Salim Yasmineh

Alternative interpretation of a state vector

Introduction

Conventionally, the startling features of quantum mechanics such as "measurement" and the "particle-wave duality" are illustrated by the double-slit experiment. When particles such as electrons are sent one at a time through a double-slit plate (hereafter called slit A and slit B), single random impacts are observed on a screen behind the plate as expected out of individual particles. However, when the electrons are allowed to build up one by one, the cumulative effect of a great number of impacts on the screen reveals an interference pattern of light and dark bands characteristic of waves arriving at the screen from the two slits. Meanwhile, the interference pattern is made up of individual and sequential impacts and although these sequential impacts are separate and independent, yet it seems as if the electrons work together to produce the interference pattern on the screen. This phenomenon seems to entail that the electrons embody a wave-like feature in addition to their particle nature hence illustrating a particle-wave duality structure.

When the electrons are made to build up one by one while detectors D A and D B are placed at slits A and B respectively to find out through which slit each electron went, the interference pattern disappears, and the electrons behave solely as particles. It seems thus impossible to observe interference and to simultaneously know through which slit the particle has passed. The best explanation that can be made from these strange features is that the same electron seems to pass simultaneously through both slits when no detectors are present and through only one slit when detectors are present [START_REF] Cohen-Tannoudji | Laloë Mécanique quantique I[END_REF][START_REF] Rickles | The Philosophy of Physics[END_REF]. This seemingly paradoxical statement is in conformity with the experimental data.

The state vector of an electron passing through slit A may be denoted , similarly, the state vector of an electron passing through slit B may be denoted . An electron passing through both slits A and B at the same time is said to be in a superposition state and its state-vector is denoted , where "a" and "b" are called the probability amplitudes. The mod-square of " " represents the probability of the particle to be measured by the D A detector at the slit A and likewise the mod-square of " " represents the probability of the particle to be measured by the D B detector at the slit B.

Conventionally, when no detectors are present, the state-vector of the electron is said to evolve per a deterministic continuous unitary evolution U whereas, when detectors D A and D B measure from which slit the electron passes, the deterministic evolution of the state-vector is transformed into a probabilistic discontinuous and non-linear state reduction R as explained by Penrose [START_REF] Rickles | The Philosophy of Physics[END_REF]. The two processes U and R create a conflict in the formalism of quantum mechanics. Different ontologies have been proposed to interpret the strange combination of the deterministic continuous U process with the probabilistic discontinuous R process.

In general, a quantum system (e.g. spin or position of a particle) can be defined by a statevector in a Hilbert space. For any observable Q, the state-vector is defined by a superposition of vector projections in an orthonormal eigenbasis . In other words, the state-vector is defined as a linear combination of the different possible states . The normalized conventional state-vector of the quantum system is expressed as follows:

(1) where

(2)

The coefficients are complex numbers ( ) that define the "probability amplitudes" in the specific orthonormal eigenvector basis and are orthonormal states of the quantum system verifying (Kronecker delta).

According to the Copenhagen interpretation [START_REF]Penrose The Road to Reality[END_REF][START_REF] Wimmel | Quantum physics & observed reality[END_REF], the state-vector and the U and R processes should be regarded as a description of the experimenter's knowledge. There exist several other interpretations amongst which the Everett interpretation or what is more commonly known as the many-world interpretation [START_REF] Everett | The Theory of the Universal Wave function[END_REF][START_REF] Everett | [END_REF], according to which there is no wave function collapse and all measurement results exist but in different worlds. In line with this interpretation, it is claimed [START_REF] Wallace | Emergent Multiverse[END_REF] that when a measurement is conducted on an electron in the superposition state , a deterministic branching takes place where on one branch detector A detects the electron while detector B doesn't and at the same time but on the other branch (i.e. another world), detector A doesn't detect the electron while detector B does detect it. However, this interpretation pauses some probabilistic as well as ontological problems. In particular, the axioms of quantum mechanics say nothing about the existence of multiple physical worlds [START_REF] Kent | [END_REF].

Another interpretation is the De Broglie-Bohm deterministic theory according to which particles interact via a quantum potential and are assumed to have existing trajectories at all times. This model seems to make more sense of quantum mechanics than the other interpretations as discussed in detail by Jean Bricmont in his book "Making Sense of Quantum Mechanics [START_REF] Bricmont | Making Sense of Quantum Mechanics[END_REF].

In this paper, it is intended to introduce an alternative explanatory hypothesis that makes sense of some remarkable features of quantum mechanics, and in which the process of measurement does not come in conflict with the deterministic evolution of the states of a particle.

Introducing a time-thickness into the state-vector

It is learned from the above that a particle can be at different positions at the same instant of time and that the state of the particle can be described by a state-vector as a linear combination of possible states with complex coefficients according to the above equations [START_REF] Cohen-Tannoudji | Laloë Mécanique quantique I[END_REF][START_REF] Rickles | The Philosophy of Physics[END_REF].

It does not seem absurd to suppose that a straightforward implication of the above observations would be the fact that an instant of time is not a geometrical point but rather a plurality of elementary instants.

In particular, we suppose that a local referential (u, v) of complex numbers is associated to each point (i.e. to each time index t) of the ordinary time-axis . Each local referential (u, v) has its origin at the corresponding time index t and is perpendicular to the ordinary time-axis. Moreover, each local referential is limited by a circle of an infinitely small radius δ.

In other terms, instead of being a simple point on a real axis, an instant of time becomes according to the present model a sort of a "time-slice" or section in a cylindrical manifold, hereinafter referred to as an "elementary-time-thread" having an infinitely small but non-zero radius δ. The original real axis can be considered as the central longitudinal direction of the "elementary-time-thread" and thus, each ordinary instant of time determines the position of a corresponding time-slice . On the other hand, each point belonging to the time-slice is defined by a complex number with respect to the local referential (u, v) in the plane of the time-slice. Points belonging to the time-slice are complex numbers hereinafter called "state-time-indices" that account for the complex probability amplitudes as will be shown underneath.

Thus, each point belonging to the time-slice is refenced by a complex number s (statetime-index) in addition to the common ordinary time index t referencing the ordinary temporal position t of the time-slice itself. Thus, a time-slice can be generally defined as a set of points hereinafter called "elementary-time-instants"

, as follows:

(

It should be emphasised that for each ordinary time index t, there exists one and only one corresponding slice and vice-versa. The fact that a time-slice , associated to a unique index , is made up of an infinite number of elementary-time-instants enables a particle to be at different positions at the same ordinary-time-index .

According to the present model, a quantum system can be represented by a fundamental-statevector -noted hereafter where the states of the system are well defined. For example, the position as well as the momentum of a particle are well defined at each elementary-timeinstant . The fundamental-state-vector is then written as follows:

(4)

The above formulation expresses the fact that at each elementary-time-instant , the particle has a definite position and a definite momentum that can be defined in a phase space constructed out of and . Both position and momentum are "simultaneously" defined with respect to an elementary-time-instant . The set of elementary-time-instants forms a curve that belongs to the time-slice and with respect to which the positions and momenta of the particle are well defined.

However, if it is made abstraction of the complex time , then position and momentum cannot be "simultaneously" defined with respect to the ordinary time . Indeed, if the curve is subdivided into a set of subsets where each subset corresponds to the elementary-timeindices that are associated to the same position , then at least one of these subsets may be associated to different momenta and inversely the same momentum may be associated to different subsets.

In other terms, it is not possible to construct out of the fundamental-state-vector , a state vector that determines the definite position and definite momentum of a quantum particle only with respect to the ordinary time-index (i.e. without considering the state-time-indices ). Indeed, by omitting the state-time-indices , it would be possible to find that the position at one elementary-time-instant is equal to the position at another elementary-time-instant , i.e. while the momenta and at these same elementary-time-instants and are different. Thus, if we know that the position of the particle is , we don't know whether its momentum is or . The contrary is of course true, creating thus an uncertainty relation between the position and momentum of the particle.

For simplicity reasons, we will first illustrate the fundamental-state-vector defining the position and momentum of a quantum system in a discrete manner before expressing it in a continuous one.

In order to describe the different positions of the particle at a given ordinary time-index , we subdivide into a set of elementary instants chosen in such a manner that each interval or arc joining to represents a "stateperiod" during which the particle is at a given position . Thus, the curve is made up of all the arcs : .

On the other hand, let (j=1, 2, ..) be all the different arcs belonging to that are associated to the same position state , then the "domain of state-time-indices" (or subcurve) during which the particle is found in the state is given by : (

Moreover, "the total state-time-period" or "state-life-time" during which the particle is in the state is:

(7)
On the other hand, in order to describe the different momenta of the particle at the same given ordinary time index , we subdivide into a set of elementary instants chosen in such a manner that each arc joining to represents a "state-period" during which the particle presents a given momentum . Thus, the curve is made up of all the arcs :

. ( 8
)
It is evident that the subdivision into intervals referencing equal momenta should not be necessarily the same as the subdivision into intervals referencing equal positions.

On the other hand, let (h=1, 2, ..) be all the different arcs belonging to that are associated to the same momentum state , then the "domain of state-time-indices" (or sub-curve) during which the particle is found in the state is given by : (

It is even less likely that the union of all the intervals associated to the same position (i.e. ) be equal to the union of all the intervals associated to the same momentum (i.e.

