Monarchy in Hobbes, or The Role of Sovereign


Hobbes took up to History and carried on his historical studies with a view of politics in mind. He always considered Thucydides as his favourite author and commented on him as ‘the most political historiographer that ever writ’. Hobbes wished to communicate to his fellow citizens that Democracy is faulty and Monarchy is to be preferred. In the introduction to the translation of Thucydides, Hobbes summarizes Thucydides, ‘opinion touching the Government of the State’ to the effect that ‘Thucydides ‘least of all liked the Democracy’ and ‘best approved of the regal Government’.  Thus from the very outset, Hobbes was an ardent opponent of Democracy and an upholder of a monarchic form of Government. This view he held till the rest of his life. In the introduction to the translation of Thucydides, he formally considers the monarchic Government of Peisistratos and the nominally democratic but monarchic Government of Pericles as equivalent.  But he considers in all his expositions of political philosophy the possibility of elective monarchy, comparing it with the Roman institution of dictatorship, under which the people is ‘sovereign in property’, but not ‘in use’. Hobbes regarded absolute monarchy and dictatorship as the only practical form of Government.

Hobbes’ position with regards to monarchy never changed throughout his life, but his conception of the term ‘monarchy’ did change. In earlier presentations, Hobbes makes mention of the traditional arguments, according to which monarchy is the only natural, original form of authority, the only form which corresponds to the nature’s original order, whereas Aristocracy and Democracy are artificially produced by men, namely ‘cemented’ by human wit. Moreover, he maintained till the end of his life that paternal authority and consequently patrimonial monarchy is, if not the legal, nevertheless the historical origin of all or majority of the States. 

Hobbes at all times maintained the distinction between the natural and the artificial State. He distinguished between ‘Commonwealth by acquisition’, which is based on natural force, and ‘Commonwealth by institution’, which comes into being by voluntary subjection to an elected Government i.e. artificially. In discussing the artificial State he treats of institutional and therefore artificial State monarchy. But a noteworthy difference is compounded in the Leviathan, the right of succession is treated as a specific problem of monarchy in the discussion of ‘Commonwealth by institution’, but in the earlier presentations it is mentioned only in connection with the distinction of the natural State. Since in Hobbes’ original point of view, monarchy and the natural State were identical, this specific problem of monarchy was included in the discussion of the basis for a natural State.

Hobbes distinguishes between two kinds of natural State: the despotic State, which is based on conquest, and the patrimonial monarchy, which is based on paternal authority. The monarchy, which, Hobbes originally identified with the natural State, was patrimonial monarchy and not despotic monarchy. For Hobbes, monarchy and patrimonial kingdom were originally identical. Later on, he did come to consider, the monarchy based on paternal authority and the monarchy based on conquest as identical. This turn is the result of his conception of the idea of an instituted monarchy; compared with all forms of authority, which are not of artificial production and are not based on voluntary delegation, seem natural. In the ‘Elements of Law’, it is said in passing: ‘the monarch’s subjects are to him as his children and servants’. Monarchy is to cease to be personal Government in any higher degree than Democracy and Aristocracy. The more sharply Hobbes elaborates the idea of representation, the more clarity he achieves as the essence of institutional monarchy and the differences between the King as the natural person and the King as the political person, the less important does the natural State, patrimonial monarchy, and the affinity between monarchy and the paternal authority become for him. Towards the end, despotic Government and monarchy are diametrically opposed: ‘The King though as a father of children, and a master of domestic servants command many things which bind those children and servants; yet he commands the people in general never but by a precedent law, and as a politic, not a natural person’.

Initially, Hobbes considered Democracy as a primary form of the artificial State. In the Elements of Law, it is said: ‘Democracy precedeth all other institutions of Government’. Aristocracy and institutional monarchy are developed from the original Democracy. Thus, according to Hobbes’ original opinion, the artificial State is primarily democratic, as the natural State is the patrimonial monarchy.

It happens that the earliest systematic exposition of Hobbes’ views is the most democratic. That the precedence of Democracy over the other artificial forms of state is addressed most decisively in the Elements of Law. In the Elements of Law, Aristotle’s assertion that the object of Democracy is freedom meets with more justice at Hobbes’ hands, in spite of his rejection of that opinion, than it does later. In the Elements of Law, there is a remark about the artificial State which seems to be a residue of an argument in favour of democracy. In the Elements of Law, he says,

The subjection of them who institute a commonwealth amongst themselves, is no less absolute, than the subjection of servants. And herein they are in equal estate; but the hope of those is greater than the hope of these. For he that subjecteth himself uncompelled, thinketh there is a reason he should be better used, than he that doth it upon compulsion; and coming in freely, calleth himself, though in subjection, a Freeman; whereby it appeareth, that liberty is…a state of better hope than theirs that have been subjected by force and conquest.

