Integral Biomathics

Historically, mathematics developed hand-in-hand with the physical sciences. While biological processes must obey the laws of physics, biology is not reducible to physics (otherwise we would not be able to distinguish one set of phenomena from the other!), and therefore mathematics that have been adequate for describing physical processes are often inadequate to describe biological ones. In consequence, I argue that the a new phase of scientific development is required in which mathematicians turn to biological processes for inspiration in creating novel forms of mathematics appropriate to describe biological functions in a more useful manner than has been done so far. Many the kinds of problems that seem to remain unaddressable at present involve forms of mathematics that currently have competing assumptions. For example, biologists need to describe phenomena that involve discrete and continuous functions simultaneously (control of metabolism through binding of single molecules to unique gene promoters; the statistical description of continuously varying molecular complexes); they need to handle spatial descriptors (geometry?) at the same time as kinetic data (calculus?) to explain developmental processes; they need to explain how scalar processes (random diffusion) gave rise to vectorial ones (facilitated transport). These, and other hybrid problems described in this paper, suggest that a fertile field of enquiry exists for mathematicians interested in developing new forms of biologically-inspired mathematics. I predict the result of the development of this new field of biologically-inspired mathematics will be as fundamentally revolutionary as physics-inspired mathematics was during the original Scientific Revolution.

Information processing in the brain is performed by propagating data through an array of neuronal networks, each having unique structural and topological architectures. However, the mechanisms that specify these architectures are not well understood. We found that neuronal networks

in vitro

determine the pattern and strength of their connectivity by designing the way dendrites overlap. The branches of neighboring dendrites converge in a collective and ordered fashion, leading to a network configuration that enables axons to innervate multiple and remote dendrites using short wiring lengths. In addition, the convergence sites are associated with synaptic clusters of higher density and strength than found elsewhere, leading to patchy distribution of synaptic strength in the network. Thus, controlled design of the overlap among dendrites patterns and strengthens neuronal connectivity in neuronal networks.

How do higher mental processes, learning, intentions, thoughts, emotions, arise from the functioning of the brain? That is the question which, with Jean-Paul Vanbremeersch, we have attempted to approach in the model MENS (for

Memory Evolutive Neural Systems

), proposing a unified frame for the functioning of the neural, mental and cognitive systems. It is an application to neuro-cognitive systems of our Memory Evolutive Systems, a model for self-organized multi-scale dynamic systems, based on a ’dynamic’ theory of categories (a summary on MES is given by Ehresmann & Simeonov, 2011, in this volume). Here I just indicate the main ideas; for more details, cf. Ehresmann & Vanbremeersch (2007, 2009).

Given the tremendous advances that have been made in our understanding of the mechanics of neural systems, there has been remarkably little progress in understanding how they process information. Here is it proposed that a major obstacle has been confusion about the concepts of information and probability. It is suggested that the correct definition of probabilities is strictly Bayesian, in which probabilities are always entirely conditional on information. It is further proposed that to best understand the brain, we should use Bayesian principles to describe what the brain knows about its world. Although such a “first-person” Bayesian approach has recently become prominent, its success has so far been almost entirely restricted to accounts of phenomena such as perception and cognition. The present work demonstrates how the Bayesian approach can be grounded in biophysics. Boltzmann’s distribution from statistical mechanics is used to derive probability distributions that are conditional entirely on the information held within single molecular sensors. By integrating information from a multitude of sensors within its membrane voltage, a neuron thereby reduces its uncertainty about the state its world. A major virtue of this integrated view of information and biophysics is that it allows us to identify a single and general computational goal for the function of the nervous system, which is to minimize its uncertainty (about the biological goals of the animal). This computational goal has recently served as the basis for a general theory of information processing within the nervous system (Fiorillo, 2008).

The Escherichia coli is a bacterium that comfortingly lives in the human gut and one of the best known living organisms. The sensitivity of this cell to environmental changes is reflected in two kind of movements that can be observed in a swimming bacterium: “run” towards an attractant, for example food, and “tumbling”, in which a new direction is chosen randomly for the next “run”.