).

Moreover, "the total state-time-period" or "state-life-time" during which the particle is in the state is:

(10

)
where again is different from .

In view of the above, it becomes clear that by omitting the complex time , the fundamentalstate-vector can only be described by two separate and independent statevectors and with respect to position and momentum respectively as follows:

(11) (12)
where is a normalizing parameter called hereafter the "total-state-life-time" at a given , such that:

(13) And thus, (

By comparing for example, the position state-vector of equations ( 11) and ( 14) to equations ( 1) and ( 2), one can easily deduce that: It should be noted that the phase term in equation ( 16) may naturally be dependent on the ordinary-time-index and its associated state-time-indices .

The state-vector can thus be considered as a "normalised weighted sum" or almost as a sort of a "centroid" or "weighted arithmetic mean" where each "weight" (i.e. probability amplitude) represents the "state-time-ratio" visited by the state at the physical-time-index .

In that case, the probability associated to the state is:

(17

)
It seems logical that for a given physical-time-index , the greater is the value of the "statelife-time" the higher is the probability to find the quantum system in the state .

It should be noted that equation (15) takes account of the state-time-indices in an implicit or "hidden" manner via the coefficients . Thus, when a measuring apparatus is used to measure the state of a quantum system, it cannot be explicitly known at which elementarytime-instant the measure has been undertaken and thus, the measured outcome would seem as if it has resulted out of a wave-function collapse.

Similarly, to describe the position and momentum of a quantum system in a continuous manner with respect to the ordinary time-index without explicitly taking into account the state-time-indices , we construct two different state-vectors: a position state-vector out of the fundamental-state-vector and a momentum state-vector out of fundamental-state-vector as above.

The position state-vector can be expressed as the integral of the fundamental-statevector with respect to the state-time-indices over the curve as follows:

(18

)
where is the "total-state-life-time" (i.e. a normalizing parameter representing the total length of the curve ).

By decomposing the curve at a given time-index , into a set of intervals such that each interval represents the "state-period" spent by the fundamental-state-vector at the same position , the above integral (18) can be expressed as follows:

(19) represents the ratio of the state-time-life spent by the states at the same position . This integral can be considered as the "centroid" of the states with complex coefficients: . However, and thus, . Therefore, represents the probability associated to the states having the same position .

In a similar manner, the momentum state-vector can be expressed as the "centroid" of the states of the fundamental-state-vector as follows:

(20)

where the interval represents the "state-period" spent by the fundamental-state-vector at the same momentum , and where represents the ratio of the state-timelife spent by the states at the same momentum .

Similarly, and thus, . Therefore, represents the probability associated to the states having the same momentum .

Free particle and uncertainty

The "centroid" as defined in equation ( 19) can be considered as a "bloc of superpositions" that evolves according to the usual Schrodinger equation with respect to ordinary time . Thus, a free particle occupies a volume in space at each ordinary-time index and can thus be viewed as a spatial cloud formed by the different positions visited by the particle at the different state-time-indices of its state-time curve

. Indeed, at each , the particle may be considered as having an oscillatory-like movement in space with respect to the state-time-indices and thus, at each , the particle has multiple positions as if there is not only one particle but plenty of particles.

In view of the above model, the uncertainty principle arises from the fact that a particle may have different states with respect to the state-time-indices at any given physical-time-index .

Indeed, consider a particle whose position is defined by a one-dimensional representation along the x-axis according to equations ( 18) and (19). Equation (18) implies that when the state-time-index spans the state-time curve , the position of the particle at a given can be considered as a continuous random variable that takes its values in R. Equation ( 19) implies that the probability distribution density of the position is given by: (21)

It should be noted that the probability distribution reflects a statistical distribution of the different positions of the particle along the state-time curve at a given ordinary-timeindex .

On the other hand, Fourier analysis shows that the variance for the distribution of position and the variance for the distribution of momentum satisfy the following well-known classical mathematical relation [START_REF] Cohen-Tannoudji | Laloë Mécanique quantique I[END_REF], [START_REF] Bricmont | Making Sense of Quantum Mechanics[END_REF]:

(22)
However, it should be emphasised that according to the present model the above uncertainty relation ( 22) comes from the statistical distribution at one given ordinary-time-index of the different positions and momenta of a single particle visited by the different state-time-indices belonging to the time thickness. It does not come from a statistical distribution of the different positions and momenta of different particles neither from a statistical distribution of the different positions and momenta of a particle at different ordinary-time-instants . It should be clear that here we are considering only one particle at only one ordinary-time instant and the statistical distribution is generated by the time thickness.

For simplicity and illustrative reasons only, we suppose that the movement of the particle along the x-axis with respect to the state-time-indices obeys the following equation of a harmonic oscillator:

(23)

The solution of the above equation may be expressed as follows:

(24)

The above solution shows that the particle may undergo a combination of diverging and converging oscillatory movements around depending on the values of and . It can thus be implied that the spatial points of the cloud furthest away from are visited less "frequently" by the particle than those nearest to . Here, the term "frequently" is to be understood with respect to the state-time and not with respect to the ordinary-time . Thus, it is sensible to suppose that at a given ordinary-time , the ratio of the state-time-life spent by the particle at the same position follows the following square-root of a Gaussian:

(25)

It should be noted that the down bound of the uncertainty relation ( 22) is attained when the probability distribution is Gaussian.

On the other hand, it is known [11] that the normalised wave-function of a particle of momentum in the one-dimensional space representation is given by: (26)

The probability amplitude of momentum of the particle at a given can thus be expressed as follows:

Equation ( 29) expresses the uncertainty principle between position and momentum.

Spin

Spin can be considered as the rotation of a point particle around a sphere with respect to the complex time . More precisely, an electron may be considered as a point-particle turning around a sphere of radius while covering almost all the surface of the sphere at any given ordinary time (i.e. rotating around circles of radius with respect to and according to different directions of ).

Thus, the spin of the electron can be defined as an angular momentum as follows:

(30)

At any given , the point particle rotates a plurality of times around the sphere along different directions with respect to the state-time . In other words, what may be called as the radius of the particle is in fact the radius of a sphere around which the point-particle revolves with respect to the complex state-time .

Thus, at any given , the electron would seem as if it is a sphere of radius presenting a superposition of different spins generated by the different directions around which the pointparticle revolves with respect to the state-time . These different directions may be organised along , or where for example, divides the sphere into an upper hemisphere and a lower hemisphere where all directions lying in the upper hemisphere are defined as and all others as .

The value of the spin may be expressed as:

(31) where is the instantaneous complex velocity with respect to the state-time . The value of the spin in spherical coordinates may be expressed as follows:

(32) However, by considering the velocity to be analytic, the distance covered by the electron around the sphere at a given between the extremities and of the state-time curve is:

(33) Thus, the average velocity may be defined as the covered distance divided by the module of the difference between the extremities and of the state-time curve :

where is the number of revolutions around the sphere at a given . It should be noted that the average velocity is an "apparent velocity" and may be much greater than the speed of light.

Indeed, another velocity, named hereafter "average effective-velocity" may be defined as the covered distance divided by the total state-time-span spent by the particle around the sphere at a given (i.e., the length of the state-time curve

) knowing that the length may be much longer than the difference between the extremities and :

In other words, the average effective-velocity is smaller than the average apparent-velocity and thus, it is possible for the latter to be greater than the speed of light but not for the former.

On the other hand, it is to be noted that the state-time curve with respect to which the spin of a particle is defined may be different and completely independent from the one that defines the general movement of the particle in space (or more precisely, the movement of the sphere's centre around which the dot particle revolves).

Uncertainty and Measurement

When the complex time is taken into account the position as well as momentum of a particle are definite (i.e. at each there exists a well-defined position and a well-defined momentum. However, when we make abstraction of the complex time , position and momentum cannot be defined simultaneously. Indeed, as explained above (in section 3), if we classify all the same 's in a separate x-class and all the same 's in a separate p-class, the complex time indices may overlap (i.e. the set of indices of a given p-class may intersect several sets of different x-classes. In other words, constructing a state-vector by factorising with respect to the 's (see equation (18) rewritten underneath as equation ( 36)) gives a different state-vector from a one constructed out of factorisation with respect to the 's:

(36) (37) According to the above expressions, if we know the value of , we cannot know the value of simply because the set of complex indices that correspond to may correspond to a plurality of different 's. Thus, the "uncertainty principle" is only an uncertainty of our knowledge due to our incomplete representation (i.e. by omitting complex time ).

The same is true for spin which is considered as the rotation of the particle around a sphere of fixed radius in all different orientations covering all the sphere's surface (section 4). This rotation takes place with respect to the complex time and not with respect to the ordinary time . Thus, for a given , the spin is a superposition of different angular momenta directions due to the fact that the revolution keeps changing with respect to complex time while its value remains constant (same mass of the particle and same sphere's radius). However, by arbitrarily classifying the spin into three directions , , implies that knowing one direction leads to an uncertainty in the other directions. Indeed, if we know that the spin is in the direction (i.e. upper hemisphere), then we cannot know whether it is tilted towards the right or left hemisphere neither whether it is tilted towards the forward or backword hemisphere.