From this, this opinion seems to be implied: the motive that leads to the natural State is fear; the motive that leads to the artificial State is hope or trust. This antithesis, in so far as Democracy is the primary form of an artificial State, means the preference for Democracy over patrimonial monarchy.

It is probable from the outset that Hobbes was open to democratic ideas in his humanist period. In the later years he always named the classical authors as the chief causes of democratic ideas in his age. It is not to be assumed that, at a time when he was occupied with these authors, before he could confront their authority with his own political philosophy which raised a claim to mathematical certitude, and when only the authority of Thucydides was on his side, he was as steady in his rejection of the democratic tradition as he later became, to say nothing of the fact that Thucydides after all was not an absolutely indisputable authority for Hobbes’ view in favour of absolute monarchy. The earliest presentation of Hobbes’ political philosophy is at one and the same time the one most in favour of patrimonial monarchy and Democracy. The paradox disappears if one reflects that the ideas of patrimonial monarchy and of Democracy, which are brought out most clearly in the Elements of Law, are traditional ideas, that the untraditional union of these ideas, was not fully successful until the Leviathan, and that, therefore, these ideas are of necessity imperfectly united in the earlier presentations, and as a result, stand side by side in self-contradiction. In his humanist period, Hobbes had not yet found the means of reconciling these opposed traditional ideas i.e. he had not yet developed his final conception of institutional artificial monarchy with sufficient clarity. From the starting, Hobbes’ theory of the State represents the union of two opposed traditions. Hobbes follows the monarchist tradition, in so far as he contends that patrimonial monarchy is the only natural, and thus the only legitimate form of State. In its contrast, the democratic State contends that all legitimacy has its origin in the decree of the sovereign people. With reference to natural states he follows to the end the monarchist tradition, at least as far as the historical origin of already existing states is concerned. With reference to artificial states, he follows, at least to begin with, the democratic tradition, taking pains from the beginning to show that Democracy can do no better than to transform itself into an absolute monarchy.

As far as sovereignty is concerned, Hobbes reconciles two fundamental theories of sovereignty. In one, sovereignty is the right, which is finally based on the authority of the father, thus completely independent of the will of the individual. In second, all sovereignty is to be traced back to the voluntary delegation of authority on the part of the majority of free citizens. In Hobbes’ final theory of sovereignty, the involuntary as well as the voluntary nature of subjection is more systematically reconciled; the individuals and not the fathers; at the founding of the artificial State delegate the highest power to the man or an assembly from mutual fear, in itself compulsive, is consistent with freedom. Compulsive mutual fear is voluntarily replaced by the again compulsive fear of a neutral third power, the Government, and thus they substitute for an immeasurable, endless, and inevitable danger; the danger threatened by an enemy; a measurable, limited and avoidable danger which threatens only the law breakers from the courts of law. When Hobbes reconciled the two opposed theories of sovereignty, he did reject as illegitimate those governments whose foundations could be explained neither by the traditional monarchy, nor by the traditional democratic principles. He says in the translation of Thucydides: Thucydides ‘commandeth (the Government of Athens), both when Peisistratos reigned (saving that it was an usurped power), and when in the beginning of the war it was democratical in name, but in effect monarchical under Pericles’. So Hobbes could distinguish between legitimate and usurped power and thus he originally considered only the patrimonial monarchy as the natural State, and not the despotic rule of the conqueror. His final theory is effective in the sense that it is legitimate in nature thus paving way for ‘tyranny’ and ‘despotism’ to lose all significance.

