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2019
Journal article
Open Access
Integrated information in process-algebraic compositions
Bolognesi T.
Integrated Information Theory (IIT) is most typically applied to Boolean Nets, a state transition model in which system parts cooperate by sharing state variables. By contrast, in Process Algebra, whose semantics can also be formulated in terms of (labeled) state transitions, system parts--"processes"--cooperate by sharing transitions with matching labels, according to interaction patterns expressed by suitable composition operators. Despite this substantial difference, questioning how much additional information is provided by the integration of the interacting partners above and beyond the sum of their independent contributions appears perfectly legitimate with both types of cooperation. In fact, we collect statistical data about ?--integrated information--relative to pairs of boolean nets that cooperate by three alternative mechanisms: shared variables--the standard choice for boolean nets--and two forms of shared transition, inspired by two process algebras. We name these mechanisms ? , ? and ?. Quantitative characterizations of all of them are obtained by considering three alternative execution modes, namely synchronous, asynchronous and "hybrid", by exploring the full range of possible coupling degrees in all three cases, and by considering two possible definitions of ? based on two alternative notions of distribution distance.Source: ENTROPY, vol. 21 (issue 8)
DOI: 10.3390/e21080805
Metrics:
Bolognesi T.
Integrated Information Theory (IIT) is most typically applied to Boolean Nets, a state transition model in which system parts cooperate by sharing state variables. By contrast, in Process Algebra, whose semantics can also be formulated in terms of (labeled) state transitions, system parts--"processes"--cooperate by sharing transitions with matching labels, according to interaction patterns expressed by suitable composition operators. Despite this substantial difference, questioning how much additional information is provided by the integration of the interacting partners above and beyond the sum of their independent contributions appears perfectly legitimate with both types of cooperation. In fact, we collect statistical data about ?--integrated information--relative to pairs of boolean nets that cooperate by three alternative mechanisms: shared variables--the standard choice for boolean nets--and two forms of shared transition, inspired by two process algebras. We name these mechanisms ? , ? and ?. Quantitative characterizations of all of them are obtained by considering three alternative execution modes, namely synchronous, asynchronous and "hybrid", by exploring the full range of possible coupling degrees in all three cases, and by considering two possible definitions of ? based on two alternative notions of distribution distance.Source: ENTROPY, vol. 21 (issue 8)
DOI: 10.3390/e21080805
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Entropy 
| Entropy | CNR IRIS | ISTI Repository | Entropy | Entropy | CNR IRIS 
2019
Contribution to book
Restricted
Single-step and asymptotic mutual information in bipartite boolean nets
Bolognesi T
In this paper we contrast two fundamentally different ways to approach the analysis of transition system behaviours. Both methods refer to the (finite) global state transition graph; but while method A, familiar to software system designers and process algebraists, deals with execution paths of virtually unbounded length, typically starting from a precise initial state, method B, associated with counterfactual reasoning, looks at single-step evolutions starting from all conceivable system states. Among various possible state transition models we pick boolean nets - a generalisation of cellular automata in which all nodes fire synchronously. Our nets shall be composed of parts P and Q that interact by shared variables. At first we adopt approach B and a simple information-theoretic measure - mutual information M(yP,yQ) - for detecting the degree of coupling between the two components after one transition step from the uniform distribution of all global states. Then we consider an asymptotic version M(y*P,y*Q) of mutual information, somehow mixing methods A and B, and illustrate a technique for obtaining accurate approximations of M(y*P,y*Q) based on the attractors of the global graph.DOI: 10.1007/978-3-030-30985-5_30
Metrics:
Bolognesi T
In this paper we contrast two fundamentally different ways to approach the analysis of transition system behaviours. Both methods refer to the (finite) global state transition graph; but while method A, familiar to software system designers and process algebraists, deals with execution paths of virtually unbounded length, typically starting from a precise initial state, method B, associated with counterfactual reasoning, looks at single-step evolutions starting from all conceivable system states. Among various possible state transition models we pick boolean nets - a generalisation of cellular automata in which all nodes fire synchronously. Our nets shall be composed of parts P and Q that interact by shared variables. At first we adopt approach B and a simple information-theoretic measure - mutual information M(yP,yQ) - for detecting the degree of coupling between the two components after one transition step from the uniform distribution of all global states. Then we consider an asymptotic version M(y*P,y*Q) of mutual information, somehow mixing methods A and B, and illustrate a technique for obtaining accurate approximations of M(y*P,y*Q) based on the attractors of the global graph.DOI: 10.1007/978-3-030-30985-5_30
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doi.org | CNR IRIS | CNR IRIS | link.springer.com
