Quantum Music

Human neurophysiology suggests that artistic beauty cannot easily be disentangled from sexual attraction. It is, for instance, very difficult to appreciate Sandro Botticelli’s Primavera, the arguably “most beautiful painting ever painted,” when a beautiful woman or man is standing in front of that picture. Indeed so strong may be the distraction, and so deep the emotional impact, that it might not be unreasonable to speculate whether aesthetics, in particular beauty and harmony in art, could be best understood in terms of surrogates for natural beauty. This might be achieved through the process of artistic creation, idealization and “condensation.”

1200px-Botticelli-primavera

In this line of thought, in Hegelian terms, artistic beauty is the sublimation, idealization, completion, condensation and augmentation of natural beauty. Very different from Hegel who asserts that artistic beauty is “born of the spirit and born again, and the higher the spirit and its productions are above nature and its phenomena, the higher, too, is artistic beauty above the beauty of nature” what is believed here is that human neurophysiology can hardly be disregarded for the human creation and perception of art; and, in particular, of beauty in art. Stated differently, we are inclined to believe that humans are invariably determined by (or at least intertwined with) their natural basis that any neglect of it results in a humbling experience of irritation or even outright ugliness; no matter what social pressure groups or secret services may want to promote.

Thus, when it comes to the intensity of the experience, the human perception of artistic beauty, as sublime and refined as it may be, can hardly transcend natural beauty in its full exposure. In that way, art represents both the capacity as well as the humbling ineptitude of its creators and audiences.

Leaving these idealistic realms and come back to the quantization of musical systems. The universe of music consists of an infinity – indeed a continuum – of tones and ways to compose, correlate and arrange them. It is not evident how to quantize sounds, and in particular music, in general. One way to proceed would be a microphysical one: to start with frequencies of sound waves in air and quantize the spectral modes of these (longitudinal) vibrations very similar to phonons in solid state physics.

For the sake of relating to music, however, a different approach that is not dissimilar to the Deutsch-Turing approach to universal (quantum) computability, or Moore’s automata analogues to complementarity: a musical instrument is quantized, concerned with an octave, realized by the eight white keyboard keys typically written c, d, e, f, g, a, b, c′ (in the C major scale).

In analogy to quantum information quantization of tones is considered for a nomenclature in analogy to classical musical representation to be further followed up by introducing typical quantum mechanical features such as the coherent superposition of classically distinct tones, as well as entanglement and complementarity in music…..quantum music

Beginning of Matter, Start to Existence Itself

__beginning_of_matter___by_ooookatioooo

When the inequality

μ+3p/c2 >0 ⇔ w > −1/3

is satisfied, one obtains directly from the Raychaudhuri equation

3S ̈/S = -1/2 κ(μ +3p/c2) + Λ

the Friedmann-Lemaître (FL) Universe Singularity Theorem, which states that:

In a FL universe with Λ ≤ 0 and μ + 3p/c2 > 0 at all times, at any instant t0 when H0 ≡ (S ̇/S)0 > 0 there is a finite time t: t0 − (1/H0) < t < t0, such that S(t) → 0 as t → t; the universe starts at a space-time singularity there, with μ → ∞ and T → ∞ if μ + p/c2 > 0.

This is not merely a start to matter – it is a start to space, to time, to physics itself. It is the most dramatic event in the history of the universe: it is the start of existence of everything. The underlying physical feature is the non-linear nature of the Einstein’s Field Equations (EFE): going back into the past, the more the universe contracts, the higher the active gravitational density, causing it to contract even more. The pressure p that one might have hoped would help stave off the collapse makes it even worse because (consequent on the form of the EFE) p enters algebraically into the Raychaudhuri equation with the same sign as the energy density μ. Note that the Hubble constant gives an estimate of the age of the universe: the time τ0 = t0 − t since the start of the universe is less than 1/H0.

This conclusion can in principle be avoided by a cosmological constant, but in practice this cannot work because we know the universe has expanded by at least a ratio of 11, as we have seen objects at a redshift 6 of 10, the cosmological constant would have to have an effective magnitude at least 113 = 1331 times the present matter density to dominate and cause a turn-around then or at any earlier time, and so would be much bigger than its observed present upper limit (of the same order as the present matter density). Accordingly, no turnaround is possible while classical physics holds. However energy-violating matter components such as a scalar field can avoid this conclusion, if they dominate at early enough times; but this can only be when quantum fields are significant, when the universe was at least 1012 smaller than at present.

Because Trad ∝ S−1, a major conclusion is that a Hot Big Bang must have occurred; densities and temperatures must have risen at least to high enough energies that quantum fields were significant, at something like the GUT energy. The universe must have reached those extreme temperatures and energies at which classical theory breaks down.

Single Asset Optimal Investment Fraction

Protecting-your-nest-egg_investment-outcomes

We first consider a situation, when an investor can spend a fraction of his capital to buy shares of just one risky asset. The rest of his money he keeps in cash.

Generalizing Kelly, we consider the following simple strategy of the investor: he regularly checks the asset’s current price p(t), and sells or buys some asset shares in order to keep the current market value of his asset holdings a pre-selected fraction r of his total capital. These readjustments are made periodically at a fixed interval, which we refer to as readjustment interval, and select it as the discrete unit of time. In this work the readjustment time interval is selected once and for all, and we do not attempt optimization of its length.

