Laurent Limat
email: laurent.limat@univ-paris-diderot.fr

Dewetting with conical tail formation: how to include a line friction of microscopic origin, and possibly evaporation?

Keywords: wetting, contact line, free-surface flows, lubrication

Most studies of dewetting fronts in 3D with a "corner formation", as happens behind a drop sliding down an incline are based on a generalisation of Voinov theory, with (at least implicitly) a slip length at small scale. I here first examine what happens, if instead of considering a free slip at small scale, one admits a non-zero additional line friction of microscopic origin. Concerning the selection of cone angles, I show that most features of the model are unchanged, except that the "slip length" must be replaced in the equations with an "effective" cut off that can become apparently unphysically small. I suggest that these results could explain problematical cut-offs in the hydrodynamical modelling observed recently by Winkels et al on water drops. The sole difficulty with this interpretation is the law ruling the radius of curvature of the corner tip at small scale, which remains unsatisfactory. I suggest that evaporation of the liquid should also be considered at these very small scales and propose a preliminary "toy model" to take this effect into account. The orders of magnitude are better recovered without changing the structure of the equations developed initially for "classical" wetting dynamics with silicon oil drops.

I -Introduction

Despite decades of studies, wetting dynamics on a solid is still the focus of an intense activity [1][START_REF] Blake | Liquid film coating[END_REF][START_REF] Coninck | [END_REF][4][5]. In this context, one of the the perhaps simplest experiment consists in observing the shape of a drop sliding down an incline [6][7][8][9][10][11][12]. Several works have shown that a conical tail develops at the drop rear when the velocity is large enough [6,7], the structure of both the flow [8] and the interface being well described [7][8][9][10] by an appropriate 3D generalization [13] of the "hydrodynamical model" of wetting dynamics [14,15]. On the other hand, depending on the liquid used, the slip cut-off assumed in this approach can be of reasonable magnitude (polymer lengths for silicon oils) [7,10] or on the contrary, completely unreasonable, i.e. extremely small for liquids such as water or liquid metals [11][12]. Understanding these effects is important for further progresses in wetting dynamics and for several applications in the field of coating, for instance immersion lithography [11]. Indeed this "corner formation" is ubiquitous and has been reported very early on liquid films extracted from a bath by a moving tape [16], as well as for air films trapped below the coating at the advancing front [17][18][19][20].

In the present paper, I suggest that these surprising apparent cut-offs could be explained by assuming some extra-dissipation at small scale [START_REF] Coninck | [END_REF]21,22], that could be represented by a contact line friction in the framework of combined models [23,24] that mix the hydrodynamic approach with possible thermally activated jumps at small scales [21,22]. In this framework, I show that the large scale flow structure is still solely governed by the same hydrodynamical model, with exactly the same equations, but with an apparent cut-off modified by the contact line friction. This one can indeed be very small, and in appearance unphysically small, when this line friction is sufficiently large. These ideas, that I briefly suggested in a recent focus article in JFM [25] on a paper from Puttenvethil et al [12], are qualitatively compared with measurements performed on water drops by Winkels et al [11]. Most features of these experiments are recovered, and in particular the fact that the laws governing the large scale geometrical structure of the interface are unchanged, but with this very small renormalized effective cut-off. I also show that the same occurs for straight contact lines, where the same apparent cut-off can be invoked, which perhaps explains some puzzling observations of similar unphysical cut-off on water and mercury in these conditions when data are considered from a purely hydrodynamical perspective [12,25,26]. However, in our 3D geometry, there is still a difficulty on the law giving the curvature at the corner tip. The singularity of the interface is limited at small scale by the same cut-off, but this one is clearly too small for what is observed, and can obviously not hold, especially as it is now the model that reaches apparently unphysical values... More technically, it appears that the exponential law involved is affected at the level of its prefactor instead of in the argument of the function, which is also inconsistent with the obtained curves. I suggest here that evaporation should perhaps be considered before the tip structure reaches these very small scales. The question of evaporation interacting with contact line dynamics is a major question in recent modelling of contact lines [START_REF] Rednikov | [END_REF][29][30][31] trying to remove the hydrodynamic singularity, and also in the context of drying to interpret unusual aspects of "coffee-stain" effect [32][33][34][35][36]. I propose a tentative law including these evaporation effects, which would remain to be tested in more details on well controlled surfaces and volatile liquids, and also reconsidered with a more advanced modelling.

II -Drops sliding down a plane revisited with a microscopic friction line.

Typical pictures of a drop sliding down a plane and of its conical tail are reproduced on fig. 1, where the notations are also precised. The flow inside the tail results from a balance between viscous losses and the gradient of capillary pressure linked to the conicity. Assuming an approximate parabolic cross section for the interface,

h(x, y) ≈ x tanΩ 1- y 2 x 2 tan 2 φ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ (1)
together with a local balance of flow given, in the lubrication limit, by [13] Vh

x = γ 3η ∇. h 3 ∇ h xx + h yy ( ) x ( ) , (2)
one can easily derived a relationship linking the cone angles with the capillary number Ca= ηV/γ (V drop velocity, η liquid viscosity, γ surface tension of the liquid). This one reads [8]

tan 3 Ω = 35 16 Ca tan 2 φ , (3)
and is remarkably well satisfied by most of available data (see figs 2-e and 2-f in the next section). To obtain some predictions on these angles, one needs to precise the microscopic modelling of wetting at the contact line. I here propose to use Petrov "combined model" [23] (see also Appendices below), mixing both the bulk hydrodynamic dissipation with a microscopic line friction , which reads on the two inclined contact lines:

θ 3 = 2Ω / sinφ ( ) 3 = θ m 3 -9CaLog b / a ( ) sinφ (4-a) θ m 2 = θ r 2 -ACasinφ (4-b)
where θ r is the static receding contact angle, b a macroscopic size (typically the drop size, at which the conical tail has to match, a is a small-scale cut-off, below which a line friction of microscopic origin develops, modelled by the constant A. This constant A can be related to the more classical concept of line friction ζ used in molecular kinetic theory [START_REF] Duvivier | Comportement de gouttes de mélange en situation de mouillage extrème[END_REF]39], where (2-b) should be usually written as:

γ cosθ r -cosθ m ( ) = ζV sinφ (5)
which implies A≈2ζ/η in the low angle limit. If one now considers the limit of small capillary numbers and/or slender cone of low φ value, even for "large" values of A, these equations lead to the following equation linking φ to Ca:

Ca θ r 3 = 2φ 35 + 18φ 2 Log b a' ( ) with a' = a exp -Aθ r / 6 ( ) (6)
As one can see, these equations are the same as those developed in refs. [9][10][11], but in which a' plays the role of an apparent cut-off that can become extremely small in the limit of a strong microscopic slip constant A. The same kind of argument can be developed for the modelling of the curvature radius R=1/κ r of the contact line at the corner tip [10], where one has to match the large scale interface slope on the symmetry axis Ω to the same modelling of the contact line at the scale of the corner tip width R/φ 2 . Roughly, one has:

Ω 3 = θ r 2 -ACa ( ) 3/2 -9CaLog 2R aφ 2 (
) , which finally yields, again in the low Ca limit:

R ≈ a'φ 2 2 exp θ r 3 9Ca ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ (7)
which is the same form as the one used in [10], but with the same apparent cut-off as the one used in eq.( 6). Finally, let us conclude this section with the even more simple case of a straight contact line receding normally to itself, in the vicinity of which the local slope can be written as (see more details in Appendix):

θ 3 = θ r 2 -ACa ( ) 3/2 -9CaLog(b / a) ( 8
)
In the limit of large A, but small enough Ca, the first term can be developed as θ r 3 -(3 / 2)ACaθ r 2 , in such a way that (8) can be rewritten as:

θ 3 ≈ θ r 3 -9CaLog(b / a') (9)
at first order upon Ca, where a' is the effective cut-off introduced above. [10]), (b) similar shapes observed for water drops maintained static on a glass turning table (Winkels et al. [11]); (c) dynamic contact angle observed for both experiments (SD silicon oil sliding drops, TT turning table measurements with water) at the dewetting front, fitted by eq.( 9), and followed at larger Ca by the cone angle defined in a vertical plane [11]; (d) Cone angle viewed from above as a function of the capillary number for both situations, compared to the theory [11], a being replaced with a' for water (TT); (e) check of eq. ( 1) for silicon oils (from Snoeijer et al [8]), (f) check of eq. ( 1) for water (Winkels et al [11], TT). Eq.( 3) corresponds to the dotted line on both figures, the continuous line being a better numerical approximate (but not analytical) obtained in refs. [8,13].

The agreement with hydrodynamics, possibly combined with a extra line friction is good, except for two things: a noticeable departure for water (TT curve) on fig. 2-d, possibly linked to the breakdown of the slender approximate for the cone, and a certain irreproducibility of data for silicon oil (second trace on fig 2-f, SD, still unexplained).

In summary, in the three cases considered, straight contact line receding normally to itself, inclined contact line on each cone side, curved contact line at the cone apex, the large scale spatial structure should be ruled by the "hydrodynamical" model of wetting, i.e. by a balance between capillarity and viscous bulk dissipation, but with an apparent slip length that is modified by the extra friction introduced microscopically by other mechanisms. In this point of view, one should not oppose the hydrodynamical model to others (and in particular to the MKT "chemical" model of wetting), as they describe in fact complementary aspects of the same puzzle.

III -Qualitative comparison with experiments: contact angle and cone angles.

