arXiv subjects

Stuart Kauffman

Publications and source records attributed to Stuart Kauffman.

At least 37 records · Page 2Linked to original sources

arXiv2020

The expected number of viable autocatalytic sets in chemical reaction systems

The emergence of self-sustaining autocatalytic networks in chemical reaction systems has been studied as a possible mechanism for modelling how living systems first arose. It has been known for several decades that such networks will form within systems of polymers (under cleavage and ligation reactions) under a simple process of random catalysis, and this process has since been mathematically analysed. In this paper, we provide an exact expression for the expected number of self-sustaining autocatalytic networks that will form in a general chemical reaction system, and the expected number of these networks that will also be uninhibited (by some molecule produced by the system). Using these equations, we are able to describe the patterns of catalysis and inhibition that maximise or minimise the expected number of such networks. We apply our results to derive a general theorem concerning the trade-off between catalysis and inhibition, and to provide some insight into the extent to which the expected number of self-sustaining autocatalytic networks coincides with the probability that at least one such system is present.

q-bio.MN↗

arXiv2019

Self-referential basis of undecidable dynamics: from The Liar Paradox and The Halting Problem to The Edge of Chaos

In this paper we explore several fundamental relations between formal systems, algorithms, and dynamical systems, focussing on the roles of undecidability, universality, diagonalization, and self-reference in each of these computational frameworks. Some of these interconnections are well-known, while some are clarified in this study as a result of a fine-grained comparison between recursive formal systems, Turing machines, and Cellular Automata (CAs). In particular, we elaborate on the diagonalization argument applied to distributed computation carried out by CAs, illustrating the key elements of Gödel's proof for CAs. The comparative analysis emphasizes three factors which underlie the capacity to generate undecidable dynamics within the examined computational frameworks: (i) the program-data duality; (ii) the potential to access an infinite computational medium; and (iii) the ability to implement negation. The considered adaptations of Gödel's proof distinguish between computational universality and undecidability, and show how the diagonalization argument exploits, on several levels, the self-referential basis of undecidability.

cs.LO↗

arXiv2019

Ensembles, Dynamics, and Cell Types: Revisiting the Statistical Mechanics Perspective on Cellular Regulation

Genetic regulatory networks control ontogeny. For fifty years Boolean networks have served as models of such systems, ranging from ensembles of random Boolean networks as models for generic properties of gene regulation to working dynamical models of a growing number of sub-networks of real cells. At the same time, their statistical mechanics has been thoroughly studied. Here we recapitulate their original motivation in the context of current theoretical and empirical research. We discuss ensembles of random Boolean networks whose dynamical attractors model cell types. A sub-ensemble is the critical ensemble. There is now strong evidence that genetic regulatory networks are dynamically critical, and that evolution is exploring the critical sub-ensemble. The generic properties of this sub-ensemble predict essential features of cell differentiation. In particular, the number of attractors in such networks scales as the DNA content raised to the 0.63 power. Data on the number of cell types as a function of the DNA content per cell shows a scaling relationship of 0.88. Thus, the theory correctly predicts a power law relationship between the number of cell types and the DNA contents per cell, and a comparable slope. We discuss these new scaling values and show prospects for new research lines for Boolean networks as a base model for systems biology.

q-bio.MN↗

arXiv2018

A Simple Combinatorial Model of World Economic History

We use a simple combinatorial model of technological change to explain the Industrial Revolution. The Industrial Revolution was a sudden large improvement in technology, which resulted in significant increases in human wealth and life spans. In our model, technological change is combining or modifying earlier goods to produce new goods. The underlying process, which has been the same for at least 200,000 years, was sure to produce a very long period of relatively slow change followed with probability one by a combinatorial explosion and sudden takeoff. Thus, in our model, after many millennia of relative quiescence in wealth and technology, a combinatorial explosion created the sudden takeoff of the Industrial Revolution.

econ.GN↗

arXiv2018

Taking Heisenberg's Potentia Seriously

It is argued that quantum theory is best understood as requiring an ontological duality of res extensa and res potentia, where the latter is understood per Heisenberg's original proposal, and the former is roughly equivalent to Descartes' 'extended substance.' However, this is not a dualism of mutually exclusive substances in the classical Cartesian sense, and therefore does not inherit the infamous 'mind-body' problem. Rather, res potentia and res extensa are proposed as mutually implicative ontological extants that serve to explain the key conceptual challenges of quantum theory; in particular, nonlocality, entanglement, null measurements, and wave function collapse. It is shown that a natural account of these quantum perplexities emerges, along with a need to reassess our usual ontological commitments involving the nature of space and time.

