Cthulhu Swims Left, Cthulhu Like Strauss, is not Christian

Nevertheless, Strauss’s unhappiness with the Left in the Cold War period is not tantamount to a categorical rejection of all leftist or modern thought per se….Strauss and his students largely agree with the traditional leftist dismissal of Christianity as an irrational influence on the political philosophy of the West. This fundamental consensus between Strauss and the Left, which has been neglected in most of the literature on Strauss, gravely affects their understanding of Anglo-American political thought. For Strauss was compelled to read out of this tradition any sign of a serious indebtedness to Christianity. Unlike the anti-democratic Far Right, which often faults Christianity for its universalist morality (e.g. charity) that made modern democracy possible, Strauss is ultimately critical of Christianity as a foundation for Anglo-American democracy because it is not sufficiently universalist (that is, intelligible to all human beings): it is sheer historicism to hold up one faith as the principal foundation of the West. As as result of this hermeneutical rationale, the very tradition that Strauss and his students wish to preserve as a  repository of rational accessible “eternal principles” is reinvented as a secular liberal artifice. (Leo Strauss and Anglo-American Democracy: Grant Havers)

Neoconservative thought is ultimately based on the notion that Christianity does not matter. In fact, Strauss’s understanding of European civilisation rejects the notion, first given express formulation by Aquinas, that there is no incompatibility between the Christian faith and reason. For Strauss, faith and reason were incompatible, yet influential upon each other. Whatever Strauss’s view of religion, it is clear that he felt that it had no obligatory right on reason: it existed in a separate domain. Sure, religion may be an influence, an inspiration, a tradition, etc.,  but if reason came to a conclusion separate to religion, reason had to be given its “latitude.” At its best, Straussian Neoconservatism is a secularism that is “respectful” towards religion, at worst, it plays cynical lip service to it.

Indeed, Strauss’s separation of faith and reason is contra to the Christian understanding of the two. Strauss may not have said much against Christianity, but the system he espouses is inherently incompatible with Christianity. In fact the lip service given to Christianity by the Neoconservative moment disguises the fact that that the secular agenda is still given primacy, and while attacks by an openly hostile Left may be easy to spot, the undermining of the Right goes unnoticed by an agent which talks about the importance of  “Athens and Jerusalem”, while pushing the metaphysics of the Left.

The importance of the dualistic hermeneutic in Strauss’s thought is hard to overstate, since it makes any significant attempt to spy rationality in faith almost impossible. It also throws into question Strauss’s respect for the tradition of Anglo-American democracy, whose main defenders, mightily attempted to distinguish “true religion” from superstitious dogma. If Strauss believes that no distinction is possible, does the religious basis for this civilization fall by the wayside? And, if this is the case, does the irreligious Left score the ultimate victory over the Right?

Athenian Secularism, Jacobin Secularism, Managerial Secularism, Socialist Secularism, Natsoc Secularism, Right secularism, Left secularism…….secularist market specialisation is still secularism. Cthulhu swims left because Cthulhu is a secularist.

Cthulhu swims left, Cthulhu like Strauss, is not Christian.

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Is There a Philosophy of Bundles and Fields? Drunken Risibility.

The bundle formulation of field theory is not at all motivated by just seeking a full mathematical generality; on the contrary it is just an empirical consequence of physical situations that concretely happen in Nature. One among the simplest of these situations may be that of a particle constrained to move on a sphere, denoted by S²; the physical state of such a dynamical system is described by providing both the position of the particle and its momentum, which is a tangent vector to the sphere. In other words, the state of this system is described by a point of the so-called tangent bundle TS² of the sphere, which is non-trivial, i.e. it has a global topology which differs from the (trivial) product topology of S² x R². When one seeks for solutions of the relevant equations of motion some local coordinates have to be chosen on the sphere, e.g. stereographic coordinates covering the whole sphere but a point (let us say the north pole). On such a coordinate neighbourhood (which is contractible to a point being a diffeomorphic copy of R²) there exists a trivialization of the corresponding portion of the tangent bundle of the sphere, so that the relevant equations of motion can be locally written in R² x R². At the global level, however, together with the equations, one should give some boundary conditions which will ensure regularity in the north pole. As is well known, different inequivalent choices are possible; these boundary conditions may be considered as what is left in the local theory out of the non-triviality of the configuration bundle TS².

Moreover, much before modem gauge theories or even more complicated new field theories, the theory of General Relativity is the ultimate proof of the need of a bundle framework to describe physical situations. Among other things, in fact, General Relativity assumes that spacetime is not the “simple” Minkowski space introduced for Special Relativity, which has the topology of R⁴. In general it is a Lorentzian four-dimensional manifold possibly endowed with a complicated global topology. On such a manifold, the choice of a trivial bundle M x F as the configuration bundle for a field theory is mathematically unjustified as well as physically wrong in general. In fact, as long as spacetime is a contractible manifold, as Minkowski space is, all bundles on it are forced to be trivial; however, if spacetime is allowed to be topologically non-trivial, then trivial bundles on it are just a small subclass of all possible bundles among which the configuration bundle can be chosen. Again, given the base M and the fiber F, the non-unique choice of the topology of the configuration bundle corresponds to different global requirements.

