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Are Borders Inside or Outside?

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Abstract

When a boat disappears over the horizon, does a distant observer detect the last moment in which the boat is visible, or the first moment in which the boat is not visible? This apparently ludicrous way of reasoning, heritage of long-lasting medieval debates on decision limit problems, paves the way to sophisticated contemporary debates concerning the methodological core of mathematics, physics and biology. These ancient, logically-framed conundrums throw us into the realm of bounded objects with fuzzy edges, where our mind fails to provide responses to plain questions such as: given a closed curve with a boundary (say, a cellular membrane) how do you recognize what is internal and what is external? We show how the choice of an alternative instead of another is not arbitrary, rather points towards entirely different ontological, philosophical and physical commitments. This paves the way to novel interpretations and operational approaches to challenging issues such as black hole singularities, continuous time in quantum dynamics, chaotic nonlinear paths, logarithmic plots, demarcation of living beings. In the sceptical reign where judgements seem to be suspended forever, the contemporary scientist stands for a sort of God equipped with infinite power who is utterly free to dictate the rules of the experimental settings.

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References

  • Achar, Y. J., Adhil, M., Choudhary, R., Gilbert, N., & Foiani, M. (2020). Negative supercoil at gene boundaries modulates gene topology. Nature, 577, 701–705.

    Article  Google Scholar 

  • Autrecourt N. 1940. The Universal Treatise. Marquette University Press, Milwaukee, Wisconsin, 1971.

  • Badiou, A. (2015). Being and Event. London: Bloomsbury.

    Google Scholar 

  • Bak, P., Tang, C., & Wiesenfeld, K. (1987). Self-organized criticality: an explanation of the 1/f noise. Physical Review Letters, 59, 381–384.

    Article  Google Scholar 

  • Bekenstein, J. D. (1973). Black holes and entropy. Physical Review D, 7(8), 2333–2346.

    Article  Google Scholar 

  • Bianconi, G., & Rahmede, C. (2016). Network geometry with flavor: From complexity to quantum geometry. Physical Review E, 93(3), 032315. https://doi.org/10.1103/PhysRevE.93.032315.

    Article  Google Scholar 

  • Bonalda D, Seveso L, Paris MGA. 2019. Quantum sensing of curvature. arXiv:1903.06905.

  • Borsuk, K. (1933). Dreisatzeuber die n-dimensionale euklidischesphare. Fundamenta Mathematicae, 20(1), 177–190.

    Article  Google Scholar 

  • Bradwardine, Thomas (1349?), 1955 [B-TP], Tractatus proportionum seu de proportionibus velocitatum in motibus, (H. Lamar Crosby, Jr. ed. and trans.) in Thomas of Bradwardine His Tractatus de Proportionibus. Its Significance for the Developement of Mathematical Physics, Madison, WI: University of Wisconsin Press.

  • Cao, Y., Fatemi, V., Fang, S., Watanabe, K., Taniguchi, T., et al. (2018). Unconventional superconductivity in magic-angle graphene superlattices. Nature, 556, 43–50.

    Article  Google Scholar 

  • Ceruti, M., & Damiano, L. (2018). Plural embodiment(s) of mind. Genealogy and guidelines for a radically embodied approach to mind and consciousness. Frontiers in Psychology. https://doi.org/10.3389/fpsyg.2018.02204.

    Article  Google Scholar 

  • Chesler PM. 2019. Singularities in rotating black holes coupled to a massless scalar field. arXiv:1905.04613

  • Collins, G. P. (2006). Computing with quantum knots. Scientific American, 294(4), 56–63.

    Article  Google Scholar 

  • Constant, A., Ramstead, M. J. D., Veissière, S. P. L., & Friston, K. (2019). Regimes of expectations: An active inference model of social conformity and human decision making. Frontires in Psychology. https://doi.org/10.3389/fpsyg.2019.00679.

    Article  Google Scholar 

  • de Arcangelis, L., & Herrmann, H. J. (2010). Learning as a phenomenon occurring in a critical state. Proceedings of the National Academy of Sciences, 107, 3977–3981.

    Article  Google Scholar 

  • Di Concilio, A., Guadagni, C., Peters, J. F., & Ramanna, S. (2018). Descriptive proximities. Properties and interplay between classical proximities and overlap. Mathematics in Computer Science, 12, 91–106.