This simple bimodal behavior of the

E. coli

constitutes in itself a paradigm of adaptation in which roboticists and cognitive psychologists have found inspiration. We present a new approach to synaptic plasticity in the nervous system by scrutinizing

Escherichia coli

’s motility and the signaling pathways that mediate its adaptive behavior. The formidable knowledge achieved in the last decade on bacterial chemotaxis, serve as the basis for a theory of a simple form of learning called habituation, that is applicable to biological and other systems. In this paper we try to establish a new framework that helps to explain what signals mean to the organisms, how these signals are integrated in patterns of behavior, and how they are sustained by an internal model of the world. The concepts of adaptation, synaptic plasticity and learning will be revisited within a new perspective, providing a quantitative basis for the understanding of how brains cope with a changing environment.

The traditional research method of the natural sciences chooses an element paying attention to the various elements in the natural world and analyzing their characteristics and components. To analyze the complicated structure of nature, one normally applies a highly precise device and the sophisticated expertise. This method will exclude other elements of the natural world, and will ignore mutual relations between elements that the network has. Such methods and results contribute to human profit immediately. On the other hand, by ignoring the function within the whole of the natural world, naturally we will face the environmental disruption threatening our survival. Thus modern technology resembles the person who is preoccupied with a specific thing in a forest, and loses his way. Because nature has a simpler aspect as a whole, it may not need the high quality technology for the understanding of nature as the whole. We have changed natural environments towards our profit for a long time. But, a protozoan (the lower animals) such as the myxomycetes let themselves adapt themselves to their environment by changing their lifestyle. Such a protozoan gives us valuable suggestions for our survival, and the new findings of a natural system provide a good opportunity to re-examine the scientific method. To understand nature as a whole, regardless of creatures and inanimate objects, it is necessary to understand how the systems of nature connect each other. Therefore, to obtain new findings on the mutual relations between environment and living creatures, in general, the ecosystem (or the behaviors of creatures) are investigated. The myxomycetes which have the time period of amoeba and a short life cycle, are considered best for observation of behaviors in environment.

In the plasmodium of

Physarum polycephalum

, we confirmed that galvanotaxis causes dilation of the tubular vein, the increment of resting potential, phase reversal of movement, and rapid flow of protoplasm streaming. In this paper, we show that the electric field strength can be used as an effective stimulus to motion control of a plasmodium on an agar-agar surface. (1) Galvanotaxic reinforcement: Our results show that the velocity of crawling increases in proportion to the DC electrical stimulus, up to a specific velocity. (2) Remaining galvanotaxis: A synthetic plasmodium composed of a experienced plasmodium which has been stimulated by the electric field strength and an inexperienced plasmodium which has not been stimulated, shows more rapid crawling than plasmodium which has not been stimulated. (3) Galvanotaxic application: In the experiment using a T-shaped path consisting of one path of feeble electric field strength and one with no electrical field, an experienced plasmodium, chooses almost always a path without the electrical field. On the other hand, the path chosen by an inexperienced plasmodium is always random. Our method has significant possibilities to find new findings for origin of memory and learning by a simple animal model, the plasmodium of

Physarum polycephalum

.

This paper claims that biological systems will more effectively create organized complexity if they use probabilistic inference that is context-sensitive. It argues that neural systems combine local reliability with flexible, holistic, context-sensitivity, and a theory, Coherent Infomax, showing, in principle, how this can be done is outlined. Ways in which that theory needs further development are noted, and its relation to Friston’s theory of free energy reduction is discussed.

Cells are the basic components from which living systems are composed. We describe an abstract version of a cell, and use it to discuss what cells really are doing, particularly in terms of information and information processing. Cells are characterised in terms of traffic across their boundary. We discuss the issues posed by an information-based view of this.

We develop a hierarchical model for an organism which is primarily based on structural scale. This is then compared with the Kronig-Penney model for electron propagation in a crystal. Both models exhibit similar multi-level structure, where the levels are separated by complex or forbidden regions. We conclude that cross-modeling between natural hierarchy and electron band structures may help in formulating future models of biological systems.

