Enigma – Synonymous with the Name of
Turing
The word “enigma” refers to something or someone that is, or, who is, mysterious or difficult to understand. The Enigma Machine was thus, aptly named. By the beginning of the twentieth-century it had become necessary to mechanize encryption and in 1918 a German engineer, Arthur Scherbius, patented the Enigma Machine – a solution to fulfil the growing need for encryption. Originally this device was sold to banks, railway companies and other organizations that needed to communicate secret information. By the mid-1920s the German military had also started to use the Enigma Machine, with some technical variation from the commercial version of the device.
By World War II, this machine
was at the very heart of encryption techniques applied to many thousands of highly
sensitive coded messages transmitted by the German Armed Forces each day. These messages ranged from top-level signals,
such as detailed situation reports prepared by generals at the battle fronts, the
movement of troops and orders signed by Hitler himself, to even the important
minutiae of war such as weather reports and the inventories of the contents of
supply ships. Being able to access the information that was being transmitted was
not very difficult as these messages were transmitted as radio signals and were
easily detected. The critical step was to interpret the true substance of these
encrypted messages and this could only be done if they were first decoded.
The
Enigma Machine
Essentially,
the Enigma Machine is just a large circuit. When you type in a letter on the
Enigma Machine it completes a circuit and lights up another letter on a lamp-board.
The circuit comprises plugboards and several rotors. By configuring the
plugboards and rotors in a specific manner, an input letter being typed-in would
result in a different output letter of the alphabet being produced. The
permutations allowed by the plugboards and rotors enabled encrypted
combinations of words into the billions to be created. In the World War II scenario, the level of
complication was further compounded as each day the German Armed Forces would
change the relative positions of the plugboard connections and on alternate days, the
rotor orientations as well, with only sender and receiver knowing specific plugboard /
rotor positions applicable for that day. Thus, the task of deciphering these
messages, for the purposes of Allied military intelligence gathering, was
mammoth.
Polish
Efforts to Break Enigma
Enigma
was used by the German military throughout World War II. Therefore, breaking
the Enigma cipher became a top priority, first by the Polish, then later, by
the British and Americans. Polish
Intelligence initially tried to break the German Enigma using conventional code-breaking
techniques but to no avail. Driven by the imperative of trying to mitigate ever-threatening
German military tactical moves, they, uniquely among other nations at that
time, decided to try a mathematical approach. In 1932 a team of young
mathematicians was set up. It included Jerzy Rozycki, Henryk Zygalski and
Marian Rejewski. A great deal of the foundation work towards the eventual breaking
of the Enigma code (from a mathematical perspective), was undertaken by this team of
Polish researchers.
Breaking
Enigma During World War II
On 1
September 1939, Germany invaded Poland. World War II was now underway. It was now even more important to crack Enigma.
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Communications to the German battlefront were done via coded radio messages. The encryption and decryption of the coded messages were done by the Enigma Machine |
On 4
September 1939, the day after Britain declared war on Germany, Alan Mathison
Turing, a young English mathematician, computer scientist, and logician
reported to Bletchley Park, the wartime station of the Government Code and
Cipher School (GCCS). Turing, an individual of immense intellect, was to become
instrumental in the battle to decrypt messages generated by Germany using
Enigma. An alumnus of Cambridge University and Princeton University, he initially
helped adapt a device originally developed by the Polish researchers, to
create the “bombe”. The prototype model of his anti-Enigma "bombe",
named “Victory”, was installed in the spring of 1940 as he pitted machine
against machine to deliver results.
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First Day Cover from the United Kingdom showing the "Bombes" and honouring Alan Turing |
But the evolution of encryption in Germany was not static and it was left to Turing to discover a way to break into the vast torrent of messages suddenly emanating from a new, and much more sophisticated Nazi cipher machine. The British named the new machine “Tunny” and Tunny was the heart that pumped secure messages through the communication arteries that connected Hitler and the Military High Command in Berlin to the generals on the frontlines. Turing's breakthrough in 1942 yielded the first systematic method for cracking Tunny messages. His method was simply known at Bletchley Park as “Turingery” and the broken Tunny messages provided detailed knowledge of German strategy - information that changed the course of the war.
