediate future. In the third part, I continue reasoning and studying in the same plane the historical curves of the future of the already mentioned powers and with them I have a final synthesis for the cold war and the hot war of the continuity of the world’s present situation.B.H. Liddell says in his work “Historie Mondiale de la Strategie”: “If the horizon of the strategy is limited by war, the Great or High Strategy looks beyond war, towards peace that should follow it. It should not only dedicate itself to combine the diverse instruments of was, but also regulate its employment in order to avoid that which could be prejudicial to future peace that should be solid and prosperous”.The deplorable state of peace in which both parties participate right after the majority of wars, could be due to the fact that, contrary to strategy, the air of high strategy mostly remains in an “unknown land“ that hopes to be explored and comprehended. In the second and third part, I have explored that “unknown land” with the mathematical-historical principles and with the human means as a strategic synthesis of the mathematics of history, thus opening a new field without prospection and leaving the mathematics of history as an basic element of future studies, in its application for war and for peace.It should be remembered that this is a High Strategy or National Strategy work, which is formed by four particular strategies: Political, economical, psycho-social and armed force. Wherefore, it is a work of general interest. And to end, I quote from the Mathematical-Historical Principles deduced in my strategic synthesis:“There should not be friction between these and classical principles. They give the result of war or, in other cases, govern the global strategy or high strategy, since they are a military synthesis of the law of history, that is, eternal laws of the art of war that dominated the whole set. Accordingly, it is necessary to keep them in mind in times of peace and in times of war in this planet”.THE CYCLICAL CONCEPT OF HISTORYThe principal currents in the conceptions regarding the course of history can be reduced to two. One of them seen in history as a cycle or series of cycles that follow each other and, the other, sees an infinite straight line, without a beginning nor a foreseen end.The concept of cycle is something very ancient and permanent in the human spirit. In the Brahmaniantheory, cycles form the calendar of the gods. In ancient India the human year is made up of 360 days, without including the interpolatedones; the divine year is made up of 360 human years. One Haha Yugais formed by 120,000 divine years and is divided into four eras of unequal duration and similar rhythm. An era is preceded by an ascending period and is followed by a phase of expiration;each one of them lasts one tenth of the principal era. The Krita Yugais composed of 400 divine ascending years, 4,000 divine years of a principal year and 400 divine years of expiration.The periods of the Near East are nearer to the current concepts of time. They are based on the direct observation of the stars, their interpretation of sacred books, cabalisticmultiplications of the magic number, seven.One Jewish historian in Rome during the I century, Josephus Flavius, says that the most ancient times were divided into eras of 600 years.Sirius’ traslationmovement of 1,461 years, that was the great astronomical discovery of the Egyptians, gave way to the appearance of mythological-historical conceptions on the sky. Within this period of 1,461 years, not only the processes are repeated but also the lands, in the same order of succession.Another Egyptian cycle has a structure similar to the Indian divine year. It is made up of 36,525 years and it is said that once this cycle ends, the Golden Age will begin again on earth.The Greeks have worked on this, they were searching for the “great cosmic year”, the rhythmic unit of universal evolution. From the era of Plato comes the idea of a universal cycle of 700.000 years, after which everything begins again. A later calculation to the II Century gives the universal year a duration of 9,977 earthyears.The conceptions of Plato and Aristotleare also cyclical. For Plato the perfect number by which universal events are governed is the “cycle of that which is created by God”. At the same time it is converted into one of the fundamental laws of ethics. Aristotle reaches similar results through very different roads: the mathematical and physical reflection. He said that there is only one perfect and lasting form of movement, that is circular, such as is shown by celestial bodies with the greatest purity. The transformation of terrestrialthings are nothing more than movements in circles that are more or less perfect.The Stoa that during 500 years has had a maximum influence on the intellectual formation of the Greeks and the Romans, proclaim the cyclical rhythm of universal events, explaining them as an eternal return to what is equal and not only similar. When stars return to being in the same position, a Socrates and Plato will appear again, and each individual person will be born again with the same friends and fellow citizens, he will suffer identically and will perform the same activities and, each city, place, nation and field will again arise in the same manner. Epicurean rejects as superstition the search for the great universal year and the theory of the third rebirth. “In nature, everything can return, but not in human life. Every human life is unique and individual and only for this reason does it have a value and an incentive. Man’s birth and death are accidents”.In reference to this, says Richard Lewinsohn in his book “The revelation of the future”: “Now then, if millions of individual lives are not the sameit would not be possible for entire repeated eras to exist for humanity”. It is true that the conception of the typical world of Epicureandoes not leave an adequate margin for historical studies, because, what lessons could be taken out of history? The conception of Epicurean could be debated with multiple arguments. Isn’t man a living being? Is he exempt of the law that governs everything? I think that the mathematics of history of Dr. Deulofeu, that are facts, make the school of philosophy of the epicurean fall on the wayside.In the Christian arena, in the beginnings of Christian literature, the 22 books of Saint Augustine “On the City of God”, it can be considered that the idea of the cyclical event is still alive. It is found with little change in the ecclesiastical texts: “.... that terrestrial states appear and succumb as a result of men’s sins”. In the “History of the Future” of the Jesuit Priest Antonio Vieira: “.... but at the end, there is always God’s kingdom, that which is terrestrial flows into the supernatural where everything is perfect and eternal, and where periodical catastrophes are already impossible”.In the Renaissance the ancient example again starts the search for the great universal year. The word renaissance itself gives out a sense of cycle. The Italian humanist, Julio Cesar Scaliger, combines astronomical cycles with the tax collecting Roman period of fifteen years, period that is still used today as a unit of time in the papal bullaof 15 years. He thus obtains a cycle of 7,890 years. This cycle, that has the name of its discoverer: “The Julian Period”, had begun in the year 5,713 B.C., so that in Scaliger’s time in order to reach its end, 1,700 years would have to pass.Nietzsche in his “Will to Power”, where he shows a magnificent song on the return to that which is equal, makes us understand that the cycle, for him, is no more than a vital principle, not a measurable magnitude. Other intellectuals of lesser importance found strength in their own era and showed that universal happenings are developed according to a fixed rhythm. In 1937 we have the case of a book that had the honor of being presented in the Academy of Moral and Political Sciences of France by one of its members, “Les Rythmes dans l’Historie”, by Gaston Georgel. It is part of a cabalisticnumber upon discovering in a passage of the Bible the formula 77 x 7, being a product that is equal to 539. This figure provides the author with the key to the true knowledge of the course of history. Every 539 years, its duplicate (1,078) and its quadruplicate (2,156), also years derived from the same figure, historical events of the same type are to repeat themselves. Georgel, using his formula, has closely studies history and has discovered multiple parallels therein, some of them having small deviations, facts that, according to him, imply an affirmation of the thesis.More persuasive parallels could be discovered using Sirius’cycle of 1,461 years. If we go back as many years from the first world war, we arrive at the V Century, in which the expeditions of the