Sir William Rowan Hamilton (1805-1865) was Ireland’s most ingenious mathematician. When he was just fifteen years old, Hamilton and a schoolfriend invented a semaphore-like signalling system. On 21 July 1820, Hamilton wrote in his journal how he and Tommy Fitzpatrick set up a mark on a tower in Trim and were able to view it from a neighbouring hill using a telescope. This gave them the idea of devising a telegraph to signal between these points.
Just a week later, the two boys were able to exchange messages using their scheme. and could maintain a long-distance conversation. Hamilton wrote: “By a telegraph which I contrived myself, each having a telescope, we have repeatedly transmitted questions and answers correctly. It is somewhat on the plan of our secret language.”
In the following week Hamilton and Fitzgerald adjusted their plan to the use of the letter array signalled by five positions of the arms (see letter table in Figure) and, apparently, by Friday 28 July their system had become satisfactory.
The Coding System
The coding system used a square array of five rows and five columns. To send a letter, both arms were raised to the position the number of which corresponded to the row in which the letter occurs. Immediately following this, the arms were moved to the position whose number corresponded to the column of the letter. For the vowels, the first movement was repeated.
Thus, Hamilton’s system did not use the left and right hands in different ways: both arms were used symmetrically to signal the row and then the column. While one arm might have sufficed, the use of both reduced the risk of errors. An object, such as a book, was held in the hands to make the signs easier to read through a telescope.
Semaphore Systems
The term semaphore, coming from the Greek words for ‘sign’ and ‘carry’, signifies a form of optical telegraph. It is a system for sending messages by holding in the arms two flags or poles in certain positions according to an alphabetic code.
Semaphore systems were devised to transmit signals over a distance using visual means. They were used in several ancient civilisations. Smoke signals were a popular means of messaging in several contexts. Signals were also formed using fire, lights, flags, sunlight or moving arms. In 1794 an extensive mechanical semaphore network became operational in France and elsewhere. Chains of relay towers were built at separations of 20 km or more, so that messages could be sent over long distances.
The modern lighthouse is a semaphore system using a tower that emits light signals. Flag semaphore is the telegraphy system conveying information by means of signals with hand-held flags or, at night, illuminated wands. In 1867, the Royal Navy began using signal lamps. Different letters or numbers were encoded by the positions of the lamps. After the invention of the electric telegraph and Morse code, semaphore systems fell out of use.
In 2007, the Internet Engineering Task Force standards organization published the Semaphore Flag Signalling System, for transmitting Internet traffic via a chain of flag semaphore operators; the publication date was 1 April.
Recreational Mathematics: an Evening Course.
“Marvellous Maths: The Mysteries and Magnificence of Mathematics” will be presented this Autumn by Prof Peter Lynch at UCD. Registration at: http://ucd.ie/lifelonglearning
Sources
https://datatracker.ietf.org/doc/html/rfc4824 (1 April 2007).
ThatsMaths 