Cthulhu Swims Left, Cthulhu Like Strauss, is not Christian

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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.

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

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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 Mön (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 Mön 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 Mö2k allow never-vanishing sections (i.e. field configurations) while the odd ones Mö2k+1 do not.

Perverse Ideologies. Thought of the Day 100.0

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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 + kφa) 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)φa), with positive proportionality factor. If, finally, we reparametrize γ3 so that its tangent vector at q is equal to (t ̃a + 2(1 + √2)φa), 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 rc/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 + kφa) 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 gab, 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 rc. Once again, that is the “critical radius” at which the rotational Killing field φa is null. Call this dotted circle the “critical circle.” The circles that pass through p and have radius r = rc/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 rc.

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Figure: Projections of timelike and null geodesics in Gödel spacetime. rc is the “critical radius” at which the rotational Killing field φa 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.)

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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 + αra, with α positive), we can reach a point p1 with coordinate value r > rc. At that radius, we know, φa is timelike and future-directed. So we can find an ε > 0 such that (−εt ̃a + φa) 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 + φa) (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 + αra, 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

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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.

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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.