arXiv:2604.28021physics.soc-phcs.CL2026-04

发现菜谱遵循类似语言的统计规律,揭示烹饪背后的通用设计原理。

Universal statistical laws governing culinary design

  • 通过分析全球菜谱,发现食材使用符合齐普夫定律
  • 菜谱多样性随数量增长呈亚线性关系,营养成分分布呈对数正态
  • 简单生成模型可复现这些规律,适合对符号系统感兴趣的研究者

烹饪是人类创造力的文化表达,如同语言通过词汇与句法跨越地理与时间。然而,尽管菜谱看似多样,其是否遵循类似其他符号系统的统计规律尚不明确。本文分析了一个涵盖全球传统菜谱的大规模语料库,利用先进的命名实体识别算法标注出食材、烹饪技法、厨具等属性。结果发现:食材使用呈现类齐普夫的秩频缩放;菜谱多样性随语料规模增长呈亚线性,符合希普斯定律;菜谱复杂度符合门泽拉特-阿尔特曼型关系,即组成单元数量与平均信息量之间存在反比关联。此外,与加工食品一致,菜谱中宏营养素浓度也表现出对数正态特征。基于优先重用、受限采样与渐进修改的最小生成模型能重现这些规律,表明跨文化菜谱结构由简单且受约束的生成过程塑造。这些发现确立了菜谱作为组合性符号系统,其复杂结构源于基本的生成机制。

原文摘要 · Abstract (English)

Cooking is a cultural expression of human creativity that transcends geography and time through the orchestration of ingredients and techniques, much like languages do through words and syntax. Yet, beneath the apparent diversity of culinary traditions, whether recipes obey statistical laws comparable to those of other symbolic systems remains unknown. Here we analyze a large corpus of traditional recipes spanning global cuisines, annotated using a state-of-the-art named entity recognition algorithm into ingredients, cooking techniques, utensils, and other culinary attributes. We find that ingredient usage exhibits Zipf-like rank-frequency scaling, that culinary diversity grows sublinearly with corpus size in accordance with Heaps' law, and that recipe complexity follows Menzerath-Altmann-type relations between the number and average information of constituent units. Consistent with observations in packaged foods, macronutrient concentrations across recipes also display a log-normal signature. Minimal generative models based on preferential reuse, constrained sampling, and incremental modification recapitulate these regularities, suggesting generic processes that shape recipe architecture across cultures. Together, these findings establish recipes as a compositional symbolic system in which complex structure emerges from simple, constrained generative processes.

符号系统统计规律烹饪科学生成模型

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