25 May 2008

The tide predicter of the U.S. Coast and Geodetic Survey

Robert Merkin of Northampton, Massachusetts, USA, recently sent me a photo of the tide predictor that was in use at the U.S. Coast and Geodetic Survey from 1912 to 1965. It was built by Rollin A. Harris and E. G. Fisher, who modeled it on Lord Kelvin's Tide Predicter, and can handle 37 tidal constituents. It is also known as "Old Brass Brains". Here is Bob Merkin's photo.

Bob also pointed me to a site that offers an animation of Kelvin's Tide Predicter. It shows the workings of the Predicter much clearer than my own description and offers a choice of seven port locations to try it out. Unfortunately it comes under the heading "Fourier Analysis of Ocean Tides".

Fourier Analysis uses multiples of a base period; but the tidal constituents are not multiples of a base period, they are set by the movement of the earth and the moon. Tides are therefore predicted by adding the effect of the various tidal constituents with their known periods. This method is called Harmonic Analysis in oceanography.

In mathematics the term Harmonic Analysis describes an extension of classical Fourier Analysis. When the term Harmonic Analysis is used in the context of tide prediction it does not carry that meaning; it refers to a method that is based on the known periods of the tidal constituents. This has lead to confusion on occasions. Kelvin's Tide Predicter is a very helpful tool to clarify the situation.

11 May 2008

Science and the aristocracy

In a study of the history of science it is important to realize that progress in science is not determined by the genius of a few individuals but by the conditions of society. In the age of feudalism only a wealthy aristocrat could afford to pursue scientific interests and go down in history as genius. Ordinary people had little chance to show their potential.

In a footnote to lecture 8 I used the example of Tycho Brahe, the Danish aristocrat turned astronomer. A study of the history of astronomy described his birth in 1546 as "fortunate" for the development of science. I queried that and said: "What honours him and secures his place in the history of science is not his fortunate birth but his decision to turn his back on the idle life of the ordinary nobleman and apply his gifted mind to science." Brahe did not care much about the aristocracy; he married a peasant's daughter and embarked on a career as imperial mathematician and astronomer.

It is instructive to compare Brahe's attitude to science with that of the English nobleman Joseph Banks, the resident naturalist during James Cook's fist expedition into the South Pacific. Banks brought along a second naturalist, a secretary, two artists and four servants, all paid for from his own wealth.

The large amount of work done by Banks and his party in the field of botany and taxonomy was an immense contribution to science. But Banks clearly did not see science as an important part of his life; he saw it more as what Galiliei called the "regal sport" of the ruling class. This became obvious when Cook invited Banks to join his second voyage into the South Pacific on the Resolution. Banks agreed, on the condition that he could increase his party to fifteen, including two musicians to while away the time. He even managed to talk the Navy into adding an extra deck to the ship to accommodate his party.

When the time came to sail the Resolution out of the shipyard one of Cook's lieutenants called her "by far the most unsafe ship I ever saw or heard of." The pilot declared her top-heavy and prone to capsize and refused to even move her off the dock. The ship was restored to her original state and Banks, swearing and sulking, withdrew from the expedition.

The story demonstrates that when it comes to evaluating the role of individuals to science, looking at their contribution to science alone does not produce a balanced assessment. Banks clearly had the capacity and gift to play a much larger role in the history of botany, but he chose the idle life of the aristocracy.


Allen, O. E. (1980): The Seafarers, the Pacific Navigators. Time-Life Books, Alexandria, Virginia, 176 pp.

The Catholic Church and the destruction of America's civilizations

Wherever the Spanish conquerors went they were accompanied by friars, whose role was to bring Christianity to the heathens. The Dominican order made missionary activity during the conquest one of its primary undertakings.

There is no doubt that some Dominican friars tried to soften the treatment of the indigenous people by the conquerors and prevented the worst excesses. But there is also no denying that even such intellectual interest as the study of indigenous languages (mainly to enable the Christian gospel to be preached in the local vernacular) was aimed at the final destruction of a "pagan" civilization. Any historical assessment of the role of Christianity has to admit that the muskets and guns of the conquistadors were not the only instruments that brought great civilizations to an end but also the book burnings and destruction of places of worship by the representatives of the Church.

The Convent of San Esteban in Salamanca, Spain, was and remains the centre of the Dominican mission. It features a display of the Dominican role in the conquest of South America. There are exhibits of souvenirs brought back by Dominican missionaries, but one searches in vain for any indication of regret for what happened under their spiritual supervision. Instead, vague and obfuscating texts attempt to conceal their contribution to the destruction of great civilizations.

A book exhibit "San Esteban, Search and Encounter; America, the universalist Dominican vocation" declares: "The world expanded itself, and it became necessary to invent new norms. What was known and understood was no longer sufficient. The search for the truth extended itself to the other side of the ocean." The main inscription on the wall of the Convent is more direct; it concedes that it was not the world that drove the action by expanding itself, admits that actions involved people, and identifies the actors: "The thoughts and the action of the Dominicans of San Esteban in America demonstrate that the battle for the freedom and the dignity of all people is the way to the TRUTH – And the only medium: the WORD." The South American Indians should be thankful for the freedom and dignity they received!

The role of profit in scientific exploration during the "Age of Discovery"

The early European ocean voyages of the Age of Discovery did not always lead to the discovery of unknown lands. Their main objective was to obtain as much profit as could be made. Exploration of new coasts, with the associated benefits for science, was a secondary consideration, performed only to the degree necessary to bring success to the economic purpose of the voyage.

The early Portuguese and Spanish sea captains were true explorers, in the sense that their contract with the crown (four fifth of the profit to the explorer, one fifth to the crown) was based on voyages to unknown destinations and therefore carried great risk. The British crown found it more profitable to raid the Spanish outposts in regions already discovered. It financed Francis Drake, Thomas Cavendish and other "privateers" to sack Spanish settlements and capture Spain's ships.

The profitability of marauding voyages was beyond doubt. When Drake captured a Spanish galleon in 1579 he obtained 13 chests of silver coin, 26 tons of silver bullion, 80 pounds of gold, and uncounted jewellery. Cavendish sacked Puna Island off Peru, slaughtering its Indian inhabitants, in 1587; he returned from his two year marauding voyage with a booty worth 125,000 pounds, nearly half of the Crown's annual revenue. Such adventurism did not contribute much to science.