Yoann Hériveaux

Vu-Hieu Nguyen

Christine Biateau

Bertrand Audoin

Guillaume Haïat
email: guillaume.haiat@cnrs.fr

MEASUREMENT OF THE PROPAGATION OF A GUIDED WAVE IN A DENTAL IMPLANT

Ultrasound techniques can be used to characterize and stimulate dental implant osseointegration. The acoustical energy transmitted to the bone-implant interface is an important parameter for both applications since it should be sufficiently low to avoid damaging the surrounding tissues, but sufficiently high for stimulation purposes to enhance bone growth. However, the interaction between an ultrasonic wave and a dental implant remains unclear. The objective of this study combining experimental, analytical and numerical approaches is to investigate the propagation of an ultrasonic wave in a dental implant by assessing the amplitude of the displacements along the implant axis.

An ultrasonic transducer was excited in transient regime at 10MHz. Laser interferometric techniques were employed to measure the amplitude of the displacements, which varied between 3.2 to 8.9 nm according to the position. The results show the propagation of a guided wave mode along the implant axis with a first arriving signal velocity equal to 2110 m.s-1 and frequency components lower than 1 MHz, which was confirmed by the analytical and numerical results. This work paves the way to improve techniques for the characterization and stimulation of the bone-implant interface.

INTRODUCTION

Dental implants are routinely used in the clinic and have allowed substantial progresses in oral and maxillofacial surgeries [START_REF] Albrektsson | Osseointegrated oral implants. A Swedish multicenter study of 8139 consecutively inserted Nobelpharma implants[END_REF]. However, a lack of implant osseointegration may lead to aseptic loosening and to surgical failures, which are difficult to anticipate [START_REF] Pilliar | Observations on the effect of movement on bone ingrowth into porous-surfaced implants[END_REF]. The evolution of the implant biomechanical stability is a strong determinant of the surgical success [START_REF] Haïat | Effects of Biomechanical Properties of the Bone-Implant Interface on Dental Implant Stability: From In Silico Approaches to the Patient's Mouth[END_REF] and may be assessed by measuring the biomechanical properties of the implant-bone interface (IBI) [START_REF] Mathieu | Biomechanical determinants of the stability of dental implants: influence of the bone-implant interface properties[END_REF].

Biomechanical techniques such as impact methods [START_REF] Schulte | Periotest--a new measurement process for periodontal function[END_REF][START_REF] Michel | Assessing the Acetabular Cup Implant Primary Stability by Impact Analyses: A Cadaveric Study[END_REF] or resonance frequency analysis [START_REF] Meredith | Quantitative determination of the stability of the implant-tissue interface using resonance frequency analysis[END_REF] have been applied ex vivo and in vivo to investigate the BII properties. In an ex vivo study using a coin-shaped implant model [START_REF] Mathieu | Influence of healing time on the ultrasonic response of the bone-implant interface[END_REF], the reflection coefficient of a 15 MHz ultrasonic wave interacting with the IBI significantly decreases as a function of healing time, which may be explained by a decrease of the gap of acoustical properties at the IBI. More recently, a 10 MHz QUS device was validated first ex vivo using cylindrical implants [START_REF] Mathieu | Ultrasonic Evaluation of Dental Implant Biomechanical Stability: An In Vitro Study[END_REF], then in vitro using dental implant inserted in bone tissue [START_REF] Vayron | Assessment of In Vitro Dental Implant Primary Stability Using an Ultrasonic Method[END_REF] and, eventually, in vivo [START_REF] Vayron | Ultrasonic evaluation of dental implant osseointegration[END_REF]. The sensitivity of this QUS device on changes of the periprosthetic bone tissue was shown to be significantly higher compared to the resonance frequency analysis in vitro [START_REF] Vayron | Evaluation of dental implant stability in bone phantoms: Comparison between a quantitative ultrasound technique and resonance frequency analysis[END_REF] and in vivo [START_REF] Vayron | Comparison of Resonance Frequency Analysis and of Quantitative Ultrasound to Assess Dental Implant Osseointegration[END_REF].

Ultrasound and more specifically low intensity pulsed ultrasound (LIPUS) may also be employed to stimulate bone remodeling [START_REF] Duarte | The stimulation of bone growth by ultrasound[END_REF]. Different studies have shown the potential of ultrasound to stimulate osseointegration using animal models with dental implants [START_REF] Hsu | Effects of near-field ultrasound stimulation on new bone formation and osseointegration of dental titanium implants in vitro and in vivo[END_REF][START_REF] Liu | The effect of low-intensity pulsed ultrasound on the osseointegration of titanium dental implants[END_REF][START_REF] Nakanishi | Low-intensity Pulsed Ultrasound Stimulation Significantly Enhances the Promotion of Bone Formation Around Dental Implants[END_REF]. More recently, an ultrasonic therapy was assessed clinically and confirmed that LIPUS can be used to promote dental implants osseointegration [START_REF] Akram Abdulhameed | The Effect of Low Intensity Pulsed Ultrasound Therapy on Osseointegration and Marginal Bone Loss Around Dental Implants[END_REF]. However, the precise mechanism of action of LIPUS remains poorly understood [START_REF] Claes | The enhancement of bone regeneration by ultrasound[END_REF][START_REF] Padilla | Stimulation of bone repair with ultrasound: A review of the possible mechanic effects[END_REF] and strongly depends on the nature of the signal corresponding to the stimulation.

The amount of energy transmitted to the IBI is an important parameter for applications corresponding to the ultrasonic characterization and stimulation of the IBI. Concerning the characterization, the acoustical energy should be sufficiently low so that the tissues around the implant would not be damaged due to excessive micromotion which could be detrimental to osseointegration [START_REF] Szmukler-Moncler | Timing of loading and effect of micromotion on bone-dental implant interface: review of experimental literature[END_REF]. Concerning the stimulation, the acoustical energy must be sufficiently high to obtain a significant impact on the implant osseointegration.

However, the interaction between an ultrasonic wave and a dental implant still remains unclear due to the complex geometrical configuration. Numerical simulation of wave propagation in a dental implant [START_REF] Vayron | Assessment of the biomechanical stability of a dental implant with quantitative ultrasound: A three-dimensional finite element study[END_REF] has already been carried out using finite element modeling, and the guided nature of the ultrasonic wave propagating in cylindrical implants has been evidenced [START_REF] Vayron | Finite element simulation of ultrasonic wave propagation in a dental implant for biomechanical stability assessment[END_REF]. However, no previous study was able to show whether guided waves could propagate in dental implants.