We also assume that on the time-scale of this readjustment interval the asset price p(t) undergoes a geometric Brownian motion:

p(t + 1) = eη(t)p(t) —– (1)

i.e. at each time step the random number η(t) is drawn from some probability distribution π(η), and is independent of it’s value at previous time steps. This exponential notation is particularly convenient for working with multiplicative noise, keeping the necessary algebra at minimum. Under these rules of dynamics the logarithm of the asset’s price, ln p(t), performs a random walk with an average drift v = ⟨η⟩ and a dispersion D = ⟨η2⟩ − ⟨η⟩2.

It is easy to derive the time evolution of the total capital W(t) of an investor, following the above strategy:

W(t + 1) = (1 − r)W(t) + rW(t)eη(t) —– (2)

Let us assume that the value of the investor’s capital at t = 0 is W(0) = 1. The evolution of the expectation value of the expectation value of the total capital ⟨W (t)⟩ after t time steps is obviously given by the recursion ⟨W (t + 1)⟩ = (1 − r + r⟨eη⟩)⟨W (t)⟩. When ⟨eη⟩ > 1, at first thought the investor should invest all his money in the risky asset. Then the expectation value of his capital would enjoy an exponential growth with the fastest growth rate. However, it would be totally unreasonable to expect that in a typical realization of price fluctuations, the investor would be able to attain the average growth rate determined as vavg = d⟨W(t)⟩/dt. This is because the main contribution to the expectation value ⟨W(t)⟩ comes from exponentially unlikely outcomes, when the price of the asset after a long series of favorable events with η > ⟨η⟩ becomes exponentially big. Such outcomes lie well beyond reasonable fluctuations of W (t), determined by the standard deviation √Dt of ln W (t) around its average value ⟨ln W (t)⟩ = ⟨η⟩t. For the investor who deals with just one realization of the multiplicative process it is better not to rely on such unlikely events, and maximize his gain in a typical outcome of a process. To quantify the intuitively clear concept of a typical value of a random variable x, we define xtyp as a median of its distribution, i.e xtyp has the property that Prob(x > xtyp) = Prob(x < xtyp) = 1/2. In a multiplicative process (2) with r = 1, W (t + 1) = eη(t)W (t), one can show that Wtyp(t) – the typical value of W(t) – grows exponentially in time: Wtyp(t) = e⟨η⟩t at a rate vtyp = ⟨η⟩, while the expectation value ⟨W(t)⟩ also grows exponentially as ⟨W(t)⟩ = ⟨eη⟩t, but at a faster rate given by vavg = ln⟨eη⟩. Notice that ⟨lnW(t)⟩ always grows with the typical growth rate, since those very rare outcomes when W (t) is exponentially big, do not make significant contribution to this average.

The question we are going to address is: which investment fraction r provides the investor with the best typical growth rate vtyp of his capital. Kelly has answered this question for a particular realization of multiplicative stochastic process, where the capital is multiplied by 2 with probability q > 1/2, and by 0 with probability p = 1 − q. This case is realized in a gambling game, where betting on the right outcome pays 2:1, while you know the right outcome with probability q > 1/2. In our notation this case corresponds to η being equal to ln 2 with probability q and −∞ otherwise. The player’s capital in Kelly’s model with r = 1 enjoys the growth of expectation value ⟨W(t)⟩ at a rate vavg = ln2q > 0. In this case it is however particularly clear that one should not use maximization of the expectation value of the capital as the optimum criterion. If the player indeed bets all of his capital at every time step, sooner or later he will loose everything and would not be able to continue to play. In other words, r = 1 corresponds to the worst typical growth of the capital: asymptotically the player will be bankrupt with probability 1. In this example it is also very transparent, where the positive average growth rate comes from: after T rounds of the game, in a very unlikely (Prob = qT) event that the capital was multiplied by 2 at all times (the gambler guessed right all the time!), the capital is equal to 2T. This exponentially large value of the capital outweighs exponentially small probability of this event, and gives rise to an exponentially growing average. This would offer condolence to a gambler who lost everything.

We generalize Kelly’s arguments for arbitrary distribution π(η). As we will see this generalization reveals some hidden results, not realized in Kelly’s “betting” game. As we learned above, the growth of the typical value of W(t), is given by the drift of ⟨lnW(t)⟩ = vtypt, which in our case can be written as

vtyp(r) = ∫ dη π(η) ln(1 + r(eη − 1)) —– (3)

One can check that vtyp(0) = 0, since in this case the whole capital is in the form of cash and does not change in time. In another limit one has vtyp(1) = ⟨η⟩, since in this case the whole capital is invested in the asset and enjoys it’s typical growth rate (⟨η⟩ = −∞ for Kelly’s case). Can one do better by selecting 0 < r < 1? To find the maximum of vtyp(r) one differentiates (3) with respect to r and looks for a solution of the resulting equation: 0 = v’typ(r) = ∫ dη π(η) (eη −1)/(1+r(eη −1)) in the interval 0 ≤ r ≤ 1. If such a solution exists, it is unique since v′′typ(r) = − ∫ dη π(η) (eη − 1)2 / (1 + r(eη − 1))2 < 0 everywhere. The values of the v’typ(r) at 0 and 1 are given by v’typ(0) = ⟨eη⟩ − 1, and v’typ(1) = 1−⟨e−η⟩. One has to consider three possibilities:

(1) ⟨eη⟩ is realized at r = 0 and is equal to 0. In other words, one should never invest in an asset with negative average return per capital ⟨eη⟩ − 1 < 0.

