Category Archives: the titbits

Best-of-Three Coin Toss: The Most Likely Way to Win

Always pick whatever side of the coin comes up first, i.e. if heads comes up on the first toss, always choose heads thereafter.

The reasoning: There’s probably some kind of minimal bias one way or another in the coin or in the tosser’s toss. Assuming there’s no data to help you out beforehand for determining the bias, as soon as you get your first piece of data in the form of the first coin toss, chances are the bias is towards whatever side of the coin turns up.

The complication: If the probability distribution is 90% heads and 10% tails and tails happens to come up up first, well, you’re very likely to lose a best-of-three coin toss series by always choosing tails. But if no one actually knows the probability distribution beforehand, you’re better off always choosing the side of the coin that comes up first for a short coin-toss series. Larger coin-toss series, i.e. a best of twenty series, will mean that if the bias is sufficiently skewed, it is indeed better to change your coin-flip choice in light of results.

King James and His Remembrance of Things Past

So I was reading the King James Bible, as one does, and I stumbled across this in the Wisdom of Solomon, 11-12:

For a double grief came upon them, and a groaning for the remembrance of things past.

From the Bible to Shakespeare to Proust (in a liberal translation) to Anagrammatically — not a bad lineage.

A Short Documentary on Cryptic Crosswords and David Astle (DA)

I love cryptic crosswords, so much so that I run, with a little help from some friends, The DA Trippers, a site devoted to David Astle’s crosswords.

A bunch of RMIT students wanted to film a short documentary on cryptic crosswords and asked DA, as he’s known in the biz, to be involved. Being the genial guy that he is, DA agreed, and a series of coincidences meant that I ended up in the documentary as well, along with fellow DA-Trippers founder, RC.

And that doco — it’s right here: http://www.youtube.com/watch?v=c4GurqnVAF4

The Indo-Europeans: The Undisputed World Champions

The whole world might play soccer (I’m Australian and I prefer soccer to football), but only a tiny portion of nations have ever held the World Cup aloft or even played off for the honour. Of the 202 nations that FIFA have given a world ranking to, only 8 have ever won the World Cup the 19 times the festival of soccer has been held and only 12 have ever made the final.

But here’s what’s really interesting: if we organise nations by language group, only 2 language groups have ever won the World Cup and 4 reached the final.

And even more interesting: if we organise nations by language family, of the 20 or so that exist (some are disputed), only 1, the Indo-European, has ever won the World Cup and only 2 have ever reached the final (those pesky Uralic Hungarians the only thorn in the Indo-European side).

If ever there was proof that language influences sporting ability, we have it here.

Nabokov’s Ratings

Everytime I read this, I giggle:

My loathings are simple: stupidity, oppression, crime, cruelty, soft music. My pleasures are the most intense known to man: writing and butterfly hunting.

It’s Nabokov, being droll yet again, and so effective at doing so because of the last item on a list of otherwise humdrum loathings and pleasures.

Duke Ellington on the Whole World Going Oriental

Duke Ellington went rock and began taking on musical influences from around the world on his ridiculously good The Afro-Eurasian Eclipse. Not only is the album a landmark of reinvention, it begins with a startlingly mad and entertaining Duke monologue, one so good I’ve transcribed it for posterity below:

This is really this chinoiserie. Last year, we, about this time, we premiered a new suite titled The Afro-Eurasian Eclipse. And of course the title was inspired by a statement made by a Mr. Marshall McLuhan of the University of Toronto. Mr. McLuhan says that the whole world is going oriental and that no one will be able to retain his or her identity, not even the orientals. And of course, we travel around the world, a lot, and in the last five or six years we too have noticed this thing to be true. So as a result, we have done a sort of a thing, a parallel or something, and we’d like to play a little piece of it for you.

In this particular segment, ladies and gentlemen, we have adjusted our perspective to that of the kangaroo and the didgeridoo. This automatically throws us either down under and/or out back, and from that point of view it’s most improbable that anyone will ever know exactly who is enjoying the shadow of whom.

Harold Ashby has been inducted into the responsibility and the obligation of possibly scraping off a tiny bit of the charisma of his chinoiserie, immediately after our piano player has completed his rikki-tikki.

The Unexpected Properties of Circles

Let’s say a tennis ball has a diameter of 6 cms and a basketball a diameter of 46 cms.

