From Logic to Biology via Physics: a survey
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paper_title: Life Itself: A Comprehensive Inquiry Into the Nature, Origin, and Fabrication of Life

paper_content:

1. Prolegomenon2. Strategic Considerations: The Special and the General3. Some Necessary Epistemological Considerations4. The Concept of State5. Entailment Without States: Relational Biology6. Analytic and Synthetic Models7. On Simulation8. Machines and Mechanisms9. Relational Theory of Machines10. Life Itself: The Preliminary Steps11. Relational Biology and Biology
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paper_title: Laplace, Turing and the "imitation game " impossible geometry: randomness, determinism and programs in Turing's test 1.

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From the physico-mathematical view point, the imitation game between man and machine, proposed by Turing in his 1950 paper for the journal "Mind", is a game between a discrete and a continuous system. Turing stresses several times the laplacian nature of his discrete-state machine, yet he tries to show the undetectability of a functional imitation, by his machine, of a system (the brain) that, in his words, is not a discrete-state machine, as it is sensitive to limit conditions. We shortly compare this tentative imitation with Turing's mathematical modelling of morphogenesis (his 1952 paper, focusing on continuous systems, as he calls non-linear dynamics, which are sensitive to initial conditions). On the grounds of recent knowledge about dynamical systems, we show the detectability of a Turing Machine from many dynamical processes. Turing's hinted distinction between imitation and modelling is developed, jointly to a discussion on the repeatability of computational processes in relation to physical systems. The main references are of a physico-mathematical nature, but the analysis is purely conceptual.
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paper_title: Model theory: an introduction

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This book is a modern introduction to model theory which stresses applications to algebra throughout the text. The first half of the book includes classical material on model construction techniques, type spaces, prime models, saturated models, countable models, and indiscernibles and their applications. The author also includes an introduction to stability theory beginning with Morley's Categoricity Theorem and concentrating on omega-stable theories. One significant aspect of this text is the inclusion of chapters on important topics not covered in other introductory texts, such as omega-stable groups and the geometry of strongly minimal sets. The author then goes on to illustrate how these ingredients are used in Hrushovski's applications to diophantine geometry. David Marker is Professor of Mathematics at the University of Illinois at Chicago. His main area of research involves mathematical logic and model theory, and their applications to algebra and geometry. This book was developed from a series of lectures given by the author at the Mathematical Sciences Research Institute in 1998.
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paper_title: A computable expression of closure to efficient causation

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In this paper, we propose a mathematical expression of closure to efficient causation in terms of lambda-calculus; we argue that this opens up the perspective of developing principled computer simulations of systems closed to efficient causation in an appropriate programming language. An important implication of our formulation is that, by exhibiting an expression in lambda-calculus, which is a paradigmatic formalism for computability and programming, we show that there are no conceptual or principled problems in realizing a computer simulation or model of closure to efficient causation. We conclude with a brief discussion of the question whether closure to efficient causation captures all relevant properties of living systems. We suggest that it might not be the case, and that more complex definitions could indeed create crucial some obstacles to computability.
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paper_title: SOME BRIDGING RESULTS AND CHALLENGES IN CLASSICAL, QUANTUM AND COMPUTATIONAL RANDOMNESS

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We encountered randomness in our dierent elds of interest, as unpredictable phenomena are omnipresent in natural and articial processes. In classical physical systems (and by this we mean also relativistic ones) randomness may be dened as 'deterministic unpredictability'. That is, since Poincare's results (on the Three Body Problem) and his invention of the geometry of dynamical systems, deterministic systems include various forms of chaotic ones, from weak (mixing) systems to ones highly sensitive to border conditions, where random behaviours are part of the deterministic evolutions. Randomness got a new status with the birth of quantum mechanics: access to information on a given systems passes through a nondeterministic process (measurement). In computer sciences, randomness is at the core of algorithmic information theory, all the while nondeterministic algorithms and networks present crucial random aspects. Finally, an extensive use of randomness is made also in biology. Thus we wondered: all these dierent sciences refer to a concept of randomness, but is it really the same concept? And if they are dierent concepts, what is the relation between them?
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paper_title: Biological Phase Spaces and Enablement

paper_content:

This chapter analyzes, in terms of critical transitions, the phase spaces of biological dynamics. The phase space is the space where the scientific description and determination of a phenomenon is given.We first hint to the historical path that lead physics to give a central role to the construction of a sound notion of phase space, as a condition of possibility for physico-mathematical analyses to be developed. We then argue that one major aspect of biological evolution is the continual change of the pertinent phase space and the unpredictability of these changes. This analysis will be based on the role of theoretical symmetries in biology and on their critical instability along evolution. Our hypothesis deeply modifies the tools and concepts used in physical theorizing, when adapted to biology. In particular, we argue that causality has to be understood differently, and we discuss two notions to do so: differential causality and enablement. In this context constraints play a key role: on one side, they restrict possibilities, on the other, they also enable biological systems to integrate changing constraints in their organization, by correlated variations, in un-prestatable ways. This corresponds to the formation of new phenotypes and organisms.
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paper_title: Comparing Symmetries in Models and Simulations

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Computer simulations brought remarkable novelties to knowledge construction. In this chapter, we first distinguish between mathematical modeling, computer implementations of these models and purely computational approaches. In all three cases, different answers are provided to the questions the observer may have concerning the processes under investigation. These differences will be highlighted by looking at the different theoretical symmetries of each frame. In the latter case, the peculiarities of agent-based or object oriented languages allow to discuss the role of phase spaces in mathematical analyses of physical versus biological dynamics. Symmetry breaking and randomness are finally correlated in the various contexts where they may be observed.
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paper_title: Symmetry and Symmetry Breakings in Physics

paper_content:

Symmetries play a major theoretical role in physics, in particular since the work by E. Noether and H. Weyl in the first half of last century.
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paper_title: Scaling and Scale Symmetries in Biological Systems

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This chapter reviews experimental results showing scaling, as a fundamental form of “theoretical symmetry” in biology. Allometry and scaling are the transformations of quantitative biological observables engendered by considering organisms of different sizes and at different scales, respectively. We then analyze anatomical fractal-like structures, the latter being ubiquitous in organs’ shape, yet with a fair amount of variability. We also discuss some observed temporal fractal like structures in biological time series. In the final part, we will provide some examples of space-time and of network configurations and dynamics.
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paper_title: Phase Transitions and Renormalization Group

paper_content:

1. Quantum Field Theory and Renormalization Group 2. Gaussian Expectation Values. Steepest Descent Method . 3. Universality and Continuum Limit 4. Classical Statistical Physics: One Dimension 5. Continuum Limit and Path Integral 6. Ferromagnetic Systems. Correlations 7. Phase transitions: Generalities and Examples 8. Quasi-Gaussian Approximation: Universality, Critical Dimension 9. Renormalization Group: General Formulation 10. Perturbative Renormalization Group: Explicit Calculations 11. Renormalization group: N-component fields 12. Statistical Field Theory: Perturbative Expansion 13. The sigma4 Field Theory near Dimension 4 14. The O(N) Symmetric (phi2)2 Field Theory: Large N Limit 15. The Non-Linear sigma-Model 16. Functional Renormalization Group Appendix
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paper_title: Mean field theory, the Ginzburg criterion, and marginal dimensionality of phase transitions

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By applying a real space version of the Ginzburg criterion, the role of fluctuations and thence the self‐consistency of mean field theory are assessed in a simple fashion for a variety of phase transitions. It is shown that in using this approach the concept of ’’marginal dimensionality’’ emerges in a natural way. For example, it is shown that for many homogeneous structural transformations the marginal dimensionality is two, so that mean field theory will be valid for real three‐dimensional systems. It is suggested that this simple self‐consistent approach to Landau theory should be incorporated in the teaching of elementary phase transition phenomena.
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paper_title: Critical Phase Transitions

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In this chapter, we first present the basic principles of a relatively new area of physics, the analysis of critical phase transitions and more generally the theory of criticality. Then, we will introduce some mathematical methods that set the physics of criticality on robust grounds.We will also discuss briefly some variation on the theme of criticality such as self-organized criticality, often used in theoretical approaches to biology. Following the current analyses in physics, we present them here as point-wise transitions, with respect to (usually) one control parameter. This will constitute an opening towards the approach to criticality in the following chapters seen as an “extended” phenomenon in biology, that, we propose, is ranging on a non-trivial interval of definition.
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paper_title: Renormalization group theory: Its basis and formulation in statistical physics

