Towards measuring the semantic capacity of a physical medium demonstrated with elementary cellular automata
Introduction
Understanding the origin of life and its further evolution should include understanding how the first organic semantic information systems appeared (Küppers, 2015, Walker et al., 2017) and how the processing of semantic information evolved over time (Hernández and Jagus, 2016, Barbieri, 2015). The contingency between physical information carriers has been identified as a key property of semantic information (Monod, 1971, Barbieri, 2008). Examples are the mapping of an external signaling molecule to a second messenger inside a cell, or the mapping from triplets to amino acids in the genetic code, which are examples of organic codes (Barbieri, 2015). The development of such arbitrary symbol-meaning mappings may have added great flexibility in an organism's control system and increased its evolvability.
Following this line of thought, a formal method to asses the capacity of a chemical reaction network to process semantic information has been recently suggested (Görlich and Dittrich, 2013) and applied (Görlich et al., 2014, Neu et al., 2017). The basic idea is to measure semantic capacity as the number of molecular codes a network can implement. According to Görlich and Dittrich (2013), a molecular code is a contingent mapping between molecular species, that is, a mapping that cannot be inferred from knowing the network and the species alone. So far, the algorithms for finding all molecular codes of a given reaction network consider only the network's structure and do not require any kinetic information. A computational analysis of some chemical systems has pointed to a large spectrum of semantic capacities (Görlich and Dittrich, 2013, Neu et al., 2017). Basically no semantic capacity was found in a model of the atmosphere chemistry of Mars and combustion chemistries, whereas bio-chemical systems posses very high semantic capacities. Consequently, the hypothesis has been derived that life over the course of evolution is gaining access to (chemical) systems with increasing semantic capacity, that is, with an increasing ability to implement contingent mappings.
This paper develops further the idea that the semantic capacity of a physical medium can be measured by assessing its ability to implement a contingent mapping, called a code. For that, contingency (also called arbitrariness) is understood as a property of a mapping with respect to a medium. The medium can be physical (e.g., the combustion chemistry of hydrogen) or formal, e.g., a particular metabolic reaction network model or a cellular automaton as studied here. Furthermore, it is required that the medium can be configured in different ways, allowing to implement the mapping using particularly configured instances of the medium. So, it can be assumed that the mapping maps elements of the medium (called signs) to other elements of the medium (called meanings). Such mapping is called contingent, if an alternative mapping on the same domain of signs to the same codomain of meanings can be implemented by the same medium using a different configuration (called alternative context). Note that those mappings must be non-trivial, e.g., not constant, which is necessary for useful information processing.
For demonstration and evaluation, the approach is applied to elementary cellular automata (ECA) (Wolfram, 1984), which can represent certain physical media (Wolfram, 2002). Despite their simplicity, ECAs display a wide spectrum of different behaviors (Martinez, 2013), including computational universality (Cook, 2004). Because there are only 256 different ECAs, each denoted by a number in a standard way (Wolfram, 1984, Wikipedia, 2017), the space of all ECAs can be easily explored computationally.
Furthermore, in this work a link to information theory (Shannon, 1948) is established by taking multivariate mutual information (MMI) (McGill, 1954) for quantifying contingency. A negative value of MMI applied to three random variables representing sign, meaning, and context, respectively, is taken as as an indication of contingency.
The following results show how ECAs differ in their semantic capacities and that there is not a trivial relation to a CA's behavioral class (Martinez, 2013), shown for the classification according to Oliveira et al. (2001). Furthermore it is shown that the semantic capacity depends on how a meaning is defined. Interestingly, if the meaning should persist for a certain while, the highest semantic capacity is found in CAs with apparently simple behavior, i.e., the fixed-point and two-cycle class.
The choice of a medium, how signs, meanings and contexts are defined, how the meaning is used to implement mappings, all those decisions influence strongly the measures of semantic capacity, as is also shown in the subsequent study of ECAs. However the study also suggests a certain robustness of classifying the semantic capacity. Furthermore, it is possible to understand how a particular choice influences the results, which might lead to a concept of relative semantic capacity, i.e., relating the semantic capacity to how signs and meanings are actually used. This will add a pragmatic level to the theory, which needs to be carefully investigated in the future.
