Alan Kay Rebuffs Dijkstra to Defend Software as New Kind of Math

vermilyer

Evaluating computing through classical mathematics fails because software engineering operates as a constructive mathematics at structural scales traditional math never envisioned.

AI-assisted summary of Alan Kay on Dijkstra — original source. Check the original for full context.

Source published: 2011-06-07

Key ideas

Alan Kay shares the classic computing industry joke that 'arrogance in computer science is measured in nano-Dijkstras.' (0:00)
Edsger W. Dijkstra criticized American computer science in a polemical paper titled 'On the fact that the Atlantic has two sides,' arguing that American computing was insufficiently mathematical. (0:20)
Alan Kay penned a direct rebuttal titled 'On the fact that most of the software in the world is written on one side of the Atlantic,' asserting that computing is a practical, constructive new mathematics operating at unprecedented scale. (1:20)

Detailed notes

## Background Published on YouTube by vermilyer on June 7, 2011, this short clip captures computer scientist Alan Kay reflecting on Edsger W. Dijkstra. No description or show notes were provided with the upload.

## TL;DR Alan Kay recounts his historical interactions with Dutch computer scientist Edsger W. Dijkstra, opening with the classic industry quip that arrogance is measured in 'nano-Dijkstras.' He describes Dijkstra's paper criticizing American computing for lacking European mathematical rigor, which prompted Kay to write a rebuttal noting that most of the world's software is produced on the American side of the Atlantic. Kay argues that computing is not merely an offshoot of classical mathematics, but a distinct practical math characterized by building consistent structures at unprecedented scale while still bearing the burden of rigorous case-by-case proof.

## Atmosphere & style The clip carries an informal, witty, and wryly humorous tone, eliciting frequent laughter and applause from the audience. Kay speaks with relaxed authority, transitioning effortlessly from playful, irreverent jabs about academic pomposity into sharp philosophical reflections on the nature of software engineering. It feels like intimate, erudite shop talk delivered by a pioneer reflecting on the foundational cultural debates of his field.

## Bulletin - [00:00](https://www.youtube.com/watch?v=9KivesLMncs&t=0s) Alan Kay shares the classic computing industry joke that 'arrogance in computer science is measured in nano-Dijkstras.' - [00:20](https://www.youtube.com/watch?v=9KivesLMncs&t=20s) Edsger W. Dijkstra criticized American computer science in a polemical paper titled 'On the fact that the Atlantic has two sides,' arguing that American computing was insufficiently mathematical. - [01:20](https://www.youtube.com/watch?v=9KivesLMncs&t=80s) Alan Kay penned a direct rebuttal titled 'On the fact that most of the software in the world is written on one side of the Atlantic,' asserting that computing is a practical, constructive new mathematics operating at unprecedented scale.

## Key takeaways - [00:00](https://www.youtube.com/watch?v=9KivesLMncs&t=0s) Alan Kay humorously highlights Edsger W. Dijkstra's famously sharp persona by citing the joke that arrogance in computer science is measured in 'nano-Dijkstras.' - [00:20](https://www.youtube.com/watch?v=9KivesLMncs&t=20s) Dijkstra authored a polemical paper titled 'On the fact that the Atlantic has two sides,' critiquing the cultural and philosophical divide between European and American computer science. - [00:45](https://www.youtube.com/watch?v=9KivesLMncs&t=45s) Dijkstra emphasized the Dutch academic viewpoint, claiming American computing practitioners lacked sufficient mathematical rigor. - [01:05](https://www.youtube.com/watch?v=9KivesLMncs&t=65s) Dijkstra highlighted European academic status by noting that full professors in the Netherlands were appointed directly by the Queen. - [01:20](https://www.youtube.com/watch?v=9KivesLMncs&t=80s) Alan Kay responded with a paper titled 'On the fact that most of the software in the world is written on one side of the Atlantic.' - [01:35](https://www.youtube.com/watch?v=9KivesLMncs&t=95s) Kay, holding a mathematics degree, argues that computing represents a new kind of mathematics that cannot be properly judged through the lens of classical math. - [01:45](https://www.youtube.com/watch?v=9KivesLMncs&t=105s) Kay contends that attempting to fit software strictly into classical math amounts to an indulgent and misguided exercise. - [02:05](https://www.youtube.com/watch?v=9KivesLMncs&t=125s) Computing functions as practical mathematics requiring the construction of consistent structures on a scale far larger than classical mathematics ever attempted. - [02:20](https://www.youtube.com/watch?v=9KivesLMncs&t=140s) Software engineering shares the core challenge of large-scale formal math: proving and convincing others that every single case has been thoroughly accounted for.