A simple purely geometrical example can be considered to sustain this claim. Let us consider M = S¹ and F = (-1, 1), an interval of the real line R; then ∃ (at least) countably many “inequivalent” bundles other than the trivial one Mö₀ = S¹ X F , i.e. the cylinder, as shown

Furthermore the word “inequivalent” can be endowed with different meanings. The bundles shown in the figure are all inequivalent as embedded bundles (i.e. there is no diffeomorphism of the ambient space transforming one into the other) but the even ones (as well as the odd ones) are all equivalent among each other as abstract (i.e. not embedded) bundles (since they have the same transition functions).

The bundles Mö_n (n being any positive integer) can be obtained from the trivial bundle Mö₀ by cutting it along a fiber, twisting n-times and then glueing again together. The bundle Mö₁ is called the Moebius band (or strip). All bundles Mö_n are canonically fibered on S¹, but just Mö₀ is trivial. Differences among such bundles are global properties, which for example imply that the even ones Mö_2k allow never-vanishing sections (i.e. field configurations) while the odd ones Mö_2k+1 do not.

Perverse Ideologies. Thought of the Day 100.0

Žižek (Fantasy as a Political Category A Lacanian Approach) says,

What we are thus arguing is not simply that ideology permeates also the alleged extra-ideological strata of everyday life, but that this materialization of ideology in the external materiality renders visible inherent antagonisms that the explicit formulation of ideology cannot afford to acknowledge. It is as if an ideological edifice, in order to function “normally,” must obey a kind of “imp of perversity” and articulate its inherent antagonism in the externality of its material existence.

In this fashion, Žižek recognizes an element of perversity in all ideologies, as a prerequisite for their “normal” functioning. This is because all ideologies disguise lack and thus desire through disavowal. They know that lack is there, but at the same time they believe it is eliminated. There is an object that takes over lack, that is to say the Good each ideology endorses, through imaginary means. If we generalize Žižek’s suggestion, we can either see all ideological relations mediated by a perverse liaison or perversion as a condition that simply helps the subjects relate to each other, when signification fails and they are confronted with the everlasting question of sexual difference, the non-representable dimension. Ideology, then, is just one solution that makes use of the perverse strategy when dealing with Difference. In any case, it is not pathological and cannot be determined mainly by relying on the role of disavowal. Instead of père-vers (this is a Lacanian neologism that denotes the meanings of “perversion” and “vers le père”, referring to the search for jouissance that does not abolish the division of the subject, her desire. In this respect, the père-vers is typical of both neurosis and perversion, where the Name-of-the-Father is not foreclosed and thereby complete jouissance remains unobtainable sexuality, that searches not for absolute jouissance, but jouissance related to desire, the political question is more pertinent to the père-versus, so to say, anything that goes against the recognition of the desire of the Other. Any attempt to disguise lack for instrumental purposes is a père-versus tactic.

To the extent that this external materialization of ideology is subjected to fantasmatic processes, it divulges nothing more than the perversity that organizes all social and political relations far from the sexual pathology associated with the pervert. The Other of power, this fictional Other that any ideology fabricates, is the One who disavows the discontinuities of the normative chain of society. Expressed through the signifiers used by leadership, this Other knows very well the cul-de-sac of the fictional view of society as a unified body, but still believes that unity is possible, substantiating this ideal.

The ideological Other disregards the impossibility of bridging Difference; therefore, it meets the perversion that it wants to associate with the extra-ordinary. Disengaging it from pathology, disavowal can be stated differently, as a prompt that says: “let’s pretend!” Pretend as if a universal harmony, good, and unity are feasible. Symbolic Difference is replaced with imaginary difference, which nourishes antagonism and hostility by fictionalizing an external threat that jeopardizes the unity of the social body. Thus, fantasy of the obscene extra-ordinary, who offends the conformist norm, is in itself a perverse fantasy. The Other knows very well that the pervert constitutes no threat, but still requires his punishment, moral reformation, or treatment.

The Only Maximally Extended, Future-directed, Null and Timelike Geodesics in Gödel Spacetime are Confined to a Submanifold. Drunken Risibility.

Let γ₁ be any maximally extended, future-directed, null geodesic confined to a submanifold N whose points all have some particular z ̃ value. Let q be any point in N whose r coordinate satisfies sinh²r = (√2 − 1)/2. Pick any point on γ₁. By virtue of the homogeneity of Gödel spacetime, we can find a (temporal orientation preserving) global isometry that maps that point to q and maps N to itself. Let γ₂ be the image of γ₁ under that isometry. We know that at q the vector (t ̃^a + kφ^a) is null if k = 2(1 + √2). So, by virtue of the isotropy of Gödel spacetime, we can find a global isometry that keeps q fixed, maps N to itself, and rotates γ₂ onto a new null geodesic γ₃ whose tangent vector at q is, at least, proportional to (t ̃^a + 2(1 + √2)φ^a), with positive proportionality factor. If, finally, we reparametrize γ₃ so that its tangent vector at q is equal to (t ̃^a + 2(1 + √2)φ^a), then the resultant curve must be a special null geodesic helix through q since (up to a uniform parameter shift) there can be only one (maximally extended) geodesic through q that has that tangent vector there.

