Alan Turing’s legacy: computers, AI and queer mathematics
A slate statue of mathematician Alan Turing at Bletchley Park, Milton Keynes, UK.
(Photo credit: lenscap50 / Adobe Stock )
The Turing Test for whether a machine can ‘think’ is as relevant in today’s world of rapid AI adoption as it was when it was first outlined in the 1950s.
Its 75th anniversary is the perfect time to reflect on Alan Turing as a mathematician, computer scientist, and LGBTQIA+ icon. It is also an opportunity to celebrate the people who are carrying his legacy forward.
The 1930s Turing machine
Mathematicians in the early 20th century had a lofty ambition to make all of mathematics computable - ideally you could build a machine that, given any mathematical statement, would tell you whether it was true or false.
Their plan was upended in the 1930s when Kurt Gödel showed there were mathematical statements that could never be logically proven or disproven. Shortly after, Alan Turing showed that there were fundamental and impassable limits to computation.
Turing's method still permeates mathematics and computer science today.
Essentially, he described an ingenious abstract model of a computer, a machine that could read and write information to a tape (its memory), moving back and forth along the tape according to what it read.
He then made a simple and ingenious argument that, if such a machine could decide whether another process could terminate, one could create a logical paradox by asking the machine to analyse itself.
The fact that Turing did this work in the 1930s before computers existed is remarkable.
Props from the The Imitation Game at Bletchley Park. The film was based on a biography of Alan Turing.
(Photo credit: lenscap50/Adobe Stock)
Breaking wartime codes
Some of Turing's most famous work was in cryptanalysis, the mathematical art of codebreaking. He was a central figure in breaking the Enigma, the German cipher machine used (and frequently upgraded) before and during World War II.
The 20th century was the first time cryptographers used machines in a serious way to encrypt messages using an ever-changing cipher with vast numbers of possible cryptographic keys, making linguistic and statistical codebreaking techniques useless.
Mathematicians rose to the machine challenge. As the war raged, Turing was central to the development of cryptological ‘bombes’, mechanical devices that made logical deductions to identify potential cryptographic keys.
These extraordinary machines gave the Allies crucial intelligence in the battle against German U-boats in the Atlantic, and arguably significantly shortened the war.
The question of thinking machines
After the war, Turing turned his interest to what we now know as artificial intelligence.
In a pioneering essay published in 1950, he asked, ’Can machines think?’. Instead of arguing over what it meant to think, he took the approach of describing an explicit way to measure it.
He called it the ‘imitation game’, and we now know it as the Turing test. A machine passes the test if, using only text-based conversations, a human examiner cannot tell the machine apart from a human.
Turing argued that a machine would likely be able to pass his test within 50 years and gave some concrete ideas on how to build such a machine.
Today as we often find ourselves struggling to determine what content is generated by humans versus AI, Turing's predictions do appear to have come to pass.
His essay makes for a very interesting read 75 years on, given what we know now, and still offers up significant food for thought.
Alan Turing on the £50 note.
(Photo credit: Abdul/Adobe Stock)
A beacon for visibility
To me personally, the legacy of Alan Turing is not only his mathematics (which can be seen throughout much of my own research), but also his visibility as an LGBTQIA+ mathematician.
In the 1950s, when homosexuality was illegal in Britain, he was convicted of ‘gross indecency’, stripped of his security clearance, and given a choice between jail or the injection of drugs referred to as chemical castration.
He died at the age of 41 of cyanide poisoning, for reasons that remain subject to speculation today.
Moving forward to the 21st century, he was pardoned by Queen Elizabeth II in 2013, and in 2017 a broader ‘Alan Turing law’ was enacted to automatically pardon others with similar convictions. Now Turing is on the UK’s 50-pound note.
LGBTQIA+ scientists are now more visible than ever.
An event to honour Alan Turing and the 75th anniversary of the Turing Test at UQ also celebrated LGBTQIA+ researchers in Science, Technology, Engineering, and Mathematics (STEM) and there are dedicated global conferences in geometry and topology.
Alan Turing has given us an amazing legacy to build on.
Scroll through images from the UQ event marking the 75th anniversary of the Turing Test.
Professor Benjamin Burton delivers the public lecture: Some Very Queer Mathematics.
"Marking the Turing Test anniversary wasn’t just about history; it was about visibility. I wanted LGBTQIA+ mathematicians to look around and see that our community is larger, prouder, and more present than many of us realise," Dr Matthew Holden, UQ School of Mathematics and Physics.
"Alan Turing showed that ideas outside the mainstream can change the world. Our work in AI follows that spirit, translating ecological knowledge in every language, including voices often ignored in conservation science," Dr Violeta Berdejo Espinola, Postdoctoral Research Fellow, Centre for Biodiversity and Conservation Science.
"Turing's work is integral to our modern understanding of algorithms and computers. Within my work I find algorithms for essentially solving Sudoku puzzles, and this wouldn't be possible without the computational power we have today. The story of Alan Turing's life is a reminder to us all that we never know what impact our work and actions will have in the future," Tara Kemp, PhD candidate in the UQ School of Mathematics and Physics.
"People forget that Alan Turing did some biology. He did fundamental work on pattern formation: how leopards get their spots and how zebras get their stripes," Associate Professor Simone Blomberg, School of the Environment.
Professor Benjamin Burton is from UQ's School of Mathematics and Physics. His public lecture on Alan Turing is available on YouTube.
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