## Detailed walkthrough ### [00:00](https://www.youtube.com/watch?v=9KivesLMncs&t=0s) Measuring Arrogance and Dijkstra’s Transatlantic Critique

Opening his talk, Alan Kay reflects on how to ease into his topic and recalls an interaction rooted in the ideas of the influential Dutch computer scientist Edsger W. Dijkstra. Kay pokes fun at Dijkstra's notoriously sharp personality, drawing laughs from the audience with an old industry joke: “I don’t know how many of you have ever met Dijkstra, but you probably know that arrogance in computer science is measured in nano-Dijkstras.”

Kay recounts a particular paper Dijkstra authored—characteristic of the polemics he frequently produced—entitled *On the fact that the Atlantic has two sides*. In that paper, Dijkstra examined the profound philosophical and cultural divide between the European and American approaches to computer science. Dijkstra placed heavy emphasis on the Dutch academic perspective, asserting that American computing practitioners were far from mathematical enough. Dijkstra also pointed out European academic prestige, noting that a full professor in the Netherlands held the distinction of being officially appointed by the Queen.

- Dijkstra's critique centered on the divide between the rigorous, mathematical traditions of Europe (specifically the Netherlands) and the more empirical, engineering-driven style in the United States. - The unit of arrogance in computer science was famously joked to be the "nano-Dijkstra."

[01:20](https://www.youtube.com/watch?v=9KivesLMncs&t=80s) Software, Scale, and Computing as a New Kind of Mathematics

Spurred by Dijkstra's paper, Kay—who holds a degree in mathematics himself—decided to pen a direct rebuttal titled *On the fact that most of the software in the world is written on one side of the Atlantic*, prompting immediate laughter and applause from the audience. Kay’s core thesis was that computing represents an entirely new discipline that cannot simply be evaluated through the lens of traditional mathematics. Addressing those who insisted on treating software solely as classical math, Kay remarked: “it was basically about that computers form a new kind of math you can't judge them they don't really fit well into classical math and people who try to do that are basically uh indulging in a form of masturbation maybe even realizing it”.

Kay argues that computing operates as a practical mathematics. The central challenge of software engineering is constructing systems of consistent structures on a scale far vaster than classical mathematics ever dreamed of attempting. At the same time, computing still faces the exact challenge encountered by any large-scale formal math: the burden of proving and being thoroughly convincing that every single case has been accounted for.

- Kay’s rebuttal title: *On the fact that most of the software in the world is written on one side of the Atlantic*. - Kay views computing not as a branch of classical mathematics, but as a practical, constructive math operating at a vastly larger structural scale. - Both disciplines share the difficult burden of formal rigor: convincing oneself and others that all possible cases have been addressed.

## Mentioned Alan Kay, Edsger W. Dijkstra, On the fact that the Atlantic has two sides, On the fact that most of the software in the world is written on one side of the Atlantic, Netherlands, United States

[Source](https://www.youtube.com/watch?v=9KivesLMncs)

