Jul 052020
 

John Conway

生命游戏之父约翰·康威于4月11日由于新冠肺炎去世,享年83岁。作为普林斯顿大学数学系教授的约翰·康威,从小就对数学表现出强烈的兴趣和天赋,因为发明“生命游戏”被人熟知,他在组合博弈论、数论、群论等多个领域都颇有建树。

康威证明了生命游戏具有图灵完备性,允许在生命游戏中模拟任何其他生命游戏规则。在理论上,如果网格空间足够大,计算能力足够强,生命游戏甚至可以模拟出与真实生命相当的复杂度。

康威最为世人所知的创造是《生命游戏》。上世纪70年代初,全世界四分之一的电脑运行过这款游戏。一份美国军方的研究报告显示,人们在岗位上偷闲观看游戏的进展,损失的工作量价值百万美元。直至今天,油管上有关它的最新视频仍在收获数十万的点击量。

游戏的世界是一张方格棋盘,被细胞棋子占据。每个细胞接下来的命运取决于相邻8个方格中其他细胞的数量。生存或死亡,规则看似简单:活着的时候,周围生命分布得太多太少都会导致死亡。死去后,周围生命多起来则会带来重生。

生命在棋盘之上自寻出路,组合、震荡、碰撞,变幻出无穷无尽的图像。它激发了细胞自动机的研究热潮,有计算机的数学家都开始运行模拟,发掘更新更复杂的图样,探索其中蕴含的优美规律。2013年11月,第一个可以克隆自身及规则的《生命游戏》复制体问世。

John Conway

John Horton Conway 小传

透过 Bultheel, Adhemar的书评(《Book Review: ‘Genius at Play: The Curious Mind of John Horton Conway (S. Roberts)》)可以了解这位传奇的数学家。

这是一位具有非常规职业的数学家,他的思考方式与众不同。

他于1937年出生在利物浦——有两个姐姐的家庭。康威在11岁时已定下志愿:去剑桥大学,做一个数学家。他是个多面手,几乎在现代数学的每一方面都有所建树,包括群论、拓扑、数论、几何。

1964年,他在剑桥获得博士学位,后成为普林斯顿大学数学系教授。

在剑桥大学,他是个才华横溢的迷惘年轻人。毕业前很长一段时间,他连找什么工作都没想好。一日闲逛路遇老师,老师建议他向自己申请本校教职,他则连申请书都不知道怎么写。老师只得现场拿出纸笔替他写好,而他只负责签名。几天后,回信寄至:“您的申请失败了,但我还能给您第二选择。”

这是一份助理教授的职位,他在“第二选择”的位置上工作了22年,直到1986年任教普林斯顿。工作的头5年里,他没有做成一件“正事”,终日在教员休息室里发明新游戏,或者为老游戏制定新规则——旧规则太“无聊”了。以粉笔为赌注,他与同事争锋于“豆芽游戏”和“哲学家足球”——用围棋棋子玩的抽象足球。一组数学家在多年后发表论文证明,这球要踢好真的很难啊。

1966年8月,在莫斯科,一位博士生向他介绍了“Leech晶格”:在24维的欧几里得空间里,一堆球体紧密排布,每个球都挨着周围196560个球。他的想象力被激活了,开始寻找这个晶格的空间对称群。他成功了。

他非常健谈,可以同时思考许多显得很混乱的事情。他将自己再普林斯顿(Princeton)的办公室变成一个住所,装满了悬挂在天花板上的纸质多面体模型、书籍、纸张、未打开的信件以及桌子,

椅子和地板上的午餐包装纸。不坐任何整理,也不保留任何文件、信件或档案。

他是充满魅力的数学教师,一位从口袋里变出趣味问题的魔术师,一个侃侃而谈的数学天才。在公众面前,他可能就是数学本身:敏锐,跳脱,灵光闪现在大胡子上,频繁得像静电噼里啪啦闪现在干燥的毛衣上。有时他会随口瞎扯,描述在一场剑桥的酒席上,一个古老家族归还保存了150年的克伦威尔的头颅——他根本就不在现场。

他选择成为这样的康威。成年以前,这个身形单薄的利物浦男孩总坐在教室最后一排,因为内向被老师戏称“玛丽”。在18岁前往剑桥上学的路上,他决定要做一个外向的人,能言善辩,大讲段子,高声笑。

退休之后,他仍出没于各大数学夏令营,和年轻人讨论数学。他多次公开表示越来越不相信自己的记忆力,因为记忆老是撒谎。这可能是实情,也可能是他逃避采访的又一次瞎扯。

Siobhan Roberts 写过一本Conway 的传记 Genius At Play: The Curious Mind of John Horton Conway

