# Alan Turing: Who was Alan Turing and what did he do in the War?

An Interview with Alan Turing: Who was Alan Turing and what did he do in the War?

Michael F. Shaughnessy –

1) In a recent movie, Alan Turing was featured as a key person involved in World War II. First of all, what do we know about his early life and childhood?

Turing’s mother, Ethel, was living in London, England when her son Alan Turing was born in 1912. Turing’s father, Julius, had a temporary leave of absence from his position with the Indian Civil Service (ICS) in British India, so he did not miss the arrival of his second son.

Because of his commitment to ICS, Julius was obligated to live in India and Ethel chose to accompany him while Alan and his brother John resided in Hastings, England with a retired army couple. The Turing brothers interacted with their parents only on occasional visits. There was not a regular, biological parental presence.

2) Where did he go to school?

It appears that Turing did not have much continuity and stability during his youth where education is concerned. At the age of six, Turing attended St. Michael’s school. Four years later, he was admitted to Hazelhurst Preparatory School in Sussex, England. By the age of 13, Turing was off to yet another boarding school. This new school was located in Dorset called the Sherborne School. Turing rode his bicycle 60 miles to attend the school on account of the 1926 General Strike in the United Kingdom. Though the strike lasted only nine days, it altered transportation and industry alike. Millions of workers went on strike, making it impossible for young Turing to rely on public transportation to chauffer him to the Sherborne School. He must have been highly motivated to attend that school to ride such a long distance, at such a young age, all by himself.

While attending the Sherborne School, Turing apparently did not perform well in the classics (literature), but was quite talented with the math and science curriculum. One of his teachers remarked that he showed extraordinary talent in the topics he loved, solving advanced mathematical problems despite lacking knowledge of calculus. Turing apparently was exposed to some of Einstein’s work and not only understood it, but also comprehended Einstein’s questioning of Newton’s laws of motion. Such an achievement requires a profound understanding of the subject matter.

Turing spent his undergraduate years at King’s College, in Cambridge. It may not be surprising that he was brilliant in mathematics. Turing proved the central limit theorem for his dissertation. Upon its completion, he was elected a fellow at King’s College.

In 1938, Turing earned his PhD from Princeton University in New Jersey. Turing researched mathematics and cryptology at the Institute for Advanced Study in Princeton. One of his accomplishments while there includes constructing three of four stages of an electromechanical binary multiplier.

After graduation, Turing found employment back in Cambridge at the Government Code and Cypher School (GC-CS). It is interesting to note that Turing was offered a postdoctoral position to work with John von Neumann, but headed back to England instead.

3) Mathematical biology—how do these two fit together and what were his contributions?

Mathematical biology combines the academic disciplines of mathematics with biology. Mathematical biology allows for reasoning across diverse fields of study, thus enabling a wide array of applications. Sometimes this field is referred to as biomathematics to emphasize the mathematical side. At other times, it is referred to as theoretical biology to emphasize the biological side. By combining the two disciplines, one can use the quantitative qualities of mathematics when predicting possible outcomes for experiments. New techniques for experimentation have been developed by using mathematical biology.

4) ACE—what does it stand for and why is it important?

Turing designed an electronically powered stored-program computer. He dubbed it the Automatic Computing Engine (ACE). The unique feature of ACE was that it functioned using an early form of programming language. Because of the complexity of required engineering work, a Pilot ACE version was constructed in 1950, which used punch cards. See Figure 1.

Figure 1

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The idea for creating ACE came from Turing’s theoretical work “On Computable Numbers” and his German military code-breaking work at Bletchley Park. Bletchley Park was the main location for British codebreakers during World War II. The machine is now referred to as the Universal Turing Machine.

During World War II, Turing was a prominent contributor in the breaking of German encryptions. An Enigma machine, consisting of electro-mechanical rotors, was used to protect business-related, political, and armed forces communications. See Figures 2 and 3.

Figure 2

Figure 3

Turing designed an electromechanical machine that could help break Enigma more efficiently. This machine was named Bombe. He also undertook another problem involving German naval Enigma. Turing’s development of Hut 8 had a special feature incorporated into its design that he called the ban. This ban could eliminate certain arrangements of the Enigma rotors. This was critical because it significantly reduced the time needed to test settings on the bombes.

5) Now, please tell us the definition of an algorithm and why it is important to mathematicians and its implications for Turing’s work?

A mathematical algorithm is a procedure or formula for solving a mathematical problem, based on performing a sequence of indicated actions. Turing used an algorithm to simulate a chess game. I’ll discuss that in more detail later in the interview.

The code-breaking work Turing participated in during World War II also used machines programmed with algorithms. The Enigma rotors were intricate and sophisticated. The British bombe was created out of necessity to decrease the possible wheel orders and scrambler positions that required additional investigation, down to a more practical number. After all, there was no time to squander with this imperative project.

