The book of nature is written in the language of mathematics.

Our motto is a frequently cited short form of a quote from Galileo
Galilei's work *The Assayer (Il saggiatore)*, written in 1623.
(Translation supplied by
Stephen J. Summers):

Philosophy is written in that great book which continually lies open before us (I mean the Universe). But one cannot understand this book until one has learned to understand the language and to know the letters in which it is written. It is written in the language of mathematics, and the letters are triangles, circles and other geometric figures. Without these means it is impossible for mankind to understand a single word; without these means there is only vain stumbling in a dark labyrinth.

In the original Italian:

La filosofia è scritta in questo grandissimo libro che continuamente ci sta aperto innanzi a gli occhi (io dico l'universo), ma non si può intendere se prima non s'impara a intender la lingua, e conoscer i caratteri, ne' quali è scritto. Egli è scritto in lingua matematica, e i caratteri sono triangoli, cerchi, ed altre figure geometriche, senza i quali mezi è impossibile a intenderne umanamente parola; senza questi è un aggirarsi vanamente per un'oscuro laberinto.

## Featured articles

### Uncertainty Relations for Angular Momentum

Prof. Dr. Reinhard F. Werner, Lars Dammeier#### Video Abstract

#### Abstract

In this work we study various notions of uncertainty for angular
momentum in the spin-*s* represen- tation of *SU*(2). We
characterize the “uncertainty regions” given by all vectors, whose
components are specified by the variances of the three angular momentum
components. A basic feature of this set is a lower bound for the sum of
the three variances. We give a method for obtaining optimal lower bounds
for uncertainty regions for general operator triples, and evaluate these
for small *s*. Further lower bounds are derived by generalizing
the technique by which Robertson obtained his state-dependent lower
bound. […]

### Equilibration of Quantum Gases

#### Video Abstract

#### Abstract

Finding equilibration times is a major unsolved problem in physics with few analytical results. Here we look at equilibration times for quantum gases of bosons and fermions in the regime of negligibly weak interactions, a setting which not only includes paradigmatic systems such as gases confined to boxes, but also Luttinger liquids and the free superfluid Hubbard model. To do this, we focus on two classes of measurements: (i) coarse-grained observables, such as the number of particles in a region of space, and (ii) few-mode measurements, such as phase correlators and correlation functions. We show that, in this setting, equilibration occurs quite generally despite the fact that the particles are not interacting. […]