Posted in Psychology & Medicine

The Silent Twins

The story of June and Jennifer Gibbons is a fascinating case of linguistics.

June and Jennifer were twin sisters born in 1963 from Barbadian parents. They were raised in Wales, where they were bullied in school due to their dark skin. This was a traumatising event that led to the twins becoming more and more isolated as children, often choosing to hermit themselves in their own secluded world.

An interesting phenomenon that developed at the time was that June and Jennifer would talk in an unintelligible language between the two of them. At first, it started with a mix of English and Bajan Creole (an English-based Caribbean language) spoken very rapidly. However, over the years, their shared language became more and more cryptic to the point that only the two of them could understand each other (and their younger sister Rose).

To add to this, the two made a pact with each other that they would never speak to other people, based on their trauma of being ostracised by their schoolmates. Furthermore, the twins exhibited mirroring movements and mannerisms, and would become catatonic when forcibly separated from each other.

In their teenage years, June and Jennifer started writing various plays, poems and stories. They also began experimenting with drugs and alcohol, leading to them committing crimes such as arson, theft and vandalism. Instead of being sent to juvenile prison, they were admitted to a psychiatric hospital due to their mutism.

The two would be admitted at Broadmoor Hospital for a total of 12 years, where they were treated with antipsychotics despite not having objective signs of psychotic illnesses. Their institutionalisation resulted in the worsening of their “symptoms”.

Later on, it was revealed by June that this was the point that the two came to an agreement that their pact could only be broken if one of the sisters died. In other words, one person had to die for the other to live a normal life. Jennifer decided to make the sacrifice.

At the age of 30, they were finally discharged from Broadmoor to be transferred to a more open clinic. When they arrived at the clinic, Jennifer was found to be unconscious. She was transferred to a hospital where she was diagnosed with acute myocarditis (heart muscle inflammation), resulting in her demise. The cause of the myocarditis was never found and had appeared unprovoked.

After a period of grief, June started to speak to other people. Regarding Jennifer’s sacrifice, she said:

“I’m free at last, liberated, and at last Jennifer has given up her life for me”.

June would go onto give interviews detailing her and Jennifer’s life journey and suffering, giving us insight into a remarkable case of cryptophasia.

Cryptophasia is a common phenomenon in twins, where they develop a language spoken only between the two of them. This may be accompanied by mirroring actions. It is thought that up to 50% of twins invent some form of language or code between the two. Cryptophasia is possibly a result of speech delay, with the twins compensating for each other by creating a language that they find more relatable. As in the case of June and Jennifer, environmental and social factors are also likely to play a crucial role.

The desire for connection is innate to human beings. When we feel isolated in the world, we may cling to the few connections we feel comfortable with, even if it means causing further isolation and loneliness. This may manifest in a healthy way, such as investing more time and energy cultivating a fulfilling relationship with friends and family. However, it may also result in co-dependent or toxic relationships, social isolation, addiction and restricting ourselves from leading a full life.

June and Jennifer Gibbons are reminders to us of the importance of connection in our life. How far would you go to feel connected to something – anything – in life?

Cuombajj Witches by Seb McKinnon
Posted in Life & Happiness

Hidden Messages

Communication is easy on paper. We say what we think or feel, the other person hears it, and understands it. But in practice, so much can go wrong. Failure to communicate has been the cause of so much grief for people throughout history, even resulting in wars and disasters. Most importantly, poor communication is one of the greatest barriers to building a deep connection with another person.

The problem lies in the fact that despite being social animals, we are quite bad at being social. We care too much about how others may judge us, so we avoid being direct and literal when we communicate our thoughts and feelings. Instead, we choose to encrypt our messages and hope (or worse, expect) that the other person will understand the hidden meaning behind our words.

For example, instead of telling our partner that we are angry at them over something they did, we act passive-aggressively or pick a fight over an unrelated manner. Instead of speaking up about something that is unfair or unjust, we choose to stay silent and accept it to avoid conflict. We will flirt and tease with someone without telling them just how much we adore them. Instead of just saying what is on our mind, we try to package what we want to say in a cryptic form through vague, suggestive messages. Sometimes, we act out like a little boy pulling at the ponytail of a girl he likes on the playground, by sulking or being cruel to our loved ones.

Because we all tend to hide our feelings behind our words and actions, we become conditioned to try and analyse and decode messages to interpret the true meaning of what other people say. But because we are not mind readers, this often leads to misunderstandings. Instead of trying to talk openly with the person, we assume that we have unraveled their true intentions and act on it, which often leads to even more misunderstandings. In time, the relationship breaks down.

