A Madman Dreams of Turing Machines

Kurt Goedel and Alan Turing  Highlight Perimeter Institute Lecture

at the Bruce County Museum and Cultural Centre on Wednesday May 14, 2008 at 2 pm in the Bruce Theatre. Donations appreciated...

Two of the Greatest Mathematicians of all time are highlighted in this engaging lecture by Janna Levin  Both considered eccentric to an extreme, these men have had a vast influence on 21st Century thought ... in fact .... how we think.

Kurt Goedel

One of the most significant logicians of all time, Goedel's work has had immense impact upon scientific and philosophical thinking in the 20th century, a time when many, such as Bertrand Russell, A. N. Whitehead and David Hilbert, were pioneering the use of logic and set theory to understand the foundations of mathematics.

Goedel is best known for his two incompleteness theorems, published in 1931 when he was 25 years of age, one year after finishing his doctorate at the University of Vienna. The more famous incompleteness theorem states that for any self-consistent recursive axiomatic system powerful enough to describe the arithmetic of the natural numbers (Peano arithmetic), there are true propositions about the naturals that cannot be proved from the axioms. To prove this theorem, Goedel developed a technique now known as Goedel numbering, which codes formal expressions as natural numbers.

 

(next column)

(continued)

Alan Turing

Turing is often considered to be the father of modern computer science. Turing provided an influential formalisation of the concept of the algorithm and computation with the Turing machine. With the Turing test, he made a significant and characteristically provocative contribution to the debate regarding artificial intelligence: whether it will ever be possible to say that a machine is conscious and can think. He later worked at the National Physical Laboratory, creating one of the first designs for a stored-program computer, although it was never actually built. In 1948 he moved to the University of Manchester to work on the Manchester Mark I, then emerging as one of the world's earliest true computers.

During the Second World War Turing worked at Bletchley Park, Britain's codebreaking centre, and was for a time head of Hut 8, the section responsible for German naval cryptanalysis. He devised a number of techniques for breaking German ciphers, including the method of the bombe, an electromechanical machine that could find settings for the Enigma machine.