"Kant described a mechanism as a functional unity, in which the parts exist for one another in the performance of a particular function.
An organism, on the other hand, is a functional and structural unity in which the parts exist for and by means of one another in the expression of a particular nature.
This means that the parts of an organism – leaves, roots, flowers, limbs, eyes, heart, brain – are not made independently and then assembled, as in a machine, but arise as a result of interactions within the developing organism."
— Brian Goodwin, How the Leopard Changed His Spots
If we try to cross this lake by following only the stepping stones that lead toward our objective, we’ll soon get stuck. But what if we let go of our objectives? What if we focused on trying to find new stepping stones instead? This is novelty search. Instead of looking for something specific, you look for something new.
Novelty search isn’t just random, it’s chance plus memory. Together, these ingredients do something interesting.
...Stepping stones are also combinatorial. Each new stepping stone we discover expands our potential to find even more stepping stones. Collecting stepping stones is a luck maximization algorithm. By collecting and combining stepping stones, we might arrive at our destination by accident, or somewhere more interesting!
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.