Perhaps Sir Roger
Penrose just didn't want
people wiping their
butts on his math.

Toilet Paper Plagiarism

by D. Trull
Enigma Editor

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. I think there's a lesson here for anyone who stumbles across an undiscovered part of the universe and tries to claim it as his own. You can presume to hold on tight and never let it go, clenching up your retentive grip with constipated determination. But in the end, your "creation" will rightly return to nature's anarchy with a victorious plop, leaving you to wipe yourself clean of any residual pretensions.

And don't forget to flush.

Sources: Electronic Telegraph; Associated Press; "World of Escher" web page <>

(c) Copyright 1997 ParaScope, Inc.

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