( Read more... )

The next instalment in this exciting saga of family feuds and cyberwarfare. Tybalt has sent an invitation email to Romeo, impersonating Juliet in order to tempt Romeo to reveal himself.

Romeo opens his mail and finds this message waiting for him:

From: “Juliet” juliet@capulet.net
To: “Romeo” romeo@montague.net
Subject: secret ( Read more... )

Some more on information theory. Last time I covered issues to do with the reliability of the ‘channel’, the medium used to transfer the data between sender and receiver. To summarise what was in the last post:

• Information is data transferred between sender and receiver, so that the receiver then learns something that they didn’t know before.
• All ( Read more... )

According to Darrell Huff, it’s easy to lie with statistics. But it’s just as easy to lie with any kind of science, for the same reason - there’s a lot of knowledge out there and most people aren’t familiar with the basics. So people can come up with intuitively plausible ideas like homeopathy using some quantum-theoretic means of healing, and many ( Read more... )

I occasionally listen to a podcast called Computational Complexity. They recently had an interesting blog post explaining a zero-knowledge proof for a Sudoku puzzle.

A zero-knowledge proof is an interesting beast. It involves two parties, the Prover (who knows something) and the Skeptic (who doesn’t). The Prover has to convince the Skeptic that ( Read more... )

I mentioned in my last post on computational models that a Turing machine is the pinacle of computational power. There is nothing that can be computed that can’t be computed by a Turing machine. The only limit is the set of rules (the states and transitions) used by the Turing machine.

But there’s one thing we haven’t really broached yet. One ( Read more... )

In my last post on computational models I finished with a question. I had introduced the concept of a finite state machine, and then a pushdown automaton - essentially a finite state machine with a simple memory. The memory was represented as a ‘stack’, where only the top item was visible.

My questions was - does adding more stacks to a system ( Read more... )

The general trend of this series of posts is about slowly adding features to the idea of a machine until it becomes as sophisticated as we can make. Last time I mentioned the finite state machine, the simplest possible abstraction of computation.

A finite state machine is nothing but a table of rules. It can only act on an input or not, and there ( Read more... )

It’s hard for most people to think about things abstractly. People understand abstractions only by generalising from specific examples, rather than learning the abstraction first. It’s difficult to say what the idea of a chair is, for example, but if you’ve seen enough examples you can form your opinion. You begin to generalise and so don’t make a ( Read more... )

If you were paying attention to the field of pseudoscience a couple of weeks ago you’ll remember the story of the maths teacher who revolutionised division by zero and without a by-your-leave was teaching it to secondary school pupils. Not only was he subverting the standard procedure of childhood education (by teaching his pet fantasies as the ( Read more... )