This document discusses Alan Turing's ideas about computation and Turing machines. It proposes building a Turing machine emulator using Lego to explore Turing's ideas. Turing machines provide a precise definition of computation, and Turing showed that a universal Turing machine could compute any computable sequence, meaning a single machine could emulate all others. Turing also introduced the idea of programs as data that could be used as input for other programs.

1. Presented by Melvin Zhang
melvinzhang@gmail.com
@melvinzhangzy
Build a Turing Machine emulator
to explore Turing’s great ideas

2. Lego Turing Machine

4. A precise definition of
computation

5. Alonzo Church
Computation = λ Calculus
Church Thesis (Apr 1936)

6. Kurt G¨odel
“Thoroughly unsatisfactory”

7. Alan Turing

8. http://www.kurzweilai.net/passing-of-the-typewriter

9. Computation = Turing Machine
Turing’s Thesis (Nov 1936)

10. Kurt G¨odel
“That this really is the correct
definition of mechanical
computability was established
beyond any doubt by Turing.”

12. A universal machine

13. “It is possible to invent a
single machine which can be
used to compute any
computable sequence.”

14. “If it should turn out that the basic logics of a machine
designed for the numerical solution of differential equations
coincide with the logics of a machine intended to make bills for
a department store, I would regard this as the most amazing
coincidence that I have ever encountered.” –
Howard Aiken in 1956

15. http://www.rdrop.com/ half/General/UTM/UTMStateTable.html

16. Program = Data

17. Automatic Computing Engine,
proposed in 1946 and built in 1950

18. Turing’s Great Ideas:
• Turing machines as a model for computation
• A single machine can emulate all others
• Programs as data for other programs

19. Turing’s Great Ideas:
• Turing machines as a model for computation
• A single machine can emulate all others
• Programs as data for other programs
Further readings: