# Recursion **Domain:** Computation / Mathematics / Language / Cognition **Doc Type:** Concept Node **Maturity:** Developed **Related:** [[Self-Reference]], [[Recursive Self-Modification]], [[Formal Systems]], [[Twittering Machine]] --- ## Definition **Recursion** is a process in which a rule, function or structure refers to or operates upon instances of itself. In computation, recursive procedures solve a problem through smaller instances governed by a base condition. In language, art and philosophy, recursion can describe embedded structures, feedback and self-reference. Recursion is not identical to repetition. Repetition produces another occurrence; recursion re-enters a rule or structure at another level. ## Corpus Function Recursion links [[Formal Systems]], [[Self-Reference]], [[Recursive Self-Modification]] and the machine-intelligence readings in [[articles/Bauhaus Architects of AI|Bauhaus Architects of AI]]. [[Twittering Machine]] supplies a visual metaphor of repeated mechanical activation, but the work’s artistic loop should not be mistaken for a formal recursive algorithm without further specification. ## Key Insight **Recursion becomes generative when re-entry changes the scale, state or context of the operation.** ## Simple Reminders, Quotations, and Thoughts > “Recursion resides at the core of all intelligence. Recursion requires the ability to reference an algorithm or procedure, and keep the reference distinct from the contents. And this capacity to refer is a centerpiece of the way that organisms form models of the world around them and even of themselves. Recursion is a profoundly computational idea and lies at the heart of Godel’s incompleteness theorem and the philosophical consequences that flow from that work. Turing’s own work on computable numbers requires recursion at its center. It’s an open question about how recursion is implemented biologically, but one could speculate that it has been discovered by evolution many times.” > **— Read Montague**, *2017, Edge Annual Question, “WHAT SCIENTIFIC TERM OR CONCEPT OUGHT TO BE MORE WIDELY KNOWN?”* [[reminders/Information/Recursion Resides at the Core of Intelligence by Read Montague|Recursion Resides at the Core of Intelligence by Read Montague]] > “The word "computations" is aptly chosen, for it turns out that all the "magic" of cognition depends, just as life itself does, on cycles within cycles of recurrent, re-entrant, reflexive information-transformation processes from the biochemical scale within the neuron to the whole brain sleep cycle, waves of cerebral activity and recovery revealed by EEGs. Computer programmers have been exploring the space of possible computations for less than a century, but their harvest of invention and discovery so far includes millions of loops within loops within loops. The secret ingredient of improvement is always the same: practice, practice, practice.” > **— Daniel C. Dennett**, *2011, Edge Annual Question, “WHAT SCIENTIFIC CONCEPT WOULD IMPROVE EVERYBODY'S COGNITIVE TOOLKIT?”* [[reminders/Information/Cognition Depends on Cycles Within Cycles by Daniel C. Dennett|Cognition Depends on Cycles Within Cycles by Daniel C. Dennett]]