(2) ⟨eη⟩ > 1 , and ⟨e−η⟩ > 1. In this case v’typ(0) > 0, but v’typ(1) < 0 and the maximum of v(r) is realized at some 0 < r < 1, which is a unique solution to v’typ(r) = 0. The typical growth rate in this case is always positive (because you could have always selected r = 0 to make it zero), but not as big as the average rate ln⟨eη⟩, which serves as an unattainable ideal limit. An intuitive understanding of why one should select r < 1 in this case comes from the following observation: the condition ⟨e−η⟩ > 1 makes ⟨1/p(t)⟩ to grow exponentially in time. Such an exponential growth indicates that the outcomes with very small p(t) are feasible and give dominant contribution to ⟨1/p(t)⟩. This is an indicator that the asset price is unstable and one should not trust his whole capital to such a risky investment.

(3) ⟨eη⟩ > 1 , and ⟨e−η⟩ < 1. This is a safe asset and one can invest his whole capital in it. The maximum vtyp(r) is achieved at r = 1 and is equal to vtyp(1) = ln⟨η⟩. A simple example of this type of asset is one in which the price p(t) with equal probabilities is multiplied by 2 or by a = 2/3. As one can see this is a marginal case in which ⟨1/p(t)⟩ = const. For a < 2/3 one should invest only a fraction r < 1 of his capital in the asset, while for a ≥ 2/3 the whole sum could be trusted to it. The specialty of the case with a = 2/3 cannot not be guessed by just looking at the typical and average growth rates of the asset! One has to go and calculate ⟨e−η⟩ to check if ⟨1/p(t)⟩ diverges. This “reliable” type of asset is a new feature of the model with a general π(η). It is never realized in Kelly’s original model, which always has ⟨η⟩ = −∞, so that it never makes sense to gamble the whole capital every time.

An interesting and somewhat counterintuitive consequence of the above results is that under certain conditions one can make his capital grow by investing in asset with a negative typical growth rate ⟨η⟩ < 0. Such asset certainly loses value, and its typical price experiences an exponential decay. Any investor bold enough to trust his whole capital in such an asset is losing money with the same rate. But as long as the fluctuations are strong enough to maintain a positive average return per capital ⟨eη⟩ − 1 > 0) one can maintain a certain fraction of his total capital invested in this asset and almost certainly make money! A simple example of such mind-boggling situation is given by a random multiplicative process in which the price of the asset with equal probabilities is doubled (goes up by 100%) or divided by 3 (goes down by 66.7%). The typical price of this asset drifts down by 18% each time step. Indeed, after T time steps one could reasonably expect the price of this asset to be ptyp(T) = 2T/2 3−T/2 = (√2/3)T ≃ 0.82T. On the other hand, the average ⟨p(t)⟩ enjoys a 17% growth ⟨p(t + 1)⟩ = 7/6 ⟨p(t)⟩ ≃ 1.17⟨W (t)⟩. As one can easily see, the optimum of the typical growth rate is achieved by maintaining a fraction r = 1/4 of the capital invested in this asset. The typical rate in this case is a meager √(25/24) ≃ 1.02, meaning that in a long run one almost certainly gets a 2% return per time step, but it is certainly better than losing 18% by investing the whole capital in this asset.

Of course the properties of a typical realization of a random multiplicative process are not fully characterized by the drift vtyp(r)t in the position of the center of mass of P(h,t), where h(t) = lnW(t) is a logarithm of the wealth of the investor. Indeed, asymptotically P (h, t) has a Gaussian shape P (h, t) =1/ (√2π D(r)t) (exp(−(h−vtyp(r)t)2)/(2D(r)t), where vtyp(r) is given by eq. (3). One needs to know the dispersion D(r) to estimate √D(r)t, which is the magnitude of characteristic deviations of h(t) away from its typical value htyp(t) = vtypt. At the infinite time horizon t → ∞, the process with the biggest vtyp(r) will certainly be preferable over any other process. This is because the separation between typical values of h(t) for two different investment fractions r grows linearly in time, while the span of typical fluctuations grows only as a √t. However, at a finite time horizon the investor should take into account both vtyp(r) and D(r) and decide what he prefers: moderate growth with small fluctuations or faster growth with still bigger fluctuations. To quantify this decision one needs to introduce an investor’s “utility function” which we will not attempt in this work. The most conservative players are advised to always keep their capital in cash, since with any other arrangement the fluctuations will certainly be bigger. As a rule one can show that the dispersion D(r) = ∫ π(η) ln2[1 + r(eη − 1)]dη − v2typ monotonically increases with r. Therefore, among two solutions with equal vtyp(r) one should always select the one with a smaller r, since it would guarantee smaller fluctuations. Here it is more convenient to switch to the standard notation. It is customary to use the random variable

Λ(t)= (p(t+1)−p(t))/p(t) = eη(t) −1 —– (4)

which is referred to as return per unit capital of the asset. The properties of a random multiplicative process are expressed in terms of the average return per capital α = ⟨Λ⟩ = ⟨eη⟩ − 1, and the volatility (standard deviation) of the return per capital σ = √(⟨Λ2⟩ – ⟨Λ⟩2. In our notation, α = ⟨eη⟩ – 1, is determined by the average and not typical growth rate of the process. For η ≪ 1 , α ≃ v + D/2 + v2/2, while the volatility σ is related to D ( the dispersion of η) through σ ≃ √D.

