Penrose’s Patent and the Battle of the Tissue Tiles (Contains Mathematics)

Penrose bar 2

This drama has got it all – art, law, maths, a genius professor/knight, a multi-national company, a courtroom…

I was reading about Roger Penrose and I realised that today is the 30th anniversary of his success in applying for a patent on Penrose tiling. So this isn’t exactly news, but the anniversary is my excuse to post up some cool links.

Penrose tiling was discovered in 1974. You can pick up the idea behind it pretty quickly.

We’re familiar with bathroom tiles and similar types of designs that have translational symmetry. In other words, they repeat after a while. Penrose tilings don’t repeat. They are non-periodic. But they also have five-fold rotational-symmetry.

This combination of properties had never been seen before. People assumed it was impossible until Penrose came along and drew one. Awesome scenes, no?

If you want to investigate this for yourself, you can start with some pretty pictures and then delve into the actual maths.

Penrose successfully got the patent through on 9th January 1979. And that’s where it gets contentious as there are people who would take issue with this. It was undeniably an innovative step and in this instance a patent can incentivise further discovery and get some pay-off for a mathematicians’s hard work. But is it right to award patents to mathematicians who discover stuff that’s lying around in the Universe? I’m not at all sure it is right, but that’s what happened. Happy birthday patent!

Much later on, in 1997, Mrs Penrose came home with some Kleenex toilet roll from the supermarket. Her husband, the prof, was shocked to discover that the pattern on the roll of tissue was based on his tiling. There’s a good summary of the beginning of the story here. It couldn’t have been an exact copy because the original is non-repeating. Apparently the design prevents bunching of the roll because it’s non-periodic. Penrose sued the company and later won.

I think I’m right in saying the patent will have expired by now, if you want to make anything with the design.

I first heard this story in a mathematics lecture in 2002, my final year at Cardiff University. It was during a module called Non-Commutative Geometry. I won’t try and pretend otherwise – in truth that module was an absolute beast, every bit as difficult as it sounds.

I’m not totally sure why I find myself continually revisiting school and university in this blog. Maybe I have unfinished mental tidying to do.

Anyway, my lecturer at the time showed us Penrose tiling and related the Kleenex story. In a flourish (and this was a flourish by maths undergrad standards, yours may differ), he ended the story by saying “Of course, the company had to withdraw the item from the shelves… BUT NOT before I had a chance to snap up THIS!”. At which point he reached under the desk and produced a bog roll. “And what is more, the top 3 scorers in the exam will each get a free sheet – with my compliments”.

This was, comparatively, one of my highlights of that year.

I was actually mildly disappointed not to win a sheet. If I ever manage to catch one on eBay it’s going to feel like cheating.

5 Replies to “Penrose’s Patent and the Battle of the Tissue Tiles (Contains Mathematics)”

  1. Roger Penrose is a true genius! It’s a charming story when a mathematician invents something like a breakthrough geometrical pattern. Mathematicians across the world must have bubbled with excitement at the time. The rest of the world would probably have been asking why? We have a Penrose book at home called the Emperor’s New Mind. It’s a chunky beauty all about artificial intelligence, computers and the physics. That work was breakthrough stuff too! I wish so much to read it, but it will mean devoting a lot of brain power time!

  2. Hi Carl,

    Interesting stuff.
    But I think you’ll find, if you dig a little deeper, is that a lot of this geometry is derived from Islamic art and mathematics.
    I’m not sure why I know this but I think it was in a novel by Russel Hoban – Pilgermann I think?


  3. S’mai Carl,

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    Darllenais dy sylw are Metastwnsh ble soniais am dy fwriad i greu fideos o phodlediadau Cymraeg.

    “Bydda i postio fideos gyda syniadau DIY, lefel mynediad am y person ifanc/dechrauwr.”

    Mae’n swnio’n ddiddorol – sut fath o DIY oedd gyda ti mewn golwg, gosod silff yn y tŷ bach, neu rhyweth ychydig mwy geeky fel sut i ddechrau blog/golygu erthygl ar Wicipedia? Dw i ddim yn berson ‘techy’ ofnadyw (nac yn pync nac yn secsi!) ond os wyt ti eisiau help, gyda rhywbeth fel sgriptio er enghraifft, rho floedd, byddwn i wrth fy modd yn helpu.

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  4. Thanks all.

    Sam, Emperor’s New Mind has been on my to-read list for years. It’s kind of daunting. I guess you have to start on the first page and work from there!

    Ian, I knew about the existence of the Islamic art but after a quick search I was surprised by the similarities. It’s frustrating that they didn’t write down their understanding of the maths to go along with the designs! Or at least, we no longer have it. All the same, I’m pretty sure Penrose made a unique breakthrough by using only two tiles. I guess the US Patent Office saw fit to award the patent to the Penrose tilings without considering the earlier work to be a prior art – which the court later upheld. But I haven’t delved into their process to see if they even considered the work of the Islamic guys. I wonder if there are any other treasures out there ripe for rediscovery. Haven’t read that book, sounds interesting..

    Rhys, diolch ond cadwch ar y pwnc! Dw i’n amateb trwy ebost yn union.

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