I was challenged at the very start of this, the first Chapter in Section Four, to describe what symmetry is – and indeed, describe the opposite; asymmetry as well.
A dictionary informed me that symmetry is best described by placing a mirror along the axis of symmetry of any object. A casual observer will then see the object as if it is whole. But that presupposes that you know what an axis is.
An easier to understand description of symmetry is that if you are able to cut an object so that you make two identical halves (think of an apple here) it is said to be symmetrical along the cut and thus the object possesses symmetry.
I suggest that many man-made objects (e.g. door, car, airplane, building, mat) have virtually exact symmetry and many things in nature (e.g. tree, apple, animal, flower, human) have approximate symmetry.
Have a look at the three pictures below, Figures A, B and C.
Very precise symmetry is observed in the drawing (Figure A) of the butterfly, with the green line being the axis of symmetry. (That is, if we cut along the green line we will be left with two identical halves). Figure B is Leonardo da Vinci’s famous picture of man, with the axis of symmetry down the middle of the human body – but because it is of nature it is not precisely symmetrical. Figure C is a random shape that I found on the Internet. This does not have an axis of symmetry. That is to say, there is no way we can cut it to make two identical halves.
So Figure C is said to be asymmetrical.
When I was in primary school we had inkwells and pens. This was very messy for us young children to deal with – but at least we had a bit of fun spilling ink on pages and then folding the page to make inkblots which were random shapes which, when dry, were symmetrical along the fold when we opened the page again.
Nowadays, using a biro, it’s not as easy for children to do this!