The above uncertainty can be called an "uncertainty of knowledge" so as to be differentiated from an "uncertainty of measurement". A measurement is a restriction of the state of the particle to a certain domain in addition to the "uncertainty of knowledge". For example, the measurement of the position of a particle means the restriction of the position of the particle with respect to to a certain domain which leads to an increase in the domain of momentum .

Similarly with spin, measuring the spin of the particle to be means the restriction of the particle to the northern hemisphere and thus, we cannot know simultaneously whether it is or , or whether it is or .

Measurement can thus be considered as a combination of two phenomena:

-restriction of the state of the particle to a certain domain (e.g. ), that leads to an expansion of the conjugate state. For example, restricting the motion to a certain volume, certainly increases the momentum; and -knowing one state of the particle leads to an "uncertainty in knowledge" of the conjugate state of the particle.

Discussion

According to the above model, the complex-time is considered to be hidden in the complex amplitudes of the superposition states determined by the Schrodinger's equation. This implies that there should be a more basic equation that explicitly accounts for the complex time and out of which Schrodinger's equation can be derived.

This may be illustrated with a simple example where the Lagrangian of a particle is supposed to have the following expression: (38) where is a field supposed to be a function of space , ordinary time and complex time . The Lagrangian depends on and some partial derivatives of with respect to the coordinates of space and time. In the above example, the Lagrngian is expressed only with respect to kinetic energy which is considered to have space as well as time derivatives. The first kinetic term mixes the coordinates of ordinary time and complex time . However, as complex time is a complex variable, a complex multiplicative constant is introduced into the spatial kinetic energy terms for dimensional consistency.

By applying the following Euler-Lagrange equations on the above Lagrangian (39) where stands for space and time coordinates , , , one gets the following equation of motion:

(40)

In order to derive Schrodinger's equation, complex time should not be explicit and thus, we integrate the above equation of motion on the state-time curve with respect to the complex time :

(41) By supposing that there are no mixed terms of space and time, the second differential derivatives ( with respect to space are thus independent of complex time and thus, the Laplacian can be put outside the integral:

(42)

Moreover, by supposing that the interval between the complex limits of the integral is invariant at each ordinary time , we get:

(43)

where is the module of the interval between the limits of the integral at each ordinary time and where is the phase (i.e. is the difference between the extremities of the state-time curve

). Thus, equation (42) becomes:

(44)

According to the present model, quantum phenomena are supposed to be derived from the thickness of time, it is thus reasonable to suppose that the energy of the particle is related to the "thickness of time" as follows:

(45) Equation ( 45) leads to:

(46)

And thus, by replacing and by taking , equation (44) becomes:

(47)

Finally, we consider that the wave function is the integral of the field with respect to the complex time :

(48)

By replacing equation (48) into equation (47), we obtain Schrodinger's equation:

Equation ( 46) shows that the module of the difference between the extremities of the statetime curve decreases when the energy increases and thus, the quantum phenomena would be unnoticeable at high energies.

Using equation (46) an estimate of the value of related to an electron may be calculated as follows:

(50) It is to be reminded that represents the module of the difference between the extremities of the state-time curve whose "length" could have a much bigger value.

  (27) By calculating the Gauss integral, the above equation (27) becomes:


Marcin Lenart

Andrzej Bielecki

Marie-Jeanne Lesot

Teodora Petrisor

Adrien Revault D'allonnes

Dynamic Trust Scoring of Railway Sensor Information

Keywords: information scoring, sensor, trust, reliability, likelihood, credibility

A sensor can encounter many situations where its readings can be untrustworthy and the ability to recognise this is an important and challenging task. It opens the possibility to assess sensors for forensic or maintenance purposes, compare them or fuse their information. We present a proposition to score a piece of information produced by a sensor as an aggregation of three dimensions called reliability, likelihood and credibility into a trust value that take into account a temporal component. The approach is validated on data from the railway domain.

Introduction

Information scoring (see e.g. [START_REF] Batini | Data and Information Quality[END_REF]) aims at assessing the quality of available pieces of information and, in particular, the trust that can be put in them. It plays a crucial role in any decision-aid system. For instance, in an information fusion system, equally considering reliable and unreliable sources may severely cripple the results. Sensors are not an exception, the information they produce is often used to get enhanced knowledge about a given situation and the ability to differentiate between them in terms of quality is a much needed feature. Indeed, sensors do not always produce correct information. There are many situations in which a sensor can fail, e.g. producing out of range values, when encountering unfavourable operating conditions, communication problems or other interferences. Knowing whether the information produced by sensors is trustworthy can be key in many aspects, for instance, to choose the ones with the highest quality level for a given time interval. It can also be used to predict maintenance operations for sensors with decreased quality of information.

As detailed in Section 2, current quality measurements for sensors are mainly based on scoring reliability either from meta-data [START_REF] Destercke | Evaluating data reliability: An evidential answer with application to a web-enabled data warehouse[END_REF][START_REF] Florea | Dempster-Shafer Theory: combination of information using contextual knowledge[END_REF] or ground truth evaluation [START_REF] Blasch | Derivation of a reliability metric for fused data decision making[END_REF][START_REF] Florea | Dynamic estimation of evidence discounting rates based on information credibility[END_REF]. Other systems include credibility to further improve scoring by com-paring information with other sources [START_REF] Florea | Dynamic estimation of evidence discounting rates based on information credibility[END_REF]. These solutions can suffer from lack of external knowledge (meta-data or ground truth) which can make them unusable.

This paper aims to address these limitations by decreasing the dependence on meta-data or ground truth and incorporating statistical analysis into the computation. It proposes new definitions for three dimensions chosen such that different aspects of the source and the information can be captured.

The paper is organised as follows: Section 2 presents some of the current approaches to score information quality for sensors, in Section 3 the proposed process of information scoring is explained and in Section 4 the approach is illustrated on real-world data. Section 5 concludes the paper and discusses future research directions.

Literature Review

This section briefly discusses general Information Quality scoring and describes approaches dedicated to the special case where the considered information is provided by sensors.

General Information Quality Assessment. The task of information scoring is mainly addressed through the decomposition of its quality into components, assessed on different dimensions whose list and definitions vary depending on the author. Some examples are relevance and truthfulness [START_REF] Pichon | Relevance and truthfulness in information correction and fusion[END_REF], reliability and certainty [START_REF] Lesot | Proposition of a semi-automatic possibilistic information scoring process[END_REF], source-trustworthiness and information-credibility [START_REF] Besombes | An extension of STANAG2022 for information scoring[END_REF], sincerity, competence, intention of the source and plausibility [START_REF] Lesot | Information quality and uncertainty[END_REF] or trust [START_REF] Young | Pedigree and confidence: Issues in data credibility and reliability[END_REF][START_REF] Demolombe | Reasoning about trust: A formal logical framework[END_REF][START_REF] Florea | Dynamic estimation of evidence discounting rates based on information credibility[END_REF][START_REF] Revault D'allonnes | Formalising information scoring in a multivalued logic framework[END_REF], see [START_REF] Sidi | Data quality: A survey of data quality dimensions[END_REF] for a complete list. One recent approach, introduced in [START_REF] Revault D'allonnes | Formalising information scoring in a multivalued logic framework[END_REF], considers trust evaluation in a multivalued logic framework based on four dimensions: reliability and competence, which evaluate the source, and plausibility and credibility, which relate to the information content, spanning the range from source to information, from general to contextual and from subjective to objective.

Information Quality Dimensions in the Context of Sensor Measurement Many papers [START_REF] Destercke | Evaluating data reliability: An evidential answer with application to a web-enabled data warehouse[END_REF][START_REF] Florea | Dempster-Shafer Theory: combination of information using contextual knowledge[END_REF][START_REF] Guo | Evaluating sensor reliability in classification problems based on evidence theory[END_REF][START_REF] Pon | Data quality inference[END_REF] focus on the case of information provided by sensors. They often consider three dimensions, called reliability, contextual reliability and credibility, but vary in the way they are scored, as detailed below.

Reliability is generally understood as the ability of a system to perform its required functions under stated conditions for a specified time. It is an a priori assessment of the source.

Different approaches are considered to score reliability. In [START_REF] Florea | Dempster-Shafer Theory: combination of information using contextual knowledge[END_REF][START_REF] Destercke | Evaluating data reliability: An evidential answer with application to a web-enabled data warehouse[END_REF] meta-information on the source are considered, e.g. its specification, protocol or environment. The gathered knowledge is then combined to propose a final reliability score. This approach is limited to the case where valuable meta-data are available.

A second approach to define reliability consists in viewing it as accuracy [START_REF] Florea | Dynamic estimation of evidence discounting rates based on information credibility[END_REF][START_REF] Blasch | Derivation of a reliability metric for fused data decision making[END_REF] in the case where ground truth is available, i.e. knowledge about the expected results. This suffers the same limitation as the previous approach since ground truth is not always available. Blasch [START_REF] Blasch | Derivation of a reliability metric for fused data decision making[END_REF] views it as a compound notion that aggregates several sub-dimensions. He enriches the previously mentioned approach by considering that reliability requires accurate, confident and timely results. However these three are not always achievable simultaneously, e.g. sometimes having more accurate or confident data leads to longer collecting time, which induces a choice between accuracy and timeliness.

