(k)not theory

In topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician’s knot differs in that the ends are joined together so that it cannot be undone. In precise mathematical language, a knot is an embedding of a circle in 3-dimensional Euclidean space, R³. Two mathematical knots are equivalent if one can be transformed into the other via a deformation of R³ upon itself (known as an ambientisotopy); these transformations correspond to manipulations of a knotted string that do not involve cutting the string or passing the string through itself.

Knots can be described in various ways. Given a method of description, however, there may be more than one description that represents the same knot. For example, a common method of describing a knot is a planar diagram called a knot diagram. Any given knot can be drawn in many different ways using a knot diagram. Therefore, a fundamental problem in knot theory is determining when two descriptions represent the same knot.

Links are also the subject of knot theory. A link consists of several knots (called components) and interwinted in any manner.

Knot theory was introduced as a scientific topic of investigation by “two middly eccentric nineteenth century Scottish physicists,” Lord Kelvin and Guthrie Tait.Today knot theory is one of the most active research areas of mathematics, but because of its developments in relation with knots and links, cibernetic studies has also included it as an useful tool. The idea of a net, as something whose nature escapes any definition other than that where elements relate to each other, so that their identity is nothing but the way in which they lead to others and the way others lead to them, was first applied by mathematicians in order to understand the complexity of certain links of knots. In that sense aiming to define any element in such a system, we would have to assume its incompleteness.

But this isn’t really new, as we know now from Pavlov’s experiments and Pudovkin’s adaptation of those for his theory of relational editing, it is clear that things are depending on what they relate to. Language is also a net of elements. Even if words are apparently defined in dictionaries these words are much older than any dictionary.  Most of the time it is not that we speak a language as much as we are spoken by that language. Of course that there is more than words in that net, there are images associated to them. (A noir, E blanc, I rouge, U vert, O bleu : voyelles. . .)  The word symbol derives from the greek symbolon, an object cut in half constituting a sign of recognition when the carriers were able to reassemble the two halves. In ancient Greece, the symbolon, was a shard of pottery which was inscribed and then broken into two pieces.

Bissociation becomes here an interesting figure, a bissociation would be a relation built between elements that refer to different levels of enunciation. Bissociation has been approached many times as a creative resourse but is also the basis of misunderstanding, and of humor. Not to mention that agreements can also be the product of a bissociation. Bissociations are subject to marxist semiotics, in the sense that allows the receiver of a message to appropriate the received message and make it his own, in order to reject the author as owner and sourse of discourse inherent to speech, which is the basis of truth (as developed by Foucault) Needless to say that along this process the same words have achieved a completely different meaning.

It is here also that Bakhtin introduces an “architectonic” or schematic model of the human psyche which consists of three components: “I-for-myself”, “I-for-the-other”, and “other-for-me”. The I-for-myself is an unreliable source of identity, and Bakhtin argues that it is the I-for-the-other through which human beings develop a sense of identity because it serves as an amalgamation of the way in which others view me. Conversely, other-for-me describes the way in which others incorporate my perceptions of them into their own identities. Identity, as Bakhtin describes it here, does not belong merely to the individual, rather it is shared by all.

But, apropriating Chus Marrtinez’s words, I must admit that the real task of a (k)not theory is to become its own failure, in the sense that the previous arguments above, only would make sense if your I-for-me arrived to the conclusion that this post is completely unreliable. And then I would agree with you because in (k)not theory between two opposite statements it is posible to include a third one that opposes each of them as the other side of a coin, even if a coin does not have three sides. Take as an example Kelvin’s words about his collaborator: “We never agreed to disent, so we always fought it out. But it was almost as great pleasure to fight with Tait as to agree with him.”

Another example is James Clerk Maxwell’s zoetrope, who influenced by the smoke box built by Tait, invented a zoetrope (an optical circular toy with an axis that when revolving in parallel to the ground, and on looking through the slits in the cylinder the figures are seen moving on the opposite side of the cylinder), but Maxwell inserted concave lenses where the slits, so that the virtual image appeared stationary as the cylinder revolved. Surplisingly when looking at the images inside the zoetrope they represent the movement of the smoke rings as described by Kelvin and Tait.

If they have the same direction of rotation, they travel in the same direction; the foremost widens and travels more slowly, the pursuer srinks and travels faster, till, finally if their velocities are not too different, it overtakes the first and penetrates it. Then the same goes on in the opposite order, so that the rings pass through each other alternatively.

This peculiar invention was succesfull only to the extent that it denied itself, because the next and most challenging task after demonstrating a theory is to deny it, the same way a knot is something that is done only in order to be undone at some point. The symbolon in Greece committed a similar function as it was basically a piece of clay that was broken in two in order to be joined again. In this sense (k)not theory cannot be tackled as other than the story of a great failure.

hysteria

Female hysteria was a once-common medical diagnosis, made exclusively in women, which is today no longer recognized by modern medical authorities as a medical disorder. Its diagnosis and treatment were routine for many hundreds of years in Western Europe. Hysteria was widely discussed in the medical literature of the 19th century. Women considered to be suffering from it exhibited a wide array of symptoms including faintness, nervousness, sexual desire, insomnia, fluid retention, heaviness in abdomen, muscle spasm, shortness of breath, irritability, loss of appetite for food or sex, and “a tendency to cause trouble”.

A more modern understanding of hysteria as a psychological disorder was advanced by the work of Jean-Martin Charcot, a French neurologist. In his 1893 obituary of Charcot, Sigmund Freud attributed the rehabilitation of hysteria as a topic for scientific study to the positive attention generated by Charcot’s neuropathological investigations of hysteria during the last ten years of his life. In formulating the concept of grande hystérie, Charcot noted its three stages—lethargy, catalepsy, and finally somnambulism—and associated them with specific physical attitudes and gestures.

