I speak as my understanding instructs me: Information Mobility, Withdrawal and the Echo Chamber of The Winter's Tale

Ondřej Polák, Charles University, Prague

The greatest advance that we have witnessed in the 20 th and early 21 st century cannot be subsumed under a single invention such as the combustion engine, the plane, or the internet. But together, these inventions give people access to unprecedented mobility, and mobility is what defines our time. It seems impossible for us to imagine a world where we do not have access to planes, trains and automobiles. However, mobility of people is only one facet of the globalized world, as there are other mobilities with a far greater impact than we have hitherto realized, with one in particular, mobility of information, being a source of crisis.

Mobility of information is inseparable from the mobility of people, as Peter Adey writes in

The Routledge Handbook of Mobilities: "Whilst people are mobile, the equally differentiated mobilities of information, capital, goods and services that are essential for contemporary life are a sustained feature of mobilities research." 1 While today´s discussions of mobility relate primarily to the movement of people, it is crucial to remember that the mobility -or circulation -of information and knowledge plays a crucial role in the globalized world. In fact, sharing information, news and knowledge is a cornerstone of our society. As Flavio Soares writes, "Information structures and personal information structures have been prerequisites for the construction of our society." 2 The result of the hyper-increase in the circulation of information is twofold. On the one hand, access to knowledge is unprecedentedly easy, but in the age of the internet, social networks, instant messaging and mass media, we are also overwhelmed by a constant flow of information, and the ability to process this body of data proves to be a challenge and a weakness that can be exploited by Soares, et al., Information Flow and Knowledge Sharing (Amsterdam: Elsevier, 2008) 17.

http://www.new-faces-erasmusplus.fr/ those who manipulate information to their will; a fact that is now becoming painfully clear.

Soares notes that information in a digitalized and global world is "the means to approach reality" 3 , but this reality can be easily distorted. Recently, a new dangerous phenomenon has arisen: "With the digital age and the rise of social media phenomena such as filter bubbles, echo chambers, and algorithms have emerged." 4 These algorithmically generated echo chambers make individuals withdraw from the circulation of new information and create cutoff social circles where pre-existing anxieties are validated and multiplied, while at the same time making objective discussion impossible, thus making echo chambers into a breeding ground for misinformation. Interestingly, the theme of withdrawal from the circulation of information and its negative effects finds its reflection in one of William Shakespeare's plays.

Circulating, sharing or withholding information: all these play a crucial role in Shakespeare´s The Winter's Tale; a play defined by mobility of individuals, but also of the information about them -from the very first scene, when we are told of the visit of Polixenes to Sicilia, to the penultimate scene of the play when the climactic moments are being relayed to us. Particularly act I, scene II, describing Leontes' quick turn from friend to tyrant serves as a warning about what happens when the circulation of knowledge is distorted, or when an individual actively avoids objective discussion. This scene inevitably results in crises that define the destinies of individual characters, but also the entire nation of Sicilia, and it is only when the free flow of information and people are restored in Sicilia that the play can come to a peaceful conclusion. In this paper, we will examine the importance of the circulation of information in the play, show the disruption of the flow of information in act I scene II and reveal its effects on the rest of the text. Finally, we will mirror the themes in the contemporary 3 Soares,17. 4 Vincent D. Guffy, ed. Digital Human Modeling and Applications in Health, Safety, Ergonomics and Risk Management (New York: Springer, 2019) 442.

http://www.new-faces-erasmusplus.fr/ crises. However, first we must briefly explore mobility of information in The Winter's Tale as a whole.

Mobility in all its forms plays an important role in The Winter's Tale. Each act is bookended by acts of mobility, from Polixenes' arrival to his escape, from Perdita´s banishment all the way to her return in the final act. However, these acts are always preceded or followed by information spreading through the world of the play. The necessity to relate and mediate information is established at the very start. The introductory scene merges the themes of physical mobility and the circulation of information as Archidamus and Camillo discuss the relationship of their respective rulers and, while doing so, they relate the information not only to each other, but to the audience as well: CAMILLO Sicilia cannot show himself over-kind to Bohemia. They were trained together in their childhoods; and there rooted betwixt them then such an affection, which cannot choose but branch now. Since their more mature dignities and royal necessities made separation of their society, their encounters, though not personal, have been royally attorneyed with interchange of gifts, letters, loving embassies; that they have seemed to be together, though absent, shook hands, as over a vast, and embraced, as it were, from the ends of opposed winds. The heavens continue their loves!5

Most importantly for us, this information precedes the physical appearance of the characters and serves as an integral part in the creation of their image. While we never learn to what extent the stories about the young princes and their supposed friendship are real, they are the only pieces of information we have and are therefore essential in our view of the following scene and the rest of the play. This effect of judging people based on the circulation of information about them extends from the audience to the characters on stage, as they too rely on the stories. When Archidamus says: "I think there is not in the world either malice or http://www.new-faces-erasmusplus.fr/ matter to alter it."6 -he bases his assumptions on the stories; they are enough for Archidamus to judge the reality of the friendship between Leontes and Polixenes. Indeed, the construction of reality based on circulation of information and the following subversion of that reality are Leontes's quick turn from a brotherly friend to a mortal enemy of Polixenes, and from a loving husband to a blind tyrant to Hermione, is famous for its incongruous nature and chaotic delivery. It encapsulates the mental processes of a person overtaken by jealousy and the phantoms of their own imagination. Leontes jumps from one argument to another, he hastens from conclusion to conclusion. At moments, he seems willing to believe that his train of thought is only a flight of fancy: LEONTES I' fecks! Why, that's my bawcock. What, hast smutch'd thy nose? They say it is a copy out of mine.9

But he then dismisses these thoughts as folly and goes on pursuing his hunch about Hermione's infidelity. Finally, he says: Affection! thy intention stabs the centre: Thou dost make possible things not so held, Communicatest with dreams; -how can this be? -With what's unreal thou coactive art, And fellow'st nothing: then 'tis very credent Thou mayst co-join with something; and thou dost, And that beyond commission, and I find it, And that to the infection of my brains And hardening of my brows. 10 http://www.new-faces-erasmusplus.fr/ Only after he is fully convinced that Polixenes and Hermione are in a romantic relationship, Leontes turns back to them and resumes the conversation. The thing that defines this scene, other than Leontes´ chaotic speech, is the cut that occurs when Leontes gets the first hints of suspicion. What had been up to that point going on as a conversation where the three involved freely exchanged stories of days past, suddenly turns into two separate conversations, one of which involves Leontes reverting into himself and completely cutting himself off from Hermione and Polixenes. As Siemon notes, this is emblematic of The Winter's Tale, as "The ritual action of the play takes the form of a withdrawal from the world followed by a return to it." 11 Leontes withdraws himself from the reality surrounding him and begins constructing a reality of his own. His own past, his marriage, his son, even the stories about his own life -so important to the reality constructed by the dramatic fiction -no longer apply once Leontes withdraws from the world. He is no longer willing to listen to his wife and friend, who are literally meters away. Once the flow of information is broken, Leontes enters a downward spiral which is driven, as he says himself, by "affection". And affection does not require objectivity or facts to construct truth, it makes "possible things not so held, communicates with dreams" and is coactive "with what's unreal". It would be possible to prevent the entire Although he is certain that his version of events is the definitive truth, Leontes also feels the need for confirmation from a higher source, believing that it will cement his beliefs in the eyes of the public and convict both Hermione and Polixenes: Though I am satisfied, and need no more Than what I know, yet shall the oracle Give rest to th'minds of others, such as he Whose ignorant credulity will not Come up to th' truth. 13 To do so, Leontes commands his lords, Cleomenes and Dion to travel to Delphi and seek the oracle, who should provide the divine and unquestionable truth, one that Leontes believes is correspondent to his own. This plan, however, does not work since the message from the oracle reads: Hermione is chaste; Polixenes blameless; Camillo a true subject; Leontes a jealous tyrant; his innocent babe truly begotten; and the king shall live without an heir, if that which is lost be not found. 14 The oracle, whose visions are eventually fulfilled, is understood as the bearer of definitive truth, and therefore a source of objective information. However, once Leontes undergoes his change objective reasoning and the search for truth loses all meaning to him. He can no longer relate to truth and, when faced with the prophecy, he dismisses it: "There is no truth at all i' the oracle: The sessions shall proceed: this is mere falsehood." 15 Since even divine truth no longer has any power in the reality Leontes has constructed, he freely proceeds to take action 12 The Winter's Tale, II, i, 38-41. 13 The Winter's Tale, II,ii,[189][190][191][192][193] The Winter's Tale, III, ii, 131-134. 15 The Winter's Tale, III, ii, 139-140. http://www.new-faces-erasmusplus.fr/ that ruins the lives of everyone involved and changes the face of Sicilia for more than a decade.

