Where are all the typical numbers — 2

In this two-part article, we are trying to discover patterns in the decimal digits of numbers between zero and one. In Part I we started showing that each digit occurs with frequency 1/10. We reduced the problem with the help of Borel-Cantelli Lemma and Markov inequality to show certain sums of integrals are finite. In this concluding part we bring in an essentially new ingredient and conclude the proof.     

Sundials: Ancestors of our clocks

This article deals with the timekeepers of the past, the sundials. Apart from discussing the structure of a few common sundials, we point out the reasons for the variation between sundial time and the time shown by mechanical timekeepers.     

Israel Moiseevich Gelfand (1913–2009)

In this homage to the late I M Gelfand, we try to give an overview of some of his contributions to the theories of Banach algebras in general and C*-algebras in particular, and briefly elaborate on the celebrated Gelfand-Naimark-Segal construction which gives a way of passing from positivity-preserving linear functionals to representations on Hilbert space.     

Dawn of science

What was remarkable about the most misunderstood medieval scientist’s discoveries was the way he arrived at them — by direct observation.     

Effect of foster care on young children's language learning

This report examines 174 young children's language outcomes in the Bucharest Early Intervention Project, the first randomized trial of foster placement after institutional care. Age of foster placement was highly correlated with language outcomes. Placement by 15 months led to similar expressive and receptive language test scores as typical age peers at 30 and 42 months. Placement from 15 to 24 months also led to dramatic language improvement. In contrast, children placed after 24 months had the same severe language delays as children in institutional care. Language samples at 42 months confirmed that placement after 24 months led to lower expressive skill.