Olivier Capra
email: olivier.capra@univ-catholille.fr

Florent Berthaut
email: florent.berthaut@univ-lille.fr

Laurent Grisoni
email: laurent.grisoni@univ-lille.fr

Levels of Detail in Visual Augmentations for the Novice and Expert Audiences

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Introduction

Digital Musical Instruments offer countless opportunities for musical expression as they allow artists to produce sound without the physical constraints of acoustic instruments. This control dislocation [START_REF] Miranda | New digital musical instruments: control and interaction beyond the keyboard[END_REF], by breaking the intuitive link between gestures and sound, may however hinder the audience experience making the musician's contribution and expressiveness difficult to perceive. Consequently, it also contributes to degrading spectator's attributed agency [START_REF] Berthaut | Liveness Through the Lens of Agency and Causality[END_REF], that is the level of control they perceive from the musician. Such difficulties in the integration of the musician's gestures can lower the interest of observers [START_REF] Schloss | Using contemporary technology in live performance: The dilemma of the performer[END_REF] and lead them to doubt the genuine contribution of the artist compared to the one of autonomous processes such as prerecorded audio samples or computer controlled sequences. Furthermore, the diversity and complexity of DMIs makes it difficult for the audience to build a familiarity with every instrument. Thus, audience experience progressively became an important aspect in the creation of Digital Musical Instruments (DMIs), either as an evaluation method [START_REF] Barbosa | Considering Audience's View Towards an Evaluation Methodology for Digital Musical Instruments[END_REF] or as a dimension which should be addressed at the design [START_REF] Fels | Mapping transparency through metaphor: towards more expressive musical instruments[END_REF][START_REF] Jordà | Interactive music systems for everyone: exploring visual feedback as a Computer Music Journal January 11, 2021 way for creating more intuitive, efficient and learnable instruments[END_REF]Correia and Tanaka 2017) or performance stages [START_REF] Reeves | Designing the Spectator Experience[END_REF][START_REF] Benford | Designing the Audience Journey through Repeated Experiences[END_REF]. Artists and researchers alike have designed techniques which augment the instruments with additional information to improve the audience experience and restore the trust of spectators in the musician's involvement. While these techniques explore different modalities (visual, haptic, auditory) and address different aspects of the performance (technical, gestural, intentional), they mostly offer a fixed level of information to all spectators.

However, we think that augmenting the audience experience can be more effective when considering spectators from an individual perspective. The information needed by each spectator can differ depending on their personal sensitivity and expertise. In order to ensure an optimal experience for spectators, we propose to allow the audience to dynamically change this level of information using visual augmentations with variable levels of detail (LODs).

Augmenting the audience experience

A number of augmentation techniques for spectator experience have been designed.

Here we only provide a few examples, a more detailed analysis can be found in the taxonomy that we proposed in Capra et al. (2020b).

Perhaps the simplest is the organisation of pre-concert demonstrations, such as described by [START_REF] Bin | Skip the Pre-Concert Demo: How Technical Familiarity and Musical Style Affect Audience Response[END_REF]. More common is the use of visual projections that represent the instrument structure and parameters or musician's gestures. Examples can be found in many electronic performances, with accompanying visuals displaying changes in sound processes as abstract or figurative elements. [START_REF] Perrotin | Visualizing Gestures in the Control of a Digital Musical Instrument[END_REF] have proposed to display the musical controls of musicians in an orchestra with a video projection, to help the audience perceive the actions of each orchestra member by representing both gestures and musical parameters. Similarly, Correia et al. (2017) discuss the role of visuals in live performances and insist on the importance of showing both the gestures (interface) and parameters to the audience. [START_REF] Berthaut | Rouages: Revealing the Mechanisms of Digital Musical Instruments to the Audience[END_REF] describe an augmented reality which can be used to reveal the mechanisms of DMIs. Haptic augmentations can also be created to increase the audience's engagement, as proposed by [START_REF] Turchet | Haptification of Performer's Control Gestures in Live Electronic Music Performance[END_REF]. All these augmentation techniques however only offer a fixed set of information for the whole audience. [START_REF] Benford | Designing the Audience Journey through Repeated Experiences[END_REF] go beyond fixed information by combining projected visual augmentations during the performance and visual/textual augmentations on a mobile app after the performance, thus allowing spectators to access two different levels of representation. Finally, [START_REF] Capra | Toward Augmented Familiarity of the Audience with Digital Musical Instruments[END_REF] propose adaptive augmentations as part of a pipeline for augmented familiarity, but they do not provide an implementation or evaluate the impact of the described levels. In contrast, we propose to adapt the amount and the type of information provided by visual augmentations using a Level Of Detail approach.

Contribution

In this paper, we first introduce the concept of Level of Details (LOD) for visual augmentations, gathering LOD approaches from research fields, other than those in music.

Second we describe the design and implementation of dynamic and controllable LODs for the audience of digital musical performances. Third, through a controlled experiment based on a protocol that we proposed in Capra et al. (2020a), we study the effect of LODs on the experience of novice and expert spectators, and investigate how they could be used in performance settings.

Levels of Detail for the Visual Augmentation of DMIs

The concept of Level of Detail (LOD for short) originates from the field of computer graphics [START_REF] Luebke | Level of detail for 3D graphics[END_REF] where 3D models and scenes complexity are adapted in order to reduce rendering load. It takes inspiration from existing signal analysis tools, such as wavelets [START_REF] Stollnitz | Wavelets for Computer Graphics: Theory and Applications[END_REF] or more basic simplifications systems such as down-sampling. LODs are meant to bring some flexibility in terms of calculus cost in all possible aspects of 3D representations (geometric models, textures, collision detection, etc.) by allowing one to adapt the representation to the context of use. Such adaptations are usually made thanks to the context of visualisation (expectations of users, hardware possibilities, etc.).

In the Human Computer Interaction (HCI) literature, LODs allow users to access different levels of complexity in the interface, such as with Zoomable User Interfaces [START_REF] Bederson | Pad++: A Zooming Graphical Interface for Exploring Alternate Interface Physics[END_REF], or in a musical context to build and manipulate complex musical structures [START_REF] Barbosa | Illusio: A drawing-based digital music instrument[END_REF]. Finally, LODs have been also used in augmented reality [START_REF] Sung | Level-of-detail AR: Managing points of interest for attentive augmented reality[END_REF] to provide access to more or less detailed information on physical objects and in the field of information visualisation to adapt quantity of information in order to limit visual overload [START_REF] Holten | Hierarchical edge bundles: Visualization of adjacency relations in hierarchical data[END_REF][START_REF] Wang | Visualization of Large Hierarchical Data by Circle Packing[END_REF].

Practical existing applications fields where LODs are used involve two classes of techniques, depending on the nature of data to handle. Such data may be discrete (i.e. sampling from a continuous phenomenon, whatever its nature), in which case most of the existing digital techniques can be adapted from interactive graphics and signal analysis.

Such data may also be symbolic (i.e. referring to a dimension of information that is mostly conceptual and can not be directly represented by any sampling set), in which case LODs may be achieved by drawing inspiration from other communities, such as data visualisation and HCI.

LODs applied to augmentations for the audience

In this paper, we propose to apply the LODs approach to the design of augmentations for the audience of digital musical performances. As discussed above, digital musical interactions can prove highly difficult to perceive and understand, due to potentially small or hidden sensors and gestures, potentially complex mappings between sound and gestures, and complex and partly autonomous (pre-defined or automated) sound generating processes. Augmentations proposed in the literature aim at compensating this by providing the audience with information to enrich their experience.

Technically, there are no major obstacles for these augmentations to provide access to all information from the instrument : the exact sensor values, the audio graph that results in the sound with all the used processes and their corresponding parameters, the list of mappings between all the sensors and all the sound parameters.

However, this volume of information might not benefit the audience due to various reasons, such as:

• too much information at once;

• information requiring some expertise on DMIs to be understood;

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• inconsistency with the audience preference when attending a performance, which might range from trying to understand the musician's actions to only focusing on the music.

