Einstein claimed that the fundamental dynamical insight of special relativity was the equivalence of mass and energy. I disagree. Not only are mass and energy not equivalent (whatever exactly that means) but talk of such equivalence obscures the real dynamical insight of special relativity, which concerns the nature of 4-forces and interactions more generally. In this paper I present and defend a new ontology of special relativistic particle dynamics that makes this insight perspicuous and I explain how alleged cases of mass-energy conversion can be accommodated within that ontology.

The QAnon conspiracy theory claims that a cabal of (literally) bloodthirsty politicians and media personalities are engaged in a war to destroy society. By interpreting cryptic «drops» of information from an anonymous insider calling themselves Q, adherents of the conspiracy theory believe that they are being led by Donald Trump in an active fight against this cabal. QAnon has been covered extensively by the media, as its adherents have been involved in multiple violent acts, including the January 6th, 2021 seditious storming of the US Capitol building. Nevertheless, we still have relatively little understanding of how the theory evolved and was spread on the Web, and the role played in that by multiple platforms.

We review, for a general audience, a variety of recent experiments on extracting structure from machine-learning mathematical data that have been compiled over the years. Focusing on supervised machine-learning on labeled data from different fields ranging from geometry to representation theory, from combinatorics to number theory, we present a comparative study of the accuracies on different problems. The paradigm should be useful for conjecture formulation, finding more efficient methods of computation, as well as probing into certain hierarchy of structures in mathematics.

“En el fondo del fondo, constata G.B., la humanidad está haciendo un supremo experimento no el de ser semejante a los dioses, que no da para gran cosa, sino ser en el fondo dioses en persona” (AF 25).

A central topic in recent artificial intelligence technologies is deep learning, which can be regarded as a multilayer feedforward neural network. An essence of deep learning is the information propagation through the layers, suggesting a connection between deep neural networks and dynamical systems, in the sense that the information propagation is explicitly modeled by the time-evolution of dynamical systems. Here, we present a pattern recognition based on optimal control of continuous-time dynamical systems, which is suitable for physical hardware implementation. The learning is based on the adjoint method to optimally control dynamical systems, and the deep (virtual) network structures based on the time evolution of the systems can be used for processing input information.

With the challenge of quantum computing ahead, an analysis of number and representation adequate to the task is needed. Some clarifications on the combinatorial nature of representation are presented here; this is related to the foundations of digital representations of integers, and is thus also of interest in clarifying what numbers are and how they are used in pure and applied mathematics. The author hopes this work will help mathematicians and computer scientists better understand the nature of the Generalized Knapsack Code, a lattice-based code which the author believes to be particularly promising, and the use of number in computing in general.

We briefly overview how, historically, string theory led theoretical physics first to precise problems in algebraic and differential geometry, and thence to computational geometry in the last decade or so, and now, in the last few years, to data science. Using the Calabi-Yau landscape — accumulated by the collaboration of physicists, mathematicians and computer scientists over the last 4 decades — as a starting-point and concrete playground, we review some recent progress in machine-learning applied to the sifting through of possible universes from compactification, as well as wider problems in geometrical engineering of quantum field theories.

Technological cumulativeness is considered one of the main mechanisms for technological progress, yet its exact meaning and dynamics often remain unclear. To develop a better understanding of this mechanism we approach a technology as a body of knowledge consisting of interlinked inventions. Technological cumulativeness can then be understood as the extent to which inventions build on other inventions within that same body of knowledge. The cumulativeness of a technology is therefore characterized by the structure of its knowledge base, which is different from, but closely related to, the size of its knowledge base

The overall objective is to apply logical methods in these disciplines to provide a sound foundation for obtaining exact and correct algorithms. At the same time, the conference was the third annual meeting of the COMPUTAL project, which is a research network between Europe, Russia, South Africa, and Japan funded by the European Union under the FP7-IRSES programme scheme. A major motivation for the project collaboration is the fact that in safety-critical applications it is not sufficient to produce software that is only tested for correctness: its correctness has to be formally proven. This is true as well in the area of Scientific Computation.

Until relatively recently this theory has been regarded as the foundation of modern cosmology, the branch of science devoted to the study of the Universe as a whole. I am talking now to one of the most well-known, outspoken critics of the Big Bang, the American physicist Eric J Lerner.Readers of my articles in Asia Times will know the name: Eric is also the founder and chief scientist of the company LPP Fusion, which is developing the Dense Plasma Focus, a revolutionary type of fusion reactor which could provide a shortcut toward realizing nuclear fusion as an energy source.