Historicity at the Heart of Biology Maël Montévil

Historicity at the heart of biology Maël Montévil

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Maël Montévil. Historicity at the heart of biology. Theorie in den Biowissenschaften / Theory in Biosciences, Springer Verlag, 2020, 10.1007/s12064-020-00320-8. hal-02398755v2

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Maël Montévil* July 3, 2020

Abstract implicitly or explicitly. The reasoning is predom- inantly anhistorical in physics. However, some Most mathematical modeling in biology relies ei- classes of phenomena are radically historical. It ther implicitly or explicitly on the epistemology is the case in evolutionary biology and most hu- of physics. The underlying conception is that the man and social sciences such as linguistics or eco- historicity of biological objects would not mat- nomics. ter to understand a situation here and now, or, at Why is physics fundamentally anhistorical? least, historicity would not impact the method of Physics studies phenomena by static equations, modeling. We analyze that it is not the case with they stem from the older notion of the laws of concrete examples. Historicity forces a conceptual nature. In models, the changes of an object are reconfiguration where equations no longer play changes of position in a theoretical space, for ex- a central role. We argue that all observations de- ample, the space of positions and velocities in clas- pend on objects defined by their historical origin sical mechanics. These changes derive from the instead of their relations as in physics. Therefore, equations. In other words, change stems from an we propose that biological variations and historic- underlying invariance. In historical phenomena, ity come first, and regularities are constraints with the ability to find such invariance at any level is limited validity in biology. Their proper theoreti- doubtful. cal and empirical use requires specific rationales. In this discussion, we describe physics by its method: physics has a specific use of mathematics keywords: Historicity, Organization, Episte- to understand phenomena. However, there are mology, Mathematical modeling, Constraints other uses of the word that we want to review succinctly in order to avoid confusions and mis- understandings. Contents • First, physics can refer to the theories of 1 The shadow of historicity on mathemat- physics such as quantum mechanics, statis- ical models 2 tical mechanics, or hydrodynamics. These theories are not genuinely reducible to one 2 Biological historicity takes another stab another. Nevertheless, they display a unity at physics epistemological principles 4 thanks to theoretical bridges. The Interna- tional System of Units is valid for all these 3 historicity shapes the observation of bi- theories and materializes this unity. ological matter 5 • Second, physics may also refer to the mathe- 4 A castling move on the epistemological matical apparatus of these theories and more board 8 broadly to the models of physics. Physi- 1 cists sometimes use these models to study other objects. For example, physicists describe flocks of birds with statistical mechan- Introduction ics. In their work, the elementary objects are birds and no longer molecules. From the per- For many scientists and philosophers, physics re- spective of the theories of physics, it is not mains the paradigm of scientific thinking, either indisputable that birds would behave similarly to molecules. Nevertheless, the strong *Institut de Recherche et d’Innovation, Centre Pompidou. points of this approach are that these mod- [email protected] els may have a broader generality than their 1Published as: Montévil, M. Historicity at the heart of biology. Theory Biosci. (2020). https://doi.org/10.1007/ use in the theories of physics and that these s12064-020-00320-8 mathematical apparatus are well known.

