Quasi-crystals are not proof of intelligent design

Every once in a while, a new discovery is made in science that is only partially-understood. Inevitably, this gets reported to the masses in a watered-down way by news writers who do not understand science, and there is a great cry: “The foundations of science are crumbling! Science discovers thing that is impossible to explain! Everything you know is wrong!”  And, naturally, there are plenty of people who take this opportunity to tack on: “…therefore, there really must be a God!”

Perplexing Poutry PiecesOne example of this centers around the decades-long debate over quasi-crystals. To give you a sense of what quasi-crystals are and why they matter, I’d like to introduce you to the “Perplexing Poultry” game.  This is a puzzle game in which you have a large collection of tiles that come in two shapes: two different (slightly mutant-looking) chicken shapes.

The game is quite simple: arrange the shapes in a tiling.  In other words, fit them together into a pattern that covers the surface that you are working on with no gaps. You are familiar with “tiles,” of course, although most of the time they are not poultry: usually the pieces are squares or rectangles, or sometimes triangles and hexagons. There was a time when it was quite fashionable to cover floors this way.

Perplexing Poutry Small TilingBut when you use the Perplexing Poultry tiles, you immediately realize that there is a problem here. It’s possible, but it’s extremely hard.  You can put together the first several pieces very easily, of course. But as the pattern grows, it gets more and more difficult.  You sometimes actually have to back-track, because you realize you have “worked your way into a corner.”  In other words, you’ve built a pattern up part-way that makes a completely space-filling solution impossible: you have a gap that you cannot fill.  That’s why this is interesting as a puzzle or a game: you cannot simply do it mechanically. You have to plan ahead, think about what you want the larger shape to look like. Picking the “next piece” isn’t just something you can do based on what you see on the board: you have to take into consideration the pattern produced by pieces that you have not yet put down.

Perplexing Poultry Large TilingSo creating a Perplexing Poultry tiling is possible, but hard. It seems to require intelligence or planning.  This is different from tiling a floor with, say, squares or hexagons. Those produce a repeating pattern, or in the language preferred by mathematicians, those tilings have “translational symmetry.” You can create them by following very simple rules. You could easily write a computer program to generate a repetitive pattern tiling, or you could even imagine some natural system following simple physical laws producing the same result.

The problem with Perplexing Poultry is that the pattern never repeats.  Ever. No matter how big you make the tiling, you will never “start over” and be able to say: “OK, now I can just do the same thing again.” Instead, every single step of the way, you will have to follow the same complicated process of planning ahead, envisaging a pattern with no gaps, and trying to move forward… and backtracking if you make a mistake and force yourself into creating a “gap.”

Symmetrical Penrose TilingThis type of non-repeating pattern was first discovered by Roger Penrose in the 1970’s. As a result, they are called Penrose Tilings. The key features of a Penrose Tiling are 1) they completely fill the space with no gaps, 2) they are made up of a limited number of predefined shapes that are used over and over again, and 3) the pattern never, ever repeats. Penrose discovered that these tilings tend to happen when the pieces have five-fold symmetry (e.g. pentagons). You will notice that the Perplexing Poultry pieces are basically deformed pentagons.

Penrose Tilings can be radially symmetrical: in other words, they can have rotational symmetry (although they do not necessarily have this property, as you can see with the perplexing poultry).  However, as you move from left to right (or top to bottom) they a completely non-repeating. You could go on literally indefinitely and never see the same pattern twice.

Now, let’s talk about crystals. Most crystals are regular tilings.  They are made up of atoms that bond with each other so that they fit together like squares or hexagons and produce normal “tiling patterns.” This is actually what a “crystal” is: a tiling pattern of atoms. It is very repetitive, and it’s very easy for them to form using simple laws of physics.  There is no “foreknowledge” or planning needed to make sure that no gaps appear. There would never need to be any “backtracking” in the creation of the pattern arising from the system growing into a pattern that could not be solved.  Instead, each piece can fit into the system based only on what is already there, in a mindless and mechanical way, and the crystal will continue to grow.