This is the reason why practising good communication is such a crucial relationship advice. Why waste our time and energy crafting delicate riddles and trying to be codebreakers, when it will only result in misunderstandings? It would be far more efficient to fight through our awkwardness and insecurities to talk about what is really on your minds.

That said, this is not a simple task and takes a lot of courage and trust. That is why the other takeaway point is how lucky it is to find someone who truly “gets you” – someone who has the patience to listen to you talk in a roundabout way, and spend the effort to try to understand what you really mean. If you find someone who knows you well enough that they can decipher your messages and actually listen to what you are really trying to say, then that is something to be grateful for.

Because the greatest gift we can receive from another person is for them to truly understand us.

Posted in History & Literature

Morse Code

In 1825, an artist by the name of Samuel Morse was travelling to a city far from his home to paint a commission. While working on his painting, he received a letter from his father, which informed Samuel that his wife was ill with an infection. The next day, another letter came, but this time detailing his wife’s sudden death. Upon receiving the letter, Morse immediately returned to his home as fast as possible, but he arrived after they had already buried his wife. This was the age before fast long-distance communication, where messages could only be sent as fast as the horses that carried them.

Frustrated by the inefficient communication methods of his time, Morse became dedicated to devising a better way to send messages over long distance at a much faster speed. After intensive studying of electromagnetism, Morse eventually developed the first concept of a single-wire telegraph. The telegraph could send electrical signals of variable length at fast speeds down wires with a simple button.

Together with the telegraph, Morse devised a code alphabet so that messages could be sent encoded into short and long signals on the telegraph. A dot (“dit”) represents a short press, a dash (“dah”) represents a long press (three times longer than a short press). Each letter is separated by a space the length of 3 dots. Words would be spaced out by a slightly longer pause – the length of 7 dots. Morse designed the code to be efficient and so he made the most common letters (E, I, S, T and so forth) the shortest in length.


Posted in Science & Nature


Pi (π) a mathematical constant that is defined as the ratio of a circle’s circumference to its diameter. It is approximately equal to 3.14159, but since it is an irrational number (cannot be expressed as a ratio), the decimal places go on and on with no repeating segments. The history of pi extends back to almost 5000 years ago, as it plays such a crucial role in geometry, such as finding the area of a circle (A = π ²). It is not an understatement to say that pi is among the top five most important numbers discovered in history (0, 1, i and e being the others).

The interesting thing about pi is that it is an irrational number. As mentioned above, this means that pi has an infinite number of non-repeating decimal places, with numbers appearing in random sequence. For example, pi to a 30 decimal places is 3.141592653589793238462643383279… Because of this feature, pi contains all possible sequences and combinations of numbers at a certain point. The corollary to this fact is, if pi is converted into binary code (a number system of only 0 and 1, used by computers to encode information), somewhere in that infinite string of digits is every combination of digits, letters and symbols imaginable. The name of every person you will ever love. The date, time and manner of your death. Answers to all the great questions of the universe. All of this is encoded in one letter: π.

That, is the power of infinity.

Posted in History & Literature

Spelling Alphabet

One weakness with the English alphabet is that when they are spelt out aloud, some letters are too similar and end up being confused. For example, B sounds like D and M sounds like N. Although this is not too major an issue in normal life, it becomes very problematic when giving important information over the phone, such as an identification number. The same problem applies in the military where precise orders are required. To overcome the issue of similar-sounding letters, many systems have been developed to replace the letters with words when spelling words aloud over the phone or radio. For example, if the ID number EFS9201 has to be told to the other person, it can be read as “echo-foxtrot-sierra-nine-two-zero-one”. It is also used in the military to say abbreviations, such as “oscar mike” for “on the move”. As the spelling alphabet system is designed so that no two words sound similar, it is a very effective way of accurately transmitting information over the phone.

The spelling alphabet (NATO phonetic alphabet) is as follows:


Posted in Science & Nature

Cryptography: Book Cipher

So far, the three ciphers introduced could all easily be cracked using frequency analysis and the Kasiski examination. Is there a cipher that is easy to implement yet difficult to break for a beginner cryptanalyst? An extremely popular and surprisingly powerful cipher is the book cipher. Essentially, the book cipher replaces a keyword with an entire book. Instead of replacing a letter for a letter or symbol in a systematic and mathematical way (such as a set shift number or using a tabula recta), the book cipher replaces letters for numbers that refer to a certain text within a book. As the only way to decode the message is to have the book, it is an extremely secure way of enciphering a message given that both parties have an identical copy of the book.