Within the framework of info-computationalism, morphological computation is described as fundamental principle for all natural computation (information processing).

This paper compares two complementary theories, Simeonov’s Wandering Logic Intelligence and Ehresmann’s & Vanbremeersch’s Memory Evolutive Systems, in view of developing a common framework for the study of multi-scale complex systems such as living systems. It begins by a brief summary of WLI and MES, then analyzes their resemblances and differences. Finally, the article provides an outlook for a future research.

There have recently been some computational or mathematical formalization studies on closedness of living systems such as autopoiesis and (M,R) systems. In particular, some have mentioned relationships between cartesian closed categories and

λ

–calculus. Following this line, the paper proposes a framework to formalize autopoiesis by combining category theory and

λ

–calculus more strictly, by introducing an equivalence between the category of cartesian closed categories and that of

λ

–calculi while providing a formalization of the distinction between organization and structure in autopoietic systems.

Multi-agent systems have been studied in various contexts of both application and theory. We take Dynamic Epistemic Logic (DEL), one of the formalisms designed to reason about such systems, as the foundation of the language we will build.

BioAmbient calculus is an extension of

π

-calculus, developed largely for applications to biomolecular systems. It deals with ambients and their ability to communicate and to execute concurrent processes while moving.

In this paper we combine the formalism of Dynamic Epistemic Logic together with the formalism of BioAmbient Calculus in order to reason about knowledge maintained and gained upon process transitions. The motivation lies in developing a language that captures locally available information through assignment of knowledge, with potential application to biological systems as well as social, virtual, and others.

We replace the ambients of BioAmbient Calculus with agents, to which we attribute knowledge, and explore the parallels of this treatment. The resulting logic describes the information flow governing mobile structured agents, organized hierarchically, whose architecture (and local information) may change due to actions such as

communication

,

merging

(of two agents),

entering

(of an agent into the inner structure of another agent) and

exiting

(of an agent from the structure of another). We show how the main axioms of DEL must be altered to accommodate the informational effects of the agents’ dynamic architecture.

The origin of life from matter and the subsequent emergence of mind were fundamental events. Our work is based on the idea that the chemical/genetic/mathematical framework developed over the last 150 years to explain the first is conceptually similar to the neural/psychological/mathematical framework needed to understand the second. First we outline the first, seemingly adequate, framework and then we explain some related, unusual and controversial, ideas that offer a “translation” into neural terms. The core idea is that the extraordinary, mysterious and qualitatively unique features of “life” and “mind” arise because of extraordinary (though completely explicable) levels of accuracy of the relevant elementary processes (base-copying and synaptic strengthening). The living and the mental might hinge on prosaic, though accurate, lower-level machinery.

Research into natural and artificial intelligence can overlook that natural intelligence capable of anticipating the future has a potential cost, mediated by cognitive factors involved in the stress response, leading to high allostatic load (‘wear and tear’). This theoretical paper suggests that nature may have partly resolved the problem by using the same mechanism—an adaptation of the stress response enabling a new and flexible balance of accurate and inaccurate assessments of the animal’s control over the environment—to (a) generate flexible, high-level general intelligence in humans and (b) reduce allostatic load to within adaptive parameters. This new form of intelligence, probably appearing in early hominins, acts as a buffer between the animal and its environment. A tentative framework for information processing around the primate brain is proposed, showing where and how such ‘buffer intelligence’ could have arisen and been exploited in early hominins. This appears to be a development of a function undertaken in non-human primates by the neural correlates of consciousness, an area of the non-human primate brain where there is no, or very little, intelligence. There is a brief discussion of whether this principle might enable the spread of a capacity for intelligence throughout a complex adaptive system, with flexible linguistic syntax in humans as an example.