The aim of the present study is to investigate the interaction between an ultrasonic wave and a dental implant using experimental and numerical approaches.

MATERIAL AND METHODS

Dental implant

A 10 mm long and 4.1 mm diameter conical dental implant made of grade 5, Ti-Al6-V4 titanium alloy, was used in the present study. The implant was manufactured by Zimmer Biomet under the reference TSVT4B10. The geometrical configuration of the measurements is shown in Fig. 1. The implant was slightly polished locally on its extremity and laterally in regions of interest where laser ultrasonic measurements were carried out. Polishing was necessary to obtain a planar surface and therefore maximize specular reflection of the laser interferometer at the implant surface.

Ultrasonic device

The ultrasonic device composed of a 5 mm diameter planar ultrasonic monoelement contact transducer was manufactured by Imasonic. It generates a broadband ultrasonic pulse propagating perpendicularly to its active surface. The probe was used in echographic mode. Its center frequency was equal to 10 MHz, with a frequency bandwidth approximately equal to 6-14 MHz. The probe was rigidly attached to a titanium alloy dental healing abutment with a 5 mm long threaded part, which can be screwed into the implant. The ultrasonic probe was connected to a pulse generator (Sofranel, model 5052PR) via a standard coaxial cable. The pulse excitation had an amplitude of 100V and a duration of 200 ns.

Laser-ultrasonic measurements

A laser interferometer (BMI SH 140), suited for the detection of ultrasound at the surface of cylinders with millimeter diameter [START_REF] Clorennec | Investigation of surface acoustic wave propagation on a sphere using laser ultrasonics[END_REF][START_REF] Pan | Acoustic waves generated by a laser line pulse in a hollow cylinder[END_REF], was used in order to evaluate the amplitude of the displacements occurring at the implant surface. The displacements were measured at the extremity of the implant and at different positions along the implant axis. Only one channel was used for each measurement, which were made successively at each position. The surface of the implant where the displacements were measured was set perpendicularly to the axis of the beam of the laser interferometer so that the laser signal reflected by the implant could be correctly received by the laser interferometer. The size of the laser beam at the implant surface was about 100 μm. An oscilloscope was used to capture the signal given by the interferometer. Signals were averaged 500 times for each measurement. A calibration procedure allowed to derive the amplitude of the displacements at the surface of the implant and the frequency of the displacements was estimated from these signals.

Similarly as in [START_REF] Bossy | Effect of bone cortical thickness on velocity measurements using ultrasonic axial transmission: A 2D simulation study[END_REF], for all measured signals, the time of flight of the first arriving signal (FAS) was defined as the time for which signals first had an amplitude superior to a threshold equal to 0.5 nm, which is around 2.5 times higher to the magnitude of the noise.

Numerical simulation

The experimental configuration was reproduced numerically using a 2D axisymmetric model, corresponding to half of the schematic representation shown in Fig. 1a. The approach was detailed in [START_REF] Vayron | Assessment of the biomechanical stability of a dental implant with quantitative ultrasound: A three-dimensional finite element study[END_REF] and is briefly reminded in what follows. All the boundaries of the implant and of the ultrasonic transducer were considered as free. All parts considered in this model were assumed to have homogeneous isotropic mechanical properties and to be composed of Ti-Al6-V4.

The acoustical source is modeled by a broadband ultrasonic pulse with a normal stress σ11 (t) applied at the top surface of the transducer defined by:

c c ( 1
)
where A is an arbitrary constant representing the signal amplitude and fc is its central frequency.

All simulations were performed in the time domain using a finite element software (COMSOL Multiphysics). Once the solution was obtained, the displacements were determined on the extremity of the implant.

RESULTS

Experimental measurements of displacements along the implant threading

Figure 2 shows the variation of the measured displacement as a function of time at three different locations along the implant threading. The peak-to-peak amplitude of the displacement as a function of time along the implant axis was comprised between 3.2 nm and 8.9 nm. Figure 2 shows that for each position, and especially towards the end of the threading (Fig. 2c), the most energetic contribution is of relatively low frequency and arrives at a relatively short time. This low frequency contribution corresponds to the main component of the ultrasonic wave, whereas the contributions issued from multiple reflections of the ultrasonic wave on the implant boundaries are less energetic and arrive later. Moreover, a wave propagation velocity of around 2110 m.s-1 was estimated by considering the evolution of the time of flight of the FAS as a function of the position of the measurement along the x-axis.

Figure 3 represents the frequency spectra associated to the three signals shown in Fig. 2. Most components of the spectra are comprised between 0 and 1.5 MHz. For each spectrum, energetic contributions are present around 300 kHz and 900 kHz. For relatively low values of x (Fig. 3a and3b), an important number of contributions may be distinguished around 300 kHz and 900 kHz, while for higher values of x (Fig. 3c), the signal has fewer frequency components.

Numerical validation

The numerical validation of experimental results was performed through the comparison of displacements obtained at the extremity of the implant. Similarly as for experimental results, the frequency components of numerical data are lower than the central frequency of the excitation signal (fc = 10 MHz). However, frequency components obtained numerically are higher than for experimental data, and are mostly comprised between 0 and 4 MHz.

DISCUSSION

Propagation of a guided wave in the implant

Figure 3 shows that the frequency spectra corresponding to the displacement measured experimentally are mainly composed of low frequencies (mostly between 300 kHz and 2 MHz) compared to the excitation central frequency (10 MHz). Figure 3 also shows that the amplitude of high frequency components tends to decrease along the implant axis. The observation of low-frequency components may result from the attenuation of the ultrasonic wave while propagating along the 1 cm long titanium implant. Although the frequency range obtained numerically is slightly higher than that obtained experimentally, the numerical results confirm that only low frequencies (mostly between 1 and 3 MHz) are obtained in the implant.

Moreover, the wave velocity of the FAS was experimentally assessed around 2110 m.s -1 , which is significantly lower than the bulk longitudinal velocity (Cp = 5810 m.s -1 in titanium alloys). These two results (slow and low frequency wave propagation) indicate the presence of a dispersive ultrasound wave guided by the implant structure.