Fig. 2 compares series of experiments developed in Paris and Twente. The first series were performed by both teams on silicon oil drops, the last series being developed by Twente, alone, on water drops. Typical pictures of silicon oils drops observed for an increasing capillary number are suggested on Fig. 2-a, while Twente experiment on water drops is suggested on Fig. 2-b. In this last experiment, a water drop was maintained static in the framework of the lab, on a mobile substrate (Turning table, imitating a device of immersion lithography [START_REF] Riepen | Dynamics of dewetting in immersion lithography[END_REF]). This was obtained by contact with a vertical tube, itself renewing the water at constant rate while compensating any loss of mass (due for instance to evaporation...). The mobile substrate was a rotating table whose surface was made up with glass covered by some (not precised) coating, providing a receding static angle of order 65°.

A typical record versus Ca of the receding angle observed from the side is reproduced on fig. 2-c, and compared to the same trace observed on a silicon oil drops. Below some critical contact angle, of order 20°, a conical tail appears in both case, the plots displaying then the cone angle Ω, defined in a vertical plane, instead of the receding contact angle, that should now be measured in a plane normal to the contact line. Once the cone is formed, two angles are necessary to precise its geometry, Ω and 2φ the opening angle 2φ defined now in a horizontal plane. The equivalent traces for both silicon oils and water are displayed on Fig. 2d, while the correlation between the angles φ and Ω, in terms of eq. ( 3) are reproduced on fig. 2-d and2-e, respectively for silicon oils and for water.

Despite some discrepancies, it is remarkable how the whole set of data can be fitted with a hydrodynamical description. On fig. 2-b, for the receding dynamical contact angle before cone formation, the data fall exactly on Voïnov prediction (eq. 9), provided that one uses appropriate cut-offs. The same occurs after cone formation for the angles φ and Ω, with however some imperfections, for instance on fig. 2-d, presumably due to the fact that we are playing with low order theories (slender limit at low φ). Note also some lack of reproducibility, in Fig. 2-f, where the data for silicon oils seem inconsistent with earlier ones reported on fig. 2-e. Anyway, in silicon oil case, the cut-off required is equal to a= 7.5 nm [11] when one considers a macroscopic scale b≈25 µm , which is rather reasonable considering the typical size of the polymers (a few nm). On the contrary, for water, one is constrained to use an apparent cut of very low value [11], i.e. of order a'=10 -15 m (!), that is completely unphysical, unless one invokes the possibility suggested above in section (2): if one assumes that the nanometre remains the right scale for a microscopic cut-off (i.e. a≈1 nm), this would require exp(-Aθ r /6) ≈ 10 -6 , i.e. Aθ r ≈ 36 Log(10) ≈ 80. The receding angle being of order unity when expressed in radians, this is equivalent to a line friction of order ζ≈ 40 η ≈ 4 10 -4 Pa s which is a reasonable order of magnitude for water, when compared to available literature (see for instance fig. 50 of Duvivier thesis [START_REF] Duvivier | Comportement de gouttes de mélange en situation de mouillage extrème[END_REF]). One can thus here suggest two things:

(1): The classical hydrodynamical model of contact line with a slip length is enough to describe straight contact lines, as well as corner properties in 3D for silicon oils.

(2): For water, it is still necessary to include hydrodynamics in the description, to describe the large scale geometry, but the microscopic picture must be modified , by replacing the "slip length" with some molecular kinetic description, that is known to work quite well for this liquid. The coexistence of both source of dissipation is well captured by the linearized version of the mixed model combining the two effects.

These conclusions are consistent with previous works of Mons team comparing different fluids of different viscosities and surface tensions (see fig. 18 in ref. [START_REF] Duvivier | Comportement de gouttes de mélange en situation de mouillage extrème[END_REF] again, or ref. [25], showing that water experiments require absolutely to invoke some line friction in the description, not reducible to hydrodynamics), while the pure hydrodynamic modelling alone seemed enough for low surface tension liquids, such as silicon oils. Note also that despite the relatively high value found for A/2η, the observed behaviours can not be only interpreted with a line friction alone as attempted for instance in [40], that would lead to a saddle point (Ω=0) instead of the conical structure, separating two oblique contact lines of inclination given by Blake and Ruschak formula [16]. This is due to the physics contained in eq. ( 3), which has absolutely no equivalent in molecular kinetic approach of wetting dynamics.

IV -The puzzle on the corner tip: should not we include evaporation and/or inertia, here?

Another way to investigate the mechanism of corner formation consists in following the curvature at the tip for increasing capillary numbers. This study was performed for silicon oils by Peters et al [10], and generalized to water by Winkels et al [11]. Typical pictures are reproduced on Fig. 3-a where one sees clearly the progressive increase of curvature when the contact line velocity is increased. This evolution is plotted on fig. 3-b, where one sees qualitatively a sharp growth very similar to the one predicted by eq. (7). The parameters of this growth are checked on fig. 3-c, with a Logarithmic plot of curvature upon 1/Ca. In fact, again, only the data obtained with silicon oils are consistent with this law, with a cut-off a'=a of nanometre value. For water, there are two surprises:

-The slope of the line giving Log(R 0 /R) versus 1/Ca is not the right one, Winkels reporting the need to redefine the receding contact angle from its "true" value to an effective one equal to 56° instead of 65°.

-The prefactor is much larger than the scale a' calculated in section (2), and it is not a surprise as a' is much below the molecular size, and thus cannot be a reasonable scale for a "true" length measured directly on the interface structure.

To the opinion of the writer, both effects can be understood as follows: the balance between macroscopic as well as microscopic friction and capillary pressure should lead here to a very small scale for the formed singularity at the corner tip, that seems to be able to reach levels below the nanometre (!). Obviously, some other physical mechanism will happen before R reaches so small values. 7) in ref. [11] (pictures and curves extracted from Winkels et al, ref . [11]) At this step, there are two effects in which one can think: inertia of the liquid and liquid evaporation. Usually inertia is negligible in wetting problems, as the viscous stresses are diverging when one becomes closer and closer to the contact line, and dominate any residual inertia. However, recently, its effect has been invoked [41] to try to explain some departure to the Ω-φ relation, for low viscous fluids such as water, and some surprise was also observed in problems like the pearling instability of liquid filaments [START_REF] Castrejón-Pita | Proc. Nat. Acad. Sc[END_REF]. Now, if we follow Kim et al. [41], the sole effect of inertia would be to add a modification of the effective pressure via a ρV 2 term. This term has no gradient in the x-direction , or this one nearly vanishes, as the liquid must move as a whole at constant speed V. A residual effet can however be expected, if we consider 3D-effects, the flow lines being curved when reaching the contact line normally to itself [8,[START_REF] Rio | [END_REF]44]. Assuming that inertia term, in Navier Stokes equation, scales roughly as ρV y ∂V x /∂y≈ρV 2 /R while viscous effects are of order η∂ 2 V x /∂ 2 z 2 ≈ηV 2 /h 2 ≈ηV 2 /(Ωx) 2 , together with the geometrical relation R≈xφ for a slender rounded cone, one gets that inertia should matter when the following Reynolds number is larger than 1:

Re ≈ (xV / ν )(Ω 2 / 2φ) (10)
With the orders of magnitude V≈0.1 m/s, ν≈10 -5 m 2 s -1 , Ω≈0.3 rad, φ=0.6 one gets that Re>1 for only x>1 mm, which is a bit highn to influence what happens at the tip of the drop tail. At the scale of the rounded corner tip, i.e. x≈ 3 µm, Re does not exceed 3 10 -3 which remains extremely low. There are thus very few probabilities that these effects could explain our problem of R selection.

Another possible idea would be to imagine at very small scale some complex tip-splitting effects, whose average effect would limit the divergence (I thank one of the referees for this suggestion), but when looking to the pictures, we see a well defined curved and regular contact line at a scale of order 100 µm, using a camera and the required optics at a resolution of 1 µm. We do not see any rugosity or any tip formation between 1 and 100 µm.

Finally, another natural candidate is here the evaporation of the liquid, water being known as a very volatile liquid. This idea can be related to previous works performed on evaporation near contact lines by different teams. One can first mention the well known study of Deegan et al [32] who emphasize the existence of a divergence of evaporation near contact lines that scales as:

J x ( ) ≈ J 0 x ( 11
)
where x is the distance to contact line. This divergence is known to amplify the flow of the liquid towards the contact line induced by evaporation, which in turn amplifies the tendency to deposit solutes at a drying contact line ("coffee stain" effect). This divergence is ruled by the harmonic nature of water diffusion in air (Laplacian of concentration is equal to zero). In a vertical plane, normal to the contact line, this one becomes a 2D geometrical singularity around which diffusion lines are trying to escape. The mathematical description of this leads to the expression of J 0 that reads:

J 0 = D λ C w sat ρ w (12)
in which D is the diffusivity of water in air, C w sat the saturation concentration in air (supposed to hold at the free surface of water), and ρ w the mass density of water. The length scale λ is a typical length that constrains the vapour flow at large scale. It can be the thickness of some boundary layer for evaporation, imposed for instance by the air flow associated to substrate motion in Twente experiment, of, for a highly curved contact line its radius of curvature (R here). In standard conditions, for water vapour in air, D ≈ 2.4 10 -5 m 2 s -1 , ρ W =1000 kg/m 3 , C w sat ≈5 10 -3 Kg/m 3 , one has J 0 λ 1/2 ≈10 -10 m 2 s -1 .

