PERMUTATION IN MORSE CODE A STUDY OF TELEGRAPH

BY UMARU YUSUFU

International Morse Code

The International Morse Code is a system of dots and dashes that can be used to send messages by a flash lamp, telegraph key, or other rhythmic

device such as a tapping finger. As a telegraph key is moved up and down, it makes or breaks an electric circuit and transmits a signal as a series of electric pulses. The telegraph was invented by Samuel Morse in 1837. In the International Morse Code, each letter or number is represented by a combination of dashes and dots vocalized as dah and dit respectively. A dash is equal to three dots in duration. A famous Morse code signal that

signifies distress could be vocalized as dit dit dit dah dah dah dit dit dit to mean SOS an abbreviation for save our souls!

ABSTRACT

The Morse code is used in telegraph communication. In this code, the letters, numbers and punctuation marks are represented by dots and dashes.

This work is a research on the logic used in designing the codes.

What you are about to read is not a story but rather a research work I am opportune to conduct for two reasons;

I am a radio operator a telegrapher with over fifteen years experience of transmission and reception; therefore I fully understood the nature of Morse code manipulations.

I read Mathematics and when one day I visited my school library to write an assignment my eye fell on a book written by a Russian, Mr. N. Vilenkin, titled Combinatorial Mathematics for recreation and it was in it I discovered that the codes were designed using a formula of Permutation, a topic in Mathematic which could simply means rearrengement.

These two reasons guide my imaginations to write what you are about to read, hopping that it will at the end be of use in addition to the entertaining reading, because as you will come to realize; Morse code utilizing electricity and later electromagnetic waves, was to be the roots of all telecommunication utilities!

Note. for you to fully appreciate the narration, if you are not professional or not a ‘’Morse code literate’’ you have to keep in view the international Morse code, especially when you start reading where the characters are explained.

Also note, as you proceed in the narration, you will come across examples of the characters representing either an alphabets or a numbers, I usually place the characters in brackets for example (-…) for b.

INTRODUCTION

Morse code is a method for transmitting telegraphic information, using standardized sequence of short and long elements to represent letters, numerals, punctuation and special characters of a message.

The short and long elements can be formed by sounds, marks or pulses in on / off key and are commonly known as “dots” and “dashes” or dits and “dats”

Morse code can be transmitted in a numbers of ways such as:

Electrical pulses along a telegraph wire

An audio tone

A radio signal with short and long tones

A mechanical signal

A visual signal (e.g. a flashing light) using devices like an Addis lamp

The most popular current use of Morse code is by amateur radio operators but it is no longer a requirement for amateur licensing, however it is continuously in use for specialized purpose.

These codes however were designed using mathematical notations known as permutation – which is defined as an ordering of a certain number of elements of a given set.

Originally created for Samuel F.B. Morse electrical telegraph in the early 1840s, Morse code was also extensively used for early radio communication beginning in the twentieth century, the majority of high – speed international communication was conducted in Morse code, using telegraph lines, undersea cables and radio circuits.

Morse code is still being used for specialized purpose, including identification of navigational radio beacon and land mobile transmitters, plus some military communication, including flashing light between ships for tactical operations that avoids the emission of electromagnetic waves, which is detectable by the enemy.

BACKGOUND TO THE STUDY

Samuel and Alfred (1836) developed an electrical telegraph, which used electrical currents to control an electromagnet that was located at the receiving end of the telegraph wire.

The technology available at the time made it impossible to print characters in a readable form, so the inventors had to device alternate means of communication.

Earlier, William and Charles (1837) had operated electric telegraphs in England, which also controlled electromagnets in the receivers; however, their systems used needle pointers that rotated to indicate the alphabetic characters being sent.

In contrast, Morse and Vail’s initial telegraph, which first went into operation in 1844, made indentations on a paper tape when an electrical current was transmitted. Morse original telegraph receiver used mechanical clockwork to move a paper tape. When an electrical current was received, an electromagnet engaged an armature that pushed a stylus onto the moving paper tape, making an indentation on the tape.

When the current was interrupted, the electromagnet retracted the stylus, and portion of the moving tape remained unmarked.