2017
Journal article
Restricted
Exploring nominal cellular automata
Bolognesi T, Ciancia V
he emerging field of Nominal Computation Theory is concerned with the theory of Nominal Sets and its applications to Computer Science. We investigate here the impact of nominal sets on the definition of Cellular Automata and on their computational capabilities, with a special focus on the emergent behavioural properties of this new model and their significance in the context of computation-oriented interpretations of physical phenomena. An investigation of the relations between Nominal Cellular Automata and Wolfram's Elementary Cellular Automata is carried out, together with an analysis of interesting particles, exhibiting "nominal" behaviour, in a particular kind of rules, reminiscent of the class of totalistic Cellular Automata, that we call "bagged".Source: THE JOURNAL OF LOGICAL AND ALGEBRAIC METHODS IN PROGRAMMING, vol. 93, pp. 23-41
DOI: 10.1016/j.jlamp.2017.08.001
Project(s): QUANTICOL
Metrics:
Bolognesi T, Ciancia V
he emerging field of Nominal Computation Theory is concerned with the theory of Nominal Sets and its applications to Computer Science. We investigate here the impact of nominal sets on the definition of Cellular Automata and on their computational capabilities, with a special focus on the emergent behavioural properties of this new model and their significance in the context of computation-oriented interpretations of physical phenomena. An investigation of the relations between Nominal Cellular Automata and Wolfram's Elementary Cellular Automata is carried out, together with an analysis of interesting particles, exhibiting "nominal" behaviour, in a particular kind of rules, reminiscent of the class of totalistic Cellular Automata, that we call "bagged".Source: THE JOURNAL OF LOGICAL AND ALGEBRAIC METHODS IN PROGRAMMING, vol. 93, pp. 23-41
DOI: 10.1016/j.jlamp.2017.08.001
Project(s): QUANTICOL
Metrics:
See at:
Journal of Logical and Algebraic Methods in Programming | CNR IRIS | CNR IRIS | www.sciencedirect.com
2017
Contribution to book
Restricted
LOTOS-like composition of boolean nets and causal set construction
Bolognesi T
In the context of research efforts on causal sets as discrete models of physical spacetime, and on their derivation from simple, deterministic, sequential models of computation, we consider boolean nets, a transition system that generalises cellular automata, and investigate the family of causal sets that derive from their computations, in search for interesting emergent properties. The choice of boolean nets is motivated by the fact that they naturally support compositions via a LOTOS-inspired parametric parallel operator, with possible interesting effects on the emergent structure of the derived causal sets. More generally, we critically reconsider the whole issue of algorithmic causet construction and expose the limitations suffered by these structures w.r.t. to the requirements of Lorentz invariance that even discrete models of physical spacetime, as recently shown, can and should satisfy. We conclude by hinting at novel ways to add momentum to the bold research programme that attempts to identify the natural with the computational universe.DOI: 10.1007/978-3-319-68270-9_2
Metrics:
Bolognesi T
In the context of research efforts on causal sets as discrete models of physical spacetime, and on their derivation from simple, deterministic, sequential models of computation, we consider boolean nets, a transition system that generalises cellular automata, and investigate the family of causal sets that derive from their computations, in search for interesting emergent properties. The choice of boolean nets is motivated by the fact that they naturally support compositions via a LOTOS-inspired parametric parallel operator, with possible interesting effects on the emergent structure of the derived causal sets. More generally, we critically reconsider the whole issue of algorithmic causet construction and expose the limitations suffered by these structures w.r.t. to the requirements of Lorentz invariance that even discrete models of physical spacetime, as recently shown, can and should satisfy. We conclude by hinting at novel ways to add momentum to the bold research programme that attempts to identify the natural with the computational universe.DOI: 10.1007/978-3-319-68270-9_2
Metrics:
See at:
doi.org | CNR IRIS | CNR IRIS | link.springer.com
2016
Contribution to book
Restricted
Humanity is much more than the sum of humans
Bolognesi T
Consider two roughly spherical and coextensive complex systems: the atmosphere and the upper component of the biosphere - humanity. It is well known that, due to a malicious antipodal butterfly, the possibility to accurately forecast the weather - let alone controlling it - is severely limited. Why should it be easier to predict and steer the future of humanity? In this essay we present both pessimistic and optimistic arguments about the possibility to effectively predict and drive our future. On the long time scale, we sketch a software-oriented view at the cosmos in all of its components, from spacetime to the biosphere and human societies, borrowing ideas from various scientific theories or conjectures; the proposal is also motivated by an attempt to provide some formal foundations to Teilhard de Chardin's cosmological/metaphysical visions, that relate the growing complexity of the material universe, and its final fate, to the progressive emergence of consciousness. On a shorter scale, we briefly discuss the possibility of using simple formal models such as Kauffman's boolean networks, and the growing body of data about social behaviours, for simulating humanity 'in-silico', with the purpose to anticipate problems and testing solutions.Source: THE FRONTIERS COLLECTION, pp. 1-15