Amplitude of displacements and transmitted energy

The experimental results show that the amplitude of the displacement always remains inferior to 10 nm, which is far from the critical level of micromotion (around 50 μm to 150 μm) that may prevent osseointegration [START_REF] Szmukler-Moncler | Timing of loading and effect of micromotion on bone-dental implant interface: review of experimental literature[END_REF].

Regulations from the US Food and Drug Administration (FDA) indicate an exposure limit of 720 mW/cm² for diagnostic ultrasound equipment [START_REF]Marketing Clearance of Diagnostic Ultrasound Systems and Transducers[END_REF]. In our case, the average intensity transmitted by the ultrasonic wave to the implant may be derived from [START_REF] Norton | Fundamentals of Noise and Vibration Analysis for Engineers[END_REF]: [START_REF] Pilliar | Observations on the effect of movement on bone ingrowth into porous-surfaced implants[END_REF] where ZTi is the acoustical impedance of the titanium alloy and vm is the particle velocity. Considering the particle velocity measured at the extremity of the implant (around 18 mm.s-1), the average intensity sent by the ultrasonic transducer is around 460 mW/cm², which therefore respects FDA requirements.

The excitation signal sent to the transducer is similar to the one used in previous studies by our group on the QUS device aiming at assessing implant stability [START_REF] Vayron | Ultrasonic evaluation of dental implant osseointegration[END_REF][START_REF] Vayron | Evaluation of dental implant stability in bone phantoms: Comparison between a quantitative ultrasound technique and resonance frequency analysis[END_REF]. Most studies on LIPUS stimulation of implant osseointegration focused on lower intensities, around 30 or 40 mW/cm² [START_REF] Hsu | Effects of near-field ultrasound stimulation on new bone formation and osseointegration of dental titanium implants in vitro and in vivo[END_REF][START_REF] Liu | The effect of low-intensity pulsed ultrasound on the osseointegration of titanium dental implants[END_REF][START_REF] Akram Abdulhameed | The Effect of Low Intensity Pulsed Ultrasound Therapy on Osseointegration and Marginal Bone Loss Around Dental Implants[END_REF], but applied during longer duration in the harmonic regime, while we worked in transient mode. Therefore, the amplitude of the displacement measured herein are not representative of displacements generated by LIPUS stimulation. However, the present study emphasizes that mechanical stimulation induced by ultrasound is highly sensitive to the geometrical configuration and provides an estimation of the energy sent by an ultrasonic wave to the IBI.

Limitations

This study has several limitations. First, the implant measured experimentally had been partially polished on one side, which removed a small part of its threading and may have influenced the results.

Second, the present study only considered the situation where the implant was surrounded by air. The values of displacement of the implant are likely to be lower when considering an implant surrounded by bone or by soft tissues, and the energy transmitted to these media would therefore be lower.

Third, several approximations have been made in the numerical model. In particular, the acoustical source was considered to have a uniform pressure. The geometry of the implant was also approximated, since real threading cannot be thoroughly axisymmetric. A 3D model would therefore depict more precisely the real configuration.

CONCLUSION

This study emphasizes that the propagation of an ultrasonic wave in a titanium dental implant is guided by the implant structure. For characterization purposes, the results indicate that it is not necessary to consider high frequency transducers since ultrasound propagate at frequencies comprised between 300 kHz and 2 MHz in the implant. For stimulation purposes, the results indicate that the intensity transmitted to the IBI is highly sensitive to the considered structure. The reader is referred to [START_REF] Hériveaux | Ultrasonic Propagation in a Dental Implant[END_REF] for further details on the present study.

Figure 1 :

 1 Figure 1: (a) Schematic representation of the experimental setup with an ultrasonic transducer screwed into a dental implant. The x-axis corresponds to the implant axis. Arrows represent the positions corresponding to the results shown in Fig. 2. (b) Ultrasonic probe and dental implant used experimentally.

Figure 2 :

 2 Figure 2: Variation of the displacement at the implant surface measured experimentally as a function of time (a) at the beginning of the threading (x = 1.5 mm), (b) at the middle of the threading (x = 4.35 mm), and (c) at the end of the threading (x = 8.3 mm).

Figure 3 :

 3 Figure 3: Frequency spectra corresponding to the modulus of the Fast Fourier Transform (FFT) of the signals measured experimentally (a) at the beginning of the threading (x = 1.5 mm), (b) at the middle of the threading (x = 4.35 mm) and (c) at the end of the threading (x = 8.3 mm).

10.48465/fa.2020.1128

e-Forum Acusticum, December 7-11, 2020


Mitsunori Mizumachi

Tsukasa Nakashima

Mitsuhiro Nakagawara

PERFORMANCE EVALUATION OF POWER-SAVING AUDIO REPRODUCTION

INTRODUCTION

Recent audio applications make more diverse on audio reproduction. The novel transduces in the high frequency domain reproduce high resolution audio sources. The use of multiple loudspeakers enables immersive audio reproduction. On the other hand, on-demand music streaming subscription services bring about a revolution in music listening style. A massive collection of music sources can be personally reproduced using smartphones and portable devices anytime and anywhere. In such cases, the listeners give priority to extending the battery life of the mobile devices rather than audio quality.

The authors have proposed a power-saving audio reproduction algorithm based on our static auditory characteristics [START_REF] Mizumachi | Power Saving Audio Playback Algorithm Based on Auditory Characteristics[END_REF] and the auditory masking [START_REF] Nakashima | Proposal of Power-Saving Audio Playback Algorithm Based on Auditory Masking[END_REF]. Those algorithms aim at decreasing the power consumption with less perceptual distortion while reproducing audio sources. The feasibility of the proposed method was confirmed for some music sources.

In this paper, the relationship between perceptual evaluation and power consumption is investigated for both music and speech signals. The perceptual degradation in some attributes used for audio quality assessment is measured for music signals by carrying out a listening test. The diagnostic rhyme test is carried out to characterize the speech distortion.

POWER-SAVING AUDIO REPRODUCTION ALGORITHM

The power-saving audio reproduction is achieved by controlling the sub-band power in the filterbank analysis. In this study, auditory-oriented filterbanks are introduced into sub-band signal processing. Three different filterbanks are considered such as the conventional octave filterbank, mel-frequency filterbanks with triangular windows, and the gammachirp filterbank, which is designed based on both physiological and psychophysical data [START_REF] Irino | A time-domain leveldependent auditory filter: the gamma-chirp[END_REF][START_REF] Irino | A compressive gammachirp auditory filter for both physiological and psychophysical data[END_REF]. The octave and mel-frequency filterbanks are not level-depend, but the gammachirp filter broadens its main-lobe for the input with high intensity.

