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Computational philosophy is the use of mechanized computational techniques to unearth philosophical insights that are either difficult or impossible to find using traditional philosophical methods. Computational metaphysics is computational…
A mathematical definition of classical causality over discrete spacetime dynamics is formulated. The approach is background free and permits a definition of causality in a precise way whenever the spacetime dynamics permits. It gives a…
Merging disciplines has led to incredible learnings and breakthroughs throughout history, including the discovery of quantum computing: a cross between computation and quantum physics. In this paper, I will discuss how we can cross quantum…
Research on reference and naming suggests that humans can come up with very different ways of conceptualizing and referring to the same object, e.g. the same abstract tangram shape can be a "crab", "sink" or "space ship". Another common…
We offer a view of mathematics as an experimental science where axioms play the role of foundational theories like general relativity and quantum mechanics in physics. Under this view, axioms are provisional and inferred from experience…
Encoding the distance between locations in space is essential for accurate navigation. Grid cells, a functional class of neurons in medial entorhinal cortex, are believed to support this computation. However, existing theories of how…
In ancient Greek mathematics, magnitudes such as lengths were strictly distinguished from numbers. In modern quantity calculus, a distinction is made between quantities and scalars that serve as measures of quantities. It can be argued that…
We propose {\delta}-MAPS, a method that analyzes spatio-temporal data to first identify the distinct spatial components of the underlying system, referred to as "domains", and second to infer the connections between them. A domain is a…
We present the first steps of interaction spaces theory, a universal mathematical theory of complex systems which is able to embed cellular automata, agent based models, master equation based models, stochastic or deterministic, continuous…
Computation models such as circuits describe sequences of computation steps that are carried out one after the other. In other words, algorithm design is traditionally subject to the restriction imposed by a fixed causal order. We address a…
Questions concerning origin of mathematical knowledge and roles of language and intuition (imagery) in mathematical thoughts are long standing and widely debated. By introspection, mathematicians usually have some beliefs regarding these…
This paper challenges some of the common assumptions underlying the mathematics used to describe the physical world. We start by reviewing many of the assumptions underlying the concepts of real, physical, rigid bodies and the translational…
This paper studies how spatial thinking interacts with simplicity in [informal] proof, by analysing a set of example proofs mainly concerned with Ferrers diagrams (visual representations of partitions of integers, and comparing them to…
Graphs, and graph transformation systems, are used in many areas within Computer Science: to represent data structures and algorithms, to define computation models, as a general modelling tool to study complex systems, etc. Research in term…
Fog computing is a recent computational paradigm that was proposed to solve some weaknesses in cloud-based systems. For this reason, this technology has been extensively studied by several technology areas. It is still in a maturing stage,…
One often sees a sharp distinction in mathematics between descriptions from the outside and from the inside. Think of defining a set in the plane through an algebraic equation, or dynamically as the closure of the orbit of some point under…
Modern computer systems are characterized by deep memory hierarchies, composed of main memory, multiple layers of cache, and other specialized types of memory. In parallel and distributed systems, additional memory layers are added to this…
Formal concept analysis has grown from a new branch of the mathematical field of lattice theory to a widely recognized tool in Computer Science and elsewhere. In order to fully benefit from this theory, we believe that it can be enriched…
Fascinating and puzzling phenomena, such as landmark vector cells, splitter cells, and event-specific representations to name a few, are regularly discovered in the hippocampus. Without a unifying principle that can explain these divergent…
The moduli space of triangles is a two-dimensional space that records triangle shapes in the plane, considered up to similarity. We study the subset corresponding to \textit{lattice triangles}, which are triangles whose vertices have…