Such an approach also leaves open the question of the aggregation operator to be used to combine the selected components of reliability. Blasch presents a user-driven approach, where these three dimensions are weighted based on a desired utility.

Contextual Reliability aims at changing reliability depending on the task the device is used for and thus the context of each piece of information.

Mercier et al. [START_REF] Mercier | Refined modeling of sensor reliability in the belief function framework using contextual discounting[END_REF] propose to score reliability in a way where it better reflects the reality of a sensor and its working environment by enriching it with its context. Then, different situations can result in different output qualities for a given sensor. For instance in the case of target recognition [START_REF] Mercier | Refined modeling of sensor reliability in the belief function framework using contextual discounting[END_REF], the performances of a data acquisition system may depend on weather conditions and on background and target properties, making the reliability of the decision system dependent on the target at hand. A sensor that recognises between three objects (helicopter, aeroplane and rocket) can have different accuracies for each one, effectively creating a vector of three reliabilities with different contexts.

Credibility can be defined as the level of confirmation of a given piece of information by other, independent, sources and constitutes another component of information quality. There are situations where assessing reliability is difficult or even impossible. This is where scoring credibility can provide an alternative or a complement to scoring reliability.

Using a "majority vote" strategy, it is possible to either improve the quality of the acquired piece of information [START_REF] Florea | Dynamic estimation of evidence discounting rates based on information credibility[END_REF] or combine multiple similar and dissimilar sensors to improve the overall quality of calculations by aggregating all outputs into one [START_REF] Rogova | Context-based information quality for sequential decision making[END_REF][START_REF] Guo | Evaluating sensor reliability in classification problems based on evidence theory[END_REF][START_REF] Florea | Dynamic estimation of evidence discounting rates based on information credibility[END_REF][START_REF] Pon | Data quality inference[END_REF].

Credibility for a piece of information is a relation to other pieces of information provided by independent sources, which ends with two cases, information is either concurring or conflicting [START_REF] Florea | Dynamic estimation of evidence discounting rates based on information credibility[END_REF]. The more pieces of information confirming the given piece of information, the more credible it is. This presents two possibilities of usage: i/ calculating ground-truth-type-of-reference by taking as output the majority of the sensors and then comparing it to evaluated sensor's output [START_REF] Guo | Evaluating sensor reliability in classification problems based on evidence theory[END_REF][START_REF] Pon | Data quality inference[END_REF] or ii/ combining all outputs to determine information quality by grouping sensors according to the feature they measure and evaluating the degree of consensus between them [START_REF] Florea | Dynamic estimation of evidence discounting rates based on information credibility[END_REF]. This approach can suffer limitations if sources are lacking or if their information is not comparable. The information scoring model we propose is inspired by the multidimensional approach introduced in [START_REF] Revault D'allonnes | Formalising information scoring in a multivalued logic framework[END_REF] which considers source evaluation, using reliability and competence, as well as content evaluation, using plausibility and credibility. We adapt, evaluate and aggregate three among these dimensions for the case of sensors, more precisely railway monitoring sensors. The three dimensions are also aggregated into a single trust value, which, in our case, is attributed to a sensor's reading at a given time. The presented approach has, in addition, a dynamic character: to score dimensions for the current log entry, the previous log entries are considered as well as their computed trust values. This section gives a high level description of the considered data then details the process of dynamically scoring multi-dimensional trust.

Data Structure

The data structure we use for information scoring has the following characteristics: it is in the form of a log file whose entries contain a date, a time, a sensor id and a value, as shown in Table 1 for a real data example. The entries are event-triggered, i.e. they occur only when an event happens. The possible values represent the different messages given by the sensor that describe the sensor state. In the real data we consider, these messages can be occupied, clear or some type of disturbance. We aim to give a trust evaluation for each log entry, as illustrated in the last column of Table 1. We exhibit a part of data where a deficiency in quality is encountered which corresponds to a decreased trust value (see the second entry in Table 1).

For the computations, some notions need to be specified. We denote L the complete log set and L s the set of log entries produced by sensor s. The notation l corresponds to one log entry defined as a vector containing three values: l.f ullDate corresponding to date and time, l.sensor to the sensor id and l.message contains the provided piece of information describing the sensors state. The set of all sensors is denoted S, and the set of all times T .

Scoring Trust

As explained at the beginning of this section our proposition is similar to [START_REF] Revault D'allonnes | Formalising information scoring in a multivalued logic framework[END_REF], adapting and implementing this theoretical proposition to the specific case of sensors. We also consider reliability and credibility, presenting our view of scoring them in Sections 3.3 and 3.5 respectively. Regarding competence, its definition and scoring in the case of sensors appear to require knowledge about the system that is difficult to acquire e.g. external conditions or range of measurements. For instance, if competence is defined as the capacity of the sensor to provide the measurements it was designed for, this value is high when the sensor is working in its optimal conditions. The lack of that knowledge about the sensor and its surroundings makes it marginally useful in our trust calculation. Finally, we propose to replace plausibility with likelihood: whereas plausibility takes into account user background knowledge, likelihood depends only on the log file and takes into account the entry history.

The rest of this section presents our propositions for scoring each dimension, which takes into account meta-information and statistical analysis. Reliability is considered as a function of a sensor and time: r(s, t), likelihood is related to the log entry: lkh(l) and credibility applies to a log entry as well: cr(l). They are finally aggregated into a trust value: trust(l).

Reliability

Reliability, as a source metric, focuses on the specifics of the sensor, not the measures it provides. It is an a priori assessment of the source. This section first discusses the various approaches that can be proposed, organising them as constant vs. dynamic and meta-data-based vs. history-based; it then formalises the proposed definition.

Discussion. A basic approach could consist in making reliability a constant value, e.g. depending on the sensor type or brand: it might be known that specific sensors are of better quality than others and thus a priori provide more trustworthy information.

A way to enrich this basic definition is to take into account time and to define a dynamic reliability, for instance considering that this initial reliability value decreases when the sensor becomes older. This approach requires acquiring the knowledge about the obsolescence speed of the sensors, which might be difficult to know.

Note that it is possible to enrich further such a dynamic definition of reliability by taking into account maintenance operations, if their dates and types are known, although their interpretation can be debatable: they can be seen either as increasing reliability by slowing down the sensor ageing, or can be considered as the sign of the sensor needing repairs, casting doubts on the quality of the information it provides.

These approaches rely on the availability of very rich meta-information about the sensors, among which the type, brand, age, obsolescence speed and dates of maintenance operations. Another source of information that can be exploited to define sensor reliability is offered by the history of its previous outputs, which is available in the log file. Indeed, reliability can be related to the question whether the device is working properly or not, which can be derived from its downtime or from its error messages. However sensor log files usually are event-triggered, which means that the downtime is not reported as such. The next paragraph describes in more detail a reliability definition based on error messages.

Proposed Sensor Reliability Definition. The measure we propose is based on the interpretation according to which the more errors a sensor reports, the less reliable it is: error messages indicate it encounters problems. We propose a dynamical measure that automatically adapts to the current state of the sensor, depending on what happened in its recent history; formally, it is defined as:

r : S × T -→ [0, 1] (s, t) -→ 1 - |error(recent(L s , t))| |recent(L s , t)| (1)
where recent : L × T → P(L) provides the set of log entries produced by the sensor s in the considered time window t and error : L → P(L) is the function which extracts the set of error entries in this time window. The definition of the considered time window, which determines the notion of "recent history" and the value of the reference recent can take several forms: it can be directly defined as an entry number, indicating the number of previous messages one may want to take into account; it can also be a temporal window, from which the log entries to be considered must be retrieved.

Likelihood

Likelihood measures how likely a piece of information is, independently of its source, but usually depending on available external information. Its expression varies according to the type of this considered external information.

For instance, in the case where the considered piece of information describes the position of a train on a track, it might be confronted to a train schedule, so as to check the compatibility with this external knowledge.

In the case considered in this paper, as described in Section 3.1, the pieces of information indicate the sensor states. We propose to measure their likelihood according to their compatibility with a model stating the allowed state evolution. Indeed, it can for instance be known that a sensor cannot remain in the 'occupied' state at two consecutive time stamps. A more general state evolution model for our considered sensors is illustrated in Figure 1: the two main states are occupied and clear and the several error states are distinguished. It can be seen that this sensor type cannot successively report clear and disturbed but an intermediary message section disturbed is used. The proposed approach considers two cases: the message flow is compatible with the model or it is not. In the first case, the trust value of the previous log entry is considered. If it is strong, the likelihood will be high; if the log entry was untrustworthy, the likelihood will be lowered accordingly, indicating the fact that it could have been faulty. In the second case, the trust value of the previous log entry is also used to decrease likelihood: when that information was trustworthy, the likelihood will be low, otherwise the information is not considered enough to fully lower the likelihood score. The formal definition of lkh : L → [0, 1] is:

lkh(l) = trust(prv(l)), if l.message compatible with prv(l).message 1 -trust(prv(l)), otherwise (2)
where prv : L → L returns the single log entry l which is the entry provided by the same sensor just before the current entry l and l.message is compatible with l .message when that state evolution is allowed by the model.

Credibility

Credibility aims to confirm or deny a piece of information, independently of its source, by comparing it with information from other sources. Its expression depends on the type of information provided by other sources.

