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Monday, October 24, 2022

The Enigma of Blackholes and the Master of Rubik’s Cube

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.

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.

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.

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.

Black Holes – Synonymous with the Name of Hawking

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.

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.

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.

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.

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".

All stamps and First Day Covers featured in this post are from my personal collection.