 

Price Dynamics for Fundamentalists – Risky Asset – Chartists via Modeling

Substituting (1), (2) and (3) to (4) from here, the dynamical system can be obtained as

pt+1 − pt = θN[(1 − κ)(exp(α(p − pt)) − 1) + κ(exp(β(1 − µ)(pet − pt)) − 1)] pet+1 − pet = µ(pt − pet ) —– (5)

In the following discussion we highlight the impact of increases in the total number of traders n on the price fluctuation that is defined as the price increment,

rt = pt+1 − pt

We first restrict ourselves to investigating the following set of parameters:

α = 3, β = 1, µ = 0.5, κ = 0.5, θ = 0.001 —– (6)

It is clear that the two-dimensional map (5) has a unique equilibrium with pet = pt = p, namely (p¯e , p¯) = (p, p), given the above conditions. Elementary computations show that for our map (5) the sufficient condition for the local stability of the fixed point p is given as

N < (2(2 − µ))/(θ[α(2 − µ)(1 − κ) + 2β(1 − µ)κ]) —– (7)

From (7) it follows that, starting from a small number of traders N inside the stability region, when the number of traders N increases, a loss of stability may occur via a flip bifurcation. We shall now look more globally into the effect of increases in the number of traders on the price dynamics. Figure 1 shows a bifurcation diagram of the price increments rt with N as the bifurcation parameter under the set of parameters (6). For the convenience of illustration, Figure 1 is drawn using θN as the bifurcation parameter. This figure suggests the following bifurcation scenario.

0312065v1.fig1

The price increments rt converge to 0 when the number of traders N is small. In other words, the price converges to the fundamental price p when the active traders are few. However the price dynamics become unstable when the number of traders N exceeds about 1000, and chaotic behavior of the price increments occurs after infinitely many period-doubling bifurcations. If N is further increased, then the price increments rt become more regular again after infinitely many period-halving bifurcations. A stable 2 orbit occurs for an interval of N-values. However as N is further increased, the behavior of the price increment rt becomes once again chaotic, and the prices diverge. Let us investigate closely the characteristics of chaos that are observed in the parameter interval (2000 < N < 4000). Figure 2 shows a series of price increments rt with N = 4000 and the set of parameters (6). The figure shows apparently the characteristic of intermittent chaos, that is, a long laminar phase, where the price fluctuations behave regularly, is interrupted from time to time by chaotic bursts. 

0312065v1.fig2

Conjuncted: Axiomatizing Artificial Intelligence. Note Quote.

machinelearningalgorithms1

Solomonoff’s work was seminal in that he has single-handedly axiomatized AI, discovering the minimal necessary conditions for any machine to attain general intelligence.

Informally, these axioms are:

AI0 AI must have in its possession a universal computer M (Universality). AI1 AI must be able to learn any solution expressed in M’s code (Learning recursive solutions).
AI2 AI must use probabilistic prediction (Bayes’ theorem).
AI3 AI must embody in its learning a principle of induction (Occam’s razor).

While it may be possible to give a more compact characterization, these are ultimately what is necessary for the kind of general learning that Solomonoff induction achieves. ALP can be seen as a complete formalization of Occam’s razor (as well as Epicurus’s principle)  and thus serve as the foundation of universal induction, capable of solving all AI problems of significance. The axioms are important because they allow us to assess whether a system is capable of general intelligence or not.

Obviously, AI1 entails AI0, therefore AI0 is redundant, and can be omitted entirely, however we stated it separately only for historical reasons, as one of the landmarks of early AI research, in retrospect, was the invention of the universal computer, which goes back to Leibniz’s idea of a universal language (characteristica universalis) that can express every statement in science and mathematics, and has found its perfect embodiment in Turing’s research. A related achievement of early AI was the development of LISP, a universal computer based on lambda calculus (which is a functional model of computation) that has shaped much of early AI research.

Minimum Message Length (MML) principle introduced in 1968 is a formalization of induction developed within the framework of classical information theory, which establishes a trade-off between model complexity and fit-to-data by finding the minimal message that encodes both the model and the data. This trade-off is quite similar to the earlier forms of induction that Solomonoff developed, however independently discovered. Dowe points out that Occam’s razor means choosing the simplest single theory when data is equally matched, which MML formalizes perfectly (and is functional otherwise in the case of inequal fits) while Solomonoff induction maintains a mixture of alternative solutions. However, it was Solomonoff who first observed the importance of universality for AI (AI0-AI1). The plurality of probabilistic approaches to induction supports the importance of AI3 (as well as hinting that diversity of solutions may be useful). AI2, however, does not require much explanation. 

