Why this loo roll upset a professor

Mathematicians do not usually concern themselves with the trivialities of life such as which loo paper to buy. Recently, however, the distinguished Oxford theoretician Sir Roger Penrose FRS, Rouse Ball Professor of Mathematics in the Mathematical Institute at Oxford University, has been paying close attention to one particular brand - Kleenex Quilted Toilet Tissue.

The reason is that the quilting effect chosen by the manufacturers, Kimberley- Clarke, is an unusual mathematical pattern which was discovered by Sir Roger and which now bears his name. He is not best pleased, and litigation is now under way.

A few years ago, the highly acclaimed theoretical physicist and purveyor of speculative ideas (ranging from quantum mechanics and computation to theories of consciousness) discovered a certain way of tiling a surface with flat geometric shapes in a pattern which is almost but never quite repeated. This pattern is now called a Penrose tiling.

The most famous and simplest Penrose tiling shows what is known as fivefold symmetry (this is the offending design on the loo paper). This means that if you take a five-sided figure, a pentagon, and turn it through one-fifth of a whole rotation, it would still look the same.

Fivefold symmetry is of interest to some scientists because it is not supposed to exist in nature. Try tiling a floor with pentagons and they won't fit together - unlike square tiles (fourfold symmetry) or hexagons (sixfold symmetry).

Sir Roger discovered that it could be done by using two kinds of diamond shape - fat and thin - to build up pentagonal shapes. The result is a mind- boggling pattern which looks as though it should repeat itself but doesn't quite.

The pattern has deeper mathematical implications because it fits half-way between chaos and orderliness, and is one of a family of non-computable problems (a computer trying to calculate designs of this general kind would never stop). Non-computability is one of the key concepts needed to understand consciousness, according to Sir Roger's bestselling book, The Emperor's New Mind.

These lofty issues may have been missed by Kimberley-Clarke when it decided three years ago to develop a high- quality product with a quilted appearance. The company's research headquarters in Neenah, Wisconsin, US, came up with several patterns and the Penrose design was chosen.

It was Sir Roger's wife who first recognised the pattern on the loo roll (on sale in most supermarkets at pounds 1.99 for a pack of four) and brought it to his attention.

Can a mathematical discovery be owned? Well, Sir Roger already has commercial interests in the tilings. He works with a company called Pentaplex to produce puzzles based on the Penrose patterns.

"The matter is being taken up by Pentaplex and is now in the hands of their legal advisers, as there does seem to be a breach of copyright," he said. "The upshot of all this remains unknown at the moment." Kimberley- Clarke refused to comment.

The situation is complicated by the fact that Kimberley-Clarke has just bought out Scott (which makes Andrex), and the quilted product is being sold to a company called SCA to comply with EU monopoly legislation. According to SCA, the pattern is part of the deal, so the issue of copyright has to be resolved.

Until recently, the design was still to be seen clearly on the toilet roll's plastic packaging but this has now been removed, presumably as a result of the legal situation. The product is still on sale in supermarkets.