Complex projective 4-space, in mathematical terms, is a set of points described by a 5-tuple of complex numbers (v,w,x,y,z), where scalar multiples are considered equivalent. It is a geometry far more elaborate than our own boring, bog-standard, vanilla, common or garden, three-dimensional Euclidean geometry.
Informally, however, ‘complex projective 4-space’ was used in a joint Anglo-Hungarian IMO training camp to refer to a mythical world inhabited by unimaginable beasts. On reflection, these ideas are more similar than one might imagine: complex projective 4-space is indeed inhabited by such impossible-to-visualise objects as quintic threefolds.
Hence, it seemed like a reasonable title for a blog concerned with interesting aspects of mathematics. Without the ability to see into the future, I cannot anticipate what will come of this blog. It may stagnate, flourish or attract so much criticism that I am promptly assassinated.