Hobbesian Morality and State

640px-family_of_henry_viii_an_allegory_of_the_tudor_succession-e1439521969820

Political Philosophy, as that branch of knowledge which consists of moral philosophy on the one hand and, and politics on the other, was treated systematically and in details by Hobbes in three different pieces of work viz., Elements of Law (1640), in the second and third parts of the Elementa Philosophiae, and in the Leviathan (1651). In all of these three presentations, his political philosophy shows traces of Galilean science and more so of Galileo’s ‘resolutive – compositive’ method. Everyone who has written about Hobbes’ political philosophy has interpreted his treatises as heavily dependent upon natural science, either for his material or method, which he heavily incorporates through out his works. However, the recognition of this fact on closer and meticulous scrutiny proves to be extremely questionable.

The propensity of natural sciences in his political philosophy is questioned, because Hobbes very well knew the fundamental differences between the two disciplines in the contest of material and method. On this awareness lay his basic conviction that political philosophy is essentially independent of natural science. This independence is corroborated because the principles of political philosophy are not borrowed from natural science, and indeed not from any sciences, but borrowed from experience, which one has of him, or to put it more accurately, are discovered by the efforts of self-knowledge and self-examination of everyone. The evidence of political philosophy on the one hand, is much easier to understand: its subjects and its concepts are not so remote from the average man as are the subjects and concepts of Mathematics which form the basis of natural science. On the other hand, ‘the politiques are the harder study of the two’; by reason of their passions, men obscure the, in itself, clear and simple knowledge of the norms which political philosophy builds up. Moreover, man with his passions and his self-seeking is the particular subject of political philosophy, and man opposes by every kind of hypocrisy the self-knowledge on which the proof of these norms rests.

Hobbes considered both political philosophy and the natural sciences as the main components of human knowledge. It can be said that Hobbes’ classification of the sciences is based on a classification of existing things into natural and the artificial. It is not so much the artificially produced things that are basically different from all natural things as the production, the human activity itself, i.e. man as an essentially productive being, especially as the being who by his art produces from his own nature the citizen or the State, who, by working on himself, makes himself into a citizen. In so far as man works on himself, influencing and changing his nature, so that he becomes a citizen, a part of that artificial being called the State, he is not a natural being. ‘Manners of men’ are something different from ‘natural causes’. The basic classification of existing things which in truth underlies Hobbes’ classification of the sciences is classification under nature on the one side, and under man as productive and active being on the other.

The question whether his political philosophy is intended to be naturalistic or anthropological, bears not only on the method, but above all on the matter selected. The significance of the antithesis between naturalistic and anthropological political philosophy for the matter becomes fully apparent if one grasps that this antithesis is only the abstract form of a concrete antithesis in the interpretation of and judgment of human nature which extends throughout the whole of Hobbes’ work. Hobbes summed up his theory of human nature as it underlies his political philosophy in ‘two most certain postulates of human nature’. The first postulate being that of ‘natural appetite’. Eclectic as he was, this postulate takes its roots as rooted in man’s sensuousness, in his animal nature. Like that of all animals, his is constant movement. But, the specific difference between man and other animals is that of reason. Thus man is less at the mercy of momentary sense impressions, he can envisage the future much better than can animals; for this very reason he is not like animals hungry only with the hunger of the moment, but also with future hunger, and thus he is the most predatory, the most cunning, the strongest, and most dangerous animal. This view of human appetite is a specifically Hobbesian view, but then is contradicted in Hobbes’ writings by his repeated and emphatic statement that human appetite is infinite in itself and not as a result of the infinite number of external impressions. Seeing this, one can note that human appetite is essentially distinguished from animal appetite in that the latter is nothing but reaction to external impressions, and, therefore, the animal desires only finite objects as such, while man spontaneously desires infinitely and this corresponds to the intention of Hobbes’ political philosophy. The two conceptions viz., mechanistic and vitalistic conceptions differ not only in substance, but also in method. The mechanistic conception is based on the mechanistic explanation of perception and on the general theory of motion; on the other hand, the apparently vitalistic conception is based not on any general scientific theory, but on insight into human nature, deepened and substantiated by self-knowledge and self-examination. In spite of these differences, the two conceptions below the surface have something in common, which allows us to characterize them both  as naturalistic. 

The naturalistic conception of human appetite is clearly expressed in the proposition that man desires power and ever greater power, spontaneously and continuously, in one jet of appetite, and not by reason of a summation of innumerable isolated desires caused by innumerable isolated perceptions

‘…in the first place, I put for a generall inclination of all mankind, a perpetuall and restless desire of power after power, that ceaseth only in Death’. And the cause of this, is not alwayes that a man hopes for a more intensive delight, than he has already attained to; or that he cannot be content with a moderate power: but because he cannot assure the power and the means to live well, which he hath present, without the acquisition of more’.

According to him, only the irrational striving after power, which is found more frequently than the rational striving, is to be taken as the natural human appetite. The only natural striving after power, and thus man’s natural appetite, is described by Hobbes as follows: ‘men from their birth, and naturally, scramble for everything they covet, and would have all the world, if they could, to fear and obey them’.1 In the case of man, animal desire is taken up and transformed by a spontaneous infinite and absolute desire which arises out of the depths of the man himself.