quant-ph↗

arXiv2016

Toward an Evolutionary-Predictive Foundation for Creativity

Dietrich and Haider (2014) justify their integrative framework for creativity founded on evolutionary theory and prediction research on the grounds that "theories and approaches guiding empirical research on creativity have not been supported by the neuroimaging evidence". Although this justification is controversial, the general direction holds promise. This commentary clarifies points of disagreement and unresolved issues, and addresses mis-applications of evolutionary theory that lead the authors to adopt a Darwinian (versus Lamarckian) approach. To say that creativity is Darwinian is not to say that it consists of variation plus selection---in the everyday sense of the term---as the authors imply; it is to say that evolution is occurring because selection is affecting the distribution of randomly generated heritable variation across generations. In creative thought the distribution of variants is not key, i.e., one is not inclined toward idea A because 60% of one's candidate ideas are variants of A while only 40% are variants of B; one is inclined toward whichever seems best. The authors concede that creative variation is partly directed; however, the greater the extent to which variants are generated non-randomly, the greater the extent to which the distribution of variants can reflect not selection but the initial generation bias. Since each thought in a creative process can alter the selective criteria against which the next is evaluated, there is no demarcation into generations as assumed in a Darwinian model. We address the authors' claim that reduced variability and individuality are more characteristic of Lamarckism than Darwinian evolution, and note that a Lamarckian approach to creativity has addressed the challenge of modeling the emergent features associated with insight.

q-bio.NC↗

arXiv2014

Beyond the Stalemate: Conscious MInd-Body - Quantum Mechanics - Free Will - Possible Panpsychism - Possible Interpretation of Quantum Enigma

I wish to discuss a large, interwoven set of topics pointed at in the title above. Much of what I say is highly speculative, some is testable, some is, at present, surely not. It is, I hope, useful, to set these ideas forth for our consideration. What I shall say assumes quantum measurement is real, and that Bohm's interpretation of Quantum Mechanics is not true. The Stalemate: In our contemporary neurobiology and much of the philosophy of mind post Descartes we are classical physics machines and either mindless, or mind is at best epiphenomenal and can have no consequences for the physical world. The first main point of this paper is that we are not forced to this conclusion, but must give up total reliance on classical physics.

physics.hist-ph↗

arXiv2014

A Holistic, Non-algorithmic View of Cultural Evolution: Commentary on Review Article by Prof. Liane Gabora

There is surely some truth to the notion that culture evolves, but the Darwinian view of culture is trivial. Gabora does two things in this paper. First, she levels a reasoned and devastating attack on the adequacy of a Darwinian theory of cultural evolution, showing that cultural evolution violates virtually all prerequisites to be encompassed by Darwin's standard theory. Second, she advances the central concept that it is whole world views that evolve. A world view emerges when the capacity of memories to evoke one another surpasses a phase transition yielding a richly interconnected conceptual web, a world view. She proposes that cultural evolves not through a Darwinian process such as meme theory, but through communal exchange of facets of world views. Each section of her argument is completely convincing.

q-bio.NC↗

arXiv2013

A Quantum Model of Exaptation: Incorporating Potentiality into Evolutionary Theory

The phenomenon of preadaptation, or exaptation (wherein a trait that originally evolved to solve one problem is co-opted to solve a new problem) presents a formidable challenge to efforts to describe biological phenomena using a classical (Kolmogorovian) mathematical framework. We develop a quantum framework for exaptation with examples from both biological and cultural evolution. The state of a trait is written as a linear superposition of a set of basis states, or possible forms the trait could evolve into, in a complex Hilbert space. These basis states are represented by mutually orthogonal unit vectors, each weighted by an amplitude term. The choice of possible forms (basis states) depends on the adaptive function of interest (e.g., ability to metabolize lactose or thermoregulate), which plays the role of the observable. Observables are represented by self-adjoint operators on the Hilbert space. The possible forms (basis states) corresponding to this adaptive function (observable) are called eigenstates. The framework incorporates key features of exaptation: potentiality, contextuality, nonseparability, and emergence of new features. However, since it requires that one enumerate all possible contexts, its predictive value is limited, consistent with the assertion that there exists no biological equivalent to "laws of motion" by which we can predict the evolution of the biosphere.