Hobbes also assumed legal limits to sovereign power. He did mention in the introduction to the translation of Thucydides that a mixed contribution of Democracy and Aristocracy deserves primacy over Democracy on the one hand and over Aristocracy on the other. In the Elements of Law, he admits the possibility not of a division of sovereignty but of the division of the administration of sovereignty into monarchist control and an aristocratic and a democratic council. His original opinion was based on the fact that the absolute monarch is by no means obliged, but would do well, to set up an aristocratic or a democratic council, and thus unite the advantages of monarchy with those of Aristocracy and Democracy. Hobbes did recognize the obligatory limitations of sovereignty. Although it is true that in all the three presentations he rejected the view that sovereign is bound by Civil laws, and even the view that the sovereign nay be under given conditions be called to account by the subjects; but originally he did not espouse sovereignty as nearly so absolute as it is seen in the Leviathan. Finally he considered that the sovereign has no obligation of any kind; for the law of nature, which is apparently binding on the sovereign, takes on full binding force only by the command of the sovereign; and no one can be bound to himselfe; because he that can bind, can release; and therefore he that is bound to himselfe onely, is not bound. Hobbes asserts that the law of nature is obligatory not only on the basis of a sovereign command but also as ‘delivered in the word of God’. But later, according to his own assertion, the word of God itself becomes binding only on the basis of sovereign command. The theory of the Elements of Law contradicts this; as according to it natural law is binding not only by the reason of revelation but also on account of the natural knowledge of God, and thus obliges all men as rational beings and in particular the sovereign. As far as the duties of the sovereign are concerned, Hobbes originally mentions solicitude for the eternal salvation of the subjects.


Aristotelian Influence on Hobbes

Let us begin by surveying the forces, which exercised a decisive influence on Hobbes before he turned to Mathematics and Natural Sciences. From 1603 to 1608 he studied at Oxford. During this time, dissatisfied with academic teaching, he turned to classical texts, which he had already read. He read them with the interpretations of grammarians. His purpose in this study was to develop a clear Latin style. The continuation and conclusion of this study was the English translation of Thucydides, which was gradually published in 1628.

At Oxford Hobbes was introduced to scholastic philosophy. He himself recounts that he studied Aristotle’s logic and physics. He makes no mention of studying Aristotle’s morals and politics. According to the traditional curriculum, the formal disciplines viz., grammar, rhetoric, and logic were in the foreground. We may therefore assume that scholastic studies were for Hobbes in the main formal training, and that he acquired the more detailed knowledge of scholasticism, which he afterwards needed for the polemical defence of his own theories. Later on, he did not take up the studies of scholastic studies as he defected to the studies of humanities.

There were four major influences on Hobbes viz., humanism, scholasticism, Puritanism, and aristocracy. But humanism in Hobbes’ youth was the most prominent of all the influences. Hobbes after the end of his university studies read not only classical poets and historians but also classical philosophers. Which philosophers? In a foreword to his translation of Thucydides he say:

It hath been noted by divers, that Homer in poesy, Aristotle in philosophy, Demosthenes in eloquence, and others of the ancients in other knowledge, do still maintain their privacy: none of them exceeded, some not approached, by any in these later ages. And in the number of these is justly ranked also our Thucydides; a workman no less perfect in his work, than any of the former.

Hobbes later considered Plato to be the best philosopher, not the best philosopher of all, but the best philosopher of antiquity. But at the end of his humanist period he repeats without raising any objection the ruling opinion according to which Aristotle is the highest authority in philosophy. The break with Aristotle was completed only when Hobbes took to the studies of mathematics and natural sciences. The polemic against Aristotle is definitely not as violent as it is in Hobbes’ Leviathan and De Cive. In the Elements of Law, in his definition of the State, Hobbes asserts the aim of the State to be, along with peace and defence, common benefit. With this he tacitly admits Aristotle’s distinction between the reason of the genesis of the State and the reason of its being. In the later stages, Hobbes rejects the common benefit and thus defects from the above mentioned Aristotelian distinction. The linkage of Aristotle with Homer, Demosthenes, and Thucydides provides the answer i.e. Aristotle seen from the humanist point of view. Fundamentally it means the shifting of interests from Aristotle’s physics and metaphysics to his morals and politics. It also means the replacement of theory with the primacy of practice. Only if one assumes a fundamental change of this kind does Hobbes’ turning away from scholasticism to poetry and history cease to be a biographical and a historical peculiarity. Even after natural science had become Hobbes’ favourite subject of investigation, he still acknowledged the precedence of practice over theory and of political philosophy over natural science. The joys of knowledge for him was not the justification of philosophy, but rather the justification only in relation of being beneficial to man, i.e. the safeguarding of man’s life and the increase of human power. Where Hobbes develops his own view connectedly, he manifestly subordinates theory to practice. He did not, like Aristotle, attribute prudence to practice and wisdom to theory. He says: ‘Prudence is to wisdom what experience is to knowledge; wisdom is the knowledge ‘of what is right and wrong and what is good and hurtful to the being and the well-being of mankind… For generally, not he that hath skill in geometry, or any other science speculative, but only he that understandeth what conduceth to the good and Government of the people, is called a wise man’. The contrast with Aristotle has its ultimate reason in Hobbes’ conception of the place of man in the universe, which is diametrically opposed to that of Aristotle. Aristotle justified his placing of the theoretical sciences above moral and political philosophy by the argument that man is not the highest being in the universe. This ultimate assumption of the primacy of theory is rejected by Hobbes; in his contention man is ‘the most excellent work of nature’. In this strict sense Hobbes always remained a humanist, and only with the essential limitation which this brings could he recognize Aristotle’s authority in his humanist period.