As early as 1943 Turing's machines were
cracking a staggering total of 84,000 Enigma messages each month - two messages
every minute. Turing also personally broke a form of Enigma used by the Nazi
U-boats preying on the North Atlantic merchant navy convoys. It was a crucial
contribution. These convoys set out from North American ports loaded with vast
cargoes of essential war supplies such as ammunition, fuel, food and even
troops destined for the front lines. But they never got to their British destination
ports. Instead, Nazi U-boats torpedoed and sank so many of these ships that
Churchill's analysts said Britain would soon be starving and predicted the war
could be lost.
The Close Call
"The only thing that ever really
frightened me during the war was the U-boat peril," Churchill would later divulge.
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Stamp of Sir Winston Churchill from the Island of Jersey |
Just in time, Turing and his group succeeded in cracking the U-boats' coded communications to their High Command in Berlin. With the co-ordinates and intentions of the U-boats revealed, Allied convoys could avoid this submarine menace in the vast Atlantic Ocean.Turingery was the seed for the
sophisticated Tunny-cracking algorithms that were incorporated in Tommy
Flowers' Colossus, the first large-scale electronic computer. Ten such
computers were built by the end of the war and Bletchley Park became the
world's first electronic computing facility.
Turing's work on Tunny was the third
of the three strokes of genius that he contributed to the attack on Germany's codes,
along with designing the bombe and unravelling the U-boat Enigma.
It is estimated that Turing’s work
reduced the duration of the war by about two years, thus saving countless
lives. Because of the highly classified
nature of his work, Turing was never accorded much recognition for his wartime
contributions. Sadly, he was eventually disgraced by the Government he served loyally.
Chemical Castration
In 1952, it was discovered that Alan Turing had started a relationship with Arnold Murray, a
19-year-old unemployed man. During an investigation, triggered by a burglary at
his residence, Turing acknowledged a sexual relationship with Murray.
Homosexual acts were criminal offences in the United Kingdom at that time and
both men were charged accordingly. Turing, on the advice of his brother and his own
solicitor entered a plea of guilty. The case, Regina v. Turing and
Murray was brought to trial on 31 March 1952. Turing was convicted
and given a choice between imprisonment and probation. His probation would be conditional
on his agreement to undergo hormonal physical changes designed to reduce
libido, a process now known as "chemical castration”. This harsh treatment
rendered Turing impotent.
Turing's conviction led to the removal of his security clearance and barred him from continuing with his cryptographic consultancy for the Government Communications Headquarters. Sadly, on 8 June 1954, Alan Turing's housekeeper found him dead at his home at 43 Adlington Road, Wilmslow, Cheshire. He had died the previous day. He was 41 years of age. An inquest determined that he had committed suicide through the ingestion of cyanide.
A person, whose work has been
estimated to have saved approximately fourteen million lives, in the end, could
not save his own. Society had its own codes and according to the law of the
day, Alan Turing had broken these codes to his own, eventually fatal, detriment.
For many years, Black Holes were an
astronomical enigma. Initially it was John Michell (25 December 1724 – 21
April 1793), an English natural philosopher and clergyman who provided
pioneering insights into a wide range of scientific fields including astronomy
and gravitation. Whilst he shares the
same birthday as Sir Isaac Newton, and having been born a year before Newton’s death,
Michell also studied at the University of Cambridge and is considered as "one
of the greatest unsung scientists of all time". In fact, he is the first
person known to have proposed the existence of black holes and the first
to have suggested that earthquakes travelled in seismic waves.
The
Postulation of John Michell and the Findings of Einstein
Michell
postulated the idea that if a star was massive enough, the velocity required to
escape the force of its gravity might need to be greater than the speed of
light. If this was the case, then the star would be a “dark star” as no light
could escape it. More than a century later, in 1916, Albert Einstein, one of
the Fathers of Black Holes, predicted the potential existence of these
black holes with his general theory of relativity and in 1916, Karl
Schwarzschild found the first modern solution of general relativity that would characterize a Black Hole.
What is a Black Hole?
A black hole is so named as it is a
region of spacetime where gravity is so strong that nothing, not even particles
or even electromagnetic radiation such as light, can escape it. The boundary
of no escape that envelopes a black hole is called the event horizon. The event horizon is an information
membrane that partitions those places of the Universe that we can see, and it
also serves to sequester those places of the Universe of which we cannot have
sight. Once across the perimeter of the event horizon, an object is absorbed
through the pull of its’ immense gravity, into the black hole.
