Penrose Tiling v. Kleenex

What patent or copyright issues relating to computer software do this controversy suggest? Any IP paper on this subject will be considered acceptable in terms of subject matter if it manages to bring in {Baker v. Selden and/or The Rubber Tip Pencil Case} and computer software.

1. Last December, Sir Roger Penrose, the eminent British mathematician, came face to face with his own copyrighted polygon pattern in Kleenex quilted toilet paper. When his wife returned from the market with the embossed rolls, Penrose expressed "astonishment and dismay" upon seeing the use to which his discovery had been put.

Penrose devised the nonrepeating five-fold symmetrical pattern in the 1970s by using two kinds of diamond shapes—fat and thin—to create what is now called Penrose tiling. The pattern, which was thought not to exist in nature before Penrose's discovery, has subsequently been found in many physical and biological phenomena.

According to the British newspaper, The Independent, the pattern "has deeper mathematical implications because it fits halfway between chaos and orderliness and is one of a family of noncomputable problems." Noncomputability is a key concept needed to understand consciousness, according to Penrose's best-selling book The Emperor's New Mind.)

Mrs. Penrose first recognized the pattern on the loo paper in the store and brought it to her husband's attention. "He wasn't pleased," said Penrose's lawyer, as quoted in The Wall Street Journal. So Penrose and Pentaplex Ltd., the Yorkshire, England, company that owns the licensing rights to the Penrose pattern, filed a lawsuit against Kimberly-Clark for breach of copyright.

I've since tried, unsuccessfully, to find the embossed Penrose pattern in Kleenex's U.S. tissue, which although quilted doesn't offer the aperiodic design that reflects Penrose's geometric findings. The quilted British tissue is embossed with the pentagonal pattern to make it "thicker and softer," according to Kimberly-Clark literature. Penrose's writ argues that making the tissue fluffier enables manufacturers to reduce the amount of paper used on each roll. "But, if the pattern repeats itself, the tissue would likely bunch up, looking unattractive," the suit claims. "That can be corrected using a Penrose-type pattern that lets the paper sit evenly on the roll."

Quoted in The Wall Street Journal, Paul Steinhart, a physics professor at the University of Pennsylvania, notes that the Penrose discovery — the pattern, not the paper—"created a whole new phase of matter." It produced "materials with properties you never thought were possible." Creating a substance made from "quasi-crystals," which like the Penrose pattern are random or aperiodic,changes its nature.

Penrose shared the prestigious Wolf Prize for physics with Stephen Hawking of Cambridge University in 1988. Together, they have examined relativity, black holes, and the question of whether time has a beginning. He holds a knighthood as well as a chair in mathematics at Oxford University.

2. In the age of chaos theory and fractal geometry, mathematics is no longer as drab, boring and awful as it used to be. These exciting new maths escape the confines of incomprehensible geeky formulae to live and breathe in the world around us; their beauty is reflected in the grains of sand on a shifting shoreline... in the whorls of cream stirred into a cup of coffee... even in the cottony-soft quilted pattern on a roll of toilet paper.

Yes, toilet paper. Which brings us to one of the dangers inherent in dabbling in these latest breakthroughs in mathematical science: unlike Sir Isaac Newton and Rene Descartes, the guys who invented this newfangled stuff are still around to sue your ass.

In a unique accusation of copyright infringement, distinguished mathematical physicist Sir Roger Penrose has filed a lawsuit over the decorative design on a brand of toilet paper. He charges that the Kimberly-Clark Corporation unlawfully appropriated an important geometric pattern of his creation and imprinted it on rolls of Kleenex Quilted bathroom tissue. He is demanding that all existing stock of the offensively designed T.P. be confiscated and destroyed, and wants an inquiry into Kimberly-Clark's profits so that suitable damages may be assessed.

What could be so special about some little pattern on a roll of toilet paper? Quite a lot, actually. Penrose is among the luminaries of modern science, known for researching the origins of the universe in association with Stephen Hawking, and for analyzing the nature of consciousness in such works as "The Emperor's New Mind." The knighted Oxford professor also has a longstanding interest in tessellation geometry, which involves determining sets of fixed polygons that can fit together like the pieces of a jigsaw puzzle.