The corresponding argument for timelike geodesics is almost the same. Let γ₁ this time be any maximally extended, future-directed, timelike geodesic confined to a submanifold N whose points all have some particular z ̃ value. Let v be the speed of that curve relative to t ̃^a. (The value as determined at any point must be constant along the curve since it is a geodesic.). Further, let q be any point in N whose r coordinate satisfies √2(sinh2r)/(cosh2r) = v. (We can certainly find such a point since √2 (sinh2r)/(cosh2r) runs through all values between 0 and 1 as r ranges between 0 and r_c/2) Now we can proceed in three stages, as before. We map γ₁ to a curve that runs through q. Then we rotate that curve so that its tangent vector (at q) is aligned with (t ̃^a + kφ^a) for the appropriate value of k, namely k = 2 √2/(1 − 2 sinh²r). Finally, we reparametrize the rotated curve so that it has that vector itself as its tangent vector at q. That final curve must be one of our special helical geodesics by the uniqueness theorem for geodesics.

The special timelike and null geodesics we started with – the special helices centered on the axis A – exhibit various features. Some are exhibited by all timelike and null geodesics (confined to a z ̃ = constant submanifold); some are not. It is important to keep track of the difference. What is at issue is whether the features can or cannot be captured in terms of g_ab, t ̃^a, and z ̃^a (or whether they make essential reference to the coordinates t ̃, r, φ themselves). So, for example, if a curve is parametrized by s, one might take its vertical “pitch” (relative to t ̃) at any point to be given by the value of dt ̃/ds there. Understood this way, the vertical pitch of the special helices centered on A is constant, but that of other timelike and null geodesics is not. For this reason, it is not correct to think of the latter, simply, as “translated” versions of the former. On the other hand, the following is true of all timelike and null geodesics (confined to a z ̃ = constant submanifold). If we project them (via t ̃^a) onto a two-dimensional submanifold characterized by constant values for t ̃ as well as z ̃, the result is a circle.

Here is another way to make the point. Consider any timelike or null geodesic γ (confined to a z ̃ = constant submanifold). It certainly need not be centered on the axis A and need not have constant vertical pitch relative to t ̃. But we can always find a (new) axis A′ and a new set of cylindrical coordinates t ̃′, r′, φ′ adapted to A′ such that γ qualifies as a special helical geodesic relative to those coordinates. In particular, it will have constant vertical pitch relative to t ̃′.

Let us now consider all the timelike and null geodesics that pass through some point p (and are confined to a z ̃ = constant submanifold). It may as well be on the original axis A. We can better visualize the possibilities if we direct our attention to the circles that arise after projection (via t ̃^a). The figure below shows a two-dimensional submanifold through p on which t ̃ and z ̃ are both constant. The dotted circle has radius r_c. Once again, that is the “critical radius” at which the rotational Killing field φ^a is null. Call this dotted circle the “critical circle.” The circles that pass through p and have radius r = r_c/2 are projections of null geodesics. Each shares exactly one point with the critical circle. In contrast, the circles of smaller radius that pass through p are the projections of timelike geodesics. The figure captures one of the claims – namely, that no timelike or null geodesic that passes through a point can “escape” to a radial distance from it greater than r_c.

Figure: Projections of timelike and null geodesics in Gödel spacetime. r_c is the “critical radius” at which the rotational Killing field φ^a centered at p is null

Gödel spacetime exhibits a “boomerang effect.” Suppose an individual is at rest with respect to the cosmic source fluid in Gödel spacetime (and so his worldline coincides with some t ̃-line). If that individual shoots a gun at some point, in any direction orthogonal to z ̃^a, then, no matter what the muzzle speed of the gun, the bullet will eventually come back and hit him (unless it hits something else first or disintegrates).

A Time Traveler in Gödel Spacetime

Given any two points p and q in Gödel spacetime, there is a smooth, future-directed timelike curve that runs from p and q. (Hence, since we can always combine timelike curves that run in the two directions and smooth out the joints, there is a smooth, closed timelike curve that contains p and q.)

A time traveler in Gödel spacetime can start at any point p, return to that point, and stop off at any other desired point q along the way. To see why this holds, consider the figure above. It gives, at least, a rough, qualitative picture of Gödel spacetime with one dimension suppressed. We may as well take the central line to be the axis A and take p to be a point on A. (By homogeneity, there is no loss in generality in doing so.) Notice first that given any other point p′ on A, no matter how “far down,” there is a smooth, future-directed timelike curve that runs from p to p′. We can think of it as arising in three stages. (i) By moving “radially outward and upward” from p (i.e., along a future-directed timelike curve whose tangent vector field is of the form t ̃^a + αr^a, with α positive), we can reach a point p₁ with coordinate value r > r_c. At that radius, we know, φ^a is timelike and future-directed. So we can find an ε > 0 such that (−εt ̃^a + φ^a) is also timelike and future-directed there. (ii) Now consider the maximally extended, future-directed timelike curve γ through p₁ whose tangent is everywhere equal to (−εt ̃^a + φ^a) (for that value of ε). It is a spiral-shaped curve of fixed radius, with “downward pitch.” By following γ far enough, we can reach a point p₂ that is well “below” p′. Now, finally, (iii) we can reach p′ by working our way upward and inward from p₂ via a curve whose tangent vector is the form t ̃^a + αr^a, but now with α negative. It remains only to smooth out the “joints” at intermediate points p₁ and p₂ to arrive at a smooth timelike curve that, as required, runs from p to p′.

Now consider any point q. It might not be possible to reach q from p in the same simple way we went from p to p₁ – i.e., along a future-directed timelike curve that moves radially outward and upward – p might be too “high” for that. But we can get around this problem by first moving to an intermediate point p′ on A sufficiently “far down” – we have established that that is possible – and then going from there to q.

