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ESRogs comments on SotW: Be Specific - Less Wrong
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Comments (306)
I did not understand the distinction being made between a ladder and a lattice. Is the idea that the lattice is multi-dimensional? If so why was Eliezer still talking about the top and the bottom rather than some point and the origin?
He's referring to the mathematical formalism.
Sets of elements, ordered by the subset relationship, are a good example of a lattice. Lattices have a specific "top" and "bottom". Among the subsets of the letters in the alphabet, the empty set is "bottom", and the entire alphabet is "top".
The particular point of calling it a "lattice" rather than a ladder is that there are many ways to be more specific; of these, not all are more or less specific than each other. (Formally: you can have a < c and b < c such that neither a < b, a = b, nor a > b.)
Syntax note: Link is broken due to not escaping the closing parenthesis in the URL.
argle bargle. Fixed! Thanks.
Thank you! I was not aware of that concept.