1 • Third, as mentioned above, physics can be the Let us remark that, in biology, historical pro- use of physics method to study phenomena. cesses are often conflated with evolution and evo- Physics does not stick to existing theories lution is often conflated with genetic changes. or mathematical structures to study the in- There are historical reasons for this. The ideaofa ert. Otherwise, theoretical physics would be genetic program is associated with determinism at a finished field of research. Assuming that the level of functional biology sensu Mayr, while this method would be adequate to study the evolution was seen as the determination of such living, there is no reason to assume that ex- programs, where randomness is central via muta- isting theories and models would themselves tions. The idea of a genetic program is no longer be adequate. widely accepted, and it follows that we can consider that development and physiology also are • Fourth, physics etymologically means the fundamentally historical processes. knowledge of nature, that is, phenomena that We can wonder, however, whether it is sound to do not involve humans. In the history of separate historical and current aspects of biologi- thoughts, nature became matter, and, in the cal phenomena or, on the opposite, whether they materialist tradition, the matter became ev- can be deeply entangled. Authors of the extended erything there is. Physics, in this sense, en- synthesis argue against such a separation (Laland compasses everything. However, even in this et al., 2011). The core argument is that evolution tradition, it does not follow that the method and development are far more entangled than pre- of physics enables us to understand all phe- viously thought. Historicity does not just manifest nomena. Accordingly, physics method has a on the long time scales of evolution. For example, special relationship with mathematics, but biological innovations also take place at the level this relationship does not need to be the of development and can be decisive for evolution. norm for all sciences. The issue can be analyzed in terms of time scale (Pocheville, 2010, 2019). The classical perspective • Last, physics has also an institutional dimen- assumes a separation between the time scale of sion. According to this perspective, physics evolution and life cycles. In this perspective, the is everything that is done in departments of evolutionary processes would be static at the level physics. In the latter case, we think that the of life cycles and, reciprocally, life cycles would use of the method of physics is a decisive be almost instantaneous when analyzing evolutive criterion of peer recognition. processes. Alternatively, the two-time scales can meet, and life cycles and evolutionary processes In the context of biology, the confusions be- would require a joint analysis. tween these differents meaning of physics tend to In this paper, we will criticize the analytic sep- bend theoretical and philosophical work by intro- aration between the study of a life form as it is ducing artificial epistemological norms or author- right now and the historical processes that origi- ity. In this article, we will discuss the articulation nate it. Prima facie, there is indeed no apparent of physics method with biology, and more specifi- reason why a phenomenon that stems from history cally, with the historicity of biological phenomena. could be mathematized by the same method than A classical perspective to articulate historical a spontaneous phenomenon. We do not think that and anhistorical reasoning stems from linguistic. it is the case for principled reasons (Longo et al., De Saussure (2011) stated that there are two ways 2012; Montévil et al., 2016; Montévil, 2019b). In to study languages. The synchronic perspective this paper, we will focus on practical situations studies the use of a language at a given time. By where the methodology of mathematization de- contrast, the diachronic perspective investigates parts from the usual physics method. the historical processes of language transforma- tions. Along the same line, in an influential article, Mayr (1961) distinguishes functional biology and evolutionary biology. The two biologies are con- 1 The shadow of historicity on cerned with distinct kinds of causes: proximal and mathematical models distal causes, respectively. In both cases, the idea is to study short time scales phenomena ahistorically, Reasoning on quantities is central to physics. on the one side, and the historical changes, on the However, reasoning on quantities does not mean other side. In biology, Newman (2012, 2019) pro- reasoning on particular values. Instead, physicists vides another perspective along this line. Newman work with generic variables. For example, let us argues that biological development is the combi- consider the case of free fall. To describe it, physi- nation of genes and physics. Genes would be the cists do not describe an object of mass 1.51푘푔 at carrier of the historical past, and physics provides the height of 2.14푚 and velocity 0.17푚푠−1. In- anhistorical laws recruited by genes. stead, they write equations for an object of mass