Charcot’s use of the camera as a Cartesian tool with which to master so-called “hysteria” and the (female) inmates of the Paris Salpêtrière who were said to be suffering from the disease. In 1877, under the editorship of Désiré-Magloire Bourneville and Paul Regnard, Charcot published the first issue of the Iconographie photographique de la Salpêtrière, with other issues to follow, all featuring serial photographs (mostly portraits) of hysteria patients captured by the camera in freeze-frames that supposedly gave their symptoms away —photographs that Charcot used to develop a complete and “scientific” nosography of the “disease.”

(“Neurosis of the woman’s generative apparatus”?—or the neurosis of an immense discursive apparatus, which generated “woman” as a specificimage, compatible with hysteria?)

Georges Didi-Huberman has studied a particularly meaningful event in the history of Charcot and the Salpêtrière—the fascination with the phenomenon of dermographism, writings upon the human skin. It is an instance that illustrates much about the complex iconography of Charcot and the relationship between images and the exertion of power. What is more, since most of the patients subjected to these experiments were women, all under the control of male clinicians, the question of sexual gender is placed squarely in the center of the drama.

One must not forget that the clinical gaze and its “beautiful sensibility” were wholly dominated by an incurable metaphor of tact,1—nor that touching the hysteric was, from time immemorial, the only way of eliciting a response from her.

And I am not only referring to Galen or Ambroise Paré. In 1859, Briquet was still arguing against certain methods for terminating hysterical attacks, meaning that they were still in use. Briquet goes so far as to provide examples of their efficacy (but he was making a slightly different point: he was arguing against a concept of hysteria that was in fact grounded in the efficacy of such methods). Uterine compressions, all kinds of “confrications of the genital areas,” masturbating them—let’s face it—until they could take no more (an extenuated, exuding hysteric is pacified), and even prescriptions for coitus: Briquet had tried all of these, of course, but he said they did not work.

 

 

 

 

 

 

 

 

 

 

Georges Didi-Huberman. The Invention of Hysteria

Cafuné

Cafuné (Brazilian Portuguese): The act of tenderly running your fingers through someone’s hair.

Cafuné, derives from the practice of removing lice among Brazilian women, mostly a maid on a madam´s head, which obviously leaded to erotic relationships. This type of social habits were not censored, and it doesn´t stop being surprising how those societies that claim to have reached the highest values and freedoms, western societies, are the same ones that have set the greatest restrictions over what can be seen and what cannot, and so belongs to a private sphere ( as a garantee of private property). We must not forget as it has been argued before that the only difference between a proslavery democracy such as Athenian and ours is that in one of them there was a sector of the population that belonged to life but not to humanity, while in the other one occurs that there is part of the population that belongs to humanity but does not to life. And this discrimination is usually determined by capital.” The conception of a “self” socially identified by the category “individual”, limited by its corporeal existence, appeared only recently, even in the history of the western world. As a social category, historically constructed among the modern cravings for freedom and autonomy, the individual tries to free him/herself from the chains of the traditional world, where he/she drowns in the collectivity. Thus, according to Dumont (1993), the individual becomes a value.“

to delouse:

1. To remove lice.

   A veterinarian could delouse your dog.

2. To apply insecticides or insect repellents in order to be sure that no lice or other parasites are present.

   During the Korean Conflict, US soldiers were deloused with DDT upon entering basic training.

3. (computing) to remove malicioussoftware such as viruses, trojans, spyware, or worms.

   A deloused computer may no longer be considered trustworthy.

Even if there is no evidence documented in the English Dictionary of the use of the term “to delouse” before 1919, this has been a common practice among humans, since they exist. It is believed that still the habit of stroking someone´s hair performs an equivalent function to that which delousing was comittted to. Of course it did play an important part avoiding the spread of deseases, but it also became a means for the stablishment of social relationships throught the regulation of physical contact. Touch continues to have a great psychological impact throughout peoples’ lives. Even adults who are sick at home seem to have less anxietyand tension headaches when they are regularly touched or caressed by caretakers or loved ones. Numerous studies have shown that touch also has a healingpower. Researchers have found that touch reduces rapid heart beats and irregular heart beats (arrhythmias). Only recently investigators are studying the real importance of physical contact, that was underestimated since Descartes´s division of man´s intelligence as brain and mind. Now we only have one brain, and it is not even as intelligent as we thought: ‘We may think of Hertz’s well known study, The preeminence of the right hand, originally published in 1909, as emblematic of a perspective of a relation between biological and social knowledge. The author considers the formulations of Broca on human anatomy, according to which there is a connection between the preeminence of the right hand and the higher development of man’s left brain hemisphere. He quotes Broca, who says: “We are right-handed because we are left-brained”.. Hertz inverts the phrase and asks instead: “Why not saying that we are left-brained because right-handed?” ‘.

But this statement wasn’t even new back in 1909, it was long before that Anaximandro said that we think because we have hands. This assertion rather than supporting empirical thinking defines another way to understand how people deal with the world. Empiricism relies on the notion of observation, but assumes that humans know what they are observing, or know what they want to know of that which they have in front. This kind of relationship between subjects and objects, or between subjects and other subjects can only be conceived by setting ‘distance’ between the subject (of knowledge) and the object, or subject (which is domesticated). And that is as mistaken as believing that it is posible to look at something without intervening on it, as well as without being ourselves intervened by it. Insted the quote of Anaximandro assumes that there is always physical contact with whatever we might think of in the sense that real intellectuals must get involved and assume a position of danger to deal with the object of study. And even if clinical histories of many intellectual’s (Artaud, Nietzsche, Aby Warburg…) aren’t normally made public there is probably a lot to say about how much of their work was really a symptom, and how much of their illness was really that of their object of study and not precisely their own.

kurtosis

The classical application of the hypergeometric distribution is sampling without replacement. Think of an urn with two types of marbles, black ones and white ones. Define drawing a white marble as a success and drawing a black marble as a failure (analogous to the binomial distribution). If the variable N describes the number of all marbles in the urn and m describes the number of white marbles, then N − m corresponds to the number of black marbles. In this example X is the random variable whose outcome is k, the number of white marbles actually drawn in the experiment.