    Article  Google Scholar 

  • Dodson, C. T. J., & Parker, P. E. (1997). A user’s guide to algebraic topology. Dordrecht: Kluwer.

    Book  Google Scholar 

  • Don, A. P., Peters, J. F., Ramanna, S., & Tozzi, A. (2020). Topological view of flows inside the bold spontaneous activity of the human brain. Frontiers in Computational Neuroscience. https://doi.org/10.3389/fncom.2020.00034.

    Article  Google Scholar 

  • Flavahan, W. A., Drier, Y., Johnstone, S. E., Hemming, M. L., Tarjan, D. R., et al. (2019). Altered chromosomal topology drives oncogenic programs in SDH-deficient GISTs. Nature, 575, 229–233.

    Article  Google Scholar 

  • Friston, K. (2010). The free-energy principle: A unified brain theory? Nature Reviews Neuroscience, 11(2), 127–138. https://doi.org/10.1038/nrn2787.

    Article  Google Scholar 

  • Frottin, F., Schueder, F., Tiwary, S., Gupta, R., Körner, R., et al. (2019). The nucleolus functions as a phase-separated protein quality control compartment. Science, 365(6451), 342–347. https://doi.org/10.1126/science.aaw9157.

    Article  Google Scholar 

  • Fukushima, M., Betzel, R. F., He, Y., van den Heuvel, M. P., Zuo, X. N., & Sporns, O. (2017). Structure-function relationships during segregated and integrated network states of human brain functional connectivity. Brain Structure and Function. https://doi.org/10.1007/s00429-017-1539-3.

    Article  Google Scholar 

  • Gaiha, G. D., Rossin, E. J., Urbach, J., Landeros, C., Collins, D. R., et al. (2019). Structural topology defines protective CD8+ T cell epitopes in the HIV proteome. Science, 364(6439), 480–484. https://doi.org/10.1126/science.aav5095.

    Article  Google Scholar 

  • Giusti, C., Ghrist, R., & Bassett, D. (2016). Two’s company, three (or more) is a simplex: Algebraic-topological tools for understanding higher-order structure in neural data. Journal of Computational Neuroscience, 41(1), 1–14. https://doi.org/10.1007/s10827-016-0608-6.

    Article  Google Scholar 

  • Gogberashvili, M. (2019). Can quantum particles cross a horizon? International Journal of Theoretical Physics, 58, 3711–3725.

    Article  Google Scholar 

  • Golubitsky, M., & Stewart, I. (2015). Recent advances in symmetric and network dynamics. Chaos, 25(9), 097612.

    Article  Google Scholar 

  • Grant, E. (1973). Medieval explanations and interpretations of the dictum that ‘nature abhors a vacuum’. Traditio, 291973, 327–355.

    Article  Google Scholar 

  • Grant, E., & Nelson, B. (1962). Hypotheses in late medieval and early modern science. Daedalus, 91(3), 599–616.

    Google Scholar 

  • Hannan S, Villanova PMR. 2016. The Envious Instant: Material Conditions of Truth in Thomas Bradwardine https://hcommons.org/app/uploads/sites/1000608/2017/06/The_Envious_Instant_Material_Conditions.pdf

  • Hawking, S. (2005). Information loss in black holes. Physical Review D, 72(8), 084013. https://doi.org/10.1103/PhysRevD.72.084013.

    Article  Google Scholar 

  • Heytesbury W. 1979. William of Heytesbury on “Insoluble” Sentences, (Paul V. Spade ed. and transl.), Toronto: Pontifical Institute of Medieval Studies.

  • Heytesbury, W. (1984). On maxima and minima. Synthese historical library (text and study in the history of logic and philosophy). Dordrecht: Springer.

    Google Scholar 

  • Jordan C. 1893. Cours d'analyse, 1, Gauthier-Villars.

  • Jordan, D. W., & Smith, P. (2007). Non-linear ordinary differential equations: Introduction for scientists and engineers (4th ed.). Oxford: Oxford University Press.

    Google Scholar 

  • Kleineberg, K.-K., Boguñá, M., Ángeles Serrano, M., & Papadopoulos, F. (2016). Hidden geometric correlations in real multiplex networks. Nature Physics, 12, 1076–1081. https://doi.org/10.1038/nphys3812.

