In this paper we discuss various philosophical aspects of the hyperstructure concept extending ne... more In this paper we discuss various philosophical aspects of the hyperstructure concept extending networks and higher categories. By this discussion we hope to pave the way for applications and further developments of the mathematical theory of hyperstructures.
In this paper we discuss various philosophical aspects of the hyperstructure concept extending ne... more In this paper we discuss various philosophical aspects of the hyperstructure concept extending networks and higher categories. By this discussion we hope to pave the way for applications and further developments of the mathematical theory of hyperstructures.
We extend the well-known Borromean and Brunnian rings to new higher order versions. Then we sugge... more We extend the well-known Borromean and Brunnian rings to new higher order versions. Then we suggest an extension of the connection between Efimov states in cold gases and Borromean and Brunnian rings to these new higher order links. This gives rise to a whole new hierarchy of possible states with Efimov states at the bottom.
International Journal of General Systems, Feb 1, 2013
We extend the well-known Borromean and Brunnian rings to new higher order versions. Then we sugge... more We extend the well-known Borromean and Brunnian rings to new higher order versions. Then we suggest an extension of the connection between Efimov states in cold gases and Borromean and Brunnian rings to these new higher order links. This gives rise to a whole new hierarchy of possible states with Efimov states at the bottom.
When the Abel Prize was established in 2002 it was decided to award an honorary prize to the reno... more When the Abel Prize was established in 2002 it was decided to award an honorary prize to the renowned Norwegian mathematician Atle Selberg in recognition of his status as one of the world’s leading mathematicians. His contributions to mathematics are so deep and original that his name will always be an important part of the history of mathematics. His special field in mathematics was number theory in a broad sense.
We discuss the chemical synthesis of topological links, in particular higher order links which ha... more We discuss the chemical synthesis of topological links, in particular higher order links which have the Brunnian property (namely that removal of any one component unlinks the entire system). Furthermore, we suggest how to obtain both two dimensional and three dimensional objects (surfaces and solids, respectively) which also have this Brunnian property.
Gross and McMullin [Arti cial Life, 7, 355-365] criticize the conclusions of our article on dynam... more Gross and McMullin [Arti cial Life, 7, 355-365] criticize the conclusions of our article on dynamical hierarchie s [Arti cial Life, 7, 329-353]. In this note we respond to their criticisms. After clarifying our ansatz, we argue that the simulations presented by Gross and McMullin present no evidence against the ansatz, in part because their simulations use a different simulation framework, and in part because their simulations are no less complex than ours. We also clarify why the micelles in our simulations are third-order emergent structures, and why we emphasize realism in our simulation. Gross and McMullin [3] pinpoint the crucial issues in our article "Ansatz for dynamical hierarchies" [7]. We are grateful to them for helping us to clarify and sharpen our position. In the end, however, we still stand by all our original conclusions. In this brief note, we respond to the main criticisms of Gross and McMullin by clarifying some technical details and expanding some explanations.
International Journal of General Systems, Oct 1, 2004
ABSTRACT The aim of the paper is to compare two different approaches to the modeling of complex n... more ABSTRACT The aim of the paper is to compare two different approaches to the modeling of complex natural systems, in particular of their hierarchical organization with higher-order structures and their emergence processes. These approaches are, respectively, the hyperstructures (HS) of Baas and the memory evolutive systems (MES) of Ehresmann and Vanbremeersch. The HS are “structural” while MES, based on category theory, take dynamics more into account. It is shown how the dynamical organization and mechanisms developed for MES rely on simple ideas of a philosophical nature, that might be disengaged from the categorical setting and extended to the general frame of HS.
International Journal of General Systems, Dec 21, 2015
In this paper we discuss various philosophical aspects of the hyperstructure concept extending ne... more In this paper we discuss various philosophical aspects of the hyperstructure concept extending networks and higher categories. By this discussion we hope to pave the way for applications and further developments of the mathematical theory of hyperstructures.
We give a new introduction to hyperstructures and higher order structures in general. A specific ... more We give a new introduction to hyperstructures and higher order structures in general. A specific implementation of a hyperstructure we call Matter, and we argue that this is a suitable model for studying and simulating various kinds of both organic and inorganic matter — even cognitive matter.
We discuss the nature of structure and organization, and the process of making new Things. Hypers... more We discuss the nature of structure and organization, and the process of making new Things. Hyperstructures are introduced as binding and organizing principles, and we show how they can transfer from one situation to another. A guiding example is the hyperstructure of higher order Brunnian rings and similarly structured many-body systems.
