Vax Fax

There is a misconception that getting a Covid-19 vaccination stops you catching the disease. It does not. It is not designed to do so. What it does is prime your body's weapons to be ready to move on the virus quickly and cut it off at the pass. As soon as the virus invades, the antibodies, B-cells and T-cells in your alerted immune system will instantly leap into action and descend in force to neutralise it and render it harmless. It is given no chance to multiply inside your cells and wreak havoc around your body. Your symptoms, if any, will be mild and will soon disappear. But you have to 'catch' it first before your immune system can send it packing.

A vaccination has the following beneficial effects:

• It reduces the number of serious cases needing medical intervention
• It minimises the viral load in those infected and reduces transmission in the community
• It can be targeted at those most at risk

It has the same effect on the unvaccinated as catching the disease and recovering. Immunity confers protection against dangerous consequences of becoming infected but not from being initially and very mildly infected when exposed.

Slavery

The year is 1627, Shakespeare is but a decade in his grave and Charles 1 in the second year of his reign. It was an annus horribilis for the people of Iceland, then a Danish protectorate. In two raids that summer, slave traders in their corsairs from Algiers, led by two renegade Dutchmen, brutally attacked settlements along Iceland's southern coast, in particular in the Westman Islands, killing dozens, burning villages and eventually carrying off 400 Icelanders to be sold into slavery in the markets of Algiers, an audacious round-trip journey of 5,400 miles under sail; 400 human souls represented 1% of Iceland's sparse population at the time, and even today its population is only 364,000

Sally Magnusson is the author a wonderful novel, which brings vividly to life the surroundings and experiences of those captive slaves. The Sealwoman's Gift is imaginatively conceived, beautifully written and carefully researched.  She marries the bares bones of the historical record to a fully realised and thoroughly believable 17th century world. Her story spans the impoverished wind-swept landscape of dour Lutheran Iceland and the luxuriant cosmopolitan Islamic diaspora of Moors and Arabs in North Africa, and the narrative is colourfully embellished with many stories and sagas from both those cultures. She writes simply but with poetic intensity and in a few sentences can transport you almost physically into the sights, smells and sounds of her scenes and into the very presence of the men and women she so finely and sensitively observes.

The dramatic events of those times are seen through the eyes, thoughts and lived experiences of Åsta, a remarkable Icelandic woman at the centre of the story and a talented story-teller herself. This slice of history is vividly depicted from a woman’s point of view, one which is so often neglected in the telling of our past. There are many engrossing themes, especially the importance of story-telling, the meaning of love: How do you measure it? and loss: What price must you pay for losing your children forever, even losing the prospect of meeting them in heaven?

Hung out to dry?

 This nice clue from Robert Price appeared in The Sunday Times:

Jeans and shirt put outside to air (8).

All you need to solve it is a brand name for jeans and a 3-letter word for a type of shirt.

The same either way

 A week or so ago, the date was palindromic, provided one subscribes to the format DD/MM/YYYY that is. There will be another palindromic date in February next year, but then a long wait until the earlier 2030s for more. Will they go on forever? If humanity is still around at the end of the 10th millennium and still keeping track of the days in a similar fashion, it will depend on the new format. If it's DD/MM/YYYYY, then yes, they will continue to the same old irregular way.

By coincidence  this morning, I clicked on that seemingly endless source of unpredictable entertainment and bizarre novelty, Greg Ross's  Futility Closet website, and discovered some verbal palindromes that were new to me. Mathematicians Peter Hilton and Henry Whitehead, who had been codebreaking colleagues at Bletchley Park during WW2, got into a palindrome exchange in 1947. Whitehead began with STEP ON NO PETS, to which Hilton retaliated with SEX AT NOON TAXES and after a sleepless but very creative night improved upon with DOC, NOTE, I DISSENT. A FAST NEVER PREVENTS A FATNESS. I DIET ON COD. Not surprisingly that 51-letter sequence brought the exchange to an abrupt end. It certainly trumps the old one about the Panama man with his canal.

I met Peter Hilton briefly when visiting  the University of Binghamton in the 1990s. He wrote a seminal book on Topology with Shaun Wylie, another Bletchley alumnus, whose inspiring Cambridge lectures on Real Analysis (rigorous Calculus) I was privileged to attend in 1957. While at Binghamton Hilton wrote a charming book with Jean Pedersen connecting algebra to special kinds of paper folding; the title is A Mathematical Tapestry (CUP, 2010,  ISBN 0-521-12821-8).

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.