The Morse code was developed so that operators could translate the indentations marked on the paper into text messages. In his earliest code, Morse had planned to only transmit numerals and use a dictionary to look up each word according to the number, which had been sent.

However, the code was soon expanded to include letters and special characters, so it could be used more generally. The shorter marks were called “dot” and the longer one “dashes”, and the letters most commonly used in the English language were assigned the shortest sequences.

In the original Morse telegraphs, the receiver’s armature made a clicking noise as it moved into and out of position to mark the tape. Operators soon learned to translate the clicks directly into dot and dashes, making it unnecessary to use the paper tape, when Morse code was adapted to radio, the dot and dashes were sent as short and long pulses. It was later found that people become more proficient at receiving Morse code when it is taught as a language that is heard, instead of one read from a paper. To reflect the sound of Morse code, practitioners began to vocalize a dot as “dit”, and a dash as “dah”.

STATEMENT OF THE PROBLEM

Morse codes were designed from only two elements (a dot & a dash) to provide codes for all alphabets and numbers used in writing.

What the research wish to solve was the logic used in designing these puzzling codes, for at one time, one of the researchers had thought it were the symbols of some heavenly bodies!

OBJECTIVE OF THE STUDY

Results of every enquiry always expose avenues to understanding other unknowns in the same or even other field of knowledge. This study therefore, has as its objective, to expose the logic used in

designing the element variations and combinations in Morse code in order to make easier the expansion of the frontiers of knowledge in general.

SIGNIFICANCE OF THE STUDY

So many problems of this world are still defying any solution just as one time man could not solve the problems of long distance communications prior to the development of telegraphy utilizing Morse codes.

In the field of medicine for example there is still no known cure for aids. There is also no remedy to Ozone layer leakage that is causing further worming of the earth due to infrared light penetration to our atmosphere!

For solution to be found in every problem that has no “readymade” solution “brain storming” trails by errors might be required to diagnose the problem and provide a solution to it.

Mathematics being the “backbone” of science usually acts as bridge that link problem to a solution as this expository research shows, when permutation with repetition provide the necessary formula that aid in designing Morse codes.

The significance of this study therefore is to shows how mathematics when critically viewed could be the “pointer” towards solutions to so many problems.

SCOPE OF THE STUDY

The research intends to examine only the logic of the “element groupings” in Morse code.

INTRODUTION

This chapter had highlights the following which serves as literature review

The growth of an idea

Conduct of Telegraph and,

General transmission rules

THE GROWTH OF AN IDEA

The idea of using electricity to communicate over distance is said to have occurred to Morse during a conversation aboard ship when he was returning from Europe. Michael Faraday’s (1832) recently invented electromagnet was much discussed by the ships passengers, and when Morse comes to understand how it worked, he speculated that it might be possible to send coded messages over a wire.

Despite what he had learned at Yale, Morse found when he began to develop his idea that he had little real understanding of the nature of electricity, and after sporadic attempts to work with batteries, magnets and wire, he finally turned for help to a colleague at the university of the city of New York, Leonard D (c.1835) – a professor of chemistry who was familiar with the electrical work of Princeton’s Joseph H. (a true pioneer in the new field). Well before Morse has his shipboard idea about a telegraph, a research has been made on ringing a bell at a distance by opening and closing an electric circuit and had published an article, of which Morse was unaware, that contained details suggesting the idea of an electric telegraph. Gales help and his knowledge of this article proved crucial to Morse ‘s telegraph system because Gale not only pointed out flows in the system but showed Morse how he could regularly boost the strength of a signal and overcome the distance problems he had encountered by using a relay system Henry had invented. Henry’s experiments, Gale’s assistance and soon after, hiring the young technician Alfred Vail were keys to Morse’s success.

Morse had enough confidence in his new system to apply for the federal government’s appropriation and later conducted demonstrations of his Telegraph both in New York and Washington. However Morse was forced to wait for better times. Morse visited Europe again and tried to secure patent protection and to examine competing telegraph systems in England.

He met Charles Wheatstone, the inventor of one such system, where he realized although his own system was far simpler, more efficient and easier to use; his competitor had built an ingenious mechanism.

Morse’s system has an automatic sender consisting of a plate with long and short metal bars representing the Morse code equivalent of the alphabet and numbers.

