Abstract
We provide a new perspective on the relation between the space of description of an object and the appearance of novelties. One of the aims of this perspective is to facilitate the interaction between mathematics and historical sciences. The definition of novelties is paradoxical: if one can define in advance the possibles, then they are not genuinely new. By analyzing the situation in set theory, we show that defining generic (i.e., shared) and specific (i.e., individual) properties of elements of a set are radically different notions. As a result, generic and specific definitions of possibilities cannot be conflated. We argue that genuinely stating possibilities requires that their meaning has to be made explicit. For example, in physics, properties playing theoretical roles are generic; then, generic reasoning is sufficient to define possibilities. By contrast, in music, we argue that specific properties matter, and generic definitions become insufficient. Then, the notion of new possibilities becomes relevant and irreducible. In biology, among other examples, the generic definition of the space of DNA sequences is insufficient to state phenotypic possibilities even if we assume complete genetic determinism. The generic properties of this space are relevant for sequencing or DNA duplication, but they are inadequate to understand phenotypes. We develop a strong concept of biological novelties which justifies the notion of new possibilities and is more robust than the notion of changing description spaces. These biological novelties are not generic outcomes from an initial situation. They are specific and this specificity is associated with biological functions, that is to say, with a specific causal structure. Thus, we think that in contrast with physics, the concept of new possibilities is necessary for biology.
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Notes
The mathematical space used to describe an object is the combination of all the quantities that are used to describe its state. For example, a cell population can be described by the number of cells n and the corresponding mathematical space is then the positive integers.
Here randomly means, for example, a number chosen randomly in a finite interval with the uniform probability distribution.
The axiom of choice illustrates this point. The axiom of choice enables the mathematician to pick specific numbers without an explicit method to do so. In this sense, the action of choosing a specific number becomes generic. An axiom is required for this operation because such a method cannot be constructed.
For example, this notion could be implemented in a similar way than Turing’s imitation game (Turing 1950), with listeners deciding whether a piece is admissible.
This is valid, for example, in a situation without energetic constraints and with an infinite number of particles.
Indeed, a definition is needed to talk about a set of pre-possibilities. As a result, pre-possibilities are defined for some operations.
Here, genetic determinism is postulated without an explicit generic causal rule linking dna to phenotypes. This epistemological status is to be contrasted with the deterministic frame of classical mechanics where determinism follows from the generic application of the Cauchy–Lipschitz theorem on the equations provided by the fundamental principle of dynamics, see Sect. 3.1.3.
Organisms are open systems, with fluxes of matter and energy that are not straightforward to describe in classical mechanics and pertain more to far from equilibrium thermodynamics. With the natural history in mind, the only relevant isolated system would be the solar system. Moreover, biology also involves chemical reactions which, in physics, pertain to quantum mechanics and not classical mechanics.
This line of reasoning is very general, but the corresponding randomness can be interpreted in different ways depending on the theoretical context. In classical mechanics and related deterministic frameworks, this randomness stems from measurement: the state of a system cannot be determined empirically with infinite precision which entails unpredictability, see Longo and Montévil (2017) for a general discussion.
References
Adams, A., Zenil, H., Davies, P., & Walker, S. (2017). Formal definitions of unbounded evolution and innovation reveal universal mechanisms for open-ended evolution in dynamical systems. Scientific Reports, 7, https://doi.org/10.1038/s41598-017-00810-8.
Anderson, P. W. (1972). More is different. Science, 177, 393–396. https://doi.org/10.1126/science.177.4047.393.
Anderson, P. W., & Stein, D. L. (1985). Broken symmetry, emergent properties, dissipative structures, life: Are they related? In E. F. Yates (Ed.), Self-organizing systems: The emergence of order (pp. 445–458). NY: Plenum Press.
Barnes, C., Speroni, L., Quinn, K., Montévil, M., Saetzler, K., Bode-Animashaun, G., et al. (2014). From single cells to tissues: Interactions between the matrix and human breast cells in real time. PLoS ONE, 9, e93325. https://doi.org/10.1371/journal.pone.0093325.
Beatty, J. (1995). The evolutionary contingency thesis. In Concepts, theories, and rationality in the biological sciences, pp. 45–81.