Therefore, we believe that it is essential to provide a mechanism for the spectator to select the level of detail provided by these augmentations. The LOD approach can help adapt augmentation techniques, in our case visual augmentations, to the variety of expertise and preferences of spectators. In the idea of a better adaptation to personal needs, LODs on augmentations could be chosen dynamically by the spectators during the performance, either individually or as a group.

In the following sections, we describe how these LODs can be applied to visual augmentations, and how they can be implemented.

Levels of Detail in Visual Augmentation

In this paper, we apply our LOD approach more specifically to visual augmentations for the audience. These augmentations are graphical representations of the controls and mechanisms of a DMI, which are superimposed on the physical performance with the help of an augmented reality display. The purpose of visual augmentations is to reveal aspects of DMIs that are not easily perceived by the audience due to their lack of familiarity with them and the absence of physical link between gesture and sound. This includes subtle and/or hidden gestures sensed by the interface, complex or unusual mappings between the gestures and the various controllable parameters and the dynamic behaviour, potential range of output and internal structure of a DMI.

Following what [START_REF] Berthaut | Rouages: Revealing the Mechanisms of Digital Musical Instruments to the Audience[END_REF] proposed , our visual augmentations represent the three main sections of the instrument :

• the physical interface composed of sensors (e.g. a MIDI control surface);

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• the mappings, i.e. the connections between sensors and musical parameters (e.g. the first fader controls the volume of the first audio track);

• the processes (e.g. tracks, loops, patterns) that generate the sound.

An important aspect of visual augmentations is that they do not restrain the design of DMIs. Instrument designers and musicians are free to choose their interfaces, mappings and processes with expressiveness in mind, without worrying about the transparency [START_REF] Fels | Mapping transparency through metaphor: towards more expressive musical instruments[END_REF] of the musicians' actions or the familiarity [START_REF] Gurevich | Digital musical interactions: Performer-system relationships and their perception by spectators[END_REF] of the audience with the instrument, since these aspects are handled by the augmentations.

However, the potential complexity of DMIs implies that visual augmentations may become too detailed if one aims at representing all their events and components, which might in turn degrade the spectator experience that we are trying to enhance [START_REF] Leman | Embodied music cognition and mediation technology[END_REF]. Spectators might also prefer more or less detailed information for aesthetic reasons and at various times in the performance. Finally, musicians or accompanying visual artists might want to modify the level of information provided in order to alter the audience experience during the performance, e.g. to change from expressive to magical interfaces [START_REF] Reeves | Designing the Spectator Experience[END_REF].

We propose to implement LODs in visual augmentations by defining dedicated levels of detail for each section (Interface, Mappings, Processes) of the visual augmentations.

These local LODs can be chosen independently or combined as global LODs such as the ones we describe in section .

Local LODs

As illustrated in Figure 1, we propose 4 levels of detail for the Interface section, 3 levels for the Mappings section, and 5 levels for the Processes section. Each local LOD features a level 0 in which the section is not augmented. If all three sections are at level 0, no information is added to the performance. One should note that the information provided by each level can be displayed in different ways, the representations proposed in our implementation are only one of the many possibilities that artists can explore.

Interface section

Level 1 only indicates the global activity, e.g. when the musician performs a gesture sensed by the system.

Level 2 represents the activity of each sensor of the physical interface, allowing one to perceive fast and complex gestures such as bi-manual or multi-finger interactions.

Level 3 describes both the activity and the type of each sensor (discrete/continuous, shape of sensor ...).

Level 4 adds a representation of their values and range.

Mappings section

Level 1 only describes to which processes the sensors are connected.

Level 2 refines the connection to the parameter level by representing on the links the multiple parameters modified through this mapping. For example the link can change colour to show its impact on the pitch of the associated process, while changing texture to

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show that it also impacts the timbre of the sound.

Level 3 adds a representation of the operation or series of operations which transform sensor values into parameters values [START_REF] Fels | Mapping transparency through metaphor: towards more expressive musical instruments[END_REF]), e.g. scaling, inverting, combining and so on.

Processes section

Level 1 visualises the output of the system as a whole, merging the activity of all sound processes.

Level 2 provides a detailed activity for each process of the system, e.g. a distinct shape whose size indicates the volume of the corresponding sound process.

Level 3 adds a dynamic representation of parameters (i.e. inputs) that can be controlled on the processes.

Level 4 adds parameters names, types and values range, i.e. as performers would see them when performing with a GUI.

Level 5 provides a detailed representation of the complete internal graph of audio synthesis and effects that generate the sound of each process. It corresponds to what the musician would access when designing their instrument, and is potentially similar to the mental model they have when performing.

While the LOD could be chosen by spectators independently for each section, we believe a simpler solution is to define a number of global levels, i.e. presets of local LODs, so that spectators are provided during the performance with a unique control.

Global LODs

Global LODs are a combination of local LODs. They provide the spectators with a convenient way to control the level of detail by modifying several sections at a time :

Interface (I), Mappings (M) and Processes (P). For instance, "SENSORS (I4-M0-PO)" is a global LOD called "SENSORS" and uses Level 4 for the Interface section and Level 0 for the Computer Music Journal January 11, 2021

others.

In the following study, we use 7 global LODs with increasing quantity of information (See Figure 2).

NONE (I0-M0-P0) provides no information at all. The performance remains unchanged.

SENSORS (I4-M0-PO) amplifies the gestures performed by displaying representations of the types and values for all sensors of the interface. It is therefore similar to the level of details provided by [START_REF] Turchet | Haptification of Performer's Control Gestures in Live Electronic Music Performance[END_REF] with haptics, and [START_REF] Perrotin | Visualizing Gestures in the Control of a Digital Musical Instrument[END_REF] for visuals. In the case of our study, faders, knobs and buttons of a MIDI controller are displayed.

PROC (I0-M0-P2) displays the sound processes of the instrument as separate shapes with graphical parameters associated to extracted audio features (loudness with size, pitch with colour hue, brightness with colour luminance), allowing spectators to identify the broad structure of the instrument and the activity of processes. This LOD corresponds to the representations traditionally used to illustrate electronic music performances (e.g

VJiing) and defined as audiovisual entities by Correia et al. (2017).

SENS_PROC (I4-M0-P2) shows both amplified gestures and the activity of separate processes. It provides information on both the interface and processes of the instrument, without detailing its internal structure or behaviour.

MAPPINGS (I4-M1-P2) adds information pertaining to how sensors are mapped to the sound processes. It shows when a sensed gesture has an effect on a sound process but not what effect it has, i.e. not what is exactly controlled by each sensor. In our implementation, mappings are displayed as lines between sensors and processes, which appear when a control is performed and then fade out. It is similar to the level of information proposed in the Rouages project [START_REF] Berthaut | Rouages: Revealing the Mechanisms of Digital Musical Instruments to the Audience[END_REF].

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FULL_COMBINED (I4-M2-P3) refines both the Mappings and Processes sections. It

shows which parameters are controlled by each sensor and displays both the parameters and activity of the processes. In our implementation, each process is represented by a composite shape with an outer ring displaying the input parameters (i.e. gain with size, filter cutoff with color luminance, position in sample with rotation, delay feedback with shape repetition, pitch with color hue), while the activity is shown by an inner graphical element. This level is similar to the augmentations described by [START_REF] Berthaut | Liveness Through the Lens of Agency and Causality[END_REF]. As suggested by them, this LOD should improve the exclusivity dimension of attributed agency, by showing when a change in the sound actually comes from the musician and when it is automated.

FULL_GRAPH (I4-M2-P5) provides a complete overview of the instrument with parameters names and value range, processes names and mappings between each sensor and the parameters. It corresponds to the mental model musicians might have of their instrument, with the exact structure, mappings and range of sonic possibilities. In our implementation, each process is labelled and displayed as a group of graphical sliders and buttons representing each parameter, with their names, value and range of values, and another slider serves as a VU-meter. Although this global LOD uses the maximum of each local LODs, we chose to limit the Mappings section to level M2 so that the amount of information remains reasonable. Similarly, the structure of the instrument used in our study is essentially a stack of samplers and effects with one parameter each, so that level P5 adds very little information compared to level P4. This structure was chosen in order to reduce the gap in quantity of information from the previous global LOD, i.e. we do not add a complex audio graph in addition to the details on parameters when going from FULL_COMB to FULL_GRAPH. FULL_GRAPH can be seen as similar to approaches where the full complexity of the instrument is shown such as in live-coding performances.