The actions Leontes takes reverberate throughout the play and lead to further crises of mobility. Stephen Greenblatt echoes Siemon's point about the ritual withdrawal and return when he mentions that Leontes´ withdrawal forces Hermione to do the same: "The Winter's Tale then at once rehearses and reverses the ritual pattern […] the tainting of the female, her exclusion from the social contracts and her ultimate reintegration into a renewed community." 16 By making Leontes' withdrawal from the circulation of information the cause of all further trouble, The Winter's Tale critiques action that is not based on well-drawn reasoning and discussion. Siemon brings backs his notion of theories when he says that by showing us Leontes´ falsehood, the play "calls into question his easy conviction that simple theory can be directly translated into simple action" 17 Furthermore, it berates the severing of oneself from the circulation of information. Siemon says: "what [The Winter's Tale] condemns is any attempt to act upon those theories without regard to the ambiguities of appearance and the complexities of reality" 18 Luckily for the inhabitants of Sicilia, there are still those willing to listen to the objective truth the oracle represents. As Virginia Lee Strain writes, "Paulina and Camillo, safeguard the oracle's relationship to the royal family and its relevance to the political reality by enabling the return of mother and daughter: Paulina obstructs plans to have Leontes produce a new heir and secretly shelters Hermione, and Camillo directs Perdita and Florizel to run away to Sicily. The oracle's supernatural powers of truth-finding are thus directly related 16 Stephen Greenblatt, Shakespearean Negotiations: The Circulation of Social Energy in Renaissance England (Los Angeles: University of California Press, 2010) 132-133. 17 Siemon, 11. 18 Siemon, 11. http://www.new-faces-erasmusplus.fr/ to the success of the human advisors in the play." 19 It is exactly those that Leontes refused to listen to, the advisors, who are the bearers of truth. This gives further significance to the necessity of discussion, of listening to advice, in guiding action and constructing realities, a trait that Leontes has lost by withdrawing from the flow of information around him. And precisely these issues prove crucial in today's world.

As we said at the very beginning, the advances in mobility are perhaps the greatest steps that humanity has taken in the last century. No wonder then, that the anxieties we can see in The Winter's Tale are exponentially multiplied and reflected in today's events.

Information and its circulation are instantaneous thanks to the internet, and while this has brought immeasurable boons to mankind, especially in recent years the incredibly large amount of information proves to be a threat to more than one aspect of liberty and democracy, particularly since the social circulation of information has shifted from public discussion onto social media. Recently, the social media phenomenon known as filter bubbles has emerged and is described as: "digital communities of like-minded individuals that are created through algorithmic filtering" 20 which "tailor online content to users' political beliefs, partisanship, and opinions." 21 Social filter bubbles slowly enclose individuals with other individuals who echo their own opinions leading to the greatest danger of social media: echo chambers. These are an outcome of filter bubbles, where "one's opinions, attitudes and even prejudices are magnified and stoked through skewed information […] and could lead to misconceptions about the actual state of the world." 22 What echo chambers represent, is a complete withdrawal from the circulation of information into a sphere where all one hears are the No wonder then that misinformation is very common in echo chambers. Worst of all, this fact can be essentially weaponized by those so inclined. Left enclosed within themselves and detached from the outside world, these modern Leonteses of the social media will eventually construct their own reality and embolden one another in their beliefs, but the direction of their construction can be easily manipulated. As we have seen in cases such as those of Cambridge Analytica, it is frighteningly easy to target specific groups with information that then spreads and steers the internal discussions of said groups. Leontes' drastic shift of opinion and subsequent cruelties were caused only by his own fancies but imagine a situation in which an invisible character, a "virtual Iago" whispers to Leontes and spurs him on in his transformation. That is a blueprint for catastrophe. Sadly, the virtual Iagos and Leonteses are an everyday reality of our globalized world, wherein information can be twisted or completely constructed to fit nefarious goals without the knowledge of the recipients. However, while Shakespeare's play serves as a warning of the negative effects of enclosing oneself and refusing to listen to outside sources, it also shows the potential solutions to the problem.

  apparent throughout the play. In an article "'But It Appears She Lives': Iteration in The Winter's Tale", James Edward Siemon says: "Life as it is depicted in the play is a thing of wonder, constantly betraying the neat theories of men." 7 However, what Siemon calls theories in his work are not just scientific theories, he encompasses the way individuals create theories of the world around them, thus constructing their reality. And nowhere is this construction more apparent than in act I, scene II. This famous scene shows the king of Bohemia as he prepares to leave Sicilia. Despite pleas from his lifelong friend Leontes, Polixenes remains unshaken in his resolve to return to his home and tend to royal matters there, as he is spurred on by his lack of information about his home country: POLIXENES Sir, that's to-morrow. I am question'd by my fears, of what may chance Or breed upon our absence; that may blow No sneaping winds at home, to make us say 'This is put forth too truly:' besides, I have stay'd To tire your royalty. 8This brief quote again shows the importance of information on the mindset of characters. It is the lack of information that pushes Polixenes to leave. Nonetheless, once queen Hermione speaks to Polixenes but for a moment, his views change. He is suddenly willing to stay, a fact that is not lost on Leontes. In an instant, Leontes steps away from the conversation and reverts http://www.new-faces-erasmusplus.fr/ into his thoughts. He begins talking to himself and reaches the conclusion that Polixenes' willingness to listen to Hermione is not a mere coincidence. He begins to contemplate the possibility that Hermione and Polixenes have been in an ongoing romantic relationship, going so far as to assume that Polixenes is the father of Leontes´ children. Leontes eventually convinces himself that these assumptions are reality and once Hermione and Polixenes leave the scene, Leontes begins to plot Polixenes' assassination and Hermione's imprisonment.

  conflict if Leontes were willing to turn back to Hermione and Polixenes and ask them to clarify the situation in an open discussion, but that does not happen. Instead of listening to facts and information, Leontes weaves his own out of thin air. What is more, from this point onwards, Leontes is unshakable in his opinion that the conspiracy he fabricated is more real than anything anyone else can say: http://www.new-faces-erasmusplus.fr/ LEONTES How blest am I In my just censure, in my true opinion! Alack, for lesser knowledge! how accursed In being so blest! 12

  http://www.new-faces-erasmusplus.fr/ echoes of their previous beliefs, thus perpetuating a disconnection from reality and the construction of a new one. This is exactly the case with Leontes, whose fears only developed because he detaches himself from the outside reality and proceeds to creating his own version of the truth based on his own beliefs and a great dose of self-invention perpetuated by preexisting insecurities. But whereas this is only an individual's personal turn, in the era of echo chambers the construction of a false reality is a mass issue. Social media of all kinds gradually enclose individuals into impenetrable bubbles that hinder objective discussion. As we see in Leontes' example, this kind of enclosure can lead to destructive effects.What is more, such withdrawal allows for the creation of issues essentially from thin air. Affection is coactive with what is unreal and makes the unreal possible, as says Leontes.

  19 Virginia Lee Strain, "The Winter's Tale and the Oracle of the Law", Legal Reform in English Renaissance Literature, by Virginia Lee Strain, Edinburgh University Press, Edinburgh, 2018, p. 177. JSTOR, www.jstor.org/stable/10.3366/j.ctv7n0997 23 Jun 2019 23 Jun 2019. 20 Ilan Manor, The Digitalization of Public Diplomacy (New York: Springer, 2019) 137.

21

Manor, 137.

22

Manor, 137-138.

The Winter's Tale, I, i,[21][22][23][24][25][26][27][28][29][30][31][32]

The Winter's Tale, I, i, 34.

James Edward Siemon, "'But It Appears She Lives': Iteration in The Winter's Tale", PMLA, Vol.

89, No. 1 (1974): 11. JSTOR, https://www.jstor.org/stable/461662 23 Jun 2019.8 The Winter's Tale, I, ii, 10-14.

The Winter's Tale, I, ii,[120][121][122]

The Winter's Tale, I, ii,[138][139][140][141][142][143][144][145][146]


Servitude in Death: Lucrece/tia's Suicide and the Necropolitics of Representation

Jamie Rose, Charles University, Prague Revolutionary suicide does not mean that I and my comrades have a death wish; it means just the opposite. We have such a strong desire to live with hope and human dignity that existence without them is impossible. 1 Og við sverðs míns egg Loks af friður hlýst. 2 Overthrowing the current governing system and replacing it with one that is, at least theoretically, fairer and more just is never an easy task. It requires several ingredients to be added into the pot of revolution -among them mass discontent, the willingness to make sacrifices and, more often than not, an inciting incident, typically an act of violence that underscores the problems of the status quo. The Rape of Lucrece, one of Shakespeare's extended poems, takes place at such a time and it is Lucrece's rape and subsequent suicide that become Lucius Junius Brutus's casus rebelli against the Roman monarchy.

This is perhaps all well and good on a macro level, but what are we to make of the position of Lucrece's death in the matter? If this rebellion is indeed carried in her name, what sort of concern does Brutus show for her plight and that of other women, if any? As he pulls the knife out of her still-bleeding body and solemnly swears to punish the monarchical system for the crimes of the king's son, Lucrece is already fully turned from a subject into an object -or, more precisely, an instrument by which a rebellion may be carried out and justified. In a way, the old feminist adage of "the personal is political" is just as relevant as ever, as her personal experience becomes transmuted by Brutus into a microcosmic representation of all the injustices, real and imagined, that Romans suffered under the political system of monarchy. Yet, it is also a personal power-grab, as Brutus and the other aristocrats who join in his pact suddenly have the opportunity to usurp the power of the king and distribute it among themselves. This is, unfortunately, an all-too-common scenario in the script of revolutions and struggles for social change -the initially deeply personal circumstances of the inciting incident become overwritten by the political desires of those who wish to use the victim's or survivor's experience as a rallying cry. I am not suggesting that this is always necessarily to the detriment of society 3 or that this always goes against the wishes of those whose suffering and death become utilised in such ways, but I would nevertheless like to explore Livy's and Shakespeare's representation of the story of Lucretia and compare them to some modern examples in which the suffering and death of marginalised people are emptied of their personal situatedness and become, instead, a socio-political reference point. As someone coming from an activist background, I am particularly concerned about the long-term negative impact of these desubjectivised and decontextualised narratives both on the survivors/victims as well as on the stability of socially progressive movements. How do we represent individual experiences in a way that always centres and gives voice to the survivors/victims while also using them as exemplifiers of systemic issues that warrant addressing? In other words, how do we ensure that the personal and the political are allowed to exist at an equilibrium, rather than one becoming substituted by the other?

