Related papers: 25 years ago: the official farewell to the meter
These are notes from talks given at ICMS, Edinburgh, 4/2007 ("Geometry and Algorithms workshop") and at Bernoulli Center, Lausanne 5/2007 ("Limits of graphs in group theory and computer science"). We survey the following type of dichotomies…
Distances to compact sets are widely used in the field of Topological Data Analysis for inferring geometric and topological features from point clouds. In this context, the distance to a probability measure (DTM) has been introduced by…
Whereas physics in the period from about 1880 to 1910 experienced a steady growth, it was also a revolutionary period in which the foundations of the physical world picture were criticized and reconsidered. Generally speaking, from about…
On the evening after Stephen Hawking's funeral in Cambridge on March 31, 2018 a dinner for attendees who had come from far away was hosted by Paul Shellard, the Director of the Centre for Theoretical Cosmology. I was asked me to speak for…
The concept of infinity took centuries to achieve recognized status in the field of mathematics, despite the fact that it was implicitly present in nearly all mathematical endeavors. Here I explore the idea that a similar development might…
The year 2024 marks two anniversaries: The 70th anniversary of CERN and the 50th anniversary of the $J/\Psi$ discovery. At this occasion I have been asked to give review talks on the significance of these anniversaries. This article is an…
We give some personal reflections on the person and scientist Lars Brink and on some of his scientific achievements. Our relations to Lars are briefly described in [1] and [2], while the sources relevant for this text are summarised in [3].
The setting for this brief paper is R^3. Distance between two spheres is understood as distance delta between spherical centers. For instance, a Reuleaux tetrahedron T is the intersection of four unit balls satisfying delta=1 pairwise.…
While Left-Right symmetry (space parity) breaking historically appeared as a surprise, we argue that the real wonder is its restoration in long-distance interactions (at least until we find electric dipole moments!).
In this paper we investigate the Erd\"os/Falconer distance conjecture for a natural class of sets statistically, though not necessarily arithmetically, similar to a lattice. We prove a good upper bound for spherical means that have been…
The great conjunction of 21 December 2020 saw Jupiter and Saturn appear together in the sky, separated by just a tenth of a degree (equivalent to a distance five times smaller than the diameter of the full Moon). This provided a potential…
Motivated by putting empirical work based on (synthetic) election data on a more solid mathematical basis, we analyze six distances among elections, including, e.g., the challenging-to-compute but very precise swap distance and the distance…
Once considered essential to the explanation of electromagnetic phenomena, the ether was eventually discarded after the advent of special relativity. The lack of empirical signature of realist interpretative schemes of quantum mechanics,…
Overview of the determination of astronomical distances from a metrological standpoint. Distances are considered from the Solar System (planetary distances) to extragalactic distances, with a special emphasis on the fundamental step of the…
We propose detecting the moment an atom emits a photon by means of a nearly classical macroscopic clock and discuss its viability. It is shown that what happens in such a measurement depends on the relation between the clock's accuracy and…
We propose to follow the itinerary of Claude Chevalley during the last twenty years of his life, through the words of Jacques Roubaud, Denis Guedj and Alexander Grothendieck. Our perspective is that of their testimonies filled with…
We present the lessons learned about the degradation observed in several space solar missions, based on contributions at the Workshop about On-Orbit Degradation of Solar and Space Weather Instruments that took place at the Solar Terrestrial…
Despite the fact that the fundamental physical laws are symmetric in time, most observed processes do not show this symmetry. Especially the phenomenon of decay seems to involve a kind of irreversibility that makes the definition of a…
The quantum theory of measurement has been a matter of debate for over eighty years. Most of the discussion has focused on theoretical issues with the consequence that operational prescriptions, which are integral to experimental physics,…
A finite subset of a Euclidean space is called an $s$-distance set if there exist exactly $s$ values of the Euclidean distances between two distinct points in the set. In this paper, we prove that the maximum cardinality among all…