Subscribe now

Technology

How Alan Turing found machine thinking in the human mind

Turing's youthful bid for fame proved a great mathematician wrong – and accidentally created the modern computer

By Jonathon Keats

29 June 2016

Turing machine

Turing’s theoretical machines were turned into room-sized reality

Mark Dunn / Alamy Stock Photo

IN 1935, Alan Turing set out to build a reputation by outflanking the world’s leading mathematician. Turing was 22 years old, and a new fellow at Cambridge. His target, David Hilbert, was the venerated University of Göttingen professor who had single-handedly set the research agenda for 20th-century mathematics.

New Scientist Default Image

Hilbert was no match for the British upstart. In his book Turing’s Vision, Chris Bernhardt deftly shows how Turing dashed one of Hilbert’s great ambitions with a masterful proof – in the course of which he inadvertently invented the modern computer.

The title of Turing’s paper, “On Computable Numbers, With an Application to the Entscheidungsproblem” (which means “decision problem”), is hardly inviting, and reading it takes advanced training. This may explain why, as Turing’s fame exploded, most popular writing focused on his wartime codebreaking, his post-war writing on artificial intelligence – or his persecution and prosecution for being gay and posthumous royal pardon.

But what Bernhardt’s book lacks in drama, it makes up for in lucid explanation. Turing’s Vision allows careful readers to appreciate the proof that made Turing’s name and, as a bonus, to understand the basics of modern computers.

The Entscheidungsproblem was part of Hilbert’s work to show that the basic axioms of mathematics are logically consistent. To that end, Hilbert sought an algorithm – a computational procedure – that would indicate whether a given mathematical statement could be proved from those axioms alone. Turing decisively showed that there was no such algorithm.

“Turing proved that there was no mechanical set of rules for the solutions of all mathematical problems“

To do that, Bernhardt explains, Turing had to first establish a working definition for the term algorithm – to define what it means to compute. Turing looked at human “computers” – people who made computations. The task involves writing symbols on paper, he noted. “The behaviour of the computer at any moment is determined by the symbols… he is observing and his ‘state of mind’.”

Breaking down apparently complex cogitation into simple arithmetical procedures, Turing made computation explicit and eliminated the human element. “Turing’s fresh insight was to define algorithms in terms of theoretical computing machines,” writes Bernhardt. “Anything that can be computed can be computed by a Turing machine.”

That’s why the machines were central to Turing’s paper. To show there were algorithms that Turing machines would run indefinitely and inconclusively was a way of showing Hilbert was mistaken. Turing proved “that there were questions that were beyond the power of algorithms to answer”. His triumph was spectacular, and devastating to those who believed (as Hilbert did) that all problems could be solved.

Yet as crucial as the theoretical machines were to Turing’s proof, they turned out to have even more impact in their own right, providing a conceptual model for modern computers. The influence was direct, informing John von Neumann’s pioneering 1945 design for electronic computers, and the room-sized machines that applied his architecture. Like Turing’s machines, the computers used ones and zeroes to encode programs and data. This remains essential to high-level languages and networks, so in learning about Turing machines, readers pick up principles of computer science.

There are also philosophical ramifications today. Having based computers on human behaviour, Turing noted that people are really Turing machines. Computers are our mirrors: whether we marvel or shudder at the latest AI, we’re merely looking at ourselves.

Turing’s Vision: The birth of computer science

Chris Bernhardt

MIT Press (Buy from Amazon*)

This article appeared in print under the headline “Are we Turing machines?”

(*When you buy through links on this page we may earn a small commission, but this plays no role in what we review or our opinion of it.)

Topics:

Sign up to our weekly newsletter

Receive a weekly dose of discovery in your inbox! We'll also keep you up to date with New Scientist events and special offers.

Sign up