Even as a handful of smaller countries, like Israel, report having inoculated 100% of their eligible populations, hundreds of millions in Africa and other parts of the world have yet to receive even the first shot of a two-dose vaccine. Moreover, in some countries, such as the US, people are being administered booster doses, as it is believed that the vaccines so far developed provide not lifelong immunity but protection for only a few months. So, by the time the last lot of people on Earth are vaccinated, the first lot will need their third, fourth, fifth shot, and so on.
While well-meaning organisations like WHO may wring their hands in hapless dismay at this unending state of affairs, mathematicians and mythologists will shrug a shoulder at this self-evident proposition that obtains in all spheres of the human scheme of things, and is succinctly summed up in the Greek story of Sisyphus.
The wily king of Corinth, twice cheated death by trickery. A vengeful Zeus, wrathful at such mortal temerity, consigned the hoaxter to Hades where his eternal punishment was to push a large boulder up a steep hill only to have it roll down once the top had been reached, compelling Sisyphus to begin his labour anew. In 1942, Albert Camus interpreted the myth of Sisyphus as the inescapable existentialist acceptance of the inherent absurdity that underlies the human condition, permeating such realms of seeming certitude as mathematics.
A well-known mathematical puzzle, or paradox, has Achilles attempting to overtake a tortoise that has a lead of a metre on him. The Greek hero will halve the distance between himself and the slow-moving quadruped. Then he will quarter the distance, then reduce it to one-eighth, in an infinite series of subdivisions, which ensures that the great warrior will never be able to catch up with the testudine.
It’s not just ancient Greeks who are beset with such endless tasks. In his writings, Bertrand Russell narrates how as a somewhat cocky young man he took upon himself the challenge of solving what has come to be known as the problem of sets. In lay terms, all entities can be of two types: one that can be collectivised into a set; and one that is unique and not part of a set. But don’t these non-set types fall under the set of non-set entities? Having spent weeks wrestling unsuccessfully with his self-appointed mission impossible, and sharing his attempts with other logicians – like Alfred North Whitehead who, quoting Robert Browning, wrote back to Russell ruefully, ‘Never glad, confident morning again’ – he gave up.
In his 1979 book, Godel, Escher, Bach: An Eternal Golden Braid, cognitive scientist Douglas Hofstadter proposed the concept of what he called a ‘strange loop’ in the functioning of what we call ‘reality’. Drawing extensively from the works of logician Kurt Godel, composer Johann Sebastian Bach, artist MC Escher, and writer-mathematician Charles Lutwidge Dodgson (better known to us by his nom de plume Lewis Carroll), Hofstadter explained loops — or loopholes — in the fabric of reality which confound logic.
In his 2007 book, I Am A Strange Loop, Hofstadter defined a strange loop as an ‘elusive notion’ of a ‘closed cycle’ in which ‘despite one’s sense of departing ever further from one’s origin, one winds up, to one’s shock, exactly where one had started out. In short, a strange loop is a paradoxical level crossing’. And like a lot of other things, the anti-Covid vaccination process falls prey to this strange loopiness.
While technology has yet to devise a perpetual motion machine, a microscopic bug has invented a perpetual motion vaccine. How loopy can you get?