The proposed algorithm attenuates the low-frequency components up to 120 Hz in 3 dB, assuming that the lower components are mostly masked by background noises because the casual listeners are supposed to listen to music via earphones and headphones under noisy environments. In addition, 3 dB boost is applied in the mid-frequency range from 3 kHz to 4 kHz, where the human ears are more sensitive.

The power-saving audio reproduction algorithm achieves the further reduction of power consumption based on the concept of auditory masking. The psychoacoustic masking model [START_REF] Shaughnessy | Speech communication: human and machine[END_REF] is implemented to calculate the masking threshold. The proposed method attenuates the sub-band components of which amplitude levels are below the masking threshold. Finally, both high-end and low-end frequency components are omitted because popular earphones and headphones cannot reproduce the components in high fidelity below 60 Hz and upper 15 kHz.

PERFORMANCE EVALUATION

The feasibility of the proposed method is subjectively confirmed both for music and speech signals.

Subjective evaluation of music signals

The performance of the proposed method was subjectively evaluated based on the degradation mean opinion scores (DMOSs) [START_REF]Methods for subjective determination of transmission quality[END_REF] with the five-grade scale. The attributes consist of the sense of sound pressure, 10.48465/fa.2020.0321 Table 1. DMOSs on sound quality evaluation for the proposed method with tree filterbanks and non-processed conditions. clarity, perceptual distortion, resonance, and comprehensive impression. The genre of the sound sources included pops, rock, and violin solo. 50 students (12 females and 38 males) participated in the listening test, where the parameters of the proposed method are set to achieve the power reduction rate of 30% approximately.

The experimental results are given in Table 1. The proposed method does not cause fatal perceptual problems, although there is a slight difference in DMOS among the types of filterbanks.

Subjective evaluation of speech signals

Subjective evaluation was done by the diagnostic rhyme test with the Japanese word pairs [START_REF] Fujimori | Octave filterbank Gammachirp filterbank Mel-frequency filterbank Non process[END_REF]. 24 students (6 females and 18 males) participated in the diagnostic rhyme test. The parameters of the proposed method were set to achieve the power reduction rates of 22.2%, 48.6%, and 73.2%, respectively. As a reference, non-processed original word pairs were also prepared for the test.

The results of the diagnostic rhyme test are summarized in Table 2 for each of the phonetic features: voicing, nasality, sustention, sibilation, graveness, and compactness. The intelligibility scores maintain more than 80% even in the case that the power reduction rate is 73.2%.

CONCLUSIONS

The previously proposed power-saving audio reproduction algorithm was subjectively evaluated for music and speech signals. In music appreciation, there is no significant perceptual degradation when the reduction rate of power consumption is set to 30%. Concerning the speech applications, the proposed method could reduce the power consumption up to 70% for practical use.

Table 2 .

 2 Future works include performance evaluation in practical applications under real environments. Results of Japanese diagnostic rhyme test.

			Power reduction rate
		73.2%	48.6%	22.2%	0%
	Voicing	82.5	98.3	95.0	100.0
	Nasality	92.9	97.1	97.5	97.5
	Sustention	94.6	98.3	99.6	99.6
	Sibilation	97.1	99.2	99.2	99.6
	Graveness	84.2	91.3	90.4	95.4
	Compactness	95.8	98.8	100.0	100.0

10.48465/fa.2020.0321

e-Forum Acusticum, December 7-11, 2020


Anne-Françoise Schmid

Jeremy R Smith

Luka Stojanovic

Is there a field for philosophy?

Introduction

The question of a field for philosophy seems almost obvious. Indeed, we know multiple fields, and in particular, the disciplines where philosophy is exercised could be its fields. But this is not what we seek to answer the question: is there a field for philosophy. What concerns us is the investigation of a field entirely exterior or foreign to philosophy, a field where it would have no authority, but where it nevertheless will be necessary for the development of new forms of invention, and a field that it would ignore under its classical and authoritarian forms.

This investigation is in fact very difficult, and, I will add, very risky. We will see that it unsettles philosophy both in its unity and its multiplicity. On the other hand, modeled after the work that I wrote with Muriel Mambrini-Doudet, Generic Epistemology: Manual for Future Sciences (Paris: Kimé, 2019), the investigation proposes a more collective and more interdisciplinary practice of philosophy. We will substitute the solitary philosopher with the ordinary philosopher, who follows the order between the real and philosophy and seeks out Anne-Françoise Schmid 2 the original content of their practice. The ordinary philosopher is not an individual as common sense perceives them but an extended and collective individual. In its sufficient autonomy, we will come to seek a field for philosophy which not only puts it in relation with other practices but brings it into contact with "the concrete" that resists the philosophizing appetite. The philosopher will take part in an experience which puts them in relation with philosophy and gives philosophy new liberties and styles of writing.

The first epigraph manifests a change in scale: the Universe within the World, and the invisibility of this change in scale. In the world of philosophy, can we open something that philosophy itself does not recognize? This epigraph will be a focal point at each step in the development of this investigation for a field for philosophy.

The second epigraph suggests an inversion between philosophy and what it occupies itself with, another focal point.

By combining both epigraphs, perhaps we can glimpse into another field. This is the business of experimentation.

The point is to implement an experimental apparatus proposed by the two epigraphs susceptible to create or conceive a look at philosophy which will allow new possibilities of invention and writing for it, not its fixation. What are the elements of this apparatus and how do we prepare them to make them perform together?

1) Preparing the experimentation

Several factors are required to prepare for our experimentation. They are as follows:

Anne-Françoise Schmid 3 -Philosophy as an object of experience: an integrative object where synthesis is no longer assured -The transformation of principles into hypotheses: to philosophize from hypotheses -The philosopher as the experimenter: experimenting on the limits of philosophy -A generic space for philosophies where their common = X can be introduced: this common =X can be new combinations -The World and the simulation of Worlds: philosophies inhabit the world all by simulating other worlds ("the world is not enough") Ultimately, a vertical dimension will allow us to presume a Universe whose world does not have the means to be perceived. This dimension has often taken the form of the linea serpentinata in the work of François Laruelle. This figure comes to us from Michelangelo and Ravaisson. One aspect of verticality that gathers the two epigraphs, the change of scale and inversion, is the following: there is an ethics for philosophy, and not a philosophy of ethics.