Discussion. In the case considered in this paper where the piece of information describes the position of a train on tracks, it might be confirmed by its neighbouring source which should have reported the passing train shortly before. To implement this principle, the relative positions of the sensors are required, for instance in the form of sensor network. Figure 2 illustrates such a network: the nodes represent sensors and the lines between them indicate that two sensors are neighbours. For instance, when sensor S2 reports an activity, it means that the train had to pass through sensor S3 and it should have reported that fact with a log entry. Formalization. The proposed approach considers scoring credibility of the sensor's state by looking through the recent log entries to find the ones which confirm the event and the ones which contradict it. The previously computed trust values for the considered entries are aggregated, ending with the final fusion of two values representing confirmation and contradiction. Formally, the credibility function cr is thus defined as:

cr : L -→ [0, 1] l -→ agg 1 (agg 2 (conf irm(l)), agg 3 (inf irm(l))) (3)
where conf irm : L → P(L) returns a set of entries that confirm l; inf irm(l) : L → P(L) returns a set of entries that contradict l; agg 1 , agg 2 and agg 3 are three aggregation operators applied to the trust scores of their set of logs.

Selection of aggregation. An aggregation operator in general is a function which reduces a set of numbers into a single, meaningful, number. The selection of an operator opens a wide discussion due to the diversity and variety of existing aggregation operators, each with its characteristics and properties, see e.g. [START_REF] Detyniecki | Fundamentals on aggregation operators Technical report University of California Berkeley[END_REF].

The purpose of agg 2,3 is to combine the trust values of multiple entries. We propose to discard conjunctive and disjunctive operators, which can be considered as too extreme and to favour compromise operators that allow a compensation effect. As all log entries have the same impact, we consider the average. The agg 1 operator aims at combining the global confirmation trust (c) and the global infirmation trust (i). We require the following behaviour at the boundaries: if c = 1 and i = 0, the aggregated result must be 1; if c = 0 and i = 1, it must be 0.

They ensure that a fully confirmed piece of information has the highest credibility score and a fully contradicted information has the lowest credibility score. Therefore agg 1 needs to be asymmetrical. To meet these requirements we propose to define agg 1 : [0, 1] × [0, 1] → [0, 1] as:

agg 1 (c, i) = 1 + c -i 2 (4)
For the sake of simplicity, equation (3) omits its temporal dependence: confirmations and infirmations are looked for in recent entries. The notion of recent is equivalent to the one presented in Section 3.3. A too small window can result in "false negative", if the confirmation is earlier and outside the window However a too large window can result in "false positives": the confirmation does not exist but the previous train passage is included.

Trust

The final step then consists in aggregating the three dimensions: reliability, likelihood and credibility into the trust score.

We propose an approach to divide the overall trust scoring into two phases. First reliability and plausibility are aggregated. Indeed these dimensions both have an abating effect, leading to decrease trust, therefore, we propose to aggregate them using a t-norm, offering a conjunctive behaviour. The implementation described in Section 4 more specifically considers the probabilistic t-norm. Credibility can either increase or decrease trust due to its external factor as an opposite to the first two dimensions. We propose to consider a compromise operator, the weighted average. Trust is thus formally defined as

trust : L -→ [0, 1] l -→ α • r(l.sensor, l.f ullDate) • lkh(l) + (1 -α) • cr(l) (5)
where the constant α ∈ [0, 1] is set a priori to manipulate the influence of both sides.

Illustration on Real Data

This section describes the implementation of the proposed approach for realworld data from the railway domain. Among different sensors, the axle counter (AC) was chosen for its crucial role in maintaining safe and efficient train traffic. The aim is thus to verify the information it produces e.g. "the train is on this part of track", "the train left this part of track", "the sensor is not working properly". The dataset contains 60 axle counters to provide information on the train presence in the different part of tracks. The example of messages produced by AC is presented in Table 1 and all types of messages are included in the graph shown in Figure 1.

This section first describes the experimental protocol and then presents an illustrative example.

Experimental Protocol

The testing process is challenging due to the lack of a ground truth for the available dataset. We choose to illustrate our scoring by considering the original data as a reference and building a synthetic dataset from it with added random noise. We change 5% of the AC states randomly, where the changes mean replacing the message of the log entry with a different one. We constrain the noise injection to preserve the initial distribution of the sensor states, i.e. if the disturbed message appears 1% in the dataset and the clear message appears around 49%, the same proportions hold in the noisy data.

The initial values for the 3 dimensions are set to 1.0; the window defining recent entries for reliability and credibility is set to consider entries from the previous 10 minutes; for Trust, we set α = 0.75 in Equation (5).

Illustrative Example

Two approaches are considered when testing: applying noise to only one sensor or to multiple sensors.

Single Sensor Subject to Noise. In Figure 3, the trust values (y-axis) for the modified sensor are plotted over the log-entry number (x-axis). The noise is applied only to this device, its positions are highlighted by the vertical lines. It is noticeable that the corrupted entries are recognised, the trust being lowered for these log entries. Also, the trust level does not recover immediately after the decrease but takes time to do so, which is reflected by the introduction of previous logs trust into the computation. The part of the chart around entry number 220 presents one of the cases where the trust value was not able to fully recover, due to encountering another invalid entry which ended with another decrease. This example shows the ability of this tool to properly handle this scenario as well. Multiple Sensors Subject to Noise. In this case, noise is applied to all sensors to observe how different sensors affect each other's trust. Figure 4 shows the evolution of trust values for a reference sensor, vertical line show its modified entries, the ones of the other sensors are omitted. The interesting part is the smaller decrease in trust for the entries that were not modified. The explanation for it lies in other sensors and their low trust scores. Due to the correlation between sensors, one of them can influence the other's trust. The level of the decrease depends on the trust value of the correlated sensor. Even though the trust value can decrease for the entries that were not modified, the level of that decrease is noticeably weaker compared to that of modified logs.

Conclusion

The variations in information produced by sensors bring out the need for an information quality scoring system taking into account both sensors and their output characteristics. Our approach proposes a modified version of dynamical trust scoring with three dimensions: reliability, likelihood and credibility. The temporal nature of the sensor's signal is considered in the aggregated trust score. We illustrated the proposed approach on a real-world railway dataset. Future works will include performing an experimental validation with statistical study generalising the illustrative example. Another perspective lies in proposing enriched scoring methods for presented dimensions.

Acknowledgements. This work was supported in part by Thales Polska.

Fig. 1 .

 1 Fig. 1. Example of a state evolution model.

Fig. 2 .

 2 Fig. 2. Representation of the sensor locations on a portion of the railway structure

Fig. 3 .

 3 Fig. 3. Trust evolution for a single sensor affected by noise.

Fig. 4 .

 4 Fig. 4. Trust evolution for one sensor, when noise affects all sensors.

Table 1 .

 1 Example of input data structure and output trust scores for a sensor.

	Date	Time Sensor ID Message Trust
	11.03.2015 07:24:53	AC1	occupied 0.9
	11.03.2015 07:25:40	AC1	occupied 0.3
	11.03.2015 08:23:18	AC1	occupied 0.7
	11.03.2015 08:24:08	AC1	clear	0.7
	11.03.2015 09:15:23	AC1	occupied 0.8
	11.03.2015 09:16:08	AC1	clear	0.8
	11.03.2015 09:39:45	AC1	occupied 0.8
	11.03.2015 09:40:29	AC1	clear	0.8
	11.03.2015 10:22:14	AC1	occupied 0.8
	11.03.2015 10:23:03	AC1	clear	0.9