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Lengths of both sides of each end plane of a light-intensity distribution uniformizing element receiving a light flux and having an F-number of 1 are set to ½ of those of a reflecting surface of a reflecting optical-spatial modulator element, position information of uniformed light fluxes output from the light-intensity distribution uniformizing element is Fourier-transformed into diverging angle information indicated by incident light fluxes output from a first group of lenses, a relay deformed diaphragm intercepts an interference component of each incident light flux, which is expected to interfere with an outgoing light flux, to produce asymmetric light fluxes, the asymmetric light fluxes are incident on the reflecting optical-spatial modulator element, a projection lens deformed diaphragm removes stray light from outgoing light fluxes output from the reflecting optical-spatial modulator element, and an image is displayed according to the outgoing light fluxes.
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paper_title: Theoretical principles for biology: Variation

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Abstract Darwin introduced the concept that random variation generates new living forms. In this paper, we elaborate on Darwin's notion of random variation to propose that biological variation should be given the status of a fundamental theoretical principle in biology. We state that biological objects such as organisms are specific objects. Specific objects are special in that they are qualitatively different from each other. They can undergo unpredictable qualitative changes, some of which are not defined before they happen. We express the principle of variation in terms of symmetry changes, where symmetries underlie the theoretical determination of the object. We contrast the biological situation with the physical situation, where objects are generic (that is, different objects can be assumed to be identical) and evolve in well-defined state spaces. We derive several implications of the principle of variation, in particular, biological objects show randomness, historicity and contextuality. We elaborate on the articulation between this principle and the two other principles proposed in this special issue: the principle of default state and the principle of organization.
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paper_title: Theoretical principles for biology: Organization

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In the search of a theory of biological organisms, we propose to adopt organization as a theoretical principle. Organization constitutes an overarching hypothesis that frames the intelligibility of biological objects, by characterizing their relevant aspects. After a succinct historical survey on the understanding of organization in the organicist tradition, we offer a specific characterization in terms of closure of constraints. We then discuss some implications of the adoption of organization as a principle and, in particular, we focus on how it fosters an original approach to biological stability, as well as and its interplay with variation.
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paper_title: A 2-dimensional Geometry for Biological Time

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This chapter proposes a mathematical schema for describing some features of biological time. The key point is that the usual physical (linear) representation of time is insufficient, in our view, for the understanding key phenomena of life, such as rhythms, both physical (circadian, seasonal, . . . rhythms) and properly biological ones (heart beating, respiration, metabolic, . . . ). In particular, the role of biological rhythms do not seem to have a counterpart in the mathematical formalization of physical clocks, which are based on frequencies along the usual (possibly thermodynamical, thus oriented) time. We then suggest a functional representation of biological time by a 2-dimensional manifold as a mathematical frame for accommodating autonomous biological rhythms. The “visual” representation of rhythms so obtained, in particular heart beatings, will provide, by a few examples, hints towards possible applications of our approach to the understanding of interspecific differences or intraspecific pathologies. The 3-dimensional embedding space, needed for purely mathematical reasons, allows to introduce a suitable extra-dimension for “representation time”, with a cognitive significance.
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paper_title: Biological Order as a Consequence of Randomness: Anti-entropy and Symmetry Changes

paper_content:

In this chapter, we introduce the notion and the analysis of phenotypic complexity, as anti-entropy, proposed in [Bailly & Longo, 2009] and develop further theoretical consequences. In particular, we analyze how randomness, an essential component of biological variability, is associated to the growth of biological organization, both in evolution and in ontogenesis. Our approach, in particular, will focus on the role of global entropy production and will provide a tool for a mathematical understanding of some fundamental observations by S.J. Gould on how phenotypic complexity increases, on average, along random evolutionary paths, without a bias towards an increase. We also propose a preliminary analysis of biological regenerative processes, which allows to associate entropy production of adults to anti-entropy, by considering “collisions” between entropy and anti-entropy. Lastly, we analyze the situation in terms of theoretical symmetries, in order to further specify the biological meaning of anti-entropy as well as its strong correlations to randomness.
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paper_title: From Bottom-Up Approaches to Levels of Organization and Extended Critical Transitions

paper_content:

Biological thinking is structured by the notion of level of organization. We will show that this notion acquires a precise meaning in critical phenomena: they disrupt, by the appearance of infinite quantities, the mathematical (possibly equational) determination at a given level, when moving at an ``higher'' one. As a result, their analysis cannot be called genuinely bottom-up, even though it remains upward in a restricted sense. At the same time, criticality and related phenomena are very common in biology. Because of this, we claim that bottom-up approaches are not sufficient, in principle, to capture biological phenomena. In the second part of this paper, following the work of Francis Bailly, we discuss a strong criterium of level transition. The core idea of the criterium is to start from the breaking of the symmetries and determination at a ``first'' level in order to ``move'' at the others. If biological phenomena have multiple, \emph{sustained} levels of organization in this sense, then they should be interpreted as \emph{extended} critical transitions.
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paper_title: Phase Transitions and Renormalization Group

paper_content:

1. Quantum Field Theory and Renormalization Group 2. Gaussian Expectation Values. Steepest Descent Method . 3. Universality and Continuum Limit 4. Classical Statistical Physics: One Dimension 5. Continuum Limit and Path Integral 6. Ferromagnetic Systems. Correlations 7. Phase transitions: Generalities and Examples 8. Quasi-Gaussian Approximation: Universality, Critical Dimension 9. Renormalization Group: General Formulation 10. Perturbative Renormalization Group: Explicit Calculations 11. Renormalization group: N-component fields 12. Statistical Field Theory: Perturbative Expansion 13. The sigma4 Field Theory near Dimension 4 14. The O(N) Symmetric (phi2)2 Field Theory: Large N Limit 15. The Non-Linear sigma-Model 16. Functional Renormalization Group Appendix
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paper_title: From Physics to Biology by Extending Criticality and Symmetry Breakings

paper_content:

Symmetries play a major role in physics, in particular since the work by E. Noether and H. Weyl in the first half of last century. Herein, we briefly review their role by recalling how symmetry changes allow to conceptually move from classical to relativistic and quantum physics. We then introduce our ongoing theoretical analysis in biology and show that symmetries play a radically different role in this discipline, when compared to those in current physics. By this comparison, we stress that symmetries must be understood in relation to conservation and stability properties, as represented in the theories. We posit that the dynamics of biological organisms, in their various levels of organization, are not "just" processes, but permanent (extended, in our terminology) critical transitions and, thus, symmetry changes. Within the limits of a relative structural stability (or interval of viability), variability is at the core of these transitions.
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paper_title: Protention and retention in biological systems

paper_content:

This article proposes an abstract mathematical frame for describing some features of cognitive and biological time. We focus here on the so called “extended present” as a result of protentional and retentional activities (memory and anticipation). Memory, as retention, is treated in some physical theories (relaxation phenomena, which will inspire our approach), while protention (or anticipation) seems outside the scope of physics. We then suggest a simple functional representation of biological protention. This allows us to introduce the abstract notion of “biological inertia”.
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paper_title: Mathematics and the Natural Sciences: The Physical Singularity of Life

paper_content:

Introduction Incompleteness and Indetermination Space and Time in Biology Invariances and Symetries Causality and Symetries Extended Criticality Randomness and Determination Towards a Conclusion .
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paper_title: Biological Phase Spaces and Enablement

paper_content:

This chapter analyzes, in terms of critical transitions, the phase spaces of biological dynamics. The phase space is the space where the scientific description and determination of a phenomenon is given.We first hint to the historical path that lead physics to give a central role to the construction of a sound notion of phase space, as a condition of possibility for physico-mathematical analyses to be developed. We then argue that one major aspect of biological evolution is the continual change of the pertinent phase space and the unpredictability of these changes. This analysis will be based on the role of theoretical symmetries in biology and on their critical instability along evolution. Our hypothesis deeply modifies the tools and concepts used in physical theorizing, when adapted to biology. In particular, we argue that causality has to be understood differently, and we discuss two notions to do so: differential causality and enablement. In this context constraints play a key role: on one side, they restrict possibilities, on the other, they also enable biological systems to integrate changing constraints in their organization, by correlated variations, in un-prestatable ways. This corresponds to the formation of new phenotypes and organisms.
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paper_title: Randomness and multilevel interactions in biology

paper_content:

The dynamic instability of living systems and the "superposition" of different forms of randomness are viewed, in this paper, as components of the contingently changing, or even increasing, organization of life through ontogenesis or evolution. To this purpose, we first survey how classical and quantum physics define randomness differently. We then discuss why this requires, in our view, an enriched understanding of the effects of their concurrent presence in biological systems' dynamics. Biological randomness is then presented not only as an essential component of the heterogeneous determination and intrinsic unpredictability proper to life phenomena, due to the nesting of, and interaction between many levels of organization, but also as a key component of its structural stability. We will note as well that increasing organization, while increasing "order", induces growing disorder, not only by energy dispersal effects, but also by increasing variability and differentiation. Finally, we discuss the cooperation between diverse components in biological networks; this cooperation implies the presence of constraints due to the particular nature of bio-entanglement and bio-resonance, two notions to be reviewed and defined in the paper.
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paper_title: Biological Order as a Consequence of Randomness: Anti-entropy and Symmetry Changes

paper_content:

In this chapter, we introduce the notion and the analysis of phenotypic complexity, as anti-entropy, proposed in [Bailly & Longo, 2009] and develop further theoretical consequences. In particular, we analyze how randomness, an essential component of biological variability, is associated to the growth of biological organization, both in evolution and in ontogenesis. Our approach, in particular, will focus on the role of global entropy production and will provide a tool for a mathematical understanding of some fundamental observations by S.J. Gould on how phenotypic complexity increases, on average, along random evolutionary paths, without a bias towards an increase. We also propose a preliminary analysis of biological regenerative processes, which allows to associate entropy production of adults to anti-entropy, by considering “collisions” between entropy and anti-entropy. Lastly, we analyze the situation in terms of theoretical symmetries, in order to further specify the biological meaning of anti-entropy as well as its strong correlations to randomness.
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paper_title: From energetics to ecosystems : the dynamics and structure of ecological systems

paper_content:

SECTION I.- A Process-Oriented Approach to the Multispecies Functional Response.- Homage to Yodzis and Innes 1992: Scaling up Feeding-Based Population Dynamics to Complex Ecological Networks.- Food Webs, Body Size and the Curse of the Latin Binomial.- An Energetic Framework for Trophic Control.- SECTION II.- Experimental Studies of Food Webs: Causes and Consequences of Trophic Interactions.- Interplay Between Scale, Resolution, Life History and Food Web Properties.- Heteroclinic Cycles in the Rain Forest: Insights from Complex Dynamics.- Emergence in Ecological Systems.- Dynamic Signatures of Real and Model Ecosystems.- SECTION III.- Evolutionary Branching of Single Traits.- Feedback Effects Between the Food Chain and Induced Defense Strategies.- Evolutionary Demography: The Invasion Exponent and the Effective Population Density in Nonlinear Matrix Models.- Of Experimentalists, Empiricists, and Theoreticians.
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paper_title: Modeling mammary organogenesis from biological first principles: Cells and their physical constraints

paper_content:

In multicellular organisms, relations among parts and between parts and the whole are contextual and interdependent. These organisms and their cells are ontogenetically linked: an organism starts as a cell that divides producing non-identical cells, which organize in tri-dimensional patterns. These association patterns and cells types change as tissues and organs are formed. This contextuality and circularity makes it difficult to establish detailed cause and effect relationships. Here we propose an approach to overcome these intrinsic difficulties by combining the use of two models; 1) an experimental one that employs 3D culture technology to obtain the structures of the mammary gland, namely, ducts and acini, and 2) a mathematical model based on biological principles. The typical approach for mathematical modeling in biology is to apply mathematical tools and concepts developed originally in physics or computer sciences. Instead, we propose to construct a mathematical model based on proper biological principles. Specifically, we use principles identified as fundamental for the elaboration of a theory of organisms, namely i) the default state of cell proliferation with variation and motility and ii) the principle of organization by closure of constraints. This model has a biological component, the cells, and a physical component, a matrix which contains collagen fibers. Cells display agency and move and proliferate unless constrained; they exert mechanical forces that i) act on collagen fibers and ii) on other cells. As fibers organize, they constrain the cells on their ability to move and to proliferate. The model exhibits a circularity that can be interpreted in terms of closure of constraints. Implementing the mathematical model shows that constraints to the default state are sufficient to explain ductal and acinar formation, and points to a target of future research, namely, to inhibitors of cell proliferation and motility generated by the epithelial cells. The success of this model suggests a step-wise approach whereby additional constraints imposed by the tissue and the organism could be examined in silico and rigorously tested by in vitro and in vivo experiments, in accordance with the organicist perspective we embrace.
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paper_title: From Physics to Biology by Extending Criticality and Symmetry Breakings

paper_content:

Symmetries play a major role in physics, in particular since the work by E. Noether and H. Weyl in the first half of last century. Herein, we briefly review their role by recalling how symmetry changes allow to conceptually move from classical to relativistic and quantum physics. We then introduce our ongoing theoretical analysis in biology and show that symmetries play a radically different role in this discipline, when compared to those in current physics. By this comparison, we stress that symmetries must be understood in relation to conservation and stability properties, as represented in the theories. We posit that the dynamics of biological organisms, in their various levels of organization, are not "just" processes, but permanent (extended, in our terminology) critical transitions and, thus, symmetry changes. Within the limits of a relative structural stability (or interval of viability), variability is at the core of these transitions.
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paper_title: Critique of Pure Reason

paper_content:

ion of space and attend merely to the act by which we determine the internal sense according to its form, is that which produces the conception of succession. The understanding, therefore, does by no means find in the internal sense any such synthesis of the manifold, but produces it, in that it affects this sense. At the same time, how “I who think” is distinct from the “I” which intuites itself (other modes of intuition being cogitable as at least possible), and yet one and the same with this latter as the same subject; how, therefore, I am able to say: “I, as an intelligence and thinking subject, cognize myself as an object thought, so far as I am, moreover, given to myself in intuition– only, like other phenomena, not as I am in myself, and as considered by the understanding, but merely as I appear”– is a question that has in it neither more nor less difficulty than the question– “How can I be an object to myself?” or this– “How I can be an object of my own intuition and internal perceptions?” But that such must be the fact, if we admit that space is merely a pure form of the phenomena of external sense, can be clearly proved by the consideration that we cannot represent time, which is not an object of external intuition, in any other way than under the image of a line, which we draw in thought, a mode of representation without which we could not cognize the unity of its dimension, and also that we are necessitated to take our determination of periods of time, or of points of time, for all our internal perceptions from the changes which we perceive in outward things. It follows that we must arrange the determinations of the internal sense, as phenomena in time, exactly in the same manner as we arrange those of the external senses in space. And consequently, if we grant, respecting this latter, that by means of them we know objects only in so far as we are affected externally, we must also confess, with regard to the internal sense, that by means of it we intuite ourselves only as we are internally affected by ourselves; in other words, as regards internal intuition, we cognize our own subject only as phenomenon, and not as it is in itself.[23][2] [22]Motion of an object in space does not belong to a pure science, consequently not to geometry; because, that a thing is movable cannot be known a priori, but only from experience. But motion, considered as the description of a space, is a pure act of the successive synthesis of the manifold in external intuition by means of productive imagination, and belongs not only to geometry, but even to transcendental philosophy. [23][2] I do not see why so much difficulty should be found in admitting that our internal sense is affected by ourselves. Every act of attention exemplifies it. In such an act the understanding determines the internal sense by the synthetical conjunction which it cogitates, conformably to the internal intuition which corresponds to the manifold in the synthesis of the understanding. How much the mind is usually affected thereby every one will be able to perceive in himself. | Table of
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paper_title: Symmetry and Symmetry Breakings in Physics

paper_content:

Symmetries play a major theoretical role in physics, in particular since the work by E. Noether and H. Weyl in the first half of last century.
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Title: From Logic to Biology via Physics: a survey

Section 1: Introduction
Description 1: This section provides an analysis of the interdisciplinary approach necessary to gain insights into biological phenomena, drawing particularly from physical theorizing.

Section 2: A Definition of Life?
Description 2: This section discusses the challenges of defining life, emphasizing operational notions over ideal definitions and exploring the role of evolutionary theory.

Section 3: Symmetry breakings and randomness
Description 3: This section examines how symmetry changes and randomness in biological systems compare to those in physical theories, and their relevance to biological coherence structures.

Section 4: Symmetries and theoretical extensions of physical theories
Description 4: This section highlights the differences in the role of symmetries between biological and physical theories and introduces the concept of variability as a primary invariant in biology.

Section 5: Extended criticality
Description 5: This section proposes the concept of extended critical transitions to analyze biological variability and coherence structures beyond pointwise criticality in physics.

Section 6: More on critical phase transitions in physics
Description 6: This section delves deeper into the properties of critical phase transitions in physics and their theoretical significance.

Section 7: Variability and stability
Description 7: This section discusses how symmetry changes and variability relate to structural stability and autonomy in biological organism, despite their inherent instability.

Section 8: Remarks on reductionism and renormalization
Description 8: This section addresses the complexity of biological phenomena and critiques the reductionist approach, suggesting that biological systems may require new theoretical frameworks beyond existing physical theories.

Section 9: Phase spaces and enablement
Description 9: This section explores the limits of physical methods for describing biological phase spaces and introduces enablement as a unique form of causation in biological processes.