Related papers: And the math will set you free
Learning to use math in science is a non-trivial task. It involves many different skills (not usually taught in a math class) that help blend physical knowledge with mathematical symbology. One of these is the idea of quantification: that…
We present a computational model of mathematical reasoning according to which mathematics is a fundamentally stochastic process. That is, on our model, whether or not a given formula is deemed a theorem in some axiomatic system is not a…
Learning to create, use, and evaluate models is a central element of becoming a scientist. In physics, we often begin an analysis of a complex system with highly simplified or toy models. In introductory physics classes, we tend to use them…
Computation, the use of a computer to solve, simulate, or visualize a physical problem, has revolutionized how physics research is done. Computation is used widely to model systems, to simulate experiments, and to analyze data. Yet, in most…
Quantum states are the key mathematical objects in quantum theory. It is therefore surprising that physicists have been unable to agree on what a quantum state truly represents. One possibility is that a pure quantum state corresponds…
In this paper, I explore what mathematical research can tell us about ourselves, and our role in the world, using examples from my own experience. The paper is a sequel to my piece "Mathematics is a Quest for Truth", published in the…
It is first pointed out that there is a common mathematical model for the universe and the quantum computer. The former is called the histories approach to quantum mechanics and the latter is called measurement based quantum computation.…
We argue for a foundational epistemic claim and a hypothesis about the production and uses of mathematical epidemiological models, exploring the consequences for our political and socio-economic lives. First, in order to make the best use…
Cosmology differs in some respects significantly from other sciences, primarily because of its intimate association with issues of a conceptual and philosophical nature. Because cosmology in the broader sense relates to the world views held…
Recent contributions address the problem of language coexistence as that of two species competing to aggregate speakers, thus focusing on the dynamics of linguistic traits across populations. They draw inspiration from physics and biology…
Since the early twentieth century, it has been understood that mathematical definitions and proofs can be represented in formal systems systems with precise grammars and rules of use. Building on such foundations, computational proof…
Throughout this book, we discuss some open problems in various branches of science, including mathematics, theoretical physics, astro-physics, geophysics etc. It is of our hope that some of the problems discussed in this book will find…
The Universe contains everything that exists, including life. And all that exists, including life, obeys universal physical laws. Do those laws then give adequate foundations for a complete explanation of biological phenomena? We discuss…
Modern mathematics is known for its rigorous proofs and tight analysis. Math is the paradigm of objectivity for most. We identify the source of that objectivity as our knowledge of the physical world given through our senses. We show in…
Our knowledge about the universe has increased tremendously in the last three decades or so --- thanks to the progress in observations --- but our understanding has improved very little. There are several fundamental questions about our…
The purpose of this paper is to show the magic of physics by showing the physics of magic. What usually makes magic tricks interesting is that something unexpected occurs. Similarly, demonstrations are interesting inasmuch as they produce…
(transcript of a talk given by Prof.~Feshbach:) Nuclear physics has been and will be a major factor in science and technology. It makes unique and important contributions to medicine, to industry and to other sciences. Interaction with…
In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…
One source of beauty in mathematics is totally unexpected connections between two fundamentally different objects. For instance, is it not surprising that the time period of a real simple pendulum is linked with a function arising out of…
In a recent article, M. Tegmark poses the hypothesis that our known universe is a ``baggage free'' mathematical structure among many other possible ones, which also correspond to other physical universes --Mathematical Universe Hypothesis,…