Other interesting features of Gödel spacetime are closely related to the existence of closed timelike curves. So, for example, a slice (in any relativistic spacetime) is a spacelike hypersurface that, as a subset of the background manifold, is closed. We can think of it as a candidate for a “global simultaneity slice.” It turns out that there are no slices in Gödel spacetime. More generally, given any relativistic spacetime, if it is temporally orientable and simply connected and has smooth closed timelike curves through every point, then it does not admit any slices.

Negation. Thought of the Day 99.0

Negation reveals more a neurotic attitude towards jouissance, denounced as a perverse desire, that dominates both political and social life. Negation presupposes the acquisition of the meaning of “No” and it suggests a vigorous and compromising attitude between an idea remaining unconscious (repressed) and conscious at the same time. Thus, to negate means to go against the law and succumb to jouissance in a concealed way. Negating castration releases a destructive force against the paternal function, a force fuelled with jouissance. It is not the symbolic reality, but the non-symbolic real as a threatening source that is being negated. This means that the real is actually expressed through symbolic means, but in a negative form. Disavowal, involves a sexualization of the object precluding the threat of castration as punishment. But the threat is still there in the unconscious, whereas negation means that castration is negated even in the unconscious. Negation does not suggest a compromise (in the form of a splitting of the ego) between the denial of something and its acceptance, as disavowal does. Rather, it maintains the repressed status of castration by allowing the latter to be unconsciously expressed in its negated status. So, negation has a more hostile and aggressive attitude (originating in the death drive) towards castration, whereas disavowal originates in Eros. Disavowal does not go against castration, but keeps it at bay by not acknowledging it, which is different from negating it. In this way, the sexualization of the object (the mother’s phallus) remains intact. Therefore, the responsibility for extracting jouissance is also negated.

Option Spread. Drunken Risibility.

The term spread refers to the difference in premiums between the purchase and sale of options. An option spread is the simultaneous purchase of one or more options contracts and sale of the equivalent number of options contracts, in a different series of the class of options. A spread could involve the same underlying:

•  Buying and selling calls, or
•  Buying and selling puts.

Combining puts and calls into groups of two or more makes it feasible to design derivatives with interesting payoff profiles. The profit and loss outcomes depend on the options used (puts or calls); positions taken (long or short); whether their strike prices are identical or different; and the similarity or difference of their exercise dates. Among directional positions are bullish vertical call spreads, bullish vertical put spreads, bearish vertical spreads, and bearish vertical put spreads.

If the long position has a higher premium than the short position, this is known as a debit spread, and the investor will be required to deposit the difference in premiums. If the long position has a lower premium than the short position, this is a credit spread, and the investor will be allowed to withdraw the difference in premiums. The spread will be even if the premiums on each side results are the same.

A potential loss in an option spread is determined by two factors:

• Strike price
• Expiration date

If the strike price of the long call is greater than the strike price of the short call, or if the strike price of the long put is less than the strike price of the short put, a margin is required because adverse market moves can cause the short option to suffer a loss before the long option can show a profit.

A margin is also required if the long option expires before the short option. The reason is that once the long option expires, the trader holds an unhedged short position. A good way of looking at margin requirements is that they foretell potential loss. Here are, in a nutshell, the main option spreadings.

A calendar, horizontal, or time spread is the simultaneous purchase and sale of options of the same class with the same exercise prices but with different expiration dates. A vertical, or price or money, spread is the simultaneous purchase and sale of options of the same class with the same expiration date but with different exercise prices. A bull, or call, spread is a type of vertical spread that involves the purchase of the call option with the lower exercise price while selling the call option with the higher exercise price. The result is a debit transaction because the lower exercise price will have the higher premium.

• The maximum risk is the net debit: the long option premium minus the short option premium.
• The maximum profit potential is the difference in the strike prices minus the net debit.
• The breakeven is equal to the lower strike price plus the net debit.

A trader will typically buy a vertical bull call spread when he is mildly bullish. Essentially, he gives up unlimited profit potential in return for reducing his risk. In a vertical bull call spread, the trader is expecting the spread premium to widen because the lower strike price call comes into the money first.

Vertical spreads are the more common of the direction strategies, and they may be bullish or bearish to reflect the holder’s view of market’s anticipated direction. Bullish vertical put spreads are a combination of a long put with a low strike, and a short put with a higher strike. Because the short position is struck closer to-the-money, this generates a premium credit.

Bearish vertical call spreads are the inverse of bullish vertical call spreads. They are created by combining a short call with a low strike and a long call with a higher strike. Bearish vertical put spreads are the inverse of bullish vertical put spreads, generated by combining a short put with a low strike and a long put with a higher strike. This is a bearish position taken when a trader or investor expects the market to fall.

The bull or sell put spread is a type of vertical spread involving the purchase of a put option with the lower exercise price and sale of a put option with the higher exercise price. Theoretically, this is the same action that a bull call spreader would take. The difference between a call spread and a put spread is that the net result will be a credit transaction because the higher exercise price will have the higher premium.

• The maximum risk is the difference in the strike prices minus the net credit.
• The maximum profit potential equals the net credit.
• The breakeven equals the higher strike price minus the net credit.