The politics of representing suffering and the conversion of said suffering into praxis is clearly nothing new -there is a vast cornucopia of texts that deal with similar issues, particularly in the context of journalism, a field which often tries to be a medium through which personal experience is converted into transformative praxis. Among many noteworthy examples, John Hersey's Hiroshima, a 120-page article that took up an entire issue of The New Yorker magazine in August 1946, attempts to mediate, through the perspective of multiple witnesses, the otherwise unimaginable horrors of nuclear warfare. This microcosmic-to-macrocosmic nature of Hiroshima allowed for the flow of empathy and directly helped initiate the first waves of anti-nuclear activism across the anglophone world:

[…] here, for the first time, is not a description of scientific triumphs, of intricate machines, new elements, and mathematical formulas, but an account of what the bomb does -seen through the eyes of some of those to whom it did it: of those who endured one of the world's most catastrophic experiences, and lived. 4

3 Even drawing from recent Czech (and Slovak) history, it is rather clear that the Velvet Revolution protests of 1989 that led to the overthrow of the Soviet-inspired totalitarian system would not have grown to such a scale had it not been for rumours (later proven untrue) of a student being killed by the riot police. 4 John Hersey, Hiroshima, "Publisher's Note" (Harmondsworth: Penguin Books, 1946) ix.

It is for this reason that any such analysis must be inextricably linked to journalism and historiography or, if we allow ourselves a broader expression, to the practice of truthmaking.

Where does this, then, leave Lucretia/Lucrece? How did her story get told by those who approached it and where did they place their emphasis? Let us begin with a brief overview of Titus Livy's version of the tale and do so with the presupposition that not only is historiography itself an act of storytelling and ideological construction, but also that the story as recorded by One day several men, among them Collatinus, Lucretia's husband, were drinking in the quarters of Sextus Tarquinius, the son of the then ruling tyrant. Soon the subject of wives arose, and each man bragged that his wife was the most virtuous. Collatinus interrupted the rivalry urging, "What need is there of words when in a few hours we can prove beyond doubt the incomparable superiority of my Lucretia?" With this the men galloped off to Rome, where they found all of the other men's wives luxuriously enjoying themselves in their husband's absence while only Lucretia was found modestly dressed

and "hard at work by lamplight upon her spinning."

During the subsequent dinner, Tarquin was inflamed with lust by Lucretia's beauty and proven chastity. Several nights later he burst into Lucretia's bedroom, demanding she submit to him. Even when he threatened her with death, Lucretia refused. Finally, he reviled her: "If death will not move you, dishonor shall. I shall kill you first, then cut the throat of a slave and lay his naked body by your side. Will they not believe that you have been caught in adultery with a servant-and paid the price?" With this threat, Lucretia yielded.

The following day she called her father, her husband, and Brutus, a family friend, around her. She recounted the rape and demanded revenge. She would testify to her innocence, she asserted, by killing herself: "My heart is innocent, and death will be my witness".

Her family tried to dissuade her, arguing vehemently that only her body, not her honor had been violated, that without intention there could be no guilt. Refusing to listen, Lucretia plunged a dagger into her heart.

While her husband and father were lost in grief, Brutus pulled the dagger from Lucretia's breast and urged the men to join together to drive the despotic Tarquins from Rome. Roman men rallied around Brutus's call for vengeance, and Rome was subsequently liberated and Brutus named the founding father of the republic. 5

I am choosing to cite this passage in full in large part to illustrate how closely, in fact, the plot contained in Shakespeare's poem follows Livy's rather simple outline. Notable here is also the fact that, already within this account, there is some attention paid to Lucretia's inner struggle with what she's been through paired with the lack of external judgement of her as "impure" or "dishonoured" -after all, the first paragraph very strongly presents Lucretia as a paragon of Roman feminine virtue. 6 Additionally, what is more relevant to the concerns of this essay, Matthes observes the important fact that while Brutus already had a very clear casus rebelli against the Tarquin family, as they murdered his brother and father, it was actually Lucretia's rape that was the rebellion's inciting incident. 7 In this sense, Lucretia's rape and subsequent suicide actually carries more weight than even the act of murder. Brutus's reaction, which remains the same both in Livy's and Shakespeare's versions, is then both more personal and cynical. On one hand, he is once again forced to grapple with the power the Tarquins have over the lives of Roman nobility, the same power that ended the life of his brother and of his father, and these are certainly images that come back to him as he bears witness to Lucretia's suicide.

On the other hand, her death becomes the instrument through which he can not only accumulate more power by wresting it out of the hands of the king, but also as a way through which he may finally achieve his own revenge, as he begins to build his alliance of outraged noblemen. The fact that one of Brutus's goals is vengeance dramatically recontextualises his character, as he is not only the perpetrator of political violence, but also a victim of it.

Returning, then, back to Shakespeare's poem, we can now contrast its focus with that of Livy.

As stated earlier, Livy already hints at Lucretia's psychology and the tragedy of a woman who was compelled to commit suicide, despite her husband's assurances of innocence, because she was unable to cope with her trauma. The bulk of The Rape of Lucrece is comprised of depictions of two inner struggles -one on Tarquin's side, the other on Lucrece's. The important effect here is one of humanisation of both the rapist and of the survivor and the movement of action from the external into the introspective, the result of which is that far more attention can now be paid to Lucrece herself who would, otherwise, be forced to remain a fairly passive actress throughout the narrative (with the exception of her temporarily assuming agency through suicide, a trope that has historically plagued many fictional representations of women).

Shakespeare's insertion of the psychological element into Livy's outline represents a radical shift in the act of truthmaking, as it recognises that the "truth of the matter" is not merely contained in the description of observable action and social transformation, but must also seek to depict the emotion and psychology that motivates people to these actions.

In a way, this recontextualisation of the story of Lucrece follows the pattern that many contemporary activists, journalists and historians who are concerned with the praxis of radical social transformation favour over accounts of the world that are rooted in physically observable evidence and numbers -in other words, it resists the notion of empiricism as the singular valid tool through which a human and social experience should be represented.

Yet, even today, there remains a strong tension between the politics of representing the suffering of one as opposed to the oppression of the many and, more often than not, this distinction often follows social patterns of marginalisation and dehumanisation in cases where the human subject becomes reduced to a numerical figure. Broadly speaking, those who already possess some degree of privilege are given more opportunity to have their negative experiences represented as being particular to them, as being simultaneously personal as well as symptomatic of some greater socio-political issue that warrants addressing. Staying with the example of sexual violence, the #MeToo movement is a prime example of this inequality of access to subjectification. While it has been widely known that women, particularly marginalised women, experience high rates of sexual harassment and violence in the workplace, their stories were routinely denied the same media attention and, by extension, cultural and political impact that the stories of privileged, rich, typically white, Hollywood actresses. In the wider global arena, we can observe the ways in which death becomes framed along similar axes of significance. What makes the loss of certain lives "grievable" while others get reduced to statistics or to Livy-like accounts that prioritise depersonalised description over the actual circumstances of an individual internal and external life?

For this, I would like to look at an annual event that remains important to my community and that has already been subject to relevant criticism, the Transgender Day of Remembrance that occurs every 20 th November. The history of the Transgender Day of Remembrance (otherwise known as TDoR) goes back to 1999, when it was originally started as a vigil for Rita Hester, a trans woman from Allston, Massachusetts who was murdered in a transphobic attack. The modern importance of the event is two-fold: Firstly, it honours the memories of those whose lives would have otherwise been deemed ungrievable by a society that systematically devalues the lives of trans people. Secondly, this act of remembering the dead also reminds the participants of how much there is still left to be done in the field of social change as well as of their own complacency. In other words, TDoR retroactively makes the lives of trans people into lives that mattered and continue to matter through the act of grieving, putting into practice what Judith Butler describes in her introduction to Frames of War: When Is Life Grievable?: "Only under conditions in which the loss would matter does the value of life appear. Thus, grievability is a presupposition for the life that matters."8 Yet now, twenty years later, it remains dubious whether TDoR truly achieves this.

As the project itself grew, so did the list of those deemed to have been the victims of transphobic violence, a list that predominantly contains the names of trans women of colour, many of whom lived in parts of the world far away from the remembrance ceremony. Beyond their names (many of which are listed as anonymous), the only other records on the list typically contained in an entry are month of death and cause of death. Can it then, in any reasonable way, be said that this is an act of resistance to the depersonalisation of marginalised death? That we are somehow honouring the hundreds of names that list contains every year in a way that remains "Their" deaths were not in vain, one of the speakers is said to have stated: "they" made it possible for "us" to come together today. Among "them" was Tyra Hunter. Like so many of its globalizing predecessors, the Berlin TDOR thus incited a trans community into life whose vitality depends upon the ghosting of poor trans people, trans people of color, and trans people in the Global South.9

A similar, albeit a much more personal, criticism of how TDoR has been transformed from an act of remembrance into one of political activism also appears in Amber Dawn's essay "How to Bury Our Dead" where she describes her experience of attending TDoR in Vancouver in order to grieve for a trans woman she personally knew and who was brutally murdered a few months prior. She went to the event with hopes of being given some space to speak and inform people about what a resilient and strong woman Shelby Tom was, especially considering this event was held in her home city. Instead her name was simply read out from a long list that included a gruesome description of her murder, which made Amber Dawn break down in tears, as she was denied the chance to publicly honour Shelby's memory. [START_REF] Dawn | How to Bury Our Dead[END_REF] Such an approach very strongly echoes the ways in which Brutus responds to Lucretia's murder.