Even when Hobbes had come to the conclusion that Aristotle was ‘the worst teacher that ever was’, he excepted two works from his condemnation: ‘but his rhetorique and discourse of animals were rare’. It would be difficult to find other classical work whose importance for Hobbes’ political philosophy can be compared with that of the Rhetoric. The central chapters of Hobbes’ anthropology, those chapters on which, more than on anything else he wrote, his fame as a stylist and as one who knows men rests for all time, betray in style and contents that their author was a zealous reader of the Rhetoric. In the 10th chapter of Leviathan, Hobbes treats under the heading ‘Honourable’ with what Aristotle in the Rhetoric discusses. Aristotle says ‘And honourable are the works of virtue. And the sign of virtue. And the reward whereof is rather honour. And those things are honourable which, good of themselves, are not so to the owner…And bestowing of benefits…And honourable are…victory…And things that excel. And what none can do but we. And possessions we reap no profit by. And those things which are had in honour…And the signs of praise’. In reply to this Hobbes comments ‘…victory is honourable…Magnanimity, Liberality, Hope, Courage, Confidence, are Honourable…Actions proceeding from Equity, joyned with losse, are Honourable’.

Let us try to chart out a dependence of Hobbes’ theory of the passions on the Rhetoric. In the Rhetoric, Anger is desire of revenge, joined with grief, for that he, or some of his, is, or seems to be neglected. While in the Elements of Hobbes, Anger hath been commonly defined to be grief proceeding from an opinion of contempt. To kill is the aim of them that hate, revenge aimeth at triumph. In the Rhetoric Pity is a perturbation of the mind, arising from the apprehension of hurt or trouble to another that doth not deserve it, and which he thinks may happen to himself or his. And because it appertains to pity to think that he, or his, may fall into the misery he pities in others; it follows that they may be most compassionate: who have passed through misery. And such as think there be honest men…Less compassionate are they that think no man honest and who are in great prosperity. In Hobbes’ Elements, Pity is imagination or fiction of future calamity to ourselves, proceeding from the sense of another man’s present calamity; but when it lighteth on such as we think does not deserve the same, the compassion is the greater, because then there appeareth the more probability that the same may happen to us. The contrary of pity is the hardness of heart, proceeding from extreme great opinion of their of their own exemption of the like calamity, or from hatred of all, or most men.

In Rhetoric, indignation is the grief for the prosperity of a man unworthy. In the Rhetoric, envy is grief is for the prosperity of such as ourselves, arising not from any hurt that we, but from the good that they receive. Emulation is grief arising from that our equals possess such goods as are had in honour, and whereof we are capable, but have them not; not because they have them, but because not also we. No man therefore emulates another in things whereof himself is not capable. In the Elements, Emulation is grief arising from seeing one’s self exceeded or excelled by his concurrent, together with hope to equal or exceed him in time to come.

Hobbes in his later writings uses passages from the Rhetoric, of which he had made no use of in his earlier writings, it follows that when composing all his systematic expositions of anthropology he studied Aristotle’s Rhetoric afresh each time. Hobbes’ pre-occupation with the Rhetoric can be traced back as far as about 1635. in 1635, Hobbes had considered the writing of personal exposition of the theory of the passions and as just seen, his earliest treatment of the theory of the passions was clearly influenced by Aristotle’s Rhetoric. In addition, he himself recounts that he instructed the third Earl of Devonshire in rhetoric.

Hobbes’ closer study of Aristotle’s Rhetoric may be proved with certainty only for the 1630s, i.e. in the time in which he had overtly completed the break with Aristotelianism. Moreover, one gathers from his introduction to the translation of Thucydides that the phenomenon of eloquence on the one hand, and of the passions on the other, occupied his mind even in the humanist period of his. On the whole, it seems to us more correct to assume that the use and appreciation of Aristotle’s Rhetoric, which may be traced in Hobbes’ mature writings, are the last remnants of the Aristotelianism of his youth. Hobbes after exclusive pre-occupation with poets and historians

Aitareya Upanishad and Creation. Note Quote.