Catalunianfields take place (451), the scene of the Battle of Marne, which is of extreme historical importance. Going back from the Second World War we arrive almost exactly to the year 476, considered to be the year on which the Western Roman Empire ends.In the year 1725, the Neapolitan historian, Giambattista Vico, in his work “Principles of a New Science on the Common Nature of Nations”, he supports his views on an Egyptian formula and gives the names of “divine, heroic and human age”, to the three stages that every nation goes through.In the cycle of state regimes that are founded in the Aristotelian division, democracy is followed by tyranny, the latter by the oligarchy, which is followed by democracy, and so forth. One hundred years after the appearance of “Scienza Nuova” by Vico, Augusto Compte considers that the European community goes through three spiritual phases: Theological, in which faith dominates everything; another Theological, in which critical reason acts harassed by doubt, and another, Positive in which the only determining factor of action is scientific knowledge.Herbert Spencer, a disciple of Darwin, who formulated a general law of evolution, that is valid for the natural and universal history, says that “.... evolution is absolutely continuous, it has no beginning nor end, there are no periods nor other subdivisions of a rhythmic character”.The most acute criticism was presented by the French philosopher, Charles Renouvier, who, in a very ingenious manner, reduced Spencer’s extreme evolutionism into the absurd. In his book, “Uchronia”, he shows that in the history of humanity there is no infinite continuity, but that once and again cisuresare produced and where from something finished something new is started.Let us now see the cyclical aspect to war and peace. The periodicity of approximately 50 years has been found in wars having worldly importance, only in the XVIII, XIX centuries and the beginning of the XX century. In the space of approximately 200 years, five great warlike periods: the Spanish War of Succession, the three Sicilian Wars, the fist Napoleonic Wars, the Crimean War, the National Wars for the Unity of Italy and Germany, the American War of Secession, and the First World War. Toybee himself does not want to believe or admit the very optimistic forecast that the chart presents: Finding ourselves in the beginning of a great period of universal peace.Toybee’s scheme is even less useful for prediction than the most ancient theory of the 50-year cycle. There is also the interpretation of the 1:2 relationship. After thirteen years of the Spanish War of Succession (1701-1714), there followed 26 years of peace; the period of the Sicilian Wars which, with varied intervals lasted 23 years, were followed by 33 years of peace; the period of 19 years of the Napoleonic wars (1796-1815), was followed by a period of 38 years of peace that extended until the Crimean War in 1853. The period of war that begins lasts 18 years until the end of the Franco-Prussian conflict in 1871, followed by an era of relative tranquility that lasts 40 years and extends until the Italo-Turkish war in 1911.Afterwards, in Eastern Europe, before and after the First World War, there are almost uninterrupted warlike actions that extend until 1920. Peace follows this stage of 9 years. The Second World War lasted 6 years, but the annexations of Austria and Czechoslovakia in 1938 made by Hitler, without bloodshed must be added. Then, if a period of 7 to 8 years must be followed by one of peace of a double duration, according to a 1:2 relation, it could be said that in 1960 a new era of war should have begun.This 1:2 relationship regarding the periods of war and peace, coincide with a very approximate rhythm in the economic juncture. Here each period of crises is followed by one of prosperity of a double duration. This is based on good human, physiological and psychological reasons. After a stage of extreme tension, danger and scarcity, double time would be needed to recover, rest and gather new energy. This rhythm has more probability of fulfillment than the ancient formula that one same generation does not go two times to war. There exists the period of centralization and decentralization. At the beginning, great wars, as the First World War, have an annexing and centralizing character but, afterwards, they end with the dismemberment of ancient and great empires and with the formation of numerous new states.After the recognition of the independence of the United States of America by England in 1783, a first centralizing period begins in 1787, that goes beyond the French Revolution and the first decade of the Napoleonic Wars. Many small states disappear, the few states founded by Napoleon are merely vassal states. But in 1810, a new series is constituted, first in South America, where up to 1822 independent states begin, and afterwards in Europe with Greece and Belgium (1830).In 1833,with the German Customs Union, a centralized period begins that ends in the union of Italy and Germany, period that extends until 1871. But starting from then and, especially in Central and Eastern Europe, the tendency towards the independence of nations is imposed: creation of the Balkan States (1878), independence of Czechoslovakia and Yugoslavia, resurrection of Poland, foundation of the Balkan States, Syria and Irak (1.918-1.920).Afterwards, there comes the other centralistic wave that leads Italy to annex in 1936; Germany does the same with Austria and Czechoslovakia(1938-1939), and Russia takes over the Baltic States during the Second World War. Starting in 1947, a great movement of independence begins: India, Pakistan, Indonesia, Morocco, Tunisia and the foundation of Israel.Together and during a period of more than 170 years, three periods of union have alternated with each other with three periods of separation:PERIOD TENDENCY DURATION1787 - 1809 Union 23 years1810 - 1832 Separation 23 years1833 - 1877 Union 45 years1878 - 1921 Separation 44 years1922 - 1946 Union 25 years1947 - SeparationThe present period of decentralization has lead to the dissolution of unions with a determined statesystem, such as Yugoslavia in 1948 and the failed coup in Hungary in 1956. It could be predicted with great probabilities of certainty, that this period has not yet ended.Professor Gaston Bouthoul, of the High Social Studies School of France, member of the International Institute of Sociology, says in his work “Wars”: “In short, the presence of war in all types of known civilizations, the fact that it is inseparable from the most diverse mentalities and institutions and, above all, its analogy with certain biological functions, poses the question regarding its periodicity”, and continues to say: “An analogy merits, however, to be indicated: It is that of war with economic crises, they all present the same aspect of sudden eruption starting from a completely defined and identifiable point of rupture”, “....this analogy confirms the hypothesis of a certain periodicity in wars”, “....those of crisis are also elastic enough, since the classic interval among them varies in a medium value of between seven and eleven years, that is, approximately from single to double”.Once we have gone over the horizon regarding the cyclic and linear system with a very positive balance for the cyclic one, I will now enter into Don Alejandro’s system of the mathematics of history.Let us see what he says as a brief introduction: “If we observe that the birth of a child is followed by his growth, youth, his complete development, his old age and his death, on this base we can affirm that other children will follow a similar process and this can be seen as a possibility to deduce a law...” “.... It is an undeniable fact that biological processes are mathematical processes. From cariokinesis to the movements of the great collectivities, mathematics governs the evolution of living beings” and concludes: “Analogically, in collectivities in which we cannot find a common law in the moral or intellectual order, we can find the mathematical law that organizes the evolution of nations, the appearance and disappearance of great cultures”.The mathematics of history provides a most solid basis, reinforces the supports for future research of universal history, of war and peace, of the economy, finance, military history for the development and future of humanity. The cyclical conception comes from the most prudent, authorized and conscientious opinions coming from serene reasoning.If linear conceptions come from thinking minorities, that drown the words and opinions of men and, if there were still doubts that mathematics exists in universal history, let us observe the logic of the considerations of the mathematics of history, its sense, its organization of the events and its support in history itself, that are events.
