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"Musical Clock"

Musical Clock

Deleted scene from Caracol...

Description...

PAUL

At the turn of this, our third millennium, A.D., mutual-fund magnate Langdon Clay put up 7 million dollars for the solution of seven classic problems in mathematics that have resisted all attempts to solve them over the years. They are called collectively the Millennium Prize Problems. The fund was announced on the 24th of May, 2000, at a lecture offered to the general public, at the prestigious Collège de France in Paris.

Sor Juana Inés de la Cruz never went to Paris, but she would have enjoyed the occasion. In her own day, a single problem in applied mathematics had come to dominate all others. It had defied solution for almost exactly two thousand years. How to calculate the east-west position of a ship out of sight of land.

The failure to solve the problem of longitude was costing the seafaring powers of England, the Netherlands and France vast sums of money in shipping losses. For Portugal, a secure title to the colony of Brazil depended upon a definitive solution. And the stakes were even higher for Spain, since, in addition to its disputed territories with Portugal, there were the devastating losses to its silver fleets, made still worse by piracy.

In 1567, Philip II of Spain put up the first prize money. Thirty years later, Philip III put up the princely sum of 6000 ducats, plus 2000 ducats for life, and a 1000 ducats for incidentals. The greatest minds of the day were engaged in the adventure, including Galileo, Huygens and Newton.

The lectures of her lost work Caracol would have presented Sor Juana with the perfect opportunity to offer a solution all her own.

JUANA

Ladies and gentlemen, compañeros, compatriotas...

       It is often said these days that the age of discovery has ended. And yet Europe has never seemed farther away. But the age of discovery never truly ends, for it is always starting somewhere else: and it is time for us here in Mexico to make discoveries for ourselves.

       No empire has had more to gain or lose than ours in the question of longitude, for on this depends Spain's claim to all the lands lying beyond a certain meridian line imaginatively traced north-south on the sea in 1493. The trouble being that in the two centuries since, we have still found no method for tracing such a line out of sight of land. So while we have long been fond subjects of the Spanish kings, we here in Mexico may yet wake up one morning to find ourselves Portuguese....

       No country in Europe began with a greater advantage than did our Spain of the Two Faiths, for our learned Moors once had access to the writings of the mighty Persians - the astronomers of Baghdad, venerable Al-Tusi and Abu'l-Wafa, and the geometers of Kabul, Mansur and Al-Biruni. How circuitous are the tracts of history: It seems one has only to digest the problem, in 1493, to discover one has just expelled the solution, along with the Moors and the Jews, in 1492.

       It is the piratical nations of England and France that are pursuing the solution to longitude at sea most doggedly -- to catch our laggard age up with the Persian tenth century, and thereby catch up with our silver fleets.

       If anything has saved us thus far, it is that the pirates do not know where they are....

       You will say we do not know where they are either, but surely our best hope lies in finding out where we are before they do. Waking up Portuguese is not the worst fate to be imagined: we might find ourselves, not far hence, the westernmost city of France. Which could be even worse than it sounds. For if we do not know where we are, or in whose empire, or even whose language we should be speaking, it is because we do not know what time it is.

       To which problem we humbly propose a solution: the Mexican musical clock.

       The sailors tell us that if they could only tell the time with accuracy they could greatly increase the precision of their navigations out of sight of land. We begin, then, with the science of the publican, who raps on his beer casks to check their volumes. And as we have just heard with our own ears, different volumes of liquid can be calculated to make the vessels they fill sound out the hexachord. As the curtain rises here in the atrium, the musical clock we see before us is composed of six water vessels shaped like funnels, each of increasing volume, each designed to tip into the next larger as the water level rises to a given height. And so unto the largest. To the height of the water corresponds a volume, and to the volume a tone when the vessel is struck lightly with a baton.

       Aboard the ship, the water is made to flow at a constant rate from a reservoir filled each day by sailors at a water pump. Every six seconds Vessel I tips into II - and if struck at any instant it sounds with one of six notes. As the water level rises the note drops. Vessel II is a basin whose tone every ten seconds drops by a note and tips itself once a minute into Vessel III. The sum of the first two vessels gives the time-keeper his seconds. Vessel III drops by a whole note each minute and spills itself every six minutes into vessel IV, whose tone changes by a note every ten. The sum of III and IV gives the timekeeper his minutes. The sum of V and VI gives the timekeeper his hours. Vessel V changes by a whole note each hour and tips every six. Vessel VI varies by a whole note every six hours.

       The timekeeper does not need to check the time continuously. Rather, when the navigator calls Time! he takes up his baton and lightly taps each vessel, smallest to largest, yielding the precise time by way of a sequence of six notes. When the navigator is seated at his table, the timekeeper sings them out or pipes them back to him. Ut-Sol-Mi-Re-Fa-La!

       Converting these back to the corresponding values (6-2-4-5-3-1), the navigator proceeds to multiply each by the appropriate unit: 6 units of 1 second, plus 2 units of 10 seconds (equalling 26 seconds); 4 units of 1 minute, plus 5 units of 10 minutes (equalling 54 minutes); 3 units of 1 hour, plus 1 unit of four hours (equalling 7 hours). Time: 7 hours 54 minutes 26 seconds.

       Which translates, depending on one's habits, to the hour of breakfast, between Prime and Terce.

       In theory, then, we have the musical clock, and the practical demonstration that music is our most perfect and pragmatic idea of Time....

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