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# Probability in Living Systems

A special issue of Philosophies (ISSN 2409-9287).

Deadline for manuscript submissions: closed (30 November 2020) | Viewed by 14217

## Special Issue Editor

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Guest Editor
Department of Biology, Ehime University, Matsuyama, Ehime 790-8577, Japan
Interests: probability; entropy; information; semiosis; brain; consciousness; adaptation; evolution; fundamental principles of living systems
Special Issues, Collections and Topics in MDPI journals

## Special Issue Information

Dear Colleagues,

Living systems are characterized by their properties of self-organization and adaptation to their environments. Understanding principles operating in these properties is the central challenge in the science of living systems. We may say that living systems maintain their organization by producing specific internal events non-randomly, and also cope with their environments to enhance the certainty of favorable events for survival and reproduction. In other words, living systems appear to manage the probabilities of events occurring within the systems and in their environments. Here, we can connect this nature of living systems to another big challenge in the wider arena of science and philosophy, i.e., probability, which is a fundamental cross-disciplinary concept in science.

In the study of living systems, probability has received less attention than and has not been explored as effectively as information and entropy, which are also important cross-disciplinary concepts in science. However, both information and entropy can only be measured in terms of probability. Probabilistic events have been deeply explored using the mathematical theory of probability since Kolmogorov’s axiomatization, which provided mathematical consistency for the theory. However, many issues occur when the mathematical theory is applied to problems in real systems. This is because of the dual meaning of probability. Probability of an event includes mainly two interpretations: the epistemic or subjective interpretation (i.e., a degree of the certainty of the occurrence of the event for a subject); and the ontic or objective one (i.e., a proportion of the occurrence of the event in a population of events, or a system propensity or tendency to produce the event). This duality in interpretation may in turn produce the dual meaning of entropy (uncertainty/disorder) and the amount of information (reduction of uncertainty/reduction of disorder). This aspect suggests that the investigation of probability can be situated in the wider arena of research including information and entropy.

Furthermore, living systems are material systems that observe their environments. In other words, they are players within a larger system; in this sense, they may be both ontic (objective) and epistemic (subjective) entities, one aspect of which appears depending on the viewpoint. This kind of dual nature has not been explored effectively in relation to the probability concept in science as well as in traditional philosophy.

We call for papers focusing on the interconnection between probability and living systems in order to activate interdisciplinary discussions on this topic at an interface between science and philosophy. Authors may focus on a particular level or inter-level of biological hierarchy, including cells, organisms, populations and ecosystems, under a deterministic or indeterministic framework. Possible approaches may include, but are not limited to, those from quantum biology, cell biology, brain science (e.g., Bayesian brain), behavioral biology, biosemiotics, ecology, and evolutionary biology (e.g., propensity interpretation of fitness). The issue also welcomes papers based on a general, theoretical (conceptual or mathematical) models, and those based on traditional philosophy.

Prof. Dr. Toshiyuki Nakajima
Guest Editor

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## Keywords

• probability
• living systems
• information
• entropy
• Bayesian brain
• fitness
• evolution
• uncertainty
• organization