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Implementation

In order to provide such dynamic LODs to spectators, one needs to access internal parameters of DMIs and to adapt to various display strategies.

Accessing LODs

Depending on the chosen LODs, the granularity of information required by the system can increase rapidly as well as the real time processing of extracted data. For low LODs (i.e. less detail), data for both the interface and processes sections can easily be gathered by directly accessing messages (e.g. MIDI/OpenSoundControl) sent by the interface and by extracting audio features from the audio output of the instrument. In higher LODs where the mappings and internal structure of the processes need to be displayed, one must gain access to internal events and data of the software part of the Ableton Live, which are used by many electronic musicians, might offer access to their control data through plugins, or in the case of Ableton live a dedicated API. They, however, do not guarantee a full access to every settings of the instrument, e.g. the set of mappings. In general, the use of visual augmentations has implications on the design of DMIs, which need to integrate a protocol for querying their structure and state and for listening to internal events.

Displaying LODs

Once the information on the instrument's structure, state and activity is captured and translated to the visual representations proposed in the previous section, it needs to be displayed for the audience in the form of visual augmentations overlapping the performance and instrument. We envision multiple possibilities for implementing visual augmentations with LODs in a performance setting. A first one relies on individual views of the augmentations, in order to allow each spectator to choose their LOD freely. This can be implemented with a mixed-reality headset or a mobile device as shown in Figure 3.a. In our case, spectators access a web page with their mobile devices. Based on OpenCV and WebGL, it uses printed markers placed around the instrument to superimpose the augmentations on the mobile camera image in real time. Updates to the augmentations are received via WebSockets and a slider allows spectators to quickly explore the LODs.

To avoid forcing the audience to wear or hold devices which may impair their experience, another possibility is to use a single spatial AR display, either projection mapping or an optical combiner (e.g. Pepper's ghost display), such as depicted in Figure 3.b, in which case viewers all perceive the augmentations spatially aligned with the physical instrument. Another possibility is to film and re-project a close-up view of the interface integrating the augmentations, as shown in Figure 3.c. This solution however moves the focus away from the physical performer. In these scenarios, all the spectators share the same LOD. LOD control may be performed by musicians or accompanying visual artists, so that they can modulate the audience experience during the performance.

But the shared LOD can also be chosen by spectators. Voting system such as the one used in the Open Symphony project [START_REF] Wu | Open symphony: Creative participation for audiences of live music performances[END_REF]) may be used, in the form of a web interface accessible from their mobile devices, as depicted in Figure 3.b. In this case the displayed LOD reflects either the majority or the average vote.

Finally, an intermediary solution is to provide multiple views of the augmentations for groups of spectators, using video (i.e. multiple or multiscopic screens such as the one proposed by [START_REF] Karnik | MUSTARD: A Multi User See through AR Display[END_REF]) or optical AR (with mirrors at multiple angles). For each group, the LOD can be fixed at a different value, so that spectators can move towards or look at the display they prefer. A voting system may also be setup separately for each group.

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Usage and effects of LODs

In this section, we present an experiment that aims at evaluating the impact of LODs on audience experience and understanding, and studies the use of controllable LODs by spectators with different expertise.

In order to retrieve accurate and individual data on spectator experience we chose to conduct a controlled experiment in the lab. We discuss the advantages and limitations of such 'in the lab' studies in more details in (Capra et al. 2020a) and plan to address social and environmental aspects of public performances in a future work.

Hypotheses

From the literature analysis, we hypothesise that the different LODs, with their various amount and type of information, will effect the experience of participants, improving their understanding and experience up to a certain level but differently for novices and experts. We also hypothesise that, if given the choice, participants will select the LOD depending on their expertise with DMIs. 18 participants (16 M, 2 F) took part in the experiment, aged of mean 29 (±7.3 , min=20, max=43). As illustrated in Figure 4, before the beginning of the experiment, participants were presented with the details of the experiment and signed a consent form.

Procedure

Participants sat in front of a 24" screen, equipped with headphones and a Pupil-labs Core eye-tracking device (the details of the eye tracking are addressed in a forthcoming study).

We measured their expertise with the instrument presented in the study using questions regarding their practice of DMIs, their use of graphical user interfaces similar to the one in Figure 2 and their use of control surfaces. We also asked how often they attended electronic music performances. This allowed us to compute an expertise score, and we used it to separate them into two groups : 9 experts and 9 novices. The experts had a music practice of 17.3 years (±6.4, min=10, max=30) and an electronic music practice of 10.7 years (±7.3, min=2, max=25) against 1.6 years (±2.6, min=0, max=7) of music practice and no electronic music practice for the novices. Experts had all used both graphical interfaces for music and control surfaces such as the ones presented in the experiment. Per year, experts claimed going to 12.8 (±8.3, min=2, max=30) electronic music performances, while for novices the average was 0.6 (±1.5, min=0, max=5).

Dynamic stimuli

The stimuli were videos of short performances of a male musician playing with a Digital Musical Instrument. The DMI was composed of a Korg NanoKontrol controlling a set of Pure Data patches with three sound processes (melodic, rhythm, granular texture) each with multiple parameters (See Figure 2). We designed 3 sets of mappings between the interface sensors (knobs, faders, buttons) and the parameters. Each set was intended to target a different level of contribution of the musician, i.e how much of the changes in the sound are due to them vs automated. The first set is completely manual so no changes happen without a gesture. It corresponds to the maximum contribution level. The second features automations for half the parameters, the rest being manipulated by the musician.

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In the third set of mappings, most parameters are automated and the musician is able to take control of some of them temporarily, giving the highest contribution to the computer.

In order to play the videos with dynamic overlapping visual augmentations, we designed the experiment in the Godot game engine. Videos were played synchronised with the playback of control data recorded in Pure Data, so that the sound and the visual augmentations were generated dynamically during the playback. This technical setup gave us the flexibility to play the video footage of a performance and to accompany it with arbitrary audio processes and visual augmentations in real time. The experiment lasted around 45mn and was composed of 2 blocks.

Block 1 : fixed LODs

In the first block, participants watched 7 LODs x 3 contribution levels = 21 videos of short performances (20s). Each video was followed by a questionnaire of 9 order-randomised questions to evaluate their experience and comprehension. The survey included only one objective question. We evaluated the ability of the participants to correctly detect the contribution levels that we induced by the mappings by answering the question "Who from the musician or the computer contributed the most to the performance ?". They also could choose 'both equally'.(The questions were all posed in French but appear in translation here.)

The other questions evaluated the participants' subjective comprehension. They were based on 5 communication design issues introduced by [START_REF] Bellotti | Making Sense of Sensing Systems: Five Questions for Designers and Researchers[END_REF] and transposed to the spectator perspective by [START_REF] Gurevich | Digital musical interactions: Performer-system relationships and their perception by spectators[END_REF]. We complemented them with Association that targets the capacity to expose to spectators the respective and shared contributions of the user (musician) and the system (DMI) (Capra et al. 2020a).

These design challenges are well adapted to the evaluation of NIMEs as they allow for an assessment by components of the subjective experience of spectators.

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By evaluating subjective comprehension, we do not target the objective ability to detect a parameter of the interactions like we do with the first question of the block.

Instead, these questions aim at providing insights into the confidence spectators have in the inner representation of the interactions they build up along the performance.

Participants answered on 7-step scales to the question "To which extent do you agree with the following statement ?". Only the extreme values of the scales had a label : "I totally disagree" and "I totally agree".

"In this video, I know when the musician is interacting with the instrument and when he is not."(Address) Finally, the participants had to report their personal rating of the performer's virtuosity and the overall performance on a 7-point scale.

Block 2 : dynamic LODs

In the second block, participants could change with the scroll wheel the LOD of the augmentations as the video was playing. In a first task, they watched 3 short (60s) performances and were asked to select the LOD that gave them the best experience, i.e. that they preferred. In a second task, they watched the same performances and were . The levels of detail (LODs) of the visual augmentations did not impact equally the subjective perception of the interactions. Moreover, compared to novices, experts reported higher evaluations of the Bellotti/Fyans challenges (subjective comprehension) and higher ratings of their experience and the virtuosity of the musician.