3 Proposed Process for Information Scoring for Sensors


Meegan Louise

Louise Clark Meegan

Clark

Dennis Kelly Directed

Marc Munden

Rebekah Wray

Rogers Performed

Alexandra Roach

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Dennis Kelly

t think I am me. Not any more": Sacrificing the Self in Utopia

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

whether to join the King's service, 15 Libellus was published in 1516 in Louvain, in 1517 in Paris, and a more definitive version in 1518 in Basel, undergoing numerous reprints and vernacular translations by 1551. 16 The reproaches levelled against societal injustices and deficiencies are numerable and varied. Accordingly, the topics that More touches upon are tinged with concerns regarding culpability, governance, accountability and ability, far beyond the private/public dichotomy of his own being. 17 Furthermore, the trans-European audience is explicitly acknowledged: "[…] so [Hythlodaeus] rehearsed not a few points from which our own cities, nations, races and kingdoms may take example for the correction of their errors" (55), and leaves few countries exempt from direct or indirect critique. Yet the practicality of the notions put forth rests on the conceptualisation of the individual in a social context. In More's fiction the emphasis on the utility of the individual in relation to the community, and on the willing collusion, aligned with natural inclination, of the citizens of Utopia to conform to the archistic structures is remarkable. Greenblatt notes, the underlying movement of the text is of a "steady constriction of an initially limitless freedom". 18 The curtailment of individuation 19 is achieved by homogenisation, 20 and a culture of honour and shaming whilst under neigh perpetual observation. 21 Further restrictions are set in the conditional needs of the Utopian society, always prevalent, to the degree that it may be questionable to what extent any individual need or desire may arise, or rather any sense of 15 Hexter xv, xxvii-xli. 16 On the editions and printing history see Edward Surtz, "Introduction: Part III," The Complete Works of St. Thomas More: Utopia, volume 4, ed. Edward Surtz and J. H. Hexter (New Haven, London: Yale University Press, 1965) clxxxiii-cxciv; and Vibeke Roggen, "A Protean Text: Utopia in Latin, 1516-1631," Thomas More's Utopia in Early Modern Europe: Paratexts and Contexts, ed. Terence Cave (Manchester, New York: Manchester University Press, 2008) 14-31. For a tabular overview of the respective editions and vernacular translations see Terence Cave et al., Thomas More's Utopia in Early Modern Europe: Paratexts and Contexts, ed. Terence Cave (Manchester, New York: Manchester University Press, 2008) 277-286. 17 My contentions against Greenblatt's reading echo Yoran's: there is no necessity to reduce the text to a psychoanalytic reading, which arguably diminishes the project's scope of engagement, particularly regarding issues related to international cooperation, peace and war. See Hanan Yoran, Between Utopia and Dystopia: Erasmus, Thomas More, and the Humanist Republic of Letters (Lanham, New York, Toronto et al.: Lexington Books, 2010) 173, 176-177. 18 Greenblatt 40. 19 The only outlets, such as gardening, reveal a desire for it, as this exposes a competitive streak in the society (Jendrysik 35). It extends to children being seen as resources to be distributed if they choose to pursue another craft (Libellus 127), families as means of expansion (Libellus 137) and death as a communal concern, wherefore permission must be granted in euthanasia (Libellus 187). See Paola 20 Greenblatt 39-41. 21 Greenblatt 47-54. inherent self. 22 Even the plurality of opinion, be it political or religious, is strictly monitored and structured; the first in its spatial arrangement, as any deliberation of politics outside of the designated forum "is a capital offence" 23 (125), and the second by exclusion. If an individual vocally advocates a superiority of a religion, they are banished or enslaved for public incitement (219). Atheists, though, are not considered human: "[…] they do not regard him even as a member of mankind, […] so far are they from classing him among their citizens whose laws and customs he would treat as worthless if it were not for fear" (221).

However, this passage leads us to a sticking point in More's text that is of particular relevance to the question of self: Are the Utopians capable of conceiving of humanity in the abstract? And in turn, are they able to differentiate themselves as individuals from that greater unit? Davis distinguishes the two books of More's work by the hierarchies of interest promoted in the respective parts; in the first, self-interest which is dominant in Europe, and in the second, the common interest which prevails in Utopia. 24 However, the Bible proffers conflicting views as to which interest ought to take precedence, in regards to salvation. 25 It is further complicated by the precept of original sin 26 and the question of the ability to fully exercise free will, which was arguably impaired as a result of the Fall. 27 Despite Kenyon concluding that no harm or infraction was perceived in limiting the Utopians' choice of behaviours, in light of the salvation to be gained should Utopia be implemented in a real context, which would already entail an important superseding choice, namely to create Utopia; 28 Baker-Smith and Davis rather suppose an absolution of moral choice altogether. 29 Nevertheless, these readings are rooted in the premise that the Utopians are capable of conceiving themselves in isolation, in the same manner that the Europeans of Book I are, where self-interest flourishes. The reason this question is of relevance ought to be clear: If the 22 Baker-Smith also raises this question in Dominic Baker-Smith, More's Utopia (London, New York: HarperCollins Academic, 1991) 224. An example of conditional needs is when the State determines which profession ought to be pursued if an individual is proficient in more than one craft (Libellus 127). 23 Albeit this is supposedly to prevent conspiracy from fermenting amongst the representatives, by means of transparency, however it could equally be seen as a form of preventing any larger congress of likeminded people, particularly ones that might forcefully disagree with communal decisions. 24 J. C. Davis, "Thomas More's Utopia: sources, legacy and interpretation," The Cambridge Companion to Utopian Literature, ed. Gregory Claeys (Cambridge, New York, Melbourne: Cambridge University Press, 2010) 35. 25 Davis, Thomas More's 38. 26 Utopians cannot self-identify, then no oppression or comprehension of an imposition of will is possible. If they are capable of self-identification, then to what extent, as this would implicate the degree of self-interest that could potentially be generated.

In truth, the answer provided by More is inconclusive. When describing the Utopians' study of logic he touches upon the concept of second intentions:

In fact, they have discovered not even a single one of those very ingeniously devised rules about restrictions, amplifications, and suppositions which our own children learn in the Small Logicals. In addition, so far are they from ability to speculate on second intentions that not one of them could see even man himself as a so-called universalthough he was, as you know, colossal and greater than any giant, as well pointed out by us with our finger. (159) Despite the ironic tone and possible disregard for the concept of second intentions, 30 the question of their ability to abstract between the individual and humankind 31 is obfuscated due to this. On the one hand, it would seem to imply they cannot ("so far are they from ability"), but on the other hand, the split itself seems highly doubted, both by the fact that the Utopians have not mastered this, which would imply, by humanist logic, the deduction to be unnatural and thus a contrivance of erring Europeans, or "a self-regarding irrelevance", 32 despite Hythlodaeus' assertion of accepted common knowledge; and due to the metaphor of the "giant" and the act of self-anointment ("pointed out by us with our finger"), implying possibly an excessive imposing ego, suggested to be something universal, but is not -the idea being exposed as nothing more than a vanity rooted in inflated pride. Then again, elsewhere, More evinces that the Utopians are very much capable of abstraction, apart from dehumanising atheists, namely in their dealings with the Zapoletans, whose eradication achieved by carrying out Utopian wars would make them "the greatest benefactors to the human race if they could relieve the world of all the dregs of this abominable and impious people" (207-209). 33 30 Edward Surtz and J. H. Hexter, "Commentary," The Complete Works of St. Thomas More: Utopia, volume 4, ed. Edward Surtz and J. H. Hexter. (New Haven, London: Yale University Press, 1965) 437-438. 31 Susan Bruce, "Explanatory Notes: Utopia," Three Early Modern Utopias: Utopia, New Atlantis and The Isle of Pines, ed. Susan Bruce (Oxford, New York: Oxford University Press, 1999) 223-224. 32 Baker-Smith 179. 33 These segments also expose the deep-rooted transnational contemporaneity of the text in its satiric approaches to educational debates, the Italian Wars and Swiss mercenaries. The irony of describing European treaties as "holy and inviolable" upheld "partly through the justice and goodness of kings, partly through the reverence and fear of the Sovereign Pontiffs" (Libellus 197) in wake of the Popes Julius II and Alexander VI would have been immediately apparent, as is the similarity between the Zapoletans and Swiss mercenaries, as remarked in the margins (Libellus 207). Confer Edward Surtz, "Introduction: Part II," The Complete Works of St. Thomas More: Utopia, volume 4, ed. Edward Surtz and J. H. Hexter. (New Haven, London: Yale University Press, 1965) cliii; and Hexter l. Surtz also draws particular attention to parallels with Italian humanist discourse in general, noting the recent activities of the Lateran Council that would have drawn English attention (Surtz, "Introduction Part II" Accordingly, it might be surmised that the Utopians were conceived by More to be capable of differentiating between Utopians and Non-Utopians, but that within the Utopian community itself, this distinction is less clear. As Greenblatt argues, the destruction of the individual, however, is to be desired in this text 34 as it produces "a powerful sense of relatedness" 35 rather than any sense of singular selfhood within the society, which is discouraged, and a more encompassing self-perception encouraged, as noted by Hythlodaeus: "Thus, the whole island is like a single family" (Libellus 149). Additionally, the society imposes an "enforced unity", 36 however the desired pinnacle, of course, is the voluntary denial of self in favour of others, providing no self-harm occurs (which would impair the utility of said individual):