The House of Representative (1843) passed a bill containing the Morse appropriation and the senate approved it - When due to the economic recovery of the time Morse asked the congress for $30,000 that allowed him to link Washington with Baltimore successfully! And soon overhead wires connected cities up and down the Atlantic Coast – and later virtually all over the world!

CONDUCT OF TELEGRAPH

To utilize the codes for passing Information as pulses of electrical currents over wire an instrument called Morse key i.e. J-38 US Model (Manufactured during WW II and which remains in used today) is used.

A signal is “on” when the Knob is pressed and “off” when it is released. The length and timing of the short and long pulses are entirely controlled by the operator.

GENERAL TRANSMISSION RULES

1. All correspondence between two stations begins with the call signal. For calling, the calling station shall transmit the call sign (not more than twice) of the station requirement then the word DE followed by its own call sign, the appropriate abbreviation to indicate a priority telegram, an indication of the reason for the call and the signal “K” which means “over” and refers to: “I had finished transmission / I understood what you transmit and I now invite you to respond.”

Unless there are special rules peculiar to the type of apparatus used, the call shall always be made at hand speed.

2. The station called must reply immediate by transmitting the call sign of the calling station, the word DE followed by own call sign and the signal “K”,

If the station called is unable to receive, it shall give the wait signal. If it expects the wait to exceed ten minutes, the reason and probable duration shall be given.

When a station does not reply, the call may be repeated at suitable intervals.

When the station called does not reply to the repeated call, the condition of circuit must be examined.

3. The double hyphen (- …-) shall be transmitted:-

(i) To separate the preamble from the service indications

(ii) The service from each other

(iii) The service from indications from the address

(iv) The station of destination from the text.

(v) The text from the signature.

4. A transmission, once begun, may not be interrupted to give place to communication of higher priority except in a case of absolute urgency.

5. Every telegram shall be terminated with a cross signal AR (. -. -.).

6. The end of the transmission shall be indicated by the cross signal “AR” (. -. -.) Followed by the invitation to transmit signal K (-. -).

7. The end of work shall be indicated by the station that transmitted the last telegram. The correct indication is the end of work signal “VA” (…-.-)

RESEARCH DESIGN

The only methods used were historical and descriptive. For the historical, we depends on digging historical facts available in internet and for the descriptive, we depends on a translated book from Russian by George (1972) titled “COMBINATORIAL MATHEMATICS FOR RECREATION” written by Vilenkin N which described how the formula of permutation with repetition was used to designed the code.

METHOD OF DATA ANALYSIS

I had carefully grouped the codes according to the type and number of elements per alphabet or number and using the formula for number of permutation with repetition had found out the logic suggested in the Vilenkin’s book is correct.

PRESENTATION OF ANALYSIS

The dot and dashes (see above) used to design the symbols, totals 132 elements (for both Alphabets and Numbers) varied out of the two (dot and dash) out of these, 69 are dots and 63 are dashes.

The punctuation marks where formed by combining two or more Alphabets i.e. AAA (.-.-.-) for full stop (.)

From these, it could be seen that:

Some characters among the Alphabets require only a single element i.e. “E” and “T” as a symbol or code but others especially the numbers requires five elements each as codes.

Then, there are also 2 element groups, three element groups and four element groups.

The two element groups could further be subdivided into:

Those formed by only dots or by only dashes i.e. “I” and “M” respectively.

Those formed by the combination of the two i.e. “A” and “N” beginning with a dot and a dash respectively.

Similarly, the three-element group could be further grouped as:

Those formed by only dots or by only dashed i.e. “S” and “O” respectively.

Those formed by the combination of three, which could also be further subdivided as: -

Those beginning with two same elements and ending with the other i.e. “G” and “U”

Those beginning and ending with either a dot or a dash and the other in the middle i.e. “R” and “K”.

Finally, the four-element group could as well be subdivided as follows: -

Those with more dots (H, B, F, L and V) out of which “H” has no dash in its elements but “B”, “L”, “F” and “V” have single dash each, at the beginning, as a second element, a third element and the fourth element respectively.

(b) Those with more dashes (J, Q, and Y) with 3 dashes and one dot each .The dots are located as the first, second and third elements respectively.

(c) Those with two dots and two dashes (C, P, X and Z).