Results

Data was recorded, anonymised and stored in real time during the experiment by a bespoke experiment software developed in the Godot game engine. Subjective reports were obtained via likert scales and were analysed with parametric tools when the normality assumptions were met.

PERCEIVED CONTRIBUTION

NOVICES

Both equal Computer Musician EXPERTS Figure 6. Regardless of the LOD, experts perceived a higher contribution of the musician than Novices.

that the data are 2.4 times more likely to occur under a model including the corresponding effect compared to the one implying no effect (H0). The posterior odds have been corrected for multiple testing by fixing to 0.5 the prior probability that the null hypothesis holds across all comparisons. Analyses were performed with SPSS v25, R studio 1.2 and JASP (JASP Team 2019).

Block 1 : fixed LODs

Contrary to our hypothesis on objective tasks, analysis did not reveal any group effect and any effect of the levels of detail (LODs) on the objective task. Overall, the evaluation of the factual contribution ratio between the musician and the computer proved difficult.

Our hypothesis on the Bellotti/Fyans challenges was confirmed. Thus, from a subjective perspective, an interesting group effect (χ 2 = 12, p = 0.002, BF 10 = 11) showed that experts considered the musician contributed more than the computer in 62% of the stimuli compared to 45.5% for Novices (Figure 6). As depicted in Figure 7, experts reported higher evaluations of the subjective questions but did not perform better than novices in the objective task of evaluating the most contributive to the performance from

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SUBJECTIVE COMPREHENSION

Extreme evidence for H1 BF 10 > 1e+14

Anecdotal evidence for H0 BF 10 = 0.67 the musician or the computer.

OBJECTIVE COMPREHENSION

NOVICES

When detailing the Bellotti/Fyans challenges, regardless of the group, the Accident was the least rated, meaning that participants were not so confident in their capacity to detect errors. The effect of the LOD was revealed on most of the subjective questions (all p -values < 0.027, all BF 10 > 6), with the exception of Accident and Virtuosity (all p -values > 0.22, all BF 01 > 4). Two LODs were particularly effective, SENS and FULL_COMB.

Reading the experts graph (Figure 5 -left) from left to right, compared to NONE, the control condition, SENS, the level of detail exposing the sole sensors activity, presents a significant boost in all dimensions, then PROC exposes an equivalent score to NONE.

From SENS_PROC to FULL_COMB a rather linear progression is observed and extends to difference with the experts' scores. For 6 (out of 9) dimensions, the smallest difference is measured when visual augmentations are presented with FULL_COMB. This result is a good illustration of the expected role of visual augmentations, compensate the lack of expertise of novices for a better experience.

Block 2 : dynamic LODs

The score for these tasks was calculated by accumulating the time participants spent using each LOD. Both tasks, experience and comprehension, show comparable evolution characterised by a minimum for the control condition NONE and a maximum for the higher LODs (Figure 8). A decisive effect of LODs was found (F (6,90) = 9.94, p < .001, BF 10 > 10000) but with no difference between the groups (BF 01 = 4). Novices favoured FULL_COMB and SENS for experience and FULL_GRAPH for comprehension. Experts chose the highest LODs for experience and FULL_COMB and FULL_GRAPH for comprehension.

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Discussion

In this section, we complete the quantitative data with subjective insights from interviews and we discuss our results.

LODs affect subjective comprehension

The interviews confirmed and extended the quantitative analyses. Despite the absence of effect of LODs on the ability of spectators to perceive the musician objective contribution (objective comprehension), participants favoured levels FULL_GRAPH and SENSORS for understanding the performance, especially when the music got more complex with many fast changes in the sound. This indicates that LODs influence the subjective comprehension of spectators in the sense that spectators feel more confident in what they perceive from the interactions even if their factual understanding is not improved. It also suggests that amplifying the gestures (SENSORS level) might be more informative than displaying the activity of processes alone (PROC level).

The role of expertise

Our study reveals interesting insights into the nature of expertise in DMI spectators.

Results of Block 1 showed that experts perceive a higher contribution of the musician when novices perceive a higher contribution of the computer. Also, experts put more trust in their personal representation of the interactions as proven by their higher evaluation of the Bellotti-Fyans challenges (subjective comprehension). This contrast is confirmed in Block 2 where only novices favoured the SENSORS LOD over no augmentations for a better comprehension and experience (Fig. 8), as if experts already had an internal representation of the interactions with the sensors and therefore did not need that LOD.

Apart from SENSORS, both experts and novices mostly utilised FULL_COMB when they could choose their favourite LOD. But when they had to choose a LOD in order to better

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understand the interactions, experts equally used FULL_COMB and FULL_GRAPH when novices massively favoured FULL_GRAPH. As both groups scored poorly in the objective task in Block 1, whatever the LOD, these preferences in LOD are to be taken as subjective beliefs in a facilitation of understanding rather than a factual help.

In a previous study (Capra et al. 2020a), we already underlined the selective impact of visual augmentations on the sole subjective comprehension. Additionally, we showed that when participants watch DMI performances with visual augmentations, they overestimate the musician's contribution from the computer's, as the experts do when compared to novices in this study. Thus, multiple evidence support the idea of a rather subjective nature of expertise. The way we evaluate objective comprehension surely holds limitations. However, increasing data supports the hypothesis that, from a spectator perspective, experts are experts because they feel like they are, not due to a better perception compared to novices. In our results, experts do not show a superior ability in the understanding of interaction, on the contrary, we saw that their perception is biased towards a greater contribution of the musicians over automated processes.

Thus, by biasing the spectator perception towards a greater contribution of the musician (Capra et al. 2020a), and by comforting the confidence of spectators in their representation of the interactions (subjective comprehension), visual augmentations level up novices toward the rank of experts, especially when novices can select their favourite LODs.

Errors and virtuosity

The absence of effect of LODs on both the Accident dimension (i.e. the feeling of being able to perceive a potential error) and the virtuosity ratings underlines the crucial role of error perception in the emergence of a judgement of virtuosity [START_REF] Gurevich | Digital musical interactions: Performer-system relationships and their perception by spectators[END_REF].

A solution to this issue could be inspired by music video games where the virtuosity is materialised by screen indications of combinations (combos) of successful moves. Such informative contents are efficient and spectacular but imply the restriction of any improvisation or non-expected techniques. Another solution would be to design LODs that inform virtuosity, such as visualisations of input complexity or extra-ordinary values for controls and musical parameters.

LOD choice strategies

Strong differences in the choice of favoured LODs at the individual level were revealed by the data and refined by the interviews. When analysing the answers of participants regarding how they would use the LODs in public performance, we can distinguish 3 clear strategies: all or (almost) nothing: 4 participants claimed they would alternate between the maximum LOD (or just start with it) in order to form a mental image of how the instrument works (i.e. its capabilities) and then go back to no augmentations or to the SENSORS level, in order to focus on the musician's gestures.

adapting to complexity / performance: 4 participants claimed they would use LODs as a way to adapt to the complexity of the instrument or music, or change it depending on the musician playing; progression: 2 participants mentioned that their appreciation of LODs evolved over time, the more complex ones becoming more enjoyable and accessible, so that they would end up not going back to the lower LODs. One must note than even within these strategies there are interpersonal variations, again highlighting the utility of a controllable LOD on visual augmentations. thanks to cumulative data gathered about the subjective comprehension. With this study, the idea that spectators are more influenced by their inner representations than the actual objective reality of an interaction was strengthened. While this potential mismatch between perception and reality is a common phenomenon well known to illusionists and neuroscientists, here we have the possibility to infer the role of the augmentations in the constitution of more reliable inner representations.

Mediation through LODs : The role of the Augmenter

In the diversity of potential representations of a digital musical interaction, the ones expert observers can build should have a greater similarity with the ones from the musicians. As we saw it, from our data, it seems that they do not. In fact, the role of visual augmentations, and Spectator Experience Augmentation Techniques (SEATs) in general Capra et al. (2020a), may not be only to make the interactions more objectively understandable. They should not leave behind this role of a facilitation of the objective comprehension, but they should especially embed cues that contribute to the subjective comprehension, even if these cues are contradictory with objective cues. Besides, LODs are an effective way to offer rather balanced and customised information to spectators, preserving them from potential cognitive overload such as in fully descriptive visual augmentations.