The bear or sell call spread involves selling the call option with the lower exercise price and buying the call option with the higher exercise price. The net result is a credit transaction because the lower exercise price will have the higher premium.

A bear put spread (or buy spread) involves selling some of the put option with the lower exercise price and buying the put option with the higher exercise price. This is the same action that a bear call spreader would take. The difference between a call spread and a put spread, however, is that the net result will be a debit transaction because the higher exercise price will have the higher premium.

• The maximum risk is equal to the net debit.
• The maximum profit potential is the difference in the strike
  prices minus the net debit.
• The breakeven equals the higher strike price minus the net debit.

An investor or trader would buy a vertical bear put spread because he or she is mildly bearish, giving up an unlimited profit potential in return for a reduction in risk. In a vertical bear put spread, the trader is expecting the spread premium to widen because the higher strike price put comes into the money first.

So, investors and traders who are bullish on the market will either buy a bull call spread or sell a bull put spread. But those who are bearish on the market will either buy a bear put spread or sell a bear call spread. When the investor pays more for the long option than she receives in premium for the short option, then the spread is a debit transaction. In contrast, when she receives more than she pays, the spread is a credit transaction. Credit spreads typically require a margin deposit.

Žižek’s Dialectical Coincidentia Oppositorium. Thought of the 98.0

Without doubt, the cogent interlacing of Lacanian theorization with Hegelianism manifests Žižek’s prowess in articulating a highly pertinent critique of ideology for our epoch, but whether this comes from a position of Marxist orthodoxy or a position of a Lacanian doctrinaire who monitors Marxist politics is an open question.

Through this Lacanian prism, Žižek sees subjectivity as fragmented and decentred, considering its subordinate status to the unsurpassable realm of the signifiers. The acquisition of a consummate identity dwells in impossibility, in as much as it is bound to desire, provoked by a lacuna which is impossible to fill up. Thus, for Žižek, socio-political relations evolve from states of lack, linguistic fluidity, and contingency. What temporarily arrests this fluid state of the subject’s slithering in the realm of the signifiers, giving rise to her self-identity, is what Lacan calls point de capiton. The term refers to certain fundamental “anchoring” points in the signifying chain where the signifier is tied to the signified, providing an illusionary stability in signification. Laclau and Mouffe (Hegemony and Socialist Strategy Towards a Radical Democratic Politics) were the first to make use of the idea of the point de capiton in relation to hegemony and the formation of identities. In this context, ideology is conceptualized as a terrain of firm meanings, determined and comprised by numerous points de capiton (Zizek The Sublime Object of Ideology).

The real is the central Lacanian concept that Žižek implements in his rhetoric. He associates the real with antagonism (e.g., class conflict) as the unsymbolizable and irreducible gap that lies in the heart of the socio-symbolic order and around which society is formed. As Žižek argues, “class struggle designates the very antagonism that prevents the objective (social) reality from constituting itself as a self-enclosed whole” (Renata Salecl, Slavoj Zizek-Gaze and Voice As Love Objects). This logic is indebted to Laclau and Mouffe, who were the first to postulate that social antagonism is what impedes the closure of society, marking thus its impossibility. Žižek expanded this view and associated antagonism with the notion of the real.

Functioning as a hegemonic fantasmatic veil, ideology covers the lacuna of the symbolic, in the form of a fantasy, so that it protracts desire and hence subjectivity. On the imaginary level, ideology functions as the “mirror” that reflects antagonisms, that is to say, the real unrepresentable kernel that undermines the political. Around this emptiness of representation, the fictional narrative of ideology, its meaning, is to unfurl. The role of socio-ideological fantasy is to provide consistency to the symbolic order by veiling its void, and to foster the illusion of a coherent social unity.

Nevertheless, fantasy has both unifying and disjunctive features, as its role is to fill the void of the symbolic, but also to circumscribe this void. According to Žižek, “the notion of fantasy offers an exemplary case of the dialectical coincidentia oppositorium”. On the one side, it provides a “hallucinatory realisation of desire” and on the other side, it evokes disturbing images about the Other’s jouissance to which the subject has no (symbolic or imaginary) access. In so reasoning, ideology promises unity and, at the same time, creates another fantasy, where the failure of acquiring the anticipated ideological unity is ascribed.

Pertaining to Jacques Derrida’s work Specters of Marx (Specters of Marx The State of the Debt, The Work of Mourning; the New International), where the typical ontological conception of the living is seen to be incomplete and inseparable from the spectre, namely, a ghostly embodiment that haunts the living present (Derrida introduces the notion of hauntology to refer to this pseudo-material incarnation of the spirit that haunts and challenges ontological present), Žižek elaborates the spectral apparitions of the real in the politico–ideological domain. He makes a distinction between this “spectre” and “symbolic fiction”, that is, reality per se. Both have a common fantasmatic hypostasis, yet they perform antithetical functions. Symbolic fiction forecloses the real antagonism at the crux of reality, only to return as a spectre, as another fantasy.

Synthetic Structured Financial Instruments. Note Quote.