Black holes were
long considered a mathematical curiosity and it was not until the 1960s that
theoretical research work showed they were a generic prediction of general relativity.
It was only in 1967 that the
term "Black Hole" was coined by American astronomer John Wheeler.
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Stamp from the Republic of Madagascar honouring John Wheeler who coined the phrase "Black Hole" |
Much research has recently been done in the field of black holes. Today we know that there is a black hole at the centre of our own Milky Way Galaxy. We also know how stellar black holes are formed and in 2019, the Event Horizon Telescope, or EHT produced the first image of a black hole. That object sits at the center of the M87 galaxy, about 55 million light-years from Earth. More recently, a constructed image of the black hole at the center of our galaxy was also developed and widely publicized. Again, it was the Event Horizon Telescope (EHT) Collaboration that delivered this image by combining images extracted from many EHT observations and creating a single image of the supermassive black hole at the center of our galaxy, called Sagittarius A*.
Stephen Hawking
The other Father of Black Holes is the
iconic British scientist, Stephen Hawking. In 1971, Hawking derived his black
hole theorem from Einstein’s theory of general relatively.
This theorem states that it is impossible for the surface area of a black hole
to decrease over time.
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The Fathers of Black Holes - Albert Einstein and Stephen Hawking featured together on this First Day Cover from the Isle of Man. The reverse side of the FDC features a message from Professor Hawking. |
To test out Hawking’s theory,
researchers analysed gravitational waves, or ripples in the fabric of
space-time, created 1.3 billion years ago by two behemoth black holes as they
spiralled towards each other at high speed. These were the first gravitational waves ever
detected in 2015 by the Advanced Laser Interferometer Gravitational-Wave
Observatory (LIGO), a laser beam that splits into two 2.485-mile-long (4
kilometer) paths, and is capable of detecting the slightest distortions in
space-time. By splitting the received signal into two halves — before and after
the black holes merged — the researchers calculated the mass and spin of both
the two original black holes and compared it with the new combined one. These numbers, in turn,
allowed them to calculate the surface area of each black hole before and after
the collision.
The test showed that the surface area of the newly created
black hole was greater than that of the initial two combined, confirming
Hawking's area law with a more than 95% level of confidence.
Having developed his black hole area
theory from the perspective of general relativity, Hawking then applied his mind to black holes from the angle of
quantum mechanics. From his work, a concept known as Hawking Radiation emerged —
where fogs of particles are believed to be emitted at the edges of black holes through quantum
effects (based on Heisenberg’s Uncertainty Principle). Hawking predicted that this
quantum phenomenon would lead black holes to gradually shrink and eventually, over
a period of time several times longer than the age of the Universe, cause them
to completely evaporate. This evaporation through radiation is thought to occur
over timescales long enough so as not violate the area law in the short term. But nonetheless there was a disconnect and this contradiction in the findings gave rise to more research and the concept of the black hole
information paradox emerged. This concept comes into play when the predictions of general
relativity and quantum mechanics are combined.
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Special Cover from India honouring the work of Stephen Hawking |
So, on the one hand, according to
Hawking’s black hole theory (which is based on the general relativity), the
surface area of a black hole should always be preserved but deferring to his own
findings from a quantum mechanics perspective, over a long enough time period,
the effects of Hawking Radiation would cause the black hole to evaporate, thus causing its surface area to reduce with his theories relating to the
information paradox being a possible bridge that attempted to close the gap.
Stephen
William Hawking is widely respected as one of the great theoretical
physicists of the modern era. Between 1979 and 2009, he was the Lucasian
Professor of Mathematics at the University of Cambridge, widely viewed as one
of the most prestigious academic posts in the world, a post that had once been
held by Sir Isaac Newton.
The
Onset of Amyotrophic Lateral Sclerosis
In
1963, at age 21, Hawking was diagnosed with an early-onset of a slow-progressing
form of motor neuron disease (Amyotrophic Lateral Sclerosis – ALS,
for short) that gradually, over the decades, paralyzed him. After the loss of
his voice, he communicated through a speech - generating device initially
through use of a handheld switch and eventually, activated by using a single cheek
muscle. Even though he was severely medically disadvantaged, Stephen Hawking realized
that the outcomes of the laws of physics were visible for all to see but the
laws themselves had not been completely discovered. And he worked relentlessly to define the laws that produced the observable outcomes.
