# Superexponential conceptspace

### From Lesswrongwiki

In order to do inference, we constantly need to make use of categories and concepts: it is neither possible nor desirable to deal with every unique arrangement of quarks and leptons on an individual basis. Fortunately, we can talk about repeatable higher-level regularities in the world instead: we can distinguish particular configurations of matter as instantiations of object concepts like *chair* or *human*, and say that these objects have particular properties, like *red* or *alive*.

The sheer number of distinct configurations in which matter could be arranged is unimaginably vast, but the **superexponential conceptspace** of the number of different ways to *categorize* these possible objects is even vaster.

For example, given an object that can either have or not have each of *n* properties, there are 2^*n*
different descriptions corresponding to the possible objects of that kind (a number exponential in *n*). The number of possible concepts, each of which either includes a given description or doesn't, is one exponential higher:
2^(2^*n*)

Without an inductive bias, restricting attention to only a small portion of possible concepts, it's not possible to navigate the conceptspace: to learn a concept, a "fully general" learner would need to see all the individual examples that define it. Using probability to mark the extent to which each possibility belongs to a concept is another approach to express prior information and its control over the process of learning.