Among these characters: -

“C” has began with a dot followed by a dash and then repeated the sequence, ending with a dot.

“P” began with a dot and end with a dot with two dashes in the middle.

“X” which began with a dash and end with a dash with two dots in the middle.

“Z” that began with two dashes and ends with two dots.

RESEACH FINDING

At first glance, Morse codes gave some mystical puzzlement.

How was it formed? Is it heavenly symbols connected to astrology? I had then thoughts so because in an Introduction to Astrology, a book written in Hausa language titled, “Hisabi a sawake”, there are some signs representing the zodiac signs that resembles the codes!

Also, why for instance, do some characters require only a single element i.e. “E” and “T” as a symbol – while others require more?

Why up to 5 elements are required for some?

Can’t we form all by maximum of only 4 elements to save time? Since each word has to be spelt?

Now let’s look at the questions from the angle of what we want in the first place.

“The coding of Alphabets and numbers”

There are 26 Alphabets (A-z) and 10 digits (0-9) for numbers – making a total of 36 characters using two elements a dot and a dash, the science of permutation being one of several possible arrangements of things in mathematics could be utilized.

In it there is a formula for number of permutation with repetitions, 2 rests to the power of n, i.e. (2n) where the 2 refers to the 2 elements of Morse code (a dot and a dash), and the n represent number of element (s) to be used in forming the character or symbol.

A character is a symbol made from either of or the combination of the elements (dot and dash) mentioned earlier in a particular pattern of arrangement, for example, (-.--) made from four elements: a dash a dot and to two other dashes to represents the Roman Alphabet Y.

This system of coding alphabets and other writing symbols can be utilized to have a symbol for each of the characters (alphabets, numbers and combing the alphabet codes to designs punctuation marks).

These characters are of varying number of elements and arrangements.

Some characters belonging to alphabets are of single elements while some have two elements, others three; some four, but all the numbers have five elements each.

However all these characters of varying numbers of elements were formed from the only two basic elements, a dot (.) and a dash (_) as you must have noticed?

Why? Because;

Utilizing a single element for a character, we can be able to form any 21 = 2 different symbols (.) for “E” and (-) for “T” vocalized as dit and dah respectively.

Utilizing two elements to form a character we can be able to form 22 = 4 other characters – these are (.-) for “A”, (..) for “I”, (--) for “M” and (-.) for “N” vocalized as dit dah, dit dit, dah dah, and dah dit respectively.

Also utilizing three elements in forming a character it was possible to form as much as 23 =8 more characters out which (-..) is for “D”, (--.) for ”G”, (-.-) for ”K”, (---) for “O”, (.-.) for “R”, (…) for “S”, (..-) for “U” and (.--) for “W” vocalized as dah dit dit, dah dah dit, dah dit dah, dah dah dah, dit dah dit, dit dit dit, dit dit dah and dit dah dah respectively, were designed.

Finally utilizing four elements to code an alphabet, it will yield as much as 24 = 16 more characters which include (-…) for “B”, (-.-.) for “C”, (..-.) for “F”, (….) for “H”,(.---) for “J”, (.-..) for “L”, (.--.) for “P”,(--.-) for “Q”, (…-) for “V”, (-..-) for “X”, (-.--) for “Y” and (--..) for “Z” vocalized as dah dit dit dit, dah dit dah dit, dit dit dah dit, dit dit dit dit, dit dah dah dah, dit dah dit dit, dit dah dah dit, dah dah dit dah, dit dit dit dah, dah dit dit dah, dah dit dah dah, and dah dah dit dit respectively.

It should be noted here that only 12 out of the 16 possible different types of arrangements were chosen, the remaining 4 were not utilized, these are(---.), (----), (..-- ) and (.-.-) to have been vocalize as dah dah dah dit, dah dah dah dah, dit dit dah dah, and dit dah dit dah respectively.

In writing, sometimes we require numbers, so we need ten more codes for the numbers 0 to 9 and since the four unutilized codes could not be sufficient because the total number of characters that can be transmitted by utilizing 2 +4+8+16 different code arrangements = 30, we require 6 more for the 26 Roman alphabets and 10 Arabic digits (making a total of 36 different types of arranging the two elements, a dot and a dash) and taking the combination of 5 elements per character in addition, we get 25 = 32 more possible types of arrangements and adding the 30 different types of possible arrangements or codes with the new 32, the we get 62, which are quite sufficient for telegraph communications.