We have perhaps here a much more convincing candidate to explain the R selection at small scale as we have now an effect that increases when the scale x goes to zero, instead of having an effect rather at large scale, when x increases. To get some order of magnitude, we can seek now at which scale evaporation will be able to modify appreciably the flow of the liquid. Very close to the tip, we can assume that there is only one scale that rules evaporation, i.e. that the evaporation flux towards air is of order DC w sat /(ρ w x), which implies a flux of liquid leaving the cone between 0 and x of order (DC w sat /(ρ w x))(x 2 φ)≈(DC w sat xφ)/ρ w . This 1/x divergence estimate is consistent with rworks from Popov and Witten, on evaporation of liquid triangular sectors [45] (apart some slight geometrical modification of the exponent -1). This must be compared to the flux linked to sliding velocity of the drop across a section located at x, i.e. to Vx 2 φΩ. This means that evaporation will perturb the flow when the following adimensional number is larger than 1, i.e. when

Dc w sat 3ρ w V Ωx > 1 (13)
Again, with the available orders of magnitude, D≈2.4 10 -5 m 2 s -1 , r W =1000 kg/m 3 , C w sat ≈5 10 -3 Kg/m 3 , Ω≈0.3 rad, evaporation should matter only for x smaller than 1 nm… This apparently rather deceiving value means that the corner flow structure is not influenced by evaporation, in practice, and that we can still trust equations such as eq.( 3). However this does not mean that the radius of curvature, at the tip will remain unaffected. There is another effect that will matter: In fact, the strong evaporation flow near contact line will modify a lot the effective static and dynamic contact angle which must have some effect on the matching procedure that was used to calculate R. This idea is at the basis of the next section.

V -A tentative calculation of R, in presence of liquid evaporation.

The influence of a diverging evaporation has been only recently considered in hydrodynamical models of contact lines dynamics [START_REF] Rednikov | [END_REF][29][30][31], and it has even been proposed that evaporation is a general phenomenon that regularizes the hydrodynamical singularity at contact lines [30]. A difficulty is here that no models are available combining hydrodynamics, evaporation and a possible line friction of molecular origin (or related to pinning/depinning events on the solid surface, as in [21]). It is however possible to develop a semi-qualitative argument by a slight heuristic generalization of the expression of dynamic contact angle proposed by Berteloot et al [33] for a receding evaporating contact line:

θ d 3 ≈ θ m 3 -9CaLog x a ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ + 24 ηJ 0 γθ m 1 a 1/2 - 1 x 1/2 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ (14)
in which we have replaced the static, macroscopic, receding angle by the one assumed in molecular kinetic theory (eq. 4-b), assuming also that all the angles here are small and slowly varying with x (which is not really the case here...). Using exactly the same argument as in ref. [10][11], i.e. that θ d ≈Ω at a distance of order x≈2R/φ 2 >>a of contact line (matching condition between the cone and its rounded tip), one finally yields the obtained value for the tip radius:

R ≈ a'φ 2 2 exp θ r 3 9Ca 1+ 24 ηJ 0 γa 1/2 θ r 4 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ (15-a) with: a' ≈ a exp - Aθ r 6 1-12 ηJ 0 γa 1/2 θ r 2 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ (15-b)
As one can see, now, the decrease of a' scale will be limited by evaporation. At low Ca, we can expect that the spatial scale λ that rules J o will be some constant thickness (or at least slowly varying with Ca) of a boundary layer for evaporation near the glass plate, and at higher capillary number, we can imagine that λ will progressively adjust itself to R, which implies that eqs. (15) will prevent R to reach very low values. Not also that these ideas are perhaps consistent with the two regimes observed on the curve Log(Ro/R) versus 1/ Ca observed on fig. (3-c), that could correspond to the two different regimes of evaporation for λ. An interesting feature is also that we recover in (15-a) that the argument of the exponential function is modified, which will lead to an apparent contact angle θ r that will differ from the expected one, as observed by Winkels, but unfortunately the sign of the effect is reversed, the effective angle being larger (and not smaller) than the macroscopic one... A more refined analysis would be here required, as eq.( 14) is just a "toy model", imagined for very small contact angles, that also needs improvements, and whose predictions must be taken with cautions. We now just limit ourselves to some calculations of orders of magnitude, in order to see if our idea to invoke evaporation is reasonable or not.

For a static drop of millimetre size, with low contact angles, in standard conditions, the orders of magnitude reminded above lead to J o ≈ 5 10 -9 m 3/2 s -1 [32,33]. In addition, this quantity scale as R -1/2 , where R is the radius of the drop, which equivalent is here the radius of curvature R of the corner tip, itself of order 10 to 100 µm [11], which implies here a larger effective value J o ≈ 5 10 -8 m 3/2 s -1 . With typical viscosity and surface tension values for water of order η=10 -3 Pa s, and γ=80 mN/m, and speculating on a microscopic scale a, of molecular size , the typical correction in (10) is of order : 24 η J o /(γ a 1/2 ) ≈ a few 10 -3 which is just too small to have a measurable effect here. Now, we have to take care on the angle dependencies, this factor being divided in (15-a) and (15-b), respectively by θ r 2 and θ r 4 ... which are here unfortunately of order unity (!). This may seem again a bit deceiving, but we have also to remind that we are here dealing with theories valid for very low interface slopes, extrapolated to larger values, and in addition slowly varying with the distance to the contact line. All these approximates allow us to develop something analytical, but are clearly not valid here.

In such conditions, one would have to generalize the modelling to a non-linear high angle situation, which is difficult, or to focus on linearized theories in a low range of capillary numbers. In such a situation, it is not obvious that the macroscopic receding angle is the relevant reference angle here, on the new branch of solutions that appear at cone onset, and not for instance a fraction of this angle or even some other reference angle. One can think for instance to the cone angle Ω at cone onset, for which, in addition, there is still no model available. For all these reasons, one can question globally this modelling that is very rough and suggests that other typical angles could be involved in a "true" theory. For instance, if one replaces θ r by something more relevant to the cone structure, for instance Ω≈ 0.1 rad at cone onset, one gets some effective parameters 12 η J o /(γ a 1/2 Ω 2 ) and 24 η J o /(γ a 1/2 Ω 4 ) of order 1 and 10, both having orders of magnitude able to perturb eq. (15). So, though the present picture is at first look not completely satisfactory, I think that evaporation should indeed be considered in this question of corner tip radius selection with water, but presumably with a more advanced description that the present one. Kelvin effect linked to the strong curvature of the interface should be included, for instance, as in refs. [START_REF] Rednikov | [END_REF][29].

V -Conclusion

In short, I have examined the replacement of the classical no-slip condition at contact line by some line friction inspired by the molecular kinetic theory on the "corner formation" by dewetting in 3D, as observed at the rear of sliding drops of water. This approach, in terms of the "combined model" imagined by Petrov and Petrov seems able to explain why the same laws could hold as for the first experiments with silicon oils, but with apparently unphysical spatial cut-off of very low values. Now it fails to describe what happens with the selection of the contact line curvature at the tip of the corner. I have suggested that liquid evaporation should be included in the description to get a more reasonable description and provided a "toy model" to do this. Again, this approach preserves the structure of the equations found initially when considering silicon oil drops, and improves the problem with orders of magnitude for the cut off, but the predicted influence of the reference static receding contact angle remains problematical.

Further works are necessary to get a complete understanding, with new and better controlled experiments (substrate properties, liquid volatility, etc.), as well as new and more refined approaches of wetting dynamics, especially with respect to the consistency of Ca developments, or to the physical basis of a line friction of microscopic origin, and also with respect to evporation [28-31, 46, 47]. A question that remains asked is also what happens for large static contact angles, the theory developed here holding only in the limit of low interface slopes. Though observations of a conical structure has been reported, experimentally in such conditions [12], recent numerical simulations by molecular dynamics are unable to reproduce it in the same limit [44], despite a well defined transition to pearling very similar to experiments. To conclude, I mention that this idea to combine a line friction with standard hydrodymical models to interpret dewetting data from immersion lithography has been first proposed independently during the coating symposium ECS2013 in Mons by M. Riepen [START_REF] Riepen | Dynamics of dewetting in immersion lithography[END_REF].

Strictly speaking, eq. ( 7) and, consequently eq. ( 15), is a bit more complex that what we present here. There is an additional, weak dependence upon the φ angle, that was yet omitted in refs. (10)(11), and that reads as follows:

R ≈ a'φ 2 2 exp θ r 3 9Ca ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ exp - 35 144 φ 2 ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ (A-1)
This factor should also be taken into account in eq. ( 13) that reads in fact:

R ≈ aφ 2 2 exp - Aθ r 6 1-12 ηJ 0 γa 1/2 θ r 2 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ⎡ ⎣ ⎢ ⎤ ⎦ ⎥exp θ r 3 9Ca 1+ 24 ηJ 0 γa 1/2 θ r 4 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ⎡ ⎣ ⎢ ⎤ ⎦ ⎥exp - 35 144 φ 2 ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ (A2) Appendix B.
Reminding Voinov approach for a single receding contact line with a slip length.

