To live to a ripe old age, untroubled by health problems, physical or mental, is an almost universal aspiration. But most people are not so lucky and will likely be in care homes for their final years, with varying levels of disease, disability and dementia. Kinley et al [1] maintain that over a fifth of the population of developed countries die in care homes. Moreover, the financial cost of this end of life care, which is the focus of this paper, can be daunting and require much planning [2]. It was reported in 2017 that, in the UK, care home costs are rising up to twice as fast as inflation [3]. Consequently the question arises about the long term affordability of such care to those having to fund it, a question that ever more people both nationally and globally are having to confront.

If anything were calculated to make me anxious to do justice to my theme to-night it would be the association with your society of the men to whom I owe my earliest introduction to dynamics—at St. Paul’s School to Mr Pendlebury, your Secretary, and at Trinity College, Cambridge, to Professor Forsyth, your incoming President. The interest that they implanted has survived for half a century; and the applications to sport that I propose to describe are the immediate outcome of that interest.

The growing importance of the elements of group theory in sixth form teaching has been recognised by a number of recent publications, but a very simple presentation of the theory of groups by means of free variable axioms which was introduced by Lorenzen more than twenty-five years ago, and which is particularly well suited for elementary teaching, does not appear to be as well known as it deserves to be.

Lorenzen defines a group in terms of division x/y, instead of multiplication, a device which obviates the need to postulate the existence of a neutral element and an inverse.