中文简报

艾伦·凯驳斥迪杰斯特拉，捍卫软件作为新型数学的地位用经典数学来衡量计算是行不通的，因为软件工程是一种构造性数学，其运作的结构规模是传统数学从未设想过的。艾伦·凯回顾了他与荷兰计算机科学家艾兹格·W·迪杰斯特拉的过往交集，并以业内流传的经典调侃开场，称傲慢是用“纳迪杰斯特拉”来衡量的。他讲述了迪杰斯特拉曾撰文批评美国计算学界缺乏欧洲数学严谨性，这促使凯撰文反驳，指出世界上绝大多数软件都是在大西洋的美国这一侧编写的。凯认为，计算不仅是经典数学的一个分支，而且是一门独特的实用数学，其特点是在空前的规模上构建一致的结构，同时仍需承担严密逐案证明的责任。艾伦·凯分享了计算行业的经典玩笑，即“计算机科学中的傲慢是用纳迪杰斯特拉来计量的”。 (0:00) 艾兹格·W·迪杰斯特拉曾在一篇题为《论大西洋有两岸这一事实》的论战文章中批评美国计算机科学，认为美国计算缺乏足够的数学性。 (0:20) 艾伦·凯直接撰写了一篇题为《论世界上大部分软件都在大西洋一侧编写这一事实》的反驳文章，坚称计算是一种在空前规模上运作的实用、构造性新数学。 (1:20)

Reading summary

Alan Kay argues that computing constitutes an entirely new, practical form of mathematics operating at unprecedented structural scales, challenging Edsger W. Dijkstra’s critique that American software development lacked classical mathematical rigor. The Transatlantic Divide in Computer Science (0:00) Alan Kay examines the philosophical rift between European and American computing traditions, highlighted by Dutch computer scientist Edsger W. Dijkstra in his polemical paper, On the fact that the Atlantic has two sides. Dijkstra criticized American computer scientists for being insufficiently mathematical compared to their European counterparts, particularly emphasizing the academic prestige and formal rigor of the Dutch system, where full professors receive official appointments from the Queen. Kay acknowledged Dijkstra’s famously sharp personality, citing the computing community's joke that arrogance is measured in "nano-Dijkstras." Scale and Computing as Constructive Mathematics (1:20) Holding a degree in mathematics himself, Kay drafted a rebuttal titled On the fact that most of the software in the world is written on one side of the Atlantic. Kay posited that computing represents a distinct, practical mathematics that cannot be judged through the lens of classical mathematics, arguing that treating software strictly as traditional math misinterprets the discipline's nature. According to Kay, the central challenge of software engineering is building consistent systems on a structural scale far larger than classical mathematics ever attempted. Despite this difference in medium, Kay emphasized that computing still shares classical mathematics' fundamental burden: the formal difficulty of thoroughly proving and verifying that every possible case has been accounted for. Kay’s argument leaves software engineering positioned between pragmatic construction and formal proof, tasking practitioners with managing systemic scale while satisfying the rigorous requirement of accounting for every operational state.

精炼阅读摘要

Alan Kay回顾了他与Edsger W. Dijkstra关于计算学科本质的论争，指出计算机科学不能单纯用经典数学来衡量，而是一种在巨大结构规模上运行的新型实用数学。大西洋两岸的分歧与经典数学视角 (0:00) Alan Kay谈到了荷兰计算机科学家Edsger W. Dijkstra及其尖锐鲜明的学术风格。在计算机科学界，同行曾开玩笑将傲慢的度量单位戏称为“纳狄克斯特拉”（nano-Dijkstras）。Dijkstra在其论战性文章《论大西洋有两面》（On the fact that the Atlantic has two sides）中，强调了欧洲与美国在计算机科学方法上的文化与哲学鸿沟。 Dijkstra从荷兰的学术传统出发，批评美国计算机从业人员严重缺乏数学严谨性，更偏向经验主义与工程风格。为了凸显欧洲学术界的权威与地位，Dijkstra还在文中特别提及荷兰的正教授是由女王正式任命的。新型实用数学与软件规模的严谨性 (1:20) 针对Dijkstra的论调，拥有数学学位的Kay撰写了一篇题为《论世界上大多数软件都写在大西洋的一侧》（On the fact that most of the software in the world is written on one side of the Atlantic）的驳文。Kay主张，计算科学代表了一门全新的学科，根本无法直接套用经典数学的框架去审视；他认为硬将软件开发塞入经典数学范畴的做法脱离了实际。 Kay将计算定义为一种实用性、构造性的新型数学。软件工程的核心挑战在于构建庞大的一致性结构系统，其规模远超经典数学以往的想象。尽管两者形态不同，计算科学与大型形式数学仍面临相同的严谨性考验：从业者必须承担起形式化证明的责任，彻底确认并证明系统已经毫无遗漏地覆盖了每一种可能的情况。 Kay与Dijkstra的分歧揭示了软件在工程规模与数学纯粹性之间的深层张力：软件系统虽然脱胎于工程实践且规模远超传统数学体系，但其对逻辑完整性与边界情况严密证明的要求，与形式数学并无二致。