Speedcubing
– Today,
Synonymous with the Name of Max Park
The Rubik Cube was a puzzle cum toy invented by an Hungarian architecture professor named Erno Rubik. The toy first became popular in the early 1980s and as its inventor, Rubik was the first person to solve the Cube. Apparently, Rubik spent a month struggling to unscramble it, if only to prove to himself that it could be done. Over the years, the time required to unscramble this cubic conundrum has reduced and global competitions are held to determine if new records may be created in this space.
According to information to be found in Wikipedia, Max Park was born on November 28, 2001, in California. When Park was two years old, he was diagnosed with moderate to severe autism. His parents, Miki and Schwan Park, were advised that he might need lifelong care. Max Park's motor skills were severely impaired because of his autism so his mother, Miki Park, taught Max how to solve a Rubik’s Cube. He began learning "speedcubing" and soon was performing at competitions. At his second competition, he came in at first place in the 6×6×6 event.
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Stamp commemorating the 1982 World Rubik Cube Tournament held in Budapest, Hungary |
Over the years, Park has set multiple world records in
solving the 4×4×4, 5×5×5, 6×6×6, and 7×7×7 cubes, and 3×3×3 one-handed. He
has won 374 events across many Rubik's cube competitions.
Apparently,
an average person takes more than 3 hours to solve the cube on a first try.
There are algorithms that may be learnt to help solve the cube faster. Like
some other Rubik's cube solving methods, one can solve the cube with a
two-look system (two algorithms) or a one-look system (one algorithm). The
two-look system has 20 potential algorithms to be learned, while the one-look
system has a whopping 493 potential algorithms. Hand and finger dexterity are also
required if one intends to compete.
Incredibly, Max Park currently ties the world record average for 3x3x3 of 4.86 seconds with Tymon Kolasinski.
Concluding
Comments
Alan Turing was an outlier who was finally constrained by the wishes and rules of the general population. Here was an individual who may well have changed the course of history through his wartime contributions but was eventually branded a criminal.
But the words on a plaque set below Turing’s statue currently located in Sackville Park, Manchester, begins to set the record straight, referring to him as a “Victim of Prejudice”. As values changed over many decades, it became necessary to act. In 2014, Queen
Elizabeth II officially pronounced Turing pardoned. The Queen's action was only
the fourth royal pardon granted since the conclusion of the Second World
War. Pardons are normally granted only when the person is technically
innocent and a request has been made by the family or another interested party. In the case of Turing's conviction, neither condition was met.
In
September 2016, the government announced its intention to expand this
retroactive exoneration to other men convicted of similar historical indecency
offences, in what is described as the Alan Turing Law.
The Alan Turing Law is
now an informal term for the law in the United Kingdom, contained in the Policing
and Crime Act 2107, which serves as an amnesty law to retroactively pardon
men who were cautioned or convicted under historical legislation that outlawed
homosexual acts. The law applies in England and Wales. The Bank of England further honoured Alan Turing when his image was included as part of a new STG 50 note which went into circulation in 2021, 67 years after his premature death.
Stephen Hawking lived with ALS for over 50 years.
Whilst his body deteriorated, his mind continued to evolve, and he increasingly
challenged himself to resolve the most complex problems of modern physics which
try to explain the biggest question of all – how was the Universe created?
He once said from the confines of a wheelchair that
transported his frail body for decades:
“We are just an advanced breed of monkeys
inhabiting a very minor planet, rotating around a very average star. But we can
understand the Universe. That makes us something special.”
As for Max Park, surely, he is the living example
of a quote from the movie “The
Imitation Game” which tells the story of the life and work of Alan Turing. The quote goes like this:
“Sometimes it’s the people no one imagines anything
of, who do the things that no one can imagine.”
The hallmarks of greatness and genius are to make those things which are difficult to do appear simple. Turing, Hawking and even Park – who would have ever imagined
their achievements given their personal challenges?
In the case of Turing, he may well have changed the course of history.
Stephen Hawking has helped us understand some elements of our creation.
And Max Park?
Max is most definitely an inspiration to the parents of children who are medically classified as "autistic" through his redefinition of this sometimes misunderstood word.
With that, I hope you are inspired by the music of Sia. The song is entitled "Never Give Up".
https://www.youtube.com/watch?v=NEsQfb4xWY0
All stamps and First Day Covers featured in this post are from my personal collection.