E.The Battle of Tours in the year 732, Charles Martel against the Arabs, the latter commanded by the brave Abderraman. It was a warlike action of the second aggressive process of the French Empire against the Arabs. The French Empire developed its first aggressive process from the year 250 to 561 (a duration of 311 years), its great depression from 561 to 688 (a duration of 125 years), the second period of great strategic victories from 688 to 815 (a duration of 129 years) and disintegration from 815 to 879 (64 years), resulting in a total of 629 years. The Arabs, owners of Spain and after one century of victories, attack Gaulin the year 732. After the defeat of Tours, they retreat to Spain for eight centuries until they return to their continent due to Hispanic weapons.
F.The Battle of Saratoga (October 7, 1778). This battle decides the independence of the United States of America. Great Britain was practically at the beginning of its great depression when it faced its then colony in this decisive battle.
G.The Battle of Lepanto(October 7, 1571). In the historical process of Europe and adjacent areas, where it concerns the first mathematical-historical cycle, in chronological order, the Persian, Carthaginian, Macedonian, Roman, Visigoth,French,and Teutonic Empires developed. It was the mathematical substitution of the supremacy of some for others respectively. The second mathematical-historical cycle begins with the TurkishEmpire, then the Spanish, French, English Empires and the Federal Republic of Germany. The Turkish Empire is followed by the Spanish, so that the Battle of Lepanto, a warlike decisive event in this process, expresses the phase of decadence and disintegration of the Turkish Empire and the first period of great victories of the Spanish Empire. This is the reason for the result of this battle.
“Great strategic victories belong to the phases corresponding to two great aggressive processes. Victory is a constant and it is the conclusion of every attack. That is the phase of great offensives”. This was the phase of the Spanish Empire.
“Decadence and disintegration is the phase in which strategic offensives are useless to back up the continental or intercontinental empire. Effective strategic potentiality is effective for the imperial body or nation, but it is always useless for the second empire of the mathematical-historical cycle, that is, when the nation is about to go through the era of great demographic fractionation”.
The Turkish Empire had gone through the phases of the first period of great victories (1250-1392), the great depression (1392-1422), second period of great victories (1432-1572) and was about to develop the phase of decadence and disintegration with a brief duration of the conservation phase. Although Lepanto was at the end of 1571 is it considered as the beginning of the phase of decadence.
H.The Battle of Valmy(September 28, 1792). The ethnic group of the Germanic area was undergoing the Great Demographic Fractionation era. France was ending its phase of Great Depression (1697-1793), in which, generally, the Empire is invalid in order to afterwards be able to expel the invaders. At the end of this phase, begins the second period of great victories in 1793. “Victory in the defense is a characteristic of the era of great demographic fractionation. Strategic victories are reserved for the defensive. Successful offensive is only achieved in order to enforce the defense of the region. It is the defense and counter-offense phase”.
According to this mathematical-historical principle, the Germanic ethnic group did not have an offensive strategic ability. On the other hand, France was about to end its second period of Great Strategic Victories.
I.The Battle of Bailen (July 15, 1808). The result of this battle was due to the independent value that territories in the historical process of the corresponding ethnic group have. An empire is developed, it expands towards its neighbors, when they are undergoing the depressive phase, but when they recover they expel the invader. There is no permanent occupation but it is rather temporary. Thus, there exists a historical force that provides unity and sovereignty to each geographical area, with its corresponding ethnic group. To the expansion of the French Empire in its second period of Great Victories, there follows a setback that is known as the Military Disaster, which was the Battle of Waterloo in the year 1815. Likewise, as in the French retreat from Spain, essentially marked by the Battle of Bailen.
“Conservation is a phase of Empire maintenance. Any strategic operation in this phase should be closely analyzed, including the human means factor. Victories and defeats alternate with each other. It is more a phase of the defensive in the maintenance of conquered geographical regions of the imperial body”. This mathematical-historical principle was influential in the victory of Bailen.
J.The Battle of Bleinheim(August 15, 1704). This Battle that is called, Hochstedby the French and Belinheim,by the Germans, gather a series of European Countries, among which was the British Empire, in the phase of the first period of Great Strategic Victories (1609-1783).
K.The Battle of Orleans (May 7, 1942). At this time, the English and French were undergoing an era of Great Demographic Fractionation, and, according the mathematical-strategic concept, England did not have a strategic offensive capacity and, as we have already seen: “Victory in the defense if a characteristic of the era of great demographic fractionation. Strategic victories are reserved to the defensive. A successful offensive is only obtained to enforce the defense of the region”. It was thus impossible to detain the French mathematical-historical process.
The destruction of the undefeatable Armada of Phillip II in the year 1558. The Spanish Empire was at that time in the first period of great strategic victories (1479-1643). However, England was in an era of Great Fractionation and soon to begin the year 1783, year in which that phase was to end. We already know by the mathematical-historical principles of the characteristics of nations during that era and, in this case, furthermore, the advance of the creative force, developing, in chronological order the Turkish, Spanish, BritishEmpires and the Federal Republic of Germany, and this second cycle of Europe and its adjacent area.
This is then the mathematical-historical reason for the result of this Battle, the truth and its pure cause.
L.The Battle of the Boyne(July 1, 1690). The BritishEmpire was in the phase of the first period of Great Victories (1609-1783) and so was the French Empire, but the phase was coming to an end, so that in 1697 the Great Depression ended. The reason for the result of this Battle is that the phase which the English were undergoing, has as a characteristic, the unification of the geographical area with ethnic groups, that is, Great Britain. In this manner, then, the mathematical-historical process of the era of Unification in its second cycle of 1,700 years, had begun in the year 1609 to end various centuries later, estimated to be five or five and one-half centuries later.