We find a more detailed definition of the irrational striving after power:

‘because there be some, that taking pleasure in contemplating their own power in the acts of conquest, which they pursue farther than their security requires; if others, that otherwise would be glad to be at ease within modest bounds, should  not by invasion increase their power, they would not be able, long time, by standing only on their defence, to subsist. And by consequence, such augmentation of dominion over men, being necessary to a man’s conservation, it ought to be allowed him’.

It is clearly seen here that rational permissible striving after power is in itself finite. The man guided by it would remain ‘within modest bounds’, would ‘be content with a moderate power’. Only the impermissible, irrational, lustful striving after power is infinite.

In four different arguments, Hobbes designated the characteristics in the difference between man and animal as the striving after honour and positions of honour, after precedence over others and recognition of this precedence by others, ambition, pride, and the passion for fame. Since man’s natural appetite is a striving after precedence over others and recognition of this precedence by others, the particularities of natural appetite, the passions, are nothing other than particular ways of striving after precedence and recognition. Speaking about the cause of madness, Hobbes says: “The Passion, whose violence, or continuance maketh Madnesse, is either great vaine-glory; which is commonly called Pride, and selfe-conceipt; or great Dejection of mind”. All passions and all forms of madness are modifications of conceit or of a sense of inferiority, or in principle, of the striving after precedence and recognition of that precedence.

The same conclusion is reached if one compares the arguments by which Hobbes in the three presentations of his political philosophy proves his assertion that the war of everyone against everyone arises of necessity from man’s very nature. Every man for that reason is the enemy of every other man, because each desires to surpass every other and therefore offends every other. The discrepancies between the three presentations shows that Hobbes himself never completed the proofs of his fundamental assertion, and, as is seen on closer inspection, did not complete them simply because he could not make up his mind explicitly to take as his point of departure the reduction of man’s natural appetite to vanity. At the end of the most important part of his work, “Leviathan”, Hobbes says:

‘Hitherto I have set forth the nature of Man, (whose Pride and other passions have compelled him to submit himselfe to Government;) together with the great power of the Governour, whom I compared to Leviathan, taking that comparison out of the last two verses of the one and fortieth of Job; where God having set forth the great power of Leviathan, called him the King of the Proud’.

The state is compared to Leviathan, because it and it especially is the ‘King of all the children of pride’. Only the State is capable of keeping pride down in the long run, indeed it has no other raison d’etre except that man’s natural appetite is pride, ambition, and vanity. 

Why could not Hobbes take man’s natural appetite, which is vanity as the basis of his political philosophy?  If this conception of natural appetite is right, if man by nature finds his pleasure in triumphing over all others, then man is by nature evil. But he did not dare to hold this consequence of his theory. For this very reason, in the Leviathan, he puts vanity in the end. Because man is by nature animal, he is not by nature evil, therefore he is as innocent as the animals; thus vanity cannot characterize his natural appetite. Hobbes in defence against the reproach that according to his theory man is by nature evil does not mention vanity at all. In laying the foundations of his political philosophy, Hobbes puts vanity more and more into the background in favour of innocent competition, innocent striving after power, innocent animal appetite, because the definition of man’s natural appetite in terms of vanity is intended as a moral judgment. He is finally obliged to attribute to the judges the wickedness which he disallows in the case of the guilty, the criminals; he betrays particularly in his description of the striving after power itself, that the innocence, neutrality, and moral indifference of that striving is only apparent. The apparent moral indifference arises simply and solely through abstraction of the necessary moral difference. Hobbes’ political philosophy rests not on the illusion of an amoral morality, but on a new morality, or, so to speak according to Hobbes’ intention, on a new grounding of the one eternal morality.

The second of the ‘two most certain postulates of human nature’ is ‘the postulate of human reason’. In accordance with the naturalistic reasoning this postulate is reduced to the principle of self-preservation: since the preservation of life is the condition sine qua non for the satisfaction of any appetite, it is the ‘primary good’. As a logical conclusion of this thought, Hobbes attempts to deduce natural right, natural law, and all the virtues from the principle of self-preservation. It is noteworthy that Hobbes prefers the negative expression ‘avoiding death’ to the positive expression ‘preserving life’. That preservation of life is the primary good is affirmed by reason alone. On the other hand, that death is the primary evil is affirmed by passion, the passion of fear of death. And as reason itself is powerless, man would not mind to think of the preservation of life as the primary and the most urgent good, if the passion of fear of death did not compel him to do so. According to Hobbes, the preservation of life is the primary good, an unhindered progress to ever further goals, a ‘continuall prospering’, in a word, happiness is the greatest good, but there is no supreme good in the enjoyment of which the spirit might find repose. On the other hand, death is the primary as well as the greatest and the supreme evil. For death is not only the negation of the supreme good; but at the same time, it is the negation of all the goods. Only through death has man an aim, the aim that is forced upon him by the sight of death, the aim of avoiding death. For this reason, Hobbes uses the negative expression ‘avoiding death’ to the positive expression ‘preserving life’. This is also because we fear death infinitely more than we desire life. 