After years of effort, Penrose discovered aperiodic patterns that had never before been seen in human history. They did not predictably repeat, yet formed reliable patterns indefinitely. This was a demonstration of five-fold symmetry, which was previously thought to be impossible. To make Penrose's feat all the more impressive, his discoveries did not come courtesy the calculational brawn of a computer; these patterns belong to a weird set of "non-computable" problems that have to be solved by hand.

Speaking of doing things by hand, let's get back to the toilet paper. When Penrose noticed a pack of Kleenex Quilted his wife had purchased, he immediately recognized the design embossed on its ill-fated 2-ply sheets. It was a very near facsimile of an aperiodic pattern he had created twenty years ago. Widely known in the geometry field as "Penrose tilings," this particular pattern is notable for using only two polygons to cover a surface. A thin diamond and a thick one form an endlessly interlocking field of five-pointed stars and decagons, sort of like a mildly psychedelic bathroom tile.

And that's as close an association with the lavatory as Sir Roger would care for. Unamused to find his work transfigured at the hand of some Bizarro Marcel Duchamp, Penrose is taking legal action against Kimberly-Clark Ltd., the British division of the Dallas-based Kleenex corporate empire. The Kleenex Quilted brand is reportedly Britain's #3 most popular premium bog roll. Backing Penrose in his lawsuit is Pentaplex Ltd., a company that licenses Penrose tilings and other of Sir Roger's creations for use in puzzles and games.

"So often we read of very large companies riding rough-shod over small businesses or individuals," said David Bradley, director of Pentaplex. "But when it comes to the population of Great Britain being invited by a multi-national to wipe their bottoms on what appears to be the work of a Knight of the Realm without his permission, then a last stand must be made."

Hear, hear. Talks between Kimberly-Clark and Pentaplex about a possible settlement apparently broke down, with Kimberly-Clark denying any violation of copyright laws. Nevertheless, the company has announced that Kleenex Quilted will be "re-launched" with a new look -- undoubtedly a less mathematically significant one.

Now, even though I think Penrose deserves the fullest respect for his achievements, and I'm all for fighting the encroachments of evil corporations everywhere, I still have to question the legitimacy of Sir Roger's complaint. First off, the design Kimberly-Clark used on their toilet paper wasn't an exact ripoff. It must have repeated itself in some regular pattern, in order to have been mass-produced in 500-sheet rolls. Thus it couldn't be more than a kissing cousin to the Penrose original, which is noteworthy for never repeating itself.

Nitpicking aside, here's a more important point: you have to wonder if these scientist guys aren't a little possessively paranoid, sometimes. For instance, there was the late astronomer who sued Apple Computer over a Macintosh model with the internal code-name "Carl Sagan." Then we have researchers applying for copyrights and patents on such items as genetic material, artificial life forms and clones. In 1995, computer expert Roger Schlafly received a patent on two extremely large prime numbers. Among the chorus of protesters against the idea of someone claiming ownership to a number: the eminent Sir Roger Penrose.

"It's absurd," Penrose said of the Schlafly case. "Mathematics is out there for everybody."

It sure is... for better and for worse.

3. Penrose Working 'In Partnership' with SCA Hygiene Products UK

Sir Roger Penrose and Pentaplex Limited have resolved their differences with SCA Hygiene Products UK, current holders of the Kleenex toilet tissue and kitchen roll brands. The three came into contact when SCA Hygiene Products UK took over the Kleenex range. The embossed pattern on Kleenex Quilted toilet tissue is the subject of a dispute between Kimberly Clark Limited, which formerly marketed the product, and Sir Roger and Pentaplex Limited. Sir Roger and Pentaplex Limited are suing Kimberly Clark Limited for copyright infringement, and are considering whether to join the US-based Kimberly Clark Corporation into the action. The dispute does not involve SCA Hygiene or any of its products.

Pentaplex Ltd and SCA Hygiene Products UK have now developed a working relationship, described by both sides as "cordial and constructive." Pentaplex Limited is undertaking technical consultancy work for SCA Hygiene Products UK. "Undoubtedly the expertise behind Pentaplex Ltd will ensure a bright future for both our private label and branded lines, particularly since we now have our hands totally free on the Kleenex Quilted products," comments Mr Harry Tintner, General Manager for SCA Hygiene Products UK. "Intelligence by design is most definitely our style: we look forward to working with Sir Roger and the Pentaplex team."