… began in 2012, though I only started to archive them on my website the following year.  That fact indicates a decade of specialist Christmas gifts delivered, and a recognition of the next one due.  As usual, the sending of cards has been replaced by a donation to charity.  As ever, I have been racking my brain (apparently ‘wracking’, though common, is less correct) for this year’s offering via website and email.  As always, it will need to be useful, carbon-neutral, capable of immediate digital delivery, easily digested, appropriate for all ages and – I very much hope – welcome.

So, as another year rolls towards its phoenix moment, I ask myself what would constitute a suitable gift this time round.  A scan of the list so far shows that you will have received a microparticle, three dots – each for a different purpose, some space, some silence, the present moment, an ellipsis (another three dots, I suppose) and an apostrophe.

I could continue with punctuation marks, but what is the point?  Furthermore, when it came to mind to gift you all a ‘dash’, that item carried with it the memories of hurry and concern: not the message I wanted to send.  ‘Colons’ sounded too medical, and ‘commas’ too common.  Accents have a happy resonance of Europe, but the situation in our post-“taking control” world is acutely grave, and so I am looking elsewhere.

To cut a long story short, I have decided to give you all a number.  And not just any old number, but a prime example.  And, please note, not merely a number ‘of’ something.  No, I wish for you the number itself, fresh, magisterial and ready for general use.

But, you may ask (please do, if you wish) how could I know in advance which particular number would be of most use to you at any particular moment?  And this is a good question.  Therefore, for this very reason I have chosen to proffer a variable, which will be suitable for use anywhere and at any time.

With all this in mind, I had thought to give you ‘x’.  Further reflection, however, showed that it did not seem quite right, as this symbol might give rise to accusations of inconstancy.  This was not what I wished for my friends.

Therefore, I have decided that your gift this year will include a bonus: a cardinal constant as well as a variable, and I hereby give you


How wonderful: a gift that you may choose yourself how to use.  Take it with you in your pocket when next shopping, when visiting friends, or when out for a walk.  Then, when something of interest presents itself to your attention, apply the formula.  The pleasure of the encounter will be doubled.  For that is the essence of the function.

(If, I hasten to add, something unpleasant occurs, never fear – there is no need to multiply that unwelcome item by two.  To pre-empt any problem, a simple precaution applies.  In your other pocket keep one of the dots given to you previously.  By carefully introducing the dot before the new gift, you will have


and the discomfort will be diminished considerably.  By a full 80%, in actual fact.)

My very best wishes to you for Christmas and the New Year. And, dare I say it, much love.