However, this Universe does not belong to only one philosopher. The philosopher knows how to construct worlds, but it is in this gesture that the philosopher touches upon something that they cannot see while remaining a philosopher. This is one of the hypotheses of non-philosophy: the philosopher must become human and recognize their humanity without qualities to be able to perceive their gesture and objectivate it. But to do this, the philosopher needs help from another discipline. The auto-modeling of philosophy fails here. There is no theory of philosophy without the help of another discipline and of another practice.

Our experimentation will engage as much the difference in scale as the inversion of the word "of" into an operator which contributes towards unbinding Anne-Françoise Schmid 4 the philosopher from philosophical authority and philosophical sufficiency.

Inverting "of" makes us see the philosopher's act.

There are two personages in this experimentation: philosophy and the philosopher are not alike. The "I" of the philosopher is introduced to the experience of contingency within the multiplicity of philosophies. This experience and experiment are fundamental for the investigation into a field independent of philosophy but where philosophy, now transformed and treated, can take its place.

What about the negation that intervenes in both epigraphs? Negation in nonphilosophy is to put at a distance, whereas negation in non-standard philosophy is an extension of the field. We can compare this use of negation with the notion of non-music. In music, negation adjoins its timbre and noise (cf. Brazilian composers included Jean-Pierre Caron who is inspired by Yacinto Scelsi).

Extension, as a non-classical negation, allows one to articulate logics that are often seen as contradictory, for example Russell's principle of external relations and the use of relations in Deleuze.

These epigraphs have the function to deprive philosophy of its sufficiency, to limit philosophy, but by leaving it with a greater freedom of invention, a greater freedom than what sufficiency constantly uses and abuses: critique. With the help of intermediary axioms, namely, the obscure cogito and the open secret, we will bind invention to the exercise of the de jure multiplicity of philosophies.

The Kampflatz and fields within philosophy that depend on it Philosophers have spoken of "matter" in philosophy, such as Husserl in his Logical Investigations. There, matter allows one to better distinguish the scope and the contents within complex intentional acts by making the part of what is lived intentional. Further, it allows one to distinguish the object of a description, which is what of this lived experience is expressed. However, this matter is within Anne-Françoise Schmid 5 philosophy, even if it is but one material condition of possibility. Philosophy requires a degree of matter, but philosophy does everything to ensure that it does not go beyond its sphere of influence.

The idea of a sphere for philosophy, distinct from the famous Kantian Kampflatz which would be a space proper to philosophy, has no special significance in the philosophical gesture. The field of philosophy is within philosophy itself. The field is held between two edges, two contraries, as is custom in philosophy: the a priori and the empirical. From the point of view of the a priori, the philosophers who see some other disciplines as their own field or those who, like Wittgenstein, think it would be nonsense to attribute a field to philosophy if it is not language. According to Wittgenstein, the Logos is but one outgrowth devoid of meaning. As for the empirical, determined by the a priori of philosophies, it is one sort of internal field whose limits are drawn in advance by principles and concepts. The empirical objects of each philosophy do not completely overlap.

There is a nearly infinite possibility of development of the empirical, giving to the empirical a certain mystery: what is its "theoretical" place if it is not to distinguish philosophies otherwise than through principles.

Philosophy had the ability to distribute fields to other disciplines as one of its functions. But disciplines are often rebellious and seek out their own autonomy.

Anthropology or ethnology no longer wanted to be guided by philosophy.

Sometimes we want to forge new bonds with philosophy but without submitting these bonds to its hierarchies.

We can suppose that to forge these new bonds assumes the creation of new fields for philosophy in the sense where the field will no longer be the point of application of philosophy. The field will be a semi-rebel that proposes a part of the unknown to philosophy, and not only a part of classical astonishment. To realise this change, we will see that we must comprehend the principles of philosophy like Anne-Françoise Schmid 6 hypotheses and begin to philosophize from hypotheses. We know that Leibniz and Russell knew to give importance to hypotheses within philosophy while it was customarily relegated to the sciences.

Let us begin with a variation of the first epigraph:

The Field is "within" philosophy, but philosophy did not notice it.

There is a mode of exteriority to philosophy which is "within" philosophy, without which philosophy does not notice and which, despite everything, it could not do without. Without this mode of exteriority, philosophy would not be "philosophy."

How do we demonstrate this and how can such an assertion change the practice of philosophy? Can we imagine a field that does not depend on philosophy from philosophy? There are some fields that philosophy delegates, but the very gesture of delegation subsists.

I propose a series of propositions to make a place for an exteriority outside of the philosophical field. In a certain way, it is to add intermediary axioms to nonphilosophy and non-standard philosophy. These axioms are necessary because non-philosophy is interested in philosophy as a unity more than as a diversity.

Concerning one preposition…

First, let us reprise some philosophical habits. Its relation to other disciplines nearly each time makes use of the word "of" (in French "de"): such as in philosophy of sciences, philosophy of art, philosophy of religion, philosophy of technics. It is in this position that philosophy nearly always appears in the singular.

There are sciences in the plural, but one philosophy of the sciences or one philosophy of science. There is a trajectory already made for philosophy. It chooses historical cases and texts that it projects some of its characteristic Anne-Françoise Schmid 7 properties such as opposition or complementarity among the conceptual and the experimental. In philosophy of art, it creates commentaries which project a philosophical signification over painting, sculpture, installations, and even music.

It knows how to transform technics, which respond each time to finite problems, into an infinite technology which ends by being represented as autonomous.

Obviously, all these traits are caricatures because these operations are made with technical means and subtle, varied stylistics which make up the bonds between philosophies. Within these technical means, there is a beginning of formalization that some will bring to the side from mathematics or physicsrarely from chemistry, biology, or the human sciences.

The use of the word "of" manifests the voracity of philosophy: if philosophy is found with another discipline, then it seeks to interiorize some traits from it, perhaps even those which most often allow to put it in relation with other further disciplines, for example through mathematization and even now digitization.

There exists an inverse use of the word "of": the science of philosophy, the technics of philosophy, and the religion of philosophy has another signification or another use. It is philosophy as a science, philosophy in its technical aspect, and philosophy as a religion. It is then philosophy that is characterized, rather than its voracious relation with other disciplines. They are what we can call its disguises.