In this study, the alternation of the passively active and actively passive attitudes is considered as the basic scheme of communication in a society-like system. We construct a model for swarming behavior based only on mutual anticipation implementing this basic scheme of communication, and we estimate a swarm as a mobile network consisting of mutual anticipation structures. In particular, we show that a mutual anticipation structure can be expressed as a fixed point with respect to equivalence classes in a network and that redundant connections in a mutual anticipation structure can contribute to generating and maintaining a robust and dynamic swarming behavior.

This position paper discusses the potential contributions of the ‘operator hierarchy’ theory to the INBIOSA project. The operator hierarchy offers a fundamental, theoretical, multilevel methodology for analysing natural organisation. In this theory, the word ‘operators’ generically represents the physical particles and the organisms. The operators theory may act as a backbone for modelling approaches because it offers a general theory describing how hierarchical levels of organisation emerge along three dimensions: from interactions between operator, from the complexity increases within operator and from the complexity increases leading to higher level operators.

In this paper we explore a variant of a two dimensional realization of the model presented in Ref. [1], in particular examining the structure of the distributions of species produced by the model, and exploring the ways in which the functions defining competition and carrying capacity interact to give rise to these structures.

The development of engineered systems having properties of autonomy and intelligence has been a visionary research goal of the twentieth century. However, there are a number of persistent and fundamental problems that continue to frustrate this goal. Behind these problems is an outmoded industrial foundation for the contemporary discourse and practices addressing intelligent robotics that must be superseded as engineering progresses more deeply into molecular and biological modalities. These developments inspire the proposal of a paradigm of engineered synthetic intelligence as an alternative to artificial intelligence, in which intelligence is pursued in a bottom-up way from systems of molecular and cellular elements, designed and fabricated from the molecular level and up. This paradigm no longer emphasizes the definition of representation and the logic of cognitive operations. Rather, it emphasizes the design of self-replicating, self-assembling and self-organizing biomolecular elements capable of generating cognizing systems as larger scale assemblies, analogous to the neurobiological system manifesting human cognition.

We have applied the concepts from the mathematical theory of cellular automata – as developed to understand the emergence of spacetime at Planck scale – to consciousness. This gives rise to a digital, spacetime solution to the mind/body problem.

This article attempts to resolve the age-old conflict of determinism and free will. The problem is approached from two directions: biological information processing and physical determinism at the ontological and the epistemological levels. It is shown that biological information processing is neither absolutely deterministic nor completely random. It is shown that Laplace’s determinism can neither be proved nor disproved and is, therefore, an epistemological choice. It is further shown that a) Boltzmann’s statistical mechanics is irreconcilable with Newtonian mechanics, contrary to Boltzmann’s own claim, b) microscopic reversibility cannot possibly give rise to macroscopic irreversibility, c) Zermelo’s recurrence paradox and Loschmidt’s velocity-reversal paradox are valid arguments against Boltzmann’s claim, and d) in breaking the tie with Newtonian mechanics, Boltzmann was actually the hero that had freed us from the bondage of absolute physical determinism. Last but not least, it is impossible to design a scientific experiment to test the existence or non-existence of free will because of the impossibility to maintain the required homogeneity of human test samples. However, individuals who believe in the existence of free will have a more consistent worldview than non-believers. If free will does not exist, it is futile and meaningless to attempt to convince others that free will does not exist.

It is argued that at a sufficiently deep level the conventional quantitative approach to the study of nature faces difficult problems, and that biological processes should be seen as more fundamental, in a way that can be elaborated on the basis of Peircean semiotics and Yardley’s Circular Theory. In such a world-view, Wheeler’s

observer-participation

and emergent law arise naturally, rather than having to be imposed artificially. This points the way to a deeper understanding of nature, where meaning has a fundamental role to play that is invisible to quantitative science.

A quantum mechanism for nomogenesis is conjectured.

I have been invited to make a short comment on an essay by Brian Josephson. My comment will be more general, in the sense that what I have to say can be seen as a critique of science as it is done since the closure of Plato Academy in Athens about 1500 years ago. This comment is also inspired by Brian Josephson’s talk ”Which Way for Physics” easily accessible on the Net.

