Related papers: Some Thoughts on Hypercomputation
There exists a growing literature on the so-called physical Church-Turing thesis in a relativistic spacetime setting. The physical Church-Turing thesis is the conjecture that no computing device that is physically realizable (even in…
The simulation hypothesis has recently excited renewed interest in the physics and philosophy communities. However, the hypothesis specifically concerns {\textit{computers}} that simulate physical universes. So to formally investigate the…
Hyperdimensional (HD) computing is a set of neurally inspired methods for obtaining high-dimensional, low-precision, distributed representations of data. These representations can be combined with simple, neurally plausible algorithms to…
The history of computer science and brain sciences are intertwined. In his unfinished manuscript "The Computer and the Brain," von Neumann debates whether or not the brain can be thought of as a computing machine and identifies some of the…
What is computable with limited resources? How can we verify the correctness of computations? How to measure computational power with precision? Despite the immense scientific and engineering progress in computing, we still have only…
Significant advances in the development of computing devices based on quantum effects and the demonstration of their use to solve various problems have rekindled interest in the nature of the "quantum computational advantage." Although…
We propose a definition of quantum computable functions as mappings between superpositions of natural numbers to probability distributions of natural numbers. Each function is obtained as a limit of an infinite computation of a quantum…
If we define classical foundational concepts constructively, and introduce non-algorithmic effective methods into classical mathematics, then we can bridge the chasm between truth and provability, and define computational methods that are…
The last century saw dramatic challenges to the Laplacian predictability which had underpinned scientific research for around 300 years. Basic to this was Alan Turing's 1936 discovery (along with Alonzo Church) of the existence of…
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…
Computability theory is a discipline in the intersection of computer science and mathematical logic where the fundamental question is: given two mathematical objects X and Y, does X compute Y in principle? In case X and Y are real numbers,…
Quantum computers, if fully realized, promise to be a revolutionary technology. As a result, quantum computing has become one of the hottest areas of research in the last few years. Much effort is being applied at all levels of the system…
One of the fundamental results in computability is the existence of well-defined functions that cannot be computed. In this paper we study the effects of data representation on computability; we show that, while for each possible way of…
The Turing machine halting problem can be explained by several factors, including arithmetic logic irreversibility and memory erasure, which contribute to computational uncertainty due to information loss during computation. Essentially,…
Experimental science usually relies on laboratory procedures that, after finitely many steps, terminate with numerical reports on physical quantities. This paper argues that such procedures can be understood as algorithmic once the…
High Performance Computing (HPC) aims at providing reasonably fast computing solutions to scientific and real life problems. The advent of multicore architectures is noticeable in the HPC history, because it has brought the underlying…
The hypercomputers compute functions or numbers, or more generally solve problems or carry out tasks, that cannot be computed or solved by a Turing machine. Several numerical simulations of a possible hypercomputational algorithm based on…
In recent years we observed rapid and significant advancements in artificial intelligence (A.I.). So much so that many wonder how close humanity is to developing an A.I. model that can achieve human level of intelligence, also known as…
The world of mathematics is often considered abstract, with its symbols, concepts, and topics appearing unrelated to physical objects. However, it is important to recognize that the development of mathematics is fundamentally influenced by…
The Web has made it possible to harness human cognition en masse to achieve new capabilities. Some of these successes are well known; for example Wikipedia has become the go-to place for basic information on all things; Duolingo engages…