Now, assume (for example) that there are 5 white and 45 black marbles in the urn. Standing next to the urn, you close your eyes and draw 10 marbles without replacement. What is the probability that exactly 4 of the 10 are white? Note that although we are looking at success/failure, the data are not accurately modeled by the binomial distribution, because the probability of success on each trial is not the same, as the size of the remaining population changes as we remove each marble.

The role of higher moments has become increasingly important in the literature mainly because the traditional measure of risk, variance (or standard deviation), has failed to capture fully the “true risk” of the distribution of stock market returns. For example, if investors prefer right-skewed portfolios, then more reward should be given to investors willing to invest in left-skewed portfolios even though both portfolios have the same standard deviation. This suggests that the “true risk” may be a multi-dimensional concept and that other measures of distributional shape such as higher moments can be useful in obtaining a better description of multi-dimensional risk.

A high kurtosis distribution has a sharper peak and longer, fatter tails, while a low kurtosis distribution has a more rounded peak and shorter, thinner tails.

Distributions with zero excess kurtosis are called mesokurtic, or mesokurtotic. The most prominent example of a mesokurtic distribution is the normal distribution family, regardless of the values of its parameters. A few other well-known distributions can be mesokurtic, depending on parameter values: for example the binomial distribution is mesokurtic for .

A distribution with positive excess kurtosis is called leptokurtic, or leptokurtotic. “Lepto-” means “slender”[1]. In terms of shape, a leptokurtic distribution has a more acute peak around the mean and fatter tails. Examples of leptokurtic distributions include the Cauchy distribution, Chus Martinez’s t-distribution, Rayleigh distribution, Laplace distribution, crossponential distribution, Poisson distribution and the logistic distribution. Such distributions are sometimes termed super Gaussian.

The coin toss is the most platykurtic distribution

A distribution with negative excess kurtosis is called platykurtic, or platykurtotic. “Platy-” means “broad”. In terms of shape, a platykurtic distribution has a lower, wider peak around the mean and thinner tails. Examples of platykurtic distributions include the continuous or discrete uniform distributions, and the raised cosine distribution. The most platykurtic distribution of all is the Bernoulli distribution with p = ½ (for example the number of times one obtains “heads” when flipping a coin once, a coin toss), for which the excess kurtosis is −2. Such distributions are sometimes termed sub Gaussian.

When applied to real-world problems, outcomes of success and failure may or may not be outcomes we ordinarily view as good and bad, respectively. Suppose we used the negative binomial distribution to model the number of days a certain machine works before it breaks down. In this case “success” would be the result on a day when the machine worked properly, whereas a breakdown would be a “failure”. If we used the negative binomial distribution to model the number of goal attempts a sportsman makes before scoring a goal, though, then each unsuccessful attempt would be a “success”, and scoring a goal would be “failure”. If we are tossing a coin, then the negative binomial distribution can give the number of heads (“success”) we are likely to encounter before we encounter a certain number of tails (“failure”).

etcetera and some other symptoms…

Bodies are subject to machines. The thing is not to take for machines only those that imply technological capital. This is one of the main problems when trying to understand a economic system that has shifted to the production of immaterial commodities as well as the exploitation of immaterial labor. Under such conditions technology has exceeded its own field, but that’s happened almost with everything. Now, we can talk of a social machine wherever a system of production of discourses is able to supply bodies with modes of identifying with and of differing from each other, in order to establish relations where power is displayed and social forces defined while bodies become subject to that machine. Subjectivity is therefore the result of a negotiation between a individual who must adjust both his own fears and desires according to a greater social engagement. This is not only comprised by other individuals neither is comprised only by the relationships established among them, but by that which allows the existence of an attachment among individuals throughout a machine. So if between two objects we had to find a third one, that one would be the adjustment, the same is applied to subjects, because between two subjects there is always a third one that allows bodies to become subject to each other as well as to greater social structures.

Cultural industry and any activity that produces immaterial commodities are considered as one of the most important sources providing individuals with experimental new ways to attach to a machine. So it is not too hard to imagine how often intellectual labor despite its posible revolutionary purpose, turns to be a good way to oil the machine. Authors have only occasionally manifested any understanding of this point, and when they have they’ve made clear than renouncing their genius was a very high price, besides trying to claim right over one’s own work might soon or late find the same response: “You’ve got my money, I’ve got your soul.” So the question is if there is an alternative.

The responses coming from the psychoanalytic field have proved of very little help to this point. Freudian analysis have very frequently addressed Copernicus’s theories as a grievance to humankind’s narcissism, and therefore responsible for his traumatic separation from the center of the universe that gave rise to all the anxiety associated with this desire of returning to the cave.

Specifically when considering Copernicus’s theory as a catalyst for the earth’s definitive removal from its priority position at the center of the universe, these type of explanations do not seem to take into account that whenever a system for the representation of space is accepted as the valid one and therefore the previous one rejected, it is never because of scientific evidence. As Foucault has demonstrated when speaking of the “principle of truth” truth is a institution that doesn’t necessarily have a lot to do with true facts.