While her husband and father bicker over which one of them has a greater claim to grief (which in some ways mirrors other discussions surrounding TDoR that have to do with whether certain people memorialised were truly victims of transphobic violence or of violence that had a different motive), Brutus wastes no time as he pulls the knife from her body and immediately begins instrumentalising her corpse as well as the weapon for his own needs. Furthermore, as Melissa M. Matthes catalogues in The Rape of Lucretia and the Founding of Republics, the mythological event of Lucretia's rape has been used to justify different forms of society and constitutes a "[…] memory designed to ignite political action even as it aims to occlude femininity." [START_REF] Matthes | The Rape of Lucretia and the Founding of Republics[END_REF] In other words, issues such as masculinity, power, ideal constructions of womanhood etc. become overwritten with what philosophers and historians (often one and the same) would consider to be more "pressing matters" -the political system at large as it pertains to the distribution of power among privileged men. As Brutus and the two other men go "To show her bleeding body throughout Rome, / And so publish Tarquin's foul offence," [START_REF] Shakespeare | The Complete Works of William Shakespeare[END_REF] the suffering of this Lucretia undergoes an irreversible transformation from the personal to the political, employed to change the Roman system to one that is just as unfair to women as the previous one. In a way, as Tarquin forcibly claimed Lucretia's living body, so does Brutus claim her corpse to sate his own desires for power and revenge. It is unavoidable to think of the realworld parallels to Brutus's instrumentalisation of Lucretia's death, some of which have already been outlined here, but the question remains of how we should transform our praxis in order to be fairer to both the living and the dead.

An example presents itself in the recent coverage around the five-year anniversary of the death of Eric Garner, an African-American New Yorker killed by a member of the NYPD, which became one of the sparks that ignited the Black Lives Matter movement across the United States. While much of the recent re-emergence of coverage had to do with the fact that the statute of limitations would run out if none of the cops were charged with his murder -which they were ultimately not, not even the one who put Mr Garner into an illegal chokehold which eventually caused him to suffocate -and the fact that New York City mayor Bill DeBlasio, a self-proclaimed progressive and a Democratic candidate for the presidential office, refused to punish the perpetrators through some of the extra-judicial means available to him, such as firing them, progressive media outlets like Democracy Now! provided space for the voices of Mr Garner's family to be heard, bringing grief and personal outrage to the forefront. 13 Decisions such as these regarding the presentation of socio-politically important violence and death ensure that, while the act itself may be instrumentalised by movements with which the victim/survivor may or may not have allied themselves with, the personal impact of this violence is not forgotten in the protests that it helped spark. In fact, this polarity between the personal and the political can be seen in how another event that had to do with racism and police brutality is remembered in name -the Rodney King Riots are also known as the 1992 LA Riots. One preserves the name of the man who was beaten for the LAPD's entertainment, the other does little but tell us where and when the event took place. This is, to some extent, the same barrier that separates Livy from Shakespeare. Livy cares little for who Lucretia may have been as a person, what things must have been going through her head for her to take her own life even as she was ensured that her honour had not been sullied.

While glimpses of the internal may be spotted in his account, she remains a mere tool for his narrative of social progress, more useful as a corpse than as a living woman. On the other hand, Shakespeare is far more interested in the living woman and, in order to present her as such, he is forced to take Livy's story and begin writing in its margins, breathing new life into the void of Lucretia and transforming her into Lucrece. Yet, as I praise Shakespeare for the act of giving her an interiority, it is important to also keep in mind that the Lucrece of his poem only comes to life at the moment of her rape -her mind is hidden to us up until that point and we are instead forced to witness Tarquin's thoughts -which presents a whole new challenge of its own, one that similarly echoes the ethical issues of grievable violence, where the perpetrator's background is often picked apart and analysed while what we know of the victims/survivors rarely extends beyond the event they had been through, as was the case with the 2016 Pulse Nightclub shooting in Orlando, Florida. It is in this regard that I find my edition of Shakespeare's work, a reprint of the 1904 Stratford Town Edition, to be quite striking, as it refers to the poem simply as Lucrece -the rape is nowhere to be found in the title. While we may speculate over this particular choice, the impulse for which was likely a conservative one, it does remove the character of Lucrece from the traumatised state, the only state in which she appears to us in the poem, and opens up new possibilities for us to think of what she may have been like as a person, as a woman and a human being. The title, Lucrece, is the next step on the road towards genuine compassion and empathy, a step that many people, be they activists, writers, journalists or readers, have, unfortunately, yet to take. This is because the politics of representation not only represent what happened, but they also alter the memory of the very thing they are representing, as Susan Sontag writes in Regarding the Pain of Others:

"Something becomes real -to those who are elsewhere, following the 'news' -by being photographed. But a catastrophe that is experienced will often seem eerily like its representation." 14 In order for a shred of ethicality to be preserved in how we write about events as personally catastrophic as rape, suicide and murder, we must build our representation from the experience rather than constructing the experience around its representation.

  aware of each individual life? Are we truly grieving for people or are we, instead, grieving for the concept of transphobic violence? As the organiser of last year's Transgender Day of Remembrance in Prague, these were questions that weighed quite heavily on me and which, over time, made me inherently suspicious of similar depersonalised representations of the suffering and pain of others. I did not want to instrumentalise the lives and deaths of people I never knew for the benefit of my own local activism, a criticism raised against Berlin-based trans activists by C. Riley Snorton and Jin Haritaworn in "Trans Necropolitics: A Transnational Reflection on Violence and the Trans of Color Afterlife":

  WORKS CITED "'They Didn't Do Their Job': Eric Garner Family Outraged DOJ Won't Prosecute His Death by Police." Democracy Now!. Democracy Now!. 17 July 2019 <www.democracynow.org/2019/7/17/eric_garner_justice_dept_no_charges> 23 July 2019. Web. Amber, Dawn. "How to Bury Our Dead". How Poetry Saved My Life: A Hustler's Memoir. Vancouver: Arsenal Pulp Press, 2013. 90-99. Butler, Judith. "Introduction: Precarious Life, Grievable Life". Frames of War: When Is Life Grievable?. London: Verso, 2013. 1-32. Hersey, John. Hiroshima. "Publisher's Note". (Harmondsworth: Penguin Books, 1946) v-ix.

Huey P. Newton, Revolutionary Suicide (New York: Penguin Books,

2009) 3. 2 Austin Wintory, "Only We Few Remember It Now," The Banner Saga 3, track 22, Bandcamp <https://austinwintory.bandcamp.com/track/only-we-few-remember-it-now>.

Judith Butler, "Introduction: Precarious Life, Grievable Life," Frames of War: When Is Life Grievable? (London: Verso, 2016) 14.

C. Riley Snorton and Jin Haritaworn, "Trans Necropolitics: A Transnational Reflection of Violence and the Trans of Color Afterlife," The Transgender Studies Reader vol. 2 (New York: Routledge, 2013) 74.


From Privilege to Necessity: The Dual Nature of Mobility in The Winter's Tale and Today

Barbora Šedivá, Charles University, Prague

The twenty-first century might be described as the age of mobility. If we approach the term in its literal meaning as a geographical displacement, we will observe that the members of our society are constantly on the move. However, there are different kinds of mobility and not all people travel for the same reasons. Generally speaking, there are two kinds of mobility -one driven by interest, the other by compulsion. While some people travel in order to visit exotic places and learn about distant cultures, others are driven on the road to escape from danger and to save their lives. The first kind of mobility is enabled by privilege and freedom of movement, the second by necessity and the lack of freedom. The former focuses on arrival, the latter on departure. People with the desire and the means to travel do so with the vision of eventually returning back home. Those, who run away from their homes for salvation, can only hope to find a new home somewhere else.

Both of these kinds of mobility are represented in Shakespeare's The Winter's Tale.

Although the conditions of traveling are vastly different from our own, the characters in this play experience similar reasons for mobility as we might encounter today. Polixenes, the King of Bohemia, travels to Sicilia in order to pay a visit to his friend King Leontes. Due to a sudden change of circumstances, his visit ends prematurely and Polixenes needs to escape the country in order to save his life. Similarly, but contrariwise, his son Florizel is driven from Bohemia in order to save his marriage and, through a sudden revelation of some hidden facts, his refuge in Sicilia turns into a pleasant visit. In this way, the contrary movements of these two characters reflect the two kinds of mobility present in our own age. It is, therefore, still relevant to read Shakespeare, for his plays often provide a valuable commentary on contemporary issues. In this particular case, I am going to show how The Winter's Tale presents the way in which a simple change of circumstances might result in the transformation of mobility from something pleasant to something imperative, from privilege to necessity.

In his lecture entitled "Des Espaces Autres"1 (Of Other Spaces) delivered in March 1967, the French philosopher Michel Foucault suggested that as opposed to the nineteenth century, which had been marked by its obsession with history, the subject of the present age would be space. While before, the emphasis was on the development of events on a temporal scale, today we are more interested in the spatial experience of reality. However, what we need to be focusing on is the combination of these two dimensions, for there is an inevitable link between them. As Foucault observed, "space itself has a history in Western experience, and it is not possible to disregard the fatal intersection of time with space."2 In this essay, I will observe the role of this intersection and its representation through the theme of mobility in Shakespeare's The Winter's Tale.

