Most numbers are not normal

Normal Numbers Are Normal

A number is normal in base b if every sequence of k symbols in the letters 0, 1, . . . , b− 1 occurs in the base-b expansion of the given number with the expected frequency b−k. From an informal point of view, we can think of numbers normal in base 2 as those produced by flipping a fair coin, recording 1 for heads and 0 for tails. Normal numbers are those which are normal in every base. In this...

Most 1.6 Earth-radius Planets Are Not Rocky

The Kepler mission, combined with ground-based radial velocity (RV) follow-up and dynamical analyses of transit timing variations, has revolutionized the observational constraints on sub-Neptune-sized planet compositions. The results of an extensive Kepler follow-up program including multiple Doppler measurements for 22 planet-hosting stars more than doubles the population of sub-Neptune-sized ...

Most General First Order Theorems are not Recursively Enumerable

Most Real Bars are Not Made by the Bar Instability

Having once thought that we understood how some galaxies were barred and had difficulty accounting for the absence of bars in others, it now seems that we have the opposite problem. Most real galaxies have centres dense enough to inhibit bar formation, even if they have massive discs. This is also true for barred galaxies, which therefore could not have acquired their bars as a result of a self...

Are most species small? Not within species-level phylogenies.

The robust macro-ecological observation that there are more small-bodied species implies that small-bodied organisms have experienced elevated net rates of diversification. We investigate the role of body size in creating non-random differences in rates of cladogenesis using a set of 38 species-level phylogenies drawn from a range of animal groups. We use independent contrasts to explore the re...