2 푚 at a height 푥 and vertical velocity 푣. Since the compatible with our existence (Friederich, 2018). height and velocity change over time, it is deci- This example shows that setting particular values sive that equations are valid for any value of the of the parameters cannot be done for free, and variables. explaining situations that do not correspond to Moreover, such values do not have any intrin- generic values of the parameters sometimes leads sic meaning; they depend on the arbitrary choice to rather ontologically costly hypotheses. of a reference frame. Objectivity requires to take However, in biology,in numerous cases, specific into account all possible reference frames, thus a values of external quantities are used in models collection of descriptions (Longo and Montévil, and are necessary to explain the intended behavior. 2014a). In a nutshell, physicomathematical rea- For example,Mora and Bialek (2011) argue that in soning is not about particular values; it is about many situations, biological systems seem “poised” generic variables and their relations. Equations at criticality. usually describe these relations. The underlying evolutionary history is used to However, equations are not the only element justify such tuning of the parameters. However, determining a situation. Parameters, initial condi- there is usually no investigation of the natural his- tions, and boundary conditions complement them tory per se. Instead, the modeler identifies that to entail trajectories. The equations do not de- specific values are required for the model to lead termine the value of such quantities; as a result, a functional configuration. For example, Lesne we will call them “external quantities” in this text. and Victor (2006) observe that a model of the Choosing arbitrarily the value of external quanti- chromatin leads to a functional configuration only ties can yield all kinds of patterns, and this move when the properties of two otherwise indepen- is not allowed in physics. Let us illustrate why dent molecules are equal. Similarly, modelers in with a simple dynamical system. Consider that ecology can use the fact that initial conditions are (푡) the value 푥 = 푥0.푥1푥2푥3... in decimal writing is not random but correspond to a viable configu- (푡+1) transformed into 푥 = 푥1.푥2푥3... at the next ration for all populations involved. This configu- time step. For the initial condition 휋 = 3.1415..., ration does not stem from a dynamic intrinsic to the integer part of the state will span the deci- the model but the underlying history (Jane et al., mals of 휋 one by one. However, this dynamical 2007). system has nothing to do with 휋 specifically. The In these cases, natural history justifies a specific link with 휋 stems only from the initial condition, configuration. However, in practice, this specific and different initial conditions would yield differ- configuration is not genuinely singled out by his- ent results. Actually, this dynamical system can torical reasoning. Instead, modelers find it be- produce all possible patterns of sequences of num- cause it leads to specific properties in the model. bers. As a result, the equation of the dynamics This line of reasoning can be pursued further by cannot genuinely explain why the system spans postulating that a quantity reaches an optimum specifically the decimal of 휋. in evolution because of its functional role. For Without additional hypotheses, such a dynam- example, modelers have assumed that evolution ical system can only explain the qualitative prop- has maximized the exchange surface of the lungs erties obtained for all possible initial conditions (West et al., 1997, 1999). or almost all initial conditions. “Almost all” is a These relatively simple cases and examples show mathematical notion. Let us assume a measure on that historicity interferes with the epistemology initial conditions, for example, based on probabili- of mathematical modeling. Tuning parameters ties or a metric. The properties valid for almost all and initial conditions can be allowed in biology initial conditions are valid for all initial conditions while it is forbidden in physics. However, we have except for a set of measure 0. For example, almost seen that choosing the value of external quanti- all real numbers are not integers, rational numbers, ties can yield unacceptable explanations; therefore, or 휋. modelers cannot do it freely. Let us analyze the Physicists consider that only generic values of corresponding reasoning more deeply. The central external quantities appear spontaneously. In cos- argument is that we can single out a specific con- mology, this fundamental epistemological point figuration by their corresponding function. At the leads to a troublesome situation: models do not level of the model, the specific configuration may lead to the formation of complex matter in the entail qualitatively distinct trajectories, or they can universe except for a narrow range of parameter be optimal without qualitative discontinuity. In values. Some theologians argue that this situa- both cases, understanding the situation requires a tion is evidence of intelligent design. In physics, a hypothesis on biological functions. This hypoth- popular way to justify this unlikely situation is to esis does not stem from the causal relationships assume there are universes with all possible values described in the model and requires analyses be- of the parameters, and we are in a universe that is yond its boundaries.