[…] unless a man neglects these advantages to himself in providing more zealously for the pleasure of other persons or of the public, in return for which sacrifice he expects a greater pleasure from God -but otherwise to deal harshly with oneself for a vain and shadowy reputation of virtue to no man's profit […] -this attitude they think is extreme madness and the sign of a mind which is both cruel to itself and ungrateful to nature […] (179) 37 Of course, as soon as a difference between self and others is perceived, the potential for selfinterest as a destructive force emerges. Yet, as we have also noted, although More conceived of the Utopians as being capable of this discernment, it is implied that the Individual, in the more abstract and embodied sense, is not perceived or even perceivable (as noted in their inability to comprehend second intentions) 38 -the question remains if this is by choice or by nature. If one decides this is not by choice, then this in turn would lead us to the questions as to whether human nature can change, and, if so, then how, and at what cost? 39 The tone More clxxii-clxxviii, clxxii). Also consult Surtz, "Introduction Part II" cxlvii-cliii for a more detailed account of the satiric components. 34 Greenblatt 41. 35 Greenblatt 47; It is a modification of Hexter's "patriarchial familialism" (Hexter xli), due to the differences in conceptualising family life (Greenblatt 42-44). 36 Jendrysik 34. 37 Their founder would be an embodiment of this perceived virtue, as Baker-Smith notes that Utopus was completely "self-denying; [… and] legislates himself out of existence," rejecting his absolutist potential (153). See Baker-Smith also on the combinations of theories of pleasure that reconcile self-sacrifice, solidarity and the after-life (174). 38 Baker-Smith explains that a modern conception of the Individual distorts More's Utopia to be perceived as more totalitarian than his contemporaries might have (221). 39 It is noteworthy to mention here, that it is Hythlodaeus' inability to disregard his own inclinations, even at the cost of benefitting his family, that prevents him into entering any court, irrelevant of the (in)efficiency, as such self-sacrifice is too high a cost for him. " […] As for my relatives and friends, […] I am not greatly troubled about them, for I think I have fairly well performed my duty to them already" (Libellus 55) and "As it is, I now live as I please […]" (Libellus 57). It is also ironic as he professes the Utopian way of life, where this behaviour would be presumably abhorred, to be the best and "[…] the only one which can rightly claim the name of a generally adopts though, is of felicitous complicity and individual freedom to pursue happiness within guiding constraints laid down to optimize production and the chances of salvation, and where Utopians perceive themselves as an extension of one another, where noone is beholden unto themselves. 40 "As We See Fit": Splitting the Self and Role in Bacon Bacon, however, does not take up the underlying radical tendencies of More's work, in regard to the suppression of individual and its self by social negation, but rather plays a tune of outward conformity. Despite partially touching upon the topics Libellus raised, but more ostensibly engaging in issues of structuring scientific endeavours and their relation to power, 41 Bacon's New Atlantis 42 seems to be driven by the latter and is concerned far more with worldly comfort than spiritual. 43 Published posthumously in 1627, it is preceded by a prefatory note, claiming the unfinished "fable" contained "a model or description of a college instituted for the interpreting of nature and the producing of great and marvellous works for the benefit of men […]" (127). 44 Framing its concerns thus, as to primarily pertaining to knowledge production, transmission, and application, although not necessarily limited commonwealth" (Libellus 237). Accordingly, it is presumably his European capacity to discern between himself and universal humankind, by means of his education in the "Small Logicals," that blinkers him from ever being able to fully live in Utopia or bring it about. 40 This would comply with Freeman's reading of the books and their composition, reconciling the text with More's life (esp. 308-309) but would also be iterated in the parerga of Libellus where Busleyden writes of More as "Regarding yourself as born not for yourself alone but for the whole world […]" (Libellus 33) which might very well encompass the general ethos of Utopian living. 41 Bierman notes More's silence regarding the establishments of scientific institutions and endeavours (494). See also Judah Bierman, "Science and Society in the New Atlantis and Other Renaissance Utopias," PMLA 78.5 (1963) hereto, 45 rather than a European-scale systemic societal crisis as More perceived, the narrative itself is much more contained. 46 This shift in focus might account for some peculiar dissonances that riddle the text, 47 yet it may also just be a further opening of the tension between individuals and their community that More seemed at pains to explain away.

Bensalem is formally archistic but belies, as Weinberger has skilfully shown, 48 an anarchistic underbelly. 49 It is this duality, or split, of seeming (role) and being (self), that seems to pervade the Bensalemite society. 50 This is explicitly signalled when the visitors' fate is to be revealed by a stranger who introduces himself thus, "I am by office governor of the House of Strangers, and by vocation I am a Christian Priest; and therefore am come to you

[…], both as strangers and chiefly as Christians" (135; emphasis added). Although vocation might quite simply refer to a prior training, it could also imply a calling, a distinction that would be fostered by enforcing a duplication of labels unto the Europeans, one denoting a public perception ("strangers") and another pertaining to a more internal dimension of their identities ("Christians"). It is this tenuous relation that seems unsettling in the text, especially when applied to their societal structure. Bierman considers the political power as being 45 62), when focusing on the text's silence regarding social structures, I consider these approaches equally valid and not exclusive. 46 This does not mean that New Atlantis has no interest in other contemporary issues or those limited to England. For example, Jowitt astutely contextualises New Atlantis in relation to Bacon's shifting relationship to James I and his colonial policies, in addition to the spectre of 'the Jew' in politics. Although I do not share all of her assessments, a full engagement with the issue lies outside the scope of this paper. See Claire Jowitt, "'Books will speak plain'? Colonialism, Jewishness and politics in Bacon's New Atlantis," Francis Bacon's New Atlantis: 47 The narrative itself a very paradox given the Bensalemite laws enforcing secrecy (Weinberger, Science and Rule 873). 48 Weinberger, "Science and Rule"; "On Bacon's New Atlantis". 49 Whereas More constantly seems to open up limitless freedom only to restrict considerably (Greenblatt 40), Bacon seems to do the exact opposite, most notably in regard to Bensalemite concerns about murder, prostitution and the exacerbation the Adam and Eve pools pose (Weinberger, "Science and Rule" 881-882). 50 Pohl calls them Atlantan (61). separate from the House of Salomon, 51 possessing "isolation and autonomy" 52 despite their activities taking place everywhere, 53 essentially the State being "an almost foreign body of which they are scarcely a part"; 54 contrarily though, it is an institution driven by individuals 55 who are only subject to their own restraint and morality which may restrict their pursuits. 56 Pohl justly contends, "They are indeed the true rulers of the Atlantan society", 57 and given the extent of their interests and potential for manipulative intercessions, 58 Weinberg's speculation of mass manipulation via psychedelics ought not to be dismissed entirely as misplaced modern conjecture. 59 What follows then is two parallel existing societies, Bensalem -a monarchy and patriarchy adapted to longer lifespans, their society obscured, and a "fellowship" 60 of I's, the roots of their individuality presumably based on merit, but subject only unto themselves, who assume an almost occult quasi-stewardship of the former, revealing and concealing "as we think fit" (165; emphasis added). Between the first lack of identity due to a collapse into a faceless mass, roles and functions their only descriptors, and the second lack due to a superior nebulous "we," the constituents described similarly with a degree of inclination visible in their pursuits, the impression conveyed is of the insignificance of any and all individuals and their selfhood, the choice of volition irrelevant in face of self-perpetuating dynamic of discovery, wherein morality (and arguably personality) poses an obstruction to total knowledge. 61 "No. I Don't Think I Am Me. Not Anymore": 62 Positivizing Eradication Dennis Kelly's 2013 television show Utopia revolves around the questions More raised as to whether human nature can change, and, if so, then how, and at what cost, with an inversion: 51 Bierman 500. 52 Bierman 496. 53 Bierman 498. 54 Reiss 93. 55 Reiss 92. 56 Weinberger, "Science and Rule" 881-885. 57 Pohl 61. 58 Of especial note is the ancillary material denoting their goals e.g. "Exhilaration of the spirits, and putting them in good disposition" (New Atlantis 167). 59 Weinberger, "On Bacon's New Atlantis" 151. 60 Bierman 500, 497. 61 Weinberger also perceives a Bensalemite irreverence for morality ("Science and Rule" 881; "On Bacon's New Atlantis" 144). The aspect of perpetuity is arguably also evident in the feast of the Tirsan, promoting a vision of asexual perpetual existence, the mother kept out of sight or mind (New Atlantis 149). 62 Utopia, specifically season 2, episode 6; hereafter abbreviated as (2:6) and all subsequent references to this edition are in parentheses in the text.

Set in contemporary British society, where self-perception is utterly undoubtable, it is the ability to participate in any larger sense of self beyond immediate embodiment that is scrutinised. The individual is at once all-compassing, yet therefore perceived as completely irrelevant, embedded in a set of seemingly self-perpetuating machinations of power, both political and capitalist -not unlike Bacon's utopia of continual discovery. As in Bacon's piece, it is also replete with shadowy parallel structures, simultaneously on the outside but essentially above, who operate and influence the highest levels of politics, the economy and society, though unelected and unaccountable, officially non-existent, and unfettered by policy, the necessity of transparency, or national borders, incumbent only unto goals they themselves define. What starts out as a group of fans of a graphic novel, all outcasts of a kind, searching for a sequel manuscript, quickly spirals into being caught up in a conspiracy, their adversaries a collective known only as The Network, seeking to impose sterility onto the majority of humanity as to ensure the future of humanity on the cusp on an eco-pocalypse. We have been living in a dystopic utopia since the onset of modernity, it would seem to argue. 63 With morality spinning on a gyroscope of conflicting interests to a countdown of a species-level self-annihilation and irrevocable implosion, the individuals are at once thrust into the midst of a situation where their actions may have an immediate impact: averting the release of a sterilising virus. Yet their involvement is almost coincidental, constantly placing them on the back foot, hence their preoccupations are determined by immediacy and propinquity, initially limited to survival. Accordingly, they provide an inadequate response to the adversaries' greater objectives, governed by long-term global forethought, engaging primarily with the threat of the sterilising virus rather than the issues of overpopulation and consequent ecological, energy and food supply crises The Network seeks to address.

