Path-Constrained Search in Discrete Time and Space

This chapter examines the possibility of discrete time. At first sight, the answer seems trivial, but actually, it raises a number of interesting questions, both philosophical and scientific. First, the chapter explains what interpretations of discrete time are not considered. Then, it addresses two key philosophical problems: if there are such things as chronons, smallest “bits” of time, do they have extensions and can a distance function, that is, a duration, be defined on them? Second, the chapter discusses the relation between discrete time and discrete space, showing that the former implies the latter. Thus, with applications in mind, both time and space are to be seen as discrete. This leads, third, to the hardest problem of all: whether discrete time is applicable in physical theories.

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Grief in Times of Corona (Envoi)

Qualitative Inquiry ◽

10.1177/1077800420960140 ◽

2020 ◽

pp. 107780042096014

Author(s):

Cathy Fowley

Keyword(s):

Discrete Time ◽

Time And Space ◽

Close Relationship ◽

Relationship Of

This autoethnographic poem tells of personal grief happening in a time of lockdown. It draws on the concept of chronotope, a discrete time and space unit, a parenthesis of sorts, which I have chosen to illustrate as a bubble. In our daily speech, we see bubbles as related to both time and space, now with the added meaning of close relationship of people, those who belong to the same COVID bubble. In this autoethnographic piece, relationships are mediated by technology which anchors our bubbles together, with multimodal links carrying affect and emotion.

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Theoretical foundation for the discrete dynamics of physicochemical systems: Chaos, self-organization, time and space in complex systems

Discrete Dynamics in Nature and Society ◽

10.1155/s1026022697000058 ◽

1997 ◽

Vol 1 (1) ◽

pp. 31-43 ◽

Cited By ~ 8

Author(s):

V. Gontar

Keyword(s):

Discrete Time ◽

Theoretical Foundation ◽

Reaction Dynamics ◽

Second Law Of Thermodynamics ◽

Dynamic Equations ◽

Self Organization ◽

Second Law ◽

Discrete Dynamics ◽

Time And Space ◽

Physicochemical Reaction

A new theoretical foundation for the discrete dynamics of physicochemical systems is presented. Based on the analogy between theπ-theorem of the theory of dimensionality, the second law of thermodynamics and the stoichiometry of complex physicochemical reactions, basic dynamic equations and an extreme principle were formulated. The meaning of discrete time and space in the proposed equations is discussed. Some results of numerical calculations are presented to demonstrate the potential of the proposed approach to the mathematical simulation of spatiotemporal physicochemical reaction dynamics.

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Analysis of bifurcation, chaos and pattern formation in a discrete time and space Gierer Meinhardt system

Chaos Solitons & Fractals ◽

10.1016/j.chaos.2018.11.013 ◽

2019 ◽

Vol 118 ◽

pp. 1-17 ◽

Cited By ~ 6

Author(s):

Jinliang Wang ◽

You Li ◽

Shihong Zhong ◽

Xiaojie Hou

Keyword(s):

Pattern Formation ◽

Discrete Time ◽

Time And Space ◽

Bifurcation Chaos

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The dynamics of living and thinking systems, biological networks, and the laws of physics

Discrete Dynamics in Nature and Society ◽

10.1155/s1026022604401058 ◽

2004 ◽

Vol 2004 (1) ◽

pp. 101-111 ◽

Cited By ~ 1

Author(s):

V. Gontar

Keyword(s):

Mathematical Models ◽

Discrete Time ◽

Difference Equations ◽

Biological Networks ◽

Information Exchange ◽

Artificial Life ◽

Chaotic Dynamics ◽

Time And Space ◽

Self Organized ◽

Interacting Agents

Discrete chaotic dynamics (DCD) of living and thinking systems are presented in a form of networks of interacting agents with the abilities of energy and information exchange. Special dynamical principles followed by the systems of basic discrete time and space difference equations are introduced. Emergent, self-organized behavior of complex living and thinking systems is presented by the different patterns generated by the DCD algorithms. Artificial life and brain systems based on DCD principles and mathematical models are proposed.

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Discrete Time and Space

10.1093/oso/9780198810339.003.0008 ◽

2018 ◽

Author(s):

Alexander R. Pruss

Keyword(s):

Discrete Time ◽

Time And Space ◽

Continuous Space ◽

Space And Time

There is a strong intuitive argument that if causal finitism is true, then space and time are discrete. Discreteness, especially of time, is discussed, and varieties are distinguished. The implication fromcausal finitism to discretenesswould be problematic for causal finitism asmany physical theories involve continuous space and time.However, the argument from causal finitism to discreteness is challenged, and it is argued that while causal finitism does provide intuitive support for the discreteness thesis, it does not require it. Interpretations of physics, and specifically of QuantumMechanics, are offered on which time is continuous but nonetheless causation is discrete in a way that coheres with causal finitism.

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