A quick anecdote about quasicrystals

Today the Nobel Prize for Chemistry was awarded to Daniel Shechtman for the discovery of quasicrystals – a material whose components are arranged in a seemingly ordered pattern, but one that never repeats itself.


Earlier this year I interviewed mathematician Edmund Harriss for an unrelated feature about design and science, and he told me a wonderful anecdote about these curious materials:

I work on aperiodic tiling, sets of shapes that fit together but never becomes periodic – there’s never one single unit that repeats again and again. The initial example by Robert Berger had 10,000 different shapes, very much an abstract theoretical object, but that was brought down, to Penrose tiling, which has just two different shapes. Even today we don’t understand a lot about how this process works.

Most people regarded it as recreational mathematics, just an interesting problem. Then in the 1980s, Dan Shechtman managed to get a crystal structure in an x-ray diffraction pattern that had a five-fold symmetry. In three dimensional space, you can’t have a periodic structure with five-fold rotational symmetry. This showed that the structure of this crystal couldn’t be periodic. This ran against the central beliefs that chemists had about how crystals form. The discovery of these non-periodic crystals disappeared without a trace, and one of the arguments was that it was mathematically impossible. The mathematicians then refined what was mathematically possible, so when quasicrystals were observed again you had models for what was happening.

Alongside the transcript I’d jotted the note: “So we ignored the existence of quasicrystals until someone figured out their underlying design?”.

Sometimes, even in science, things need to be believed in to be seen.


  1. #1 Edmund Harriss
    October 5, 2011

    Just to add a little flesh to the story. Non-periodic crystals were initially discussed back in 1931, in studying the properties of the mineral Calaverite:

    In particular this paper:

    Goldschmidt. V. Palache, C. and Peacock, M. (1931).
    Uber Calaverit
    Neves Jahrbuch fur Mineralogic. 63. pp. 1–58

    Shechtmann was able to use modern techniques to show more convincingly that something unusual was happening, but he also benefited from the fact that that there were mathematical models that had the right property, such as the Penrose tiling (and 3d variants) first published just a few years before:

    Gardner, Martin (January 1977), “Extraordinary non-periodic tiling that enriches the theory of tiles”, Scientific American 236: 110–121

    (Gardner is reporting on Penrose’s discovery, but not for the only time, his report is also the first publication!)

  2. #2 Greg Laden
    October 5, 2011

    You have to go over here and explain to everybody on the internet why they are wrong:

  3. #3 Frank the SciencePunk
    October 5, 2011

    Greg, wow. You need to be more liberal with the comment nuke button.

  4. #4 bill beaty
    October 6, 2011

    > even in science, things need to be believed in to be seen.

    But they were seen, no? Instead, science appears to often work backwards. Rather than theory being confirmed by evidence, evidence undergoes selection based on current theory.

    Here’s an excellent if long appropriate quote:

    “The mind likes a strange idea as little as the body likes a strange protein and resists it with similar energy. It would not perhaps be too fanciful to say that a new idea is the most quickly acting antigen known to science. If we watch ourselves honestly we shall often find that we have begun to argue against a new idea even before it has been completely stated.” – W. Trotter 1941

  5. #5 Birger Johansson
    October 6, 2011

    Bill, to illustrate your quote:
    From the field of Archaeology, I have a little anecdote. No one believed there were bronze age rock carvings in northern Sweden, because the textbooks said so. Then one such rock carving was found in my home village Norrfors. Suddenly, when people started looking, rock carvings turned up all over the place…

    And in regard to avian dinosaurs, fifty years ago a Swedish paleontologist suggested that dinosaurs may very well have had feather plumage, but was ridiculed. Everyone knew dinosaurs were “just reptiles”, and reptiles do not have feathers. It was not until those marvellously preserved Chinese specimen turned up that people started looking for traces of feathers.

    However, in the long run Sagan’s motto “extraordinary claims require extraordinary evidence” is sound. For instance, Aberhalden’s “abwehrfermente” (defense enzymes) were quickly discounted outside Germany, but in Germany this myth took root and lasted a generation.
    And let’s not get into Lysenkoism and the mass starvations it caused.

  6. #6 Sarani Rangarajan
    October 6, 2011

    Isn’t quite a chunk of vision/psychological research devoted to what people see when they look at a picture being drawn from the context of what they expect to see?

    Bill, that’s the nature of human experience, isn;t it? I mean, grad students are told to “go where the data takes you” (or the equivalent of grounded theory in social science research) — but who really does? IT’s a scary world out there without the theories to codify it for you; and the weight of existing research is SO very heavy. Plus, if you don’t understand it, you discount it (or at least I did — the reason why my thesis is being rewritten right now. I had the paper that turns things around all along, but I never ‘got’ it.)

  7. #7 Collin
    October 7, 2011

    “Even today we don’t understand a lot about how this process works.”

    I suppose actual quasicrystals are poorly understood, but hasn’t an exact description already been found for the Penrose Tiling itself?

  8. #8 Hanan Cohen
    October 10, 2011


    I am now in the process of preparing a presentation about the Nobel Prize for the Bloomfield Science Museum Jerusalem and see the same mistakes all over.

    Shechtmans’ discovery was achieved using electron diffraction – not x-ray diffraction and certainly not using an electron microscope.

  9. #9 osmanlı iksiri
    October 12, 2011

    Isn’t quite a chunk of vision/psychological research devoted to what people see when they look at a picture being drawn from the context of what they expect to see?