An option is common form of a derivative. It’s a contract, or a provision of a contract, that gives one party (the option holder) the right, but not the obligation to perform a specified transaction with another party (the option issuer or option writer) according to specified terms. Options can be embedded into many kinds of contracts. For example, a corporation might issue a bond with an option that will allow the company to buy the bonds back in ten years at a set price. Standalone options trade on exchanges or Over The Counter (OTC). They are linked to a variety of underlying assets. Most exchange-traded options have stocks as their underlying asset but OTC-traded options have a huge variety of underlying assets (bonds, currencies, commodities, swaps, or baskets of assets). There are two main types of options: calls and puts:

• Call options provide the holder the right (but not the obligation) to purchase an underlying asset at a specified price (the strike price), for a certain period of time. If the stock fails to meet the strike price before the expiration date, the option expires and becomes worthless. Investors buy calls when they think the share price of the underlying security will rise or sell a call if they think it will fall. Selling an option is also referred to as ”writing” an option.
• Put options give the holder the right to sell an underlying asset at a specified price (the strike price). The seller (or writer) of the put option is obligated to buy the stock at the strike price. Put options can be exercised at any time before the option expires. Investors buy puts if they think the share price of the underlying stock will fall, or sell one if they think it will rise. Put buyers – those who hold a “long” – put are either speculative buyers looking for leverage or “insurance” buyers who want to protect their long positions in a stock for the period of time covered by the option. Put sellers hold a “short” expecting the market to move upward (or at least stay stable) A worst-case scenario for a put seller is a downward market turn. The maximum profit is limited to the put premium received and is achieved when the price of the underlyer is at or above the option’s strike price at expiration. The maximum loss is unlimited for an uncovered put writer.

Coupon is the annual interest rate paid on a bond, expressed as percentage of the face value.

Coupon rate or nominal yield = annual payments ÷ face value of the bond

Current yield = annual payments ÷ market value of the bond

The reason for these terms to be briefed here through their definitions from investopedia lies in the fact that these happen to be pillars of synthetic financial instruments, to which we now take a detour.

According to the International Financial Reporting Standards (IFRS), a synthetic instrument is a financial product designed, acquired, and held to emulate the characteristics of another instrument. For example, such is the case of a floating-rate long-term debt combined with an interest rate swap. This involves

• Receiving floating payments
• Making fixed payments, thereby synthesizing a fixed-rate long-term debt

Another example of a synthetic is the output of an option strategy followed by dealers who are selling synthetic futures for a commodity that they hold by using a combination of put and call options. By simultaneously buying a put option in a given commodity, say, gold, and selling the corresponding call option, a trader can construct a position analogous to a short sale in the commodity’s futures market.

Because the synthetic short sale seeks to take advantage of price disparities between call and put options, it tends to be more profitable when call premiums are greater than comparable put premiums. For example, the holder of a synthetic short future will profit if gold prices decrease and incur losses if gold prices increase.

By analogy, a long position in a given commodity’s call option combined with a short sale of the same commodity’s futures creates price protection that is similar to that gained through purchasing put options. A synthetic put seeks to capitalize on disparities between call and put premiums.

Basically, synthetic products are covered options and certificates characterized by identical or similar profit and loss structures when compared with traditional financial instruments, such as equities or bonds. Basket certificates in equities are based on a specific number of selected stocks.

A covered option involves the purchase of an underlying asset, such as equity, bond, currency, or other commodity, and the writing of a call option on that same asset. The writer is paid a premium, which limits his or her loss in the event of a fall in the market value of the underlying. However, his or her potential return from any increase in the asset’s market value is conditioned by gains limited by the option’s strike price.

The concept underpinning synthetic covered options is that of duplicating traditional covered options, which can be achieved by both purchase of the underlying asset and writing of the call option. The purchase price of such a product is that of the underlying, less the premium received for the sale of the call option.

Moreover, synthetic covered options do not contain a hedge against losses in market value of the underlying. A hedge might be emulated by writing a call option or by calculating the return from the sale of a call option into the product price. The option premium, however, tends to limit possible losses in the market value of the underlying.

Alternatively, a synthetic financial instrument is done through a certificate that accords a right, based on either a number of underlyings or on having a value derived from several indicators. This presents a sense of diversification over a range of risk factors. The main types are

• Index certificates
• Region certificates
• Basket certificates

By being based on an official index, index certificates reflect a given market’s behavior. Region certificates are derived from a number of indexes or companies from a given region, usually involving developing countries. Basket certificates are derived from a selection of companies active in a certain industry sector.

An investment in index, region, or basket certificates fundamentally involves the same level of potential loss as a direct investment in the corresponding assets themselves. Their relative advantage is diversification within a given specified range; but risk is not eliminated. Moreover, certificates also carry credit risk associated to the issuer.

Also available in the market are compound financial instruments, a frequently encountered form being that of a debt product with an embedded conversion option. An example of a compound financial instrument is a bond that is convertible into ordinary shares of the issuer. As an accounting standard, the IFRS requires the issuer of such a financial instrument to present separately on the balance sheet the

• Equity component
• Liability component

On initial recognition, the fair value of the liability component is the present value of the contractually determined stream of future cash flows, discounted at the rate of interest applied at that time by the market to substantially similar cash flows. These should be characterized by practically the same terms, albeit without a conversion option. The fair value of the option comprises its

• Time value
• Intrinsic value (if any)

The IFRS requires that on conversion of a convertible instrument at maturity, the reporting company derecognizes the liability component and recognizes it as equity. Embedded derivatives are an interesting issue inasmuch as some contracts that themselves are not financial instruments may have financial instruments embedded in them. This is the case of a contract to purchase a commodity at a fixed price for delivery at a future date.