Let us consider, as on the figure, a receding contact line in situation of partial wetting, the liquid thickness being called h(x,t) and the fluid velocity component, parallel to the substrate, U(x,y,t). Mass conservation imposes that:

∂h ∂t + ∂ ∂x h < U(x, t) > [ ] = 0 (B-1)
where <U> is the mean velocity integrated over the thickness h. Seeking for a solution propagating at uniform velocity, i.e. h=h(x-Vt), with ∂h/∂t=-V∂h/∂x, one will find easily that the quantity (V-U>)h is constant and uniform, and equal to zero if there exists a point at which h goes to zero (contact line). Thus, in the lubrication approximation, one has everywhere

< U >= V = - h 2 3η ∂ ∂x (-γh xx ) (B-2)
where the term γh xx represents the capillary pressure excess linked to curvature, whose gradient drives the fluid motion. This leads to the well-known equation:

h xxx = 3Ca h 2 (B-3)
in which Ca designates the capillary number, i.e. Ca=ηV/γ. Instead of seeking for h(x), it is simpler to seek, following Voïnov, for a first integral [14], i. e. to seek for θ≈h x =f(h) where θ is the local slope of the profile, which, after noting that ∂/∂x=θ∂/∂h, leads to:

3Ca h 2 = θ ∂ ∂h θ ∂ ∂h θ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ≈ ∂ ∂h θ 2 ∂ ∂h θ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ (B-4)
where the second equation holds for Ca not too large. This finally leads to a Logarithmic solution, when the curvature at large-scale ∂θ/∂x is supposed to be negligible:

θ 3 (h) = θ 3 (a) -9CaLog(h / a) (B-5)
If we select now the reference scale a, as a very small thickness below which some free slip will occur, one can consider that viscous stresses will be inefficient to affect the contact angle selection at very small scale. θ(a) will reduce to some static equilibrium value i. e. θ(a) =θ e that , for simplicity, is identified to the static receding contact angle on fig. 2-c. In fact, it is possible to be more rigorous with the slip length concept. If one assumes a Navier boundary condition on the solid instead of U(y=0)=0:

λ ∂U ∂y = U for y = 0 (B-6)
it is easy to show that eqs. (B-4) will reduce to:

∂ ∂h θ 2 ∂ ∂h θ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ≈ θ ∂ ∂h θ ∂ ∂h θ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = 3Ca h 2 + 3λh (B-7)
The same process of integration as above gives now:

θ 3 (h) = θ e 3 + 9Ca Log 1+ h 3λ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ + h 3λ Log 1+ 3λ h ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ (B-8)
In the limit h>>λ, this expression reduces to:

θ 3 (h) = θ e 3 -9CaLog he 3λ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ (B-9)
in which e≈2.732… is the well-known exponential constant. This expression is completely consistent with eq. B-7 , with a = 3λ/e and allows us to establish some bridge more recent versions of Voïnov description [4,48]. Rather close to the contact line, one can assume that h≈xθ e , which allows us to have an approximate expression for the x-dependence of θ:

θ 3 (x) ≈ θ e 3 -9CaLog e 3λ xθ e ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ (B-10)
which exactly coincides with Eggers formula [48] at leading order upon Ca. Note that the advancing case can be deduced from above by changing V into -V, which gives here:

θ 3 (x) ≈ θ e 3 + 9CaLog e 3λ xθ e ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ (B-11)
More generally, in all the above formula -Ca can be replaced with +Ca , while one replaces also when necessary, the receding static angle θ r with the advancing static angle θ a . Finally all this shows that this approach leads to an apparent contact angle at a macroscopic scale b given by: θ 3 (b) ≈ θ e 3 ± 9CaLog b / a ( )

(B-12)

Fig. 1 :

 1 Fig. 1: (a) Top and side views of a silicon oil drop sliding down a inclined plane (from le Grand et al. [7]), under partial wetting conditions; (b) magnified vision of the cone tip at the drop rear, rounded at small scale R=1/κ r (from Peters et al. [10]); (c) notations used here.

Fig. 2 :

 2 Fig. 2: (a) Typical shapes observed for silicon oil drops sliding down a plane under partial wetting conditions, Ca increasing from left to right (Peters et al[10]), (b) similar shapes observed for water drops maintained static on a glass turning table(Winkels et al. [11]); (c) dynamic contact angle observed for both experiments (SD silicon oil sliding drops, TT turning table measurements with water) at the dewetting front, fitted by eq.(9), and followed at larger Ca by the cone angle defined in a vertical plane[11]; (d) Cone angle viewed from above as a function of the capillary number for both situations, compared to the theory[11], a being replaced with a' for water (TT); (e) check of eq. (1) for silicon oils (from Snoeijer et al[8]), (f) check of eq. (1) for water(Winkels et al [11], TT). Eq.(3) corresponds to the dotted line on both figures, the continuous line being a better numerical approximate (but not analytical) obtained in refs.[8,13]. The agreement with hydrodynamics, possibly combined with a extra line friction is good, except for two things: a noticeable departure for water (TT curve) on fig.2-d, possibly linked to the breakdown of the slender approximate for the cone, and a certain irreproducibility of data for silicon oil (second trace on fig 2-f, SD, still unexplained).

Fig. 3 :

 3 Fig. 3: (a) Pictures of the corner tip obtained for increasing capillary numbers by Twente team (Winkels et al,[11]) , (b) divergence of tip curvature normalized by its initial value, (c) same as (b), to test the equivalent of eq. (7) in ref.[11] (pictures and curves extracted from Winkels et al, ref .[11])

This week dependence is negligible compared to the strength of the exp[θ r 3 /(9Ca)] diverging central term, when Ca is progressively reduced, but should be taken into account in a more advanced modelling.

Acknowledgments: I thank T. Blake, P. Colinet, C. Colosqui, A. Daerr, M. Riepen, M. Roché, J. Snoeijer, K. Winkels, for exchanges and discussions. This paper has also greatly benefited from a stay in University of Mons, and discussions with J. de Coninck.

where b is the macroscopic scale considered and a is some microscopic scale below which slip occurs, both being defined in the y-direction, rather.

Appendix C.

Introduction of an extra line friction in Voïnov approach: towards "combined models".

The point of view developed in Apendix B is not the sole possible, even from a hydrodynamical perspective. Instead of considering a "free slip" at small scale, one can imagine that viscous stresses are on the contrary replaced by a strong, non zero friction of microscopic origin, linked to some mechanisms that can be very diverse. It can be adsorption/desorption molecules on the solid [2-3, 21, 38-39], or pinning/depinning of the contact line by very small defects of the solid surface [4,22]. The simplest idea, in this case, is to introduce some line friction ζ representative of these mechanisms, the local contact angle at very small-scale θ m resulting from a balance between capillarity and friction:

This line friction can be calculated in the framework of molecular kinetic models [21], which finally leads to a value proportional to the fluid viscosity [START_REF] Duvivier | Comportement de gouttes de mélange en situation de mouillage extrème[END_REF][39], with some prefactor depending upon the adhesion parameter, but the concept is here more general. One can assume very generally a line friction representative of microscopic effects, even without a precise knowledge of these ones, and develop calculations on this sole basis [40].

To reconnect with Voinov model, one can assume that large scale hydrodynamics have to match with his microscopic situation at some microscopic scale called again "a", which finally yields:

with A =2ζ/η as used in (4-a) and (4-b) in a direction perpendicular to the contact line. This idea is the point of departure of what is often called "combined models" of wetting dynamics as initially proposed by Petrov and Petrov [23], that we tried to use in the present paper for the cone structure formation in dewetting experiments.


Giuseppe Longo

Information, science and democracy, for an ethics of scientific knowledge 1

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

notions or properties that can be transferred from one context to another, while preserving that which matters. In both cases, typically, the characteristics of information do not depend neither on the code chosen (apart from the negligible price of coding, be it by 0s and 1s or by numbers from 0-9 or any other sequence of signs) nor on the material support: one can elaborate information on transistors, chips, silicon, and can transmit signals by wires, drums, smoke... This ancient invention, formalized in a revolutionary manner by Turing in 1936 and by Shannon in 1948, has enabled us to distinguish between software and hardware and to propose an autonomous theory of programming, i.e. of elaboration of information, or of transmission of information (Shannon) -both independent of the specific coding and of the material support (the hardware), a fantastic theoretical and practical feat. In Manchester, in 2012, at a conference marking 100 years from the birth of Turing, the students constructed a Turing Machine (1936), the mathematical prototype of modern computers... out of Legos. This machine worked, although of course a little bit slowly.... More precisely, in the 1930s, Gödel, Church, Turing ... each of these mathematicians gave his own, very different definition of the notion of "computable function"-these turned out to be all equivalent. In short, a function is computable when it can be described by an algorithm -a set of instruction or formal rules in a sufficiently powerful language. The consequence of that nonobvious equivalence results is that this notion does not even depend on a formal language or system of calculation used. Independence or invariance of a notion, typically from the formal system used, the coding and the material support, it is the force and the scientific relevance, in particular, of the notions of information and program.

-Mysticism and Scientism

As it often happens, the mystics have taken the beautiful mathematical invariance in the two theories of information as an absolute and have applied it to all phenomena, including natural ones. Thus, when one of the leaders of the Human Genome Project writes that, soon, we will be able to transfer genetic information on a compact disk and claim/assert "Here is a human being, this is me!" (Gilbert 1992), he applies the distinction between software and hardware, fundamental in computer sciences but catastrophic when it is about understanding the living. Gilbert's statement, a rather common attitude in molecular biology, betrays an alphanumerical, linguistic vision of biology as just an analysis of software, independent of coding, of its material realization and, of course, even physical dimensions -in discrete data types, phenomena in any finite physical dimension be encoded in one dimension, a string of 0s and 1s. This "linguistic" approach is very well described by François Jacob and Jacques Monod, two great scientists, protagonists of molecular biology, rare among those who have made explicit a broad theoretical reflection on the subject: "The surprise is that genetic specificity is written out, not with ideograms like in Chinese, but with an alphabet" (F. Jacob, opening lecture, Collège de France, May 1965).

All this would reassure us that God is on our side, as confirms Francis Collins, director of the National Human Genome Research Institute, in June 2000, publicly announcing the decoding of five human genomes together with Venter, Clinton and Blair: "we have caught the first glimpse of our own instruction book, previously known only to God". Mysticism and theology, or researchers' enthusiasm about an extraordinary technical performance? Which philosophy and which practice of biology are they proposing? Which vision of the human?