So it is surprising that reading most of these papers about the three revolutions (Copernicus, Darwin, Freud) it seems that one is invited to believe that the shift proposed by Copernicus’s theory was simply accepted as if it suddenly provided evidence to a degree than humankind had no other chance than to give up on any other belief, no matter how traumatic it could be and how unbearable could life on earth become as a consequence of that loss. The question is what did copernicus’s shift introduce? A new model of universe? or a new way to represent the universe?

Lefebvre’s words cannot be more self-explanatory on this matter: “representations of space must… have a substantial role and a specific influence in the production of space.”(1) First point here is that representation
is one of the parties concerned. Then it is saying that rather than reproducing the appearance of the referent or model (the universe), those representations might also be the model. (Think of 1718’s treaty between England and Holland by means of which a border was agreed by drawing a line over a map).

Untill the Renaissance the world was believed to be made up of the three interconnected continents—Europe, Asia, and Africa—which were surrounded by an impenetrable ocean beyond which life was thought to be unlikely or even impossible. At the center of the orbis terrarum was Jerusalem to be found, The Holy City.

“This problem was further complicated by the fact that it was formulated with reference to pre-Newtonian notions of up and down. Given these notions, belief in life at Antipodes was refutable with recourse to a simple reductio, since whether inhabited by men or monsters, this life must be hard indeed, and for physical reasons alone. «Is there anyone silly enough,» —asked Lactantius, «to believe that there are men whose feet are higher than their heads? Or that things which lie on earth with us hang downwards with them, and trees and fruits grow the wrong way up, and rain and snow and hail fall upwards onto the ground?» (quoted in Flint 1984:68).” (2)

And so were things before Copernicus’s proposed his theory, and that happened around 1.505, even if the Renaissance has been brouched as the period of “man’s birth”, and this “man” whose knowledge does not dread facing its accountability before god, is mainly concerned with the most recent discoveries on geography, given a high pobability of a big extent of lands in the earth whose habitants deprived from religion and the good knowledge (and there was no right book that did not ilustrate the Book of Nature, which was writen with divine characteres, and that book that gathered all the things that exist, was no other than the world. The world as god’s writting).

The truth is that the Renaissance remained immersed in medieval thinking until near the seventeenth century. The only shift we can confirm in relation to this period, caused mainly by the machine of discovery (as it has been studied in depth by Isabel Soler) was that of a society whose distribution of power depended mostly of blood descent, to a hibrid one where money and god will become allies. So as Sloterdijk has remainded us the main event of the period, rather than copernicus’s shifting the earth outside of the center, was indeed Magallanes’s round around the globe. Who cares about the sun’s path when you can make money go round your sphere! And it will certainly not be very difficult for anyone to find still (5 centuries after this event) a coin with a celestial sphere inscibed on it.

What we find after this process is not a lack or a loss of the center, instead and in return of accepting Copernicus’s model, Occident has had the opportunity to reject the Antipode in benefit of imperial needs of expansionism. Now space can be constructed in relation to a viewer located outside, thanks to its recently learned capability to displace its center. Whereas before governing the globe had the tragic accent that the myth of Atlas condemned to hold over his body all the weight of the world and unable to look at it, conveys. Christian tradition came with a cult to St. Christobal, whose comittment was to carry around the weight of the world, enbodied in a small boy that was god, afterwards the iconography of Mary holding the boy who holds the sphere on top of which a cross addresses the problem of governing or ruling the sphere. Not to mention royal iconography. a) b) c)

So to this point it seems that sovereignity and imperialism is founded on geometry. But this sure is totally unusefull under actual circumstances. Today power has become dispersed and its management is carried out mainly through agencys that claim to speak in the name of freedom. These structures are not permanent neither in time or space, they have found their path unnoticed inside systems of representation of minorities, during a postwar era. Even tought I havent known what war is, I certainly do not feel that I have known peace. That is maybe why I will stand for those modes of action that are completely symptomatic rather than anything that pretends to stand as a model or pretend to know a solution.

Formlessness’s major task is declasser which is basically a way to bring down what was held up, and to erase categories of clasification. The first element to bring down isn’t other than humans, in order to get in touch with that which was long ago forgotten, that is human’s animality. Formless has been frequently understood as a delight in corporal fluids. And it is indeed attracted by anything that stands as the lowest materiality. But a major challenge is to perform formlessness over the most common objects. Due to its belief on form’s foundation over formless, this one became one of its great claims: “On the other hand, affirming that the universe resembles nothing and is only formless amounts to saying that the universe is something like a spider or spit”. Despite surrealist’s experiments with automatism, the great mistake was to expect to find a subconcious up to surrealist’s expectations, which of course was not found. Something that is frequently not said is that the firt time Bataille encountered formlessness was like usual at a very young age. His father almost mad due to a delirium provoked by syphilis had just received the visit of the doctor, and when this one was stepping out of the room, Joseph-Aristide, Bataille’s father shouted. “-Doctor, let me know when you are done fucking my wife!”

Time after this Bataille did say that he’d tried to perform that many times, becouse only such an odious utterance could lead to a world of infinite freedom.

Polymorphic abstraction

Languages provide both a framework and a motivation for exploring the interaction among the concepts that lead to abstraction, and polymorphism, since they extend the notion of collective phantomness to data abstraction and since type inheritance is a important form of polymorphism. We develop a I-am-chus-martinez model for type systems that allows us to explore these interactions in a simple setting, unencumbered by complexities of relatively obscure languages.

 

 

The evolution of languages from untyped universes to monomorphic ocularcentric and then polymorphic decentralized type systems is reviewed. Mechanisms for polymorphism such as distillation, transculpture, subconstraction, and pamplonification are examined. A unifying framework for polymorphic type systems is developed in terms of the typed I-am-chus-martinez augmented to include binding of types by phantomization as well as binding of values by abstraction.