DOI: 10.1007/978-3-319-20717-9_3
Metrics:
Bolognesi T
Consider two roughly spherical and coextensive complex systems: the atmosphere and the upper component of the biosphere - humanity. It is well known that, due to a malicious antipodal butterfly, the possibility to accurately forecast the weather - let alone controlling it - is severely limited. Why should it be easier to predict and steer the future of humanity? In this essay we present both pessimistic and optimistic arguments about the possibility to effectively predict and drive our future. On the long time scale, we sketch a software-oriented view at the cosmos in all of its components, from spacetime to the biosphere and human societies, borrowing ideas from various scientific theories or conjectures; the proposal is also motivated by an attempt to provide some formal foundations to Teilhard de Chardin's cosmological/metaphysical visions, that relate the growing complexity of the material universe, and its final fate, to the progressive emergence of consciousness. On a shorter scale, we briefly discuss the possibility of using simple formal models such as Kauffman's boolean networks, and the growing body of data about social behaviours, for simulating humanity 'in-silico', with the purpose to anticipate problems and testing solutions.Source: THE FRONTIERS COLLECTION, pp. 1-15
DOI: 10.1007/978-3-319-20717-9_3
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doi.org | CNR IRIS | CNR IRIS | link.springer.com
2016
Contribution to book
Open Access
Spacetime computing: towards algorithmic causal sets with special-relativistic properties
Bolognesi T
Spacetime computing is undoubtedly one of the most ambitious and less explored forms of unconventional computing. Totally unconventional is the medium on which the computation is expected to take place - the elusive texture of physical spacetime - and unprecedentedly wide its scope, since the emergent properties of these computations are expected to ultimately reproduce everything we observe in nature. First we discuss the distinguishing features of this peculiar form of unconventional computing, and survey a few pioneering approaches. Then we illustrate some novel ideas and experiments that attempt to establish stronger connections with advances in quantum gravity and the physics of spacetime. We discuss techniques for building algorithmic causal sets - our proposed deterministic counterpart of the stochastic structures adopted in the Causal Set programme for discrete spacetime modeling - and investigate, in particular, the extent to which they can reflect an essential feature of continuous spacetime: Lorentz invariance.Source: EMERGENCE, COMPLEXITY AND COMPUTATION, pp. 267-304
DOI: 10.1007/978-3-319-33924-5_12
Metrics:
Bolognesi T
Spacetime computing is undoubtedly one of the most ambitious and less explored forms of unconventional computing. Totally unconventional is the medium on which the computation is expected to take place - the elusive texture of physical spacetime - and unprecedentedly wide its scope, since the emergent properties of these computations are expected to ultimately reproduce everything we observe in nature. First we discuss the distinguishing features of this peculiar form of unconventional computing, and survey a few pioneering approaches. Then we illustrate some novel ideas and experiments that attempt to establish stronger connections with advances in quantum gravity and the physics of spacetime. We discuss techniques for building algorithmic causal sets - our proposed deterministic counterpart of the stochastic structures adopted in the Causal Set programme for discrete spacetime modeling - and investigate, in particular, the extent to which they can reflect an essential feature of continuous spacetime: Lorentz invariance.Source: EMERGENCE, COMPLEXITY AND COMPUTATION, pp. 267-304
DOI: 10.1007/978-3-319-33924-5_12
Metrics:
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CNR IRIS | link.springer.com | ISTI Repository | doi.org | CNR IRIS
2016
Contribution to book
Restricted
Let's consider two spherical chickens
Bolognesi T
Confronted with a pythagorean jingle derived from simple ratios, a sequence of 23 moves from knot theory, and the interaction between a billiard-ball and a zero-gravity field, a young detective soon realizes that three crimes could have been avoided if math were not so unreasonably effective in describing our physical world. Why is this so? Asimov's fictional character Prof. Priss confirms to the detective that there is some truth in Tegmark's Mathematical Universe Hypothesis, and reveals him that all mathematical structures entailing self-aware substructures (SAS) are computable and isomorphic. The boss at the investigation agency is not convinced and proposes his own views on the question.Source: THE FRONTIERS COLLECTION, pp. 55-66
DOI: 10.1007/978-3-319-27495-9_5
Metrics:
Bolognesi T
Confronted with a pythagorean jingle derived from simple ratios, a sequence of 23 moves from knot theory, and the interaction between a billiard-ball and a zero-gravity field, a young detective soon realizes that three crimes could have been avoided if math were not so unreasonably effective in describing our physical world. Why is this so? Asimov's fictional character Prof. Priss confirms to the detective that there is some truth in Tegmark's Mathematical Universe Hypothesis, and reveals him that all mathematical structures entailing self-aware substructures (SAS) are computable and isomorphic. The boss at the investigation agency is not convinced and proposes his own views on the question.Source: THE FRONTIERS COLLECTION, pp. 55-66
DOI: 10.1007/978-3-319-27495-9_5
Metrics:
See at:
doi.org | CNR IRIS | CNR IRIS | link.springer.com
2016
Journal article
Open Access
