A Space of Knowledge
21 Feb 2016This is a very informal preliminary argument about constructing a classification space of knowledge.
3 Dimensions
X: Density \(\Longleftrightarrow\) Dispersity
Y: Formality \(\Longleftrightarrow\) Informality
Z: Representative \(\Longleftrightarrow\) Unrepresentative
Density
The amount of entropy/ information (across time and space) “contained” in a piece of knowledge per bit of information in the medium it’s manifested.
Basically, it’s data compression. Divide the amount of information in the description of a system by the entropy of that described system.1
Formality
The degree to which statements of knowledge are shown to follow from a certain set of axioms under a defined set of rules. Insofar as the axioms and rules are stated and shown to lay the foundation for the asserted statement, the statement is formal; insofar as they are not stated and not shown to follow, the statement is informal.
Formality is basically concerned with the language used. Insofar as the language used can be type-checked, that is shown to follow from some axioms according to some rules, the language is formal. Insofar as it can’t, it’s informal.
And formality can be quantified through some sort of static analysis of statements, where the statements are taken as programs and type-checked. The degree of formality can be taken to be the concentration of formal language used within the sequence of either informal or formal statements (where informal statements use language that doesn’t necessarily directly contain either the axioms or statements that have already shown to follow directly from the axioms).
Representation
The degree to which a piece of knowledge actually represents what it claims to represent. Also the degree to which a statement accurately simulates what it claims to simulate.
This is basically what it means for something to be true, so it’s not easy/ quite subtle to prove. As such of the three this dimension might be the hardest to quantify. This axis could also be labeled truth versus fiction.