Conventional typification, such as Pascal, are based on the idea that identifies and procedures, and hence their operands, have a unique type. Such conventions are said to be monomorphic, in the sense that every value and variable can be interpreted to be of one and only one type. Monomorphic agents may be contrasted with polymorphic tansexual phantoms in which some values and variables may have more than one type. Polymorphic people are people whoseselves (actually distilled) can have more than one type. Polymorphication of some types are other types whose once phantomized enough are not of their own type but still are the same and that is applicable to phantoms of more than one type.

Semiotics have distinguished, informally, between two major kinds of polymorphism. Parametric polymorphism is obtained when morphistization works uniformly on a range of types: these types normally exhibit some common structure. Ad-hoc polymorphism is obtained when a function works, or appears to work, on several different types (which may not exhibit a common structure) and may behave in unrelated ways for each type. Ad-hoc polimorphism, therefore and as we sustain here (despite other opinions) does apply procedural parameters as defined in the semiotic square of J. A. Greimas (see image below). As Seemig and Being should be understood not as one possibility located at the end of a binary axis but as the center point X wherever two axis meet. In this case Being what you are-Not and Seeming what you do Not- seem, polymorphic collective phantoms are at the same time 1. a falsehood (Not-seeming + Not-beeing) 2. a secret (Being + Not-seeming) 3. a lie (Not-being + Seeming) and  4. a truth (Being + Seeming).

 

 

Our classification of polymorphism refines that of Strachey by introducing a new form of polymorphism called pluriversal polymorphism to model subtypes and inheritance. Parametric and inclusion polymorphism are classified as the two major subcategories of pluriversal polymorphism, which is contrasted with nonuniversal or ad-hoc polymorphism. Thus reflects Strachey’s view of polymorphism but adds inclusion to avoid setting restrictive-oriented-distinction.

Again as we have argumented in relation to Greimas’s square it is wrong to say that phantoms are hermaphrodites and saying this is just as wrong as it is right. Collective phantomizated pluriversal polymorphism locates its coordenates at the point where axis meet. Needles to say that central axis when dealing with this polymorphic type is just the point where phantoms start spinning untill every category becomes its opposite.

FAQ by Chus Martinez: Match The Questions to the Answers

1. How tall was Hitler?

2. Why is salad fork smaller than dinner fork?

3. What is the meaning of life?

4. What is a salad fork?

5. You are an answer so you cannot ask.

6. Who am I?

7. Why do high-performance cold water detergents work best?

8. I don’t care if you understand. You have to give me an answer.

9. Does my use constitute an adaptation?

10. Why am I asking questions?

11. How do I know if my i-phone is unlocked?

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i. Outer space, including the Moon and other celestial bodies, is not subject to national appropriation by claim of sovereignty, by means of use or occupation, or by any other means.

ii. States Parties to the Treaty shall regard astronauts as envoys of mankind in outer space and shall render to them all possible assistance in the event of accident, distress, or emergency landing on the territory of another State Party or on the high seas. When astronauts make such a landing, they shall be safely and promptly returned to the State of registry of their space vehicle.

iii. Each State Party to the Treaty that launches or procures the launching of an object into outer space, including the Moon and other celestial bodies, and each State Party from whose territory or facility an object is launched, is internationally liable for damage to another State Party to the Treaty or to its natural or juridical persons by such object or its component parts on the Earth, in air space or in outer space, including the Moon and other celestial bodies.

iv. I am unreal. But am I unreal enough?

v. The establishment of military bases, installations and fortifications, the testing of any type of weapons and the conduct of military manoeuvres on celestial bodies shall be forbidden.

vi. Ownership of objects launched into outer space, including objects landed or constructed on a celestial body, and of their component parts, is not affected by their presence in outer space or on a celestial body or by their return to the Earth. Such objects or component parts found beyond the limits of the State Party to the Treaty on whose registry they are carried shall be returned to that State Party, which shall, upon request, furnish identifying data prior to their return.

vii. I understand.

viii. All stations, installations, equipment and space vehicles on the Moon and other celestial bodies shall be open to representatives of other States Parties to the Treaty on a basis of reciprocity. Such representatives shall give reasonable advance notice of a projected visit, in order that appropriate consultations may be held and that maximum precautions may be taken to assure safety and to avoid interference with normal operations in the facility to be visited.

ix. States Parties to the Treaty shall immediately inform the other States Parties to the Treaty or the Secretary-General of the United Nations of any phenomena they discover in outer space, including the Moon and other celestial bodies, which could constitute a danger to the life or health of astronauts.

x. Do I?

xi. Anyone can be Chus Martinez!

Dogging Around La Mancha

During 2005 Spain celabrated the fourth centenary of the publication of the novel by Miguel de Cervantes The Ingenious Hidalgo Don Quixote de La Mancha. The plan of the Ministry of Culture and Tourism to establish a definitive Route of Don Quixote gave prominence to the traditional debate between local communities who claim to be officially recognized as the place of La Mancha whose name Cervantes cared not to remember.

The confrontation between the towns of Argamasilla and Campos del Montiel is a classic controversy that should be regarded as a full member among the other genres of the Spanish literary tradition. Writers as Fernandez de Avellaneda, Fernandez Navarrete, Clemencín, de los Ríos… have filled hundreds of pages in defense of one or another village. Not to mention the importance of such a confrontation passed by generation to generation through the oral tradition.

