Jack Copeland Lectures – Københavns Universitet

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13. januar 2015

Jack Copeland Lectures


Visiting professor Jack Copeland gives two lectures on hypercomputation and Alan Turing

3th February 2015 13.00-15.00: Hypercomputation at CCC, Center for Communication and Computing, the Faculty of Humanities (Room 27.0.17)

4th February: 2015 15.15-17.30: Alan Turing: From Cracking Enigma to Deciphering the Mind, IVA, Birketinget 6 (Auditorium).


Hypercomputation is the computation of functions or numbers that cannot be computed in the sense of Turing's 1936 paper 'On Computable Numbers', i.e. cannot be computed with paper and pencil in a finite number of steps by a human clerk working effectively. It is often forgotten that, in 1936, a computer was not a machine at all, but a human being, a mathematical assistant who calculated by rote. This is the sense in which Turing used the term computer and its cognates, such as computable, in his 1936 paper; and the Turing machine (or as Turing called it, 'computing machine') is an idealization of the human computer.

A hypercomputer, on the other hand, is any information-processing machine, notional or real, that is able to achieve more than the traditional human clerk working by rote. Hypercomputers compute functions or numbers, or more generally solve problems or carry out tasks, that lie beyond the reach of the standard universal Turing machine of 1936. The additional computational power of a hypercomputer may arise because certain of the restrictions customarily imposed on the human computer are absent—for example, the restriction that data take the form of symbols on paper, or that all data be supplied in advance of the computation, or that the rules followed by the computer remain fixed for the duration of the computation. Or the additional power may arise because the machine has, among its repertoire of primitive capacities, one or more operations that no human rote-worker can carry out. All computation takes place relative to some set or other of primitive capacities, and the richer the capacities that are available, the greater the extent of the computable.

In this lecture I explore some simple logical models of hypercomputation. I also examine some apriori objections to the possibility of hypercomputation. Will hypercomputation ever be observed? I argue that this is an empirical question, whose answer is not yet known.

Turing: From Cracking Enigma to Deciphering the Mind, Abstract

At the turn of the millennium Time magazine listed Alan Turing among the twentieth century's 100 greatest minds, alongside the Wright brothers, Albert Einstein, DNA busters Crick and Watson, and the discoverer of penicillin, Alexander Fleming. Turing's achievements during his short life of 42 years were legion. Best known as the genius who broke some of Germany's most secret codes during the war of 1939-45, Turing was also the father of the modern computer. Today, all who click or touch to open are familiar with the impact of his ideas. To Turing we owe the brilliant innovation of storing applications, and the other programs necessary for computers to do our bidding, inside the computer's memory, ready to be opened when we wish. We take for granted that we use the same slab of hardware to shop, manage our finances, type our memoirs, play our favourite music and videos, and send instant messages across the street or around the world. Like many great ideas this one now seems as obvious as the cart and the arch, but with this single invention—the stored-program universal computer—Turing changed the world.

Turing was a theoretician's theoretician, yet like Leonardo da Vinci and Isaac Newton before him he also had immensely practical interests. In 1945 he designed a vast stored-program electronic computer called the Automatic Computing Engine, or ACE. Turing's sophisticated ACE design achieved commercial success as the English Electric Company's DEUCE, one of the earliest electronic computers to go on the market. In those days—the first eye-blink of the Information Age—the new machines sold at a rate of no more than a dozen or so a year. But in less than four decades, Turing's ideas transported us from an era where 'computer' was the term for a human clerk who did the sums in the back office of an insurance company or science lab, into a world where many have never known life without the Internet.

'Turing: From Cracking Enigma to Deciphering the Mind' is an introduction to Turing and his ideas, from the universal computing machine of 1936, through Bletchley Park and his post-war electronic digital computers, to his still highly controversial views on computability and the mind. His results on computability and uncomputability have implications regarding searching and Big Data (showing, for example, that the Algorithmic Search Completeness Thesis is untrue).

Jack Copeland, January 2015

Jack Copeland, Biography

Jack Copeland FRS NZ is Distinguished Professor in Humanities at the University of Canterbury, New Zealand, where he is Director of the Turing Archive for the History of Computing. He is also Honorary Research Professor of Philosophy at the University of Queensland, Australia, and in 2012 was Royden B. Davis Visiting Chair of Interdisciplinary Studies in the Department of Psychology at Georgetown University, Washington DC. His books include The Essential Turing (Oxford University Press), Colossus: The Secrets of Bletchley Park’s Codebreaking Computers (Oxford University Press), Alan Turing’s Electronic Brain (Oxford University Press), Computability: Turing, Gödel, Church, and Beyond (MIT Press), Logic and Reality (Oxford University Press), and Artificial Intelligence (Blackwell); and he has published more than 100 articles on the philosophy and history of computing, and mathematical and philosophical logic.

He is recognised as a leading authority on Turing's work, and in June of 2004, the 50th anniversary of Turing’s death, he delivered the first annual Turing Memorial Lecture at Bletchley Park National Museum and also lectured on Turing’s life and work at the Royal Institution of London. He received the Scientific American Sci/Tech Web Award for his on-line archive www.AlanTuring.net. He has been script advisor, co-writer, and scientific consultant for a number of documentaries on Turing. One of these, the BBC's Code-Breakers: Bletchley Park's Lost Heroes, won two BAFTAs (British Academy of Film and Television Arts awards) in 2012, and was listed as one of the year's three best historical documentaries at the 2013 Media Impact Awards in New York City. 

A Londoner by birth, Jack earned a B.Phil. with Distinction from the University of Oxford—where he was taught by Turing's great friend Robin Gandy—and followed by a D.Phil. in mathematical logic. Jack has been a visiting scholar at the University of California at Los Angeles, a visiting professor at the universities of Sydney, Aarhus, Melbourne, and Portsmouth, a senior fellow of the Dibner Institute for the History of Science and Technology at the Massachusetts Institute of Technology, and most recently Gastprofessor in the Departments of Philosophy and Computer Science at the Swiss Federal Institute of Technology (ETH Zurich) and, of course, Visiting Professor at IVA. He is a past president of the U.S.-based Society for Machines and Mentality and is the founding editor of the Rutherford Journal for the History and Philosophy of Science and Technology.

Oxford University Press published his latest paperback last month, a highly accessible biography of Turing titled Turing, Pioneer of the Information Age.