Detailed notes — zh

## Background 该视频由 YouTube 频道 vermilyer 于 2011 年 6 月 7 日发布，视频时长约为 2 分 38 秒。视频页面并未提供任何文字说明或简介。 ## TL;DR 艾伦·凯（Alan Kay）在演讲中调侃了计算机科学家艾兹格·W·戴克斯特拉（Edsger W. Dijkstra）以傲慢著称的性格，并引用了戴克斯特拉探讨欧美学术文化鸿沟的文章《论大西洋有两岸这一事实》。戴克斯特拉曾批评美国计算机科学不够数学化，而凯则以《论世界上绝大多数软件都是在大西洋某一岸写出来的这一事实》为题进行犀利反驳。凯强调计算技术构成了无法硬塞进古典框架的新型数学，它是处理超大规模一致性结构并在现实工程中证明覆盖所有情况的“实用数学”。 ## Atmosphere & style 现场气氛轻松幽默且充满智慧火花，艾伦·凯以极具个人特色的睿智和辛辣辞藻掌控全场，几句精妙的调侃便引得观众席阵阵哄堂大笑。虽然充斥着学术圈的阵营交锋与火药味，但叙事风格风趣从容，既有令人会心的尖锐讽刺，也有对计算科学本质的深刻洞察，观感快节奏而发人深省。 ## Bulletin - [00:00](https://www.youtube.com/watch?v=9KivesLMncs&t=0s) 艾伦·凯调侃戴克斯特拉名声在外的傲慢性格，称计算机科学界的自负程度是以“纳戴克斯特拉”为基准单位来衡量的。 - [00:25](https://www.youtube.com/watch?v=9KivesLMncs&t=25s) 戴克斯特拉曾撰文指出大西洋两岸在计算机科学研究上的鸿沟，批评美国的研究进路缺乏欧陆传统的古典数学严谨性。 - [01:20](https://www.youtube.com/watch?v=9KivesLMncs&t=80s) 艾伦·凯以撰写反驳文章回应，强调全球绝大部分软件均产自大西洋一岸（美国），计算机科学本质上是一种超越古典数学框架的全新“实用数学”。 - [02:00](https://www.youtube.com/watch?v=9KivesLMncs&t=120s) 凯指出计算所构建的一致性系统规模远超古典数学的想象极限，但同时仍需解决穷尽并证明覆盖所有分支情况的终极难题。 ## Key takeaways - [00:00](https://www.youtube.com/watch?v=9KivesLMncs&t=0s) 计算机科学界流传着将艾兹格·W·戴克斯特拉的名字作为衡量学者傲慢程度单位（纳戴克斯特拉）的幽默梗。 - [00:25](https://www.youtube.com/watch?v=9KivesLMncs&t=25s) 戴克斯特拉在其论文《论大西洋有两岸这一事实》中探讨了欧洲与美国在学术文化与计算机科学研究范式上的巨大分歧。 - [00:45](https://www.youtube.com/watch?v=9KivesLMncs&t=45s) 戴克斯特拉代表的欧陆学术传统重视严格的形式化推演与体制地位（如荷兰正教授由女王亲自任命），批评美国研究“不够数学化”。 - [01:20](https://www.youtube.com/watch?v=9KivesLMncs&t=80s) 艾伦·凯撰写反驳论文，题为《论世界上绝大多数软件都是在大西洋某一岸写出来的这一事实》，以此捍卫工程实践与实用主义价值。 - [01:35](https://www.youtube.com/watch?v=9KivesLMncs&t=95s) 凯认为计算机技术开创了一种全新的数学形态，无法直接用古典数学的标准进行评判。 - [01:45](https://www.youtube.com/watch?v=9KivesLMncs&t=105s) 凯辛辣批评那些强行将现代计算塞入古典数学框架的人，直言这种做法无异于自知或不自知的自慰。 - [02:00](https://www.youtube.com/watch?v=9KivesLMncs&t=120s) 计算机科学属于“实用数学”，其构建的大规模一致性系统结构远远超出了古典数学曾经设想的极限。 - [02:15](https://www.youtube.com/watch?v=9KivesLMncs&t=135s) 新型实用数学仍需面对数学核心难题，即必须证明系统已经严密且完备地覆盖了所有可能的边界和运行情况。 ## Detailed walkthrough ### [00:00](https://www.youtube.com/watch?v=9KivesLMncs&t=0s) 计算机科学中的“傲慢计量单位”与大西洋两岸的争论在演讲的开场部分，艾伦·凯（Alan Kay）试图寻找一个合适的切入点，随后他回忆起了计算机科学家艾兹格·W·戴克斯特拉（Edsger W. Dijkstra）撰写过的一篇代表性论文。凯在切入主题前先调侃起戴克斯特拉那名声在外的性格，引得全场哄堂大笑：“I don't know how many of you have ever met Dijkstra, but you probably know that arrogance in computer science is measured in nano-Dijkstras.”（我不知道你们当中有多少人见过戴克斯特拉，但你们大概都知道，计算机科学领域的傲慢程度是以‘纳戴克斯特拉’为单位来衡量的。）随后，凯提到了戴克斯特拉非常热衷撰写的那类文章，其中一篇题为《论大西洋有两岸这一事实》（*On the fact that the Atlantic has two sides*）。