As a spatial transformation enabled by temporal progression, mobility might serve as one of the most vital expressions of the intersection of the time and space. Over the course of its plot, The Winter's Tale observes many mobile developments that propel the action and influence the timespan. It is precisely through movement that most of the events in the play are initiated and the plot moves forward. This strategy is not, of course, exclusive to this particular play, as it was often employed by previous literary texts. In fact, the merging of time and space and its reflection in movement was used both as a theme and as a vehicle of plot development in literature ever since ancient times. This representation was most famously described by the Russian philosopher Mikhail Bakhtin. By observing the intersection of time and space in its fictional representation, Bakhtin opened up a field of research that has been considered relevant in our discourse ever since. He applied the term "chronotope" (from the Russian xронотоп, a portmanteau of the Greek words χρόνος, meaning "time," and τόπος, "space") to refer to "the intrinsic connectedness of temporal and spatial relationships that are artistically expressed in literature." 3 According to Bakhtin, the chronotope plays a significant role in the definition of literary genres; it is, in fact, the main defining factor in generic distinctions. He recognizes several different types of chronotopes, among which the one involving the act of taking to the road could be considered the paramount one. "The importance of the chronotope of the road in literature is immense," Bakhtin asserts, "it is a rare work that does not contain a variation of this motif, and many words are directly constructed on the road chronotope, and on road meetings and adventures." 4 The Winter's Tale is precisely one of these works of literature that incorporates the chronotope of the road as the main driving force of the plot. Whether physical or imaginary, the theme of journey and movement seem to govern this play. While the two chief locations, Sicilia and Bohemia, are hardly described with any degree of geographical accuracy, they function more as symbolic spaces endowed with exotic quality and characterized by spatial separation and cultural estrangement. It is the ceaseless movement between these two spaces that propels the action of the plot. This is not, however, any haphazard kind of movement. In Creswell's influential study provided the definition of mobility as it is understood in contemporary theory. According to his now-familiar formula, mobility is the realization of movement equipped with meaning and power. In other words, the difference between simple movement and mobility is that the latter has "been given meaning within contexts of social and cultural power." 6 Since there is no inherent value in movement, it is only through society and culture that it becomes mobility; "its meaning is created in a constant process of cultural give and take." 7 This is precisely the case with all the geographical dislocations in The Winter's Tale.

Since the movement between Sicilia and Bohemia is always driven by certain purpose and endowed by cultural or social significance, it should be understood as mobility in our present comprehension of the term as suggested by Cresswell. The play itself begins with a situation brought about by such mobility. It is the trip of king Polixenes to the kingdom of his friend Leontes, which takes place before the play's opening scene and which sets in motion the dynamics of the plot. The social function of this trip has many layers. It is not only a friendly visit paid by the king of Bohemia to his lifelong acquaintance, the king of Sicilia, but also the performance and consolidation of a relationship between the two kingdoms. In this sense, the figure of the head of the nation serves as a metonymy for the nation as a whole. This is demonstrated in the official quality of the language used by the two kings, as well as in the way they are referenced in the speech of others.

The short opening scene witnesses this kind of reference in the dialogue between Camillo, a lord of Sicilia, and Archidamus, a lord of Bohemia. When talking about the kings, Camillo makes the following observation: "Sicilia cannot show himself over-kind to Bohemia… [emphasis mine]."8 The use of the highlighted pronoun "himself" betrays the actual referent of "Sicilia," which is not the country as such but rather the king. At the same time, the body of the king serves as a representation of the whole nation and all of his acts are to be interpreted on a national level. The mobility of king Polixenes from Bohemia to Sicilia thus acquires even a greater degree of significance precisely for it is to be understood as a symbolic movement of the kingdom as a whole. Polixenes' departure from Sicilia is followed by yet another, less observed, kind of mobility. It is the removal of Leontes's newborn daughter, who is deemed to be his wife's illegitimate child and whose presence at the court is thus seen as undesirable. This occurrence concludes the first half of the play and sets the stage for the events of the second one. These will come to mirror the incidents of the first half, especially as regards mobility. The two parts are separated by a passage of time, sixteen years to be precise, during which period the mobility between the two kingdoms is halted along with any significant events shaping the plot. The second half of The Winter's Tale begins with happenings that soon call for another mobility.

Although physical movement has been on pause for sixteen years, there was yet another kind of mobility that took place during this passage of time. It was the motion of growth and personal development, especially in the case of Perdita, the daughter of king Leontes. Brought up far from her birthplace -in a shepherd's house in the land of Bohemia -Perdita grew up to be a beautiful young woman, whose evolution as a human being had a profound effect on the subsequent events in the play. As Florizel, the prince of Bohemia, finds himself in love with the young princess, whose royal status is yet unknown, his father Polixenes is faced with a new challenge -how to deal with a situation that might result in his son marrying bellow his social class? When Polixenes finds out about his son's objective of marrying Perdita, a similar kind of inner motion takes place in his mind that characterized the previous change of thought in king Leontes. Although this transformation is much more justified and understandable than the former one, the result is virtually the same: another need for physical mobility, again in the form of a flight. Similar to Polixenes himself in the first half of the play, Florizel is now forced to leave the country in order to save what is dear to him -the prospect of his marriage with the love of his life. Interestingly enough, Florizel finds refuge where, many years before, his father found a threat to his life -at the court of king Leontes. The distressing conditions of Florizel's parting with Polixenes and the escape to the kingdom of Sicila are, fortunately, not to last long.

Soon after their arrival to Sicilia, Florizel and his bride are delivered from their predicament by the revelation of Perdita's real origin and social status. After many years of hostility between the two kingdoms, Leontes's error is brought to light and the friendly relation between Sicilia and Bohemia is allowed to resume. The marriage of Florizel and Perdita serves to foster this relationship and secure its positive future course. In order to give this event a proper share of attention and celebrate the happy conclusion of all events, the last instance of mobility brings king Polixenes and Camillo on the scene, and the reunion of the two kingdoms is thus complete. The end of the play brings us to the same geographical location where we started and the joyous meeting of the two kings is again described through the words of secondary characters rather than being displayed directly on stage. Polixenes and Leontes are again referred to as representatives of their kingdoms and their encounter is depicted by one of the witnesses as the happiest of all occurrences.

In my analyses of the theme of mobility in The Winter's Tale, I have shown the way in which movement, both physical and spiritual, acquires social and cultural significance within the play and contributes to the development of the plot. What I am going to argue in the following section of the present study is that not only does movement acquire meaning in the context of the play's dynamics but this meaning also rises in importance when perceived in relation to our contemporary age.

Mobility has been an essential part of western culture for centuries. In order to emphasize this relevance, I am going to borrow from Ingrid Horrocks, who, in her observance of literary texts at the turn of the nineteenth century, distinguished the traveler as "the emblematic modern subject."9 With the contemporary, tourism-driven nature of our society, the importance of traveling and mobility seems only to have increased. However, it is not only the touristic endeavors that provoke movements in the twenty-first century. Just as I have described in the introduction, the current migrant crises in Europe shows that there are, in fact, other kinds of motivations for mobility. These are not, however, exclusive to our present age. Although the migrant crises might be described as a contemporary issue, mobility as a means of escape and salvation was always present in our society. This might be demonstrated by the use of if as a theme in many works of literature, including Shakespeare's The Winter's Tale.

In the following discussion of the play's events in relation to the present age, I will desist from comparing the situation of Shakespeare's characters to that of the modern refugees, for that would not only be historically inaccurate but also gravely disrespectful and underestimating in terms of the seriousness of the latters' situation. Instead, I am going to point out some of the instances within the play that might make the modern reader aware of the thin line between mobility as a privilege and as a necessity. As the play shows, the need to take to the road for the purpose of refuge does not necessarily befall people in distressful economic or social situations. In fact, it is the members of the royal family itself that experience the need to escape their predicaments in The Winter's Tale.

The beginning of the play witnesses the king of Bohemia enjoying his visit in a distant land, a situation one might perceive in terms of his royal privilege. However, a slight change of circumstances soon drives even the king himself back on the road. While his trip to Sicilia was endowed with positive prospects of his stay abroad, the expeditious return home acquires the character of an escape one would hardly associate with a king. The situation of his son in the second half of the play is different in that Florizel has no home to escape to. Instead, he needs to escape from home if he wants to remain true to his principles. In this way, although he is the prince of Bohemia and his domestic situation is thus hardly in danger, Florizel finds his own concerns that challenge the peaceful quality of his dwelling in Bohemia and drive the young prince into exile. Neither the king's nor his son's relationship to home or the road should be thus taken for granted. The nature of their mobility is constantly affected and shaped by the physical and imaginary movements of others around them and the privileges afforded by their social status are not always sufficient in determining their motivation for traveling.

If social conditions were not ample to secure a stable role of mobility in one's life already in the Early Modern period, nor should they be considered so today -in an age defined by a much greater degree of uncertainty and transience. What I am trying to achieve in this study is to point out the volatile status of our present approach to mobility and to reemphasize the need for compassion with those who do not possess the same privileges in this field as we do. Whereas mobility remains an attractive option for the majority in the modern western world, there are many subjects throughout Europe, as well as the rest of the world, for whom physical displacement and permanent departure from home forms an unavoidable condition of survival. The first step towards assisting these people in their struggles is the ability to understand their situation and sympathize with their hardships.

While reading Shakespeare's plays will not by itself solve the migrant crises that Europe is currently facing, it might raise awareness of the conditions surrounding mobility in general as well as the unstable nature of our own relationship to movement.

