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1446Marriages of Mathematics and Physics: A Challenge for BiologyProgress in Biophysics and Molecular Biology 131 179-192. 2017.The human attempts to access, measure and organize physical phenomena have led to a manifold construction of mathematical and physical spaces. We will survey the evolution of geometries from Euclid to the Algebraic Geometry of the 20th century. The role of Persian/Arabic Algebra in this transition and its Western symbolic development is emphasized. In this relation, we will also discuss changes in the ontological attitudes toward mathematics and its applications. Historically, the encounter of g…Read more
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317From physics to biology by extending criticality and symmetry breakingsProgress in Biophysics and Molecular Biology 106. 2011.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 sy…Read more
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301Protention and retention in biological systemsTheory in Biosciences 130 107-117. 2011.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 …Read more
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299A 2-dimensional geometry for biological timeProgress in Biophysics and Molecular Biology 106. 2011.This paper proposes an abstract mathematical frame for describing some features of biological time. The key point is that 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 …) and properly biological (heart beating, respiration, metabolic …). In particular, the role of biological rhythms do not seem to have any counterpart in mathematical formalization of physical clocks, wh…Read more
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294The Inert vs. the Living State of Matter: Extended Criticality, Time Geometry, Anti-Entropy - An OverviewFrontiers in Physiology 3 39. 2012.The physical singularity of life phenomena is analyzed by means of comparison with the driving concepts of theories of the inert. We outline conceptual analogies, transferals of methodologies and theoretical instruments between physics and biology, in addition to indicating significant differences and sometimes logical dualities. In order to make biological phenomenalities intelligible, we introduce theoretical extensions to certain physical theories. In this synthetic paper, we summarize and pr…Read more
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256No entailing laws, but enablement in the evolution of the biosphereIn G. Longo, M. Montévil & S. Kauffman (eds.), Genetic and Evolutionary Computation Conference, Acm. 2012.Biological evolution is a complex blend of ever changing structural stability, variability and emergence of new phe- notypes, niches, ecosystems. We wish to argue that the evo- lution of life marks the end of a physics world view of law entailed dynamics. Our considerations depend upon dis- cussing the variability of the very ”contexts of life”: the in- teractions between organisms, biological niches and ecosys- tems. These are ever changing, intrinsically indeterminate and even unprestatable: w…Read more
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250Randomness Increases Order in Biological EvolutionIn M. Dinneen, B. Khoussainov & A. Nies (eds.), Computation, Physics and Beyond. pp. 289-308. 2012.n this text, we revisit part of the analysis of anti-entropy in Bailly and Longo (2009} and develop further theoretical reflections. In particular, we analyze how randomness, an essential component of biological variability, is associated to the growth of biological organization, both in ontogenesis and in evolution. This approach, in particular, focuses on the role of global entropy production and provides a tool for a mathematical understanding of some fundamental observations by Gould on the …Read more
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207Mathematical intuition and the cognitive roots of mathematical conceptsTopoi 29 (1): 15-27. 2010.The foundation of Mathematics is both a logico-formal issue and an epistemological one. By the first, we mean the explicitation and analysis of formal proof principles, which, largely a posteriori, ground proof on general deduction rules and schemata. By the second, we mean the investigation of the constitutive genesis of concepts and structures, the aim of this paper. This “genealogy of concepts”, so dear to Riemann, Poincaré and Enriques among others, is necessary both in order to enrich the f…Read more
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192The Deluge of Spurious Correlations in Big DataFoundations of Science 22 (3): 595-612. 2016.Very large databases are a major opportunity for science and data analytics is a remarkable new field of investigation in computer science. The effectiveness of these tools is used to support a “philosophy” against the scientific method as developed throughout history. According to this view, computer-discovered correlations should replace understanding and guide prediction and action. Consequently, there will be no need to give scientific meaning to phenomena, by proposing, say, causal relation…Read more
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110Reflections on Concrete IncompletenessPhilosophia Mathematica 19 (3): 255-280. 2011.How do we prove true but unprovable propositions? Gödel produced a statement whose undecidability derives from its ad hoc construction. Concrete or mathematical incompleteness results are interesting unprovable statements of formal arithmetic. We point out where exactly the unprovability lies in the ordinary ‘mathematical’ proofs of two interesting formally unprovable propositions, the Kruskal-Friedman theorem on trees and Girard's normalization theorem in type theory. Their validity is based on…Read more
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81Big Data e Intelligenza Artificiale: Che Futuro Ci Aspetta?Scienza E Filosofia 20. 2018.BIG DATA AND ARTIFICIAL INTELLIGENCE: A LOOK INTO THE FUTURE To say or write something innovative on the ongoing revolution in the fields of Big Data and Artificial Intelligence is very difficult. The advent of these two new technologies is in fact among the most relevant events in human history since in a little more than a decade it will likely lead to the creation of the First Artificial Intelligence of the Fourth level: i.e capable to think and create autonomously. This is a strong statement…Read more
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76The differential method and the causal incompleteness of programming theory in molecular biologyFoundations of Science 12 (4): 337-366. 2007.The “DNA is a program” metaphor is still widely used in Molecular Biology and its popularization. There are good historical reasons for the use of such a metaphor or theoretical model. Yet we argue that both the metaphor and the model are essentially inadequate also from the point of view of Physics and Computer Science. Relevant work has already been done, in Biology, criticizing the programming paradigm. We will refer to empirical evidence and theoretical writings in Biology, although our argu…Read more
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51Solomon Feferman. Weyl vindicated: “Das Kontinuum” 70 years later. Atti del congresso, Temi e prospettive della logica e della filosofia della scienza contemporanee, Organizzato dalla Società Italiana di Logica e Filosofia delle Scienze , Cesena, 7–10 gennaio 1987, Volume I, Logica, edited by Carlo Cellucci and Giovanni Sambin, CLUEB, Bologna1988, pp. 59–93 (review)Journal of Symbolic Logic 58 (3): 1085-1086. 1993.