戴克斯特拉在文章中重点探讨了欧洲与美国在计算机科学研究进路上的巨大鸿沟，尤其是以荷兰为代表的欧洲学术传统与美国学界的差异。在戴克斯特拉的论调中，美国这边的计算机研究“不够数学化”；同时文中还罗列了两种文化之间的许多阶层与体制区别，比如在荷兰，一旦晋升为正教授，实际上是由荷兰女王亲自任命的。戴克斯特拉借此强调了欧罗巴理论传统与美国实用主义之间的截然不同。 - **纳米戴克斯特拉（Nano-Dijkstra）**：计算机科学界流传的经典幽默梗，将戴克斯特拉的名字作为衡量学者“自负/傲慢”程度的基准度量衡。 - **大西洋的两岸文化差异**：欧洲（特别是荷兰）讲求严格的形式化、数学严谨性与崇高的学术地位（如女王亲自任命正教授）；而美国则偏向工程实现与务实产出，常被欧陆传统批评为“缺乏足够的数学底蕴”。 --- ### [01:20](https://www.youtube.com/watch?v=9KivesLMncs&t=80s) 艾伦·凯的反驳：计算机是一种全新形态的数学面对戴克斯特拉的观点，拥有数学学位的艾伦·凯撰写了一篇火药味十足的针锋相对的反驳论文。凯在演讲中公布了自己当时拟定的反击标题，立刻引发了听众席热烈的掌声与笑声：“I wrote a rebuttal paper is called *On the fact that most of the software in the world is written on one side of the Atlantic*.”（我写了一篇反驳论文，题目叫《论世界上绝大多数软件都是在大西洋某一岸写出来的这一事实》。）凯进一步阐述了自己反驳的核心哲学。他指出，计算机技术实际上开创了一种全新的数学范畴，根本无法直接套用古典数学的评价标准去衡量。对于那些硬把现代计算往古典数学框架里生搬硬套的人，凯给出了毫不客气地辛辣讽刺，直言这种做法就像是在自我沉溺：“Computers form a new kind of math, you can't judge them, they don't really fit well into classical math, and people who try to do that are basically indulging in a form of masturbation maybe even realizing it.”（计算机构成了一种新型数学，你不能照搬旧逻辑去审判它们，它们与古典数学并不相容，而那些试图这么做的人，基本上是在沉溺于一种甚至自知或不自知的自慰行为。）凯解释道，计算是一种兼顾理论与工程的“实用数学”（practical math）。它所构建的一致性系统结构的庞大规模，远远超出了古典数学曾经敢于梦想尝试的极限。然而，这种新型实用数学又必须面对古典数学在任何规模下都必须解决的终极难题——即如何令人信服地证明系统已经严密覆盖了所有的边界与分支情况（all of the cases）。 ```mermaid flowchart TD accTitle: 古典数学与计算科学的分歧对比 accDescr: 对比戴克斯特拉代表的欧陆古典数学视角与艾伦·凯代表的计算机实用数学视角 subgraph Classical["戴克斯特拉：古典数学与形式主义视角"] C1["欧洲/荷兰学术传统\n（由女王任命的教授体制）"] C2["严格的古典数学规范"] C3["批评美国研究\n不够数学化"] C1 --> C2 --> C3 end subgraph NewMath["艾伦·凯：计算科学即新型实用数学"] K1["大西洋西岸的工程实践\n（产出全球绝大多数软件）"] K2["构建超大规模一致性结构\n（规模远超古典数学所想）"] K3["必须证明覆盖所有运行分支与情况\n（Covering all cases）"] K1 --> K2 --> K3 end C3 -.->|"反驳与范式冲突"| K1 ``` - **反驳文章的核心立足点**：大西洋彼岸（美国）虽然常被欧洲指责不够严谨，但全球绝大部分真正运行的软件都诞生于此。 - **全新形态的实用数学**：计算不仅是公式推演，而是去组织前所未有的超大规模一致性逻辑实体；计算系统同样必须解决数学核心的完备性问题，即确凿无误地穷尽并处理所有可能的状态和案例。 ## Notable quotes > [01:20](https://www.youtube.com/watch?v=9KivesLMncs&t=80s) Computers form a new kind of math, you can't judge them, they don't really fit well into classical math, and people who try to do that are basically indulging in a form of masturbation maybe even realizing it. — Alan Kay ## Mentioned Alan Kay, Edsger W. Dijkstra, On the fact that the Atlantic has two sides, On the fact that most of the software in the world is written on one side of the Atlantic [Source](https://www.youtube.com/watch?v=9KivesLMncs)