Mobility is an issue, the significance of which in our culture has been constantly on the rise. Instead of promoting the freedom of movement for certain segments of society while denying it to others, we should interrogate the motives behind global migration and consider the fragile relationship between mobility as a privilege and as a necessity. Reading the works of the Early Modern period might prove extremely helpful in this endeavor, for it gives us different perspectives on this issue and forces us to reconsider our own standpoint. If reading is an exercise in critical thinking, as it is commonly deemed to be today, and mobility a pervasive thematic concern in literature, as it has been ever since its earliest manifestations, then approaching texts such as The Winter's Tale can only bear fruit. Through the analyses of the meaning and function of movement in this particular play, I have shown that the status of mobility in the lives of individuals is rather unstable. What we might learn from the overseas voyages of king Polixenes and his son is that the privilege of voluntary mobility enjoyed by the majority of the modern western world is not to be taken for granted, for all our trips might at any point turn into flights.

3

  Mikhail Bakhtin, "Forms of Time and of the Chronotope in the Novel," The Dialogic Imagination: Four Essays by M. M. Bakhtin, trans. Caryl Emerson and Michael Holquist (Austin: University of Texas Press, 1981) 84. 4 Bakhtin 98. fact, most of the geographical displacements undertaken by the characters in the play have their own designs and they acquire certain significance within the plot. It is for this reason that we describe the present kind of motion as mobility rather than a simple movement, employing the distinction introduced by Tim Cresswell in his influential study of mobility in the modern west. According to Cresswell, "mobility is central to what it is to be human. It is a fundamental geographical facet of existence." 5 Considering this prominence of mobility in our culture, it is quite baffling that the term itself should have been present in critical discourse for so long without being properly defined. It was only a decade ago, in 2006, that

  The peaceful visit is suddenly interrupted by mobility of a different kind. It is the inner motion of thought in king Leontes's mind that gives way to a new series of incidents leading up to Polixenes' eventual departure from Sicilia. The internal movement thus becomes reflected in the external dynamics of the play. Although it remains unclear what gave Leontes the reason for his abrupt change of thought, this spiritual kind of mobility nevertheless plays an important role in the development of the plot. The result of this inner motion is the presumed infidelity of Leontes's wife and Polixenes' alleged betrayal. The friendly status of the relationship between the two kingdoms is disrupted and Polixenes' own life is put in danger. In this way, the pleasant visit turns into a troubling situation, the only solution of which is another mobility, a physical one this time -a flight.

  BIBLIOGRAPHY Bakhtin, Mikhail. "Forms of Time and of the Chronotope in the Novel." The Dialogic Imagination: Four Essays by M. M. Bakhtin. Translated by Caryl Emerson and Michael Holquist. Austin: University of Texas Press, 1981. Cresswell, Tim. "Mobility as Resistance: A Geographical Reading of Kerouac's On the Road." Transaction of the Institute of British Geographers 18.2 (1993): 249-262. JSTOR <http://www.jstor.org/stable/622366> Accessed 12 Feb 2019.

This text, entitled "Des Espaces Autres," and published by the French journal Architecture Mouvement Continuité in October, 1984, was the basis of a lecture given by Michel Foucault in March 1967. Although not reviewed for publication by the author and thus not part of the official corpus of his work, the manuscript was released into the public domain for an exhibition in Berlin shortly before Michel Foucault's death. Translated from the French by Jay Miskowiec.

Michel Foucault, "Of Other Spaces," trans. Jay Miskowiec, Diacritics 16 (1986): 22, Foucault.info <http://foucault.info/documents/heteroTopia/foucault.heteroTopia.en.html> 22 July 2019.

The Winter's Tale I, i,[20][21]

Ingrid Horrocks, Women Wanderers and the Writing of Mobility, 1784-1814 (Cambridge: Cambridge University Press, 2017) 67.


Olivier Lombard

Nicolas Viard

Valentin Leroy

Christophe Barrière

Multiple scattering of an ultrasonic shock wave in bubbly media

Keywords: numbers: 43, 35, +d, 43, 20, +g

This experimental study deals with the propagation of an ultrasonic shock wave in a random heterogeneous medium, constituted of identical 75-µm radius bubbles, trapped in a yield-stress fluid. The fundamental frequency of the incident wave (in the MHz range) was much larger than the resonance frequency of bubbles (38 kHz). A well expanded coda, resulting from the multiple scattering of the incident shock wave through the heterogeneous medium, was experimentally measured in transmission. Despite the significant amplitude of the shock wave (90 kPa), no sign of nonlinear response of the bubbles was detected. Both the coherent and incoherent fields were successfully described by linear theories. Using a shock wave presents the advantage of characterizing the medium over a large frequency range (1.5-15 MHz).

I. INTRODUCTION

Acoustic propagation in strongly scattering heterogeneous media has been widely studied for years [START_REF] Ishimaru | Wave Propagation and Scattering in Random Media[END_REF][START_REF] Lagendijk | Resonant Multiple Scattering of light[END_REF][START_REF] Rytov | Principles of Statistical Radiophysics 4, Propagation Through Random Media[END_REF][START_REF] Skypetrov | Wave scattering in Complex Media From Theory to Applications[END_REF][5][6][7][8][9][10][11][12][13]. In such media, the wave is multiply scattered as it encounters successively several heterogeneities. Consequently, transmitting an acoustic pulse through such a medium provides a typical signal generally showing a ballistic part at the first times of flight, followed by a multiply scattered coda, possibly lasting for a long time. When the positions and/or the shapes of the scatterers are random, the acoustic propagation through the medium is modeled as a random process. The transmitted wave is then the sum of a coherent [6][7][8][9] and an incoherent fields [10][11][12][13].

A simple criterion to determine whether multiple scattering occurs in a medium is L > s , where L is the medium's thickness and s its scattering mean free path, which can be though at as the average length over which the wave propagates between two scattering events [6][7][8][9]. For a random medium, without absorption, the scattering mean free path is also defined as the characteristic length of the attenuation of the coherent intensity. In presence of absorption, the characteristic length of the attenuation of the coherent intensity is the extinction mean free path ext , that takes both effects into account: scattering and absorption. When the medium is constituted of identical discrete scatterers, the scattering mean free path depends on the concentration and strength of the scatterers and the following simple formula usually applies: s ≈ 1/(nσ), where n is the number of scatterers per unit volume and σ the scattering cross-section of one scatterer. It follows that strong multiple scattering can be obtained with a thick assembly (large L) of numerous (large n) and strong scatterers (large σ). In this case, the incoherent part of the field can be modeled as if the wave was a particule flux, where no interference occurs. The incoherent intensity obeys then to the Radiative Transfert Equation, which can be simplified to a diffusion equation, assuming the medium is statistically isotropic and using the pre-isotropic approximation, i.e. considering that the direction of the incoming wave is rapidly lost in the medium. [10][11][12][13].

Gas bubbles are good candidates as strong acoustic scatterers. A typical scattering cross-section as a function of frequency is given in figure 1, here for a 75 µm radius bubbles. The bubble (black solid line) is a much stronger scatterer than a steel bead of the same size (dashed line), especially at its resonance [16], at ν 0 = 38 kHz. However, in the frequency range of the resonance, the absorption scattering cross-section (red line) is also large, even larger than the scattering one. It means that this regime is not favorable for the observation of coda, because most of the energy incoming on a bubble is dissipated, not scattered. Nevertheless, even for frequencies much higher than ν 0 , the bubble still exhibits a strong scattering cross-section, with negligible absorption.

In this paper, we study experimentally stable samples made with 75 µm radius bubbles trapped in a yield-stress fluid. Those samples had a typical gas volume ratio φ 1 %, and they were studied over a large "high" frequency range (ν 0 1.5 MHz < ν < 15 MHz), produced by ultrasonic shock waves. Using shock waves to probe these bubbly media also raises the interesting question of a possible coupling between nonlinear effects and multiple scattering.

The article is organized as follows. We first describe the experimental setup designed to study multiple scattering of ultrasonic waves in our samples. Then, we study the coherent wave transmitted by such bubbly media. The scattering mean free path s is deduced from measurements, and compared to results provided by the ISA model. Finally, the incoherent energy of the coda is measured and compared to a diffusion equation, allowing to estimate the diffusion coefficient D as a function of frequency.

II. EXPERIMENTAL SETUP A. Bubbly media synthesis

Bubbly media were made with the same technique as in reference [17]: nitrogen bubbles were injected in a yield-stress fluid, with a 20-µm diameter capillary driven by motorized linear stages. The yield-stress fluid was a commercial hair gel diluted with water, whose frequencydependent viscosity was determined with a rheometer: η = 5/ f /1 Hz. The yield-stress was high enough to efficiently trap bubbles of radii below 100 µm, and it was checked that the bubbles positions were not affected by the ultrasound. Addition of C 6 F 14 to nitrogen slowed down ripening, thus increasing the sample stability, approximately up to ten hours. Samples were contained in a 3 cm thickness cell (see figure 2), whose walls were as thin as possible to ensure a good transmission of ultrasounds. In practice, 14-µm thickness Mylar membranes were used as walls. In this cell, the bubbles were injected regularly in a volume of 10 × 10 × 1 cm 3 . Then the sample was mixed to randomize the bubble positions. It was checked, by image analysis, that the thickness of the sample was not appreciably modified by this mixing: L = 1, 00 ± 0.02 cm.

Following this whole process, we made disordered bubbly media composed of R 0 = 75 µm radius bubbles, with a gas volume fraction up to about 1%. Experimental results shown in this article are almost all obtained with a sample having a gas volume ratio φ = 0.96 % (except on the inset of figure 4.b), which corresponds to a concentration of n = 5.4 bubbles/mm 3 .