In whatever way we turn, it is very difficult to speak of philosophy without making any allusion to other disciplines. Its autonomy is paradoxically guaranteed by its relation to other disciplines. I draw the following idea: philosophies among themselves have relations which are indirectly bound to the relations that they give to other disciplines, in particular the sciences.

Anne-Françoise Schmid 8

From the word "of" to the concept of "operator"

We replace the word "of" through an inversion: there is no philosophy "of" the future, but, rather, a future-philosophy, as Laruelle proposed in a colloquium on philosophers and the future. The inversion of the "of" leads to the invention of operators on philosophy; any discipline can be an operator on philosophy.

Science-philosophy will manifest the interventions of philosophy in the fragments of science so heterogeneously that the connections and adjustments cannot depend on the disciplines concerned. Art-philosophy demonstrates the inchoative series and the dynamic movements, process, consumption, and inscription, within philosophy.

2) The hypothesis of a Real preceding philosophy

The hypothesis that I propose is that the autonomy of philosophy only makes sense if we consider at the same time and identically the philosophies which make up its tradition, and I posit the primacy of the de jure multiplicity of philosophies over philosophy. Is this multiplicity just the material of philosophy (or philosophies)? A philosophy which would be in total isolation could not be recognized as philosophy, perhaps as intention, process, and inscription rather than philosophy.

But this multiplicity is equivocal: it allows us to treat the relation of philosophies to the real in the form of compatibilities which themselves are part of this multiplicity. Being isolated, one philosophy makes a representation of the real created through its own arrangements and techniques without being able to be recognized as philosophy. This philosophical horizon allows any philosophy to preserve a kind of authority to think that the more one advances in their philosophical thought, the more they have chances to "encounter" the real. The authentic real is at the end of philosophy, and not vice versa. It is what grounds the Anne-Françoise Schmid 9 authority or the sufficiency of philosophy. The de jure multiplicity manifests the desire of sufficiency of each untreated multiplicity not in a chronological succession of type: for example, a caricatural response where my philosophy is better than the previous one, but in a systematics which can support diverse interpretations of time and chronology. Each philosophy thus manifests an "active indifference" to the other philosophies, to take up an expression from Laruelle's early Nietzschean writings.

Non-Philosophy has changed this problematic radically with the following hypothesis: the Real precedes philosophy and is indifferent to it. There is something Real which cannot be philosophized, there is philosophy which can develop as it desires and consume itself (like the desiring-machine in Deleuze, or philosophy is a "skin disease" as Laruelle said in the "vomit scene").

In his thesis General Economy of the Effects of Being (to be published by Temple University, Tokyo, edited by Jordančo Sekulovski) Laruelle undoes the identities of phenomenology in a system, such as intention, process, inscription on a Topos, all of which already bring out something of the dynamics of his subsequent works. It was necessary to separate phenomenology from its identities to find the One or the Real. And each philosophical and/or non-philosophical wave will be in a constant motion, each work being something of a "freeze frame" of a moment in this dynamic.

There is a form of materiality of philosophy that philosophy cannot notice If philosophy does not co-construct the Real, it becomes contingent.

3) On the contingency of philosophy and the philosopher

An experience of philosophy is then lived that its contingency liberates. In a practice without foundation, the philosopher herself appears contingent. But her experience eclipses the object, philosophy, for a moment, or in any case eclipses it as isolated and auto-productive.

That philosophy would be without foundations can give rise to several conceptions of its possible field. For example, think of the philosopher Robert Frodeman (North Texas University, Denton) who sent his students to the field directly in a social group and would give a very interdisciplinary philosophical teaching at the same time. Or think of William Gonzales in Cali (Universidad del Valle) who sent his doctoral students into the country towns to start up masters' programs in philosophy almost everywhere in the hopes to be a pledge for peace in a country coming out of war.

The research of intermediaries

But one can also see philosophy as a function that the philosopher bears.

Thus: to be a philosopher among the scientists, philosophers among the artists, etc.

Think of the philosopher Fernando Zalamea (UNAL, Bogota) who admirably read Poincaré and currently works on a publication by Grothendieck all while writing on Proust. Is this the same gesture as Hegel's? I do not believe so. This does not concern the Aufhebung, but rather the research of intermediaries and intermediary fields which no longer directly depend on philosophy. According to Zalamea, we can no longer practice contemporary mathematics by making them exclusively repose on set theory, however complex and difficult it may be. To comprehend contemporary mathematics, we must create theories of an intermediary scope to take account of the current wealth of mathematics. The same termstheories of the intermediary rankhave also been utilized by the philosopher Jean Gayon to manifest the diversity of the disciplines of biology, biology being one spectrum of heterogeneous theories. All these works change the idea of unity and its dream which have been directors within the epistemology of physics.

There is heterogeneity within the sciences, and the sciences can perceive it if they get rid of the dream of unity, like the epistemology of physics has done, relying on the reduction of heterogeneity that its functional use of mathematics Jouy-en-Josas). We hesitated to call this work "Intermediary Fields." Also, in the arts, the philosopher's place will no longer be to comment but to eventually write texts to accompany and allow, along with the artist, to think the bonds between art and philosophy which could be common, perhaps ephemeral, in a new way. It is what we have done in different ways with Ivan Liovik Ebel, Alice Lucy Rekab, and in another way, for an exhibition in Hanover, with Gallien Déjean.

Therefore, the philosopher's role is no longer grounded in their work, their experience in the research of intermediaries opens her to new styles. There is a fusion of styles and techniques with style becoming an intermediary for the technique and inversely to a near displacement. Philosophy without foundation flies away like fictions or experimental texts where neither totality nor the result are given. It is in this experience and experiment that the philosopher makes use of hypotheses more than principles: the correlations among intermediaries result from hypotheses that are more local than the principles which remain impermeable to the experience of the philosopher.

4) The Point of Exteriority

With the intermediaries, it is now possible to pose a point of exteriority independent of philosophy and to ask ourselves what of philosophy manifests from this point of exteriority. At once a unity, philosophy, and a multiplicity: philosophies, at the same time separately and identically.

Anne-Françoise Schmid 13

Let us think of Vernadsky when he imagines himself looking at the Earth from afar. He sees first a mineral, then a place of animals which modify the vegetal world, and human thought modifying the animal world. He concludes that human thought is found in the earth's crust. Despite the different scales, we still have the Earth. Thought was in the Earth and the Earth was not aware of it. The point of exteriority was there: the geologist who could not be separated from Stalin, and the philosopher who tried to organize interdisciplinary platforms in Europe.