3 The theories and models of physics do not pro- By contrast, external quantities such as initial vide a theory of biological functions. It follows conditions and parameters are of secondary epis- that in many cases, modelers make functional as- temological importance. They stem from circum- sumptions on very informal bases. This situation stances, and their value is contingent to a large leads to a diversity of hypotheses, even in the case extent. As discussed above, since physicists usually of a single structure and function. For example, study the consequences of generic values of these lungs have a function of gas exchange; however, quantities, no specific hypothesis is required to the latter can be formalized in many ways (West justify them. We have seen that it is not always et al., 1999; Sapoval et al., 2001; Gheorghiu et al., the case in biology. This problem alone suggests 2005, for example). Moreover, in a model, the already that we should confer an equal or similar robustness of this function is not necessarily com- epistemological status to hypotheses concerning patible with its maximum efficiency (Mauroy et al., equations and external quantities. 2004). This example shows that assumptions on There are further reasons to argue for this biological functions require great care and a proper change in epistemological status. Since model- theorization. ers confer most of the epistemological weight to There are several philosophical interpretations equations, it follows that using a single equation of biological functions that may become starting to explain a diversity of phenomena is more parsi- points for such a theory. A trait may be functional monious in physics. in the sense that it has been selected because of its This logic is exported to biology. For example, consequences (Godfrey-Smith, 1994), or it may Zhu et al. (2010) aim to understand vertebrate be functional in the sense that it is maintained forelimbs morphogenesis. To this end, they use by a whole and contributes to maintaining this a single equation describing a system of reaction- whole (Mossio et al., 2009; Montévil and Mossio, diffusion. They show that this equation can leadto 2015). To be operational, the first concept of func- a diversity of configurations encountered in nature. tion requires a historical investigation. The second However, these configurations require a diversity concept of function is more systemic; the presence of hypotheses on external quantities. We are not of a function is justified when the trait contributes interested in discussing the validity of this model to maintaining another part of the organization per se. Since one of the authors argues that this but is also maintained actively. The origin of this method is general (Friederich, 2018), we assess situation remains historical. This concept of func- the general methodology of modelization and its tion cannot justify optimization; it can only justify epistemological validity. that a functional effect requires a specific config- Like in physics, let us consider that equations uration and that this configuration is plausible come first epistemologically. From this perspec- because processes maintain it. tive, this model is very parsimonious because it Let us sum this discussion up. In physics, it is subsumes a diversity of situations by a single equa- not possible to assume specific values of parame- tion. The use of a single equation carries heavy ters or initial conditions without justification. In epistemological weight. biology, there is a reason to use specific values of On the opposite, let us consider that hypothe- such quantities: natural history and organization, ses on equations and external quantities are on an that is to say, the presence of a function. equal epistemological footing. In this perspective, the model is not particularly parsimonious be- 2 Biological historicity takes cause many hypotheses on external quantities are required to explain the different forms observed. another stab at physics epis- This situation alone is not necessarily a problem. temological principles There is no way around the notion that natural history generates novelties that require specific In physics,equations play a central role. They build hypotheses (Montévil, 2019b). However, the sion the notion that permanence underlies changes: multaneous use of a single equation and a diversity equations do not change but enable physicists to of patterns for external variables is an oddity that understand objects’ changes. They materialize the may be acceptable in specific cases but is not a classical notion of natural laws, a central, tradi- sound general method. As a result, it does not tional aim of scientific inquiry. In modern terms, carry any epistemological weight; on the opposite, equations manifest fundamental invariants and it may very well be an artifact steming from the symmetries that are at the core of theories (Bailly inappropriate use of physics epistemology. and Longo, 2011; Longo and Montévil, 2014a). We think that the second perspective is the They also articulate different concepts. For exam- right one in biology. Let us examine further this ple, Einstein’s famous equation 퐸 = 푚푐2 articu- model of morphogenesis. In this model, equations lates energy and mass. describe interacting molecules and their diffusion

