Zen is to do things without purpose or reason? I thought that the idea of Zen is that I eat when I am hungry, I drink when I am thirsty, and I sleep when I am tired. I thought Zen is asking yourself "What is lacking in this moment?". Sounds like a purpose to me.
Perhaps it's trying without trying too hard? Or, doing things without the need of some fixed goal as the purpose for doing? I can ask what's lacking in this moment and come up with enough answers to keep me from doing any one thing...speaking from my own experiences, at any rate.
It a koan of sorts isn't it? The unaimed arrow never misses: an "arrow" with enough skill can find use where ever it lands. Something like that perhaps?