It is firstly the sense of radical materiality of life that one loses, that within which one cannot distinguish the software and the hardware: The living state of matter is made of this DNA, RNA, only, of these membranes and their physics-chemistry and of nothing else …. Synthetic biology in fact transfers fragments of these from one to the other: The DNA or fragments of DNA in a membrane taken from another cell; it does not re-write neither transfer software onto another hardware, a practice common in computer science. When the colleagues from molecular biology will know how to transfer information and biological programs in a DNA on Lego and make a cell that works-then we will be able to affirm that they have finally "extracted" and separated information and instructions, the software of the living, written by God or not, from its hardware, in the mathematical and informational sense of the words. Are these only innocent metaphors? No: The characteristic of a metaphor is that it transfers and enriches the meaning of a theoretical proposition. In our case, it is a reference to commonsensical, vague, poorly defined notions of information and program (where is the operating system, the compiler in a cell? Which are the proper invariant properties of computing and information mentioned above?), but from which strong consequences have been derived, heavy weight onto knowledge, as it may be shown in reference to cancer research (Longo, 2018a). This is unacceptable in science, because this imposes a bias without rigorously specifying its origin and forces research onto tracks whose principles remain implicit, a form of "scientism" that affects science and trust in science. For example, as molecules, DNA in particular, are the obvious locus for discrete/digital coding of information, it follows that "everything is molecular", or even "everything is genetic", the most organized chemical structure in an organism. Thus, the claim that "any phenotype has a causal origin in the genotype", including, say, the gene for monogamous behavior (Nature, 1999), as, for many, genes should broadly encode also behavioral information [START_REF] Plomin | BLUEPRINT How DNA makes us who we are[END_REF] 2 . Instead, DNA is the extraordinary physico-chemical trace of Evolution, a fundamental constraint in ontophylogenesis, as I will hint below.

-Strong consequences from vague hypotheses

As for an analogy, the genocentric/informational approach in biology strictly parallels the geocentric approach to the Universe. They are both based on commons sense: Everybody knows what information and programs are, as it is evident that the Earth does not move … Then, from both vague "evidences", complicated theories and strong consequences have been derived, based on ad hoc epicycles on top of epicycles for every planet, genes controlling gene expression for every phenotype. Science instead is made by putting forward strong and rigorous hypotheses, which go against common sense, against the idea that the Sun raises on motionless Earth, that light travels along a Euclidian line, or that a measurement remains the same if one changes the order between position and momentum (the non-commutativity of quantum physics) ... From vague hypothesis on information and programs, which have for too long governed molecular biology, an understanding of how transmission and elaboration of information may work on macromolecules has been deduced. That is, the strong idea of the "Necessarily stereospecific molecular interactions explain the structure of the code ... a Boolean algebra, like in computers" (Monod, 1970) was derived. This prevented observing the stochastic character of these interactions, already known in physics-chemistry, whose probability depends on the context -the cell, the organism, the ecosystem -for a classic reference, see [START_REF] Elowitz | Stochastic Gene Expression in a Single Cell[END_REF] and for more references [START_REF] Bravi | The Unconventionality of Nature: Biology, from Noise to Functional Randomness[END_REF]. In this way, little attention has been payed to the possible role of endocrine disruptors of finite combinations of the 82,000 molecules that we have produced and thrown into the ecosystem in a little more than a century [START_REF] Diamanti-Kandarakis | Endocrine-disrupting chemicals: an Endocrine Society scientific statement[END_REF], as most of them are far from presenting exact affinities with bio-molecules. Yet, they do affect hormonal cascades as they modify the probabilities of interactions, in particular with cellular receptors. Or, they may even replace hormones, in low, but sufficient, probabilities due to lower chemical affinities or by changes of affinity constants due to modifications of the chemical context, [START_REF] Vandenberg | Hormones and endocrine-disrupting chemicals: low-dose effects and non-monotonic dose responses[END_REF]. Of course, stochastic macromolecular interactions and stochastic gene expression, in a cell, a tissue, an organism constraining those interactions, are incompatible with the current notions of information and program, their determinism and their focus on DNA, elaborating and transmitting information in the exact Boolean fashion we find in computers.

In this way, by affirming that "the organisms are simple vehicles of genetic information" (to take a 2002 reference text in molecular biology of evolution) in the service of the "selfish gene" (as in a popular philosophy), it has been believed, for example, that we could completely pilot the development of plants by genetically modifying them (GMOs). To be more precise, GMOs are the children of the "central dogma" of molecular biology (Crick, 1958), according to which information propagates from DNA to RNA to proteins in a one-way and linear manner (except for some retroactions RNA-DNA). To the contrary, today, we understand the strong interactive and retroactive eco-systemic effects, acting on a number of levels. For example, GMOs heavily affect the microbiome and roots' mushrooms, essential symbionts of plants. As a consequence, they gradually transform humus into a sort of sterile sand [START_REF] Bizzarri | The New Alchemist. The Risks of Genetic Modification[END_REF]. Again, the exact macromolecular interactions (stereo-specificity, the key-lock paradigm) were derived from the informational/programming myth, which justified or gave a pseudo-rigorous frame to the genocentered approach, against empirical evidence. And this is massively affecting our lives and, in many, the general trust in science.

When we speak of the consequences of this "programmatic/informational" and DNA-centered vision in cancer research, the organismal perspective in [START_REF] Sonnenschein | The society of cells: cancer and control of cell proliferation[END_REF]) may be an alternative reference. It was confronted by harsh criticisms for at least a decade. But a paradigm shift is taking place [START_REF] Baker | Recognizing Paradigm Instability in Theories of Carcinogenesis[END_REF]. Recent articles by leading researchers in the informational perspective acknowledge the failure of the search for the "signal" from the carcinogen "deprogramming" the genetic program. So, R. Weinberg, a biologist from the MIT, is among those working for long on search for genetic therapies for reprogramming DNA, promises made over and over since 1971, the beginning of "War on Cancer" by Nixon, and still today. In [START_REF] Weinberg | Coming Full Circle -form endless complexity to simplicity and back again[END_REF], he acknowledges the failure of the programming/informational, genocentered approach to cancer. Similarly, Gatenby, another leading personality in the field, in a 2017 paper in Radiology, acknowledges the little or absence of causal relation between DNA mutations and the various forms of cancer, see (Longo, 2018a) for this and more references. Where has information gone? Should it be just diluted in epigenetics? Ok, then one should define the invariant properties that make the sciences of information robust and that should be used in an epigenetic frame: is the proteome and its interactions that support the biologically relevant information? Or use another word and concept or another explicit theory.

But, careful: Molecular biology has given us an immense quantity of data and has shown evidence of fundamental mechanisms. It is extraordinary to see the experimental fineness and originality of methods that enabled Changeux, Jacob, Monod and Lwoff to discover the mechanism of chemical allostery and of the lactose operon, a regulation of the genetic expression by DNA itself. However, on the basis of the operon specific case, they leave aside the epigenetics, to say the least: genes regulate gene expressions… So, they do not cite Barbara McClintock, the first author to analyze the epigenetic regulation of gene expression. In fact, since the 1950s, the studies of major geneticists like McClintock and Waddington, suspected of "Lamarckism" (by giving a role to external influences on DNA), have been abandoned, for decades. They had always studied the chromosomes, an extremely important component of the cell, in a context: the proteome, the cell, the organism. Evelyn Fox-Keller tells this story in a book on Barbara McClintock. In this way, for decades, molecular biologists have researched regulators of genetic expression in DNA, assigning it the role of the complete informational description of an organism, like an Aristotelian humunculus, very small indeed, but completely codified in chromosomes and therefore "programmed" (yes, we are modern). On the contrarysome geneticists have known this for 60 years-every relevant molecular cascade, from DNA to RNA, to proteins, depend causally on the context and on its material, physico-chemical, realization. The activity of these macromolecules is context driven or used by the context -the cell, the tissue, the organism -in its irreducible tri-dimensionalty and materiality: No software as a mathematical invariant, no information as independent of coding, hardware, dimensions etc. And since several years we know that the individual cells, taken in small groups from cancerous tissues and transferred into healthy tissues take up normal function, without necessarily "reprogramming" their DNA.

-Randomness and bio-resonance

The concept of randomness in science is a delicate one. It is not an absolute. It depends on theories. It should be understood as the unpredictability with reference to the intended theory (Calude & Longo, 2016): it is what the theory shows/assumes to be unpredictable. In physics, classical and quantum dynamics propose two concepts of randomness, epistemologically and mathematically distinct. The first depends upon the joint role of non-linearity and of the physical measurement, namely upon the interactions in a dynamic and upon the access to the world given by measurement. A fluctuation/perturbation below measurement is the hidden cause of a phenomenon observable and measurable after some time -non-linearity may amplify the hidden fluctuation (Poincaré wrote in 1902: "and we then have a random phenomenon"). It is about a chaotic determinism of throwing dice, of a double pendulum or the solar system (luckily for us, in quite different temporal scales!). Quantum mechanics proposes another definition, which is intrinsic to the theory and starts from the indetermination (and non-commutativity) of measurement. Moreover, the phenomenon of "entanglement" distinguishes quantum randomness, mathematically, from the classical one. In biology, or at least in the cell, these two forms of randomness overlay each other. There is significant evidence of quantum phenomena with phenotypic effects [START_REF] Buiatti | Randomness and multilevel interactions in biology[END_REF]) and these may be amplified or dumped, according to the context, by classical phenomena. Moreover, the interaction of different levels of organization (molecules, tissues, organism) produces effects of bio-resonance, as we defined it, which may destabilize and stabilize an organism. But the most important thing is that this randomness, in biology, is not "noise" as in (Monod, 1970), a notion related to information, and like many claim still today [START_REF] Bravi | The Unconventionality of Nature: Biology, from Noise to Functional Randomness[END_REF]. It is instead an essential component of the variability, adaptability and diversity of the living and thus of its structural stability on the level of species, of populations and also in an organisms. They are all "more stable" when adaptive and diverse and this is partly due to the peculiar form of randomness one has to describe in biology, as we hinted above (for more about unpredictability in Evolution, see (Longo, 2016)).

