## Archive for March, 2020

### Bang! Bang! Bang! Explosively Large Numbers

Typical Comic-book `bang’ mark [Image from vectorstock ].

Enormous numbers pop up in both mathematics and physics. The order of the monster group, the largest of the 26 sporadic groups, is

$\displaystyle 808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000$

which is approximately ${8\times 10^{53}}$. The number of atoms in the universe is estimated to be about ${10^{80}}$. When we consider permutations of large sets, even more breadth-taking numbers emerge.

### Covid-19: Modelling the evolution of a viral outbreak

The illness is called Covid-19 but the virus is known as SARS-CoV-2 (Severe Acute Respiratory Syndrome coronavirus 2) [Image from US agency Centers for Disease Control and Prevention].

There is widespread anxiety about the threat of the Covid-19 virus. Mathematics now plays a vital role in combating the spread of epidemics, and will help us to bring this outbreak under control. For centuries, mathematics has been used to solve problems in astronomy, physics and engineering. But now biology and medicine have become topics of mathematical investigation, and applications in these areas are certain to expand in the future [TM183 or search for “thatsmaths” at irishtimes.com].

How rapidly will the viral infection spread? How long will it remain a problem? When will it reach a peak and how quickly will it die out? Most important, what effective steps can we can take to control the outbreak and to minimize the damage caused? When vaccines become available, what is the optimal strategy for their use? Models provide valuable evidence for decision makers.

### Samuel Haughton and the Twelve Faithless Hangmaids

In his study of humane methods of hanging, Samuel Haughton (1866) considered the earliest recorded account of execution by hanging (see Haughton’s Drop on this site). In the twenty-second book of the Odyssey, Homer described how the twelve faithless handmaids of Penelope “lay by night enfolded in the arms of the suitors” who were vying for Penelope’s hand in marriage. Her son Telemachus, with the help of his comrades, hanged all twelve handmaids on a single rope.

### Samuel Haughton and the Humane Drop

Samuel Haughton (1821-1897).

Samuel Haughton was born in Co. Carlow in 1821. He entered Trinity College Dublin aged just sixteen and graduated in 1843. He was elected a fellow in 1844 and was appointed professor of geology in 1851. He took up the study of medicine and graduated as a Doctor of Medicine in 1862, aged 40 [TM182 or search for “thatsmaths” at irishtimes.com].

In addition to his expertise in geology and medicine, Haughton was a highly talented applied mathematician. His mathematical investigations included the study of the motion of solid and fluid bodies, solar radiation, climatology, animal mechanics and ocean tides. One of his more bizarre applications of mathematics was to demonstrate a humane method of execution by hanging, by lengthening the drop to ensure instant death.