Abstract
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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Notes
After reading a draft of this article, L. Manning gave us references to IRM data confirming the neurophysiological and neuroimaging evidence for protention and the dependence of protention on retention: Szpunar et al. (2007), Botzung et al. (2008). Further, more specific experiments would be required in order to quantify the coefficients we introduce here and check/adjust the linearity of this dependence.
Relaxation functions are among the simplest decreasing functions enabling to define a characteristic time τ in physics, they often represent the basic model for the return to the equilibrium of a system that was initially brought out of equilibrium, with the speed at which the system returns to the equilibrium f e of the system’s f function \(({\frac{{\hbox{d}}f}{{\hbox{d}}t}})\) remaining proportional to this interval \({\frac{{\hbox{d}}f}{{\hbox{d}}t}} = - {\frac{|f-f_e|}{\tau}}\).
Without forgetting Giordano Bruno who had an informal yet quite relevant notion of inertia, a few years prior to Galileo. It then became possible to understand planetary movements without God being required to push the planets around at all times. We similarly aim at a concept of inertia for living phenomena with no reference to “vital impetus” or divine thrust.
A paramecium manages the movements of about 2,000 cilia during highly complex swimming activities; some of its cilia also serve to direct food towards a “mouth” (opening upon the membrane), by means of very articulate movements.
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Acknowledgments
We would like to thank the anonymous referee for his/her critical comments and suggestions. Longo’s articles are downloadable from http://www.di.ens.fr/users/longo/.
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This paper was made possible only as part of an extended collaboration with Francis Bailly (see references), a dear friend and “maître à penser”, who contributed to the key ideas. Francis passed away in february 2008: we continue here our inspiring discussions and joint work.
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Longo, G., Montévil, M. Protention and retention in biological systems. Theory Biosci. 130, 107–117 (2011). https://doi.org/10.1007/s12064-010-0116-6
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DOI: https://doi.org/10.1007/s12064-010-0116-6