Would the philosopher be then the point of exteriority, which would make philosophy manifest itself at once as singular and multiple? They would be like the one who inhabits the world (=a philosophy), while simulating others. The philosopher never delivers only one philosophy, but rather simulates others at the same time. The philosopher thus has a responsibility before philosophy, to respond to philosophies in an unstable and each time singular equilibrium.

Genericity and the common = X

In front of the identity and the multiplicity of philosophy(s), we can suppose a genericity, a place, which is a common=x, always guarding a part of the unknown. It is not given, it is to be constructed as an unknown, and not as a simple uncertainty, which leaves the concepts unchanged.

Let us suppose that this unknown is an X. There are alternatives and knowledges that allow one to determine it, at least partially. But what knowledge? It is possible to use very heterogeneous ones because it is possible to echo them through the intermediaries. These allow a reorganization of knowledge.

How can these commons be developed? It is possible to do it by matrices as Laruelle suggested in Non-Standard Philosophy, with, on one coordinate, the conditions of experience and, on the other, the characteristics of philosophy. The Anne-Françoise Schmid 14 "spaces" of the matrix are places of invention for philosophy. And it is a method which allows us to work in commons, even with heterogeneous or contradictory hypotheses, if we consider the variety of uses of "non-".

Decomposition of the logos and invention in philosophy

To decompose philosophy, the question is neither to destroy philosophy nor the "real world" or the "field", but to undo the entanglements, both will have new dimensions, liberated by the bracketing of complementarity and the opposition of the two notions. There is the concept and the empirical, let us not make them opposites. This obliges us to consider the contingency of our concepts and our field.

Let us look for a philosophy that does not see present daily life in necessary darkness, but rather that is attentive to the lights and the shadows of contemporary objects. Let us look for a philosophy that is not supposed to be the creator of these objects and one that is not persuaded that it must be accountable for them. Let us present philosophy without its opposites, without its sufficiency. Let us present the field without its auto-position, but by seeking the tools to recognize it as such.

For this task, it is necessary to be able to recognize the limits to philosophy but not from above. It can go up as far as it wishes with the help of other disciplines according to Laruelle, such as the generic, the quantum and philosophy, by stages, where a philosophical thought and scientific and philosophical thought are linked. This is already a limit to omnipotence. But there is another, this time from below, that are not inhabitants of the Earth rather than the world, that have been internalized by philosophy as abstract beings. Katerina Kolozova has shown this beautifully. The animal, man, woman, pain, and sorrow are not abstractions that philosophy presents to us. We are no longer in the era of all-philosophy, as we speak of the all-powerful, but in an era where philosophy takes its place and its Anne-Françoise Schmid 15 field just where it stumbles towards the concrete. Not a particular concrete, in a worldly situation, but a rough concrete that makes us feel something of the human that philosophy, having forgotten it, has not been able to transmit to us.

The animal, the man, and the woman see philosophy which on the contrary does not see them. The living was in the philosophy, but philosophy did not consider it in its concreteness. Rather than a philosophy of the living, let us practice philosophy in another style, that of the fiction, passing from the real to another point of the real, or that of the experimental text, of which, in a certain way, this essay is a part.

Let's imagine operative fictions, such as a man-philosophy, a womanphilosophy, an animal-philosophy, which makes us relive the intentions, processes, inscription, and topoi closest to living matter without qualities.

What would then be the field for philosophy? One, rough and robust, where it could find its limits of omnipotence through something concreteor through a "ject" according to Laruelle (a ject without jection or without an ob-ject), resisting all abstraction.

The concrete was not in philosophy, and philosophy did not realize it. This is its limit and its strength.

The force of invention of philosophy does not come from criticism, but from its transformation by the concrete which returns to it the reality of the de jure multiplicity of philosophy: to philosophize by hypotheses rather than by principles. Fiction is the combination of a concept with knowledges under heterogeneous knowledges. Rather than working with the uncertain, fiction works with the unknown = X which reorganizes knowledges in an unexpected way within its realizations.

In philosophy, it is possible to choose a concept and recombine it with other philosophies under the guarantee of another discipline as an under-determination.

What is an experimental text?

An experimental text touches the concrete. The formula is the following:

K/K' ⊃ Hyp
An experimental text is a text that seeks to produce new hypotheses through heterogeneous knowledges to comprehend contemporary integrative and complex objects (To appear in: Scripts Philosophiques 1: le silence du futur, edited by Anne-Françoise Schmid 17

Jordančo Sekulovski, Temple University). The experimental text works on uncertainty rather than the unknown, and as Wittgenstein reminds us, "uncertainty extends to the roots."

The bond of fiction and experimental text: non-synthesis?

In this new practice which admits a field that does not depend on philosophy, philosophy becomes an integrative object, an object without definitive synthesis, within an unstable equilibrium between fiction and the experimental text.

New work on contemporary objects then can be done, superseding complexity. Such contemporary objects are the following: climate change, nanotechnologies, GMOs, which are equally partially unknown Xs, and the work can practice an orchestration where all these disciplines have the same weight, with this work included. Therefore, it is no longer the organizing of this orchestration alone, but it makes a part of this orchestration as the possibility of the creations of bonds between propositions and other disciplines. This allows the generic to organize a hyper-compatibility between disciplines, but this does not make the whole of philosophy nor the whole of science.

In this generic space, philosophy encounters the real otherwise, where the The long notes have the obligation to receive and take care of the short ones, which give the rhythm. Among those who invented long notes, we can play Bruckner, Wagner, Scelsi. Among the short ones we have percussion, anything that sounds from tactile pressure. Perhaps we could feel music by the differences in air pressure, what is called noise. Any piece could be immersed in the noise. If we were Leibnizians, we could accept silence as an infinitesimal form of noise. We would then touch something like a common = X, the inchoate beginning of music, Anne-Françoise Schmid 19

but not only of it, because in this way we break the accepted frameworks which make disciplines into separate islands while assuming that we can move from to each other directly. They remain separate but allow echoing through silence and noise and the generic make them drift on the horizon without losing anything.