The ACE and the Pilot ACE are other examples of electronic stored-program computers that used algorithms to function. Procedures for handling subroutines were included in the design of ACE, but became too daunting a task to build in the fashion that Turing originally envisioned.

6) Morphogenesis—is this more scientific than mathematical- and how is it relevant to his work?

Turing was interested in studying the formation of organized patterns and varying shapes in biological organisms, known as morphogenesis. He was especially interested in plants, more specifically, their structures in relation to the Fibonacci numbers. The arrangement of leaves on a plant stem is known as phyllotaxis. Turing studied this pattern in nature and learned that a repeating spiral can be characterized by a fraction describing the angle of how the leaves spiral along the stem, leaf per leaf. For example, a “two-ranked leaf arrangement,” consists of either opposite or alternate leaf arrangements where the leaves on a stem are arranged in two upright columns on opposite sides of the stem. See Figure 4.

Figure 4

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If one examines the angle of rotation of leaf formation about the stem of certain plants, the Fibonacci sequence emerges: 1, 1, 2, 3, 5, 8, 13, 21, 34, etc. With the **alternate** two-ranked leaf arrangement, leaves have an angle of ½ of a full rotation, such as the Elm. Here are some other fractions associated with adjacent leaves on the stalk of certain plants: 1/3 for beech and hazel trees, 2/5 in oak and peach trees, 3/8 in sunflowers, roses, poplar trees, and pear trees, and 5/13 in willow and almond trees.

One might notice that both the numerator and denominator of these angles consist of a Fibonacci number. What may be even more astonishing about the relationship between the numerator and denominator values is that the numerator contains a Fibonacci number from a certain place in the Fibonacci sequence and the accompanying denominator’s value is two more places down the Fibonacci sequence.

Turing’s theory about the rotation of leaf formations involved chemical reactions dispersing across space. He demonstrated these biochemical reactions with mathematical equations, whereupon he showed a catalyst being required for a certain chemical reaction to take place. In another case, the chemical reactions yielded a catalyst and an inhibitor that delayed the production of the catalyst. Turing proposed that if the catalyst and the inhibitor circulated through the receptacle at different rates, then one could have some sections where the catalyst took over and some where the inhibitor did. Turing worked out, by hand, all the necessary calculations. His only option for working out the calculations was with linear estimates, as computers were not readily available. Turing’s work successfully produced evidence of the distribution of two different chemical signals.

The Fibonacci numbers are not exclusively associated with leaves. They are also found on the Chinese rose. See figure 5.

Figure 5

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The discovery of the structure of DNA in 1953 made it possible to comprehend the mechanisms involved in actual organisms. Thus, the development of molecular biology and biochemistry commenced.

7) I have read that he is somehow connected to that very annoying CAPCHA thing that pops up and causes me undue consternation. Did he really have something to do with this?

CAPTCHA stands for **C**ompletely **A**utomated **P**ublic **T**uring test to tell **C**omputers and **H**umans **A**part. It is used to pose a question, which requires a response in order to determine if the computer user is in fact a human. An example of this challenge-response test can be seen in Figure 6.

Figure 6

https://captcha.com/images/help/php/cakephp/basicsample.png

The CAPTCHA test is actually the reverse of what Turing developed in 1949. While working at the Victoria University of Manchester, Turing continued his work on abstract mathematics. He was focused on the problem of artificial intelligence and suggested a trial that became known as the Turing test. Turing wanted to establish guidelines for machines to be called “intelligent.”

8) And, was he really involved in Computer chess programs?

Once again, we are talking about an algorithm. Turing developed an algorithm that simulated a chess game. This program did not run on an actual computer; however, he created a notebook of sorts that required the user to perform tasks by going to specified pages in the notebook based on decisions the user makes and then moving the chess pieces on a chessboard.

9) My understanding is he won many awards and also had a number of things named in his honor- tell us about a few–

Turing won prizes for research, had buildings and memorial statues named after him, and there is even an annual conference in Istanbul named “Turing Days.”

Perhaps some of the more special or meaningful awards Turing has been honored with include the following: 1) Turing is a recipient of the Order of the British Empire shortly after World War II for his contributions at Bletchley Park. 2) Princeton University named Turing the second most significant alumnus in the history of the school. 3) In 1936, he won the Smith’s Prize for outstanding progress in mathematics. 4) In 1982, the Turing was memorialized with his own programming language. It was developed at the University of Toronto.

10) What have I neglected to ask?

Back in 2012, the Turing Centenary Advisory Committee (TCAC) coordinated the Alan Turing Year. This event commemorated the 100^{th} Anniversary of Turing’s birth. A program filled with a year’s worth of events honoring his life and achievements was scheduled.

Google even participated by developing an interactive doodle where visitors were invited to convert the instructions of a Turing Machine to Baudot-Murray code.

There is also an Alan Turing edition of Monopoly available. A collaboration between the Bletchley Park Trust and Winning Moves Games made this fun tribute possible.