Category Archives: Uncategorized

The P versus NP conjecture essentially asks whether any problem whose solution can be easily verified can also be easily solved. Here, ‘easily’ technically means ‘computed in polynomial time on a Turing machine’. If you think for a moment, it … Continue reading →

Feeling that Complex Projective 4-Space isn’t sufficiently seasonal, I was compelled to alter the colour scheme of the banner to reflect the fact that today, the 31st October, is All Hallows’ Eve, popularly abbreviated to Hallowe’en. Anyway, I actually prefer … Continue reading →

Quite a lot of interest originated from the following puzzle of unknown origin: Given two pieces of rope which burn in precisely 1 minute, time an interval of 45 seconds (3/4 minutes). The rope is not necessarily uniform, so you’re … Continue reading →

We’re quickly approaching Ebenezer Scrooge’s favourite time of the year, Greenwich Mean Time. This brief post serves as a reminder to anyone who has forgotten about the temporal adjustment due to spending too little time in real Euclidean 3-space. Of course, if … Continue reading →

We’ll begin with an intriguing set of three interlinked rings, the Borromean rings. They can’t be realised as solid circular tori, but ellipses work just fine. Here is a visualisation: If you remove any one of the three rings, the … Continue reading →

Shortly after publishing my third cipher, the second one (labyrinth) was solved by someone called Patrick. Gabriel had worked out the basis for solving the cipher ages ago, but didn’t actually do the necessary combination of brute-force frequency analysis to decipher it. I’m … Continue reading →

Forgive me if there is a slight lapse in the frequency of CP4space postings. You can attribute it to me lying in the quintuple-intersection of the following Venn diagram: This particular arrangement of ellipses partitioning the plane into 32 connected … Continue reading →

Many natural objects can be modelled by startlingly simple equations. For instance, there is a sextic surface (degree-6 polynomial equation in three variables) which resembles a heart. As such, it has been nicknamed the ‘heart surface’: Now that we’re approaching … Continue reading →

It is usual, in Cambridge, to hear a plethora of bells chiming. Being within hearing range of the chapels of both Trinity and King’s college, I am greeted with clocks chiming every quarter-hour. On Sunday mornings, however, someone plays the entire full peal … Continue reading →

The Ready gang have been doing more experiments lately, and I ought to summarise the recent discoveries in reaction-diffusion systems. You may remember Robert Munafo’s ‘U-skate’ configuration, which propagates through space even when bombarded with radiation: [youtube=http://www.youtube.com/watch?v=_sir7yMLvIo] Well, lately Tim Hutton … Continue reading →