Figure 2: Experimental setup immersed in water. The transducer emits a Gaussian pulse containing 5 periods of a sinusoidal signal at a frequency ν1 = 2 MHz or ν2 = 3.5 MHz. Its nonlinear propagation in water over a distance d = 75cm, generates a shock wave, which interacts with the bubbly sample of thickness L = 1 cm. The hydrophone (0.5-20 MHz bandwidth and 0.2 mm lateral resolution) measures 2 cm behind the sample (near field), the wave transmitted through.

B. Ultrasonic setup

The experimental setup, immersed in water, is shown in figure 2. An ultrasonic transducer (with a 3.5-MHz central frequency and a diameter 2a = 38 mm) emits a pulse with a Gaussian envelope, containing 5 periods of a sinusoidal signal. This waveform was chosen to maximize the amplitude emitted by the transducer, since it lets it resonate a bit. To compensate the narrow band of such a long time signal, we perform successively two measurements at central frequencies ν 1 = 2 MHz and ν 2 = 3.5 MHz, respectively corresponding to wavelengths λ 1 = 0.75 mm and λ 2 = 0.43 mm in water. The wave transmitted through the sample is measured, in the near field, with a hydrophone (having a 0.5-20 MHz bandwidth and a 0.2-mm lateral resolution), 2 cm behind the cell.

Choosing the distance d between the emitter and the sample depends on both diffraction and nonlinear effects in water. Firstly, to simplify the analysis of the signals transmitted through heterogeneous samples, the incident waveform has to be stable in water along the distance corresponding to the sample thickness. Consequently, we must avoid near field diffraction effects, where interferences occur. However the sample has also to be placed not too far from the emitter, to avoid the amplitude decrease resulting from the far field lost of directivity. According to the characteristic length of diffraction a 2 /λ, which is equal to 48 cm at ν 1 = 2 MHz and to 84 cm at ν 2 = 3.5 MHz, the waveform is stable from a 75 cm to 100 cm distance from the transducer, in both cases. This point has been checked precisely by numerically solving the classical diffraction integrals [19]. So limiting diffraction effects requires to place the sample at a distance d = 75 cm from the transducer.

Secondly, for sufficiently large amplitudes of emission, the nonlinear propagation in water generates harmonics of the fundamental frequencies, possibly leading up to a shock wave, with a characteristic pressure discontinuity [START_REF] Hamilton | NonLinear Acoustics[END_REF]. For a sinusoidal plane wave emitted in an homogeneous medium, the shock distance is:

L c = 1/(kβM ),
where k = 2π/λ is the wave-number, β is the nonlinearity parameter of the medium, and M = v 0 /c 0 is the acoustic Mach number, ratio of the particle velocity amplitude v 0 and the speed of sound c 0 . In our experimental configuration, in water (c 0 = 1500 m/s and β = 3.5), emitting a wave with an amplitude v 0 = 6 cm/s (corresponding to an acoustic pressure p 0 = 90kPa) leads up to a shock distance L c = 50cm. The calibration of our transducer with an optical interferometer has shown its capacity to emit such an amplitude [START_REF] Barrière | [END_REF]. Consequently, placed at the distance d = 75 cm from the emitter, the sample can be insonified by an ultrasonic shock wave [19].

As shown in figure 3a, the incident signal coming on the sample is a shock wave, with the typical sharp oscillations induced by the accumulation of harmonic components (represented in figure 3.b) during the propagation in water. Using an incident shock wave enables to study the sample over a large frequency range (1.5 MHz < ν < 15 MHz), with only two experiments driven successively at frequencies ν 1 = 2 MHz and ν 2 = 3.5 MHz. The possibility of an interaction between nonlinear effects and multiple scattering can also be investigated.

The pressure wave p i (t) is measured by the hydrophone at different spatial positions (1 ≤ i ≤ N ), by moving the sample in the (x, y) plane, perpendicular to the emitterreceiver axis z, with two motorized linear stages. We assume spatial ergodicity, implying that different realizations of the disorder can be measured at sufficiently different positions in the medium. To be certain to measure N decorrelated signals, we first measure the correlation coefficient between 8 transmitted signals truncated from t = 565 µs, by moving the sample with a 100 µm pitch. The inset of the figure 3.e shows the coefficient correlation as a function of the distance y between two sample positions. We can conclude the decorrelation length of the transmitted signal is around 400 µm. The pressure wave p i (t) is measured on N = 243 measurements, made with a 500 -µm pitch, larger than this decorrelation length.

III. EXPERIMENTAL RESULTS

A. Measurement of the coherent field

Wave p(t) transmitted through a random heterogeneous medium can be theoretically modeled as the superposition of a coherent field p(t) , i.e. the mean field averaged on an infinity of disorder realizations, and its incoherent fluctuations δp(t), specific to each realization of the medium:

p(t) = p(t) + δp(t). (1)
Assuming the spatial ergodicity, the coherent field p(t) is experimentally estimated by the average p(t) of the N = 243 measurements p i (t), acquired for different positions of the sample:

p(t) = 1 N N i=1 p i (t). (2)
Figures 3c and3d show two signals p 5 (t) and p 182 (t), arbitrarily chosen, produced by the incident shock wave p I (t) (fundamental frequency ν 1 = 2 MHz), represented in figure 3a, through the sample. They both exhibit a very well-developed coda, spreading over more than 50µs, whereas the incident wave goes down after a time T 3 µs. Note that shorter coda waves had already been reported in bubbly media [17,[START_REF] Van Der | Diffusion multiple et renversement du temps ultrasonore dans des milieux périodiques et désordonnés[END_REF][START_REF] Kol'tsova | [END_REF].

The coherent wave p(t), shown in figure 3e, still looks like a shock wave, but its waveform is quite different from that of the incident shock wave. Indeed, their phases seem to be opposite, and small secondary short peaks (high frequency contents) are visible in the coherent wave, suggesting a possible nonlinear interaction with the medium. Modeling the propagation through the sample will clarify this point.

B. Comparison with the linear ISA model

In this section, we apply the well-known linear "Independent Scattering Approximation" model to our experimental configuration. Our goals are to determine the scattering mean free path s , and to bring out possible differences with our experiments, due to nonlinear multiple scattering. If r(x, y, z) denotes the position, let us consider a sinusoidal plane wave e j( k0. r-2πν0t) , of frequency ν 0 and wave-number k 0 = 2πν0 c0 , propagating in water. The time dependence e -j2πν0t will be omitted in the following calculation, because it plays no part.

When this plane wave is scattered by a bubble (of radius R 0 ), the acoustic field becomes:

e j k0. r + f (θ) e jk0r r , (3)
where f is the scattering function of the bubble, depending on the angle θ between the incident and scattered wave-numbers. f is calculated following the reference [START_REF] Allegra | [END_REF].

The "Independent Scattering Approximation" consists in neglecting scattering loops and position correlations between scatterers. Within this framework, the coherent field propagates with an effective wave-number k eff , given by [START_REF] Ishimaru | Wave Propagation and Scattering in Random Media[END_REF]6]:

k 2 eff k 2 0 + 4πnf 0 , (4)
where f 0 = f (θ = 0) is the forward scattered wave. Following this approximation, the acoustic transmission factor T of a multiply scattering medium with a thickness L is:

T (L) = e -L 2 s e j 2πν v φ L , (5)
where s = 1/[2 (k eff )] is the scattering mean free path, i.e. the characteristic distance of attenuation of the coherent intensity (already mentioned in the introduction), and v φ = 2πν/[ (k eff )] is the phase velocity of the coherent field.

Figure 4 shows the modulus of the acoustic transmission factor |T | and the phase velocity v φ = 2πνL/ arg T , versus frequency ν.

In figure 4.a, the transmission factor of the Mylar walls in water is compared to the linear transmission through two 14 µm layers, with a mass density ρ M = 1400 kg/m 3 , and in which sounds propagates at c M = 2550 m/s. Viscous losses due to the yield-stress-fluid are also quantified from experimental data. Finally, the experimental transmission factor of the bubbly medium, deconvolved from Mylar walls effects and viscous losses, is compared to the results predicted by the linear ISA model, with a general good agreement. At highest frequencies (approximately between 13 and 15 MHz), measurements come from the fourth harmonic component of the 3.5-MHz frequency shock wave, giving a poor signal-to-noise ratio, that generates small discrepancies with the model. Assuming the exponential decay predicted by the ISA model, the scattering mean free path can be determined from |T |: s = -L/(2 ln |T |). In our sample described in section II A, s is equal to 2.5 mm at 2 MHz, and to 3 mm at 3.5 MHz. Then it increases slowly up to 3.5 mm at 15 MHz.

In figure 4.b, the phase velocity measured in the bubbly medium is in very good agreement with the velocity provided by the ISA model. Due to multiple scattering, the propagation of the coherent wave is strongly dispersive up to approximately 5 MHz, whereas no dispersion is noticed in the cell without bubbles.

Measurements were also made through four samples having different gas concentrations. In the inset of figure 4.b, measured scattering mean free paths at 2 MHz are in good agreement with those predicted by the ISA model.

The good description of our measurements by the ISA model indicates that the acoustic propagation remains strictly linear in our experiments, contrary to what the shape of the coherent wave may suggest. To bring another proof of the linear behavior of our sample, we have compared, in figure 5, the transmission factor |T | of the fundamental frequency band centered at ν 2 = 3.5 MHz and the transmission factor of the second harmonic frequency band centered at 4 MHz, resulting from the nonlinear propagation of the wave at the fundamental frequency ν 1 = 2 MHz. Although the amplitude of the second harmonic 2ν 1 is approximately half of that of the fundamental signal at ν 2 , the two acoustic transmission factors are identical, confirming the linearity of the process.