Section snippets
Elementary cellular automaton (ECA)
An elementary cellular automaton (Wolfram, 1984) is a deterministic, homogeneous, one-dimensional, binary cellular automaton with a neighborhood size of two, i.e., the new state ci(t + 1) ∈ {0, 1} of a cell i at time t + 1 depends on its own previous state ci(t) and the previous state of its two immediate neighbors i − 1 and i + 1 yielding the update scheme: ci(t + 1) = f(ci−1(t), ci(t), ci+1(t)). There are 256 different local state transition functions f : {0, 1}3 → {0, 1} and thus 256
A general approach to assess the semantic capacity of a medium
This paper follows the idea to measure the semantic capacity of a medium by assessing its ability to implement contingent mappings. A medium with a high semantic capacity can easily implement a (non-trivial) mapping f : S → M and a (non-trivial) alternative mapping f′ : S → M on the same domain (called signs) and codomain (called meanings). In order to show this, a number of assumptions are necessary and decisions have to be made that are described in the following procedure. The procedure is
Results
The result section shows how ECAs differ in their semantic capacity and how the semantic capacity is related to the behavioral class and to information theoretic properties (synergy) of the CA.
Discussion
The ability to implement a contingent mapping (code) has been found in all behavioral classes of elementary cellular automata as defined by Oliveira et al. (2001). There is even a null-class ECA, i.e. an ECA with a single fixed point as the only global attractor, able to implement a code. All two-cycle, complex, and chaotic ECAs can implement codes, if the meaning needs to persists only for a short amount of time (d = 1, Fig. 6 left).
The actual measurement depends on what is considered to be a
Conclusion
This paper indicates how a mediums capacity to implement contingent mappings, called codes, can objectively be measured; suggesting that we can also distinguish physical media by measuring their ability to implement contingent mappings. Ultimately this ability becomes a physical property. And since this ability is also suggested to be an important (or even essential) component of semantic information processing and meaningful sign-mediated communication, this work contributes also to a physical
References (24)
Universality and complexity in cellular automata
Phys. D: Nonlinear Phenom.
(1984)Biosemiotics: a new understanding of life
Naturwissenschaften
(2008)Code Biology
(2015)- et al.
Quantifying unique information
Entropy
(2014) - et al.
Chemotaxis and chemokinesis of living and non-living objects
Universality in elementary cellular automata
Complex Syst.
(2004)- et al.
Molecular codes in biological and chemical reaction networks
PLoS ONE
(2013) - et al.
Molecular codes in the human inner-kinetochore model: relating CENPS to function
Biosemiotics
(2014) - et al.
Bivariate measure of redundant information
Phys. Rev. E
(2013)
The nucleation of semantic information in prebiotic matter
Towards a synergy-based approach to measuring information modification
2013 IEEE Symposium on Artificial Life (ALIFE)
Cited by (3)
The semantic theory of language
2020, BioSystemsCitation Excerpt :The genetic code, on the other hand, was followed by many other organic codes in the first three thousand million years of the history of life, when our planet was exclusively inhabited by microorganisms (Barbieri, 2003). Among them, the sequence codes (Trifonov 1989, 1996, 1999), the histone code (Strahl and Allis, 2000; Turner, 2000, 2007; Kühn and Hofmeyr, 2014), the splicing codes (Barbieri, 2003; Fu, 2004; Wang and Cooper, 2007), the signal transduction codes (Barbieri, 2003), the compartment codes (Barbieri, 2003), the tubulin code (Verhey and Gaertig, 2007; Janke, 2014), the ubiquitin code (Komander and Rape, 2012), the molecular codes (De Beule et al., 2011; Görlich et al., 2011; Görlich and Dittrich, 2013; Dittrich, 2018) and the lamin code (Maraldi, 2018). With the origin of animals, about 600 million years ago, a second type of codes appeared on Earth, codes that are referred to as neural codes because they are rules between neural states.
A general model on the origin of biological codes
2019, BioSystemsCitation Excerpt :The genetic code was the first of a long succession of organic codes that have appeared in the history of life. Among them, the sequence codes (Trifonov, 1989, 1996, 1999), the sugar code (Gabius, 2000, 2009), the signal transduction codes (Barbieri, 2003), the splicing codes (Barbieri, 2003; Fu, 2004; Buratti et al., 2006; Wang and Cooper, 2007), the compartment codes (Barbieri, 2003), the tubulin code (Verhey and Gaertig, 2007; Janke, 2014), the nuclear signalling code (Maraldi, 2008), the ubiquitin code (Komander and Rape, 2012), the molecular codes (De Beule et al., 2011; Görlich et al., 2011; Görlich and Dittrich, 2013; Dittrich, 2018) and the lamin code (Maraldi, 2018). The evolution of life took place exclusively in single cells for about three billion years, but eventually some eukaryotes gave origin to multicellular creatures and new organic codes came into being.