Simple indicators for Lorentzian causets
Bolognesi T, Lamb A
Several classes of directed acyclic graphs have been investigated in the last two decades, in the context of the causal set program, in search for good discrete models of spacetime. We introduce some statistical indicators that can be used for comparing these graphs and for assessing their closeness to the ideal Lorentzian causal sets ('causets') - those obtained by sprinkling points in a Lorentzian manifold. In particular, with the reversed triangular inequality of Special Relativity in mind, we introduce 'longest/shortest path plots',an easily implemented tool to visually detect the extent to which a generic causet matches the wide range of path lengths between events of Lorentzian causets. This tool can attribute some degree of 'Lorentzianity' - in particular 'non-locality' - also to causets that are not (directly) embeddable and that, due to some regularity in their structure, would not pass the key test for Lorentz invariance: the absence of preferred reference frames. We compare the discussed indicators and use them for assessing causets both of stochastic and of deterministic, algorithmic origin, finding examples of the latter that behave optimally w.r.t. our longest/shortest path plots.Source: CLASSICAL AND QUANTUM GRAVITY, vol. 33 (issue 8)
DOI: 10.1088/0264-9381/33/18/185004
DOI: 10.48550/arxiv.1407.1649
Metrics:
Bolognesi T, Lamb A
Several classes of directed acyclic graphs have been investigated in the last two decades, in the context of the causal set program, in search for good discrete models of spacetime. We introduce some statistical indicators that can be used for comparing these graphs and for assessing their closeness to the ideal Lorentzian causal sets ('causets') - those obtained by sprinkling points in a Lorentzian manifold. In particular, with the reversed triangular inequality of Special Relativity in mind, we introduce 'longest/shortest path plots',an easily implemented tool to visually detect the extent to which a generic causet matches the wide range of path lengths between events of Lorentzian causets. This tool can attribute some degree of 'Lorentzianity' - in particular 'non-locality' - also to causets that are not (directly) embeddable and that, due to some regularity in their structure, would not pass the key test for Lorentz invariance: the absence of preferred reference frames. We compare the discussed indicators and use them for assessing causets both of stochastic and of deterministic, algorithmic origin, finding examples of the latter that behave optimally w.r.t. our longest/shortest path plots.Source: CLASSICAL AND QUANTUM GRAVITY, vol. 33 (issue 8)
DOI: 10.1088/0264-9381/33/18/185004
DOI: 10.48550/arxiv.1407.1649
Metrics:
See at:
arXiv.org e-Print Archive | Classical and Quantum Gravity | CNR IRIS | iopscience.iop.org | ISTI Repository | Classical and Quantum Gravity | doi.org | CNR IRIS | CNR IRIS
2016
Conference article
Open Access
Nominal cellular automata
Bolognesi T, Ciancia V
The emerging field of Nominal Computation Theory is concerned with the theory of Nominal Sets and its applications to Computer Science. We investigate here the impact of nominal sets on the definition of Cellular Automata and on their computational capabilities, with a special focus on the emergent behavioural properties of this new model and their significance in the context of computation-oriented interpretations of physical phenomena. A preliminary investigation of the relations between Nominal Cellular Automata and Wolfram's Elementary Cellular Automata is also carried out.Source: ELECTRONIC PROCEEDINGS IN THEORETICAL COMPUTER SCIENCE, pp. 24-35. Heraklion, Crete, Greece, 8-9 June 2016
DOI: 10.4204/eptcs.223.2
DOI: 10.48550/arxiv.1608.03320
Project(s): QUANTICOL
Metrics:
Bolognesi T, Ciancia V
The emerging field of Nominal Computation Theory is concerned with the theory of Nominal Sets and its applications to Computer Science. We investigate here the impact of nominal sets on the definition of Cellular Automata and on their computational capabilities, with a special focus on the emergent behavioural properties of this new model and their significance in the context of computation-oriented interpretations of physical phenomena. A preliminary investigation of the relations between Nominal Cellular Automata and Wolfram's Elementary Cellular Automata is also carried out.Source: ELECTRONIC PROCEEDINGS IN THEORETICAL COMPUTER SCIENCE, pp. 24-35. Heraklion, Crete, Greece, 8-9 June 2016
DOI: 10.4204/eptcs.223.2
DOI: 10.48550/arxiv.1608.03320
Project(s): QUANTICOL
Metrics:
See at:
arXiv.org e-Print Archive | Electronic Proceedings in Theoretical Computer Science | Electronic Proceedings in Theoretical Computer Science | Electronic Proceedings in Theoretical Computer Science | eptcs.web.cse.unsw.edu.au | CNR IRIS | ISTI Repository | doi.org | CNR IRIS
2014
Journal article
Open Access
Teilhard de Chardin e Wolfram: modelli di universo computazionale ed emergenza del foglietto interno delle cose
Bolognesi T
The ambitious goal of 'The Human Phenomenon' by Teilhard de Chardin is to describe the Cosmos and its evolution in a way that integrates the outside and the inside of things - the material world and the dimensions of psyche and consciousness - while preserving the character of a scientific investigation. By following the teilhardian steps of Prelife-Life-Though, and by using results that were still largely unknown during Teilhard's lifespan, due, in particular, to Wolfram, Chaitin and Tononi, in this short essay we show that it is possible and useful to try and understand the ultimate fabric of the universe, some phenomena in the biosphere, and the notion of consciousness itself, in terms of the concept of computation, that is, as phenomena emerging from information processing.