q-bio.PE↗

arXiv2013

Beyond Reductionism Twice: No Laws Entail Biosphere Evolution, Formal Cause Laws Beyond Efficient Cause Laws

Newton set the stage for our view of how science should be done. We remain in what I will call the `Newtonian Paradigm' in all of physics, including Newton, Einstein, and Schrodinger. As I will show shortly, Newton invented and bequeathed to us `efficient cause entailing laws' for the entire becoming of the universe. With Laplace this became the foundation of contemporary reductionism in which all that can happen in the world is due to efficient cause entailing laws. More this framework stands as our dominant way to do science. The Newtonian Paradigm has done enormous work in science, and helped lead to the Industrial Revolution, and even our entry into Modernity. In this paper I propose to challenge the adequacy of the Newtonian Paradigm on two ground: 1) For the evolution of the biosphere beyond the watershed of life, we can formulate no efficient cause entailing laws that allow us to deduce the evolution of the biosphere. A fortiori, the same holds for the evolution of the economy, legal systems, social systems, and culture. Because I have discussed this before with my colleagues Longo and Montevil (1,2) and elsewhere, (3,4), my discussion of this first point will be rather brief. 2) What I shall choose to call, after Aristotle's four causes, noted below, Formal Cause Laws derived from specific `ensemble theories' tell us about the world. But Formal Cause Laws are not reducible to efficient cause entailing laws of the Newtonian Paradigm and, critically, have already, unnoticed, crept into biology concerning the origin of life, and economics concerning economic growth. Formal cause laws appear to be a new way to do science, independent of efficient cause entailing laws. Thus Formal Cause laws can be independent of any specific material substrate. This may bear on the sufficiency of Materialism in our account of the world.

physics.hist-ph↗

arXiv2012

The Structure of Autocatalytic Sets: Evolvability, Enablement, and Emergence

This paper presents new results from a detailed study of the structure of autocatalytic sets. We show how autocatalytic sets can be decomposed into smaller autocatalytic subsets, and how these subsets can be identified and classified. We then argue how this has important consequences for the evolvability, enablement, and emergence of autocatalytic sets. We end with some speculation on how all this might lead to a generalized theory of autocatalytic sets, which could possibly be applied to entire ecologies or even economies.

q-bio.MN↗

arXiv2012

Quantum biology on the edge of quantum chaos

We give a new explanation for why some biological systems can stay quantum coherent for long times at room temperatures, one of the fundamental puzzles of quantum biology. We show that systems with the right level of complexity between chaos and regularity can increase their coherence time by orders of magnitude. Systems near Critical Quantum Chaos or Metal-Insulator Transition (MIT) can have long coherence times and coherent transport at the same time. The new theory tested in a realistic light harvesting system model can reproduce the scaling of critical fluctuations reported in recent experiments. Scaling of return probability in the FMO light harvesting complex shows the signs of universal return probability decay observed at critical MIT. The results may open up new possibilities to design low loss energy and information transport systems in this Poised Realm hovering reversibly between quantum coherence and classicality.

cond-mat.dis-nn↗

arXiv2012

No entailing laws, but enablement in the evolution of the biosphere

Biological evolution is a complex blend of ever changing structural stability, variability and emergence of new phenotypes, niches, ecosystems. We wish to argue that the evolution of life marks the end of a physics world view of law entailed dynamics. Our considerations depend upon discussing the variability of the very "contexts of life": the interactions between organisms, biological niches and ecosystems. These are ever changing, intrinsically indeterminate and even unprestatable: we do not know ahead of time the "niches" which constitute the boundary conditions on selection. More generally, by the mathematical unprestatability of the "phase space" (space of possibilities), no laws of motion can be formulated for evolution. We call this radical emergence, from life to life. The purpose of this paper is the integration of variation and diversity in a sound conceptual frame and situate unpredictability at a novel theoretical level, that of the very phase space. Our argument will be carried on in close comparisons with physics and the mathematical constructions of phase spaces in that discipline. The role of (theoretical) symmetries as invariant preserving transformations will allow us to understand the nature of physical phase spaces and to stress the differences required for a sound biological theoretizing. In this frame, we discuss the novel notion of "enablement". This will restrict causal analyses to differential cases (a difference that causes a difference). Mutations or other causal differences will allow us to stress that "non conservation principles" are at the core of evolution, in contrast to physical dynamics, largely based on conservation principles as symmetries. Critical transitions, the main locus of symmetry changes in physics, will be discussed, and lead to "extended criticality" as a conceptual frame for a better understanding of the living state of matter.

