Related papers: Definability as hypercomputational effect
Recently developed quantum algorithms suggest that quantum computers can solve certain problems and perform certain tasks more efficiently than conventional computers. Among other reasons, this is due to the possibility of creating…
The computational abilities of theories within the generalised probabilistic theory framework has been the subject of much recent study. Such investigations aim to gain an understanding of the possible connections between physical…
We present a case study featuring a first-year bio-science university student using computation to solve a radioactive decay problem and interpret the results. In a semi-structured cognitive interview, we use this case to examine the…
The theory that all processes in the universe are computational is attractive in its promise to provide an understandable theory of everything. I want to suggest here that this pancomputationalism is not sufficiently clear on which problem…
Since its inception at the beginning of the twentieth century, quantum mechanics has challenged our conceptions of how the universe ought to work; however, the equations of quantum mechanics can be too computationally difficult to solve…
We develop a notion of computability and complexity of functions over the reals, which seems to be very natural when one tries to determine just how "difficult" a certain function is. This notion can be viewed as an extension of both BSS…
This contribution argues that the notion of time used in the scientific modeling of reality deprives time of its real nature. Difficulties from logic paradoxes to mathematical incompleteness and numerical uncertainty ensue. How can the…
In the first of this pair of papers, it was proven that that no physical computer can correctly carry out all computational tasks that can be posed to it. The generality of this result follows from its use of a novel definition of…
All natural things process and transform information. They receive environmental information as input, and transform it into appropriate output responses. Much of science is dedicated to building models of such systems -- algorithmic…
Computational models are quantitative representations of systems. By analyzing and comparing the outputs of such models, it is possible to gain a better understanding of the system itself. Though as the complexity of model outputs…
With the rapid development of quantum technology, one of the leading applications is the simulation of chemistry. Interestingly, even before full scale quantum computers are available, quantum computer science has exhibited a remarkable…
Simulation models are an absolute necessity in the human and social sciences, which can only very exceptionally use experimental science methods to construct their knowledge. Models enable the simulation of social processes by replacing the…
A coherent mathematical overview of computation and its generalisations is described. This conceptual framework is sufficient to comfortably host a wide range of contemporary thinking on embodied computation and its models.
The simulation of large-scale classical systems in exponentially small space on quantum computers has gained attention. The prior work demonstrated that a quantum algorithm offers an exponential speedup over any classical algorithm in…
Computational complexity theory contains a corpus of theorems and conjectures regarding the time a Turing machine will need to solve certain types of problems as a function of the input size. Nature {\em need not} be a Turing machine and,…
We briefly review some of the scientific challenges and epistemological issues related to climate science. We discuss the formulation and testing of theories and numerical models, which, given the presence of unavoidable uncertainties in…
For the classical mind, quantum mechanics is boggling enough; nevertheless more bizarre behavior could be imagined, thereby concentrating on propositional structures (empirical logics) that transcend the quantum domain. One can also…
The problem of emergence in physical theories makes necessary to build a general theory of the relationships between the observed system and the observing system. It can be shown that there exists a correspondence between classical systems…
Quantum computing promises to provide the next step up in computational power for diverse application areas. In this review, we examine the science behind the quantum hype, and the breakthroughs required to achieve true quantum advantage in…
An intense effort is being made today to build a quantum computer. Instead of presenting what has been achieved, I invoke here analogies from the history of science in an attempt to glimpse what the future might hold. Quantum computing is…