    Article  Google Scholar 

  • Koczkodaj, W. W., Magnot, J.-P., Mazurek, J., Peters, J. F., Rakhshani, H., Soltys, M., et al. (2017). On normalization of inconsistency indicators in pairwise comparisons. International Journal of Approximate Reasoning, 86, 73–79. https://doi.org/10.1016/j.ijar.2017.04.005.

    Article  Google Scholar 

  • Maletic, S., & Zhao, Y. (2017). Multilevel integration entropies: The case of reconstruction of structural quasi-stability in building complex datasets. Entropy, 19(4), 172. https://doi.org/10.3390/e19040172.

    Article  Google Scholar 

  • Mohan, K., Ueda, G., Kim, A. R., Jude, K. M., Fallas, A. J., et al. (2019). Topological control of cytokine receptor signaling induces differential effects in hematopoiesis. Science. https://doi.org/10.1126/science.aav7532.

    Article  Google Scholar 

  • Moreva, E. V., Brida, G., Gramegna, M., Giovannetti, V., Maccone, L., & Genovese, M. (2013). Time from quantum entanglement: An experimental illustration. Physical Review A, 89, 052122.

    Article  Google Scholar 

  • Murdoch, J. E. (1964). Superposition, congruence and continuity in the Middle Ages. L'aventure de la science. Histoire de la pensée. XII Paris: Hermann.

    Google Scholar 

  • Nielsen, L. O. (1982). Thomas Bradwardine’s treatise on ‘incipit’ and ‘desinit’: Edition and introduction. Cahiers de l’Institute du Moyen Age Grec et Latin, 42, 1–83.

    Google Scholar 

  • Noé, F., Olsson, S., Köhler, J., & Wu, H. (2019). Boltzmann generators: Sampling equilibrium states of many-body systems with deep learning. Science. https://doi.org/10.1126/science.aaw1147.

    Article  Google Scholar 

  • O’ Donnell JR. 1939. Appendix: Questio de qua respondit Magister Nicholas de Utricuria. In. Nicholas of Autrecourt. Mediaeval Studies, I. Pontifical Institute of Mediaeval Studies, Toronto, Canada.

  • Offredus A. 1478. De primo et ultimo instanti ad defensionem communis opinionis adversus Petrum Mantuanum. Publisher Salomon, Bernard, ca. 1506-ca. 1561. Facsimile Publisher, 2016, ISBN-13: 978–9333632997.

  • Pelacani B. 2005. Questiones circa tractatum proportionum Magistri Thome Braduardini. Editor, Biard J. S. Rommevaux, Paris.

  • Perkins, T. J., Foxall, E., Glass, L., et al. (2014). A scaling law for random walks on networks. Nature Communications, 5, 5121.

    Article  Google Scholar 

  • Pettini, G., Gori, M., Franzosi, R., Clementi, C., & Pettini, M. (2019). On the origin of phase transitions in the absence of symmetry-breaking. Physica A: Statistical Mechanics and its Applications, 516, 376–392.

    Article  Google Scholar 

  • Porretano G. 2009. Libro dei sei principi. Eds., Paparella F. Bompiani, Testi a Fronte.

  • Richardson, M. J., Dale, R., & Marsh, K. L. (2014). Complex dynamical systems in social and personality psichology. In H. T. Reis & C. M. Judd (Eds.), Handbook of research methods in social and personality psychology (2nd ed.). Cambridge: Cambridge University Press.

    Google Scholar 

  • Rossine, F. W., Martinez-Garcia, R., Sgro, A. E., Gregor, T., & Tarnita, C. E. (2020). Eco-evolutionary significance of “loners”. PLOS biology. https://doi.org/10.1371/journal.pbio.3000642.

    Article  Google Scholar 

  • Rovelli, C. (1996). Relational quantum mechanics. International Journal of Theoretical Physics, 35, 1637–1678.

    Article  Google Scholar 

  • Schuss, Z., Basnayakey, K., & Holcmany, D. (2017). Redundancy principle for optimal random search in biology. BioRxiv. https://doi.org/10.1101/210443.

    Article  Google Scholar 

  • Shapiro, H., & Shapiro, C. (1965). De primo et ultimo instanti Des Walter Burley. Archiv für Geschichte der Philosophie, 47(1–3), 157–173.