M.The Battle of Syracuse (year 413 B.C.). In this Battle the Syracusans defeated the Athenians.The reason for this was that Athens was in the year of Great Demographic Fractionation, in its first mathematical-historical cycle, and by concept and principle, nations in this phase do not have a strategic offensive capacity to conquer, occupy and overcome. The Italiannations were also developing the era of great fractionation of the first mathematical-historical cycle of Europe.
The term “decisive battles” is a very broad concept. It must be determined if they are decisive in a war between empires, nations in conquest, or liberty of a continent or geographical areas, that make up large or medium spaces.
The battles in the 1stor 2ndperiod of Great Victories are, in their majority, decisive in the conquest of an empire or nation. Also in the phase of great depression, whether to occupy or to expel the enemy. Likewise in the military disaster, if it is one sole battle or the last one, if they are various from one or another part of the adversaries. In the phase of decadence or disintegration, the first battle that is fought indicates the beginning of the phase, and the last one, marks the end of the empire.
Lastly, in the phase of relative independence, the last one is the decisive battle to begin the phase and that provides liberty to the country. Man is the expression of the historical phase, battles are historical events that express said phase and they form the whole of the nation’s process. Everything is continuity in time and in space. Everything is decisive in the thread of the historical process.
In the field of Operational Strategy battles would be defined by the three Clausewitz rules: “The concentration of effort, the strong man’s actions and the decision for the battle in the principal theater of operations”.
In the area of National Strategy, High or Grand Strategy, its definition is given with precision, the mathematical-historical concept, the mathematical-historical principle and the mathematics of history, as has been exposed and analyzed in this modest work.
In the mathematical-historical concept, we could say that it is a mathematical and humanistic world, in which the first determines the general process of cultures and civilization, of the creations, development and duration of empires and nations, where man is the expression of historical phases. Man can change his destiny only by mental and spiritual excellence.
Evolutions and revolutions follow each other without improvisation or delay, nothing is the work of chance. In cultures, civilizations and processes of man’s life in the planet, historical happenings and events occur as a chain reaction, as a great gear of a perfect machine, and an operation having a continuity and permanence in time and space. Everything is exactly fulfilled with an admirable precision. The process of a mathematical world framed within a humanistic field, of a man who oscillates from a maximum civilization to a minimum one.
Dr. Deulofeu says: “Today we have discovered a law that arranges the evolution of nations in the same manner as we know the law that governs the evolution of the individual. Perhaps one day we may know the circumstances that have caused collective evolution, as we know the physiological circumstances that produce birth, but it is possible that man will never know what is the profound origin of life”. That is, that perhaps the cycle of life or evolutionary cycle may not be modified, neither from the individual or from the collective point of view. Be that as it may, at the present time, man has been smoothing out the individual process protecting himself more and more against the inclemency of weather and illnesses.
In like manner, he can ensure as of now that the evolution of nations be done without bloody and violent struggles, without external or internal wars. What can man do to modify his destiny? “Man follows a defined evolution, he is born, he grows up, he reaches adulthood, enters decadence and finally dies. From the individual event, lets go on to the collective one. It has been shown that nations go through phases of winter inactivity, through phases of spring growth, through summer phases of complete creativity and finally through fall phases of decadence, to again enter into the winter phase and begin the cycle again”.
“Nations follow a cyclical process that is analogous to that of plants, but just as the cycle of plants lasts 365 days, that of nations is 1,700 years. If we compare the human process with that of irrational animals, we observe a fundamental difference where they do not know how to come out of their determinism, while man constantly breaks it. Cats and dogs have been defending themselves with their nails and fangs from time immemorial, man, on the other hand, constantly modifies his means of defense. Analogically, animals walk on their hoofs starting from their origin while man discovers other means of locomotion. With plants, the same or almost the same happens when collectively considered, they continue their vegetable cycle in an identical manner through the centuries, as long as the solar system is not modified. But man, at the same time as he has been discovering the laws of nature, has modified his way of life and has progressed as a result. Why should he not progress the day he discovers the laws that govern the life of collectivities? Human progress has been evidenced in the extinction and management of great epidemics with the discoveries of bacteriology. The same progress should be expected in the political, social and cultural arena, with the discovery of the mathematical law that has been governing the life of nations up to the present time”.
“While it was not known it was not possible to do anything in this sense. All societies or nations that have been built through time in order to avoid war, have resulted to be inoperative. But knowing said law, knowing before hand what will happen, it is absurd to think that men would voluntarily launch themselves into a precipice being able to modify the trajectory. Today we know where we are and where we are going. Is it in the hands of man to deviate the helm and change the course? The transcendental operation of turning the destiny of the world, advises us to study the process and system to be followed to execute this change of course”.
“At once a fundamentalneed arises: to tone down the convulsions that entail the foreseen process; once this has been accomplished, the possibilities of totally modifying it can be considered. When he develops from infancy to old age, man does not follow a smooth and easy course, on the contrary, he, in fact, has to sustain a constant struggle in order to defend himself in the environment that surrounds him (climate, illnesses, survival). He has been improving in this struggle, that is, modifying his natural condition of life and greatly reducing natural difficulties. Housing and hygiene conditions to a great extent have lessened mortality and human suffering; medical progress tends to diminish pain. And if it has been this way, capable of eliminating collective calamities such as cholera and yellow fever, it is possible to conceive that the day will come when all illness will be eliminated and man will be able to go on with his life without these perturbances”.
“Nations, when they begin their evolutional cycle, follow a road of progress and creation, but this road is not smooth, on the contrary, in order to progress they need to sustain a constant struggle against themselves. Extinct institutions do not disappear if it were not for violence. Exhausted regimes do not resign themselves to be voluntarily substituted and fight to the death to persist. Nations in full growth, if they want to extend themselves, have to forcibly drown decadent empires. Decrepit institutions, due to their instinct of conservation and because they think that by fighting they can lengthen their time, resist disappearing”.
“But institutions and their men, if they knew the fate that awaited them in the struggle before hand, would stop fighting if they knew they were going to be defeated. As soon as they knew of the catastrophes that would be produced and their results, the nations of the world should suppress wars. Will men abolish calamities in the same manner as violence has been abolished from individual combat and taking justice by one’s own hand be replaced by the creation of courts of justice?”
So man improves mentally and spiritually in order to have a better life, is our greatest desire when we pose bellicosesubjects.
The universality of the law of History.