4 at a given developmental step. the problem is general in the study of living things (Montévil et al.,2016; Kauffman,2019), including • The equations require many assumptions to in human activities such as economy (Felin et al., be valid. For example, the organism produces 2014). the chemicals involved; a relatively homoge- In a nutshell, assigning epistemological primacy neous medium exists where they can diffuse, to equations introduces a bias in the analysis of and no other process interferes significantly, biological situations. When physics epistemology be it chemical, physical or biological (such as is applied to biology, equations are assumed to be cell differentiation). permanent while other components of modeling • Parameters describe the chemicals and also have to accommodate the historical changes of the structure of the tissue via diffusion coef- biological objects. These asymmetric roles do not ficients. Boundary conditions stem from the build on a theoretical or philosophical rationale. geometry of limbs over developmental time. This conception generates artifacts in the analysis of biological situations. In the previous section, we We argue that both kinds of assumptions have have seen that historicity pops out as a necessary fundamentally the same status. For example, as- component to assume specific external quantities. sumptions on the internal structure of the system However, from a general theoretical perspective, and assumptions on the geometry of the limb are the form of equations is no less the result of history very similar. All these properties stem from the than external quantities. previous stages of development and the underly- We have coined a concept of constraints to ad- ing evolutionary process. There is no principled dress this kind of issues. Constraints are regulari- reason to assume that the boundary conditions ties that are relevant to processes of transformation would be more labile than the equations them- (Montévil and Mossio, 2015; Soto et al., 2016). selves. For example, the recruitment of a new Constraints are not principled; they are only valid molecule in the diffusion process would be suf- at a given time scale and can be maintained ac- ficient to change the equations, and it is a likely tively. They can also change over time, and their change on evolutionary time scales. We conclude validity is contingent to an extent. This episte- that the distinction between assumptions about mological framework reinterprets the structure equations and external quantities is perspectival in of equations and external quantities of a typical biology; therefore, all theses hypothesis ultimately model. These structures are constraints or result have the same status. from constraints. Along the same line, there is no principled equa- At this point, another, similar bias appears that tion in biology. In more technical terms, let us stems from the epistemology of physics. In order recall that theoretical symmetries confer the form to fit the notion that equations do not change, of fundamental equations in physics and justify biophysicists focus on constraints that display the them. We have argued that there is no fundamen- highest stability. However, other constraints are tal symmetry in biology (Longo and Montévil, more specific and possibly also more plastic; and 2011; Longo et al., 2012; Longo and Montévil, they are also a fundamental part of biological or- 2014a; Montévil et al., 2016). Even in fields that ganizations. are mathematized such as population genetics, equations depend on the process of gene transmission from one generation to the next. How- ever, this process changed in many phyla in evolu- 3 historicity shapes the obser- tion. For example, chromosomes may be present vation of biological matter in only one or several versions, leading to haploidy, diploidy, tetraploidy, and so on. Sexual reproduc- In the theories of physics, objects are defined by tion appeared in various forms. Another example the mathematical structure that describes them is monozygotic polyembryony in organisms such (Bailly and Longo, 2011; Longo and Montévil, as armadillos (Dasypus novemcinctus): in layman 2014a; Montévil et al., 2016). For example, in terms, armadillos systematically give birth to true particle physics, particles such as electrons are de- quadruplets. fined and classified by equations describing their All these features appeared in evolution and im- behaviors, including characteristic quantities such pacted the form of equations of gene transmission. as the electrical charge. In a model, if a term fits Beyond these examples, in population genetics, the attributes of an electron, then it is an electron. the main difficulty lies in the determination offit- Reciprocally, if we are considering a real electron, ness since no computation can derive fitness from then it will follow the mathematical structure de- genotypes, and there cannot be such a computa- scribing electrons. tion since fitness is context-dependent. Ecology When physicists define a concrete phenomenon meets similar difficulties (Ulanowicz, 2009) and by mathematics, mathematicians and physicists

