Tyger! Tyger! Burning bright
In the forests of the night,
What immortal hand or eye
Could frame thy fearful symmetry?
        -William Blake

You can create:

• Mirror symmetrical pictures
• Improv symmetry performances
• Conjectures and theories about doubling - the basis of all computation

How?
These three short activities are meditations. They can put you in a certain relaxed, positive, artistic state of mind. I sometimes offer them to people if they get anxious or tired working with math, because of the refreshing effect of such change of pace. Babies as young as one can do "live mirrors," because mirroring is a strong biological need and skill.

Live mirrors. Stand in front of each other and mimic each other's gestures and expressions. That's it! First of all, it's harder than it sounds, because both people can initiate a motion or an expression. Some positions and especially motions are difficult - like the famous "pat yourself on the head while circling your tummy." The activity is usually funny and makes us feel good, for many psychological reasons. It also helps to resolve strife and conflict between people. If you do live mirrors in a group, draw the mirror line on the floor and have pairs of people face each other across the line. Children groups like to watch each other perform this way. For an advanced version, four people can play with two perpendicular lines on the floor for "mirrors." This one's hard even for most adults!

Two-handed drawing. Fold a piece of paper in two, open it and tape to the table or place a heavy object on it to hold it in place. Grab a marker in each hand and draw mirror pictures, using the line in the middle of the paper as your "mirror." This activity comes from occupational therapy, where it is used to help people with brain hemisphere disbalance, dyslexia and other left-right issues. As many occupational therapy exercises, it makes people feel good, even if they have no problems or diagnoses. The pictures also look beautiful, because humans usually see symmetry as a beautiful thing - it has to do with health instincts.

Ink and folded paper. This works the best with dark or bright liquid paints or ink, and smooth thin paper that's not too porous or too glossy. You have to experiment a bit to see which media works well. Fold the paper in two, open, drip a bit of paint into the fold, then close again and guide the paint through the paper with your fingers. It will spread around, forming weird, beautiful pictures. You can add more colors as you go.

Why?
Because these activities are meditative, artistic, therapeutic, and support doubling - the beginning of all multiplication

As you go

• Note shapes and patterns formed by mirroring
• Try to work with quantities and observe doubling

Higher and deeper

• Symmetry crops up in math subjects from algebra (symmetric functions) and beyond. Geometry is the obvious source of symmetry work.
• Doubling and mirroring have many representations in psychology and philosophy theories.