Bedau, M. A., McCaskill, J. S., Packard, N. H., Rasmussen, S., Adami, C., Green, D. G., et al. (2000). Open problems in artificial life. Artificial Life, 6, 363–376. https://doi.org/10.1162/106454600300103683.
Bergson, H. (2014). La pensée et le mouvant. Editions Flammarion.
Bich, L., & Bocchi, G. (2012). Emergent processes as generation of discontinuities. Methods, models, simulations and approaches towards a general theory of change (pp. 135–146). Singapore: World Scientific.
Borges, J. L. (1998). The library of babel. Collected fictions.
Camalet, S., Duke, T., Julicher, F., & Prost, J. (2000). Auditory sensitivity provided by self-tuned critical oscillations of hair cells. In Proceedings of the national academy of sciences, pp. 3183–3188. https://doi.org/10.1073/pnas.97.7.3183.
Chowdhury, D. (2013). Stochastic mechano-chemical kinetics of molecular motors: A multidisciplinary enterprise from a physicist’s perspective. Physics Reports, 529, 1–197. https://doi.org/10.1016/j.physrep.2013.03.005.
Cortini, R., Barbi, M., Caré, B. R., Lavelle, C., Lesne, A., Mozziconacci, J., et al. (2016). The physics of epigenetics. Reviews of Modern Physics, 88, 025002. https://doi.org/10.1103/RevModPhys.88.025002.
Danchin, E., & Pocheville, A. (2014). Inheritance is where physiology meets evolution. The Journal of Physiology, 592, 2307–2317. https://doi.org/10.1113/jphysiol.2014.272096.
David, L., Ben-Harosh, Y., Stolovicki, E., Moore, L. S., Nguyen, M., Tamse, R., et al. (2013). Multiple genomic changes associated with reorganization of gene regulation and adaptation in yeast. Molecular Biology and Evolution, 30, 1514–1526. https://doi.org/10.1093/molbev/mst071.
Dawkins, R. (1986). The blind watchmaker: Why the evidence of evolution reveals a universe without design. WW Norton & Company.
de Vladar, H. P., Santos, M., & Szathmáry, E. (2017). Grand views of evolution. Trends in Ecology & Evolution, 32, 324–334. https://doi.org/10.1016/j.tree.2017.01.008.
Feigenbaum, M. J. (1980). The metric universal properties of period doubling bifurcations and the spectrum for a route to turbulence. Annals of the New York Academy of Sciences, 357, 330–336.
Forgacs, G., & Newman, S. A. (2005). Biological physics of the developing embryo. Cambridge: Cambridge University Press.
Garson, J. (2016). A critical overview of biological functions. Berlin: Springer.
Gilbert, S. F., & Epel, D. (2009). Ecological developmental biology: Integrating epigenetics, medicine, and evolution. Sunderland: Sinauer Associates.
Godfrey-Smith, P. (1994). A modern history theory of functions. Noûs, 28, 344–362.
Gould, S. J. (2002). The structure of evolutionary theory. Harvard: Harvard University Press.
Heams, T. (2014). Randomness in biology. Mathematical Structures in Computer Science, 24, https://doi.org/10.1017/S096012951200076X.
Holzer, G., & Laudet, V. (2015). Thyroid hormones: A triple-edged sword for life history transitions. Current Biology, 25, R344–R347. https://doi.org/10.1016/j.cub.2015.02.026.
Hordijk, W., & Steel, M. (2017). Chasing the tail: The emergence of autocatalytic networks. Biosystems, 152, 1–10. https://doi.org/10.1016/j.biosystems.2016.12.002.
Huang, S. (2009). Non-genetic heterogeneity of cells in development: More than just noise. Development, 136, 3853–3862. https://doi.org/10.1242/dev.035139.
Karsenti, E. (2008). Self-organization in cell biology: A brief history. Nature Reviews Molecular Cell Biology, 9, 255–262. https://doi.org/10.1038/nrm2357.
Kauffman, S. (1996). At home in the universe: The search for the laws of self-organization and complexity. Oxford: Oxford University Press.
Kauffman, S. (2002). Investigations. USA: Oxford University Press.
Kauffman, S. A. (2016). Humanity in a creative universe. Oxford: Oxford University Press.
Koppl, R., Kauffman, S., Felin, T., & Longo, G. (2015). Economics for a creative world. Journal of Institutional Economics, 11, 1–31. https://doi.org/10.1017/S1744137414000150.