The law of History governs the process in all domains of human activity. Nations evolve, progress, decline and rise again, following some perfect cycles in the political, social, artistic, philosophical and scientific arenas. Nothing is the work of chance. The appearance and disappearance of great empires, the creation of architectural styles, the great discoveries, the great philosophical conceptions, obey a mechanism that is as precise as a clock. Up to now men have ignored it. Some have suspected it but up to now nobody had defined it. For this reason, men and nations have been following a road that, unknown to them, was traced beforehand.
Declarations of the mathematical law that determine the evolution of nations: We can resume that law in the following paragraphs:
1.All nations go through eras of Great Demographic Fractionation, alternating with other of Great Unification or imperialist eras.
2.Eras of Great Fractionation have a duration of six and one-half centuries. Eras of Great Unification last ten and one-half centuries. The cycle of evolution is made up of seventeen centuries.
3.During this process of evolution, nations go through perfectly established phases so that at the end of the cycle they occupy the same position it had at the beginning thereof.
4.The cycle of evolution covers all areas of human activity, that is, in addition to the political cycle, we must consider the social, artistic, philosophical and scientific ones.
5.All nations follow the same evolution, but it is ahead or behind, according to the geographical position of each country.
6.The creative force is not the same for all nations.
7.Imperialist nuclei that give way to eras of Great Political Unification, follow perfect biological processes that are identical to each other and with one same longevity that lasts from five to six centuries.
8.The transformation of political-social regimes is not done according to a constant ascending or descending line, but through alternative advances or reversals, some more intense than others, that produce a broken line as a result. The result of this line is equivalent to an advance in a determined sense. This is given the name of “Law of two paces towards the front and one towards the back” or “Oscillating Law”.
We are going to precisely determine and explain these paragraphs through a graphical representation of the evolutionary cycle. If in a system of Cartesian Coordinates we mark time over the X axis (horizontal axis) and the changes nations go through, from every point of view of human activity, over the Y axis (vertical axis), we can represent the evolutionary process thereof, as seen in Chart 1.
Marked on the horizontal axis, we see seventeen divisions that correspond to the seventeen centuries, that is the total duration of the cycle. The first six and one-half centuries correspond to the era of great fractionation. During this one there are no great political units, that is, nations or empires, such as we know them in our day, but, in fact, each city, with the small region that surrounds it, constitutes a real Independent State. During this era and starting from its origin (A), nations follow a life of progress in all areas of human activity, until they reach a maximum (B). We represent the evolutionary process of this first era by the ascending line that goes from A to B, that coincides with the end of this era of great fractionation.
Afterwards, an important political change occurs: nations lose their political liberty that reached up to a director nucleus. At the beginning, it will establish a military hegemony without intervening in the internal political organization of the cities, or in their particular governments. A broadly federal organization is then created. Gradually, the political regime changes and the hegemonic one accentuates its influence and intervention takes place in the local governments and, after a process of unification that lasts two centuries we see the particular governments disappearing.
Local languages and laws are substituted by the laws and languages of the hegemonic nucleus, at least in written documents, by the government.
We will call this first phase of the imperial era the Federal Phase, and is represented in the chart by the descending line B-C. Afterwards, we enter the unitary phase of great nations or empires.
The cities that form part of the empire have completely lost the conscience of their own personality and they feel identified with the hegemonic nucleus. This phase represent a regime that is completely opposed to the era of great fractionation and, in the chart it is represented by the line that goes from C to D.
From this moment on, that is, four centuries after the imperialist era began, the hegemonic nucleus starts its disintegration. The perfect unity achieved starts to deteriorate until it reaches total decomposition and substitution of the first imperial nucleus for a hegemonic one, which the unitary regime will maintain during a space of four and one-half centuries, that is, until the end of the cycle.
The two imperial nuclei do not present the same characteristics. The second enters the scene in a fully unitarian or absolute phase. The first empire considers its subjects as citizens, whether they belong to the imperial nucleus or to the other nations that form part of the empire, only with the condition that they waive their own characteristics and adopt the imperial language and law.
The disintegration of this first empire is manifested, as we have said, by a weakening of the central power, by the lack of discipline in the army, by civil war and by anarchy. Nations that make up part of the empire wish to make themselves independent and recover their own personality. Finally, disintegration of the empire is produced but the country immediately falls under the dominion of the new imperial nucleus. This one will act from the beginning as a true tyrant, will take power as well as wealth into its own hands, and will reduce the former citizens of the empire into the condition servants and slaves.
The new imperial nucleus will fulfill its evolutionary process and will enter into a phase of disintegration and decomposition. The weakening of the central power will result in turning over power into the hands of governors and sub-governments of the regions and cities until reaching the complete disintegration of the empire and to a regime known as “Feudal or Over imposedPowers”. With this one, we enter in the new era of Great Demographic Fractionation. We then begin a new cycle.
In the fourth paragraph of the law, this political cycle that we have just presented, is completed in the social, artistic, philosophical and scientific aspect, that is, that parallel to the first, we should consider a social, artistic, philosophical and scientific cycle.
The last phase of the cycle, as we have just seen, is that of the imperial and feudal aristocracy, that is, that of governors and sub-governors who have declared themselves independent from the imperial nucleus. These personalities conserve a certain vassalagewith respect to their immediate superior, and he, at the same time, considers himself the vassal of the one above him. Under this type of aristocracy, the nation is subject to a regime of servants or slaves, without any material or spiritual power.
From the cultural point of view, we find ourselves without any spiritual activity. On one hand, there is a corrupt and degenerate aristocracy, which doesn’t have any other worry or desire but to satisfy its appetite for material things. On the side of the subjected class we find ourselves with a nation that does not have any possibility of instruction and who lives under submission.
We are about to enter the fifth paragraph of the law. If its fulfillment were as simple as we exposed and there were no other complications, this law would have already been discovered many years ago. But the case is given that, although said law is fulfilled with all precision in all the nations of the Earth, cycles are not simultaneous for all of them, but are advanced or delayed in some with respect to the others.
This advance or delay is determined as a function of the geographical position. As a consequence, as long as there are nations that are in the fractionation era, others are in the imperial era, and while some are going through the phase of democracy, other live in the absolutist or priestly phase, or in the regime of servitude.
This mixture is what gives the sensation of chaos that history presents, a purely apparent chaos, since it is enough to know the law that governs the evolution of nations, so that chaos may be transformed into an order for which nations are developed obeying a perfect clock movement.
It is an undeniable fact that, up to now, little importance has been given to the precise regularity with which biological processes are unfolded and, on the other hand, it is an absolute evidence that said processes are true mathematical processes. Starting from cariokinesisup to the movement of great collectivities, mathematics govern the evolution of living beings.