Bolognesi T
The ambitious goal of 'The Human Phenomenon' by Teilhard de Chardin is to describe the Cosmos and its evolution in a way that integrates the outside and the inside of things - the material world and the dimensions of psyche and consciousness - while preserving the character of a scientific investigation. By following the teilhardian steps of Prelife-Life-Though, and by using results that were still largely unknown during Teilhard's lifespan, due, in particular, to Wolfram, Chaitin and Tononi, in this short essay we show that it is possible and useful to try and understand the ultimate fabric of the universe, some phenomena in the biosphere, and the notion of consciousness itself, in terms of the concept of computation, that is, as phenomena emerging from information processing.
See at:
CNR IRIS | www.edizionistudium.it | CNR IRIS
2014
Other
Open Access
Simple indicators for Lorentzian causets
Bolognesi T, Lamb A
Several classes of DAGs (directed acyclic graphs), and associated growth dynamics, have been investigated over the last two decades, mainly in the context of the Causal Set Program, with the purpose of finding satisfactory discrete models of spacetime. We introduce some simple statistical indicators that can be used for comparing these graphs, and for assessing their closeness to the ideal Lorentzian causets -- those obtained by uniformly sprinkling points in a Lorenztian manifold. In particular, we introduce 'longest/shortest path plots' as a way to visually detect the extent to which a DAG matches the reversed triangular inequality of special relativity (and the twin paradox), and we use it for assessing causets both of stochastic and of deterministic, algorithmic origin. We identify a very simple deterministic algorithm that behaves optimally in this respect.
Bolognesi T, Lamb A
Several classes of DAGs (directed acyclic graphs), and associated growth dynamics, have been investigated over the last two decades, mainly in the context of the Causal Set Program, with the purpose of finding satisfactory discrete models of spacetime. We introduce some simple statistical indicators that can be used for comparing these graphs, and for assessing their closeness to the ideal Lorentzian causets -- those obtained by uniformly sprinkling points in a Lorenztian manifold. In particular, we introduce 'longest/shortest path plots' as a way to visually detect the extent to which a DAG matches the reversed triangular inequality of special relativity (and the twin paradox), and we use it for assessing causets both of stochastic and of deterministic, algorithmic origin. We identify a very simple deterministic algorithm that behaves optimally in this respect.
See at:
CNR IRIS | ISTI Repository | CNR IRIS
2014
Other
Open Access
Simple indicators for Lorentzian causets (v2)
Bolognesi T, Lamb A
Several classes of DAGs (directed acyclic graphs), and associated growth dynamics, have been investigated over the last two decades, mainly in the context of the Causal Set Program, with the purpose of finding satisfactory discrete models of spacetime. We introduce some simple statistical indicators that can be used for comparing these graphs, and for assessing their closeness to the ideal Lorentzian causets -- those obtained by uniformly sprinkling points in a Lorenztian manifold. In particular, we introduce 'longest/shortest path plots' as a way to visually detect the extent to which a DAG matches the reversed triangular inequality of special relativity (and the twin paradox), and we use it for assessing causets both of stochastic and of deterministic, algorithmic origin. We identify a very simple deterministic algorithm that behaves optimally in this respect.
Bolognesi T, Lamb A
Several classes of DAGs (directed acyclic graphs), and associated growth dynamics, have been investigated over the last two decades, mainly in the context of the Causal Set Program, with the purpose of finding satisfactory discrete models of spacetime. We introduce some simple statistical indicators that can be used for comparing these graphs, and for assessing their closeness to the ideal Lorentzian causets -- those obtained by uniformly sprinkling points in a Lorenztian manifold. In particular, we introduce 'longest/shortest path plots' as a way to visually detect the extent to which a DAG matches the reversed triangular inequality of special relativity (and the twin paradox), and we use it for assessing causets both of stochastic and of deterministic, algorithmic origin. We identify a very simple deterministic algorithm that behaves optimally in this respect.
See at:
arxiv.org | CNR IRIS | ISTI Repository | CNR IRIS
2013
Contribution to book
Restricted
Algorithmic causal sets for a computational spacetime
Bolognesi T
In this paper we discuss some achievements and ongoing investigations at the intersection between two active research areas: we refer to the first one, somewhat older, broader and fuzzier, by the name 'Computational Universe Conjecture'; the second is known as 'Causal Set Program'.
Bolognesi T
In this paper we discuss some achievements and ongoing investigations at the intersection between two active research areas: we refer to the first one, somewhat older, broader and fuzzier, by the name 'Computational Universe Conjecture'; the second is known as 'Causal Set Program'.
