Countable. It contrasts with "infinite" and "unlimited" which is a product of
mathematics and the human mind. The attribute focuses attention to the
fact that (a) no observer has endless amounts of time, can make infinitisimal small distinctions and can absorb indefinitely large volumes of
data. What he can experience, what he can decide upon, and what he can do is strictly limited and the theories he may construct must take the finite nature of his
data into consideration. For similar reasons (b) the amount of
information a
computer , or more generally, any material
system may process (accept, memorize, compute, and communicate) is limited (
see bremermann's limit ) so that some problems which a computer programmer may state are definitively unsolvable or not comprehensible within finite time (e.g.,
combinatorial explosion ). Roughly anything material stops at about 10 or about 300
bits (Ashby). Finally (c) a constructivist (
see constructivism ) who accepts only those entities which can be constructed from known entities by intuitively accepted procedures must come to the conclusion that
constructs of some complexity may not be either true or false but in the absence of adequate proofs possess a third value: undecidable. (
Krippendorff )