If we were to study cellular reproduction, we would always see how, starting from the fertilization of the egg up to the division of the fertilized cell, it goes through precise phases, perfectly defined, using for each one of them the same space of time. If from the fertilization of the egg we follow the process of multicellular beings until a new being appears, we observe how each animal specie always repeats the same phases and for this it uses the same space in time. It is well known that in the human being, the gestation period lasts exactly nine months and that for each specie there is an equally fixed and determined period. This gestation process of living beings is then, mathematical.
If we go on from gestationto the evolution of living beings, from their birth to their death we see has all go through the same phases of growth, completeness, decadence and death.
In man, for example, we know that children born today will continue a generation that will follow a process through precise stages of infancy, youth, completeness and death, that permits us to predict that in 20 years they will be youths like today’s 20-year-old individuals, that when they reach between 40 and 50 years old they will have reached completeness and that in a quite fixed age, determined by the arithmetic medium of the life of today’s man on the earth, his death will take place. With this, it is evidenced that human generations also obey a mathematical process. We are going to study this process that is not isolated but global, through the centuries of history.
As in the physiological and functional aspect, all generations obey the indicated rhythm, if we study them in the order of their intellectual activities (artistic, philosophical and scientific), we will observe remarkable differences. We would see that in one same region of earth there have been generations where some have manifested great creative activity while others have remained inactive and impenetrable to all intellectual activity.
However, these differences are not arbitrary but obey a precise rhythm to an exact mathematics. In a society, in a given moment, an awakening is initiated, that awakening is transmitted to successive generations, a creative breath begins to manifest itself and the contributions accumulate themselves in forthcoming generations until a maximum creative power is accomplished that afterwards, begins a decrease of activity, diminishing the creative power and, after a very precise and determined decadence, as that in the individual being, there appears another society undergoing an ascending process that, through its generations, will repeat the same springtime growth, creative fullness and winter phases.
After the winter phase a new creative cycle begins that will follow the same stages as the prior one, using, therefor, the same space in time, made up of seven centuries.
This second cycle will give way to a new creative phase that is even more important than the first one. Once the second cycle ends, another one will begin, also creative and of a duration that is equal to the ones that came before, but with a marked decadent creative force. Once this third cycle ends, nations return to the state of primitive societies with the loss of not only the creative power, but absolutely forgetting the creative force of past generations. Within these 17 centuries, nations live a first era of Great Demographic Fractionation of six and one-half centuries and then, an era of Unification of ten and one-half centuries, for a total of the 17 centuries of a historical cycle.
In the era of great fractionation, the geographical area of the ethnic group has a material and intellectual progress that keeps accentuating with certain characteristics and laws that govern this era of the nations.
In the unification era, a city imposes itself over the other ones in the geographical area, forming the imperial power and the first unification nucleus of the era or first empire, in the true sense of the word. This first nucleus presents a first phase that is its first aggressive process, it then falls, this would be its phase of great depression, afterwards it rises again: second process. Now the military disaster follows so that the empire enters in its phase of conservation and afterwards in the phase of disintegration.
All the great Captains have appeared in the second aggressive process: Hannibal, Alexander, Julius Caesar and Napoleon.
Rome imposes and unifies dominating the whole ItalianPeninsula, thus forming the imperial body, afterwards the first aggressive process begins (the Roman Republic), afterwards it falls and great defeats take place. It rises again during the second period of great military victories (the Roman Empire), afterwards the military disaster takes place in the Battle of Teutoberg,while it tried to extend its empire in order to dominate the Germanic nations. Being that it was only a military disaster, it immediately recovers and enters into a phase of conservation and, then, disintegration.
After finishing this period of unification or first empire, there is an independence phase at the end of which a second imperial nucleus begins, having the same phases as the prior one, but more or less weak in its development, depending on the nation’s geographical position within the historical cycle in which it is being developed.
Analyzing the empires of this land since Egypt (4600 B.C.), those of Inner Asia(3700-3150 B.C.), China (2900 B.C.), Greece (2700 B.C.), Memphite (3150-2650), Sumerian (2900-2350 B.C.), Theban (2000-1450 B.C.) and Assyrius (1200-612 B.C.), all have followed the mathematical-Historical Process already mentioned in this strategic interpretation.
I would like to indicate three points before continuing:
1.Once again I would like to thank Dr. Deulofeu for making it easy for me to commit to his mathematical law, letting me have the files of his complete work, for without the summary of the published mathematics of history and the other books that cover the subject, it would not have been possible for me to make and present a complete Strategic Analysis, in such a broad domain.
2.I have worked with this law since 1961, and as involved as I am with it, I affirm one more time that we have in front of us The Law of History, Dr. Deulofeu being worthy of all the honors when he discovered in the historical process a social, artistic, philosophical and scientific cycle, in this manner covering all aspects of the life and history of the population of our planet.
3.Once the Mathematical Law has been read and comprehended, it should be directly verified in any history book, marking in the pages of text the phase that corresponds and thus obtain the desired historic curve and personally verify that we are before the true concept of history. The events of history cannot be discussed as such, at the margin of the process herein posed.
In reference to the historical past that we referred to in this first part, it is convenient to retain that if wars and battles have had a determined result due to the phases each nation was undergoing, and that these were not real struggles but disputes between an empire or ethnic group against another one, each one in determined phases with characteristics and precise laws and not as it was thought and is still thought today, then, we can project the historical event to the future in a prospective field, with the phases of those nations and reason, in this plane of High Strategy, in order to take up the matter with truth as a principle.
In the cold war or in the hot war, I have reasoned one section of the Army Staff of the National Defense, determining thus a second part or partial synthesis of the immediate and mediate future. In the third part, I continue reasoning and studying in the same plane the historical curves of the future of the already mentioned powers and with them I have a final synthesis for the cold war and the hot war of the continuity of the world’s present situation.
B.H. Liddell says in his work “Historie Mondiale de la Strategie”: “If the horizon of the strategy is limited by war, the Great or High Strategy looks beyond war, towards peace that should follow it. It should not only dedicate itself to combine the diverse instruments of was, but also regulate its employment in order to avoid that which could be prejudicial to future peace that should be solid and prosperous”.
The deplorable state of peace in which both parties participate right after the majority of wars, could be due to the fact that, contrary to strategy, the air of high strategy mostly remains in an “unknown land“ that hopes to be explored and comprehended. In the second and third part, I have explored that “unknown land” with the mathematical-historical principles and with the human means as a strategic synthesis of the mathematics of history, thus opening a new field without prospection and leaving the mathematics of history as an basic element of future studies, in its application for war and for peace.
