I would dare say that a majority of MOT readers know all about Alan Turing, and doubtless some know more than I do, but if there is such a thing as a Hero for me then one of mine has to be Alan.
Morning Open Thread is a daily, copyrighted post from a host of editors and guest writers. We support our community, invite and share ideas, and encourage thoughtful, respectful dialogue in an open forum.
This is a post where you can come to share what’s on your mind and stay for the expansion. The diarist is on California time and gets to take a nap when he needs to, or may just wander off and show up again later. So you know, it's a feature, not a bug.
Grab your supportive indulgence(s) of choice and join us, please. And if you’re brand new to Morning Open Thread, then Hail and Well Met, new Friend.
Not wanting to get too heavy into concepts I just barely understand myself, let’s just start off, uh, light?
Undoubtedly the most famous theoretical paper in the history of computing, "On Computable Numbers" is a mathematical description of an imaginary computing device designed to replicate the mathematical "states of mind" and symbol-manipulating abilities of a human computer. Turing conceived of the universal machine as a means of answering the last of the three questions about mathematics posed by David Hilbert in 1928: (1) is mathematics complete; (2) is mathematics consistent; and (3) is mathematics decidable.
Hilbert's final question, known as the Entscheidungsproblem, concerns whether there exists a definite method—or, in the suggestive words of Turing's teacher Max Newman a "mechanical process"—that can be applied to any mathematical assertion, and which is guaranteed to produce a correct decision as to whether that assertion is true. The Czech logician Kurt Gödel had already shown that arithmetic (and by extension mathematics) was both inconsistent and incomplete. Turing showed, by means of his universal machine, that mathematics was also undecidable.
To demonstrate this, Turing came up with the concept of "computable numbers," which are numbers defined by some definite rule, and thus calculable on the universal machine. These computable numbers, "would include every number that could be arrived at through arithmetical operations, finding roots of equations, and using mathematical functions like sines and logarithms—every number that could possibly arise in computational mathematics" (Hodges, Alan Turing: The Enigma [1983] 100). Turing then showed that these computable numbers could give rise to uncomputable ones—ones that could not be calculated using a definite rule—and that therefore there could be no "mechanical process" for solving all mathematical questions, since an uncomputable number was an example of an unsolvable problem.
--HistoryofInformation.com
Shorter: there can exist no algorithm (computer program) that can unequivocally decide whether some posited mathematical statement is either true or false or whether some posited equation even has a solution in the first place.
Way shorter: computers can never know everything.
What really came out of Turing’s theoretical paper, though (to a layperson like me), was the concept of a machine that could crunch numbers in any mathematical function, meaning that if you could mathematically quantify or symbolically represent a statement then you could write rules for the machine to process those quantified logical statements, i.e. what we know today as computer code, or programs. Turing never proposed actually building such a machine. He just wanted to answer the Entscheidungsproblem, and he did. I’ll recapitulate: can there exist a step-by-step process, a set of rules, that is guaranteed to return a correct decision regarding the truth (or of course, falsity) of any mathematical assertion? Turing proved such a process cannot exist.
That was 1936. World War Two was only a few years off, and while it may be true that one can never say “without [blank], we would have never won the war”, in my reasonably studied opinion without Turing and his contributions to cracking the German message encryption machine known as Enigma, the war would sure have taken a lot longer for the Allies to win and hundreds of thousands more people would have died and the destruction to the planet would have been orders of magnitude larger.
An Enigma machine is a famous encryption machine used by the Germans during WWII to transmit coded messages. An Enigma machine allows for billions and billions of ways to encode a message, making it incredibly difficult for other nations to crack German codes during the war — for a time the code seemed unbreakable. Alan Turing and other researchers exploited a few weaknesses in the implementation of the Enigma code and gained access to German codebooks, and this allowed them to design a machine called a Bombe machine, which helped to crack the most challenging versions of Enigma. Some historians believe that the cracking of Enigma was the single most important victory by the Allied powers during WWII.
…
Alan Turing and Gordon Welchman designed a machine called the Bombe machine which used electric circuits to solve an Enigma encoded message in under 20 minutes. The Bombe machine would try to determine the settings of the rotors and the plugboard of the Enigma machine used to send a given coded message.
The standard British Bombe machine was essentially 36 Enigma machines wired together, this way, the Bombe machine would simulate several Enigma machines at once. Most Enigma machines had three rotors and to represent this in the Bombe, each of the Enigma simulators in the Bombe had three drums, one for each rotor.
--brilliant.org
This machine (and a whole lotta copies of it, over two hundred)
was necessary in order to crack this one:
*****
I’m writing this diary using a Turing Universal Machine. To echo what I wrote regarding WWII, while it may be true that one can never say “without [blank], we would not have personal computers or the internet today”, in my reasonably studied opinion without Alan Turing having written that paper in 1936 it would have at least taken a lot longer to get to where we are today with computers. Others deserve great credit, of course: among many other primary pioneers of the computer age Claude Shannon came up with information theory, giving us the binary system (only two numbers, One (1) and Zero (0)) that all computers run on today; William Shockley, John Bardeen, and Walter Brattain gave us the transistor which led to the integrated circuit chip which is the heart of all computers; Paul Baran, Joseph C.R. Licklider, and Robert (Bob) Taylor came up with packet switching without which transmission of the billions and billions of binary digits (bits and bytes) across wires and now fiber optic cables worldwide would not be possible.
What makes Alan Turing a true Hero to me, though, was that he deserved medals and accolades for what he did to save lives (the Official Secrets Act prevented that at the time; do go to this link to read about the women who were also immeasurably important in the code-cracking at Bletchley Park) and instead he was criminalized and forced to undergo chemical castration for being born who and what he was as a human: gay. To some extent, that dreadful mistake has now been rectified:
After the war, Turing worked at the National Physical Laboratory, where he designed the Automatic Computing Engine (ACE), one of the first designs for a stored-program computer. In 1948, Turing joined Max Newman's Computing Machine Laboratory, at the Victoria University of Manchester, where he helped develop the Manchester computers and became interested in mathematical biology. He wrote a paper on the chemical basis of morphogenesis and predicted oscillating chemical reactions such as the Belousov–Zhabotinsky reaction, first observed in the 1960s. Despite these accomplishments, Turing was never fully recognised in Britain during his lifetime because much of his work was covered by the Official Secrets Act.
Turing was prosecuted in 1952 for homosexual acts. He accepted hormone treatment with DES, a procedure commonly referred to as chemical castration, as an alternative to prison. Turing died on 7 June 1954, 16 days before his 42nd birthday, from cyanide poisoning. An inquest determined his death as a suicide, but it has been noted that the known evidence is also consistent with accidental poisoning.
Following a public campaign in 2009, the British Prime Minister Gordon Brown made an official public apology on behalf of the British government for "the appalling way [Turing] was treated". Queen Elizabeth II granted a posthumous pardon in 2013. The term "Alan Turing law" is now used informally to refer to a 2017 law in the United Kingdom that retroactively pardoned men cautioned or convicted under historical legislation that outlawed homosexual acts.
Turing has an extensive legacy with statues of him and many things named after him, including an annual award for computer science innovations. He appears on the current Bank of England £50 note, which was released on 23 June 2021, to coincide with his birthday. A 2019 BBC series, as voted by the audience, named him the greatest person of the 20th century.
--wikipedia
Happy Anniversary, Alan.