5 can work out the consequences of a situation in parameters. abstracto. They analyze equations on a piece ofpa- In biology, we have seen that equations are as per or work with a computer far from the concrete labile as external quantities a priori. More pre- phenomenon. The causal investigation is detached cisely, they both ultimately stem from constraints from the concrete phenomenon. Because of this that can change (Montévil et al., 2016). Therefore, separation, the equations can apply to another measurement is not just about obtaining quanti- concrete phenomenon. In this sense, the objects ties; measurement has to accommodate changing theorized by physics are generic, and we can ob- constraints (Montévil, 2019a). This situation leads tain the same generic theoretical phenomenon de to several challenges that the theorization of mea- novo. surement has to accommodate. For example, physicists study convection cells Constraints are both historical and contextual. and other phenomena of self-organization occur- They are historical because they stem from an evo- ring in inert matter. They display morphogenesis lutive and ontogenetic history. For example, the and are often compared to biological morpho- geometry of forelimbs is different in a rat and a genesis. They are sometimes seen as a paradigm human. They are contextual because current and to understand them (Müller et al., 2003). How- past contexts contribute to determining a biologi- ever, the theorization of morphogenesis in physics cal organization, including its constraints (Gilbert is about generic phenomena; they always appear and Epel, 2009; Miquel and Hwang, 2016). Of in the same manner and display the same prop- course, the first and critical context in the analysis erties. Douady and Couder (1996a,b,c) provide of a biological part is the organization in which another example. These authors wrote a model it takes place, that is to say, the organism, be it to understand the property of morphogenesis in unicellular or multicellular. Since the meaning of many plants called phyllotaxis. To further justify a part, its functional role, depends on the organi- their model, they instantiated it in an abiotic sys- zation, a proper concept of measurement has to tem leading to the same mathematical structure. accommodate organizations. This kind of modelization requires and implies Moreover, the constraints of a given biologi- that the phenomenon is abstracted from the or- cal situation are mostly unknown. It is the case ganisms in which it takes place. for epistemic reasons, that is to say, because of a This epistemological situation grounds a singu- lack of knowledge. However, another reason is lar (dis)connection between theoretical descrip- principled: changes can occur in a given species tions and matter. The theoretical description is or individual situation, and further experimenta- typically a mathematical model, and its articula- tions with several organisms would be required tion with a concrete object requires only to obtain to objectivize them. In other words, biological quantities defined in the model. This operation historicity has generated new constraints that are is called measurement and has a different nature difficult to objectivize a posteriori, and this process depending on the theory (Montévil, 2019a). For never stops generating novelties even in laboratory example, in classical mechanics, states are points. conditions. However, measurement is never perfect; therefore, To accommodate these difficulties, we have ar- its outcome is an interval. Still, in physics, the gued that biological measurement specifies shared nature of the causal relations do not require some- past and contexts. For example, the existence of thing like a measurement; the theory specifies a common ancestor defines mice, Mus Musculus, them. Modelers only need to set the quantities of and all other groups used to classify living being the model to the value of a given concrete situation in systematics. Similarly, laboratory strains have to understand the latter. a controlled historical origin. The difference be- The scientific meaning of quantities depends tween the two frameworks is that the genealogy on the theoretical analysis (Houle et al., 2011), of strains is observed directly and controlled while and this meaning does not change over time, un- systematics estimates the common theoretical an- like quantities. Of course, in research situations, cestor defining a group. this meaning is not necessarily known initially, Let us emphasize the originality of this episte- but two major methodological postulates guide mology. In evolution, it is blatant that organiza- the investigation. First, physicists assume that tions change over time and that the nature of these there are underlying equations which define the changes cannot be pre-stated. It follows that we meaning of quantities. Let us recall that the exis- cannot define objects accurately by a set of stable tence of a mathematical object is a strong hypoth- properties. If we were to define tetrapods by the esis. Second, physicists assume that one quantity existence of four external limbs, we would have or another is relevant. Then, experimental work to preclude changes impacting this property or aims to unravel the underlying equations and their accept that organisms, such as snakes, can jump structure by changing external quantities such as from one group to another. Instead, systematics