q-bio.OT↗

arXiv2009

Physics and Five Problems in the Philosophy of Mind

Since Descartes' dualism, with his res extensa and res cogitans, six fundamental problems in the philosophy and natural history of mind are these: 1. how does mind act on matter? 2. If mind does not act on matter is mind a mere epiphenomenon? 3. What might be the source of free will? 4. What might be the source of a responsible free will? 5. Why might it have been selectively advantageous to evolve consciousness? 6. What is consciousness? I approach the first five of the above six problems based on two physical postulates. First the mind-brain system is a quantum coherent, but reversibly decohering and recohering system. This allows me to answer 1) above, mind does not act causally on brain at all, rather it acausally decohers to classicity (for all practical purposes), hence has consequences for brain and body as matter. Epiphenomenalism is averted. A quantum mind, because it is acausal on Copenhagen including Born, yields a free will, but a merely random free will, not a responsible free will. Second, the most radical part of this article proposes that the quantum classical interface is not always describable by a law: specifically in a special relativity setting, no function, F, maps the present state of the system mind-brain into its future. In its place is a nonrandom yet lawless process. I seek in this non-random yet lawless process a source for a responsible free will. Finally, if the quantum-classical boundary can be non-random yet lawless, then no algorithmic simulation of the world or ourselves can calculate the real world, hence the evolutionary selective advantages for evolving consciousness to know it may be great. I make no progress on problem 6, the hard problem of qualia.

physics.hist-ph↗

arXiv2004

Genetic networks with canalyzing Boolean rules are always stable

We determine stability and attractor properties of random Boolean genetic network models with canalyzing rules for a variety of architectures. For all power law, exponential, and flat in-degree distributions, we find that the networks are dynamically stable. Furthermore, for architectures with few inputs per node, the dynamics of the networks is close to critical. In addition, the fraction of genes that are active decreases with the number of inputs per node. These results are based upon investigating ensembles of networks using analytical methods. Also, for different in-degree distributions, the numbers of fixed points and cycles are calculated, with results intuitively consistent with stability analysis; fewer inputs per node implies more cycles, and vice versa. There are hints that genetic networks acquire broader degree distributions with evolution, and hence our results indicate that for single cells, the dynamics should become more stable with evolution. However, such an effect is very likely compensated for by multicellular dynamics, because one expects less stability when interactions among cells are included. We verify this by simulations of a simple model for interactions among cells.

q-bio.MN↗

arXiv2004

Random Boolean Network Models and the Yeast Transcriptional Network

The recently measured yeast transcriptional network is analyzed in terms of simplified Boolean network models, with the aim of determining feasible rule structures, given the requirement of stable solutions of the generated Boolean networks. We find that for ensembles of generated models, those with canalyzing Boolean rules are remarkably stable, whereas those with random Boolean rules are only marginally stable. Furthermore, substantial parts of the generated networks are frozen, in the sense that they reach the same state regardless of initial state. Thus, our ensemble approach suggests that the yeast network shows highly ordered dynamics.

q-bio.MN↗

arXiv1999

Phase Transition in Random Networks with Multiple States

The critical boundaries separating ordered from chaotic behavior in randomly wired S-state networks are calculated. These networks are a natural generalization of random Boolean nets and are proposed as on extended approach to genetic regulatory systems, sets of cells in different states or collectives of agents engaged into a set of S possible tasks. A order parameter for the transition is computed and analysed. The relevance of these networks to biology, their relationships with standard cellular automata and possible extensions are outlined.

adap-org↗

arXiv1998

Combinatorial dynamics in quantum gravity

We describe the application of methods from the study of discrete dynanmical systems to the problem of the continuum limit of evolving spin networks. These have been found to describe the small scale structure of quantum general relativity and extensions of them have been conjectured to give background independent formulations of string theory. We explain why the the usual equilibrium critical phenomena may not be relevant for the problem of the continuum limit of such theories and why, instead, the continuum limits of such theories are likely to be governed by non-equilibrium critical phenomena such as directed percolation. The fact that such non-equilibrium critical phenomena can be self-organized implies the possibility that the classical limit of quantum theories of gravity may exist without fine tuning of parameters.

hep-th↗