In this paper we discuss various philosophical aspects of the hyperstructure concept extending ne... more In this paper we discuss various philosophical aspects of the hyperstructure concept extending networks and higher categories. By this discussion we hope to pave the way for applications and further developments of the mathematical theory of hyperstructures.
In this paper we discuss various philosophical aspects of the hyperstructure concept extending ne... more In this paper we discuss various philosophical aspects of the hyperstructure concept extending networks and higher categories. By this discussion we hope to pave the way for applications and further developments of the mathematical theory of hyperstructures.
We extend the well-known Borromean and Brunnian rings to new higher order versions. Then we sugge... more We extend the well-known Borromean and Brunnian rings to new higher order versions. Then we suggest an extension of the connection between Efimov states in cold gases and Borromean and Brunnian rings to these new higher order links. This gives rise to a whole new hierarchy of possible states with Efimov states at the bottom.
International Journal of General Systems, Feb 1, 2013
We extend the well-known Borromean and Brunnian rings to new higher order versions. Then we sugge... more We extend the well-known Borromean and Brunnian rings to new higher order versions. Then we suggest an extension of the connection between Efimov states in cold gases and Borromean and Brunnian rings to these new higher order links. This gives rise to a whole new hierarchy of possible states with Efimov states at the bottom.
When the Abel Prize was established in 2002 it was decided to award an honorary prize to the reno... more When the Abel Prize was established in 2002 it was decided to award an honorary prize to the renowned Norwegian mathematician Atle Selberg in recognition of his status as one of the world’s leading mathematicians. His contributions to mathematics are so deep and original that his name will always be an important part of the history of mathematics. His special field in mathematics was number theory in a broad sense.
We discuss the chemical synthesis of topological links, in particular higher order links which ha... more We discuss the chemical synthesis of topological links, in particular higher order links which have the Brunnian property (namely that removal of any one component unlinks the entire system). Furthermore, we suggest how to obtain both two dimensional and three dimensional objects (surfaces and solids, respectively) which also have this Brunnian property.
Gross and McMullin [Arti cial Life, 7, 355-365] criticize the conclusions of our article on dynam... more Gross and McMullin [Arti cial Life, 7, 355-365] criticize the conclusions of our article on dynamical hierarchie s [Arti cial Life, 7, 329-353]. In this note we respond to their criticisms. After clarifying our ansatz, we argue that the simulations presented by Gross and McMullin present no evidence against the ansatz, in part because their simulations use a different simulation framework, and in part because their simulations are no less complex than ours. We also clarify why the micelles in our simulations are third-order emergent structures, and why we emphasize realism in our simulation. Gross and McMullin [3] pinpoint the crucial issues in our article "Ansatz for dynamical hierarchies" [7]. We are grateful to them for helping us to clarify and sharpen our position. In the end, however, we still stand by all our original conclusions. In this brief note, we respond to the main criticisms of Gross and McMullin by clarifying some technical details and expanding some explanations.
International Journal of General Systems, Oct 1, 2004
ABSTRACT The aim of the paper is to compare two different approaches to the modeling of complex n... more ABSTRACT The aim of the paper is to compare two different approaches to the modeling of complex natural systems, in particular of their hierarchical organization with higher-order structures and their emergence processes. These approaches are, respectively, the hyperstructures (HS) of Baas and the memory evolutive systems (MES) of Ehresmann and Vanbremeersch. The HS are “structural” while MES, based on category theory, take dynamics more into account. It is shown how the dynamical organization and mechanisms developed for MES rely on simple ideas of a philosophical nature, that might be disengaged from the categorical setting and extended to the general frame of HS.
International Journal of General Systems, Dec 21, 2015
In this paper we discuss various philosophical aspects of the hyperstructure concept extending ne... more In this paper we discuss various philosophical aspects of the hyperstructure concept extending networks and higher categories. By this discussion we hope to pave the way for applications and further developments of the mathematical theory of hyperstructures.
We give a new introduction to hyperstructures and higher order structures in general. A specific ... more We give a new introduction to hyperstructures and higher order structures in general. A specific implementation of a hyperstructure we call Matter, and we argue that this is a suitable model for studying and simulating various kinds of both organic and inorganic matter — even cognitive matter.
We discuss the nature of structure and organization, and the process of making new Things. Hypers... more We discuss the nature of structure and organization, and the process of making new Things. Hyperstructures are introduced as binding and organizing principles, and we show how they can transfer from one situation to another. A guiding example is the hyperstructure of higher order Brunnian rings and similarly structured many-body systems.
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Papers by Nils Baas