Related papers: Thinking Inside and Outside the Box
The answers people give when asked to 'think of the unexpected' for everyday event scenarios appear to be more expected than unexpected. There are expected unexpected outcomes that closely adhere to the given information in a scenario,…
In this paper the author presents some non-conventional thoughts on the complexity of the Universe and the algorithmic reproducibility of the human brain, essentially sparked off by the notion of algorithmic complexity. We must warn that…
The process of doing Science in condition of uncertainty is illustrated with a toy experiment in which the inferential and the forecasting aspects are both present. The fundamental aspects of probabilistic reasoning, also relevant in real…
I describe a puzzle I wrote for the 2018 MIT Mystery Hunt which introduced new types of people in logic puzzles. I discuss the puzzle itself, the solution, and the mathematics behind it.
The information loss paradox is often discussed from the perspective of the observers who stay outside of a black hole. However, the interior spacetime of a black hole can be rather nontrivial. We discuss the open problems regarding the…
Each market has its singular characteristic. Its inner structure is directly responsible for the observed distributions of returns though this fact is widely overlooked. Big orders lead to doubling the tails. The behavior of a market maker…
One might think that, once we know something is computable, how efficiently it can be computed is a practical question with little further philosophical importance. In this essay, I offer a detailed case that one would be wrong. In…
Complexity is an interdisciplinary concept which, first of all, addresses the question of how order emerges out of randomness. For many reasons matrices provide a very practical and powerful tool in approaching and quantifying the related…
Can AI solve all math? What do we actually mean by doing mathematics? How do we communicate mathematics? What is mathematics beyond problem solving? This essay is my attempt to answer these questions.
We investigate some versions of the famous 100 prisoner problem for the infinite case, where there are infinitely many prisoners and infinitely many boxes with labels. In this case, many questions can be asked about the admissible steps of…
The classical and quantum behavior of a particle inside a square box under the influence of the gravitational field is studied. Detailed calculations on periodic orbits, probability densities as well as expectation values and uncertainties…
Any ambitious construction project requires architects for its design and engineers who apply the design to the real world. As scientific research shifts towards large groups which focus on the engineering aspects of linking data to…
This is a collection of open problems in geometry that I think of as puzzles: they stick to my brain -- I see many grips, but no spare hands. Puzzle-charm is the only criterion for including a problem here; importance is ignored.
Can machines truly think? This question and its answer have many implications that depend, in large part, on any number of assumptions underlying how the issue has been addressed or considered previously. A crucial question, and one that is…
The Rubik's cube is a famous puzzle in which faces can be moved and the corresponding movement operations define a group. We consider here a generalization to any $3$-valent map. We prove an upper bound on the size of the corresponding…
Data integration has been recently challenged by the need to handle large volumes of data, arriving at high velocity from a variety of sources, which demonstrate varying levels of veracity. This challenging setting, often referred to as big…
Explainable artificial intelligence and interpretable machine learning are research domains growing in importance. Yet, the underlying concepts remain somewhat elusive and lack generally agreed definitions. While recent inspiration from…
In order to legitimate and defend democratic politics under conditions of computational capital, my aim is to contribute a notion of what I am calling explanatory publics. I will explore what is at stake when we question the social and…
Complex systems are characterized by specific time-dependent interactions among their many constituents. As a consequence they often manifest rich, non-trivial and unexpected behavior. Examples arise both in the physical and non-physical…
The quantum-mechanical description of the world, including human observers, makes substantial use of entanglement. In order to understand this, we need to adopt concepts of truth, probability and time which are unfamiliar in modern…