What is the Universal Turing Machine?

The Universal Turing Machine is also a Turing Machine, in the sense that it satisfies the Formal Definition of a Turing Machine. Just like any other Turing Machine, it also reads in the data that's on the paper tape, and when it finishes running, it writes the answer on the paper tape.

However, it is also a very special Turing Machine. It is a Turing Machine that can do whatever any other Turing Machine can do!

The Universal Turing Machine that was designed by Sir Roger Penrose (and which is also available as one of the sample Turing Machines included in the Excel file you can download from the Home page of this website) expects the data on the paper tape to first consist of a Turing Machine Number followed by the separator 111110 followed by some data.

When the Universal Turing Machine runs, it does the same thing with the data (that is to the right of the separator 111110) that would be done by the Turing Machine whose Turing Machine Number is on the tape (just to the left of the separator 111110).

It took the genius of Alan Turing to realize that something like this was even possible, and he explained how it can be done in his seminal paper of 1936. This idea played a role in the development of the "stored program concept" that is used by all computers today.

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The Universal Turing Machine also has a Turing Machine Number associated with it. (After all, the Universal Turing Machine is a Turing Machine too.)

When Sir Roger Penrose wrote The Emperor's New Mind (Oxford University Press, 1989), he wrote out that entire number in binary on pages 93 through 96 in this book. This binary number is 5,495 digits long! He also acknowledges his gratitude to David Deutch for converting this number to denary and lists it on page 74 of his book. This denary number is 1,654 digits long!

To the best of my knowledge, this is the first time anyone actually wrote down the Turing Machine Number of the Universal Turing Machine. I think that this itself is a great accomplishement!