Let’s also say a car tyre has a diameter of 60 cms and a monster truck tyre a diameter of 100 cms.

Now, the unexpected bit:

If we were to wrap a piece of string exactly once around the tennis ball, how much more string would we need to do the same thing around the basketball?

In the same way, if we were to wrap a piece of string exactly once around the car tyre, how much more string would we need to do the same thing around the monster truck tyre?

Believe it or not, in both cases it’s 40π cms, or approximately 126 cms!

Our intuition doesn’t like it, but even if you were to wrap a string around the Earth and then a second string around the Earth 20 cms higher than ground level (which  would increases the diameter of the circle formed by 40 cms), the difference in string length would still be 40π cms!

It feels deep in our bones like the increase in string length would be a whole lot more pronounced for the Earth-circling situation than the tyre-circling situation, yet it’s exactly the same, and here’s the maths that proves it:

Because c (circumference) = πd (diameter), whenever the radius increases by a length of x metres, the circumference will always be c = π(d + x) = πd + πx.

This means that when the diameter of a circle increases by a length of x centrimetres, the circumference is increased by πx centimetres — which is completely independent of the original circumference or radius of the circle in question!

And when we fill in the formula for the situations cited above, we’ve always got a πx cms = 40π cms ≈ 126 cms difference in circumference.

The Unreadability of French Non-Fiction

Edmund White, on French non-fiction, from his rather delightful The Flâneur: A Stroll Through the Paradoxes of Paris:

Honestly, instead of ‘like a normal feature of the present’ I almost wrote ‘without ever being inscribed within the interior of the present’. That’s how much I’ve been submerged in contemporary French nonfiction. I frequently have to stop and ask myself how a human being might put the same idea.

The Immune System is Clever

From Antonio Damasio’s Looking for Spinoza: Joy, Sorrow, and the Feeling Brain:

Curiously, it (the immune system) is also prepared to deal with chemical molecules normally contained in healthy cells in the body that can become dangerous to the organism when released from dying cells into the internal milieu (eg breakdown of hyaluron; glutamate).

Proust on Philologists

Classic extract from Proust’s Within A Budding Grove, the Moncrieff-Kilmartin-Enright translation:

The uncle in question was called Palamède, a Christian name that had come down to him from his ancestors the Princes of Sicily. And later on, when I found, in the course of my historical reading, belonging to this or that Podestà or Prince of the Church, the same Christian name, a fine renaissance medal–some said a genuine antique–that had always remained in the family, having passed from generation to generation, from the Vatican cabinet to the uncle of my friend, I felt the pleasure that is reserved for those who, unable from lack of means to start a medal collection or a picture gallery, look out for old names (names of localities, instructive and picturesque as an old map, a bird’s-eye view, a sign-board or a return of customs; baptismal names whose fine French endings echo the defect of speech, the intonation of an ethnic vulgarity, the corrupt pronunciation whereby our ancestors made Latin and Saxon words undergo lasting mutilations which in due course became the august law-givers of our grammar books) and, in short, by drawing upon their collections of ancient sonorities, give themselves concerts like the people who acquire viols da gamba and viols d’amour so as to perform the music of the past on old instruments.

The uncle for whom we were waiting
was called Palamède, a name that had come down to him from his
ancestors, the Princes of Sicily.  And later on when I found, as I
read history, belonging to this or that Podestà or Prince of the
Church, the same Christian name, a fine renaissance medal--some said,
a genuine antique--that had always remained in the family, having
passed from generation to generation, from the Vatican cabinet to the
uncle of my friend, I felt the pleasure that is reserved for those
who, unable from lack of means to start a case of medals, or a picture
gallery, look out for old names (names of localities, instructive and
picturesque as an old map, a bird's-eye view, a sign-board or a return
of customs; baptismal names, in which rings out and is plainly heard,
in their fine French endings, the defect of speech, the intonation of
a racial vulgarity, the vicious pronunciation by which our ancestors
made Latin and Saxon words undergo lasting mutilations which in due
course became the august law-givers of our grammar books) and, in
short, by drawing upon their collections of ancient and sonorous
words, give themselves concerts like the people who acquire viols da
gamba and viols d'amour so as to perform the music of days gone by
upon old-fashioned instruments.