Koutroufinis, S. (2014). Beyond systems theoretical explanations of an organism’s becoming: A process philosophical approach. In S. Koutroufinis (Ed.), In life and process (pp. 99–132). De Gruyter. https://doi.org/10.1515/9783110352597.
Koutroufinis, S. (2017). Organism, machine, process. Towards a process ontology for organismic dynamics. Organisms. Journal of Biological Sciences, 1, 23–44. http://ojs.uniroma1.it/index.php/Organisms/article/view/13878.
Leibniz, G. W. (1991). De l’horizon de la doctrine humaine. Vrin. 1666.
Lesne, A., & Victor, J.-M. (2006). Chromatin fiber functional organization: Some plausible models. The European Physical Journal E, 19, 279–290. https://doi.org/10.1140/epje/i2005-10050-6.
Longo, G., & Montévil, M. (2013b). Extended criticality, phase spaces and enablement in biology. Chaos, Solitons & Fractals, pp. 64–79. https://doi.org/10.1016/j.chaos.2013.03.008.
Longo, G., & Montévil, M. (2014). Perspectives on organisms: Biological time, symmetries and singularities. Lecture notes in morphogenesis. Dordrecht: Springer. https://doi.org/10.1007/978-3-642-35938-5.
Longo, G., Montévil, M., & Kauffman, S. (2012). No entailing laws, but enablement in the evolution of the biosphere. In Genetic and evolutionary computation conference. New York, NY: ACM: GECCO’12. https://doi.org/10.1145/2330784.2330946.
Longo, G., & Montévil, M. (2011). From physics to biology by extending criticality and symmetry breakings. Progress in Biophysics and Molecular Biology, 106, 340–347. https://doi.org/10.1016/j.pbiomolbio.2011.03.005.
Longo, G., & Montévil, M. (2013a). Extended criticality, phase spaces and enablement in biology. Chaos, Solitons & Fractals, 55, 64–79. https://doi.org/10.1016/j.chaos.2013.03.008.
Longo, G., & Montévil, M. (2017). Comparing symmetries in models and simulations. In M. Dorato, L. Magnani, & T. Bertolotti (Eds.), Springer handbook of model-based science. NY: Springer. https://doi.org/10.1007/978-3-319-30526-4.
Loreto, V., Servedio, V. D. P., Strogatz, S. H., & Tria, F. (2016). Dynamics on expanding spaces: Modeling the emergence of novelties. In M. Degli Esposti, E. G. Altmann, & F. Pachet (Eds.), Creativity and Universality in Language (pp. 59–83). Cham: Springer.
Mayr, E. (1963). Animal species and evolution (vol. 797). Belknap Press of Harvard University Press Cambridge, Massachusetts.
Mazzola, G. (2012). The topos of music: Geometric logic of concepts, theory, and performance. Birkhäuser.
Millikan, R. G. (1989). In defense of proper functions. Philosophy of Science, 56, 288–302.
Montévil, M., & Mossio, M. (2015). Biological organisation as closure of constraints. Journal of Theoretical Biology, 372, 179–191. https://doi.org/10.1016/j.jtbi.2015.02.029.
Montévil, M., Mossio, M., Pocheville, A., & Longo, G. (2016). Theoretical principles for biology: Variation. Progress in Biophysics and Molecular Biology, 122, 36–50. https://doi.org/10.1016/j.pbiomolbio.2016.08.005.
Moore, A. (2012). Life defined. BioEssays, 34, 253–254. https://doi.org/10.1002/bies.201290011.
Mossio, M., Saborido, C., & Moreno, A. (2009). An organizational account of biological functions. The British Journal for the Philosophy of Science, 60, 813–841. https://doi.org/10.1093/bjps/axp036.
Mossio, M., Montévil, M., & Longo, G. (2016). Theoretical principles for biology: Organization. Progress in Biophysics and Molecular Biology, 122, 24–35. https://doi.org/10.1016/j.pbiomolbio.2016.07.005.
Muller, G. B., & Wagner, G. P. (1991). Novelty in evolution: Restructuring the concept. Annual Review of Ecology and Systematics, pp. 229–256. https://doi.org/10.1146/annurev.es.22.110191.001305.
Neander, K. (1991). Functions as selected effects: The conceptual analyst’s defense. Philosophy of Science, 58, 168–184. https://doi.org/10.1086/289610.