Upanishads are the philosophical and spiritual sermons, forming a part of the Vedas. Isha, Kena, Katha, Prashna, Munda, Mandukya, Taittiriya, Aitareya, Chhandogya and Brihadaranyaka are the ten most famous Upanishads.

Aitareya Upanishad belongs to the Rugved. It forms part of the Aitareya Aranyaka. The Aitareya Upanishad consists of three chapters. It begins with the fourth chapter of the second Aranyaka and comprises of chapters four, five and six. The doctrines found in this Upanishad were propounded by Sage Itareya. The purpose of this Upanishad is to lead the mind of the sacrificer from the mundane world to spirituality.

The Creator of the World-Carers
‘स इक्षत। इमे नु लोका लोकपालान्नु सृजा इति’ – ‘Sa ikshata, ime nu lokã lokapãlãnnu srujã iti’ (Aitareya Upanishad: 1/1).

Just as Paramãtmã has created various worlds, he has also created the world-carers who can control and nurture those worlds. That is he gives them a suitable body by which they are capable of controlling those worlds. This has been explained here, and furthermore, a detailed description of the creation of the body and organs of those world-carers, and of the method of occupation of the deities who rule over those organs has also been given.

The Provider for the World-Carers
Compassionate Paramãtmã has created a variety of places as well as world-carers to look after those places. This Upanishad informs us that he is also concerned about nourishing them, ‘स र्इक्षतेमे नु लोकाश्र्च लोकपालाश्र्चाऽन्नमे यः सृजा इति’ – ‘Sa eekshateme nu lokãscha lokapãlãschã’nnamebhyaha srujã iti’ (Aitareya Upanishad: 1/3). That Paramãtmã desired to create food so that all these worlds and world-creators continue to be nourished. Food was created according to that wish, and all are nourished by that food. Thus, the first adhyãya prominently explains matters such as Paramãtmã creating the worlds appropriate for the jivas and ishwars to experience the fruits of their karmas; and also creating the world-carers of those worlds; and creating food for their life-long nourishment.

The Second Adhyãya
Creation of the human body

The main subject of the second adhyãya is the creation of the human body. It gives a clear presentation of how the jivãtmã attains a human body by Paramãtmã’s inspiration. The discrimination between the body and ãtmã is automatically understood by this description. Thereafter, there is a description of what happens to the jivãtmã after its life-span in this body is over. This Upanishad states that the person who lacks brahmavidyã has to repeatedly wander in the miserable cycle of births and deaths, and those that imbibe brahmavidyã attain Akshardham and experience the bliss of Paramãtmã.

The Third Adhyãya
The Upãsanã of Parabrahman

The first two adhyãyas describe the grandeur of Paramãtmã well. The third adhyãya then instructs us to perform the upãsanã of Parabrahman with knowledge of his greatness. The Upanishad says, ‘येन पश्यति येन वा शृणोति येन वा गन्घान्‌ जिघýति येन वा वाचं व्याकरोति येन वा स्वादु चाऽस्वादु विजानाति’– ‘Yena pashyati yena vã shrunoti yena vã gandhãn jighrati yena vã vãcham vyãkaroti yena vã svãdu chã’svãdu vijãnãti’ – ‘One should perform the upãsanã of Paramãtmã, by whose inspiration the ãtmã can see via the eyes, hear via the ears, smell fragrances via the nose, speak words via the tongue, and know good and bad tastes’ (Aitareya Upanishad: 3/1). If we did not have this body or these organs, then what could we do? We would not be able to perform any endeavours for liberation. Kindhearted Paramãtmã has compassionately given us all of this. He has given us a body, he has given us organs and he has poured strength into those organs. He has made everything convenient. Therefore, let us perform his upãsanã, please him and attain liberation. This has been stated here forcefully.

