CONCEPT
Trivial and Non-Trivial Machines
Heinz von Foerster’s foundational taxonomy: trivial machines return the same output to the same input forever and are certifiable; non-trivial machines have histories that make their behavior in principle analytically indeterminable—which is exactly the class large language models belong to.
Von Foerster drew a line through the world of machines that turns out to run straight through the present. A trivial machine is a device whose output is a fixed function of its input: the same key always opens the same lock, the same prompt reliably returns the same answer, the system can be fully specified and tested against that specification. On the other side stands the non-trivial machine, which has internal states, and whose response to any input depends not only on that input but on the state the machine is in—a state shaped by everything the machine has processed before. The same input, on two different days, yields two different outputs, because the machine has a history.
Von Foerster showed that the consequence of this single architectural difference is not merely practical but logical: the number of possible state-dependent input-output relations in a non-trivial machine grows so explosively with the system’s complexity