    Article  Google Scholar 

  • Sherrill SP, Timme NM, Beggs JM, Newman EL. 2020. Correlated activity favors synergistic processing in local cortical networks in vitro at synaptically relevant timescales. Network Neuroscience. 1–20.

  • Smerlak, M., & Rovelli, C. (2007). Relational EPR. Foundations of Physics, 37, 427–445.

    Article  Google Scholar 

  • Smith, R. (2013). Period doubling, information entropy, and estimates for Feigenbaum’s constants. International Journal of Bifurcation and Chaos, 23(11), 1350190.

    Article  Google Scholar 

  • Suter, T. A. C. S., & Jaworski, A. (2019). Cell migration and axon guidance at the border between central and peripheral nervous system. Science. https://doi.org/10.1126/science.aaw8231.

    Article  Google Scholar 

  • Sylla, D. E. (1998). God, indivisibles, and logic in the later middle ages: Adam Wodeham’s response to Henry of Harclay. Medieval Philosophy and Theology, 7(1), 69–87.

    Article  Google Scholar 

  • The BIG Bell Test Collaboration. (2018). Challenging local realism with human choices. Nature, 557, 212–216.

    Article  Google Scholar 

  • Thijssen JMMH. 2009. The Debate over the nature of motion: John Buridan, Nicole Oresme and Albert of Saxony. With an edition of John Buridan's "Quaestiones super libros Physicorum, secundum ultimam lecturam", Book III, Q. 7. Early science and medicine, 14, /3, Evidence and Interpretation: Studies on Early Science and Medicine in Honor of John E. Murdoch, 186–210.

  • Tozzi, A., Peters, J. F., Fingelkurts, A. A., Fingelkurts, A. A., & Marijuán, P. C. (2017). Topodynamics of metastable brains. Physics of Life Reviews, 21, 1–20. https://doi.org/10.1016/j.plrev.2017.03.001.

    Article  Google Scholar 

  • Tozzi, A. (2019). The multidimensional brain. Physics of Life Reviews, 31, 86–103. https://doi.org/10.1016/j.plrev.2018.12.004.

    Article  Google Scholar 

  • Tozzi, A., & Peters, J. F. (2019). Points and lines inside our brains. Cognitive Neurodynamics, 13(5), 417–428. https://doi.org/10.1007/s11571-019-09539-8.

    Article  Google Scholar 

  • Tozzi, A., & Papo, D. (2020). Projective mechanisms subtending real world phenomena wipe away cause effect relationships. Progress in Biophysics and Molecular Biology, 151, 1–13. https://doi.org/10.1016/j.pbiomolbio.2019.12.002.

    Article  Google Scholar 

  • Tozzi, A., & Peters, J. F. (2020). Removing uncertainty in neural networks. Cognitive Neurodynamics, 14, 339–345. https://doi.org/10.1007/s11571-020-09574-w.

    Article  Google Scholar 

  • Trifogli, C. (2017). Walter burley on the incipit and desinit of an instant of time. Vivarium, 55(1–3), 85–102.

    Article  Google Scholar 

  • Yang, J. M. (2018). A relational formulation of quantum mechanics. Scientific Reports, 8, 13305.

    Article  Google Scholar 

  • Walker GF. (2018). Nicholas of Autrecourt’ Quaestio de intensione visionis revisited: the schola Oxoniensis and Parisian masters on limit decision problems. In: Goubier F, Roques M, Duba W, Schabel C. Brill (ed.), The Instant of Change in Medieval Philosophy and Beyond. Academic Pub, ISBN-13: 978-9004367913

  • Wesson, P. S. (1980). The application of dimensional analysis to cosmology. Space Science Reviews, 27(2), 117. https://doi.org/10.1007/bf00212237.

    Article  Google Scholar 

  • Zizzi, P. (2018). Entangled spacetime. Modern Physics Letters A, 33, 1850168.

    Article  Google Scholar 

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  1. Department of Physics, Center for Nonlinear Science, University of North Texas, 1155 Union Circle #311427, Denton, TX, 76203-5017, USA

    Arturo Tozzi

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Tozzi, A. Are Borders Inside or Outside?. Found Sci 27, 489–505 (2022). https://doi.org/10.1007/s10699-020-09708-7

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