Ars magna lucis et umbrae

I also wanted to add my two cents to the series on meridians launched by Lloyd, and to present that small Italian book on the art of sundials which I bought almost twenty years ago in the Trastevere, in a secluded small shop, where they sold all kinds of self-made time-measuring devices, water hours dripping each second, candles with wick divided per hours, rings with a hole functioning as camera obscura with the inscription Carpe diem. Life, however, hastened to meet me.

Today I started to translate Umberto Eco’s new book: Storia delle terre e dei luoghi leggendari – fabulous lands, legendary places, that’s the working title, but the book adds one more twist to what you would expect. It is not simply about imaginary worlds, as we are used to from Eco, from the Baudolino to The Island of the Day Before, but about how the fanatic readers have taken bloody seriously the fictional literary locations from the antiquity to Dan Brown’s Priorate of Sion. And already in the first, ancient chapter we are greeted by our good friends, the meridians.

Che la terra fosse tonda lo sapeva naturalmente Tolomeo, altrimenti non avrebbe potuto dividerla in trecentosessanta gradi di meridiano, e lo sapeva Eratostene, che nel III secolo avanti Cristo aveva calcolato con una buona approssimazione la lunghezza del meridiano terrestre, considerando la diversa inclinazione del sole, a mezzogiorno del solstizio di primavera, quando si rifletteva nel fondo dei pozzi di Alessandria e di Syene, di cui si sapeva la distanza reciproca.

Of course Ptolemy was also aware that the Earth was round, otherwise he would not have divided it into three hundred and sixty degrees; and this was also known to Eratosthenes, who in the third century BC determined the length of the Earth’s meridian with a good approach, taking into account the different angle of incidence of the sunshine at the time of the spring equinox, when at noon it is reflected in the depth of the wells of Alexandria and of Syene, whose distance was well known.

Eco, who in his popular albums published in recent years – The Story of Beauty, The Story of Ugliness, The Infinity of Lists – seductively blends trivia with ingenious problem proposals, is like a super jongleur, who plays with a hundred balls at once, and if he drops five, never mind. The translator, however, must also seek for those five, and dust them off, as if they had not fallen. This is what I try now, too.

If at noon the sun is reflected in the depth of a well, it means that it stays exactly perpendicular above the given location. If it is reflected in two, then there is no difference between the two angles of incidence, so nothing can be calculated from it.

The reality is, that the Alexandrian librarian Eratosthenes learned from a caravan arriving from the southern Syene – today Assuan – that the sun is reflected in the depth of the cistern of the settlement, laying precisely under the Tropic of Cancer, in only one day of the year, on June 21, the summer solstice. He thus measured at the same moment the angle of incidence of the sunlight in Alexandria (7°12'), and found it to be the 1/50th part of a full circle, so he concluded that the length of the complete meridian would be fifty times the known distance of the two cities. The resulting circumference of the Earth – 39,690 km – only slightly differs from the 40 thousand known today.

The story of the measurement is well summarized by an English-language interview with Eratosthenes, including a modern diagram. But for the sake of a greater credibility, I quote it from the eccentric baroque Jesuit scholar, Athanasius Kircher himself (Ars magna lucis et umbrae, Amsterdam 1671, 638-639), whose works, as Eco admits, are preserved all (but one) in his personal library.

Hac solertia legimus Eratosthenem terrenae molis quantitatem indagasse; assumptis duabus urbibus Syene, & Alexandria sub eodem meridiano in planissima Aegypti regione sitis, quarum distantiam in stadijs 6183⅓ cognitam, ut prius, summo studio exploratam habebat. Quibus notis nihil aliud requirebatur, nisi ut eandem distantiâ in gradibus quoque notam haberet, quam ea, qua sequitur solertia invenit. Cùm tempore solstitij Syene urbs sub tropico ♋ immediatè sita, hora meridiana sit ἁσκιη, & umbra in seipsa sine ullo angulo cum gnomone facto consumatur: hoc tanquam cognito, Alexandriae eodem temporis momento dieque gnomonem erexit, diligenter angulum, quem gnomon cum umbra ad verticem faciebat, observando: hic enim erat, ut paulò post demonstrabimus, arcui meridiano inter assumptas urbes aequalis. Sed rem paradigmate demonstremus, etc.

Of Eratosthenes we read how insightfully he measured the extension of the earth, taking two cities, Syene and Alexandria, which lay in the flattest region of Egypt, under the same meridian, and whose distance of 6183 and one third stadiums were previously measured by him with the greatest care. Against this background he did not need anything more than the distance between the two cities in degrees, which he determined in the following ingenious manner. As in Syene, lying immediately under the Tropic of Cancer, on the day of the summer solstice the hour of the noon is ἁσκιη, without shadow, that is, the shadow exactly coincides with the vertical gnomon and does not deviate from it to the least angle, by observing in the same moment in Alexndria the angle of the gnomon to the vertical, he calculated, as we will soon point it out, the angular difference between the two cities. But let’s see the demonstration step by step, etc.

On the basis of all the above, my translation changed like this:

…and this was also known to Eratosthenes, who, in the third century BC on the day of the summer solstice at noon, when the sun is reflected in the depth of the well of Syene, determined the length of the Earth’s meridian on the basis of the angle of incidence measured in Alexandria, whose distance from Syene was known to him.

Such corrections, dozens per volume, are of course always sent back to the Italian editor, who always say thank for it, and never introduce it in the new editions. Therefore, as we have long known it, an educated European only reads Eco in Hungarian.