In science, disciplines are talkative, but what about the silence of science in an interdisciplinary regime? We can accept that any woman in the most distant countries, "a whole distant world" (Dutilleux), who watches her plant grow does so with a scientific gaze. It has an intuition, an intention, an elementary, an ordinary, natural, a trajectory and mobile truths, all the primitives of science, those that we find in the most complex and the most contemporary, even in the experimental holes under the earth's surface. The theory-centered conception of classical epistemology cannot quite understand this. Primitives are like long notes in musicthis music "decolonizes" science and makes it appear independent of mathematization. This does not disappear but loses its function of "universal language" for a more generic and modeling function.

The colors are not talkative, they vary between the cry and the silence, and touch us like pressure differences, if not air, at least intermediate spaces between

the eye and what makes art, the painting, the gallery, the volcano, and all the landscapes of visageity. They can "drip" into our subjectivity. Closer to earth, clay, a sculpture, which escapes classical standards -it extends into installations and contexts -but also contemporary standards by taking up the object orientation just like an object-like in context, where the gestures of the observer to approach him are part of his characterization -or of his "aura". The words of poetry also take on color, we perceive them as sounds and images, and teleported into a universe of new dimensions.

Anne-Françoise Schmid 20

Philosophies learn to see each other and to recognize their multiplicity, a multiplicity of rights, but also of functions with other disciplines. Let us remember the Poincaré conjecture: if we can on a sphere seen in two dimensions, consider a point as the reduction of a closed figure which would pass through several regions of this sphere. Suppose this sphere is three-dimensional. Can we make the same conjecture in philosophy? In mathematics, this was demonstrated by Gregori Perelman (1966), Russian mathematician, who refused the Field Prize and Medal, and just "balanced" his demonstration on the Net and not in a recognized journal… What would become of the multiplicity of philosophies in such a third dimension?

Philosophy would at least be deprived of its foundations. It would take the collective experience of philosophers, with the help of musicians, painters, poets, physicists, if we recognize that philosophy forms a body. We would be helped by Thanks to everyone involved in this thought project.

  Does this contingency lead to a critique of philosophy? This is not the right term. Contingency softens the Kampfplatz and the misunderstandings between contemporary philosophers. It gives philosophy new liberties. It admits a de jure multiplicity of philosophies as a condition for philosophical writing. How do we Anne-Françoise Schmid 10 write without considering the fact that other philosophers write under other hypotheses and anchor themselves to other disciplines or practices? There emerges a first materiality that philosophy, in its classical systematicity, cannot recognize.A philosophy without foundationA philosophy which is written by considering the de jure multiplicity of philosophies loses its own foundations. These foundations are replaced by the relations that it builds with other disciplines, as the work of Joevenn Neo has shown.I have translated this into two intermediate axioms:1. The obscure cogito: there is at least one philosophy that I do not understand. Multiplicity does not give itself. 2. The open secret: philosophies do not hide themselves and yet they are not manifest. These intermediate axioms question the overlap between philosophy and philosophies. The Cogito is out in the open but the open does not notice it.

  allows. They then must invent a new epistemology to take account of these heterogeneities and recognize them as sciences. No former paradigm suffices here in the wealth of current works. The works of epistemology all repose on past Anne-Françoise Schmid 12 examples. To project these examples, even recent ones, onto works that come about are not enough to make them visible. In this way, it is what I, side by side with Muriel Mambrini-Doudet, worked on together in our work Generic Epistemology: Manual for Future Sciences to give the tools to comprehend what is happening in the sciences. Muriel was then the president of a great center of interdisciplinary research, and I was a part of the governance of this center (INRA,

  The bonds between hypotheses (to philosophize from hypotheses in multiplicities), unknown and uncertainty: fiction and the experimental text What is a fiction? A fiction touches the real in one point to pass onto another point. Its most simple formula is the following: C x K/K Anne-Françoise Schmid 16 Where C stands for Concept and K stands for Knowledge C x x ⍴(K)/K i nformula from Generic Epistemology this formula was written by Brynn McNab, adapted from Generic Epistemology The concept of fiction then functions in an analogous way to what Laruelle calls, in Philosophy and Non-Philosophy, a first term. While engaged within knowledges under other knowledges, a first term engages the philosopher within fictions.

  colours and sounds can be reintroduced in philosophy. Philosophy then can construct spaces for its relations to other disciplines: discrete spaces, open spaces, where the fragments of disciplines act as variables, and not as differences in tension. It is in this generic space that the philosopher comes into play. For the philosopher, philosophy becomes a material where she can choose and freely combine concepts in accordance with the spaces created in relations with other practices and disciplines. Anne-Françoise Schmid 18 Concretizations in progress:  With Muriel Mambrini-Doudet: The Laboratory of Discrete Philosophy -The creation of a space for collective invention of discrete philosophies  With Ivan Liovik Ebel: Topographie discrète. Scénario pour un texte sans dimensions, Neuchâtel, le Griffon, to be published in September 2021. Then with music by Thomas Köner and video by Benoît Maire, in discussion.  With Alice Lucy Rekab, "Art and Philosophy: New Solidarities," in a work to be published, edited by Steven Shakespeare, Liverpool. One of the realizations was the latest course at the New Centre of Research and Practice: "Inventing the Non-Given Common = X Between Philosophy, Art, and Science," with Tony Yanik and Joevenn Neo. I will end this experimental essay with the final fiction of this course with Tony and Joevenn. It reprises the interventions of the participants in its own way, all whose disciplinary domains were very varied: Discoherences of disciplines and new dimensions for a common = X Anne-Françoise Schmid, translation by Joevenn Neo

  Joevenn and Tony.The geographer would help us keep the peace, limit hegemonies, invent new maps without hurting the territories too much. It could ally itself with geopoliticians, who seek to guarantee food and soil for humans who have become subjects of the arts and philosophies, as well as the sciences. Fred Moten and Edouard Glissant would inspire us for the decolonization of our prejudices on all disciplines. What would be left then? If we are lucky, a common = X, regenerated by the impossibility of representing it in two dimensions, and the games (Tony, Sub) and the abductions which will give us the means to reorganize our spaces of thought, our modes home and living. And for that, let's reverse the perspectographs of the classic perspectivists. Let us invent new solidarities, which are no longer just matters of perspective, but of faith without an object, of mysticism = X. Let us be attentive to the idea of metamorphosis (Michaël Levinas & Valère Novarina), even that of requiem and silent colors.Anne-Françoise Schmid 21