Contracts of this type have embedded in them a derivative that is indexed to the price of the commodity, which is essentially a derivative feature within a contract that is not a financial derivative. International Accounting Standard 39 (IAS 39) of the IFRS requires that under certain conditions an embedded derivative is separated from its host contract and treated as a derivative instrument. For instance, the IFRS specifies that each of the individual derivative instruments that together constitute a synthetic financial product represents a contractual right or obligation with its own terms and conditions. Under this perspective,

• Each is exposed to risks that may differ from the risks to which other financial products are exposed.
• Each may be transferred or settled separately.

Therefore, when one financial product in a synthetic instrument is an asset and another is a liability, these two do not offset each other. Consequently, they should be presented on an entity’s balance sheet on a net basis, unless they meet specific criteria outlined by the aforementioned accounting standards.

Like synthetics, structured financial products are derivatives. Many are custom-designed bonds, some of which (over the years) have presented a number of problems to their buyers and holders. This is particularly true for those investors who are not so versatile in modern complex instruments and their further-out impact.

Typically, instead of receiving a fixed coupon or principal, a person or company holding a structured note will receive an amount adjusted according to a fairly sophisticated formula. Structured instruments lack transparency; the market, however, seems to like them, the proof being that the amount of money invested in structured notes continues to increase. One of many examples of structured products is the principal exchange-rate-linked security (PERLS). These derivative instruments target changes in currency rates. They are disguised to look like bonds, by structuring them as if they were debt instruments, making it feasible for investors who are not permitted to play in currencies to place bets on the direction of exchange rates.

For instance, instead of just repaying principal, a PERLS may multiply such principal by the change in the value of the dollar against the euro; or twice the change in the value of the dollar against the Swiss franc or the British pound. The fact that this repayment is linked to the foreign exchange rate of different currencies sees to it that the investor might be receiving a lot more than an interest rate on the principal alone – but also a lot less, all the way to capital attrition. (Even capital protection notes involve capital attrition since, in certain cases, no interest is paid over their, say, five-year life cycle.)

Structured note trading is a concept that has been subject to several interpretations, depending on the time frame within which the product has been brought to the market. Many traders tend to distinguish between three different generations of structured notes. The elder, or first generation, usually consists of structured instruments based on just one index, including

• Bull market vehicles, such as inverse floaters and cap floaters
• Bear market instruments, which are characteristically more leveraged, an example being the superfloaters

Bear market products became popular in 1993 and 1994. A typical superfloater might pay twice the London Interbank Offered Rate (LIBOR) minus 7 percent for two years. At currently prevailing rates, this means that the superfloater has a small coupon at the beginning that improves only if the LIBOR rises. Theoretically, a coupon that is below current market levels until the LIBOR goes higher is much harder to sell than a big coupon that gets bigger every time rates drop. Still, bear plays find customers.

Second-generation structured notes are different types of exotic options; or, more precisely, they are yet more exotic than superfloaters, which are exotic enough in themselves. There exist serious risks embedded in these instruments, as such risks have never been fully appreciated. Second-generation examples are

• Range notes, with embedded binary or digital options
• Quanto notes, which allow investors to take a bet on, say, sterling London Interbank Offered Rates, but get paid in dollar.

There are different versions of such instruments, like you-choose range notes for a bear market. Every quarter the investor has to choose the “range,” a job that requires considerable market knowledge and skill. For instance, if the range width is set to 100 basis points, the investor has to determine at the start of the period the high and low limits within that range, which is far from being a straight job.

Surprisingly enough, there are investors who like this because sometimes they are given an option to change their mind; and they also figure their risk period is really only one quarter. In this, they are badly mistaken. In reality even for banks you-choose notes are much more difficult to hedge than regular range notes because, as very few people appreciate, the hedges are both

• Dynamic
• Imperfect

There are as well third-generation notes offering investors exposure to commodity or equity prices in a cross-category sense. Such notes usually appeal to a different class than fixed-income investors. For instance, third-generation notes are sometimes purchased by fund managers who are in the fixed-income market but want to diversify their exposure. In spite of the fact that the increasing sophistication and lack of transparency of structured financial instruments sees to it that they are too often misunderstood, and they are highly risky, a horde of equity-linked and commodity-linked notes are being structured and sold to investors. Examples are LIBOR floaters designed so that the coupon is “LIBOR plus”:

The pros say that flexibly structured options can be useful to sophisticated investors seeking to manage particular portfolio and trading risks. However, as a result of exposure being assumed, and also because of the likelihood that there is no secondary market, transactions in flexibly structured options are not suitable for investors who are not

• In a position to understand the behavior of their intrinsic value
• Financially able to bear the risks embedded in them when worst comes to worst

It is the price of novelty, customization, and flexibility offered by synthetic and structured financial instruments that can be expressed in one four-letter word: risk. Risk taking is welcome when we know how to manage our exposure, but it can be a disaster when we don’t – hence, the wisdom of learning ahead of investing the challenges posed by derivatives and how to be in charge of risk control.

Killing Fields

Let κ^a be a smooth field on our background spacetime (M, g_ab). κ^a is said to be a Killing field if its associated local flow maps Γ_s are all isometries or, equivalently, if £_κ g_ab = 0. The latter condition can also be expressed as ∇(_aκ_b) = 0.

Any number of standard symmetry conditions—local versions of them, at least can be cast as claims about the existence of Killing fields. Local, because killing fields need not be complete, and their associated flow maps need not be defined globally.