Source quotes

[1:20] Alan Kay: Computers form a new kind of math, you can't judge them, they don't really fit well into classical math, and people who try to do that are basically indulging in a form of masturbation maybe even realizing it.

Original transcript

[0:00] the other thing I want to do in the [0:03] beginning part of [0:04] this talk uh I tried to figure out how [0:07] to work my way into it and I finally [0:09] remembered the uh paper that [0:13] dyra I don't know how many of you have [0:15] ever met dyra but you probably know that [0:19] arrogance in computer science is [0:21] measured in N Nano [0:28] dyras [0:32] and he once wrote a a paper of the kind [0:36] that he liked to write a lot of uh which [0:39] had the title on the fact that the [0:41] Atlantic has two [0:44] sides and it was basically all about how [0:48] different the approaches to Computing [0:51] science were uh in Europe especially in [0:54] in [0:55] Holland and uh and in the United States [0:59] and there many interesting you [1:02] know in the US here we were not [1:04] mathematical enough [1:06] and um gee in in Holland if you're a [1:10] full Professor you're actually appointed [1:12] by the queen and there are many [1:14] other uh important distinctions made [1:18] between the the two [1:20] cultures so um I wrote a rebuttal paper [1:25] is called on the fact that most of the [1:27] software in the world is written on one [1:29] side of the [1:33] [Applause] [1:35] Atlantic and it was basically about [1:38] because I had a math degree [1:39] too was basically about that computers [1:43] form a new kind of [1:44] math you can't judge them they don't [1:47] really fit well into classical math and [1:49] people who try to do that are basically [1:52] uh indulging in a form of [1:55] masturbation maybe even realizing [1:58] it [2:03] and it was about that was a kind of a [2:06] practical math that was the balance was [2:10] between [2:12] making structures that were supposed to [2:14] be [2:15] consistent of a much larger kind than [2:18] classical math had ever come close to [2:20] dreaming of [2:22] attempting and having to deal with exact [2:25] same problems that classical math of any [2:28] size has to deal with which is uh being [2:32] able to be convincing about having [2:35] covered all of the [2:37] cases