Non-Periodic Diffraction PatternIn 1982, Dan Shechtman observed an electron diffraction pattern in an Al-Mn alloy which had been rapidly cooled after melting that appeared to have the properties of a Penrose tiling: a space-filling crystal made up of a limited set of elements that never repeated. He boldly entitled the paper “Metallic Phase with Long-Range Orientational Order and No Translational Symmetry” and declared that he had found a quasi-crystal: a crystal-like structure that was non-repeating. Plus, it had five-fold symmetry. Score!

His work was dismissed. He was mocked.  He was even asked to leave his research group for defending his findings. He was called “wrong according to the textbook.” One of Dan’s fiercest critic was Linus Pauling (Nobel Prize in Chemistry & Nobel Peace Prize laureate), who reportedly once said, “There are no quasi-crystals, only quasi-scientists.” Other scientists either went through great efforts to explain how the data had been misinterpreted, or they ignored it altogether.

Eventually, his work was supported by other findings and by other scientists. Over the next 10 years, more and more people started accepting that quasi-crystals could be manufactured in the laboratory under certain conditions. In 1992 the International Union of Crystallography even altered its definition of a crystal, reducing it to the ability to produce a “clear-cut diffraction pattern” and acknowledging the possibility of the ordering to be either periodic or aperiodic. Finally, after more than a decade of methodical hunting, scientists reported finding the first natural  quasi-crystal, a mineral found in the Khatyrka River in eastern Russia.

So almost 30 years after his initial paper on the subject,  Dan Shechtman was awarded the 2011 Nobel Prize in Chemistry for his work on quasi-crystals. They really do exist.

But wait!

How is this possible? Didn’t our little Perplexing Poultry puzzle prove that these types of crystals cannot form based on simple mechanical rules? Haven’t we demonstrated that in order for quasi-crystals to form, there would have to be planning, and decisions, and that somehow a conscious mind would have to have an idea of what the final pattern looked like in order to make it happen?

Isn’t this proof, therefore, of intelligent design? Isn’t this proof that the basic foundation of science is completely cracking??????

No, it’s not.

It’s true that many scientists made the argument that quasi-crystals were impossible because it would require “action at a distance” or a global determination about what elements fit into what positions while that crystal was forming. But while it’s true that some scientists made those arguments, it’s also possible that those arguments were simply wrong.

In much the same way that it took almost three decades from the time when the term “quasi-crystal” was coined to the point where a naturally-occurring example of it was discovered, it sometimes takes time and effort to figure out how things are possible.

The first steps have already been taken.  In 2008, Aaron Keys and Sharon Glotzer used a computer simulation to demonstrate how quasi-crystals could grow using only simple physical rules and “local information”: in other words, there didn’t have to be any planning entity who was “envisaging the whole pattern” in order to make it work. The basic mechanism has to do with the crystal forming in “clumps” or local clusters that then can maneuver to fit together.

This simulation is, I’m sure, just the first step in the development of a more sophisticated understanding of what types of processes are at work in the natural creation of quasi-crystals. It will produce deep and interesting insights about the mechanics involved in crystal formation, I’m sure.

But it’s not proof of a god.

This type of thing happens fairly often in science: there is a discovery that nobody can explain, non-scientists freak out and claim that it represents the complete failure of all science and proof that there is a god, and then science explains it.

That’s pretty much how science has worked, since the very beginning.


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  1. Kerry says:

    Hi Greg,
    I just read your post DECONSTRUCTING A QUOTE BY AYN RAND . I like it. “Similarly, there is nothing inherently noble about working things our for yourself, or trusting your own senses and pre-existing beliefs. In that complex web, if you are unwilling to cast doubt on any of the beliefs in that web, and you are unwilling to cast doubt on the experiences you thought you had, and you are unwilling to admit that one of the logical relationships that you believed might be wrong, then you are just as prone to “not distinguishing truth from error” as anyone else.

    This quotation from Ayn Rand is puffery. It’s what people who describe themselves as “rational” use to justify condescending to people whom they believe to be irrational.

    Because in the end, almost all beliefs are at least partially social; and the thing that destroys a person’s “ability to tell truth from falsity” isn’t trusting the word of the people around you, it’s unwillingness to question yourself.”