But Hobbes also does not adhere to the theory of death as the supreme evil, since for him the tortured life is a greater evil as compared to death. So for him, an agonizing death is much more evil than death. But in contradiction, if Hobbes had considered agonizing death as the supremest evil, he would have attributed an ever-greater importance on medicine, which he tends to forget. When he says of an agonizing death that it is the greatest evil, he thinks exclusively of violent death at the hands of other men. This fear of getting killed at the hands of other men, is a mutual fear, i.e. it is a fear each man has of every other man as his potential murderer. This fear of a violent death, pre-rational in its origin, but rational in its effect, and not the rational principle of self-preservation, is, according to Hobbes, the root of all right and of all morality. He finally denied the moral values of all virtues which do not contribute to the making of the State, to consolidating peace, to protecting man against the danger of violent death, or, more exactly expressed, of all virtues which do not proceed from the fear of violent death.

Since, Hobbes reduces man’s natural appetite to vanity, he cannot but recognize the fear of a violent death, not the fear of a painful death, and certainly not the principle of the preservation of life as the principle of morality. The ever-greater triumph over others, and not the ever-increasing, but rationally increasing, power is the aim and happiness of natural man. ‘Continually to out-go the next before is felicity’. Man’s life may be compared to a race: ‘but this race we must suppose to have no other goal, nor other garland, but being foremost’. Absorbed in the race after the happiness of triumph, man cannot be aware of his dependence on the insignificant primary good, the preservation of life and limb; failing to recognize his bodily needs, man experiences only joys and sorrows of the mind, i.e. imaginary joys and sorrows. Living in the world of his imagination, he need do nothing, in order to convince himself of his superiority to others, but simply think out his deeds for himself; in this world, in which indeed ‘the whole world obeys him’, everything is accomplished according to his wishes. He can awaken himself from this dream world only when he feels in his own person, by bodily hurt, the resistance of the real world. ‘Men have no other means to acknowledge their own Darknesse, but onely by reasoning from the unforeseen mischances, that befall them in their ways’. Because man by nature lives in the dream of the happiness and triumph, of a glittering, imposing, apparent good, he requires a no less imposing power to awaken him from his dream: this imposing power is the imperious majesty of death.

The ideal condition for self-knowledge is, therefore, unforeseen mortal danger. The vain man, who, in his imagination, believes himself superior to others, cannot convince himself of the rightness of his estimate of himself; he requires the recognition of hiss superiority by others. He therefore steps outside his imagination. Now, either the others take his claim seriously and feel themselves slighted, or they do not take his claim seriously and he feels himself slighted. In either case the making of the claims leads to contempt. The one slighted longs for revenge. In order to avenge him he attacks the other, indifferent whether he loses his life in so doing. Unconcerned as to the preservation of his own life, he desires, however, above all that the other should remain alive; for ‘revenge aimeth not at the death, but at the captivity and subjection of an enemy…revenge aimeth at triumph, which over the dead is not’. The struggle which thus breaks out, in which, according to the opinion of both opponents, the object is not the killing, but the subjection of the other, of necessity becomes serious, because it is a struggle between bodies, a real struggle. From the beginning of the conflict, the two opponents have, without realizing and foreseeing it, completely left the imaginary world. At some point in the conflict, actual injury, or, more accurately, physical pain, arouses a fear for life. Fear moderates anger, puts the sense of being slighted into the background, and transforms the desire for revenge into hatred. The aim of the hater is no longer triumph over the enemy, but his death. The struggle for pre-eminence, about ‘trifles’, has become a life and death struggle. In this way natural man happens unforeseen upon the danger of death; in this way he comes to know this primary and greatest and supreme evil for the first time, to recognize death as the greatest and supreme evil in the moment of being irresistibly driven to fall back before death in order to struggle for his life. Only for a moment can he free himself from the danger of death by killing his enemy, for since every man is his enemy, after killing of the first enemy he is ‘again in the like danger of another’, indeed of all others. The killing of the enemy is thus the least far-sighted consequence of the withdrawal from death. In order to safeguard his life, not only for the moment, but also in the long run, man needs companions, with whose help he can successfully defend his life against the others. Companions can be gained in two ways, by force or by agreement. The former appears as if it stands in the midway between the killing of the enemy and agreement with him; so it is natural enough for him to try out the latter. Since fear can hardly be made manifest, but by some action dishonourable, that betrayeth the conscience of one’s own weakness; all men in whom the passion of courage or magnanimity have been predominated, have abstained from cruelty…In one word, therefore, the only law of actions in war is honour. Thus arises the relationship of master and servant. The victor who has safeguarded his honour becomes the master. The vanquished, who ‘submitteth…for fear of death’, who admits his weakness and with that has forfeited his honour, becomes the servant. The dominion of the master over the servant, despotic rule, is one form of the natural State, and as the other part of the natural State, patriarchy, is construed by Hobbes entirely according to the pattern of despotic rule, we may even say: despotic rule is the natural State. The artificial State, which is as such more perfect, arises when the two opponents are both seized with fear for their lives, overcome their vanity and shame of confessing their fear, and recognize as their real enemy not the rival, but ‘that terrible enemy of nature, death’, who, as their common enemy, forces them to mutual understanding, trust, and union, and thus procures them the possibility of completing the founding of the State for the purpose of providing safeguards for the longest possible term, against the common enemy. And while in the unforeseen life-and-death struggle, in which vanity comes to grief, the futility of vanity is shown, it is revealed in the concord of living, and of living in common, to which their pre-rational fear of death leads them, that the fear of death is appropriate to human conditions, and that it is ‘rational’. It is even ostensibly shown that it is only on the basis of fear of death that life comes to concord and that the fear of death is the only ‘postulate of natural reason’.

