The Challenges of 2021

Welcome to the twenty-first year of the second millennium.  When I was a boy, 21 meant coming of age, when you got the “key of the door” and were free to go off and do your own thing. Of course, Mum and Dad were usually still around to come to the rescue if things didn’t work out first time. Well, today the United (but for how much longer?) Kingdom has set off to do its own thing, free from the thraldom of Brussels. Only time will tell if we are up for the task. If only we could pull up our island's anchor and set sail to more congenial climes, and seek out new neighbours who don't want to snaffle our fish.

The number 21 also has gambling connotations. It is the number of spots on a standard die, and the name of a card game adopted by the British as Pontoon (or Vingt-un if they wanted to sound posh). Are we still a gambling nation, are we again willing to take risks for the sake of enterprise and prosperity? Or are we lost in dreams of our “glorious past” when the sun never set on the possessions and peoples we then held in our thrall, now too tired to summon the energy, initiative and ambition to make a fresh start? We shall see. Meanwhile, let’s indulge in some trivial distractions with the number 2021 itself and briefly postpone the big challenge of facing up to a new future in an unfriendly world.

Is 2021 a prime number? To check that we only need look for prime divisors up to the square root √2021 = 44.9555… There are 14 primes less that 45 and you have to go to the wire to discover that the 14th prime 43 is the smallest prime divisor of 2021. In fact, 2021 has only two prime factors: 2021 = 43 x 47 and is not quite a perfect square. (We will have to wait four more years to find a year that is a perfect square, namely 2025 = 45² — the previous one, 44² was the year of my birth.) Anyway,, the answer to our initial question is “No”, 2021 is not a prime number.

We can represent the familiar decimal form of our current year 2021 in different bases, for example:

                    Base-2 (binary):  11111100101

                    Base-3: 2202212

                    Base-16 (hexadecimal): 7e5 = 7 x 16² + 14 x 16 + 5

Or we can devise other recipes, such as finding expressions that use the four operations of arithmetic and the digits 1 — 9 in order as follows:

                    2021 = 1 - 23 - 4 + (5 x 6 - 7) x 89 

                    2021 = 12 × (3 × 4 + 5 + 6) × 7 + 89

                    2021 = 1 x (2 + 3 ) - (((4 x 56) x (7 - 8)) x 9), or

                    2021 = (1^23 + 45) x 6 x 7 + 89 using a fifth operation exponentiation

                    2021 = (9 × 8 + 7 + 6) × 5 × 4 + 321

Instead of using all the digits, we can stick to just one digit and try to find the most efficient expression (i.e. the one with fewest  occurrences of the digit). Here are some examples:

                    2021 = ((11 - 1) - 111) x ((1 - 11) + (1 - 11)) + 1 = 

                                2/2 + (22/2 - 2) x 222 + 22 = 

                                333 x (3 + 3 ) + 3 x 3 x 3 - 3 - 3/3 =

                                (44 - 4/4) x (44 + 4 - 4/4)

or, most inefficiently, 2021 = 9/9 + 9/9 + .. (2021 terms)..  + 9/9

So I will leave readers who, like me, are amused by such bagatelle with the 2021 challenge of finding the shortest single-digit expression(s) for 2021. You have the rest of the year to improve on my best short score, which is 9.

Moral Directions

This cryptic clue

Right, second right, then a left.  (5)

was set by 'Punk' inThe Independent (a daily UK newspaper), The solution depends on a frequently-used abbreviation of the synonym 'moment' for 'second'.

Covid-19: Who passes it on?

In tracking the course of an epidemic, the R-number - the average number of infections caused by an infectious individual - is a crucial parameter in understanding the spread of a disease. Although less talked about, the dispersion rate is important too. The following cumulative frequency chart, which is taken from a large-scale study of covid-19 track-and-trace data in India, shows that 71% of infected individuals did not pass their infection on to anyone else; a further 19% accounted for 40% of the directly-transmitted infections, while the remaining 10%, the so-called 'superspreaders', were responsible for a full 60% of the transmitted cases.

Small proportion responsible for most infections

The above diagram, published in The Economist, uses data from a paper by Ramanan Laxminarayan of Princeton University and eight co-authors that analyses information from test-and-trace records in Andhra Pradesh & Tamil Nadu between March and August 2020. Their data involved 84,965 infected individuals and 575,071 of their known contacts who subsequently tested positive for covid-19. 

Slippery Surfaces

The obvious interpretation of a good cryptic crossword clue, taken at face value, should have nothing to do with the answer; in fact, the 'surface meaning' should deliberately lead you astray. This is in contrast to the non-cryptic kind where the solution is a synonym for the clue. Here are two good examples of such clever deception: 

Founder of business in Kentucky  (4 letters starting with S) by Tim Morey in The Week

Left-wingers, for instance, spouting Marxist doctrine (3 letters starting with I) by Jumbo in The Times

In one case the defining verb masquerades as a noun. In the other, what could be the defining noun is a key part of the word-play. 

Corrupting the Coronavirus Code

Inoculating with live attenuated (weakened) versions of deadly viruses has been a successful approach to eradicating viral disease. Two striking examples are: 

• The variola virus that causes smallpox.  Before smallpox was completely eradicated in 1977, an estimated 50 million cases worldwide led to 2 million deaths each year and left many survivors crippled and disfigured.
• The poliovirus that causes the sometimes-crippling disease of poliomyelitis. Protection is given with one or two doses of a vaccine delivered orally on a sugar lump. Through a concerted international campaign, the 350,000 annual cases of polio recorded worldwide in 1988 has been reduced to 179 cases in 2019, thanks to widespread inoculation with both the live attenuated and the inactivated versions of the virus.