This is a review of the article by Brian Josephson (2012) entitled “Biological Observer- Participation and Wheeler’s Law without Law”.

Developmental process in biology is manifestation of time as a marker of preserving the class identity of the participating molecules. A concrete case in point is the binding sites for transcription factors in the genome. Although each bond between the transcription factor and the DNA molecule to be transcribed is relatively weak and can easily be detached by thermal agitations available in the ambient, the transcription from the DNA to a messenger RNA molecule could smoothly proceed if the concentration of the transcription factors is not too low. The transcription could proceed without interruptions if the binding site is soon replenished by another transcription factor molecule of a similar kind available in the neighborhood. What remains significant to the transcription is the class identity of the transcription factors in the sense that it could proceed without interruptions even if the transcription-factor molecules are frequently exchanged. Characteristic to the transcription process is the occurrence of time as a marker of preserving the class identity of the transcription-factor molecules toward the DNA molecule to be transcribed. Time as a marker of preserving the class identity of molecules is ubiquitous in biology.

I attempt to point to various discursive projects that are relative to the problem of understanding change, which most current scientific perspectives cannot deal with, and never faced because the social role of the natural sciences has been to support technology development.

The division into holistic and reductionistic methods of thinking and inquiry was present in all epochs and in all domains of intellectual activity, with the former usually having an aura of mystery. The paper is providing a short exposition of the presence of, and need for the holistic methods. An approach to information integration is presented within a general framework of information understood as identification of variety. An outline of the formalism of information integration in terms of closure spaces developed in earlier papers of the author for the study of consciousness is presented here for the more general purpose. This formalism can serve as a foundation for more general methodology for holistic description of a wide class of systems, which can be associated with information. Since the level of information integration can vary from total disintegration to complete integration with many degrees in between, the formalism shows that such methodology can combine the two formerly antagonistic approaches into one.

Our knowledge related to the entailments of functionalities of different biological processes as they enable sentience to arise in the human is still limited due to the biological complexity of the body. There are two interrelated research paradigms that can be developed to approach this problem– one paradigm seeks to study the body and articulate its entailments (intra-functionalities) at multiple scales over time; the second paradigm seeks to glean knowledge from this study of biological processes and create new forms of computation to enable us to transcend the limitations of current computational modes. The nature and scope of the question necessitates an transdisciplinary approach to research through the development of a multi-perspective approach to knowledge production. Here, key solutions can in part arise at the interstices between disciplines, and potentially enable us to define and ‘chip away’ at the problem set. Central is observing the body as a distributed network of computational processes that function at different physical scales as well as across time-dependent, process-oriented accretive frames. We can articulate the study of the body by calling it an electrochemical computer— a computer whose deep functionality is not yet fully entailed. Historically the nature of the problem has been to isolate a biological system and study its entailments to ascertain its functionality. Yet, the nature of sentience asks us as researchers to take a more holistic approach, despite the complexity at play. These two paradigms then become a long-term problem set that a network of high-end researchers can collaborate on, by bringing different areas of expertise to the table. The notion of developing a biomimetic/bio-relational

Engine of Engines— A Computational Ecology

(Stengers 2005) derives from observing computational systems at work in the body and approaching them through observation— through technological, mathematical and/or computational abstraction. Where the body has been described as functioning as a computational system that transcends the Turing limit (Siegelmann 1999)(Maclennan 2003)(Penrose 1989) new approaches to computation need to be undertaken to reflect this deep complexity.

A chronological listing of ten scientific insights obtained by a theoretical biologist over half a century is presented. The circle spans many fields of science (engineering, chemistry, physics) exploring and exploding many accepted concepts. What is only touched upon is the assignment of the Now as the only place at which anything can be done and appreciated in our private qualia.

The INBIOSA project brings together a group of experts across many disciplines who believe that science requires a revolutionary transformative step in order to address many of the vexing challenges presented by the world. It is INBIOSA’s purpose to enable the focused collaboration of an interdisciplinary community of original thinkers.