There are many variations of the book cipher. The most popular type is giving a page number, with the first letter of the page being the plaintext. A variant of this is giving a set of three numbers for every letter: the page number, the line number and the word number (or just two: page and line, then take the first letter). Ironically, this may be less secure at times as it may reveal that it is a book cipher. However, doing this for each letter makes the enciphering and deciphering process incredibly long and arduous.

A shortcut method is to refer to a word within a page (using the three-number set coordinates method described above) to shorten the ciphertext. Although this method is much easier in practice, it poses the challenge of finding a book that includes all the words in the plaintext, which may be difficult if the code is for military or espionage purposes.

Because of this, and the fact that both parties (or everyone in the ring) need identical versions of the book while not standing out too much, the most common books used are the dictionary (typically a famous version such as the Oxford Dictionary) or the bible (again, a standard version is used). These books are not only good because they incorporate a massive vocabulary, but they are also inconspicuous while being carried around in an enemy territory.

The book cipher is a very difficult code to crack for most people without advanced cryptanalysis training. Thus, the easiest way to crack is to deduce what book is the keytext. There are numerous ways to do this, but one way would be to cross-match the books of two known spies until common books are found. In the setting of spies in a foreign country, a book such as a traveller’s guide or phrasebook dictionary can be considered a likely target as it can be carried around easily while containing many words. Ergo, the secret behind cracking the book cipher is less about cryptography and more about using the science of deduction.

Posted in Science & Nature

Cryptography: Kasiski Examination

The Kasiski examination can be used to attack polyalphabetic substitution ciphers such as the Vigenère cipher, revealing the keyword that was used to encrypt the message. Before this method was devised by Friedrick Kasiski in 1863, the Vigenère cipher was considered “indecipherable” as there was no simple way to figure out the encryption unless the keyword was known. But with the Kasiski examination, even the Vigenère cipher is not safe anymore.

The Kasiski examination is based on the fact that assuming the number of letters of the keyword is n, every nth column is encoded in the same shift as each other. Simply put, every nth column can be treated as a single monoalphabetic substitution cipher that can be broken with frequency analysis. Ergo, all the cryptanalyst needs to do to convert the Vigenère cipher into a Caesar cipher is know the length of the keyword.

To find the length of the keyword, look for a string of repeated text in the ciphertext (make sure it is longer than three letters). The distance between two equal repeated strings is likely to be a multiple of the length of the keyword. The distance is defined as the number of characters starting from the last letter of the first set of strings to the last letter of the second set of strings (e.g. “abcdefxyzxyzxyzabcdef” -> “abcdef” is repeated” -> distance is “xyzxyzxyzabcdef” which is 15 letters). The reason this works is that if there is a repeated string in the plaintext and the distance between these strings is a multiple of the keyword length, the keyword letters will line up and there will be repeated strings in the ciphertext also. If the distance is not a multiple of the keyword length, even if there is a repeated string of letters in the plaintext, the ciphertext will be completely different as the keyword would not match up and be different.

It is useful recording the distance between each set of repeated strings to find the greatest common factor. The number that factors the most into all of these distances (e.g. 6 is a factor of 6, 12, 18…) is most likely the length of the keyword. Once the length of the keyword is found, then every nth letter must have been encrypted using the same letter of the keyword. Thus, by recording every nth letter in one string, you can obtain what is essentially a Caesar cipher. The Caesar cipher is then attacked using frequency analysis. Once a few of these strings (of different positions on the ciphertext) are solved, the keyword can be revealed by checking the shift key against a tabula recta (e.g. if a certain string of nth letters is found to have been shifted 3 letters each, then the corresponding letter in the keyword must be “D”, which shifts every plaintext letter by 3 in the Vigenère cipher). When the keyword is deduced, every message encrypted using that keyword can now easily be decoded by you.

Although the Kasiski examination appears to be complex, attempting to try it reveals how simple the process is. Thus, it is useful to try encrypting a message using the Vigenère cipher then trying to work out the keyword using the Kasiski examination. Much like the frequency analysis, it is an extremely useful tool in the case of needing to break a secret code.