It should be remembered that this is a High Strategy or National Strategy work, which is formed by four particular strategies: Political, economical, psycho-social and armed force. Wherefore, it is a work of general interest. And to end, I quote from the Mathematical-Historical Principles deduced in my strategic synthesis:
“There should not be friction between these and classical principles. They give the result of war or, in other cases, govern the global strategy or high strategy, since they are a military synthesis of the law of history, that is, eternal laws of the art of war that dominated the whole set. Accordingly, it is necessary to keep them in mind in times of peace and in times of war in this planet”.
The principal currents in the conceptions regarding the course of history can be reduced to two. One of them seen in history as a cycle or series of cycles that follow each other and, the other, sees an infinite straight line, without a beginning nor a foreseen end.
The concept of cycle is something very ancient and permanent in the human spirit. In the Brahmaniantheory, cycles form the calendar of the gods. In ancient India the human year is made up of 360 days, without including the interpolatedones; the divine year is made up of 360 human years. One Haha Yugais formed by 120,000 divine years and is divided into four eras of unequal duration and similar rhythm. An era is preceded by an ascending period and is followed by a phase of expiration;each one of them lasts one tenth of the principal era. The Krita Yugais composed of 400 divine ascending years, 4,000 divine years of a principal year and 400 divine years of expiration.
The periods of the Near East are nearer to the current concepts of time. They are based on the direct observation of the stars, their interpretation of sacred books, cabalisticmultiplications of the magic number, seven.
One Jewish historian in Rome during the I century, Josephus Flavius, says that the most ancient times were divided into eras of 600 years.
Sirius’ traslationmovement of 1,461 years, that was the great astronomical discovery of the Egyptians, gave way to the appearance of mythological-historical conceptions on the sky. Within this period of 1,461 years, not only the processes are repeated but also the lands, in the same order of succession.
Another Egyptian cycle has a structure similar to the Indian divine year. It is made up of 36,525 years and it is said that once this cycle ends, the Golden Age will begin again on earth.
The Greeks have worked on this, they were searching for the “great cosmic year”, the rhythmic unit of universal evolution. From the era of Plato comes the idea of a universal cycle of 700.000 years, after which everything begins again. A later calculation to the II Century gives the universal year a duration of 9,977 earthyears.
The conceptions of Plato and Aristotleare also cyclical. For Plato the perfect number by which universal events are governed is the “cycle of that which is created by God”. At the same time it is converted into one of the fundamental laws of ethics. Aristotle reaches similar results through very different roads: the mathematical and physical reflection. He said that there is only one perfect and lasting form of movement, that is circular, such as is shown by celestial bodies with the greatest purity. The transformation of terrestrialthings are nothing more than movements in circles that are more or less perfect.
The Stoa that during 500 years has had a maximum influence on the intellectual formation of the Greeks and the Romans, proclaim the cyclical rhythm of universal events, explaining them as an eternal return to what is equal and not only similar. When stars return to being in the same position, a Socrates and Plato will appear again, and each individual person will be born again with the same friends and fellow citizens, he will suffer identically and will perform the same activities and, each city, place, nation and field will again arise in the same manner. Epicurean rejects as superstition the search for the great universal year and the theory of the third rebirth. “In nature, everything can return, but not in human life. Every human life is unique and individual and only for this reason does it have a value and an incentive. Man’s birth and death are accidents”.
In reference to this, says Richard Lewinsohn in his book “The revelation of the future”: “Now then, if millions of individual lives are not the sameit would not be possible for entire repeated eras to exist for humanity”. It is true that the conception of the typical world of Epicureandoes not leave an adequate margin for historical studies, because, what lessons could be taken out of history? The conception of Epicurean could be debated with multiple arguments. Isn’t man a living being? Is he exempt of the law that governs everything? I think that the mathematics of history of Dr. Deulofeu, that are facts, make the school of philosophy of the epicurean fall on the wayside.
In the Christian arena, in the beginnings of Christian literature, the 22 books of Saint Augustine “On the City of God”, it can be considered that the idea of the cyclical event is still alive. It is found with little change in the ecclesiastical texts: “.... that terrestrial states appear and succumb as a result of men’s sins”. In the “History of the Future” of the Jesuit Priest Antonio Vieira: “.... but at the end, there is always God’s kingdom, that which is terrestrial flows into the supernatural where everything is perfect and eternal, and where periodical catastrophes are already impossible”.
In the Renaissance the ancient example again starts the search for the great universal year. The word renaissance itself gives out a sense of cycle. The Italian humanist, Julio Cesar Scaliger, combines astronomical cycles with the tax collecting Roman period of fifteen years, period that is still used today as a unit of time in the papal bullaof 15 years. He thus obtains a cycle of 7,890 years. This cycle, that has the name of its discoverer: “The Julian Period”, had begun in the year 5,713 B.C., so that in Scaliger’s time in order to reach its end, 1,700 years would have to pass.
Nietzsche in his “Will to Power”, where he shows a magnificent song on the return to that which is equal, makes us understand that the cycle, for him, is no more than a vital principle, not a measurable magnitude. Other intellectuals of lesser importance found strength in their own era and showed that universal happenings are developed according to a fixed rhythm. In 1937 we have the case of a book that had the honor of being presented in the Academy of Moral and Political Sciences of France by one of its members, “Les Rythmes dans l’Historie”, by Gaston Georgel. It is part of a cabalisticnumber upon discovering in a passage of the Bible the formula 77 x 7, being a product that is equal to 539. This figure provides the author with the key to the true knowledge of the course of history. Every 539 years, its duplicate (1,078) and its quadruplicate (2,156), also years derived from the same figure, historical events of the same type are to repeat themselves. Georgel, using his formula, has closely studies history and has discovered multiple parallels therein, some of them having small deviations, facts that, according to him, imply an affirmation of the thesis.
More persuasive parallels could be discovered using Sirius’cycle of 1,461 years. If we go back as many years from the first world war, we arrive at the V Century, in which the expeditions of the Catalunianfields take place (451), the scene of the Battle of Marne, which is of extreme historical importance. Going back from the Second World War we arrive almost exactly to the year 476, considered to be the year on which the Western Roman Empire ends.
In the year 1725, the Neapolitan historian, Giambattista Vico, in his work “Principles of a New Science on the Common Nature of Nations”, he supports his views on an Egyptian formula and gives the names of “divine, heroic and human age”, to the three stages that every nation goes through.