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36Mathematical intelligence, infinity and machines: beyond GodelitisJournal of Consciousness Studies 6 (11-12): 11-12. 1999.We informally discuss some recent results on the incompleteness of formal systems. These theorems, which are of great importance to contemporary mathematical epistemology, are proved using a variety of conceptual tools provably stronger than those of finitary axiomatisations. Those tools require no mathematical ontology, but rather constitute particularly concrete human constructions and acts of comprehending infinity and space rooted in different forms of knowledge. We shall also discuss, albei…Read more
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35Prototype Proofs in Type TheoryMathematical Logic Quarterly 46 (2): 257-266. 2000.The proofs of universally quantified statements, in mathematics, are given as “schemata” or as “prototypes” which may be applied to each specific instance of the quantified variable. Type Theory allows to turn into a rigorous notion this informal intuition described by many, including Herbrand. In this constructive approach where propositions are types, proofs are viewed as terms of λ-calculus and act as “proof-schemata”, as for universally quantified types. We examine here the critical case of …Read more
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34The mathematics of computing between logic and physicsIn S. B. Cooper & Andrea Sorbi (eds.), Computability in Context: Computation and Logic in the Real World, World Scientific. 2011.
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33Symmetries and Symmetry-Breakings: The Fabric of Physical Interactions and the Flow of Time (review)Foundations of Science 16 (4): 331-333. 2011.This short note develops some ideas along the lines of the stimulating paper by Heylighen (Found Sci 15 4(3):345–356, 2010a ). It summarizes a theme in several writings with Francis Bailly, downloadable from this author’s web page. The “geometrization” of time and causality is the common ground of the analysis hinted here and in Heylighen’s paper. Heylighen adds a logical notion, consistency, in order to understand a possible origin of the selective process that may have originated this organiza…Read more
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33What is Turing's Comparison between Mechanism and Writing Worth?In S. Barry Cooper (ed.), How the World Computes, . pp. 450--461. 2012.
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31How Future Depends on Past and Rare Events in Systems of LifeFoundations of Science 23 (3): 443-474. 2018.The dependence on history of both present and future dynamics of life is a common intuition in biology and in humanities. Historicity will be understood in terms of changes of the space of possibilities as well as by the role of diversity in life’s structural stability and of rare events in history formation. We hint to a rigorous analysis of “path dependence” in terms of invariants and invariance preserving transformations, as it may be found also in physics, while departing from the physico-ma…Read more
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27Set-theoretical models of lambda-calculus: theories, expansions, isomorphismsAnnals of Pure and Applied Logic 24 (2): 153. 1983.
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26On church's formal theory of functions and functionals: The λ-calculus: connections to higher type recursion theory, proof theory, category theoryAnnals of Pure and Applied Logic 40 (2): 93-133. 1988.
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23Boris Trakhtenbrot. Comparing the Church and Turing approaches: two prophetical messages. The universal Turing machine, A half-century survey, edited by Rolf Herken, Kammerer & Unversagt, Hamburg and Berlin, and Oxford University Press, Oxford and New York, 1988, pp. 603–630 (review)Journal of Symbolic Logic 59 (4): 1434-1436. 1994.
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22C. P. J. Koymans. Models of the lambda calculus. CWI tract no. 9. Centrum voor Wiskunde en Informatica, Amsterdam1984, iii + 181 pp (review)Journal of Symbolic Logic 52 (1): 284-285. 1987.
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20Fondamenti cognitivi della matematica e analisi matematiche del viventeRivista di Estetica 37 113-124. 2008.Nel presente testo cercherò principalmente di esplicitare la correlazione tra le mie ricerche, così come ho cercato di riassumerle nel testo su La ragionevole efficacia della matematica, e l’impostazione vareliana nei confronti delle scienze cognitive. Nel tentativo di far questo, intendo prendere spunto da un aneddoto che, a dire il vero, pare sia effettivamente accaduto. Si racconta che, intorno ai sette o otto anni, il piccolo Gauss si trovò di fronte un maestro severissimo che, come puniz...
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20Quantifying the World and Its Webs: Mathematical Discrete vs Continua in Knowledge ConstructionTheory, Culture and Society 36 (6): 63-72. 2019.This short paper is meant to be an introduction to the ‘Letter to Alan Turing’ that follows it. It summarizes some basic ideas in information theory and very informally hints at their mathematical properties. In order to introduce Turing’s two main theoretical contributions, in Theory of Computation and in Morphogenesis, the fundamental divide between discrete vs. continuous structures in mathematics is presented, as it is also a divide in his scientific life. The reader who is familiar with the…Read more
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17Letter to TuringTheory, Culture and Society 36 (6): 73-94. 2019.This personal, yet scientific, letter to Alan Turing, reflects on Turing's personality in order to better understand his scientific quest. It then focuses on the impact of his work today. By joining human attitude and particular scientific method, Turing is able to “immerse himself” into the phenomena on which he works. This peculiar blend justifies the epistolary style. Turing makes himself a “human computer”, he lives the dramatic quest for an undetectable imitation of a man, a woman, a machin…Read more
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17On church's formal theory of functions and functionalsAnnals of Pure and Applied Logic 40 (2): 93-133. 1988.
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