6 defines objects by their past and not by what they identification of constraints, both constraints of do. This strategy provides stable and accurate def- the bone and the organism. initions in a context where objects can undergo As discussed above, the specification of organ- radical changes. isms relies on shared, material pasts. Biologists This situation implies a different articulation can also use quantities to assess the health of the between concrete objects and theoretical descrip- specimens, for example. However, these quantities tions. Theoretical descriptions, starting with are never sufficient to make measurement ahistor- names, cannot be detached from specific concrete ical. Measurement describes how the historicity objects. For example, mice are the descent from a of organisms defines the objects, that is to say how common ancestor which means that all mice have we establish their commensurability. For example, a material, genealogical link. No mouse can exist it is not the same to measure one strain or an- outside this material link. other, or wild animals of a given species or among Name baring types are single specimens that a larger group in the classification. define names in systematics. Names are extended To understand the meaning of biological mea- theoretically to all the descent of a common an- surement, we have introduced the concept of sym- cestor. In this manner, if the classification requires metrization (Montévil,2019a). Because biological a revision, the definition of names remains stable. objects undergo qualitative changes, they are not It follows that names correspond to specific mate- generic and thus are not equivalent. However, rial objects in biology. By contrast, the speed of choosing a shared past enables biologist to posit a light in the vacuum is an invariant of relativistic certain level of equivalence between different or- theories. The International System of Units uses ganisms that we call symmetrization. Of course, a this invariant to define lengths. There is no need priori,the more recent this shared past is, the fewer to specify which photon we are talking about; all novelties appeared in the different individual or- photons will go at the same speed in the vaccuum. ganisms, and the stronger the symmetrization is. Physics is based on generic material objects, and Symmetrization includes other methods to de- not on specific material objects. This comparison fine an equivalence between organisms. For exam- shows the deep methodological and epistemolog- ple, the metabolic rate of mammals can be mea- ical divide between biology and physics and how sured by the rate of oxygen consumption (respira- this divide shapes actual practices. tion). However, this rate strongly depends on the Now, let us go back to biological measurement. activity of organisms. Then biologists have to de- In a nutshell, defining measurement requires to cide how this activity is specified. For example, the define commensurability. For example, measure- activity of organisms in their ecosystem defines ment in quantum mechanics has unusual proper- the field metabolic rate. By contrast, the basal ties because it requires the commensurability of metabolic rate corresponds to an activity where a microscopic and a macroscopic object — the the organism is non-sleeping but does not per- measurement apparatus. Let us consider the com- form a specific activity. By suppressing specific mensurability of the length of a bone. From the activities, the latter symmetrization reduces the perspective of physics, this length seems well de- impact of novelties; therefore, it is stronger than fined: it is the largest spatial extension of the bone. the first. The bone, as a spatial object, is commensurable to At this point, the reader may think that the a ruler. Here the classical concept of measurement stronger the symmetrization is, the better. How- applies, and the resulting length is approximate. ever, stronger symmetrizations come at a cost. For However, there is another difficulty in biology. example, the basal metabolic rate is less variable The biologist would immediately wonder what and display clearer trends than the field metabolic bone and in what organism — provided that the rate (Longo and Montévil, 2014b). However, it names of bones stem from groups in the classi- does not fit the activity of organisms in ecosystems, fication of living beings. In other words, com- and the field metabolic rate is more appropriate mensurability in biology is not only about the to assess the free energy requirements of a species. commensurability of a part with an inert object. Along the same line, experimenters may prefer to Commensurability between organisms is also re- work on a specific strain of animals, with a very quired because it is this commensurability that recent common ancestor, to reduce the variability defines parts and their biological meaning. For of experimental results. However, this strategy example, the length of a bone is not necessarily its leads to results that may be specific to this strain largest spatial extension. Instead, it is also defined and may not hold with different animals of the on a qualitative basis so that different measure- same species. Therefore, there is a tradeoff be- ments have a similar meaning. For example, the tween the different symmetrization strategies and length can be smaller than the width in some spec- their scientific merits. imen or species. The underlying problem is the Let us sum this discussion up. Biological ob-