More than 150 different vaccines are now being developed around the world to combat the coronavirus SARS-CoV-2 that causes the severe respiratory disease Covid-19. A number of different immunological approaches are being tried, including several that use live attenuated viruses (LAV). Codagenix is a US company working on this approach in collaboration with with Serum Institute of India, a large-scale manufacturer of vaccines. A novel feature of their approach is the use of synthetic biology to weaken the virus strain. Whereas the process of creating LAVs previously took years to develop — requiring a patient search for naturally-occurring mutations in millions of generations of the virus hosted in animals — modern editing techniques can directly rebuild the virus genome in a matter of weeks in such a way that its replication mechanism is seriously impaired and its ability to cause bodily harm removed. Here are some of the advantages of Codagenix’s LAV approach:

• The vaccine can be administered via inexpensive nose drops. Its production scales up easily and no injections or refrigeration are required.
• A recipient’s body encounters and reacts to the entire virus rather than a just surface feature, thereby stimulating not just antibodies but also T-cells and other specialised forms of immunity that give longer-lasting and broader protection.
• The 3-letter words (codons) in the virus’s genome that specify its building blocks (amino acids) are replaced by suboptimal versions that can slow its speed of replication by a factor of 1000 and thus give the immune system more time to respond and marshal its forces to defeat the viral invasion.
• The attenuated form of the live poliovirus has only a small number of mutations and very occasionally (just once in 750,000 times) it reverts to its wild form and causes paralysis. But over 250 mutations have been introduced into Codagenix’s attenuated coronavirus so there is no chance of it mutating back to its original form. 

URGENT APPEAL: Covid-19 Symptom Study

With Covid-19 cases surging again in the UK, please download the Covid-19 Symptom Study app to your mobile phone. It takes a minute to make your daily symptom report and gives the King's College (London) team up-to-date information about new cases of coronavirus across the country; it also tells you about the current situation in your local area. 

Over four million have already signed up, but more are needed to increase the accuracy of the data, It is a quick download from the Apple and Android app stores.

Musings on a plague year in Stratford upon Avon

When in disgrace with fortune and men’s eyes,

I all alone beweep my outcast state,

During an outbreak of the bubonic plague in 1592, when London theatres were closed for 6 months, Shakespeare used the time to write two long narrative poems and quite possibly this Sonnet XXIX.

And trouble deaf heaven with my bootless cries,

And look upon myself and curse my fate,

Could those be the words of man fed up with lockdown? Shakespeare’s whole life was overshadowed by the plague. A few months after he was born in April 1564, a serious outbreak swept through England and killed nearly a quarter of the people of Stratford upon Avon. The plague was again rife in the 1590s and Shakespeare’s only son Hamnet died in 1596 aged 11; the cause of his death was not recorded but the plague was not ruled out. The plague returned in force to London in 1603 and again in July 1606 when theatres, including Shakespeare’s Globe, were once more closed; in fact, London playhouses were intermittently closed for 78 months of the following decade (60% of the time). A preacher at that time thought that “The cause of plagues is sin, and the cause of sin is plays”; fortunately we now know better: if was fleas, not sin. Theatre-goers today, perhaps, should take heart from the fact that Shakespeare’s company managed to keep the show on the road throughout those troubled times. 

Wishing me like to one more rich in hope,

Featured like him, like him with friends possessed,

He certainly sounds as though he’s “got the hump” as my mother used to say, although during  her low moments she was more like a nervous sheep than a camel. The currrent pandemic is so widespread across the world, afflicting “all conditions of men and women”, that it is hard to think  with envy of anyone “more rich in hope”. Perhaps our son who now lives in London might wish he were back in New Zealand again, or I can feel grateful for another son who lives in Japan’s northern island of Hokkaido and has not seen a single case of covid-19 in his coastal town of Shiranuka.

Desiring this man’s art and that man’s scope,

With what I most enjoy contented least;

Among the diversions of my years of retirement, I have noticed recent changes in “what I most enjoy”. For example, I have stopped drinking and watching films. Living alone since the pandemic began has made me realise these are social activities and no longer so satisfying in my outcast state. All my life I have struggled for inspiration with the tricky art of watercolour, but the muse has lately completely deserted me. My small local group of fellow greying artists has started meeting again (in the garden, of course) but now seem to gas as much as draw. I have enjoyed Zooming or WhatsApping to stay in touch and have dug up old friends from home and abroad, I have also enjoyed keeping this blog alive with commentary on the pandemic and cryptic crossword clues. I get a weekly Mindbender for the Quarantined from the New York Museum of Mathematics and spend hours writing small programs to search for solutions; off and on I append a new paragraph to my memoir (for family consumption only, I hasten to add).

Yet in these thoughts myself almost despising,

Haply I think on thee, and then my state,

Aha, at last, a welcome change of mood, a happy memory, a ray of light to banish his gloom. Begone dull care! There have been better days and there will be again. Put way introspection and melancholy, stay “Looking on the bright side” as my old maths teacher called his memoir.

Like to the lark at break of day arising

From sullen earth sings hymns at heaven’s gate;

Praise be the Lord! Heaven is not entirely deaf to his bootless cries; the lark has interceded.

For thy sweet love remembered such wealth brings

       That then I scorn to change my state with kings.

Yes, I can relate to that. For the past three months my wife has been locked away in Penzance, without a pirate in sight as far as I know. But we will soon be braving public transport to meet up in London to celebrate four family birthdays. Things are not so bad after all, for me, and even for Stratford. Sure, the RSC is closed, but they have been streaming their past productions, and their cast of actors, hopefully only temporally out of work, have been reading Shakespeare’s sonnets. Anthony Sher reads Sonnet XXIX and this reminds me that only a year ago I watched him and John Kani give an outstanding performance of Kani’s moving South African play, Kunene and the King. They will be back, the RSC will return, and then I shall scorn to change my state with kings.