In the cycle of state regimes that are founded in the Aristotelian division, democracy is followed by tyranny, the latter by the oligarchy, which is followed by democracy, and so forth. One hundred years after the appearance of “Scienza Nuova” by Vico, Augusto Compte considers that the European community goes through three spiritual phases: Theological, in which faith dominates everything; another Theological, in which critical reason acts harassed by doubt, and another, Positive in which the only determining factor of action is scientific knowledge.
Herbert Spencer, a disciple of Darwin, who formulated a general law of evolution, that is valid for the natural and universal history, says that “.... evolution is absolutely continuous, it has no beginning nor end, there are no periods nor other subdivisions of a rhythmic character”.
The most acute criticism was presented by the French philosopher, Charles Renouvier, who, in a very ingenious manner, reduced Spencer’s extreme evolutionism into the absurd. In his book, “Uchronia”, he shows that in the history of humanity there is no infinite continuity, but that once and again cisuresare produced and where from something finished something new is started.
Let us now see the cyclical aspect to war and peace. The periodicity of approximately 50 years has been found in wars having worldly importance, only in the XVIII, XIX centuries and the beginning of the XX century. In the space of approximately 200 years, five great warlike periods: the Spanish War of Succession, the three Sicilian Wars, the fist Napoleonic Wars, the Crimean War, the National Wars for the Unity of Italy and Germany, the American War of Secession, and the First World War. Toybee himself does not want to believe or admit the very optimistic forecast that the chart presents: Finding ourselves in the beginning of a great period of universal peace.
Toybee’s scheme is even less useful for prediction than the most ancient theory of the 50-year cycle. There is also the interpretation of the 1:2 relationship. After thirteen years of the Spanish War of Succession (1701-1714), there followed 26 years of peace; the period of the Sicilian Wars which, with varied intervals lasted 23 years, were followed by 33 years of peace; the period of 19 years of the Napoleonic wars (1796-1815), was followed by a period of 38 years of peace that extended until the Crimean War in 1853. The period of war that begins lasts 18 years until the end of the Franco-Prussian conflict in 1871, followed by an era of relative tranquility that lasts 40 years and extends until the Italo-Turkish war in 1911.
Afterwards, in Eastern Europe, before and after the First World War, there are almost uninterrupted warlike actions that extend until 1920. Peace follows this stage of 9 years. The Second World War lasted 6 years, but the annexations of Austria and Czechoslovakia in 1938 made by Hitler, without bloodshed must be added. Then, if a period of 7 to 8 years must be followed by one of peace of a double duration, according to a 1:2 relation, it could be said that in 1960 a new era of war should have begun.
This 1:2 relationship regarding the periods of war and peace, coincide with a very approximate rhythm in the economic juncture. Here each period of crises is followed by one of prosperity of a double duration. This is based on good human, physiological and psychological reasons. After a stage of extreme tension, danger and scarcity, double time would be needed to recover, rest and gather new energy. This rhythm has more probability of fulfillment than the ancient formula that one same generation does not go two times to war. There exists the period of centralization and decentralization. At the beginning, great wars, as the First World War, have an annexing and centralizing character but, afterwards, they end with the dismemberment of ancient and great empires and with the formation of numerous new states.
After the recognition of the independence of the United States of America by England in 1783, a first centralizing period begins in 1787, that goes beyond the French Revolution and the first decade of the Napoleonic Wars. Many small states disappear, the few states founded by Napoleon are merely vassal states. But in 1810, a new series is constituted, first in South America, where up to 1822 independent states begin, and afterwards in Europe with Greece and Belgium (1830).
In 1833,with the German Customs Union, a centralized period begins that ends in the union of Italy and Germany, period that extends until 1871. But starting from then and, especially in Central and Eastern Europe, the tendency towards the independence of nations is imposed: creation of the Balkan States (1878), independence of Czechoslovakia and Yugoslavia, resurrection of Poland, foundation of the Balkan States, Syria and Irak (1.918-1.920).
Afterwards, there comes the other centralistic wave that leads Italy to annex in 1936; Germany does the same with Austria and Czechoslovakia(1938-1939), and Russia takes over the Baltic States during the Second World War. Starting in 1947, a great movement of independence begins: India, Pakistan, Indonesia, Morocco, Tunisia and the foundation of Israel.
Together and during a period of more than 170 years, three periods of union have alternated with each other with three periods of separation:
PERIOD TENDENCY DURATION
1787 - 1809 Union 23 years
1810 - 1832 Separation 23 years
1833 - 1877 Union 45 years
1878 - 1921 Separation 44 years
1922 - 1946 Union 25 years
1947 - Separation
The present period of decentralization has lead to the dissolution of unions with a determined statesystem, such as Yugoslavia in 1948 and the failed coup in Hungary in 1956. It could be predicted with great probabilities of certainty, that this period has not yet ended.
Professor Gaston Bouthoul, of the High Social Studies School of France, member of the International Institute of Sociology, says in his work “Wars”: “In short, the presence of war in all types of known civilizations, the fact that it is inseparable from the most diverse mentalities and institutions and, above all, its analogy with certain biological functions, poses the question regarding its periodicity”, and continues to say: “An analogy merits, however, to be indicated: It is that of war with economic crises, they all present the same aspect of sudden eruption starting from a completely defined and identifiable point of rupture”, “....this analogy confirms the hypothesis of a certain periodicity in wars”, “....those of crisis are also elastic enough, since the classic interval among them varies in a medium value of between seven and eleven years, that is, approximately from single to double”.
Once we have gone over the horizon regarding the cyclic and linear system with a very positive balance for the cyclic one, I will now enter into Don Alejandro’s system of the mathematics of history.
Let us see what he says as a brief introduction: “If we observe that the birth of a child is followed by his growth, youth, his complete development, his old age and his death, on this base we can affirm that other children will follow a similar process and this can be seen as a possibility to deduce a law...” “.... It is an undeniable fact that biological processes are mathematical processes. From cariokinesis to the movements of the great collectivities, mathematics governs the evolution of living beings” and concludes: “Analogically, in collectivities in which we cannot find a common law in the moral or intellectual order, we can find the mathematical law that organizes the evolution of nations, the appearance and disappearance of great cultures”.
The mathematics of history provides a most solid basis, reinforces the supports for future research of universal history, of war and peace, of the economy, finance, military history for the development and future of humanity. The cyclical conception comes from the most prudent, authorized and conscientious opinions coming from serene reasoning.
If linear conceptions come from thinking minorities, that drown the words and opinions of men and, if there were still doubts that mathematics exists in universal history, let us observe the logic of the considerations of the mathematics of history, its sense, its organization of the events and its support in history itself, that are events.