To sum up, techniques to augment the experience of spectators should deliver a subtle ratio of objective and subjective cues and should also consider the audience's direct reactions. Such a sensitive role is not a purely technical role any more. It requires integrating a lot of information and to "feel" what should be the proper way to represent the ongoing interactions. For these reasons we think there is place on stage for one more artist, the augmenter.

The augmenter could act as an augmentations conductor and compose with the direct inputs from the musicians' instrument and connect them to visual augmentations, while selecting LODs to emphasise parts of the interactions. On the contrary the augmenter could leave the mystery on some parts, or even disturb the audience perception on purpose with disruptive augmentations. As many artistic activities, the augmenter would require training to reach the level of precision and virtuosity to personify (per-sonify ?)

the artistic intentions of the musicians. Compared to the VJs whose role is to illustrate the music with rather exclusively graphical considerations, the augmenter would perform as a human mediation between digital systems and human agents to reveal the virtuosity of the musicians and the expressiveness of instruments.

Conclusion

In this paper, we introduce the concept of Levels of Detail (LODs) in visual augmentations for the audience of Digital Musical Performances. We designed and implemented these LODs and we investigated their impact on expert and novice spectators.

The data we obtained from a controlled experiment show that whatever the LOD we used, the objective ability of spectators to perceive components of the interactions of musicians with their Digital Musical Instrument (DMI) remains relatively low, with no measurable difference between novices and experts. In particular, we found that the latter overestimate the contribution of the musician compared to the one of automated processes. Beside this newly identified bias in favour of the musician's involvement, Finally, in order to cope with the many challenges of the mediation between musicians and audience, we propose a new role in the digital musical performance ecosystem, the augmenter, who can manipulate the augmentations and their LODs during performances.

While our results provide useful insights, we believe the controlled experiment approach that we took should be combined with in the wild study of performances. As future work, we think that augmentations with LODs should be extended to other interfaces beyond control surfaces, e.g. gestural controllers or graphical interfaces such as live-coding, and that the effect of aesthetic choices on the design of augmentations should be investigated.

Figure 1 .

 1 Figure 1. (top) Local LODs (Input, Mapping, Output) refer to a specific dimension of the interaction with a DMI. We also provide examples for each level in these Local LODs. (bottom) The global LODs used in the experiment and their respective sets of local LODs.

Figure 2 .

 2 Figure 2. The 7 global levels of detail (LODs) used in our experiment, as seen by the participants. Each is built as a combination of local LODs for the Interface, Mappings and Processes sections (details in and ).

Figure 3 .

 3 Figure 3. Possible implementations 1 of visual augmentations with LODs : a) Mobile AR with individual LOD control, b) Spatial AR with an optical combiner shared between all spectators and mobile control to vote for the LOD, c) Shared close-up with Video AR projected behind the musician and artist defined LOD.

Figure 4 .

 4 Figure 4. During the experiment, participants watched videos of short performances with digital musical instruments, equipped with headphones and a lightweight eye tacking device.

  Figure5. The levels of detail (LODs) of the visual augmentations did not impact equally the subjective perception of the interactions. Moreover, compared to novices, experts reported higher evaluations of the Bellotti/Fyans challenges (subjective comprehension) and higher ratings of their experience and the virtuosity of the musician.

Figure 7 .

 7 Figure 7. Even if experts have more trust in what they think they can perceive from the interactions (subjective comprehension), they do not perform over Novices in the evaluation of the objective contribution of the musician (objective comprehension).

FULL_GRAPH.Figure 8 .

 8 Figure8. When participants could choose their favourite LODs in real time (they were asked to select it and remain on it), strategies emerged as illustrated. They confirmed and discussed their choices in the interviews.

A

  part of this work is dedicated to finding solutions to make the audience feel more aware of what is going on on stage during digital music performances. The extra mediation of visual augmentations to make more transparent interactions already mediated by technology may seem redundant. One may ask, why not explore a mediation that could suit both the musicians and the audience ? This question may find an answer Computer Music Journal January 11, 2021

  experts and novices are only distinguished by their subjective comprehension of the interactions, i.e. what they think they understand of the interactions rather than what they do (objectively) understand. These results lead us to hypothesise a rather subjective nature of the expertise, from a spectator perspective. Regarding the Levels of Detail in visual augmentations, our study revealed their impact, once again on the sole subjective aspects of the spectator experience. From quantitative data, we identified the most effective LODs with respect to the expertise of Computer Music Journal January 11, 2021observers and analysed their respective strategies during guided interviews. Our experimental approach suggests that by comforting the confidence of spectators in their representation of the interactions (subjective comprehension), visual augmentations are a particularly effective way to level up novices toward the rank of experts, especially when novices can select their favourite LODs.

All stimuli, illustration videos of the conditions, anonymised raw results, statistical analyses and implementation demos can be found here : http://o0c.eu/0NA

Computer Music JournalJanuary 11, 2021

Data analysis

The analyses were conducted under the common frequentist paradigm and were combined to Bayesian statistics [START_REF] Kay | Researcher-Centered Design of Statistics: Why Bayesian Statistics Better Fit the Culture and Incentives of HCI[END_REF]. A Bayes factor is reported as BF 01 when data better support the null hypothesis and as BF 10 when data support the alternative hypothesis (note that '01' becomes '10'). For example, the statement BF 10 = 2.4 means


Abstact In this chapter, Fabrice Bardet, a long-life student of Alain Desrosières tells the amazing academic dynamic that Alain Desrosières created around him. From the 1990s to his death in 2013, he was, without any doubt, the French scholar situated in the center of the sociological field dedicated to quantification's processes. Fabrice first comes back on the history of his master, a story that he had been told several times, by his side. Then he tells the story of the influence of his master on several generations of scholars, in France and abroad. He insists, among other things, on the importance that Alain Desrosières gave, from his main book published in 1993, The Politics of Numbers, to his most recent publications, to the influence of the writing of The Probabilistic Revolution, in the 1980s, in an international context, set up in Bielefeld, Germany. From this perspective, he explains how, in his own view, this focus made by Desrosières participated in creating a French school for sociology of quantification.

Theodore Porter, one of the main historians of the "Probabilistic Revolution", maintains that the impact of this history on the social sciences was stronger in France than anywhere else. Written after a seminar organized in the early 1980s at Bielefeld, in Germany, by the Zentrum für interdisziplinäre Forschung (Zif), this history was the fruit of a long interdisciplinary encounter envisioned by physicist and philosopher of science Lorenz Krüger and sustained by the research dynamic stemming from Thomas Kuhn's work on the structure of scientific revolutions. The revolution, which played out primarily between 1800 and 1930, placed the statistical sciences at the heart of all the activities of all the intellectual disciplines, throughout the world. The widespread use in industrial societies of "quality" tests is the product and symbol of this revolution. In France, Alain Desrosières, who had not been part of the Bielefeld group, was enthused by this masterpiece in the contemporary history of science immediately on its publication (Krüger et al. 1987, Krüger et al. 1987). He made it a basis for developing his plan for a historical sociology of quantification. He led a number of peers and students in this endeavour and was unquestionably the individual largely responsible for bringing this French school of the sociology of quantification into being. Within this school, the hypothesis of an accounting counter-revolution, dialectically linked to the probabilistic revolution, took shape as a means of shedding light on contemporary modes of government1 .

The meeting with sociology

Alain Desrosières studied the sociology that Pierre Bourdieu taught at the Ecole nationale de la statistique et de l'administration économique (ENSAE) in Paris, from 1963 to 1966. Bourdieu had just returned from Algeria where he had worked with three administrators of the Institut national de la statistique et des études économiques (INSEE), with whom he had published one of his first books [START_REF] Bourdieu | Travail et travailleurs en Algérie[END_REF]. He nurtured the hope of initiating a large-scale quantitative sociological undertaking like the one that had started to develop in the United States (Desrosières 2003). Alain Desrosières was part of that generation of INSEE administrators influenced by Pierre Bourdieu's teaching but who ended up developing an area of sociological enquiry that was actually quite distant from that of the master: not "with" but "about" statistical tools. His first objective was to establish their history (Affichard 1977[START_REF] Desrosières | Les temps forts de l'histoire de la statistique française[END_REF][START_REF] Guibert | Essai sur les nomenclatures industrielles[END_REF].