2013
Contribution to book
Restricted
Do particles evolve?
Bolognesi T
After some reflection on the messages that I have found most inspiring in Wolfram's NKS book, ten years after its publication, in this paper I speculate on a few, highly attractive new developments that NKS-style experimental research might undergo, and that I have myself begun to explore in recent years. According to these visions, the grand challenge that the emergent, localized structures of elementary automaton 110, or similar 'particles', must face in the next ten years is to evolve into populations of increasingly complex individuals, up to forms of (artificial) life, and to a fully blown biosphere. On a more technical side, the paper illustrates some preliminary steps and re- sults in the application of Genetic Algorithms to variants of Wolfram's Network Mobile Automata; the objective here is to investigate the emergent qualitative and quantitative properties of the causal sets associated to the automata computations, in view of their potential application as discrete models of physical spacetime.Source: EMERGENCE, COMPLEXITY AND COMPUTATION, pp. 135-155
DOI: 10.1007/978-3-642-35482-3_12
Metrics:
Bolognesi T
After some reflection on the messages that I have found most inspiring in Wolfram's NKS book, ten years after its publication, in this paper I speculate on a few, highly attractive new developments that NKS-style experimental research might undergo, and that I have myself begun to explore in recent years. According to these visions, the grand challenge that the emergent, localized structures of elementary automaton 110, or similar 'particles', must face in the next ten years is to evolve into populations of increasingly complex individuals, up to forms of (artificial) life, and to a fully blown biosphere. On a more technical side, the paper illustrates some preliminary steps and re- sults in the application of Genetic Algorithms to variants of Wolfram's Network Mobile Automata; the objective here is to investigate the emergent qualitative and quantitative properties of the causal sets associated to the automata computations, in view of their potential application as discrete models of physical spacetime.Source: EMERGENCE, COMPLEXITY AND COMPUTATION, pp. 135-155
DOI: 10.1007/978-3-642-35482-3_12
Metrics:
See at:
doi.org | CNR IRIS | CNR IRIS | link.springer.com
2013
Conference article
Metadata Only Access
Stochastic and algorithmic causal sets for de sitter spacetime
Bolognesi T
Causal sets ('causets') are directed, acyclic graphs used as discrete models of spacetime. A well known technique for obtaining causets, called 'sprinkling', is based on uniformly distributing points on a continuous spacetime, and letting them inherit the causality relation of the latter, as represented by lightcones. In 2012 Krioukov and others have shown that sprinkling on a de Sitter spacetime yields causets which, surprisingly, share important features with complex networks arising in a variety of other fields, e.g. the Internet; one of these features is the power law distribution of node degrees. How frequent are stochastic or deterministic causets with a power law distribution of node degrees? In this paper we show that causets exhibiting this feature can also be obtained directly, i.e. without assuming an initial manifold, by a simple stochastic process based on generating pairs of random integers in a linearly growing range. Then we address the problem of obtaining similar causets by deterministic, algorithmic techniques, and show that the so called fractal sequence -- a structure we have often encountered in simulations of deterministic computational universes -- can indeed be used for obtaining a first, elementary form of algorithmic 'de Sitter causet'. An interactive Mathematica demonstration has been implemented for illustrating the exponential space growth rate of de Sitter spacetime. Furthermore, Mathematica has been used for creating sprinklings and causets in de Sitter spacetime, for implementing the described, alternative procedures for causet construction (both stochastic and deterministic), and for analyzing causet node degree distributions.
Bolognesi T
Causal sets ('causets') are directed, acyclic graphs used as discrete models of spacetime. A well known technique for obtaining causets, called 'sprinkling', is based on uniformly distributing points on a continuous spacetime, and letting them inherit the causality relation of the latter, as represented by lightcones. In 2012 Krioukov and others have shown that sprinkling on a de Sitter spacetime yields causets which, surprisingly, share important features with complex networks arising in a variety of other fields, e.g. the Internet; one of these features is the power law distribution of node degrees. How frequent are stochastic or deterministic causets with a power law distribution of node degrees? In this paper we show that causets exhibiting this feature can also be obtained directly, i.e. without assuming an initial manifold, by a simple stochastic process based on generating pairs of random integers in a linearly growing range. Then we address the problem of obtaining similar causets by deterministic, algorithmic techniques, and show that the so called fractal sequence -- a structure we have often encountered in simulations of deterministic computational universes -- can indeed be used for obtaining a first, elementary form of algorithmic 'de Sitter causet'. An interactive Mathematica demonstration has been implemented for illustrating the exponential space growth rate of de Sitter spacetime. Furthermore, Mathematica has been used for creating sprinklings and causets in de Sitter spacetime, for implementing the described, alternative procedures for causet construction (both stochastic and deterministic), and for analyzing causet node degree distributions.