Brahman Perception
In order to understand the full glory of Parabrahman, and in order to do his upãsanã appropriately, one must become aksharrup, one must be engulfed in the sense of being like Brahman, and for this very reason, one must know Aksharbrahman. This is the essence of the whole of Vedanta. Therefore, this Upanishad has indicated the pragnãn form of Aksharbrahman with the words ‘प्रज्ञानं ब्रह्म’ – ‘Pragnãnam Brahma’ (Aitareya Upanishad: 3/3). Moreover, ‘यदेतद्‌ हृदयं मनश्र्चैतत्‌ … सर्वाण्येतानि प्रज्ञानस्य नामघेयानि भवन्ति’ – ‘Yadetad hrudayam manaschaitat … sarvãnyetãni pragnãnasya nãmadheyãni bhavanti’ – ‘This heart, mind, etc. of ours – whatever we have – are all names of pragnãna Brahman’ (Aitareya Upanishad: 3/2), that is, they are all pervaded by Aksharbrahman. Thus, we have been instructed to perceive everything as Brahman.

The Divine Fruits
This Upanishad then concludes by informing us of the fruits that one who becomes brahmarup and performs the upãsanã of Parabrahman with knowledge of his greatness attains. ‘अमृतः समभवत्‌’ – ‘Amrutaha samabhavat’ (Aitareya Upanishad: 3/4). Such a person attains divine Akshardhãm and is released from the cycles of birth and death.

In this way, by calling Paramãtmã the cause, creator, controller and nurturer of creation the Aitareya Upanishad tells us that he is the essence of creation. We should perform the upãsanã of that Paramãtmã. In order for that upãsanã to be complete and free of hindrances we should adorn our ãtmãs with a sense of being like Brahman, and thus attain ultimate liberation. By explaining such principles this Upanishad has given us a clear view of the path to liberation.

Yuanqi, Yin & Yang and Ontology of Quantum Physics. Some Chinese Import.


In ancient China, there was a saying in ‘The Book of Rites-University‘ edited by Confucius (551BC-479BC): To gain knowledge via ‘gewu’, the knowledge comes only after the “wu”(object) is “ge”. The words “gewu” was interpreted by the philosopher Cheng Yi (1033-1107, in Song dynasty) as “reaching the object” while Zhu Xi (1130-1200) explained it as “touching the object”. In Ming dynasty, Wang Shou-ren (1472-1528) interpreted it as “seeing the object” and Wang Gen (1483-1540) ex- plained it as “the measurement on the object”, yielding a considerable progress (see [10]). It was not until Mao Zedong (1893-1976) in his article “on Practice”, a principle of “the cognition being stemming from the changing” was stressed, implying that “gewu” is now interpreted as some “changing process” (“biange” in Chinese). It seems just appropriate. Just looking at the experimental methods in modern physics evolving more and more abundant, the energy being raised higher and higher, new phenomena and new particles emerge successively, we have been convinced that the replacement of the “reflection theory” by the “changing theory” in the epistemology of philosophy is indeed a big progress, a jump in conception.

In philosophy, one swam upstream from the epistemology to the “ontology”—the inquiry about the nature of universe and the origin of matters. It seems to us no surprise that in conformity with the principle in epistemology that “the information is generated from the changing process”, the “noumenon” does not contain information. There were various pronouns for the noumenon in Chinese philosophy, e.g., “emptiness(void)” or “oneness”. Sometimes, it was called the “Tao” (which means the “way” or “law”). Lao Tze (who lived in the same time with Confucius, maybe a little earlier) said: “The Tao that can be expressed is not the eternal Tao. The name that can be named is not the permanent name”. In our understanding, his saying implies that the fundamental (eternal or perpetual) law cannot be expressed in words and the permanent name in wholeness (or totality) cannot be divided and put into various categories. Actually, similar point of view was prevailing in the Eastern philosophy, e.g., in the doctrine of Hinduism or Buddhism. But it seems to us that a deep philosophy without explicit saying is also a philosophy difficult to develope in real life. Lao Tze was wise to say more. He said: “the Tao generates one and one generates two…”. Then after common efforts of many philosophers, especially Wang Chong (27-100), Zhang Zai (1020- 1077) and Wang Fuzhi (1619-1692), the theory of “yuanqi (the primary gas)” was developed. They claimed that all matters are generated from “yuanqi”, inside which there are two opposites named “yin and yang”. It is the interaction and mutual transform between yin and yang that are responsible for the motion and change of everything in the world. This is really a deep and flexible “ontology”.

Conjuncted: Forward, Futures Contracts and Options: Top Down or bottom Up Modeling?


In the top down description of theoretical finance, a security S(t) follows a random walk described by a Ito-Weiner process (or Langevin equation) as

dS(t)/S(t) = φdt + σ R(t) dt —– (1)

where R(t) is a Gaussian white noise with zero mean and uncorrelated values at time t and t′ ⟨R(t)R(t′)⟩ = δ(t−t′). φ is the drift term or expected return, while σ is a constant factor multiplying the random source R(t), termed volatility.

