Macaroni and apples

Last week, I was on holiday in Catalonia.  This has reinvigorated my interest in Spain and the Spanish language (as well as giving me a taste for Catalan).  A few more posts related to my trip will probably follow soon, but for now here’s a trilingual treat that I came across while surfing Wikipedia earlier today.  (The third language in question, though, isn’t Catalan as you might expect from the start of this paragraph, but Latin, the grand-daddy of them all.)

In English, we have a well-known saying:

An apple a day keeps the doctor away

This is probably somewhat exaggerated but it’s certainly true that apples are quite healthy and eating them regularly is likely to have a positive rather than negative effect on your general health (sadly, I’m not sure that drinking cider counts).  Actually, I read an interesting blog post fairly recently (and, sadly, have mislaid the link to it) suggesting that bananas are even healthier and we’d do better to say “A banana a day…”, but that’s digressing.

There is also a Latin saying that probably still just about qualifies as well-known (at any rate, it’s one I’ve known for a long time):

Mens sana in corpore sano

This means “A healthy mind in a healthy body”.  Presumably the point of this is to indicate a correlation between mental and physical health.

The Wikipedia page on bilingual puns lists a delightful merging of these two sayings that approximates the meaning of the English one by substituting a similar sounding Spanish word (manzana = apple) for the first couple of words of the Latin one:

Manzana in corpore sano

(Literally, “An apple in a healthy body”).



NB in case you’re wondering about the title of this post, this Wikipedia article on macaronic language might help.

Requiem pro ave mortuo

This morning, on my way to work, I cycled past a dead blue tit at the side of the road.

In the grand scheme of things, the death of one small bird is not a great tragedy.  It did, however, lead me to spend the rest of my commute considering the fleeting nature of life and trying to compose a suitable poetic epitaph for the bird.  I decided to go for a haiku, as that’s one of my favourite poetic forms in any case and, being short, is quite amenable to composition in situations (such as riding a bike) where you can’t immediately write it down.

By the time I had reached the office, about 10 minutes later, I had come up with a reasonably satisfactory haiku.  Unfortunately I got sidetracked with other things (such as my actual job) before I got a chance to make a note of it.  Now, on my lunch break, I have managed to more-or-less reconstruct it and I’m still fairly happy with the result (although I don’t think it’s one of my better haiku efforts):

Small, blue and yellow,
flying, always on the move.

Now dead on the road.

It was the middle line that gave me the most trouble.  I had considered various phrases along the lines of “a tiny bundle of life”, aiming to contrast the bird’s previous state with its current one (expressed in the final line) but this seemed a bit too figurative for a haiku. The form, as I understand it,  generally tends to stick with straight-up descriptive language aiming to evoke an impression of a scene and leave the interpretation to the imagination of the reader.

The title of this post (which could also be taken as a title for the haiku, although it’s nearly as long as the thing itself) is, in case you’re wondering, in Latin and means “requiem for a dead bird” (hopefully I’ve got all my cases and stuff right, as my Latin is woefully limited and rusty to boot).   As to why I titled it in Latin, that’s mostly because one of my first thoughts on seeing the bird (and before I started to compose the poem) was “sic transit gloria mundi” (roughly: “thus passes worldly glory”).  I’ve just realised that this is my second post in a row to have a Latin title (the other one was inspired by the name of my new bass ukulele and a parody of the refrain from “Ding dong merrily on high”).  Perhaps my subconscious is trying to encourage me to have another go at learning Latin?!



Pons asinorum

I recently discovered a draft of a blog post I started to write nearly a year ago, shortly after my previous post on the subject of Euclidean geometry.  I’m not sure why I didn’t publish it at the time (possibly because I was planning to extend it in some now-forgotten direction).  Here it is now, with minimal editing:

Undoubtedly the most famous proposition in Euclid’s Elements is I-47 (that is, the 47th proposition in book I), better known as Pythagoras’ Theorem.  This, as you probably know (though you may not have known its number in Euclid), is the statement that the square of the hypotenuse of a right-angled triangle is the sum of the squares on the other two sides.

Perhaps the second most famous one, although certainly having nothing like the same level of recognition among non-mathematicians, is I-5, which states that the two angles at the base of an isosceles triangle (i.e. one having two sides of the same length)  are equal.  Like Pythagoras’ theorem and unlike most of Euclid’s other propositions, this one has a name.  In fact, it has been known by several names, but the most popular is pons asinorum – the bridge of asses (in Latin).

There are at least two competing explanations as to the origin of this name.   One is that this is the first proposition in the Elements that might cause some people difficulty in understanding, as well as being quite necessary for the proof of many of the later propositions, so that it functions as a kind of figurative bridge that ignorant people (considered to be donkeys) are unable to cross to allow them further into the study of geometry.  Another, rather more complimentary to donkeys, is that the diagram of the construction given in Euclid’s proof resembles a steep-sided bridge that horses would have difficulty climbing but sure-footed donkeys would have no trouble with.

Interestingly, while pons asinorum is used in the English-speaking mathematical world to refer to Euclid I-5, it is apparently used in the French-speaking world to refer to I-47, i.e. Pythagoras’ Theorem.