Pachet, F., & Roy, P. (2014). Imitative leadsheet generation with user constraints. In ECAI 2014 (pp. 1077–1078). https://doi.org/10.3233/978-1-61499-419-0-1077.
Paldi, A. (2003). Stochastic gene expression during cell differentiation: Order from disorder? Cellular and Molecular Life Sciences, 60, 1775–1779.
Papadopoulos, A., Roy, P., & Pachet, F. (2016). Assisted lead sheet composition using flowcomposer. In M. Rueher (Ed.), Principles and practice of constraint programming: 22nd International conference (pp. 769–785). Cham: Springer. https://doi.org/10.1007/978-3-319-44953-1_48.
Rosen, R. (1991). Life itself: A comprehensive inquiry into the nature, origin, and fabrication of life. Columbia U. P.
Ruiz-Mirazo, K., Peretó, J., & Moreno, A. (2004). A universal definition of life: Autonomy and open-ended evolution. Origins of Life and Evolution of the Biosphere, 34, 323–346. https://doi.org/10.1023/B:ORIG.0000016440.53346.dc.
Saetzler, K., Sonnenschein, C., & Soto, A. (2011). Systems biology beyond networks: Generating order from disorder through self-organization. Seminars in Cancer Biology, 21, 165–174. https://doi.org/10.1016/j.semcancer.2011.04.004.
Soros, L., & Stanley, K. . O. (2014). Identifying necessary conditions for open-ended evolution through the artificial life world of chromaria. In ALIFE 14: The fourteenth conference on the synthesis and simulation of living systems, pp. 793–800. https://doi.org/10.7551/978-0-262-32621-6-ch128.
Stadler, B., Stadler, P., Wagner, G., & Fontana, W. (2001). The topology of the possible: Formal spaces underlying patterns of evolutionary change. Journal of Theoretical Biology, 213, 241–274. https://doi.org/10.1006/jtbi.2001.2423.
Stephan, A. (1999). Varieties of emergence. Evolution and Cognition, 5, 50–59.
Tohme, M., Fini, J.-B., Laudet, V., & Demeneix, B. (2012). Chapter 8 small model organisms as tools in food safety research. In Hormone-disruptive chemical contaminants in food (pp. 136–153). The Royal Society of Chemistry. https://doi.org/10.1039/9781849732970-00136.
Turing, A. M. (1950). Computing machinery and intelligence. Mind, 59, 433–460.
Turing, A. M. (1952). The chemical basis of morphogenesis. Philosophical Transactions of the Royal Society of London Series B, Biological Sciences, 237, 37–72. https://doi.org/10.1098/rstb.1952.0012.
Varela, F., Maturana, H., & Uribe, R. (1974). Autopoiesis: The organization of living systems, its characterization and a model. Biosystems, 5, 187–196. https://doi.org/10.1016/0303-2647(74)90031-8.
Wagner, G. P., & Lynch, V. J. (2010). Evolutionary novelties. Current Biology, 20, R48–R52. https://doi.org/10.1016/j.cub.2009.11.010.
West, G., Brown, J., & Enquist, B. (1999). The fourth dimension of life: Fractal geometry and allometric scaling of organisms. Science, 284, 1677–1679. https://doi.org/10.1126/science.284.5420.1677.
West-Eberhard, M. J. (2003). Developmental plasticity and evolution. Oxford: Oxford University Press.
Zhu, J., Zhang, Y.-T., Alber, M. S., & Newman, S. A. (2010). Bare bones pattern formation: A core regulatory network in varying geometries reproduces major features of vertebrate limb development and evolution. PLoS One, 5, 1–11. https://doi.org/10.1371/journal.pone.0010892.
Acknowledgements
I am grateful to Ana Soto, Giuseppe Longo, Carlos Sonnenschein, Marc Godinot, Paul-Antoine Miquel, Arnaud Pocheville and the anonymous reviewers for their critical insights on previous versions of this article. I also would like to thank Guillaume Lecointre for helpful discussions and Jean Lassègue for pointing out the work of Leibniz.
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Montévil, M. Possibility spaces and the notion of novelty: from music to biology. Synthese 196, 4555–4581 (2019). https://doi.org/10.1007/s11229-017-1668-5
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DOI: https://doi.org/10.1007/s11229-017-1668-5