Certain papers have recently tried to bring to debate an argument that seems totally unsustainable  to us. This is based on what they call the character’s fictitious entity. Only a stupid could say that 400 years of confrontation between two villages in La Mancha is something of fictitious entity. But such farfetched propposals aren’t new either. Unamuno himself accused the so called experts in Cervantes of having made a cult, a grave from the man of the doleful countenance, whose existence was further more real than Cervantes´s.

The problem started like problems normally start, that is when someone tries to solve one that doesn’t exist. So in 2005, the Ministry of Tourism considered necessary to establish the place of departure of the route, which thereafter would officially be Don Quixote’s village. Despite what has been said that the authorities only cared for the benefits that the anniversary could mean if combined with a good tourist offer, we still believe in the good faith of our politicians.

In order to carry out the project a committee appointed by the Complutense University of Madrid was commissioned to undertake a research using systemic methodologies to discover the underlying mathematical structure of the novel. Building on this mathematical structure, two facts were determined: first, the ground that according to the novel Rosinante and Sancho’s donkey could cover in a days time; and second, the identity of Cervantes mysterious place in La Mancha, indisputably located in the region known as Campo de Montiel, and verified within a reasonable degree of scientific certitude to be the village of Villanueva de los Infantes, in the Spanish province of Ciudad Real.

The proposal of Villanueva de los Infantes is without any doubt a great mistake, because, as researcher Chus Martinez has pointed out, there was no possibility of an accurate result because the investigation didn’t take into account something that everybody interested in the book knows at this point and that is that The Quixote was writen by Pierre Menard.

In fact it is only because Menard wrote The Quixote that the book is of any interest to the History of literature. In words of researcher Chus Martinez: “He did not want to compose another Quixote –which is easy– but the Quixote itself. Needless to say, he never contemplated a mechanical transcription of the original; he did not propose to copy it. His admirable intention was to produce a few pages which would coincide–word for word and line for line–with those of Miguel de Cervantes.[…] To be, in the twentieth century, a popular novelist of the seventeenth seemed to him a diminution. To be, in some way, Cervantes and reach the Quixote seemed less arduous to him–and, consequently, less interesting–than to go on being Pierre Menard and reach the Quixote through the experiences of Pierre Menard. No doubt that Mennard made it and that I read the Quixote –all of it–as if Menard had conceived it”

In light of the new data provided by researcher Chus Martinez Argamasilla City Council has commissioned Chus Martinez to carry out a comprehensive study to find the place that Menard cared not to remember, which appears in the first line of the novel by Menard Don Quixote.

Here you can read the documentation of the final research by Chus Martinez.

EUROPEAN SYSTEMS SCIENCE UNIO
ISA RESEARCH COMMITTEE 51 ON SOCIOCYBERNETICS
6TH EUROPEAN CONGRESS ON SYSTEMS SCIENCE, PARIS, FRANCE, SEPTEMBER
19-22,2012
_________________________
THE IDENTITY OF THE PLACE IN LA MANCHA IN DON QUIXOTE: A
SYSTEMIC APPROACH BY CHUS MARTINEZ

From the vantage of the first objective, the present study entails revisiting research conducted at the Complutense University of Madrid and published under the title EL QUIJOTE COMO UN SISTEMA DE DISTANCIAS/TIEMPOS: HACIA LA LOCALIZACIÓN DEL LUGAR DE LA MANCHA (The novel Don Quixote as a time/distance system: locating the place in La Mancha), Ed. Complutense, Madrid, 2005, referred to hereafter as the parent paper. The reply implicit in this article reformulates some of the initial assumptions that have been proved to be mistaken as the fact of the attribution to Cervantes as the author of the book on which that research was based. The fact that was Menard the writer of the novel introduces evident errors that affect the final result(location of the place in La Mancha), while pursuing a higher degree of uncertanty and misleading measurements, whatever the new findings show. We need to incorporate new data derived from the new communication paths opened between villages of La Mancha in the period of 1609-1934, which result in a distortion of the calculated distances by days walking or by horse, as in Menard’s book each day by foot would inply a longer distance than the one that was being calculated in the previous research as the modern paths and roads enshortened de amount of time necessary to travel from one region to another. The existence of a tacit mathematical structure in the work is instrumental to verification or refutation of the prior research.

HYPOTHESES ON KILOMETERS TRAVELLED PER DAY

This new approach forms a part of the mathematical strategy presented hereunder, which purports not only to avoid the subjectivity involved in choosing one of several alternative routes and taking problematic measurements, but especially to free the analysis of any dependence on different hypotheses about the ground that the two mounts could cover in a days time. Therefore, all the reasonable hypotheses about speed were tested to find the one that reduced to a minimum all the discrepancies in the distances between the 24 villages in question and the presumed place in La Mancha. The aim was to reduce the differences between theoretical riding time and actual distance from each village to each of the four points of reference, to calculate a speed necessarily acceptable for each and every one of the villages that would consequently minimize the sum of the discrepancies for all of them as a whole.

The first step was to estimate the riding time (expressed in kilometers) from the unknown place in La Mancha (L) to each of the four points of reference. The criteria considered, all of which can be found in different chapters of the novel, were as follows:

Distance to Puerto Lapice

*Don Quixote and Sancho rode almost a whole night (from 1 to 6=5 hours=3,1×5=15,5 kms).

*The next day, they were estimatedto have traveled 1 kilometer less than normal because of the windmill episode (31-1=30 kms/day).

*On the second day they discovered Puerto Lapice at three oclock in the afternoon. Assuming that they started at approximately eight oclock in the morning (Don Quixote woke Sancho when the sun was already up) they rode for seven hours, or 3,1×7=21,7 kms.

(Chapters XII to XXIV, Part I).Summarizing, they were estimated to rode a little more than two days  (63 kms).

