I enjoy gardening the most when it aligns with my broader philosophy of life, so I thought readers might like to see that philosophy and see how I apply it to gardening. These principles are in random order, just as they are applied in life. Sometimes my focus is on having fun, other times I'm focused on planning, still other times I just want to kick back and chat to my friends and neighbours.
Introduction / Pareto principle / Balance / Fun / Working for happiness / Family / Purpose / Order / Planning / Flexibility / Variety / Strategic Resilience / Motivation / Sustainability / Invest to save / Kaizen / Kindness / Giving back / Experimentation / Learning
Wang tiles (Hao Wang, 1961) are a class of formal systems. They are modelled visually by square tiles with a color on each side. A set of such tiles is selected, and copies of the tiles are arranged side by side with matching colors, without rotating or reflecting them.
The basic question about a set of Wang tiles is whether it can tile the plane or not, i.e., whether an entire infinite plane can be filled this way. The next question is whether this can be done in a periodic pattern.
In 1966, Wang's student Robert Berger solved the problem in the negative. He proved that no algorithm for the problem can exist, by showing how to translate any Turing machine into a set of Wang tiles that tiles the plane if and only if the Turing machine does not halt. The undecidability of the halting problem then implies the undecidability of Wang's tiling problem.