Related papers: Programs as the Language of Science
A logic is presented for reasoning on iterated sequences of formulae over some given base language. The considered sequences, or "schemata", are defined inductively, on some algebraic structure (for instance the natural numbers, the lists,…
Machine learning is increasingly transforming various scientific fields, enabled by advancements in computational power and access to large data sets from experiments and simulations. As artificial intelligence (AI) continues to grow in…
Human beings possess the most sophisticated computational machinery in the known universe. We can understand language of rich descriptive power, and communicate in the same environment with astonishing clarity. Two of the many contributors…
With the relentless rise of computer power, there is a widespread expectation that computers can solve the most pressing problems of science, and even more besides. We explore the limits of computational modelling and conclude that, in the…
As the twin movements of open science and open source bring an ever greater share of the scientific process into the digital realm, new opportunities arise for the meta-scientific study of science itself, including of data science and…
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…
Dirac sought an interpretation of mathematical formalism in terms of physical entities and Einstein insisted that physics should describe "the real states of the real systems". While Bell inequalities put into question the reality of…
Probabilistic programming is considered as a framework, in which basic components of cognitive architectures can be represented in unified and elegant fashion. At the same time, necessity of adopting some component of cognitive…
Affordance theory proposes that the use of an object is intrinsically determined by its physical shape. However, when translated to digital objects, affordance theory loses explanatory power, as the same physical affordances, for example,…
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…
The subject of this work is quantum predicative programming -- the study of developing of programs intended for execution on a quantum computer. We look at programming in the context of formal methods of program development, or programming…
This article introduces into the whole section on Social Sciences, edited by A. Nowak for this Encyclopedia, concentrating on the applications of mathematics and physics. Here under "mathematics" we include also all computer simulations if…
Language understanding is a key scientific issue in the fields of cognitive and computer science. However, the two disciplines differ substantially in the specific research questions. Cognitive science focuses on analyzing the specific…
A central goal of cognitive science is to provide a computationally explicit account of both the structure of the mind and its development: what are the primitive representational building blocks of cognition, what are the rules via which…
At the frontier of most areas in science, computer simulations play a central role. The traditional division of natural science into experimental and theoretical investigations is now completely outdated. Instead, theory, simulation, and…
Language models now provide an interface to express and often solve general problems in natural language, yet their ultimate computational capabilities remain a major topic of scientific debate. Unlike a formal computer, a language model is…
Over the past thirty years or so the authors have been teaching various programming for mathematics courses at our respective Universities, as well as incorporating computer algebra and numerical computation into traditional mathematics…
In this essay, I argue that mathematics is a natural science---just like physics, chemistry, or biology---and that this can explain the alleged "unreasonable" effectiveness of mathematics in the physical sciences. The main challenge for…
This article explores the evolving role of programming languages in the context of artificial intelligence. It highlights the need for programming languages to ensure human understanding while eliminating unnecessary implementation details…
This article reformulates the theory of computable physical models, previously introduced by the author, as a branch of applied model theory in first-order logic. It provides a semantic approach to the philosophy of science that…