## Published Papers (5 papers)

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# Research

19 pages, 2131 KiB
Article
The Objective Bayesian Probability that an Unknown Positive Real Variable Is Greater Than a Known Is 1/2
by Christopher D. Fiorillo and Sunil L. Kim
Philosophies 2021, 6(1), 24; https://doi.org/10.3390/philosophies6010024 - 18 Mar 2021
Viewed by 2016
Abstract
If there are two dependent positive real variables ${{x}}_{1}$ and ${{x}}_{2}$, and only ${{x}}_{1}$ is known, what is the probability that ${{x}}_{2}$ is larger versus smaller than ${{x}}_{1}$? There is no uniquely correct answer according to [...] Read more.
If there are two dependent positive real variables ${{x}}_{1}$ and ${{x}}_{2}$, and only ${{x}}_{1}$ is known, what is the probability that ${{x}}_{2}$ is larger versus smaller than ${{x}}_{1}$? There is no uniquely correct answer according to “frequentist” and “subjective Bayesian” definitions of probability. Here we derive the answer given the “objective Bayesian” definition developed by Jeffreys, Cox, and Jaynes. We declare the standard distance metric in one dimension, $d\left(A,B\right)\equiv |A-B|$, and the uniform prior distribution, as axioms. If neither variable is known, $P\left({x}_{2}<{x}_{1}\right)=P\left({x}_{2}>{x}_{1}\right)$. This appears obvious, since the state spaces ${x}_{2}<{x}_{1}$ and ${x}_{2}>{x}_{1}$ have equal size. However, if ${{x}}_{1}$ is known and ${{x}}_{2}$ unknown, there are infinitely more numbers in the space ${x}_{2}>{{x}}_{1}$ than ${x}_{2}<{{x}}_{1}$. Despite this asymmetry, we prove $P\left({x}_{2}<{{x}}_{1}\mid {{x}}_{1}\right)=P\left({x}_{2}>{{x}}_{1}\mid {{x}}_{1}\right)$, so that ${{x}}_{1}$ is the median of $p\left({x}_{2}|{{x}}_{1}\right)$, and ${{x}}_{1}$ is statistically independent of ratio ${{x}}_{2}/{{x}}_{1}$. We present three proofs that apply to all members of a set of distributions. Each member is distinguished by the form of dependence between variables implicit within a statistical model (gamma, Gaussian, etc.), but all exhibit two symmetries in the joint distribution $p\left({x}_{1},{x}_{2}\right)$ that are required in the absence of prior information: exchangeability of variables, and non-informative priors over the marginal distributions $p\left({x}_{1}\right)$ and $p\left({x}_{2}\right)$. We relate our conclusion to physical models of prediction and intelligence, where the known ’sample’ could be the present internal energy within a sensor, and the unknown the energy in its external sensory cause or future motor effect. Full article
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17 pages, 329 KiB
Article
Examining the Continuity between Life and Mind: Is There a Continuity between Autopoietic Intentionality and Representationality?
by Wanja Wiese and Karl J. Friston
Philosophies 2021, 6(1), 18; https://doi.org/10.3390/philosophies6010018 - 21 Feb 2021
Cited by 16 | Viewed by 4711
Abstract
A weak version of the life-mind continuity thesis entails that every living system also has a basic mind (with a non-representational form of intentionality). The strong version entails that the same concepts that are sufficient to explain basic minds (with non-representational states) are [...] Read more.
A weak version of the life-mind continuity thesis entails that every living system also has a basic mind (with a non-representational form of intentionality). The strong version entails that the same concepts that are sufficient to explain basic minds (with non-representational states) are also central to understanding non-basic minds (with representational states). We argue that recent work on the free energy principle supports the following claims with respect to the life-mind continuity thesis: (i) there is a strong continuity between life and mind; (ii) all living systems can be described as if they had representational states; (iii) the ’as-if representationality’ entailed by the free energy principle is central to understanding both basic forms of intentionality and intentionality in non-basic minds. In addition to this, we argue that the free energy principle also renders realism about computation and representation compatible with a strong life-mind continuity thesis (although the free energy principle does not entail computational and representational realism). In particular, we show how representationality proper can be grounded in ’as-if representationality’. Full article
16 pages, 777 KiB
Article
Living Systems Escape Solipsism by Inverse Causality to Manage the Probability Distribution of Events
by Toshiyuki Nakajima
Philosophies 2021, 6(1), 11; https://doi.org/10.3390/philosophies6010011 - 09 Feb 2021
Cited by 1 | Viewed by 2143
Abstract
The external worlds do not objectively exist for living systems because these worlds are unknown from within systems. How can they escape solipsism to survive and reproduce as open systems? Living systems must construct their hypothetical models of external entities in the form [...] Read more.