Posted in Science & Nature

Cryptography: Vigenere Cipher

It has thus been proven that the Caesar cipher, the pigpen cipher and any substitution cipher can be simply broken using frequency analysis. The basis for this is that each letter or symbol can only represent a single letter, meaning that letter frequencies (e, t, a, o…) are directly translated onto the cipher language. Ergo, by making each letter represent more than one letter, the letter frequencies can be masked and an additional level of security can be added to the cipher. This is called polyalphabetic substitution and it is the basis for a type of cipher known as the Vigenère cipher.

The cipher was first conceived in 1553 by Giovan Battista Bellaso and has been improved since. It is famous for being rather simple to use despite the difficult to decipher it at a beginner’s level. This trait earned the cipher the nickname “le chiffre indéchiffrable”, which is French for “the indecipherable cipher”.

The Vigenère cipher can be thought of a stack of Caesar ciphers (essentially a cipher within a cipher), where each letter is shifted by a variable key (in a normal Caesar shift, every letter is shifted by the same key). This is achieved by the implementation of a keyword and a table called a tabula recta. A tabula recta is simply a grid made from 26 rows of the alphabet, each row of which is made by shifting the previous one to the left. This table essentially shows all the possible outcomes of a Caesar shift.

Now, let us try encoding a message using the Vigenère cipher. The message “attack at dawn” is encoded using the keyword “nothing”. Ideally, there should be no repeating letters in the keyword for the sake of security. Therefore, if there are any repeating letters, just remove the repeated letters (e.g. “crocodile” -> “crodile”). First, repeat the keyword until it matches the number of letters of the message (e.g. “attackatdawn” is aligned with “nothingnothi”). Then, use the tabula recta to encrypt the message. The rule of thumb is “key-row, message-column”, meaning that the row of the tabula recta starting with the letter of the key is matched against the column starting with the respective letter of the message. To take the first letter as an example, the key letter is “n” and the message letter is “a”. The letter corresponding to where the “n” row and “a” column meets is “N”. If this rule is followed for each letter, the encrypted message becomes: “NHMHKXGGRTDV”. Although it takes some effort to find each letter on the table, the message becomes “indecipherable” to a beginner cryptanalyst as frequency analysis becomes useless. For example, the repeating letter “H” can represent either “t” or “a”. The longer the keyword is, the more secure the Vigenère cipher becomes.

However, the Vigenère cipher is not indecipherable. Next, we will look at a cryptanalysis method called the Kasiski examination that attacks a polyalphabetic cipher such as the Vigenère cipher to gain access to the keyword.

Posted in Science & Nature

Cryptography: Pigpen Cipher

Another well-known substitution cipher is the “pigpen cipher” or “Freemason’s cipher”. As the name suggests, it was often used by Freemasons to encrypt their messages. However, as time has passed, it has become so well-known that it is not a very secure cipher at all.

The pigpen cipher does not substitute the letter for another letter, but instead uses a symbol that is derived from a grid-shaped key. The key is made of two 3×3 grids (#)(one without dots, one with dots) and two 2×2 grids (X)(one without dots, one with dots). The letters are filled in systematically so that each shape represents a certain letter (e.g. v=s, >=t, <=u, ^=v)

The cipher has many variations that attempt to throw off an attacker by rearranging the order of the grids or the letters. Thus, even if a cunning attacker picks up on the fact that the cipher is a pigpen cipher, they may use the wrong key and get a completely wrong message. Nonetheless, it is a useful skill to recognise the unique symbols of the pigpen cipher as it is a popular cipher used commonly in puzzles.

As with any substitution ciphers, frequency analysis and pattern recognition is the key to cracking the pigpen cipher.

Posted in Science & Nature

Cryptography: Caesar Cipher

One of the earliest known uses of cryptography can be traced back to ancient Rome. Julius Caesar was well-known for his use of a type of substitution cipher dubbed “Caesar cipher” or “Caesar shift”. The encryption is very simple: shift every letter a certain value down the alphabet (the value is known as the key). For example, Caesar used a key of 3 to encrypt his messages to his general, so the message “ATTACK AT DAWN” would be encrypted into “DWWDFN DW GDZQ” (use the scheme of a=0, b=1, c=2, d=3…).

Although it was an efficient encryption system in ancient times, since then it has been revised to be much more secure. The Caesar cipher has thus been demoted to the preferred code used by children and teenagers for basic decoding puzzles.

Due to the simplicity of the encryption, cracking the Caesar cipher is quite easy with the use frequency analysis, pattern recognition and brute force analysis. Brute force analysis can be used if the attacker knows that a Caesar cipher has been used. If that is the case, the message can be decrypted using every possible key (e.g. 1, 2, 3…) until a message that makes sense is acquired.