Hurul Ain,
© Hurul Ain,

Why is there so much symmetry in the world? Sea urchins, jellyfish and other animals that sit still or float around gently have radial or rotational symmetry, so they look the same if they are rotated around a central axis. All other animals – the ones that move around – have bilateral or mirror-image symmetry.*

Flowers often have rotational symmetry, and most leaves have approximately bilateral symmetry. Five-fold symmetry is found in both plants (for an example, cut an apple in half across the core) and animals.

Symmetry can be seen in astronomy, and it is also important in chemistry – biological systems which use a specific molecule often cannot use its mirror-image. We find symmetry attractive, and people we think are good-looking tend to have very symmetrical faces.

So what lies at the root of these phenomena? In 1915 the German mathematician Amalie Emmy Noether (1882-1935) found a link between different types of symmetry and the laws of conservation in physics. Although Noether is not well-known, her work was foundational for much of modern physics.

Noether’s theorem shows that for each kind of symmetry, there is a corresponding physical law: rotational symmetry and conservation of angular momentum; spatial symmetry and conservation of momentum; time translational symmetry and conservation of energy. As a biologist I can’t pretend to understand all these concepts fully, but I am fascinated by the fact that the symmetry we see on the surface of things is linked to a deeper symmetry in the basic laws of physics.

Cynthia Yip,
Cynthia Yip,

Let me give one example. Snowflakes have a complex and famously varied structure, but they all have six-fold or hexagonal rotational symmetry. This symmetry at a (relatively) large scale reflects symmetry at an atomic scale, which is determined in turn by symmetry in the basic laws of physics.

In ice, water molecules form weak bonds between each other, with the hydrogen atoms of one water molecule interacting with the oxygen atoms of its neighbours. A hexagonal structure turns out to be the most stable, because any other would bring the oxygen atoms too near and they would repel each other.

The properties of matter are described by physical laws: the strength of the forces in the atom, the behaviour of electrons, the strength of gravity and so on. It is possible to form symmetrical crystal lattices only because the laws of physics apply equally in any direction, time or place in space. Only decay over time (the second law of thermodynamics) is not symmetrical, so as snow melts, the crystal’s hexagonal shape is destroyed.

I have heard numerous lectures on the fine-tuning of the physical properties of the universe, but I have never yet heard anything on the topic of symmetry in a science-faith context. Apparently there is indeed a link between symmetry and fine-tuning – and I want to know how. Watch this space.


Further reading

Snowflakes – Stephen Webb, Out of this World: Colliding Universes, Branes, Strings, and Other Wild Ideas of Modern Physics (New York: Praxis Publishing, 2004), pages 15-17.

Leon M. Lederman & Christopher T. Hill, Symmetry and the Beautiful Universe (New York: Prometheus Books, 2004).

Nina Byers, E. Noether’s Discovery of the Deep Connection Between Symmetries and Conservation Laws, Israel Mathematical Conference Proceedings, 12 (1999).

* There are a few exceptions to these rules. For example sponges have no symmetry, and some corals have bilateral symmetry. Some bilateral animals like flounders – develop asymmetries as adults.  Some may start with one sort of symmetry and develop another. And of course symmetry at this level is approximate – if you looked at a molecular level you would see asymmetrical differences.

4 thoughts on “Symmetry

  1. davidassender May 15, 2014 / 11:54 pm

    Very cool article, thank you. I can’t wait to see what you find.


  2. Ax-Ix May 20, 2014 / 8:19 pm

    The reason why you don’t hear anyone talk about fine-tuning and symmetry in the same breathe is that they are actually inexorably related in physics.

    Modern physics is actually dominated by not just symmetry, but by symmetry breaking. The Higgs mechanism is a notable example: by understanding how a symmetry breaks we gain insights into the physical world that we’d normally miss if we just ignored the existence of symmetry or tried to impose any symmetry as exact. Now, this can get very technical very fast, but essentially what the idea is that for any ‘small’ parameter in your theory, the idea is that it is either fine-tuned to be small (so that quantum corrections do not push it to a large number), or that there is some symmetry that makes it exactly zero and then is ‘softly broken’. It is important to note that the rules for breaking symmmetries are pretty rigid, but it is also important to note that without any symmetry at all you’d be stuck with fine-tuning. The more the symmetry gets broken, the more fine-tuning you need, the less your symmetry gets broken and you may not even need any fine-tuning.

    So fine-tuning and symmetry are, in the context of physics, mutually exclusive in a very real way.


    • Ruth Bancewicz May 21, 2014 / 9:38 am

      Thank you, that’s a very helpful explanation. I have commissioned a physicist to write a follow up to this, so hopefully she can explain some of the technical side!


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