Thus, the differences between the incident and the coherent waveforms can be ascribed to the effect of dispersion induced by multiple scattering. Figure 6.a shows the signal obtained by applying the ISA model to the incident shock wave p I (t) represented in figure 3.a. The resulting waveform is very close to that of the coherent wave p(t), represented in figure 3.b. Figure 6.b also represents the signal obtained by applying only the modulus |T | of the transmission factor given by the ISA model to p I (t), with the constant argument of the transmission factor arg(T ), measured in the yield-stress-fluid. Then the small secondary short peaks noticed in the coherent wave at the end of section (III A) are clearly due to the dispersion of the phase velocity v φ . As a conclusion, in our bubbly sample, multiple scattering dominates over nonlinear effects over the frequency range investigated.

C. Incoherent field

In an infinite scattering medium, when the propagation distance is larger than the scattering mean free path s , th and when the diffused energy becomes quasi-isotropic, the local energy density W of the incoherent field obeys to a diffusion equation governed by a coefficient D [10][11][12][13]:

∂W ∂t = D∆W. (6)
In a medium consisting of identical scatterers, the characteristic distance of this diffusion process is the trans-port mean free path:

* = s 1 -cos , (7)
where the mean cosine of the scattering angle θ is:

cos = π 0 |f (θ)| 2 cos(θ) sin(θ)dθ π 0 |f (θ)| 2 sin(θ)dθ . ( 8
)
Transport mean free path * can be interpreted as the distance required for a plane wave to lose the memory of its initial direction in the scattering medium. This distance depends both on the number of scatterers per volume unit n, and on their scattering function f . For an isotropically scattering heterogeneity, cos = 0 and * = s . At the opposite, for a heterogeneity scattering strongly forward, cos → 1 and then * → ∞.

Using the relation between * and s given by the equations ( 7) and ( 8), we can deduce * from the measurements of s made in our experiments (see section (III B)): it increases from 2 mm at 2 MHz to 7 mm at 10.5 MHz. So the diffusive regime is effective in our sample, since its thickness L = 10 mm is always larger than * .

Transport mean free path * is also related to the diffusion coefficient D and to the transport speed of the incoherent energy c by:

D = * c 3 . (9)
As described in the reference [11], the finite thickness L of our samples can be taken into account by adding boundary conditions to equation (6), leading to a modal decomposition of W :

W (z, t) = ∞ m=1 A m sin mπ(z + 2 * 3 ) L + 4 *
τ Dm = (L + 4 * /3) 2 m 2 π 2 D . (11)
Thus, for sufficiently long times, the first diffusive mode dominates all the others. In particular, the second diffusive mode becomes negligible before the first one when t > τ D 1

3 . Experimentally, we can measure the acoustic intensity of the incoherent wave, which is the average value of the Poynting vector J (density of the power flux of the wave: J = -D -→ ∇W ) over the time length T 3 µs of the incident wave. As J has the same time dependence as W , measurements can be compared to theoretical results given by equation (10).

The N measurements p i (t) are first frequentially filtered, on 6 successive 2-MHz frequency bands, centered on frequencies: ν 1 = 2 MHz, ν 2 = 3.5 MHz, 2ν 1 = 4 MHz, 3ν 1 = 6 MHz, 2ν 2 = 7 MHz, and 3ν 2 = 10.5 MHz.

Then, the envelopes of the signals p i,ν (t) resulting from this filtering, are calculated with a Hilbert transform (HT). In each 2-MHz band, the mean incoherent intensity is obtained by averaging the envelopes of the N measurements. Finally, the estimator of the mean incoherent intensity is normalized by the intensity I 0,ν of the incident wave filtered in a same way:

I ν (t) I 0,ν = 1 N N i=1 |HT(p i,ν (t))| 2 1 T T 0 p 2 I,ν (t)dt . ( 12
)
Figure 7 shows the mean incoherent intensities measured around the frequencies ν 2 = 3.5 MHz and 2ν 2 = 7 MHz, versus time. At 7 MHz, Iν (t) I0,ν tends towards a constant value, giving the noise level. For times respecting the condition t > τ D 1 3 , experimental results are fitted with exponential functions. A measurement of the characteristic time of the first diffusive mode τ D1 is directly given by the slope of the fit. In figure 8, theoretical results provided by equation ( 11) are compared to experiments, assuming that the speed of the incoherent energy is that of the yield-stressfluid: c = 1530 m/s. The error bars are calculated from the 95% confidence interval of the exponential fits. As for the coherent wave studied in section (III B), measurements are in good agreement with a linear theoretical model leading to the same conclusion: no nonlinear effect occurs in the sample, where the propagation is dominated by the multiple scattering.

The diffusion coefficient D is deduced from the measurement of τ D1 . It increases slowly from D = 1 m 2 /s at 2 MHz to D = 3.5 m 2 /s at 10.5 MHz.

IV. CONCLUSION

When an acoustic wave propagates in a stable bubbly medium, at frequencies higher than the Minnaert resonance of the bubbles, a very well developped coda is observed. In such case, the wave is the superposition of a coherent field and incoherent fluctuations resulting from the disorder of the bubbles. Using an incident shock wave, we have measured the scattering mean free path s , the coherent phase velocity v φ and the diffusion coefficient D, in our samples, over a broad frequency range. The coherent field propagation is well described by the Independant Scattering Approximation, and the intensity of the incoherent field by a diffusion equation. Following these results, the time evolution of our bubbly samples will be investigated in the future, using diffusive wave spectroscopy [14,15].

From our experiments, we can also conclude there is no coupling between nonlinear and multiple scattering effects, when a bubbly medium is excited at frequencies much higher than the Minnaert resonance of its bubbles. Indeed, all the harmonic components of the incident shock wave propagate independently. These results are coherent with litterature, where nonlinear effects were already observed in bubbly media, excited at frequencies smaller than the Minnaert resonance [26][27][28]. However, multiple scattering effects are small at these frequencies. Finally, multiple scattering effects can be observed in nonlinear regime only if bubbles are excited around Minnaert frequency [29,30].

***

We acknowledge funding support from the Agence Nationale de la Recherche (ANR-11BS09-007-03), project DiAMAN.

Figure 1 :

 1 Figure1: Scattering (black continuous line) and dissipative (red continuous line) cross-sections σ of a nitrogen bubble of radius R0 = 75 µm in water, versus frequency ν. Black doted line: comparison with the scattering cross-section of a steel bead with the same diameter, in water. All cross-sections are normalized by 4πR 2 0 , the asymptotic high frequency crosssection.

Figure 3 :

 3 Figure 3: (a) Incident ultrasonic shock wave pI (t) at the fundamental frequency ν1 = 2 MHz, measured in water at the distance d = 75 cm from the transducer. Inset : Zoom of the Incident ultrasonic shock wave. (b) Spectrum PI (ν) of the incident shock wave represented in figure 3.a. (c) and (d) Two signals transmitted through our sample, p5(t) and p182(t), arbitrarily chosen. The envelope of the coda, calculated with a Hilbert transform, is represented in red. (e) Coherent wave p(t), estimated by averaging N = 243 decorrelated measurements pi(t) (1 ≤ i ≤ N ). Inset : Correlation coefficient as a function of the pitch between two measured signals in the direction y.

Figure 4 :

 4 Figure 4: (a) Acoustic transmission factor modulus |T | versus frequency ν, of the Mylar walls alone in water (green points), of the yield-stress-fluid (blue points) and of the bubbly media (red points). For the Mylar walls, measurements are compared to the linear transmission through two 14 µm layers (mass density ρM = 1400 kg/m 3 and speed of sound cM = 2550 m/s), represented by a solid black line. Measurements in the bubbly medium are compared to the ISA model (solid blue line). (b) Phase velocity v φ in the cell with (red points) and without (blue points) bubbles, versus frequency ν. Again, measurements in the bubbly medium are compared to the ISA model (solid black line). Inset: scattering mean free path s measured at 2 MHz in samples having different gas concentrations n (blue points) compared to ISA prediction.

Figure 5 :

 5 Figure 5: Comparison, over the 3.75-4 MHz range, between the transmission factors |T | of the fundamental frequency band centered at ν2 = 3.5 MHz (in red), and the second harmonic frequency band centered at 4 MHz (in blue), resulting from the nonlinear propagation of the wave at the fundamental frequency ν1 = 2 MHz.

Figure 6 :

 6 Figure 6: (a) Pressure obtained by applying the whole ISA model to the incident shock wave pI (t). (b) Pressure obtained by applying only the modulus |T | of the transmission factor given by the ISA model to pI (t), and the constant argument arg(T ) measured in the yield-stress fluid.

  mode m exponentially decreases with a characteristic time inversely proportional to m 2 :

Figure 7 :

 7 Figure 7: Mean incoherent intensities measured around frequencies ν2 = 3.5MHz and 2ν2 = 7MHz, versus time. Experimental results are fitted with an exponential function e -t/τ D 1 .

Figure 8 :

 8 Figure 8: Measurements of the characteristic time τD 1 of the first diffusive mode (red points), compared to theoretical results provided by equation (11) (solid black line). The incoherent energy is assumed to be transported at the speed of sound of the yield-stress-fluid (c = 1530 m/s), whatever the frequency.