This difference of perspective fully explains Alain Desrosières' decision, in 1984, to support the creation establishment of the Groupe de sociologie politique et morale (GSPM). One of the group's founders, Laurent Thévenot, also an INSEE administrator, was working at the time with the sociologist Luc Boltanski on the operations of social taxonomy [START_REF] Boltanski | Finding one's way in social space: a study based on games[END_REF], and with Robert Salais, another INSEE administrator, on the conventions structuring labour markets [START_REF] Salais | Le travail : marchés, règles, conventions[END_REF]. These two research projects were to lead to the development of the "economics of conventions" [START_REF] Desrosières | The Economics of Convention and Statistics: The Paradox of Origins[END_REF]. The influence of Alain Desrosières, and in particular that of his work on the long history of French socio-occupational classifications (SOCs) [START_REF] Desrosières | Eléments pour l'histoire des nomenclatures socioprofessionnelles[END_REF][START_REF] Desrosières | Eléments pour l'histoire des nomenclatures socioprofessionnelles[END_REF]), was decisive in these entangled dynamics, as the introduction to the book that brought them together attests [START_REF] Boltanski | De la justification. Les économies de la grandeur[END_REF]. Desrosières' approach to sociology was to change as a result. This was evident in the first book that he published, with Laurent Thévenot, on SOCs, in which he explored their history on the occasion of their reform and which has remained a reference for French sociology students [START_REF] Desrosières | Les catégories socio-professionnelles[END_REF]. It was around this time that Desrosières' perspective shifted in a sense from social history to the historical sociology of statistics.

The Probabilistic Revolution as a historical and sociological tool

In fact this was more than a shift, for Alain Desrosières probably imagined the addition of a line of "tension", to use one of his favourite terms. He studied the history of sociology and that of its genetic ties with statistics, in particular [START_REF] Desrosières | Histoires de formes : statistiques et sciences sociales avant 1940[END_REF]. At the time, however, he was also regularly participating in the seminar on the history of the calculation of probabilities organized by Ernest Coumet, Marc Barbut and Bernard Bru, all of whose work he admired. That was where, in May 1987, he met Lorenz Krüger, who had been invited to MIT on the occasion of the publication of The Probabilistic Revolution. A few months later he met Lorraine Daston, whose work, following on from that of Coumet, was concerned with the development of the first probabilistic techniques by Italian city state bankers during the Renaissance [START_REF] Daston | L'interpératation classique du calcul des probabilités[END_REF]). This contact with the Bielefeld group opened up new horizons for Alain Desrosières. For several years, he had been seeking to develop links with research projects abroad. He had combed through the English-language journals, in particular, and in 1984 had come across Simon Szreter's work on the British census office [START_REF] Szreter | The genesis of the Registrar-General's social classification of occupations[END_REF]. He wrote to Szreter and, thanks to him, was invited to the 150th anniversary of the General Register Office organized in 1987 in London [START_REF] Szreter | Introduction: The GRO and the Historians[END_REF]. There he met Margo Anderson (then Conk), a specialist in census taking in the United States [START_REF] Anderson | The American Census: A Social History[END_REF]. This conjunction of research endeavours, which Bielefeld had facilitated, acted as a catalyst for Alain Desrosières' hopes for federation.

A few months after meeting Lorraine Daston, he attended a conference organized at the Ecole normale supérieure (ENS) by the Institut d'histoire moderne et contemporaine, where he delivered a paper summarising his thinking and highlighting his background [START_REF] Desrosières | Comment faire des choses qui tiennent : histoire sociale et statistique[END_REF]. He outlined his vision of a sociology of the genesis of statistical codes as being linked to Boltanski's investigation (in his book Les cadres) into "things that hold" and that of Thévenot into "investments of form" (Idem, p. 225). However, in the catalogue of work produced from this perspective, Alain Desrosières accorded a new place to the history of the calculation of probabilities. He argued that coding required thinking in terms of equivalence or resemblance between objects of the same category and posited that historians of probabilities facilitate progress on modes of comparison. He cited Coumet, Hacking and Daston (idem,p. 227). However, this intuition had yet to be developed. Alain Desrosières then soughtas the topic of his paper suggestsholding together things that did not yet hold together! Invited shortly afterwards to an international conference on the history of the social sciences, he delivered this paper translated into English. This was the first time that Alain Desrosières had published in English. This paper introduced his work to a broader audience and made his name more widely known. The fact that the conference was held in Berlin on 8 to 10 November 1989, right at the time of the fall of the Wall, certainly played its part in making the interaction there unforgettable for the participants. Anthony Giddens alludes to this in his preface to the proceedings, published as a book [START_REF] Wagner | Discourses on Society[END_REF]). The participation of Giddens, who was already widely renowned at the time, reflects above all the significant editorial work carried out by the conference organiser, Peter Wagner, to whom Alain Desrosières had been introduced two years earlier by Michael Pollack.

This was the first article by Alain Desrosières cited by Theodore Porteralthough Porter was already familiar with the French-language literaturein an article based on a paper delivered at Courmet's seminar that he published in La Revue de synthèse [START_REF] Porter | Statistics and the politics of objectivity[END_REF]. Theodore Porter now also associates his meeting with his French colleague with the title of that paper in English: "How to make things which hold together?" At the time, he saw the similarities between this article and the approach Desrosières was adopting in his work with Laurent Thévenot and Luc Boltanski (idem,. From this point of view he was supplementing the comments that Lorraine Daston had made a few months earlier on Alain Desrosières' undertaking (in an article in which Theodore Porter was thanked for reading the text), citing the work with Thévenot on socio-occupational classifications that had been published when he attended Courmet's seminar [START_REF] Daston | Objectivity and the Escape from Perspective[END_REF].

It was also in relation to this first text in English by Alain Desrosières that his research was cited for the first time, in 1993, in Accounting, Organizations and Society (AOS), which was becoming the reference journal of the sociology of accountingthe other main form of quantification, along with statistics. This citation was by two American public policy analysts who, at the time, were studying the development of statistics in audits [START_REF] Carpenter | Sampling and the abstraction of knowledge in the auditing profession: An extended institutional theory perspective[END_REF]). Carpenter and Dirsmith followed the initiative of their colleague in London, Michael Power who, with his colleague Peter Miller, had had the idea a few years earlier of inviting Theodore Porter to the LSE (where the main players in AOS worked). Their idea was to analyse possible links between the sociology of accounting and the sociology of statistics, which had resulted, in particular, in an article in AOS [START_REF] Power | From common sense to expertise: Reflections on the prehistory of audit sampling[END_REF].

It was this same paper by Alain Desrosières that appeared in Wendy Espeland's programmatic reflection several years later [START_REF] Espeland | Commensuration as a social process[END_REF]. Espeland had been working for a long time on the sociology of quantification, in fact from the time of her PhD, the subtitle of which highlights the notion of "commensuration" [START_REF] Espeland | Contested rationalities. Commensuration and the representation of value in public choice[END_REF]). However, she had also examined the evolution of accounting practices in research, which had led to a publication in AOS co-authored with a colleague at North Western University, where she had taken up a position [START_REF] Espeland | Ownership Changes, Accounting Practice and the Redefinition of the Corporation[END_REF]. From this perspective, she studied the work of Theodore Porter following his visit to the LSE [START_REF] Espeland | Legally Mediated Identities: The National Environmental Policy Act and the Bureaucratic Construction of Interests[END_REF], in particular his most recent book, which she reviewed [START_REF] Espeland | Authority By-The-Numbers: Quantification, Discretion, and the Legitimation of Expertise[END_REF]. Theodore Porter included a significant bibliography of Alain Desrosières' research. However, only one reference was in English: the same article in which Desrosières incorporated the history of the probabilistic revolution into his analysis.

