Knowledge depth is how much we know about the solutions to that problem. For instance, the problem “What is the set of 4-bit still lifes?” has a depth of 0, since we know the entirety of the problem, its facets, and its solutions. The problem “What is the population of the smallest unsynthesizable still life?” has a depth close to 1, perhaps 0.8 or so; we know it is between about 30 and about 140 (I don’t remember the exact values), but we don’t know any way to prove that. However, it has a very low Metaknowledge value.
Metaknowledge is how much we know about the problem. The still life example from earlier has a low metaknowledge as we effectively know the total space of the problem and how to solve it. A problem with very high metaknowledge cannot be articulated here, since we don’t know about it, but an example of a problem with medium metaknowledge is “What is the large-scale behavior of Life universes”. We know the gist of the problem, but we don’t have a clear vision of what to explore or what to do about it.
Knowledge accessibility is how hard it is to solve a problem. For example, take “Does an elementary (3,1)c/8 ship exist?”. This has very high depth (we haven’t found an answer), very low metaknowledge (we have a clear picture of the problem) and very high accessibility (with our current knowledge, it is very hard to solve.
Let’s look at each (octant?):
Low depth, low meta, low access: Simple problems that are easy to solve, such as the 4-bit still life problem.
High depth, low meta, low access: A very small set of problems; problems in this area are ones we don’t have good solutions to, but we know a lot about, and are easy to solve. Because of this, they’ve all been picked off already and moved into the first octant.
Low depth, high meta, low access: This one’s interesting. These are problems which we have good solutions to, and they are easy to find, but we don’t know much about the problem. Usually, this is problems that have easy existing solutions, but haven’t been articulated yet (that is, problems which we already have the answers to but not the problem itself).
High depth, high meta, low access: Problems which we do not have good solutions to, don’t have much knowledge about, and are easy to solve. This is the golden zone, or zdr-space, where sifting through it can get you cool things that nobody’s seen.
Low depth, low meta, high access: Problems that we have good answers to, we know a lot about, but are hard to solve: for example, finding more (2,1)c/6 ships.
High depth, low meta, high access: Problems that are hard to solve but we know a lot about. The elementary camelship is an example of this.
Low depth, high meta, high access: Problems which we have good solutions to, are hard to solve, and we don’t know much about. I have no clue what goes in here.
High depth, high meta, high access: Problems which we know nothing about and have no idea how to solve.
Anyway, feel free to give your thoughts