7 jects are not generic because mathematical invari- phenomena, we have to reorganize our epistemo- ance does not define them. Instead, biological logical framework and acknowledge that equa- objects are the result of a cascade of changes and tions and more generally fixed mathematical struc- continue to produce such changes. In this situa- tures cannot play a central role. Let us recall that tion, definitions of biological objects are anchored the method of physics postulates invariance in or- on specific material objects and the concept that der to explain changes. In biology, we postulate objects have a shared concrete past. In particular, instead that there is no underlying invariance be- the names of systematics are used universally in hind changes (Montévil et al., 2016; Longo and biology, and all rely on genealogical concepts — Montévil, 2017). Invariance is limited to con- in particular, the concept of a common ancestor. straints, whose validity is ascertained only at a Since all empirical works in biology rely on such given time and time scale (Montévil and Mossio, names to define their objects, there is no situation 2015; Longo, 2018). Then, in biology, changes in biology that is defined purely with the episte- come first, and invariance comes second. It fol- mology of physics. lows that invariance requires explanations. A measurement relies on a symmetrization,that Let us develop the latter idea. In physics, theo- is to say, a specific way to consider that different ries provide mathematical structures that model- organisms are equivalent despite qualitative dif- ers use. These structures have deep theoretical and ferences. Symmetrization may be more or less empirical roots and have solid justifications. In bi- strong; for example, one can study the metabolism ology, specific constraints cannot be justified this or mammals or study the metabolism of a clonal way because their validity is not general. How- population of cells. However,it is never possible to ever, there are other ways to justify constraints and consider that a symmetrization would be perfect; to choose between several possible mathematical variations are always possible. Moreover, stronger forms. symmetrizations are not always better. They tend A first theoretical justification of the stability to provide more stable results, but these results of a constraint stems from natural selection. Nat- may be specific to this symmetrization. ural selection explains the ”preservation of favored races,” that is to say the stability of certain traits in a population (Darwin, 1859; Lecointre, 2018). 4 A castling move on the epis- The organizational perspective provides another temological board justification for the validity of constraints. In this perspective,parts of an organism collectively main- We have discussed several problems that under- tain each other; this notion leads to the concept mine the ability to objectivize biological phenom- of closure of constraints (Montévil and Mossio, ena by the method of physics. External quantities 2015). Then, in an organism, the theoretical valid- such as initial conditions or parameters can be non- ity of a constraint is justified by the existence ofa generic and thus require specific hypotheses. Bio- process under constraints maintaining it. Let us logical changes can invalidate hypotheses defining take a step back. In physics, mathematical struc- equations, and these hypotheses ultimately have tures trickle down from the general framework to the same epistemological status than hypotheses particular models. Instead, in biology, at the level on external quantities. It follows that the classifica- of organisms, constraints mutually justify each tion and naming of biological objects cannot rely other by the circularity of their interdependen- on equations. Instead, naming empirical objects cies. relies on a historical epistemological framework These two methods correspond to two philo- where objects are defined by their historical origin sophical concepts of biological functions intro- and not by what they do, like in physics. Since duced briefly above. The selectionnist perspec- the physics epistemology cannot name biological tive considers that a trait has a function when it objects, it cannot accommodate empirical results has been selected because of its effects (Godfrey- alone. Smith, 1994). The organizational perspective con- However, this situation is not a checkmate for siders that a constraint has a function when it is our scientific endeavors. Our arguments only im- part of the closure of constraints (Mossio et al., ply that we can no longer assume that the method 2009; Montévil and Mossio, 2015) of physics would be adequate in biology. In other With this rationale, we hope that we have words, we cannot separate proximate causes from shown how proper biological thinking can lead the underlying history. Living beings require spe- to another perspective on the underpinnings of cific methods and epistemology to accommodate mathematical modeling in biology. By switching their historicity, even when we study how such or perspective, we can avoid artifacts stemming from such organisms behave here and now. improper use of the epistemology of physics. By To uphold our ability to objectivize biological embracing the historicity of biological phenom-

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