As a consequence of Ito calculus, differentials of functions of random variables, say f(S,t), do not satisfy Leibnitz’s rule, and for a Ito-Weiner process with drift (2) one easily obtains for the time derivative of f(S,t)

df/dt = ∂f/∂t + 1/2 σ2 S2 ∂2f/∂S2 + φS∂f/∂S + σS∂f/∂S R —– (2)

The Black-Scholes model is obtained by removing the randomness of the stochastic process shown above by introducing a random process correlated to equation 2. This operation, termed hedging, allows to remove the dependence on the white noise function R(t), by constructing a portfolio Π, whose evolution is given by the short-term risk free interest rate r

dΠ/dt = rΠ —– (3)

A possibility is to choose Π = f – S∂f/∂S. This is a portfolio in which an investor holds an option f and short sells an amount of the underlying security S proportional to ∂f/∂S. A combination of equations 2 and 3 yields the Black-Scholes equation

∂f/∂t + 1/2 σ2 S2 ∂2f/∂S2 + rS∂f/∂S = rf —– (4)

There are some assumptions underlying this result. We have assumed absence of arbitrage, constant spot rate r, continuous balance of the portfolio, no transaction costs and infinite divisibility of the stock. The quantum mechanical version of this equation is obtained by a change of variable S = ex, with x a real variable. This yields

∂f/∂t = HBSf —– (5)

with an Hamiltonian HBS given by

HBS = – σ2/2 ∂2/∂x2 + (1/2 σ2 – r) ∂/∂x + r —– (6)

Notice that one can introduce a quantum mechanical formalism and interpret the option price as a ket |f⟩ in the basis of |x⟩, the underlying security price. Using Dirac notation, we can formally reinterpret f (x, t) = ⟨x|f (t)⟩, as a projection of an abstract quantum state |f(t)⟩ on the chosen basis.

In this notation, the evolution of the option price can be formally written as |f, t⟩ = etH |f, 0⟩, for an appropriate Hamiltonian H.

In general, the description of these processes is driven by two correlated white noise functions R1 and R2

dV/dt = λ + μV + ζVαR1

dV/dt = φS + σ√V + μV + ζVαR2 —– (7)

with V = √σ and ⟨R1(t)R2(t′)⟩ = 1/ρ δ(t − t′)

ρ being the correlation parameter. However, since volatility is not traded in the market (the market is said to be incomplete), perfect hedging is not possible, and an additional term, the market price of volatility risk β(S,V,t,r), is in this case introduced. β can be modeled appropriately. In some models, a redefinition of the drift term μ in (7) in the evolution of the volatility is sufficient to hedge such more complex portfolios, which amounts to an implicit choice of β(S, V, t, r). We just quote the result for the evolution of an option price in the presence of stochastic volatility, which, in the Hamiltonian formulation are given by

∂f/∂t = HMGf —– (8),


HMG = -(r – ey/2) ∂/∂x – (λe-y + μ – ζ2/2 e2y(α – 1)) ∂/∂y – ey/2 ∂2/∂x2 -ρζ ey(α – 1)/2 ∂2/∂x∂y – ζ2 e2y(α – 1) /2 ∂2/∂y2 + r —– (9)

which is nonlinear in the variables x = log(S) and y = log(V ). For general values of the parameters, the best way to obtain the pricing of the options in this model is by a simulation of the path integral.

Forward, Futures Contracts and Options: Top Down or bottom Up Modeling?


The simulation of financial markets can be modeled, from a theoretical viewpoint, according to two separate approaches: a bottom up approach and (or) a top down approach. For instance, the modeling of financial markets starting from diffusion equations and adding a noise term to the evolution of a function of a stochastic variable is a top down approach. This type of description is, effectively, a statistical one.