Hobbes distinguishes no precisely than any other moralist between legality and morality. Not the legality of the action, but the morality of the purpose, makes the just man. That man is just who fulfils the law because it is law and not for fear of punishment or for the sake of reputation. Although Hobbes states that those are ‘too severe, both to themselves, and others, that maintain, that the First motions of the mind, be Sinnes’, he yet ‘confesses’ that ‘it is safer to erre on that hand, than on the other’. In believing that the moral attitude, conscience, intention, is of more importance than the action, Hobbes is at one with the Christian tradition. He differs from this tradition at first sight only by his denial of the possibility that just and unjust actions depend wholly on the judgment of the individual conscience. In the state of nature every action is in principle permitted which the conscience of the individual recognizes as necessary for self-preservation, and every action is in principle forbidden which according to the judgment of the individual conscience does not serve the purpose of self-preservation. If, then, in the state of nature, any and every action is permitted, even in the state of nature not every intention is permitted, but only the intention of self-preservation. Thus the unequivocal distinction between just and unjust intentions holds even for the state of nature and is, therefore, absolute.

Hobbes expressly denies the existence of a law, as if it were a natural law, which obliged man unconditionally, and therefore obliged him even in the state of nature. He says: ‘These dictates of Reason, men use to call by the names of Lawes; but improperly: for they are but Conclusions, or Theoremes concerning what conduceth to the conservation and defence of themselves; whereas Law, properly is the word of him, that by right hath command over others’. Law as an obligation is the basis of a covenant between formerly free and unbound men. Thus ‘where no Covenant hath preceded, there hath no Right been transferred, and every man has right to everything…But when a Covenant is made, then to break it unjust: And the definition of injustice, is no other than the not Performance of Covenant’. The just attitude cannot be anything but earnest striving to keep one’s given word; and is therefore far from being obedience that it is, on the contrary, nothing else but proud self-reliance. From the Leviathan, it is clearly noticeable that opinion, far from being the origin of just attitude, is rather the only origin of the unjust attitude. Not pride, and still less obedience, but fear of violent death, is according to him the origin of the just intention. It makes possible the distinction between the attitude of an unjust man who obeys the laws of the State for fear of punishment, and the attitude of the just man, who for fear of death, and therefore from inner conviction, as it were once more accomplishing in himself the founding of the State, obeys the laws of the State. 

Since man is by nature fast in his imaginary world, it is only by unforeseen mischance that he can attain to knowledge of his own darkness and at the same time a modest and circumspect knowledge of the real world. That is to say: the world is originally revealed to man not by detachedly and spontaneously seeing its form, but by involuntary experience of its resistance. The least discriminating and the detached sense is the sense of touch. This explains the place of honour which is tacitly granted to the sense of touch in Hobbes’ physiology and psychology of perception; all sense-perception, particularly that of the most discriminating and detached sense, the sense of sight, is interpreted by experience of the sense of touch.

Thus it can be seen, that the moral and humanist antithesis of fundamentally unjust vanity and fundamentally just fear of violent death is the basis Hobbes’ political philosophy. As an objection, it can be called to effect that this antithesis is to be found in Hobbes’ political philosophy only because Hobbes had not yet completely freed himself from the influence of the Christian Biblical tradition. This antithesis is the ‘secularized’ form of the traditional antithesis between spiritual pride and fear of God, a secularized form which results from the Almighty God having been replaced by the over-mighty State, ‘the Mortall God’. Is this affiliation to the antithesis in Hobbes’ moral work right by itself?

On the contrary, this antithesis is an essential indispensable element, or, more accurately, the essential basis of, Hobbes’ political philosophy. Political philosophy deprived of its moral foundations is, indeed, Spinoza’s political philosophy, but not Hobbes’. Spinoza made might equivalent to right. Thanks to the moral basis of his political philosophy, Hobbes kept the possibility of acknowledging justice as such and distinguishing between right and might. Hobbes’ political philosophy is really based on knowledge of men, which is deepened and corroborated, by the self-knowledge and self-examination of the individual, and not on a general scientific and metaphysical theory. And because it is based on experience of human life, it can never, in spite of all the temptations of natural science, fall completely into the danger of abstraction from moral life and neglect of moral difference.

The contention is that Hobbes’ humanist moral motivation of his political philosophy is more original than the naturalistic motivation. The important points of his moral motivation were firmly established well before he turned his attention to natural science and especially to Euclid’s Elements. This discovery of Euclid was an epoch in his life; everything he thought and wrote after that is modified by this happening. His discovery lent maturity to his later works and whether this is the case, can be decided only after the sparse remnants of his youthful philosophy is meticulously studied.