To take an example, the immune system is a paradigm for the "functional generation" of randomness, essential to the stability and adaptability of an organism. But even an organ of such a uniform appearance such as the liver contains up to 50% of cells with a "wrong" number of chromosomes or with all kinds of mutations. By the diversity of enzymes' production, this contributes to the resilience of the organ (and the organism) to a variety of unforeseeable toxic shocks. These biological features have nothing to do with "noise" which destroys information. Instead, adaptability, exploration of diversity, changing niche constructions … are at the core of biological dynamics. They simultaneously modify organisms and ecosystems, phenotypes and functions, and therefore the "observables" themselves in the evolutionary processes. Following a fundamental chapter of Darwin's Origin of Species, organism's "correlated variations" and its "extreme sensitivity" to internal and external conditions make it, but also the ecosystem, a conceptual challenge that cannot be envisaged merely as elementary "stacking" of elements. Machines are constructed by stacking constitutive elements, ones on top of others: We construct them by association, assemblage of components, nuts and bolts, chips and bits, simple and elementary. Occasionally, some noise may affect the construction or its functioning. Also, computers and networks of computers are superpositions and a very complicated blend of simple and elementary components, which elaborate and transmit bits of information. In the natural sciences, on the contrary, it is not necessarily the case that the fundamental is elementary, nor that elements are simple. Galileo's or Einstein's theories are fundamental but do not concern the elementary, such as Democritus's atoms or quanta. Moreover, these last ones, as much as the cells that compose the elementary of the living, are not at all simple. But, even more crucially, a multi-cell organism is not made by adding tissue to it, by attaching organs to it, putting eyes in holes ... like in all machines. On the contrary, it is made by differentiation from one cell, a zygote, which is already an organism and which, at each cellular differentiation, keeps its organismal unity. There, we have an original complex object, a cell, which further complexifies by constructing a new unity by differentiation, and not a stacking of elementary and simple bricks, glued together. All this occurs in a permanent construction of diversity, radically unpredictable, during phylogenesis: organisms co-construct niches in changing ecosystems that "enable" them [START_REF] Longo | No entailing laws, but enablement in the evolution of the biosphere[END_REF]. The changing space of possibilities singles-out biological evolution from physical dynamics (Longo, 2016).

-Information everywhere, an abuse

Besides the reinforcement of reductionists approaches in biology due to the notion of digital, programmed/transmitted information, I do not see how that sort of analyses can be improved by saying that "information is everywhere". Which are the principles of this extended and even more vague notion? Is this a reference to the remarkable new field of "Geometry of information", a new mathematical area rigorously dealing with homotopy theory and continuous symmetries and their breaking (Barbaresco, Mohammad-Djafari 2015)? Instead, in an attempt to make the commonsensical reference to digital information more rigorous, Maynard-Smith, in a 1999 article we discuss in Perret-Longo's paper in [START_REF] Soto | From the century of the genome to the century of the organism: New theoretical approaches[END_REF], confuses, in the examples, Turing-Kolmogorof and Shannon-Brillouin dual approaches to entropy and complexity as amount of information on discrete data types -in one case they are covariant in the other contravariant. In [START_REF] Longo | Digital networks, knowledge and "political" biases in their understanding and use[END_REF], [START_REF] Longo | Information at the Threshold of Interpretation, Science as Human Construction of Sense[END_REF] and [START_REF] Montévil | Entropies and the Anthropocene crisis[END_REF], we tried to be more specific as for the use of delicate concepts such as negentropy, anti-entropy etc.. More generally, we do use, as humans, gradients (variations) of energy or matter to transmit and elaborate information (modulation of frequency, of electric flows, drums, smoke … switches). Gradients of flows, in organismal and cellular exchanges typically, are very important. The claim that one has information, in a natural phenomena, any time a gradient matters more than the quantity of a flow, is an amazing abuse. It is an anthropomorphic-magic projection on nature and it blurs more appropriate scientific analyses of the role and nature of those gradients, those flows and their specific material structure. "Information" is too important today, to be left to a vague reference to an un-specified notion and then diluted on nature: robust, well adjusted theories to empirical evidence should be given, in search for bridges, dualities, unifications …. These is how the remarkable theories of information mentioned above have been constructed, their relations are still to be fully developed. Physics, since Galileo's inertia (momentum conservation) keeps proposing new observables and pertinent parameters: Force, energy, entropy … new quantum observables. A change of scale forces a change of theory: Quanta, thermodynamics, hydrodynamics, Relativity … all incompatible theories. Unity is very difficult to achieve: Newton, Maxwell, Boltzmann and Einstein and no others proposed remarkable unificationseach a scientific revolution. A book by three physicists who work on the "borderline" of theories explains this beautifully, a review is in (Longo, 2016a). In which way, claiming that both atoms and planets exchange information would help in unifying the quantum and relativistic fields, an open issue since a century? Diversity of tools and concepts, presented with rigor and facing the variety of phenomena (and scales!), is at the core of the scientific knowledge we may trust: The endeavor towards unity is a further, very difficult achievement. Scientism, against the history and the practice of science, let many believe that science is the progressive "occupation" of reality with familiar tools and concepts, possibly just one -information for example. This is a way to claim the full control on nature, by handling information, like the information in the DNA of plants (the GMOs) or the incredible fuzz made on "genome editing". A fantastic discovery, the way some viruses modify DNA, has been transformed in financial support for actions on DNA, which result in plenty of uncontrolled side-effects [START_REF] Sikandar | Genome-Editing Technologies: Concept, Pros, and Cons of Various Genome-Editing Techniques and Bioethical Concerns for Clinical Application[END_REF]. These explorations can be a component of scientific work, what is wrong is its mythical handling and the resulting distortion of research and its funding by phantasmagoric promises, see (Audédat 2015) for a survey. Finally, this hides a mechanistic view of nature, which should be controlled like our piecewise constructed machines, with no appreciation of the peculiar organismal unity and historical dynamics in animal, plants and ecosystems.

Besides "mechanisms", scientism also claims to understand and to govern the world by optimization methods. For example, the notion of "Human Resources", which analyzes work in the same way as it analyzes material resources, have been invented in the ex-USSR. Its aim was the optimization of all components of production, including human work, by the mathematical methods of "linear programming". This is how the modern idea of purely technical government is born, put in the hands of engineers of the soviet Gosplan; this is what we call, today, "governance". These methods have since found their place in our major private companies in the West and, then, also in the public and national sectors, from health to government. Shouldn't we have to govern them like we do govern (big) business? The government, should it be entrusted to the "best" entrepreneurs, like it was in Berlusconi's Italy, with a party as centralized and authoritarian as the worst Stalinist party of our democracies. Trump is a further example of this identification: Business governance rules government. This is how the circle closes. In the State Enterprise, Stalinist or neoliberal, scientism and governance blend wonderfully. Even the murdering effects may be compared: for one or two decades "only", instead of 70 years like in USSR, in Latin America neo-liberal governance has been accompanied by jailing, murders and torture ("it works!"), with the explicit economic counseling and guidance by Milton Friedman and the Chicago boys. So far, in our countries, the democratic components of the liberal tradition, Constitutions issuing from revolutions or anti-fascist resistance, allowed to restrain the authoritarian tendency of neo-liberal governance, so far.

Alain Supiot in his book Governance by Numbers (2017) more closely explains the difference between "governance" and government by law. The former is about an "objective" management, according to formal rules, potentially mechanizable, independent of all contexts. It uses methods of optimization, like in the "linear programming techniques" invented in URSS, yielding one single possible and optimal path, a "geodesic". Geodesics are produced also by the laws as equations of Walras equilibrium economy: These spontaneously determine a unique possible paths, an optimal one -societies have just to follow it. To the contrary, the law of man, the "government", is motivated by its social or human meaning, when first discussed in the agora, in the moment of its being voted, and afterwards, when it is interpreted by a government or a judge who apply it in their domains, who give it a possibly new contextual sense.

In fact, the term "natural law" has been historically articulated into the "law of man" (and of the gods) in a very interesting way. In different cultures, it is interpreted in very different ways (Longo 2017). The formal rule, based on numeric or formal writing, is instead manageable by automatisms independent of interpretative ambiguities, of which we make in the best case a "fine tuning". Governance may be largely implemented by machines elaborating information; it is claimed to be "objective". In the Merkel-Sarkozy agreements, for example, it is written that the punishment for the States that transgress the rules about the deficit will be implemented in an "automatic way", potentially mechanizable. But the essential question is that of democracy, that of law which has to be discussed and interpreted, which gives meaning to the life in a community, with the possibility of a real and organized disagreement: The analysis of Stalinism and of neo-liberalism, European or American is subordinated to it. So, similarly to the huge Soviet industrial conglomerates, Americans corporations, since the Securities and Trust Act of 1933, have the status of a medieval fiefdom or of a legal person, a State within the State.

When we talk about science, within large, once enlightened corporations, like in renaissance principalities, such as IBM, ATT-Bell Labs or Digital, with which I collaborated at the end of the 1980s, there were spaces of extraordinary freedom for research: Large groups of very diverse researchers could think freely, protected by the master/corporation, thanks to a long term, enlightened vision of industrial research. Apple, Google and Microsoft offer still today remnants of this, autonomous research centers with about a few dozens people free to think, but these are no longer hosts of hundreds of researchers who, until the beginning of the 1990s, explored all possible directions of American industry: research for immediate profit dominates. Apple and Google have begun with great innovative ideas, at the end of 70s and 80s, but today they mostly apply, in computer memories all more miniaturized, powerful and faster, about the same ideasor transfer and develop new ideas coming from public research, like the new Artificial Intelligence (the so called Deep Learning, a major technical innovation). When we talk of Microsoft, Roberto di Cosmo, professor of computer science in Paris, explains its growth in Planetary Hold-up, as a moment of disruption without research content in the 1980s. More generally, the significant reduction in industrial research in the past 20 years has been described by a number of authors, see [START_REF] Seno | Why the development engine broke down[END_REF], [START_REF] Rafols | Big Pharma, little science?: A bibliometric perspective on Big Pharma's R&D decline[END_REF], (Audedat 2015) and many others. It is one of the main consequences of the transformation of industrial property into a shareholders scheme, managed by universal managers, interchangeable, who have only to increase the value of a company's shareholders in a short or very short period of time. The permanent hype for new gadgets is transforming the public's trust in science: It is an instrument for advertising more than for knowledge construction. In this frame, note that the value of shares, in view of volatility and the evaluation of risks, is a matter of information, including on insurance assets, and on insurance based on information, far away from actual products and productivity. The continual flow of announcements of new technological applications manipulates this information and the associated shares values: It is at the heart stock market activities. This is the cultural hegemony that, in my view, dictates the universal role of the notion of information. No scientific argument nor evidence may be strong enough to oppose to a hegemony which is first economic and political.