This utilization of permutation had greatly assisted the formulation of these codes and to simplify the rather complicated code operations, all the number symbols are formed from the 5 element groups as follows:-

(.----) for 1

(..---) for 2

(…--) for 3

(….-) for 4

(…..) for 5

(-….) for 6

(--…) for 7

(---..) for 8

(----.) for 9

(-----) for 0.

Also note that most frequently used characters were assigned codes with more dots where the choice is available to minimize time of transmission and for the same season, there were more dots than dashes in the total number of the elements allocated to the Alphabets.

It should also be noted that as the numbers progresses from one to five the number of dots at the beginning increases while those of the dashes decreases until the number five is reached which has only dots, and similarly as the numbers from six progresses further the number of dashes at the beginning increases while those of the dots decreases until the digit zero is reached which has only dashes with no single dot. These I believe were deliberately designed to reduce ambiguity that may arise in conducting telegraphy because as experience had shown, as one receives numbers it is instantly

recognize as above or below the digit number five, by first element in the five element code used for coding numbers if the code began with a dah or dit respectively.

SUMMARY and CONCLUSIONS

The Morse code is used in telegraph communications to represent letters, numbers and punctuation marks utilizing dot (s) and dash (es). Some characters require only a single element (a dot or a dash) others use more (the same type of element s or combination of both).

The codes where designed using the formula for the number of permutations with repetitions 2n, where 2 represent the two elements in the set (a dot and a dash) and n represent the number of elements (single or combination) in the character.

It follows that; using one element to form a character it is possible to form only two letters (in 21

= 2), using 2 elements (22 = 4), 3 elements (23 = 8) and 4 elements (24 =16) Thus, the total number of letters that can be transmitted by means of four characters is: 2+4+8+16 = 30

Taking an Alphabet of 26 letters, number (0-9) and marks of punctuation, we see that symbols made up of four characters do not suffice. Thus taking combination of 5 elements we will have additional 25 = 32 symbols in addition to the 30 obtained from 4 elements combinations.

These 62 symbols are quit sufficient for telegraph communications.

It should be noted here however that there exist a five – digit code for telegraph communications that make use of five symbols (elements) for every latter but that is not part of these work.

This code yields exactly 25 = 32 different arrangement combinations, which is enough for all the letters, numbers and punctuations.

It has a special device for shifting from letters to numerals and back again.

5.4 RECOMMEDATION

Most major scientific breakthrough, were results of research works. Ours, though a mere expository research for academic exercise, has helped in throwing more light on the importance of mathematics in most if not all-scientific decisions.

Therefore, although, already mathematics is a compulsory subject in Nigerian school, it is yet here by further recommended to remain as such.

It is also recommended that the formula 2n used, be modified as An in which A could as well be any number of different element in a given set.

Reference:

1. N. Vilenkin (1972)

Combinatorial Mathematics for recreations, Page 11.

Translated from the Russian, by George Yankousky MIR Publishers Moscow.

2. Allied Communication Publication (ACP 131 B) used by the Allied Navy during the second World War

3. Samuel F.B.M. & Alfred (1836). The invention of Telegraphy.

Source: - Internet hppt://memory.loc.gov

4. Hisabi a Sawwake, by Al Nashirul Hajji Muhammadul Bashiru ‘Yantandu Kano- Nigeria.

s

OPERATIONAL TERMS

ALPHABET – A set of letters in a fixed order representing the sounds of a language

CHARACTER- Written sign

CODE- A system of words or symbols used to represent others.

DOT vocalized as ‘’dat’’ – is represented by small round mark (.)

DASH vocalized as ‘’dah’’ – is represented by punctuation mark (-)

ELEMENT- A unit represented in this work by either a dot or a dash referred above

MORSE CODE- A code of a signal using short and long sounds or flashes of light referred above also

NUMBER – Symbol of quantity

NUMERAL – Symbol representing a number.

STATION CALLED – The receiver of the message

TELEGRAPH – A system for sending message by electrical impulses