58 research outputs found
On the role of simplicity in science
No full textSimple assumptions represent a decisive reason to prefer one theory to another in everyday scientific praxis. But this praxis has little philosophical justification, since there exist many notions of simplicity, and those that can be defined precisely strongly depend on the language in which the theory is formulated. The language dependence is a natural feature - to some extent - but it is also believed to be a fatal problem, because, according to a common general argument, the simplicity of a theory is always trivial in a suitably chosen language. But, this 'trivialization argument' is typically either applied to toy-models of scientific theories or applied with little regard for the empirical content of the theory. This paper shows that the 'trivialization argument' fails, when one considers realistic theories and requires their empirical content to be preserved. In fact, the concepts that enable a very simple formulation, are not necessarily measurable, in general. Moreover, the inspection of a theory describing a chaotic billiard shows that precisely those concepts that naturally make the theory extremely simple are provably not measurable. This suggests that - whenever a theory possesses sufficiently complex consequences - the constraint of measurability prevents too simple formulations in any language. This explains why the scientists often regard their assessments of simplicity as largely unambiguous. In order to reveal a cultural bias in the scientists' assessment, one should explicitly identify different characterizations of simplicity of the assumptions that lead to different theory selections. General arguments are not sufficient
Renormalization constants of fermionic operators in lattice QCD with Nf=4 dynamical Wilson quarks
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Metropolis Monte Carlo integration on the Lefschetz thimble: application to a one-plaquette model
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New approach to the sign problem in quantum field theories: High density QCD on a Lefschetz thimble
No full textIt is sometimes speculated that the sign problem that afflicts many quantum field theories might be reduced or even eliminated by choosing an alternative domain of integration within a complexified extension of the path integral (in the spirit of the stationary phase integration method). In this paper we start to explore this possibility somewhat systematically. A first inspection reveals the presence of many difficulties but—quite surprisingly—most of them have an interesting solution. In particular, it is possible to regularize the lattice theory on a Lefschetz thimble, where the imaginary part of the action is constant and disappears from all observables. This regularization can be justified in terms of symmetries and perturbation theory. Moreover, it is possible to design a Monte Carlo algorithm that samples the configurations in the thimble. This is done by simulating, effectively, a five-dimensional system. We describe the algorithm in detail and analyze its expected cost and stability. Unfortunately, the measure term also produces a phase which is not constant and it is currently very expensive to compute. This residual sign problem is expected to be much milder, as the dominant part of the integral is not affected, but we have still no convincing evidence of this. However, the main goal of this paper is to introduce a new approach to the sign problem, that seems to offer much room for improvements. An appealing feature of this approach is its generality. It is illustrated first in the simple case of a scalar field theory with chemical potential, and then extended to the more challenging case of QCD at finite baryonic density
A not-too-simple solution to Goodman's new riddle of induction in the age of AI
No full textI review the works of Gärdenfors (1990) and Scorzato (2013) and show that their combination provides an elegant solution of Goodman's new riddle of induction. The solution is based on two main ideas: (1) clarifying what is expected from a solution: understanding that philosophy of science is a science itself, with the same limitations and strengths as other scientific disciplines; (2) understanding that the concept of complexity of a model's assumptions and the concept of direct measurements must be characterized together. Although both measurements and complexity have been the subject of a vast literature, within the philosophy of science, essentially no other attempt has been made to combine them. The widespread expectation, among modern philosophers, that Goodman's new riddle cannot be solved is clearly not defensible without a serious exploration of such a natural approach. A clarification of this riddle has always been very important, but it has become even more crucial in the age of AI
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