John Horton Conway 的著述

John Conway 写过很多精彩的书籍。一个不完整的清单包括:

Conway, J. H. (1970): Regular machines and regular languages;

Conway, J. H. (1976): On numbers and games;

John B Conway: Functions of One Complex Variable[经评论提醒,这书作者不是本文主角John H. Conway ]

Conway, J. H.; Berlekamp E. R.; Guy, R. K. (1982): Winning ways for your mathematical plays;

Conway, J. H.; Sloane, N.J.A. (1988): Sphere packings, lattices and groups;

Conway, J. H.; Guy, R. K. (1982): The book of numbers;

John B Conway: A Course in Functional Analysis[经评论提醒,这书作者不是 John H. Conway]

John B Conway:  A Course in Operator Theor[经评论提醒,这书作者不是 John H. Conway]

Conway, J. H.; Smith D.A. (2003): On Quaternions and Octonions

John Conway | Nov 27, 2012: All Yesterdays: Unique and Speculative Views of Dinosaurs and Other Prehistoric Animals

G. Polya and John H. Conway | Oct 27, 2014: How to Solve It: A New Aspect of Mathematical Method

John H. Conway, Heidi Burgiel, 2008: The Symmetries of Things

Tao 的纪念

正如陶哲轩所说,我们会记住这样一个有趣的灵魂,我们会怀念这样一个有趣的灵魂。

陶哲轩在他的博客写下了纪念文章,全文如下:

I was greatly saddened to learn that John Conway died yesterday from COVID-19, aged 82.

My own mathematical areas of expertise are somewhat far from Conway’s; I have played for instance with finite simple groups on occasion, but have not studied his work on moonshine and the monster group.  But I have certainly encountered his results every so often in surprising contexts; most recently, when working on the Collatz conjecture, I looked into Conway’s wonderfully preposterous FRACTRAN language, which can encode any Turing machine as an iteration of a Collatz-type map, showing in particular that there are generalisations of the Collatz conjecture that are undecidable in axiomatic frameworks such as ZFC.  [EDIT: also, my belief that the Navier-Stokes equations admit solutions that blow up in finite time is also highly influenced by the ability of Conway’s game of life to generate self-replicating “von Neumann machines“.]

I first met John as an incoming graduate student in Princeton in 1992; indeed, a talk he gave, on “Extreme proofs” (proofs that are in some sense “extreme points” in the “convex hull” of all proofs of a given result), may well have been the first research-level talk I ever attended, and one that set a high standard for all the subsequent talks I went to, with Conway’s ability to tease out deep and interesting mathematics from seemingly frivolous questions making a particular impact on me.  (Some version of this talk eventually became this paper of Conway and Shipman many years later.)

Conway was fond of hanging out in the Princeton graduate lounge at the time of my studies there, often tinkering with some game or device, and often enlisting any nearby graduate students to assist him with some experiment or other.  I have a vague memory of being drafted into holding various lengths of cloth with several other students in order to compute some element of a braid group; on another occasion he challenged me to a board game he recently invented (now known as “Phutball“) with Elwyn Berlekamp and Richard Guy (who, by sad coincidence, both also passed away in the last 12 months).  I still remember being repeatedly obliterated in that game, which was a healthy and needed lesson in humility for me (and several of my fellow graduate students) at the time.  I also recall Conway spending several weeks trying to construct a strange periscope-type device to try to help him visualize four-dimensional objects by giving his eyes vertical parallax in addition to the usual horizontal parallax, although he later told me that the only thing the device made him experience was a headache.

About ten years ago we ran into each other at some large mathematics conference, and lacking any other plans, we had a pleasant dinner together at the conference hotel.  We talked a little bit of math, but mostly the conversation was philosophical.  I regrettably do not remember precisely what we discussed, but it was very refreshing and stimulating to have an extremely frank and heartfelt interaction with someone with Conway’s level of insight and intellectual clarity.

Conway was arguably an extreme point in the convex hull of all mathematicians.  He will very much be missed.

(本文参考了几篇文章,部分段落从这里来:

1. 中国青年报,4月17日的《被新冠病毒带走的数学大玩家

2. 掌桥科研,4月12日在知乎的文章《因新冠肺炎逝世的天才数学家约翰·康威 John Horton Conway》 )

  2 Responses to “John Horton Conway”

  1. 逝世的是John H. Conway,不要把John B. Conway的书张冠李戴了。。。

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