The external worlds do not objectively exist for living systems because these worlds are unknown from within systems. How can they escape solipsism to survive and reproduce as open systems? Living systems must construct their hypothetical models of external entities in the form of their internal structures to determine how to change states (i.e., sense and act) appropriately to achieve a favorable probability distribution of the events they experience. The model construction involves the generation of symbols referring to external entities. This paper attempts to provide a new view that living systems are an inverse-causality operator. Inverse causality (IC) is an algorithmic process that generates symbols referring to external reality states based on a given data sequence. For applying this logical model involving if–then entailments to living systems involving material interactions, the cognizers-system model was employed to represent the IC process; here, living systems were modeled as a subject of cognition and action. A focal subject system is described as a cognizer composed of sub-cognizers, such as a sensor, a signal transducer, and an effector. Analysis using this model proposes that living systems invented the “measurers” for conducting IC operations through their evolution. Full article
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16 pages, 1912 KiB
Article
Is Organization of Living Systems Explained by Probability?
by Naoki Sato
Philosophies 2021, 6(1), 3; https://doi.org/10.3390/philosophies6010003 - 12 Jan 2021
Cited by 1 | Viewed by 2765
Abstract
Traditionally, life has been thought improbable without assuming a special principle, such as vital power. Here, I try to understand organization of living systems in terms of a more rational and materialistic notion. I have introduced the notion of inhomogeneity, which is a [...] Read more.
Traditionally, life has been thought improbable without assuming a special principle, such as vital power. Here, I try to understand organization of living systems in terms of a more rational and materialistic notion. I have introduced the notion of inhomogeneity, which is a novel interpretation of “negentropy”, and equivalent to “bound information”, according to the probabilistic interpretation of entropy. Free energy of metabolites is a labile inhomogeneity, whereas genetic information is a more stable inhomogeneity. Dynamic emergence can result from the conflict between two inhomogeneities, one labile and another stable, just like dialectic synthesis results from the conflict between thesis and antithesis. Life is a special type of dynamic emergence, which is coupled with reproduction mediated by genetic information. Biological membrane formation is taken as an example to formulate self-organization of biological systems through dynamic emergence. This system is ultimately driven by the Sun/Earth temperature difference, and is consistent with an increase in probability in the world. If we consider all entropy production related to life, such as degradation of materials and death of organisms, and ultimately the cooling of the Sun, probability always increases with the progress of living systems. Full article
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11 pages, 206 KiB
Article
Accommodating Probability to Durability as Facing the Onset of Biological Phenomena from Within
by Koichiro Matsuno
Philosophies 2020, 5(4), 47; https://doi.org/10.3390/philosophies5040047 - 18 Dec 2020
Cited by 3 | Viewed by 1720
Abstract
Life distinguishes itself from non-life in taking advantage of the cohesion of temporal origin which non-life cannot afford. The temporal cohesion letting the local participants adhere to each other in a contemporaneous manner refers to an instance of the precedent product being pulled [...] Read more.
Life distinguishes itself from non-life in taking advantage of the cohesion of temporal origin which non-life cannot afford. The temporal cohesion letting the local participants adhere to each other in a contemporaneous manner refers to an instance of the precedent product being pulled into the subsequent production. Setting the precedent is equivalent to preparing the conditions for the subsequent to follow. A concrete implementation of the cohesion of temporal origin, compared with the spatial cohesion common in physics, is found in the natural construction of a reaction cycle with use of the temporal affinity exerted from the immediate local environment. That construction is a temporally local phenomenon in the experiential domain, rather than in the theoretical. The cohesion originating in the local environment is due to the local act of measurement by the environment. A major component of the local environment to each reactant in the reaction cycle is the cycle itself. The cohesion specific to the reaction cycle rests upon the fact that every reaction product from the upstream production in the cycle comes to be fed upon by the immediate downstream production. Every production constituting the reaction cycle is temporally adjacent to and contemporaneous with the similar others residing in the whole cycle, in sharp contrast to the case of the open-ended linear chain of reaction. One externalist scheme of appreciating the internalist enterprise of constructing a durable reaction cycle in a contemporaneous manner may become possible as referring to the Bayesian probability. The durable reaction cycle may be made actual with probability unity under the condition that the products from the preceding production come with the protocol for the similar production to come subsequently. Full article