    You yourself refer to the problem of induction which for the secular scientist should give pause for more consideration. For the theist this poses no problem but does give confidence to his worldview. I think you would admit that all worldviews make basic presuppositions and because of such things are all taken “on faith” to some extent. To many uncritical people out there however the scientific worldview is “entirely logical” and fool proof, the assumption being that this therefore rules out the existence of God. The so-called dichotomy that many believe exist between faith and science or faith and reason is a myth. The big contention is the problem Christian theists have with the naturalist-materialist view of reality which most atheists seem to espouse. Have you read any of Alvin Plantinga’s material ? Cheers,

    • Greg Stevens says:

      “The so-called dichotomy that many believe exist between faith and science or faith and reason is a myth.”

      I agree! And I’ve written about this many times!

      I’ll admit it’s also a pet peeve of mine when atheists somehow are inherently “more rational” because they are atheists. Blech. There is plenty of rationality, just as there is plenty of irrationality, on both sides.

      Thanks for your comment!

  2. Kerry says:

    Thanks for your reference to my blog.

    I just wish to draw your readers attention to my footnote at the bottom of the post you referred to: As a footnote to this, I believe Steinhardt went on to explain that he has discovered a simple rule or formula for ensuring that these beautiful crystals conform to the complex patterns which seem to do away with the need for “longrange interaction” which is science speak for intelligent consciousness. That is really not my contention here, merely to point out the very strong bias against the idea of intelligent design- when something looks like it needed a creator to figure it out and which even had “mathematical proof” of its need for infinite longrange information the language of scepticism and incredulity is loud and clear. The fact that this complexity can be expressed in terms of a formula does nothing to detract from a creator. As Einstein has said his faith in science was underpinned by an overarching confidence that the Universe was intelligible and beautiful. Yet another formula discovered in fact adds to the theists confidence.

    Some have argued that religion stultified science because whenever problems seemed insurmountable for the scientist the temptation to throw up her hands in despair and just declare God did it has kept science in the stone age. But this is patently not true, the opposite can be cited (as it was for Einstein), it is that order, design and intelligibility are so much a part of this universe that gives rise to the confidence that steadfast efforts would be rewarded.

    For an excellent summary of the history of science I refer you and your readers to Professor of Mathematics of Oxford- John Lennox and another article I wrote on the assumptions of secular scientists that can be found here: http://struth-his-or-yours.blogspot.co.nz/2011/09/neutrino-news.html

    Key to understanding my point in the post is this: “there are some presuppositions that are so basic to the human way of thinking that they are smuggled in to the scientific enterprise at such a fundamental level that they go unquestioned, unseen.”

    There really is no such thing as “a disinterested search for the truth” The neutrality of science may be one thing, the neutrality of scientists is quite another.

    Another couple of posts that may be of interest to the open minded is one called “Mathematics and God” http://struth-his-or-yours.blogspot.co.nz/2008/11/mathematics-and-god.html and the little known or at least little acknowledged fact that much of science has at its base, what equates to a statement of faith, that means that a very basic presupposition of science does NOT strictly adhere to logic. I refer to the Problem of Induction found here: http://struth-his-or-yours.blogspot.co.nz/2010/04/problem-of-induction.html

    What is interesting in that post is that two of the most well known skeptic atheist thinkers Bertrand Russell and David Hume were the ones that brought this fact to the attention of the world.

    • Greg Stevens says:

      Thanks for your comment. I actually agree with several of the things you say.

      For example, you say, “The fact that this complexity can be expressed in terms of a formula does nothing to detract from a creator…” and this is absolutely true. Moreover, the fact that something can be given natural explanation is not evidence against the existence of a creator — it is merely NOT evidence FOR a creator, per se.

      I’ve written about this before, in the context of cognitive biases in religious belief. Many atheists like to snarkily claim that IF there is evidence that the brain has evolved a bias to believe in God, THEN that is somehow evidence against the existence of God. That is patently untrue: whether or not our brains are biased to believe in God has no bearing on whether or not God actually exists. I think that is similar to the point you are making.

      I also agree that religion is not NECESSARILY something that will stunt science. Throughout much of the middle ages, those who practiced “natural philosophy” were interested in understanding the mechanisms and rules by which the world worked. They never once doubted that God was behind it all: their explorations and research were explicitly an endeavor to understand “What are the rules that God has created for our world to work by?”

      I also talk about this in a previous post about “Divine Mathematics”: Teach Divine Mathematics if you want to… but do it right

      So thank you for your comments, and I’m sure I have some readers who will appreciate the links that you provided!

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