https://zh.wikipedia.org/zh-tw/%E9%80%92%E5%BD%92
語言中的例子
- 從前有座山，山裡有座廟，廟裡有個老和尚，正在給小和尚講故事呢！故事是什麼呢？「從前有座山，山裡有座廟，廟裡有個老和尚，正在給小和尚講故事呢！故事是什麼呢？『從前有座山，山裡有座廟，廟裡有個老和尚，正在給小和尚講故事呢！故事是什麼呢？……』」
- 一隻狗來到廚房，偷走一小塊麵包。廚子舉起杓子，把那隻狗打死了。於是所有的狗都跑來了，給那隻狗掘了一個墳墓，還在墓碑上刻了墓誌銘，讓未來的狗可以看到：「一隻狗來到廚房，偷走一小塊麵包。廚子舉起杓子，把那隻狗打死了。於是所有的狗都跑來了，給那隻狗掘了一個墳墓，還在墓碑上刻了墓誌銘，讓未來的狗可以看到：『一隻狗來到廚房，偷走一小塊麵包。廚子舉起杓子，把那隻狗打死了。於是所有的狗都跑來了，給那隻狗掘了一個墳墓，還在墓碑上刻了墓誌銘，讓未來的狗可以看到……』」
- 大雄在房裏，用時光電視看著從前的情況。電視畫面中的那個時候，他正在房裏，用時光電視，看著從前的情況。電視畫面中的電視畫面的那個時候，他正在房裏，用時光電視，看著從前的情況……
What is recursion? Is it the essence of time? What’s the difference between recursion and eternal return? （ChatGPT, 2024-12-21)
What is Recursion?
Recursion, in its simplest form, is a process where a function, structure, or phenomenon refers to itself or repeats in a self-similar way. It is commonly used in mathematics, computer science, and philosophy.
• In Mathematics/Computer Science: A recursive function solves a problem by breaking it down into smaller instances of the same problem. For example, the factorial of a number is defined recursively:
with the base case .
• In Philosophy/Systems Thinking: Recursion appears as self-referentiality or feedback loops. Systems can recursively affect themselves, leading to emergent complexity.
Is Recursion the Essence of Time?
Recursion could be seen as a metaphor for time because time itself can exhibit self-referential patterns, such as cycles, feedback loops, or layered processes:
1. Self-Similarity Across Time Scales: Natural processes often display fractal-like recursion, where patterns repeat at different temporal or spatial scales (e.g., day-night cycles vs. yearly cycles).
2. Historical Recursion: In human history, patterns (wars, cultural renaissances, collapses) repeat in ways that are reminiscent of recursive processes.
3. Temporal Feedback: Recursion mirrors how the present is shaped by the past, while simultaneously shaping the future—a feedback loop inherent in time’s flow.
However, recursion is a structural principle, whereas time also involves change, causality, and entropy, making recursion an aspect of time rather than its “essence.”
Eternal Return vs. Recursion
Eternal Return and Recursion share similarities, as both involve repetition and self-similarity, but they differ in meaning and implications:
1. Eternal Return:
• Origin: A metaphysical concept, famously associated with Friedrich Nietzsche.
• Definition: The idea that all events in the universe will recur infinitely in exactly the same way.
• Philosophical Implication: It suggests a deterministic, cyclic universe where time has no ultimate progress or end—everything repeats exactly as it was.
• Temporal Scope: Eternal return is a cosmological and ontological claim about the entire universe’s structure.
2. Recursion:
• Origin: A logical, mathematical, or structural principle.
• Definition: A process or function where the outcome refers back to itself in a dynamic, evolving manner.
• Philosophical Implication: It focuses on self-referential processes and emergence, allowing for variability and adaptability within repeated patterns.
• Temporal Scope: Recursion does not assume exact repetition but often generates new complexity through repetition with variation.
Key Differences
Aspect Eternal Return Recursion
Nature of Repetition Exact repetition of events (static cycles). Iterative self-reference (dynamic, adaptable).
Temporal Outlook Cyclical, deterministic, eternal. Open-ended, often creative or emergent.
Philosophical Context Ontological/metaphysical (cosmology). Structural/functional (systems, logic).
Variability None—everything happens exactly the same. Allows variation and evolution in cycles.
In Summary
• Recursion is a dynamic, self-referential process where patterns repeat and evolve, while eternal return suggests a static, deterministic cycle of exact repetition.
• Recursion may metaphorically describe aspects of time’s structure (e.g., feedback and patterns), but it is not synonymous with the essence of time.
• Eternal return is a more rigid, metaphysical concept, while recursion is a flexible, functional principle that underpins complexity and evolution in systems.