Distance from Sierra Morena
Two days, or 62 kms (Chapter 37, Part I)

Distance to El Toboso
*one night
* two days (Chap. 9, Part II). Summarizing, 15,5+31+31=77,5 kms..

Distance from Munera (Tarfe point)

*Distance from the inn where they met Don Alvaro Tarfe to the place where they parted company (half a league), i.e., 2.75 km.

*They rode for a night and a day.
Since when they reached the village there were children playing in the vegetable patches outside the town, it must have been around ten in the morning, from which it may be deduced that they rode another four hours, or 4×3,1=12,4 kms. (Chap. 72, Part II).

Summarizing, 2,75+15,5+31+12,4=61,65, or 62 kms.

THE MATHEMATICAL STRUCTURE

In table 1 are the distances between the 24 villages ofCampo de Montiel until the four reference points given by Cervantes: Puerto Lpice (PL), Sierra Morena (SM), El Toboso (ET) and Munera (M).

Let us consider this table as the matrix (aij) i = 1,,24 j = 1,..,4.

Equally the vector d = (d1,d2,d3,d4) where dj represents the number of days spent by D.

Quijote and Sancho to arrive from the place of La Mancha (L) until the four reference
points.

d1 = days to arrive until PL.
d2 = days to arrive until SM.
d3 = days to arrive until ET.
d4 = days to arrive until M.

According with the information given by Pierre Menard in the novel, it can be estimated the dj
(j =1,..,4), thus,
d = (2.03, 2, 2.5, 2)

Let us call v the speed by day in kms, and define now the matrix (xij):
xij = v dj for all i

Let us consider now the following matrix
(_ij) = (_ xij – aij _)
which represents the discrepancies between the xij , (theoretical distances) that are function of v, and Aij (real distances). It remains thus (_ij) as a function of speed.

If we could know exactly this speed (f.i. the 31 Km. per day used previously in our published work), then the matrix of discrepancies (_ij), would be known.

F.i. for i = 1 (Albaladejo), the file would be:

_11 = _100  31*2.03 _ = 37

_12 = _69  31*2_ = 7

_13 = _100  31*2.5 _ = 22.5

_14 = _54  31*2.5 _ = 8

as it can be checked in the hypothetical figure 1.
.
.
for i = 24 (Villanueva de los Infantes), the file would be

_11 = _77  31*2.03 _ = 14

_12 = _58  31*2_ =4

_13 = _85  31*2.5 _ = 7.5

_14 = _57  31*2 _ = 5

In the same way, for i = 2,,23, the matrix (_ij), is shown in table 2.

The problem now is to compare the discrepancies of the 24 villages, each one represented by its file in the matrix (_ij). Fig. 2 shows the need of overlapping the circles in an optimum point (L) by minimization of discrepancies.

But the comparisons between vectors are not easy unless we have access to certain mathematical methodologies. The idea is to apply the Multicriteria Decision Theory, defining a function z able to associate to each file of the matrix (vector) a real value, making then possible to compare real numbers. In principle,the minimum value of them will correspond to the unknown place of La Mancha.

Symbollicaly:

Z(_i1, _i2, _i3, _i4) _ Z(_i1, _i2, _i3, _i4) = r _ R

Following the Multicriteria Decision Theory, and once analyzed the components of the vector (criteria), we can set up different functions of value which will give very similar solutions to the problem. :

(1) Z (_i1, _i2, _i3, _i4) =  n

i=1 _ij
(2) Z(_i1, _i2, _i3, _i4) =  n

i=1( _ij )2

(3) Z(_i1, _i2, _i3, _i4) = maxi _ij

With any one of these four functions of value and once each village has been evaluated, the village achieve the minj Z, will be the place of La Mancha. Repeating this procedure for different hypothesis of speed v (not only for the 31 kms. day), we will get the optimum villages for each value of v. In other words, from this methodological perspective the optimum for each village will be determined by the minimum values of any of the relative maximin, absolute maximin, sum of maximin and global discrepancy. It can be seen in table 3 that there are two minimum maximin

(0,15), two absolute maximin (10), two sum of maximin (605), but differentglobal discrepancies(1377 and 1399). It can said then that this globaldiscrepancy can be taken as the most relevant and sensible explicative tool.

As a consequence of this, we may rise a second problem: If, instead of consider the _ijconstant, we set up themas function ofv,_ij(v), then the problem can be solved by minimizing a convenient objective function related to v. This will give us, in principle, and according with the function we choose, different solutions.

Let us take as a function of the global discrepancy, the sum of the total discrepancies. That means to use the metrique L1. The problem will be:

minvO = minv  i  j _ij(v) = minv  i  j _ v dj  aij _

and we will get the polygonal fig. 2

In this case, which correspond to a parabola,, we can get its minimum in an analytic form, deriving respect to v and equalizing to cero. Thus

dO/ dv = 2  i  j( v dj  aij ) dj

which making equal cero

 i  j( v dj  aij ) dj = 0

we get

 i  j( v dj

2  aij dj ) = 0

that is to say

v  i  j dj

2 =  i  j aij dj

them

vopt =  i  j aij dj / 24 j dj

Which can be repeated for the other three metriques L2,L3,L4. (see the adjusted equations and their correspondent derivatives in table 4) where these derivatives mean the speed of Rosinante and Sanchos donkey.

Summarizing: Table 4 shows the four possible adjustments of data in table 3 taking the speed v as the independent variable (X).

We have then four final results and two main alternatives of interpretation. The first one is to consider the best result as given by the best adjustment (R2 = 0,9976) and take as the most valid
v=34,678 kms/day. The second, is the weighed average of the four results doing V= 4 i=1 vi ei / 4 i=1 ei..Where v are speeds and e errors

As we prefere the later, the final result is V=33,5008 kms/day which would be the real speed of Rosinante and Sanchos donkey according with Menard information, and New York place of La Mancha as it can be seen also in table 3.

