Somewhere at the edge of mathematics lurks a number so large that it breaks the very foundations of our understanding - and ...

<B>Why did you think of this?</B> To some extent, I'm masochistic. Recently I've been working on a paper that involves TMs and I wrote a small simulator to check my solutions. I'm bored; therefore, we ...

When he invented Turing machines in 1936, Alan Turing also invented modern computing. In 1928, the German mathematicians David Hilbert and Wilhelm Ackermann proposed a question called the ...

One of the problems with a classic Turing machine is the tape must be infinitely long. [Mark’s] Turing Ring still doesn’t have an infinite tape, but it does make it circular to save space. That along ...

Author's rendition of a basic Turing test set-up. Sitting in between two agents (one human and one machine), a person needs to interact with both agents and determine (correctly) which is a machine.

Most people probably don’t think of mathematics when they hear “busy beavers.” But these eager little animals symbolize one of the most amazing concepts of the knotty field: not everything can be ...