Apart from the Berlin episode, Alain Desrosières also incorporated the dynamic triggered by Bielefeld into the heart of his thinking, as the introduction to the pioneering book he was writing at the time attests [START_REF] Desrosières | La politique des grands nombres[END_REF]. In his daily interaction with his colleagues he put even more emphasis, perhaps, on the seminal dimension of the dynamic that had been set off there. He engaged in research on the genesis of sampling surveys, and was joined by several colleagues: Emmanuel Didier, Einar Lie and Martine Mespoulet [START_REF] Desrosières | Three Studies on the History of Sampling Surveys: Norway, Russia-USSR, United States[END_REF]. More broadly speaking, he constantly initiated new research projects that regularly intersected with the probabilistic revolution. Personally, I owe to him my work on controversies around the introduction of survey techniques in censuses [START_REF] Bardet | Du recensement au sondage de la population. L'exception démocratique française[END_REF], on the revival of experimentation techniques in public policy [START_REF] Bardet | Les essais randomisés contrôlés, révolution des politiques de développement ? Une évaluation par la Banque mondiale de l'empowerment au Bangladesh[END_REF][START_REF] Bardet | Introduction[END_REF]) and, even more recently, on the invasion of accounting figures in organizations and policies (cf. infra).

The most significant outcome of Alain Desrosières interest in the dynamic of the probabilistic revolution was probably the fact that he was adopted by the leading members of the Bielefeld group. Apart from his above-mentioned relations with Lorraine Daston and Theodore Porter, which he nurtured, Desrosières maintained a privileged relationship with Ian Hacking. His preface in the French translation of Hacking's famous book The Emergence of Probabilities, published in English over twenty-five years earlier (Hacking, 2002), bears witness to this. On the occasion of a one-day conference organized for the launch of this French edition at the ENS on 6 February 2002, Hacking, who presented his "historical meta-epistemology" in that book, paid homage to "Alain's" brilliant reading of his work (idem, p. 14).

Considering contemporary quantifications

Even though the probabilistic revolution afforded Alain Desrosières an opportunity to return to his original sociological perspective, which was historical, he never abandoned his interest in contemporary situations and controversies. It was probably to that interest that I owe my first meeting with him, in 1994. I had been appointed a year earlier to the position of engineer at the Department for Planning and Infrastructurenow Ecology and Sustainable Developmentand had just completed my master's in political science, which had led me to his most recent article [START_REF] Desrosières | La statistique publique : analyse des besoins ou analyse des usages ? In: R. L'information Économique Et Sociale Aujourd'hui. Besoins, Usages[END_REF]. This text, the work of a group within the GSPM, part of which had been published in the Revue française des affaires sociales [START_REF] Corcuff | Entre le local et le national : des cas d'innovation dans les services publics[END_REF], focused on the implications of the career on which I was then embarking: the links between scientific expertise (here, statistics) and the governing of territories. It was therefore from the army barracks at Metz, where I was doing my military service that I sent him my thesis, asking for his comments. Very shortly afterwards I received a long reply, accompanied by an invitation to continue the discussion when I could get a pass [START_REF] Bardet | La statistique au miroir de la région. Eléments pour une sociologie historique des institutions régionales du chiffre en France depuis[END_REF]. From our first meeting, in his Rue Daguerre neighbourhood in Paris, he suggested the subject of my PhD, namely the history of the links between statistics and the French regions [START_REF] Bardet | La statistique au miroir de la région. Eléments pour une sociologie historique des institutions régionales du chiffre en France depuis[END_REF].

During our conversations, which rapidly became regular events, he showed an interest in the workings of my ministry: first, in the urban policy sector, in particular, with regard to which he put me in touch with a brilliant colleague whose work had not yet been published [START_REF] Tissot | L'État et les quartiers[END_REF]; second, in the social housing sector, on which he recommended reading the work of a colleague in Lyon with whom I had lost touch (Stavo-Debauge 2003); and finally the transport policy sector, which he encouraged me to look into [START_REF] Bardet | La statistique à la rescousse des acteurs locaux du transport. L'observatoire régional des transports Rhône-Alpes[END_REF]. He also constantly urged me to study the statistics of other sectors of the state, such as health [START_REF] Berlivet | Controverses en épidémiologie. Production et circulation de statistiques médicales[END_REF], and of other countries, such as Germany [START_REF] Labbé | Race' et 'Nationalité' dans les recensements du Troisième Reich. De l'autodéclaration au diagnostic racial[END_REF] or Russia (Mespoulet 2001), as well as other controversies in the field of statistical expertise, in which the INSEE unions were key players [START_REF] Desrosières | La statistique publique : analyse des besoins ou analyse des usages ? In: R. L'information Économique Et Sociale Aujourd'hui. Besoins, Usages[END_REF]. It was during one of them that I met his lifelong friend, Elisabeth Zucker, whose fighting spirit, in sociology and everything else [START_REF] Lucionero | Statistique et révolution en Russie. Un compromis impossible[END_REF], brought me even closer to the man who probably, at the time, became my mentor.

Apart from statistics, Alain Desrosières developed his sociological interest in scientific or rationalizing activities. He was very close to the Alexandre Koyré Centre for the Sociology of Science, and to its leading figures at the time, Amy Dahan and Dominique Pestre (Dahan Dalmedico et al. 1995). Among the rationalizing enterprises he investigated, the one devoted to the hope of quantification naturally took most of his attention, in addition to statistics per se. His enthusiasm for my master's thesis on the development of observatories in local communities [START_REF] Bardet | Observatoires et nouvelles pratiques de gouvernement[END_REF], operated aside from academia and the official state statistics dominated in France by INSEE [START_REF] Rouchet | Les observatoires économiques et sociaux[END_REF], had been the initial clue for me. He also very quickly became keenly interested in the genesis of policy evaluation in France, led by Vincent Spenlehauer who at the time was working in my research centre at the ENTPE [START_REF] Spenlehauer | L'évaluation des politiques publiques, avatar de la planification[END_REF].

From this pluralist perspective, Desrosières steered me towards Theodore Porter's work. With the publication of Porter's new book that proposed comparison of the quantification work of various professions, in various countries and at different times [START_REF] Porter | Trust in Numbers. The Pursuit of Objectivity in Science and Public Life[END_REF], he encouraged me to submit a review to the journal Genèses, of which he was an active member of the editorial committee [START_REF] Bardet | Revue : Trust in numbers. The pursuit of objectivity in science and public life, de Theodore Porter[END_REF]. In my review I presented the main hypothesis of the book, i.e. that quantification was usually the outcomecounter-intuitivelyof the initiatives of professional groups with questionable legitimacy. However, with hindsight it appears that what Theodore Porter offers throughout this book is a real epistemological feat, in which he conceptualises various forms of quantification, especially statistical and accounting quantification, within a common framework.

According to Theodore Porter himself, the core of the argument developed in Trust Numbers was already present in an article that he had published three years earlier (Porter 1992), following a talk he gave at UCLA a year before being joining that university2 . Thus this was a thesis he developed in the months following the paper which he delivered in 1990 at the LSE (Porter 1992). There is no point in seeking to pinpoint the specific role of this meeting between sociologists of accounting at LSE in the dynamic of the Porter's career as a sociologist of statistics. However, it is certain that this role was decisive, especially since one of the members of the LSE team, Michael Power, embarked on publication of the ideas generated by this meeting, in which the work of Theodore Porter featured prominently (Power 1996[START_REF] Power | From the Science of Accounts to the Financial Accountability of Science[END_REF]

Michael Power did not extend the common framework applied to the various sociologies of quantification4 . Theodore Porter did, however, especially in the course of a new collaboration with Alain Desrosières, who had been enthused by the perspective opened by Trust in numbers. When the new edition of La politique des grands nombres was published in 2000, he added a postscript in which he mentioned the sociology of accounting research stream that had developed around AOS and the team at LSE (p. 438). He also wrote numerous papers (published several years later) in which he sought the means to bring together the sociologies of statistics and of accounting, based on the work of Theodore Porter and Michael Power (Desrosières 2003[START_REF] Desrosières | How Real are Statistics? Four Possible[END_REF]. To this end he worked with Michel Armatte on the historical junction between (probabilistic) econometrics and national accounting [START_REF] Armatte | Méthodes mathématiques et statistiques en économie : nouvelles questions sur d'anciennes querelles[END_REF].

However, it was with Eve Chiapello, with whom he was collaborating at the time, that he had the idea of the Premières journées de sociologie de la quantification held in Paris on 23 and 24 May 2002. This gathering afforded an opportunity to prolong discussions with Theodore Porter, who was the guest of honour. He opened the first day of the conference, devoted to the sociology of statistics, whose organization Desrosières had entrusted to me. Also highly symbolically, Peter Miller opened the second day, devoted to the sociology of accounting, which Eve Chiapello had organized with her young colleague Carlos Ramirez. The proceedings of these two days were not published in a single opusto my great regret -but Alain Desrosières continued his collaboration with Eve Chiapello [START_REF] Chiapello | La quantification de l'économie et la recherche en sciences sociales : paradoxes, contradictions et omissions. Le cas exemplaire de la positive accounting theory[END_REF]).

In the footsteps of Alain Desrosières, who sought to rally the accounting side from the statistical side, Béatrice Touchelay was probably the first to have accomplished the entire crossing. Béatrice Touchelay was the author of an encyclopaedic thesis on the history of the INSEE from its origins up to the 1960s [START_REF] Touchelay | L'INSEE des origines à 1961 : évolution et relation avec la réalité économique, politique et sociale[END_REF]) and which, thanks to Desrosières, provided crucial material for my own PhD. At the time, she opened up a new research front in the history of accounting quantification (Touchelay 2005, Touchelay 2005), which led to her habilitation à diriger des recherches [START_REF] Touchelay | L'État et l'entreprise[END_REF].

More or less at the same time, I organized an international seminar in October 2007 at ENTPE in Lyon on "Globalization of quantitative tools of government", to which we invited Margo Anderson, Wendy Espeland and Julia Mensink (a PhD student of Mary Morgan), as well as researchers in France, including Eve Chiapello, Roser Cussó, Florence Jany-Catrice and Béatrice Touchelay5 . This seminar produced a number of publications. The first was an article by Wendy Espeland published several months later with Michael Stevens [START_REF] Espeland | A Sociology of Quantification[END_REF]. It was entitled "A Sociology of Quantification" and was enriched with references to work presented at the seminar, notably research in France [START_REF] Bruno | Europeanization through its Instrumentation: Benchmarking, Mainstreaming and the Open Method of Coordination... Toolbox or Pandora's Box?[END_REF][START_REF] Cussó | From development comparatism to globalization comparativism: towards more normative international education statistics[END_REF], but also in the US [START_REF] Anderson | Who Counts? The Politics of Census-Taking in Contemporary America[END_REF], as Wendy Espeland herself points out with amusement. A few months later, Desrosières published a collection of articles under the title : Pour une sociologie historique de la quantification [START_REF] Desrosières | Pour une sociologie historique de la quantification[END_REF]. However, the introduction to this volume focused mainly on statisticsreflected in the titleand did not resume the line of enquiry initiated during the late nineties, in relation to the work of Porter and Power, which comprised Chapter 12. The most explicit outcome of this seminar, however, was the publication of some of the original papers written for the event in an issue of the Revue française de socio-économie [START_REF] Bardet | Les politiques de la quantification[END_REF].

The improbable conjunction of the sociologies of quantification

Over twenty years have passed since the idea of a sociology of quantification was put forward, in which the two main forms that had existed historically, namely accounting and statistics, would be combined. Even though the main founders of this project have enjoyed international academic recognition, their work has not yet resulted in the institutionalization of a discipline, or even of an autonomous field of enquiry. Several explanations can be found for this incompleteness. The most apparent seem to be structural, related to the academic trajectories of the various promoters. However, a return to the genesis of this project has also revealed a historical cause, the nature of which could naturally turn out to be more conjunctural, thus reviving the founding hopes.

We do of course first need to consider the difficulty of conceptualizing statistical and accounting quantifications together, as they have old and disjointed histories and academies. These two professional worlds communicate little, if at all. As a result, sociologists specialized in one can hardly be specialized in the other. Alain Desrosières was first trained in statistics for the French statistics administration, and his interest in the probabilistic revolution project was obviously related to that history, which was also his own. It was only much later that he opened up multiple research fronts, which steered him away from statistics. He reacted very quickly to Isabelle Bruno's research on benchmarking [START_REF] Bruno | À vos marques®, prêts… cherchez ! La stratégie européenne de Lisbonne, vers un marché de la recherche[END_REF]) and placed much hope in the research programme she Emmanuel Didier launched soon afterwards [START_REF] Bruno | Benchmarking : l'Etat sous pression statistique[END_REF]. In recent years he also focused on budgetary policy [START_REF] Lemoine | Les valeurs de la dette. L'État à l'épreuve de la dette publique[END_REF]) and accounting policy [START_REF] Eyraud | Une comptabilité d'entreprise pour l'État. Sociologie d'un dispositif de quantification économique[END_REF], constantly fascinated by new encounters that changed his horizon. Fundamentally, however, statistics remained the core of his framework of analysis, as attested by the last paper that he wrote, for a conference in Rome that he was too weak to attend [START_REF] Desrosières | Quantifier les sciences sociales : une perspective historique et comparative[END_REF].

When I started writing the thesis for my habilitation a few months earlier, I imagined myself presenting the family of the sociology of quantification, naturally starting with the three pioneers: Porter, Desrosières and Espeland. First with Wendy Espeland, who honoured me by including me in her 2008 panorama (cf. supra), I sought to resituate her first article published in AOS within her research dynamic. Finding other AOS articles, I remembered Desrosières' suggestion that the history of this journal should be studied. So I pulled the AOS thread, that of its founder, Anthony Hopwood, of his American history, of his encounter with public policy analysis, of his return to the UK, of the establishment of his journal, of his sense of academic enterprise, and of his great curiosity [START_REF] Bardet | La contre-révolution comptable. Ces chiffres qui (nous) gouvernent[END_REF].

Alain Desrosières, enthusiastic about the idea of this history, asked about its progress every week. In the autumn, when he was bed-ridden, he questioned me a last time, asking me to find "the reason" for this history, its title. The hypothesis of an accounting counterrevolution then occurred to me, probably linked to the conjunction of three dynamics that the history of AOS enabled me to envisage. The first was this hypothesis, which was based on my scrutiny of twenty years of issues of AOS (1976AOS ( -1995) ) and accounting's gradual encroachment into organizations and public policy, which gathered momentum from the early 1970s in the USA. To that was added my discovery of accounting's resistance to the probabilistic revolution, which was inspired by Michael Power's early work published in AOS (cf. supra). Finally, going through AOS also enabled me to identify an episode in which, in the early 1990s, the editors of AOS for a while considered bringing together their sociology of accounting project with others in the sociology of statistics, notably that of Theodore Porter. Thus what emerged from my reading of AOS was paradoxical: accounting had conquered the world but at the same time had been antagonistic towards probabilistic measures. This in turn suggested the hypothesis of an accounting counter-revolution.

This hypothesis proposes that we conceptualise statistical and accounting quantifications not only in conjunction with each other but also dialectically. This would mean separating forms of quantification that are the result of simple counting from those that stem from counting but are then provided with the tools of statistical science, in other words, probabilistic measurements. A distinction such as this may enable progress to be made in the characterization of contemporary quantificationsperhaps those of neo-liberal governments. The hypothesis would need to be tested, and challenged. I would like to think that Alain Desrosières would have been very happy to participate in this endeavour which, for me, is in a way his own.

Fabrice

  Bardet, "Learning from the history of the probabilistic revolution: the French school of Alain Desrosières" in I. Bruno, F. Jany-Catrice, B. Touchelay (eds) The Social Sciences of Quantification. From Politics of Large Numbers to Target-Driven Policies, Springer, 2016.

I would like to thank Roser Cussó, Elisabeth Zucker, Morgane Labbé and Philippe Corcuff for their suggestions and comments.

Email to the author, on 22 July 2013.

The first publication was a special issue of the journal Science in Context, after which a book was published by Cambridge University Press, with identical content except for the preface by Bruno Latour.

Interview with the author, July 2013.

http://erstu.ens-lyon.fr/spip.php?rubrique79