A bottom up approach, instead, is the modeling of artificial markets using complex data structures (agent based simulations) using general updating rules to describe the collective state of the market. The number of procedures implemented in the simulations can be quite large, although the computational cost of the simulation becomes forbidding as the size of each agent increases. Readers familiar with Sugarscape Models and the computational strategies based on Growing of Artificial Societies have probably an idea of the enormous potentialities of the field. All Sugarscape models include the agents (inhabitants), the environment (a two-dimensional grid) and the rules governing the interaction of the agents with each other and the environment. The original model presented by J. Epstein & R. Axtell (considered as the first large scale agent model) is based on a 51 x 51 cell grid, where every cell can contain different amounts of sugar (or spice). In every step agents look around, find the closest cell filled with sugar, move and metabolize. They can leave pollution, die, reproduce, inherit sources, transfer information, trade or borrow sugar, generate immunity or transmit diseases – depending on the specific scenario and variables defined at the set-up of the model. Sugar in simulation could be seen as a metaphor for resources in an artificial world through which the examiner can study the effects of social dynamics such as evolution, marital status and inheritance on populations. Exact simulation of the original rules provided by J. Epstein & R. Axtell in their book can be problematic and it is not always possible to recreate the same results as those presented in Growing Artificial Societies. However, one would expect that the bottom up description should become comparable to the top down description for a very large number of simulated agents.

The bottom up approach should also provide a better description of extreme events, such as crashes, collectively conditioned behaviour and market incompleteness, this approach being of purely algorithmic nature. A top down approach is, therefore, a model of reduced complexity and follows a statistical description of the dynamics of complex systems.

Forward, Futures Contracts and Options: Let the price at time t of a security be S(t). A specific good can be traded at time t at the price S(t) between a buyer and a seller. The seller (short position) agrees to sell the goods to the buyer (long position) at some time T in the future at a price F(t,T) (the contract price). Notice that contract prices have a 2-time dependence (actual time t and maturity time T). Their difference τ = T − t is usually called time to maturity. Equivalently, the actual price of the contract is determined by the prevailing actual prices and interest rates and by the time to maturity. Entering into a forward contract requires no money, and the value of the contract for long position holders and strong position holders at maturity T will be

(−1)p (S(T)−F(t,T)) (1)

where p = 0 for long positions and p = 1 for short positions. Futures Contracts are similar, except that after the contract is entered, any changes in the market value of the contract are settled by the parties. Hence, the cashflows occur all the way to expiry unlike in the case of the forward where only one cashflow occurs. They are also highly regulated and involve a third party (a clearing house). Forward, futures contracts and options go under the name of derivative products, since their contract price F(t, T) depend on the value of the underlying security S(T). Options are derivatives that can be written on any security and have a more complicated payoff function than the futures or forwards. For example, a call option gives the buyer (long position) the right (but not the obligation) to buy or sell the security at some predetermined strike-price at maturity. A payoff function is the precise form of the price. Path dependent options are derivative products whose value depends on the actual path followed by the underlying security up to maturity. In the case of path-dependent options, since the payoff may not be directly linked to an explicit right, they must be settled by cash. This is sometimes true for futures and plain options as well as this is more efficient.

Conjuncted: Sheaf Cohomology as the Mathematical Tool Necessary to Describe a Conformally Invariant Isomorphism. Twistors and Spinors Theoreticals. Note Quote.

Via Cosmological Framework.

The characterization of gravitational forces is nothing but the effect on matter and energy of a modification of the geometry of space-time. This major property of General Relativity remains unchanged. The main difference concerns the dynamics that this geometry obeys. In GTR the dynamics of the gravitational field depends on the curvature invariants; in the Spinor Theory of Gravity such a specific dynamics simply does not exist: the geometry evolves in space-time according to the dynamics of the spinors. The metric is not a field of its own, it does not have an independent reality but is just a consequence of the universal coupling of matter with the fundamental spinors. The motivation of walking down only half of Einstein’s path to General Relativity is to avoid certain known problems that still plague this theory, including its difficult passage to the quantum world and the questions put into evidence by astrophysics involving many discoveries such as the acceleration of the universe, the problems requiring dark matter and dark energy. It seems worthwhile to quote Dark Energy Task Force here :

Dark energy appears to be the dominant component of the physical Universe, yet there is no persuasive theoretical explanation for its existence or magnitude. The acceleration of the Universe is, along with dark matter, the observed phenomenon that most directly demonstrates that our theories of fundamental particles and gravity are either incorrect or incomplete. Recent observations in Cosmology are responsible for an unexpected attitude: to take seriously the possibility of alterating Einstein’ s theory of gravity.

The Spinorial Theory of Gravity presents the possibility of a way out of these difficulties. The reason, which will be explained later on, can be understood from the fact that in the STG there is no direct relationship between the acceleration of the scale factor of the universe and the matter/energy distribution, contrary to the case of GTR, in which the Friedman equation that controls the dynamics of the universe relates the matter-energy content to the geometry through the evolution of the scale factor a(t): ä/a = -1/6 (ρ + 3ρ)