Each and every one of the characters is overwhelmed at one point or another, if not constantly by the personal ethical and moral ramifications of the situations they are faced with, and to a certain extent the resultant implications at large. Wilson Wilson is a particularly interesting figure in this regard. He is introduced both driven by an extreme sense of selfinterest, evident in his refusal to dress in blue, by which the group had intended to identify one another when meeting in real life for the first time, as "[I] don't look good in blue", and as being excessively possessive of his personal details, to the point of having blotted himself from all digital history (1:1), revealing a nihilistic drive compounded in his narcissism, with an almost paranoid, schizoid grasp on reality. 64 Nevertheless, he simultaneously longs to belong to a community, evinced in his online forum presence, and is yet unable to, due to lacking social decorum and an almost amoral willingness to embrace blunt facts of reality. 65 It is the latter trait that increasingly comes to dominate, quickly adapting to engage in violence, wherefore it ought not to surprise us, when he is converted, for lack of a better term, to The Network's cause, by Letts' and later Milner's relentless speeches on the state of the environment (1:5; 2:4). Despite grappling with the violence the choice inflicts, the spoon in season 2 increasingly symbolising his victimhood, lack of agency and his semblance of self as Wilson Wilson, 66 he ultimately sacrifices that Self -in wilfully killing Lee, when otherwise unnecessary (2:6), in order to regain agency in the communal identity of The Network with the role of Mr Rabbit; 67 to act in a manner he deems moral in the grand scheme of time, to exert influence in a problem that he would otherwise only be subject to. He is very aware of the implications and his own moral stance, neither fully agreeing nor disagreeing with The Network: "We should at least think about it […] because if they are right and we stop them, what does that make us?" (1:5) but also: "Losing that much life is never acceptable. But losing some is. […] I promise you, I'll be better than her" (2:6).

Conclusion

As I have attempted to outline, the works investigated provide different takes on the relationship between the individual and society, they are essentially reimaginings redressing failures of the societies the authors lived in. More tries to maintain both a sense of selfidentity whilst sacrificing it in part in favour of a communal identity, resulting in an extended self that may not be entirely natural, in order to achieve salvation, yet not succumbing entirely to predestination or resignation. According to Greenblatt his crisis was located in a perception 64 His deep conviction of conspiracy theories and defence of the graphic novel as "opening a door … to reality" (Utopia 1:1). 65 He blatantly admits to not expecting Ian to be black (Utopia 1:1) and seems romantically interested in Becky at times. 66 Problematically, he is almost overly inscribed with symbolic signifiers even upon introduction, reflected both in his duplicated name, the t-shirt he wore initially bearing a stag on it -the relationship between animals and death is intriguingly subtle, but seems to function as harbingers in season 1, and well worth a more thorough analysis but also his repeated conversion; physical inscriptions of violence; and relationships to Arby and Milner, which figure as inverted mirrors; his colour coding and audio cues would be interesting to pursue in future elsewhere, as would the symbolic significance of his right eye being removed, however all this lies outside the scope of this paper. 67 Interestingly, when inflicting the Chinese character upon his body -a scar associated with Mr Rabbit -, the act bears a momentary resemblance to the Japanese act of Seppuku (Utopia 2:6), yet again inscribing himself with symbolic significance and negating the counter-argument of an imposed Self, as his action avows to a deep degree of self-reflexivity. of a world of madness; 68 an envisioned collapse or rather harmonious reconciliation of the private and public distinction, by means of relinquishing a possessive self-perception, was

More's answer. 69 Bacon, however, produces a split between seeming (role) and being (self), akin to More's dichotomy between the private and public, in order to address the crisis of a restriction of scientific endeavour, whilst the self though is either disavowed or else sacrificed on the altar of knowledge-worship in order to be unencumbered by morality, as Weinberger speculates. 70 Nevertheless a degree of self, as a constitutive part of a restricted "we", remains or is regained by means left deliberately obscure. Also of note is the openness towards intervening in human nature in order to achieve the necessary disposition.

Wilson Wilson, of Kelly's Utopia, also operates with the distinction between role and self that Bacon used, but sacrifices anything he may have considered his self in order to regain agency within a role that offers an identity within a species-identification, in light of the burgeoning crisis of overpopulation. Contrary to Jendrysik's assertion that "[i]n all utopias, individual political activity is reduced to exit", 71 here Wilson Wilson embraces the obliteration of self and actively engages in the maintenance of our critical utopia; it is the implication of this action and the dystopic tendencies it reveals that is unsettling. However, in truth, the choices proffered in these Utopias between self-repression with a resignation of agency and self-sacrifice in order to perceive an attainment of agency, when faced with crises, are by no means comfortable. It is Bacon's legacy, though, the willingness to intervene in the construction of human nature, as explored by a number of post-and transhumanist authors, that is proving more fruitful for Utopian literature as means of envisioning alternative relationships between the Self and larger units, or to make the transition more palatable; with biochemical tweaking of aggression, for example, or by means of technologies that may bring about more compromising hive minds or swarm intelligences.

It is these science-fiction speculations that maintain the spirit of Utopia and would be exceedingly engaging to explore in their precise manifestations, as they continue to force us to ask: What makes us human? What do we want to become? How? And, at what cost? But they also enable us to not only interrogate how we might be able to achieve a sustainable 68 Greenblatt 14-16. 69 Greenblatt would assert that this relinquishment does not fully occur (56-58), but his subject is More rather than the Individual in Libellus proper. 70 Weinberger, "Science and Rule" 881-885. 71 Jendrysik 37. equilibrium between the I and Us -but whether we should. With recent investment in technologies of neural interfacing by companies such as Neuralink and Kernel, [START_REF] Cade | Elon Musk Isn't the Only One Trying to Computerize Your Brain[END_REF] these projects need to be addressed now in their inception, as the far-reaching implications for the social contract hold an extreme potential for generating systemic and fundamental crises that will undoubtedly exceed traditional national borders as we currently conceive them.

  Spinozzi, "Acerba illa vita velut carcere atque aculeo: Health or Death in More's Libellus vere aureus: Early Modern Thought and Contemporary June 2017, on the utilitarian approach on life in Utopia and for greater elaboration. Arguably the only distinctions that remain are sex and marital status.

	Debate,"	Utopian	Studies	27.3	(2016):	586-600,	JSTOR	<http://www.jstor.org/stable//
	10.5325/utopianstudies.27.3.0586> 15

  : 492-500, JSTOR <http://www.jstor.org/stable/460726> 15 May 2017; Eleanor D. Blodgett, "Bacon's New Atlantis and Campanella's Civitas Solis: A Study in Relationships," PMLA 46.3 (1931): 763-780, JSTOR <http://www.jstor.org/stable/ 457860> 16 May 2017; and Timothy J Reiss, "Structure and Mind in Two Seventeenth-Century Utopias: Campanella and Bacon," Yale French Studies 49 (1973): 82-95, JSTOR <http://www.jstor.org/stable/2929569> 16 May 2017; for more comprehensive, in-depth analyses and comparisons to other Utopias. 42 James Spedding, et al., The Works of Francis Bacon, volume 3, ed. James Spedding, Robert L. Ellis and Douglas D. Heath (London: Longman and co., 1857). Hereafter abbreviated as New Atlantis and all subsequent references to this edition are in parentheses in the text. 43 That is not to say it has no part. 44 Bronwen Price, "Introduction," Francis Bacon's New Atlantis: New Interdisciplinary Essays, ed. Bronwen Price (Manchester and New York: Manchester University Press, 2002) 1-2, 23 n.2, Directory of Open Access Books <https://www.doabooks.org/doab?func=fulltext&uiLanguage=en&rid=12662> 5 Jan. 2018. New Atlantis is considered as complete in this text, in line with Weinberger's reading. Cf. J. Weinberger, "Science and Rule in Bacon's Utopia: An Introduction to the Reading of the New Atlantis," The American Political Science Review 70. 3 (1976): 869-872, 882-885, JSTOR <http://www.jstor.org/stable/1959872> 11 July 2017; and J. Weinberger, "On Bacon's New Atlantis," New Atlantis and the Great Instauration, ed. J. Weinberger. 2 nd Edition (Chichester: Wiley Blackwell, 2017) 133-134.

  David Colclough, "Ethics and politics in the New Atlantis," Francis Bacon's New Atlantis: New

	Interdisciplinary Essays, ed. Bronwen Price (Manchester and New York: Manchester University Press, 2002)
	67-72,	Directory	of	Open	Access	Books	<https://www.doabooks.org/
	doab?func=fulltext&uiLanguage=en&rid=12662> 5 Jan. 2018. Counter to Colclough's dismissal of other
	readings, which he argues "ask[s] the wrong questions of the work" (

  Jan. 2018. Also on the contextualisation of New Atlantis in colonial issues, see Irving, who stresses Bacon's underlying anxieties whilst linking it to his concerns on knowledge, and Lux, who draws attention to the relevance of China in New Atlantis. Sarah Irving, "'In a pure soil': Colonial anxieties in the works of Francis Bacon," History of European Ideas 32.3 (2006): 249-262; ScienceDirect <http://www.sciencedirect.com/science/article/pii/S0191659906000143> 3 Jan. 2018. Jonathan E. Lux, "'Characters reall': Francis Bacon, China and the entanglements of curiosity," Renaissance Studies 29.2 (2014): 184-20, Wiley Online Library <http://onlinelibrary.wiley.com/doi// 10.1111/rest.12060/epdf> 3 Jan. 2018.

	New Interdisciplinary Essays, ed. Bronwen Price (Manchester and New York: Manchester University Press,
	2002)	129-155,	Directory	of	Open	Access	Books	<https://www.doabooks.org/
	doab?func=fulltext&uiLanguage=en&rid=12662> 5