(M, g_ab) is stationary if it has a Killing field that is everywhere timelike.

(M, g_ab) is static if it has a Killing field that is everywhere timelike and locally hypersurface orthogonal.

(M, g_ab) is homogeneous if its Killing fields, at every point of M, span the tangent space.

In a stationary spacetime there is, at least locally, a “timelike flow” that preserves all spacetime distances. But the flow can exhibit rotation. Think of a whirlpool. It is the latter possibility that is ruled out when one passes to a static spacetime. For example, Gödel spacetime, is stationary but not static.

Let κ^a be a Killing field in an arbitrary spacetime (M, g_ab) (not necessarily Minkowski spacetime), and let γ : I → M be a smooth, future-directed, timelike curve, with unit tangent field ξ^a. We take its image to represent the worldline of a point particle with mass m > 0. Consider the quantity J = (P^aκ_a), where P^a = mξ^a is the four-momentum of the particle. It certainly need not be constant on γ[I]. But it will be if γ is a geodesic. For in that case, ξⁿ∇_nξ^a = 0 and hence

ξⁿ∇_nJ = m(κ_a ξⁿ∇_nξ^a + ξⁿξ^a ∇_nκ_a) = mξⁿξ^a ∇(_nκ_a) = 0

Thus, J is constant along the worldlines of free particles of positive mass. We refer to J as the conserved quantity associated with κ^a. If κ^a is timelike, we call J the energy of the particle (associated with κ^a). If it is spacelike, and if its associated flow maps resemble translations, we call J the linear momentum of the particle (associated with κ^a). Finally, if κ^a is spacelike, and if its associated flow maps resemble rotations, then we call J the angular momentum of the particle (associated with κ^a).

It is useful to keep in mind a certain picture that helps one “see” why the angular momentum of free particles (to take that example) is conserved. It involves an analogue of angular momentum in Euclidean plane geometry. Figure below shows a rotational Killing field κ^a in the Euclidean plane, the image of a geodesic (i.e., a line) L, and the tangent field ξ^a to the geodesic. Consider the quantity J = ξ^aκ_a, i.e., the inner product of ξ^a with κ^a – along L, and we can better visualize the assertion.

Figure: κ^a is a rotational Killing field. (It is everywhere orthogonal to a circle radius, and is proportional to it in length.) ξ^a is a tangent vector field of constant length on the line L. The inner product between them is constant. (Equivalently, the length of the projection of κ^a onto the line is constant.)

Let us temporarily drop indices and write κ·ξ as one would in ordinary Euclidean vector calculus (rather than ξ^aκ_a). Let p be the point on L that is closest to the center point where κ vanishes. At that point, κ is parallel to ξ. As one moves away from p along L, in either direction, the length ∥κ∥ of κ grows, but the angle ∠(κ,ξ) between the vectors increases as well. It should seem at least plausible from the picture that the length of the projection of κ onto the line is constant and, hence, that the inner product κ·ξ = cos(∠(κ , ξ )) ∥κ ∥ ∥ξ ∥ is constant.

That is how to think about the conservation of angular momentum for free particles in relativity theory. It does not matter that in the latter context we are dealing with a Lorentzian metric and allowing for curvature. The claim is still that a certain inner product of vector fields remains constant along a geodesic, and we can still think of that constancy as arising from a compensatory balance of two factors.

Let us now turn to the second type of conserved quantity, the one that is an attribute of extended bodies. Let κ^a be an arbitrary Killing field, and let T_ab be the energy-momentum field associated with some matter field. Assume it satisfies the conservation condition (∇_aT^ab = 0). Then (T^abκ_b) is divergence free:

∇_a(T^abκ_b) = κ_b∇_aT^ab + T^ab∇_aκ_b = T^ab∇(_aκ_b) = 0

(The second equality follows from the conservation condition and the symmetry of T^ab; the third follows from the fact that κ^a is a Killing field.) It is natural, then, to apply Stokes’s theorem to the vector field (T^abκ_b). Consider a bounded system with aggregate energy-momentum field T_ab in an otherwise empty universe. Then there exists a (possibly huge) timelike world tube such that T_ab vanishes outside the tube (and vanishes on its boundary).

Let S₁ and S₂ be (non-intersecting) spacelike hypersurfaces that cut the tube as in the figure below, and let N be the segment of the tube falling between them (with boundaries included).

Figure: The integrated energy (relative to a background timelike Killing field) over the intersection of the world tube with a spacelike hypersurface is independent of the choice of hypersurface.

By Stokes’s theorem,

∫_S2(T^abκ_b)dS_a – ∫_S1(T^abκ_b)dS_a = ∫_S2∩∂N(T^abκ_b)dS_a – ∫_S1∩∂N(T^abκ_b)dS_a

= ∫_∂N(T^abκ_b)dS_a = ∫_N∇_a(T^abκ_b)dV = 0

Thus, the integral ∫_S(T^abκ_b)dS_a is independent of the choice of spacelike hypersurface S intersecting the world tube, and is, in this sense, a conserved quantity (construed as an attribute of the system confined to the tube). An “early” intersection yields the same value as a “late” one. Again, the character of the background Killing field κ^a determines our description of the conserved quantity in question. If κ^a is timelike, we take ∫_S(T^abκ_b)dS_a to be the aggregate energy of the system (associated with κ^a). And so forth.