The Symmetrical Patch

For the past couple of weeks, on my patch walks, I’ve been symmetry spotting.

To see if something is symmetrical:

1. Pick it up
2. Transform it (rotate, scale, reflect, flip etc)
3. Put it down again
4. If it looks the same as before the transformation it’s symmetrical

Popular items for this kind of transformation are spoons, static caravans and grandparents.

The most obvious kind of symmetry is reflectional (or bilateral).  An object has reflectional symmetry if there is a line going through it which divides it into two pieces which are mirror images of each other. There are several other kinds, however, and it's flippin' well everywhere.

Symmetry in the Physical world

Bubbles have rotational symmetry as do a the sun, moon, earth and the Death Star. 

In a bubble, surface tension pulls molecules of water into the tightest possible groupings.  A sphere is the tightest possible grouping that any collection of particles can achieve.

Symmetry Animals
99% of members of the animal kingdom have two identical halves - they are bilaterally symmetrical. This is a consequence of two things - locomotion and gravity.  Animals mostly move around in their environment, one end inevitably encounters stimuli before the other end. It makes sense, therefore, to have a head  - with all the sense organs. This head will also encounter food first, so it makes sense to put the mouth there.

Elephant hawk moth
locomotion so front / back; gravity so top / bottom; identical environment on either side so reflectional symmetry

Much about the way a body is organized - with a nervous and digestive system - follows on from this. Internal organs, on the other hand, are often  laid out asymmetrically - the space inside the body is best utilised, by packing them to one side or the other. The environment will tend to be the same on both left and right so sense organs can be the same on either side. Having two identical halves is genetically economical - you only need DNA that codes for one half, then 'flip this stuff'. Furthermore you'll be more streamlined and it's easier for the brain to propriocept  - to know where the body is in space. When considering your next body plan - this is the one I heartily recommend to clients. Do you live on Earth? If you have answered 'yes' to this question then you're living on a planet where gravity is constantly pulling you downwards.  You'll probably, therefore, want some legs to hold you up (if on land). In fact, the whole top / bottom carry-on is a result of gravity. To see how the left / right symmetry differs from the top / bottom asymmetry you just have think about easy it would be for a mirror image of yourself to function. Now compare that to an upside down copy of yourself.  Furthermore, an upside down copy of yourself would look quite ridiculous.

Sense organs placed symmetrically on this jumping spider - Salticus scencius White legged snake millipede segmented animals display  strip pattern symmetry repetitions of a pattern in one direction

Symmetry in plants

Symmetries in an Oak Tree - Oaks don't locomote so there is no underlying head / tail, bilateral symmetry at play.  They do exhibit symmetry though - sometimes it's less obvious. 

• Leaf - approximate reflectional symmetry
• Truck / whole tree / catkins - rotational symmetry about a vertical axis 
• Branches - a branch is approximately a copy of the whole tree - Oaks are 'self similar' therefore they display fractal symmetry. (my blog post on fractals)
• The crown / root system is (very approximately) reflectionally symmetrical

Plant growth is very modular in nature - it is governed by simple rules. The genes often code for perfectly symmetrical structures, however very little in nature is perfectly symmetrical - to paraphrase John Lennon 'life gets in the way'. There are always asymmetries - environmental factors such as weather, light & wind direction, disease, a squirrel building a drey, come into play.

Although most trees don't locomote the exception are The Ents of Lord of the Rings fame...they can walk...obviously. Who can forget that line of Frodo Baggins's - "cor blimey Charlie! look at that walking tree exhibiting reflectional symmetry!!"

Symmetries in flowers on the patch - flowers demonstrate that there can be degrees of symmetry - the number of ways you can transform them symmetrically. There are an infinite number of ways a circle can be rotated, about its center, for it to look the same. A Bee Orchid flower has just one line of reflectional symmetry. A Yellow Flag iris has 3 lines of reflectional symmetry and three of rotational symmetry.

Flowers often act as targets for insects - the petals radiate from a central points. They are like arrows pointing  to the 'goodies' - the nectar at the centre. Experiments have shown that bees prefer flowers which are symmetrical.

Orchids, Peas, Himalayan Balsam etc, have pollination strategies which result in the bilateral symmetry of insect bodies being passed on to the flower design.

Seeing Symmetry

Humans are naturally attracted to symmetry. A symmetrical face is often considered beautiful. We are drawn to even proportions, as are many of our fellow creatures. Animals often choose mates, partly, on the basis of symmetry. Female Swallows prefer males with tail streamers of equal length.

It is believed that the absence of asymmetry is an indicator of genetic fitness. Only a healthy organism can resist environmental stresses throughout its development to maintain a symmetrical plan. Healthy animals make the best mates, with the best chance of producing offspring.

Our brains are constantly on the look out for symmetry. If we are in a jungle, and we see something symmetrical, we know it is likely to represent an island of order in the sea of chaos. This, in turn, probably represents something we can eat, or is going to eat us. Symmetry is important, therefore, in that it carries a message. Symmetry has been described as nature's language - a language our brains are adapted to understand.

It's been speculated that the whole realm of aesthetics, art, beauty, and even truth, follows on from the way our brains perceive our environment. Symmetry makes visual processing easier for our brains. - so we respond with a sensation of pleasure.<sup>1 


1</sup> There other kinds of symmetry which I haven't touched on - language, music, time, physical laws Get this