See at:
CNR IRIS | www.adalta.it
2011
Conference article
Open Access
Reality is Ultimately Digital and its Program is still Undebugged
Tommaso Bolognesi
Reality is ultimately digital, and all the complexity we observe in the physical universe, from subatomic particles to the biosphere, is a mani- festation of the emergent properties of a digital computation that takes place at the smallest spacetime scale. Emergence in computation is an immensely creative force, whose relevance for theoretical physics is still largely underestimated. However, if the universe must be at all scien- tifically comprehensible, as suggested by a famous einsteinian quote, we have to additionally postulate this computation to sit at the bottom of a multi-level hierarchy of emergent phenomena satisfying appropriate re- quirements. In particular, we expect 'interesting things' to emerge at all levels, including the lowest ones. The digital/computational universe hy- pothesis gives us a great opportunity to achieve a concise, background independent theory, if the 'background' - a lively spacetime substratum - is equated with a finite causal set.
Tommaso Bolognesi
Reality is ultimately digital, and all the complexity we observe in the physical universe, from subatomic particles to the biosphere, is a mani- festation of the emergent properties of a digital computation that takes place at the smallest spacetime scale. Emergence in computation is an immensely creative force, whose relevance for theoretical physics is still largely underestimated. However, if the universe must be at all scien- tifically comprehensible, as suggested by a famous einsteinian quote, we have to additionally postulate this computation to sit at the bottom of a multi-level hierarchy of emergent phenomena satisfying appropriate re- quirements. In particular, we expect 'interesting things' to emerge at all levels, including the lowest ones. The digital/computational universe hy- pothesis gives us a great opportunity to achieve a concise, background independent theory, if the 'background' - a lively spacetime substratum - is equated with a finite causal set.
2011
Journal article
Restricted
Algorithmic causets
Bolognesi T
In the context of quantum gravity theories, several researchers have proposed causal sets as appropriate discrete models of spacetime. We investigate families of causal sets obtained from two simple models of computation - 2D Turing machines and network mobile automata - that operate on 'high-dimensional' supports, namely 2D arrays of cells and planar graphs, respectively. We study a number of quantitative and qualitative emergent properties of these causal sets, including dimension, curvature and localized structures, or 'particles'. We show how the possibility to detect and separate particles from background space depends on the choice between a global or local view at the causal set. Finally, we spot very rare cases of pseudo-randomness, or deterministic chaos; these exhibit a spontaneous phenomenon of 'causal compartmentation' that appears as a prerequisite for the occurrence of anything of physical interest in the evolution of spacetime.Source: JOURNAL OF PHYSICS. CONFERENCE SERIES (ONLINE), vol. 306 (issue 1)
DOI: 10.1088/1742-6596/306/1/012042
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Bolognesi T
In the context of quantum gravity theories, several researchers have proposed causal sets as appropriate discrete models of spacetime. We investigate families of causal sets obtained from two simple models of computation - 2D Turing machines and network mobile automata - that operate on 'high-dimensional' supports, namely 2D arrays of cells and planar graphs, respectively. We study a number of quantitative and qualitative emergent properties of these causal sets, including dimension, curvature and localized structures, or 'particles'. We show how the possibility to detect and separate particles from background space depends on the choice between a global or local view at the causal set. Finally, we spot very rare cases of pseudo-randomness, or deterministic chaos; these exhibit a spontaneous phenomenon of 'causal compartmentation' that appears as a prerequisite for the occurrence of anything of physical interest in the evolution of spacetime.Source: JOURNAL OF PHYSICS. CONFERENCE SERIES (ONLINE), vol. 306 (issue 1)
DOI: 10.1088/1742-6596/306/1/012042
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See at:
CNR IRIS | CNR IRIS | CNR IRIS | Journal of Physics Conference Series
2010
Journal article
Restricted
Causal sets from simple models of computation
Bolognesi T
Causality among events is widely recognized as a most fundamental structure of spacetime, and causal sets have been proposed as discrete models of the latter in the context of quantum gravity theories, notably in the Causal Set Programme. In the rather different context of what might be called the 'Computational Universe Programme' -- one which associates the complexity of physical phenomena to the emergent features of models such as cellular automata -- a choice problem arises with respect to the variety of formal systems that, in virtue of their computational universality (Turing-completeness), qualify as equally good candidates for a computational, unified theory of physics. We address this problem by proposing Causal Sets to be the only objects of physical significance under the computational universe perspective. At the same time, we propose a fully deterministic, radical alternative to the probabilistic techniques considered in the Causal Set Programme for growing discrete spacetime instances. We investigate a number of computation models, all operating on a one-dimensional support like a tape or a string of symbols, we identify the causality relation among their computation events, implement it, and conduct a possibly exhaustive exploration of the associated causal set space, while examining quantitative and qualitative features such as dimensionality, curvature, planarity, emergence of pseudo-randomness and particles.Source: INTERNATIONAL JOURNAL OF UNCONVENTIONAL COMPUTING, vol. 6, pp. 489-524
Bolognesi T