As a matter of fact, all of this is of little help in facing the problems of our world's complexity: This requires first discussing the method and processes of research. Any research activity has its own method and concepts to be spelled out explicitly, as hinted above as for the notion of information, possibly on the grounds of an ethics: questioning one's own principles and motivations of knowledge, by making a "step aside", look at them at a distance. This requires giving oneself time to think, without knowing exactly where one is going, open to being judged, and severely so, in order to be hired, promoted, closely evaluated on the basis of one's past creative work, beginning with a PhD. Thesis work and so on, say, and not on promises. The computational governance of research by numbers, by "bibliometrics" typically, does not work either, nor financing (only) huge projects. Bibliometrics reinforces dominant fashions, kills diversity and critical thinking, an essential component of science and … democracy. The identification of democracy with the majority vote, disregarding the division of powers and the formation of alternative views, is a major danger in all our countries. It similarly endangers science by the "vote of the majority" of all colleagues on Earth, counted by the number of quotations, by machines searches on Internet, in the short term (the impact factor concerns at latest two or five years from publication, which is nothing in fundamental science). If we do not appreciate the risky and isolated exploration of new paths, by analyzing contents, and we do not respect the ethics of individual or team research, the passion for knowledge, no institutional engineering will allow us to correctly evaluate our activity, nor to finance scientific projects, which is also necessary; big problems of the ecosystem, for example, would really need it.... But if we do only Big Science, we kill science: No project whose final application is told in advance can never be very innovative. The real novelty, even technical, is always achieved from research that does not imagine it -and often long after or as an indirect finding.

-Following the mechanical rule vs. the imagination of configurations of sense

We are confronted by an important crossroads: extraordinary instruments of interaction and exchange of information can enrich our knowledge and our scientific practices, or they can be employed to normalize us and to make us "follow the rules", to render us all homogeneous. Networks put everyone in an unprecedented position of being able to meet at a distance, of accessing the knowledge of all of humanity in its diversity. The exchange of cultures, ideas, objects, was at the heart of major moments in our history, such as ancient Greece and Renaissance Italy, to mention only two examples. But with this new speed of interaction we could do much better. Or, to the contrary, information networks can be used like "average fields" in physics: With too many neighbors, there are no more singularities, we cannot any more have individuality, we become all grey. We have discussed above the monochromatic images of the world of this type: DNA, the brain, human law, they are all seen as sets of formal rules, instructions and programs, of the same type, like in computers, but enriched -in the best caseby some network "noise". An instrument, a computer, an excellent assistive tool used by science to understand the world, in mathematical modeling for example, may also be employed to flatten the world, or, worse, to be identified with the world, a new, common sense of mechanicity. It happens that it also organizes our activities, by computational evaluations of work, bibliometrics being only one example. Rigid medical protocols are yet another terrifying example, as sets of formal instructions. This is the world of pure information, elaborated and transmitted by machines, with no interpretation, nor material body, the flesh at the origin of meaning. Living organisms are always acting, moving, in a protensive gesture: They interpret by this any "friction" on the world, any hit arriving -this is the bodily and material origin of meaning.

The modes of life are profoundly changed by the "everything is information" approaches. We are constantly under the pressure of computing devices that, as many promised since the 1960s, were going to replace man in everything. This was the dream of Classical Artificial intelligence (AI), based on deductive machines, that is on Turing's Logical Computing Machine, as he called it, but well beyond Turing's lucid analysis, (Longo 2018b). Yet, today, the paradigm has changed: The connectionist approach, based on continuous deformations of multi-layer neural nets ("Deep Learning") prevailed, far away from the old "deductive" AI. It is no longer an "imitation" of human intelligence, in Turing's sense (his 1950 paper on the Imitation Game), but a tentative "model" of the morpho-dynamics of the brain -that is of changes of forms, including electric variations and wiring, a model that may implement a highly simplified "learning" process. This is a much more effective approach, much closer to the way animal brains may seem to work. So, not a day passes without hearing: "Attention, do accept no matter which working condition, accept to lose your rights because if not, you will be replaced by machines!" -a voluntary construction of a collective imaginary. This substitution already started since decades, and it continues to happen in offices, and above all, in production chains, since the '70s, in storage centers, today, thanks to old style digital control machines -that is to say in professions which require reiteration of identical gestures -the original competence of the digital, Turing-like, machine. Since then, we observe a construction of an imaginary adapted to the subordination to the rules, to mechanical evaluation, to the governance which replaces the government, as observed above. Because also the neural nets machines just elaborate information, as they also are input-output devices. They somehow model the brain, somehow learn, but they are remote shadows of an actual animal brain. This is an always active organ, whose "default" state is a chaotic dynamics. In absence of sensations and perceptions, for example by torturing someone by complete silence, immersed in body-temperature water, in the dark, the brain gets "crazy", its activity goes out of control. The brain is not an input-output machine, but an always super-active organ, constrained by a changing context. Its continual activity is canalized by and works only in its preferred ecosystem: The skull of an animal as part of a sensing body in an ecosystem -and in history, as for humans. Its material flesh, the only one we can witness, is essential for this.

Intelligence is not just "elaboration of information", but it is first production of sense, within a biological and historical body in an active friction with the world. Our humanity probably started when we singled-out by interpolation and named non-existing forms of stars' constellations and thus gave "meaning" to the non-sense of the little lights in the sky. Or, when we interpreted phenomena by inventing and naming ancestors and gods, by establishing the law, very differently in different communities. This is not elaboration of information but the "imagination of new configurations of sense", in the stars, in the human community. Our specific, material body and its gestures, in a common history of the communicating community, are essential to this. And these invention are often historical: only the Greek geometers, say, invented the "line with no thickness" (Euclid's definition beta). An abstraction from movement, a trajectory, the invention of the notion of border, which originated the a-logos of the diagonal or the infinity of the Greek π. The extraordinary Nine Chapters of the Chinese geometer Lu Hui, III century, do not imagine this limit construction: The construction of mathematical sense then took a different path. This what I mean by a "historical formation of sense", its reduction to "elaboration of information" is a parody of knowledge construction.

Today, when we speak of constant novelty, certainly, we are surrounded by a million of new fantastic gadgets exchanging bits and bytes of information, but publicity on this matter is often more important than scientific innovation, as hinted above. If you read newspapers from the end of 1990s, you will find similar announcements to those of today's Self-Driving Car ... and what has become of the Google Glass in the past two years? It was presented as a revolutionary way to elaborate visual information ... So many promises are continually formulated whose realization ends up as gadgets that decorate our cars, typically. In Pittsburg (PA, USA), a couple of years ago, Uber has launched a big project of driverless taxis, driven by robots that elaborate input information. For the moment, they declare that there will still be an "employee" in the vehicleas the experiment has been a major failure. Is it possible that such a smart company that earns so much money by just selling information, with no "hardware" (no cars' ownership), is wrong? But no, the primary objective is the increase, in short term, of stock market value of the concerned companies, by the effect of advertising. As for driving automation, we will perhaps channel, by means of electronic tracks, the driving done by robots and humans as well, so that their coexistence on the road can be possible. As long as we are channeled as car drivers, it is great. But the myth of mechanization, by all kinds of algorithms from genetics to evaluation, the necessity of interacting by subordination to machines elaborating digital information -at first theoretical, conceptual and then practical, can have as a goal or as an effect to completely channel our human and social behavior. The too much computational modeling of various forms of "meteorology of social dynamics" seem to go in the same direction: Social information is extracted for the historical context and elaborated by optimization techniques -more than a botched analysis, it seems a method for guidance.

-Spurious

Correlations and non-sense in Big Data. Taking a step aside. This is the social pressure underlying and justifying the "everything is information" myth. The reduction of human activities and intelligence to "elaboration/transmission of information" by input-output devices continually compares human activities to machines, a fantastic tool when soundly used, but often overestimated in their performances and presented as threatening the human intellect. The worst example is perhaps the new fashion of un-scientific Data Mining on Big Data, as immense reservoirs of information. Big Data and their sound statistical analysis are an opportunity without precedent if they are used to produce hypotheses, to (in-)validate theories and to propose new ones. But, to the contrary, and in a truly viral manner, some think today that we can optimize thought, by reducing it to zero: sufficiently powerful algorithms could in the end "replace scientific knowledge" (sic!). This is supposed to predict all kinds of dynamics and to direct action, without the need of a hypothesis, a theory or knowledge. The bigger a database, yotta of yotta bites, the more, they claim, we can avoid thinking: "machines will discern regularities that the science does not see", but which are sufficient to predict and act [START_REF] Anderson | The End of Theory: The Data Deluge Makes the Scientific Method Obsolete[END_REF]. "We kill based on Data Mining on metadata" declared the former CIA director, M. Hayden, in a debate ( https://www.youtube.com/watch?v=UdQiz0Vavmc ).