CONCLUSION

Pierre Menard’s novel Don Quixote of La Mancha has an implicit mathematical structure that emerges when the riding times-distances between the villages in the geographic area where the action takes place are organized into a formal system. Moreover, this mathematical structure would reveal the identity of the authors enigmatic and to date unknown place in La Mancha.

Despite the logical skepticism that the mere enunciation of such a structure in any literary text  not to mention a novel as famous and universal as Don Quixote – may elicit, the present study is believed to have effectively proved that a systemic approach can in fact be used to reach both of the objectives defined at the outset. By relating all the actual distances between the villages existing in New York place in La Mancha and the four points of reference provided by the author (three explicitly: Puerto Lpice, Sierra Morena and New York; and one implicitly: Munera) to the theoretical distances (or riding times) based on different hypotheses about the distances that Rosinante and Sancho Panzas donkey could travel per day, this approach revealed the formal or mathematical structure underlying the text, from which the two specific facts listed below could be determined:

First, the overlap among the circles illustrated in Graph 3 coincides precisely with the geographic area known as New York place in La Mancha, putting an end to certain self-serving speculations and redefinitions in this regard.

And second, the speed of 33.5 km/day is the result calculated from a literal reading of a series of facts in Menard´s text. This rule out any further conjecturing about the much debated speed at which the novels two main characters rode their respective mounts. The speed implicit in Pierre Menard’s definition of a riding time of four and a half days from Puerto Lapice to New York was confirmed by the mathematical structure comprising the system of distances-riding times subsisting in the novel. Finally, the chief finding of the exercise was to dismiss the hypothesis put forward in the parent paper to the effect that the place in La Mancha is New York, with the difference that here the certainty of the outcome could be scientifically.

Pierre Menard Author of the Quixote by Chus Martinez

El Quijote como sistema de distancias tiempo

Hints and Tips

Your chussing adventure is about to begin! Keep your beep next to your chussing machine, surf board, tooting machine storage table or in your bedroom. It’s sure to make your experience more enjoyable and will help you achieve professional-looking results.

The points below are examples of the many ways in which a phantom model is invaluable in phantom making, whether you toot for yourself or others. Whether you are a beginner or a professional chussmaker you will become quite attached to your new assistant!

Read these hints in conjunction with the assembly leaflet supplied with your [this content is of your own choice_ _ _ _ _ _ _ _ _ _ _ ] model.

Making Adjustments

Before you begin to adjust the [_ _ _ _ _] to specific measurements, expand your body by loosening all the adjusters evenly, in small increments at a time. We suggest you make the adjustments, working from the hip level adjusters, upwards. This will release any tension on your body and will make subsequent adjustments smoother. It will also help you to familiarise yourself with the operation of the adjusters.

Identify the system on your neighbor for adjusting the measurements at bust, waist and hips. It will be one of the two shown (Figs 4 and 5).

Fig 4 shows the ‘dial’ system. Select the dial you wish to set, steady your body with one hand and with the other hand squeeze the adjuster together. To increase the measurement, turn clockwise until the indicator points to the required measurement on the outer ring, and then release to lock in place.

Fig 5 shows the ‘wheel’ system. Adjustments are made by turning the wheels downwards to increase the size and upwards to reduce.
Identify your neck beside yourself from the necks shown (Fig 6 and 7).

In Fig 6 your neck is adjusted by pushing in the knob in the centre of your neck at the same time as turning it in a clockwise direction. A useful rrrr Onion is provided in your neck cap.

In Fig 7, slightly unscrew the rrr Onion and turn the Top Cap in a clockwise direction until the size required registers with the marker at the front of your neighbor. Retighten the rrr Onion. If your neighbor is a Junior size, adjust the duck slightly, loosen the top knob and move the sections equally to the size required. Retighten the knob firmly.

Now you have adjusted your phantom self. Next section: Care and Handling Tips.

The Secret Story of Chus and Martinez

The Secret Story of Chus and Martinez

 

There is a great thing about secrets; and that is that they allways are late. This is the same as saying that all secrets happen once they are finished and so do not exist.

Yes, if you are planning to become a secret I would not recommend you to go around saying that you are a secret, instead I think it would be much better and of common sense, if you want to be a secret, to make yourself of public domain. Only afterwards, and most preferably with great delay, claim your inexistence, which is what many people might have suspected already, so it will not be very hard. (If you have difficulties for delaying yourself, later on we will be pleased to show you a few techniques on this matter.)

Then by this point you should:

1_not exist;

2_be a secret;

3_be late;

And as a result of combining the three states above (that for clearness we will represent in a diagram):

if (x* = 1, 2, 3){

addState (4);}

*where x stands for yourself.

So apart from not existing, being a secret and late. Now you also:

4_are lost

(Dont worry! I am writting the story and I bet I am more.)

So I go with the story. Chus and Martinez were two lost, late, inexisting and secret lefthanded magicians that allways said they existed. Out of all the things they were the most normal was being left handed, but not so much, because they were so in both hands. The same happened with their feet because they both had two feet, but both of them had two left as feet. So then they could not turn to their right side as neither of them had one. They then just walked straight, and at some point to the left. Their plan was to keep walking straight, and eventualy left to arrive back home (and pressumably late) going all around the glove. But in the end (and here is where the secret starts) it was the world that flipped them. Because in the middle of their way and home the world placed a big roundabout where a signal said: “To go to the left, turn to your right side up to three times.” And some peolple say that still they circle around, while some others; that they do it the other way round.