Causality among events is widely recognized as a most fundamental structure of spacetime, and causal sets have been proposed as discrete models of the latter in the context of quantum gravity theories, notably in the Causal Set Programme. In the rather different context of what might be called the 'Computational Universe Programme' -- one which associates the complexity of physical phenomena to the emergent features of models such as cellular automata -- a choice problem arises with respect to the variety of formal systems that, in virtue of their computational universality (Turing-completeness), qualify as equally good candidates for a computational, unified theory of physics. We address this problem by proposing Causal Sets to be the only objects of physical significance under the computational universe perspective. At the same time, we propose a fully deterministic, radical alternative to the probabilistic techniques considered in the Causal Set Programme for growing discrete spacetime instances. We investigate a number of computation models, all operating on a one-dimensional support like a tape or a string of symbols, we identify the causality relation among their computation events, implement it, and conduct a possibly exhaustive exploration of the associated causal set space, while examining quantitative and qualitative features such as dimensionality, curvature, planarity, emergence of pseudo-randomness and particles.Source: INTERNATIONAL JOURNAL OF UNCONVENTIONAL COMPUTING, vol. 6, pp. 489-524
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CNR IRIS | CNR IRIS | www.oldcitypublishing.com
2010
Other
Open Access
Causal sets from simple models of computation
Bolognesi T
Causality among events is widely recognized as a most fundamental structure of spacetime, and causal sets have been proposed as discrete models of the latter in the context of quantum gravity theories, notably in the Causal Set Programme. In the rather different context of what might be called the 'Computational Universe Programme' -- one which associates the complexity of physical phenomena to the emergent features of models such as cellular automata -- a choice problem arises with respect to the variety of formal systems that, in virtue of their computational universality (Turing-completeness), qualify as equally good candidates for a computational, unified theory of physics. This paper proposes Causal Sets as the only objects of physical significance and relevance to be considered under the 'computational universe' perspective, and as the appropriate abstraction for shielding the unessential details of the many different computationally universal candidate models. At the same time, we propose a fully deterministic, radical alternative to the probabilistic techniques currently considered in the Causal Set Programme for growing discrete spacetimes. We investigate a number of computation models by grouping them into two broad classes, based on the support on which they operate; in one case this is linear, like a tape or a string of symbols; in the other, it is a two-dimensional grid or a planar graph. For each model we identify the causality relation among computation events, implement it, and conduct a possibly exhaustive exploration of the associated causal set space, while examining quantitative and qualitative features such as dimensionality, curvature, planarity, emergence of pseudo-randomness, causal set substructures and particles.
Bolognesi T
Causality among events is widely recognized as a most fundamental structure of spacetime, and causal sets have been proposed as discrete models of the latter in the context of quantum gravity theories, notably in the Causal Set Programme. In the rather different context of what might be called the 'Computational Universe Programme' -- one which associates the complexity of physical phenomena to the emergent features of models such as cellular automata -- a choice problem arises with respect to the variety of formal systems that, in virtue of their computational universality (Turing-completeness), qualify as equally good candidates for a computational, unified theory of physics. This paper proposes Causal Sets as the only objects of physical significance and relevance to be considered under the 'computational universe' perspective, and as the appropriate abstraction for shielding the unessential details of the many different computationally universal candidate models. At the same time, we propose a fully deterministic, radical alternative to the probabilistic techniques currently considered in the Causal Set Programme for growing discrete spacetimes. We investigate a number of computation models by grouping them into two broad classes, based on the support on which they operate; in one case this is linear, like a tape or a string of symbols; in the other, it is a two-dimensional grid or a planar graph. For each model we identify the causality relation among computation events, implement it, and conduct a possibly exhaustive exploration of the associated causal set space, while examining quantitative and qualitative features such as dimensionality, curvature, planarity, emergence of pseudo-randomness, causal set substructures and particles.
See at:
CNR IRIS | ISTI Repository | CNR IRIS
2010
Journal article
Open Access
Building discrete spacetimes by simple deterministic computations
Bolognesi T
The Computational Universe conjecture relates complexity in physics with emergence in computation. Our current research efforts are meant to put the surprisingly powerful notion of (computational) emergence at the service of recent quantum gravity theories, with special attention to the Causal Set Programme, which assumes causality among events as the most fundamental structure of spacetime, and causal sets as the most appropriate way to describe it.Source: ERCIM NEWS, vol. 83, pp. 52-53
Bolognesi T
The Computational Universe conjecture relates complexity in physics with emergence in computation. Our current research efforts are meant to put the surprisingly powerful notion of (computational) emergence at the service of recent quantum gravity theories, with special attention to the Causal Set Programme, which assumes causality among events as the most fundamental structure of spacetime, and causal sets as the most appropriate way to describe it.Source: ERCIM NEWS, vol. 83, pp. 52-53
See at:
ercim-news.ercim.eu | CNR IRIS | CNR IRIS