The 5 x 5 Grid
Iterative Relativization allows us to simplify The Grid without losing essential functionality. Before iterative relativization all patterns were relativized to a slot in an 8 x 8 or 9 x 9 grid. Before the Analytic Metaphysics of Quality all patterns were relativized to one of four levels. But we have found out that no grid can account for an arbitrary amount of patterns of arbitrary value. This is because two different patterns might both be intellectual so that one of them is nevertheless more valuable. We cannot express this difference by placing these two patterns on the same level or in the same slot. But iterative relativization bypasses this limitation. Because of iterative relativization the resolution of the grid becomes largely irrelevant for exact modeling. We don't need a 100 x 100 grid for modeling small value differences. Therefore, to keep things simple, we might as well try using the lowest possible resolution.
Iterative relativization already works on a resolution of 5 x 5. Only testing will reveal whether this is more convenient to use than 9 x 9. The 5 x 5 grid is simpler but a larger resolution does have the advantage of providing vague information of value differences without a need for iterative relativization. That is to say, if you compare quantum mechanics to a rock you should find the rock less valuable, but you should also find the rock less valuable than society. In a 9 x 9 grid you don't need to do any iterative relativization to express this. In a 5 x 5 grid you need to do lots and lots of iterative relativization for modeling any large amount of data. I think the 5 x 5 grid is more suitable for computers than human operators because it's simpler and the computer shouldn't mind doing lots of iterative relativization.
The 5 x 5 grid might also have another advantage. If we wanted to do relativization with a normal mechanical keyboard we might want to have one key stand for one slot on the grid. There are not enough neighboring keys on the keyboard for a decent user interface for a 9 x 9 grid but there are enough for a 5 x 5 grid. I would assign keys within the area defined by Q, R, Z and V for relativizable slots, the area defined by B and 5 for vertical nonrelativizable slots except NOTHING, the area defined by 6 and 9 for horizontal nonrelativizable slots except NOTHING and 0 for NOTHING.
Since the 5 x 5 grid is so simple it makes lots of sense to try to make a somewhat detailed description of how to select the appropriate slot. Earlier, we have simply described the slots. In theory, this might suffice in the sense that all relevant information perhaps can be derived from the descriptions. But it would still be more helpful if, instead of mere descriptions, we would provide an informal algorithm or a list of checks that explains how slot memberhood is determined instead of what is there in the slot.
There are only two "levels" and only two "clusters" per quadrant in this model. Once a pattern has been assigned a quadrant in can be assigned a slot by asking two questions:
- Is the pattern classically remarkable? Answer yes if it could under some plausible circumstances turn out very important. Answer no if it makes no sense to expect such circumstances.
- Is the pattern romantically remarkable? Answer yes if its importance is actually felt. Answer no if the pattern feels or should feel boring.
As for more interface design: iterative relativization would benefit of us being able to assign two patterns as identical and not merely equal. This cannot be done on the grid because belonging to the same slot doesn't specify patterns as identical or not. They might be identical or they might be equally valuable but unrelated. This evaluation can be performed at the same step of iterative relativization in which one pattern is declared inferior or superior to another. We could use - for inferior and + for superior and perhaps O for identical and P for equal.