Luckily, mathematics allows to demonstrate the absurdity of these perspectives. In (Calude & Longo, 2016a), by a simple application of classical, not trivial results, we pointed out the "Deluge of Spurious Correlations in Big Data". In short, for any given "correlation between numbers", one can compute a number of elements, let's say m, such that any set of data (of numbers) having at least m elements satisfies the pre-given correlation. It is therefore also the case for a set of numbers, a database, produced by a random process, by throwing of dice or quantum measurements: The correlation will appear there as well and will then be "spurious", because it occurs by chance. In other words, the presence of correlations may only depend on the size of the database and do not grant themselves in any case prediction nor taking action. In this way, in order not to think, these authors of algorithms who say they in principle ignore theories, including the ergodic theory, theories of algorithms and of finite combinatorics, that we applied for our result, are confronted with internal limits demonstrated by and within these theories: Spurious correlations inevitably infiltrates very large sets of numbers. This makes any kind of prediction risky when this one is not based on a thought that gives meaning and that enables us to choose what counts, beginning with the choice of what and how to measure and thus to associate it to a number. This thought is necessary to understand and theorize and, if possible, predict. Moreover, the power of scientific knowledge resides also in the fact of revealing the limits of the intended theory; this helps in better understanding, delimiting but also reinforcing the perspective that enables us to do science. Those who pretend to understand everything and to be able to make everything from a single object or concept, such as the DNA in biology or information, algorithms in all sciences ... they are certainly wrong. But I insist: the DNA, information, algorithms... are all very important, the science around them is essential. The former is a fundamental chemo-physical trace of evolution, continuously employed by cells in order to produce proteins, largely using the Brownian motion of the proteome, which is the first functional random dynamics in biology. The latter, the algorithms, are about to change our lives, potentially for the better, if we keep in mind the limitations of any monomaniacal approach to knowledge [START_REF] Longo | On the Relevance of Negative Results[END_REF](Longo, , 2018)).

In this "everything is information" or even "instructions and formal rules" craze, with the peak in the use of Big Data with no meaning, many often make reference to Alan Turing, inventor of the Logical Computing Machine (1936) -the mathematical foundation of computers -but with a dangerously incorrect interpretation of his work, see (Longo 2018b). We need to go beyond a collective imaginary in order to think the "next machine", just as Turing was able to show the falsity of common hypotheses by his result of "non-computability". In fact, between us, this digital machine and its powerful networks are perhaps a little boring, with their always identical iterations: If one initiates over and over a digital simulation of the wildest turbulence, with the same initial data, or if one opens a web page in Japan, they are always the same. But when faced with a non-linear physical dynamics such as a hurricane or a linguistic structure, all this is suddenly meaningless because no hurricane or human being will ever repeat anything identically. When digital information is networked, the sophisticated methods of "interleaving" and "semaphores" render the randomness, proper to the spatial-temporal continuum and of networks, ineffective. This randomness is considered as a "do not care", as the experts-the real onessay. In the areas of concurrency and network analyses in computer science, experts are able to make them function with computational certainty, according to the rules, eliminating noise. In fact, against computing's common-sense view, which belongs more to molecular biology and to formally regulated governance, computer science today analyses and makes large use of randomness, including in continua, by stochastic calculus, analyses of networks dynamics, in techniques of coding, although in a way different from biology. Networks' noise is thus analyzed and used in a very useful way, in cryptography for example. Yet, this has nothing to do with evolutionary "bricolage" of rare events, the unpredictable changes of the phase space (the space of observable and pertinent parameters), which are proper to biological dynamics and functional to them (Longo, 2016). The historical processes in natural and human sciences as well, economics in particular, require a different insight far away from the analysis by and the imposition of the optimal path in pre-given spaces of possibilities, see [START_REF] Koppl | Economics for a creative world[END_REF].

It is the job of science to single-out the role of diversity of the human within the human, starting from the biological. Evolutionary diversity and adaptability is the result of the unexpected variant, the "hopeful monster" that is not noise which needs to be removed, like in information theories, or averaged out as in stochastic approaches, but it is that which makes life possible, according to Darwin's great intuition. This may also allow us to better use this fantastic discrete state machine for the elaboration of information, and its networks, and to invent new machines. Human beings will certainly invent yet another machine, if we do not identify this one and its algorithms for elaborating information with the world, if we abandon the necessity to work in the same computational modalities, evaluated, or with our actions predicted, by normalizing techniques without thought, like in the science handled by Big Data and bibliometrics. Making the founding principle explicit, in order to re-think them critically, is at the core of the scientific approach and its ethics. Science is not "elaboration of information", even less the extrapolation from Big Data, but a historical construction of sense of the world, by a continual invention of new concepts and structures. In order to trust science, its ethics requires a critique of one's own principles of knowledge, making a "step aside", understanding different viewpoints. A good scientific practice is a major democratic training by this critical attitude, while contributing to democracy also by knowledge construction. It may only be the result of a difficult dialogue between remote or contrasting perspectives, a collaboration between different knowing subjects, based on ideas that may be unlikely but must be profound, proposed by small groups of thinkers who see things differently. Disagreement and diversity are not noise to be eliminated by the absolute dominance of the majority vote, such as the short term quotations in bibliometrics. They are instead at the core of science, since its invention by the democratic and the scientific debate on the Greek Agora. To do science, we need democracy, and science is an essential component of democracy, the only way to trust both.

Extended and revised synthesis of an interview by P. Bartolini in Italian (ROARS, september

2016), translated into English by M.R. Doyle and S. Savic. In A. Fabris (ed.), Trust, Studies in Applied Philosophy, Epistemology and Rational Ethics 54, Springer 2020.

Unfortunately, these simplistic views of genetic determination reach the general public: " Being Rich and Successful Is in Your DNA" (Guardian, July 12, 2018); "A New Genetic Test Could Help Determine Children's Success" (Newsweek, July 10, 2018); ''Our 'Fortunetelling Genes' make us''(Wall Street Journal, Nov. 16, 2018).


Thinking beyond

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

Thinking beyond the "epidemic of epidemics"1

Giuseppe Longo

Centre Cavaillès, CNRS et Ens, Paris and School of Medicine, Tufts University, Boston http://www.di.ens.fr/users/longo/ One of the major challenges of any historical science is the role of forecasting. Biology is a historical science, because organisms can only be understood in a temporal, phylogenetic and ontogenetic, perspective.

In particular, the time of biology, and therefore of correlated sciences (ecology etc.), is a time of change in the "space of possibilities" (of "phases" as we say in physics, of ecosystems and species in biology), punctuated by rare events -evolutionary novelties, speciation. In physics, the space (of phases) is fixed as "a priori" of knowledge, as "condition of possibility" for "writing equations", explain Newton and Kant: it a priori contains all possible trajectories -unpredictability is within these trajectories (the randomness of a die concerns six possibilities, no more, no less). In biology, to physical randomness is added the unpredictability of changes of the space of possibilities and of rare events, to which one cannot even assign probability values, see (1). The historian of human affairs will recognize there elements of his theorization, although, of course, symbolic culture, in all its forms, imposes an important change in the tools of analysis.

Faced with the intrinsic unpredictability of the history of the living, should we remain silent? No, science is not (or not only) the analytical game of "experience/observation, theory, prediction, verification/ falsification", but first of all a construction of objectivity, or even objects of knowledge, through difficult operations of "carving-out" (separating/distinguishing) and "qualification" of reality. This is how Darwinian theory offers us a remarkable historical theory of the living, of "species", a notion that is constantly being recarved-out and re-qualified. This theory does not allow us to predict, but, by making us understand, it allows us to act, if we assume the risk of relying on the best available knowledge. We then decide to measure "biodiversity", an admittedly arbitrary partition of species and life forms, which is always open to discussion and revision; to assess the impact of man on an ecosystem, a difficult qualification of the consequences of activities that are sometimes centuries old. We can also give ourselves a measure of the notion of 'epidemic' and draw the historical diagram shown here (''The Evolution of the number of epidemics of infectious diseases in the world from 1950 to 2010'').

Partial and revisable knowledge: is it enough to act? Yes, it is. Since the 1990s, many epidemiologists have been warning us: the notion of "epidemic of epidemics" dates back to 1993 and this 2015 diagram shows it to us. The reasons are well described in (2): some cases may be due to a synthetic biology that claims to be all-powerful and let us believe that we can fully control living organisms by modifying (''editing'') their DNA/RNA, but more than 70% of these emerging infectious diseases come from animals, at new interfaces with the environment. Deforestation for agricultural settlement accompanied by intensive livestock farming enables the passage of bacteria and viruses from wild animals to livestock and then to humans. None of these cases and microorganisms were individually predictable, and none will be in the future: they and their causes are known a posteriori.

The self-serving denial of the history of life, of the evolutionary construction of ecosystems, of their specificity and diversity, is the main cause of the activities that destroy them. Often this denial finds its justification in a new scientism, which rules our science: on the one hand, the spontaneity of the man/economy/nature dynamics would choose the best possible path -a misuse of the mathematics for the equilibrium physics of the 19th century; on the other hand, nature itself would be an adjustable, even programmable machine, with disposable material and biological "resources". A new awareness and a science of these phenomena is being built, change is possible: the knowledge of a history, as in the diagram above, and a vision of organisms in their autonomy and their dependence on the ecosystem make it possible to act.

(1) Longo G. 2020. Naturalizing Physics. To appear : https://www.di.ens.fr/users/longo/files/NaturPhysics.pdf

(2) Morand S., Figuié M. (coord.) 2015. Émergence de maladies infectieuses. Éditions Quae https://www.quae.com/produit/1365/9782759224920/emergence-de-maladies-infectieuses

A paraître dans "Penser l'épidémie Covid-19 autrement", Institut d'Etudes Avancées de Nantes,

(in French).