I think I love ideas. I like a story that’s got some concrete you know structure but also holds abstractions. Life is filled with abstractions and the way we make heads tails of it is through intuition. And so people get used to film that pretty much explains itself a hundred percent. And they kind of turn off that you know beautiful thing of intuition when they’re looking at a film that has some abstractions. And some people on the other hand love these abstractions. And it gives them room to dream.

A abstractions to me is a thing that cinema can say. And it’ so beautiful for me anyway to think about these pictures and some sounds flowing along together in the time in a sequence making a thing that can only really be said in cinema. It’s not words. It’s not just music. It’s the whole bunch of things coming together and making a thing that didn’t exist before. And that’s what i really love about it.

And then to answer your question a little further. It’s up to the people you know to you know find their own your know interpretation. It’s doesn’t really matter what I think. It’s all every screening no matter what even if all the frames of the film are exactly the same. But there no two screenings that are exactly the same. It’s the viwer and the picture and the sound and it makes a circle and it just goes like that. And so you just feel it and think it. That’s kind of intuition emotion and thinking together and come up make it have a sense to you.

译: 我想我钟爱的是理念本身. 我喜欢那种既有具象结构又蕴含抽象思维的故事. 生活本就充满抽象, 而我们理解它的方式就是通过直觉. 人们已经习惯了那些将一切解释得明明白白的电影, 当看到带有抽象元素的影片时, 他们往往会关闭那种美妙的直觉感知. 而另一些人却恰恰痴迷这种抽象, 因为这给了他们造梦的空间.

对我而言, 抽象正是电影独有的表达方式. 当画面与声音在流动的时间中交织, 形成唯有电影才能言说的意境 $—$ 这不是文字能描述的, 也不仅是音乐能呈现的, 而是所有元素共同创造出前所未有的存在 $—$ 这种构想本身就已美得令人心醉.

进一步回答你的问题: 观众完全可以根据自己的理解来诠释作品. 我的想法其实无关紧要. 每一次放映都是独特的相遇, 即便胶片帧数分毫不差, 但银幕光影与观者感受却不可重现. 这种循环生生不息, 你只需去感受, 去思考, 让直觉情感与理性交融, 最终形成属于你自己的体验.

The preface to the 1957 edition of Jorge Luis Borges’ collection of essays The Book of Imaginary Beings (幻兽辞典) contains the comment that monsters will always stalk mythic stories because real animals are a deeply important part of human experience and because monstrous beings are combinations of the real and the imagined, the stuff of nightmares and dreams. The Classical mythic centaur, which melds the forms of man and horse, has its Celtic counterpart in the Welsh horse-woman, Rhiannon. The Cretan Minotaur (米诺陶洛斯), a hideous blend of bull and human, can perhaps be seen transmuted in Irish mythology to become the great fighting bulls of Ulster and Connacht, which had human speech and understanding, or, in Wales, the enchanted boar Twrch Trwyth (图鲁夫图鲁维斯). Borges even goes so far as to argue that monsters are ‘necessary’ for human society. In our own day, fascinated by space and the possibility of worlds beyond, we conjure up fantastic images of galactic monsters, nowhere more clearly presented than in the Star Wars cantina, in which Skywalker and Solo encounter a collection of weird and wonderful beings from all over the Universe. Such are our modern mythic creations. 26

A persistent feature of both Irish and Welsh mythology is the theme of the magical cauldron, a vessel capable of raising the dead and of providing ever-replenishing supplies of food. The Irish god Daghdha, (‘the Good God’), possessed a huge inexhaustible cauldron. The central focus of the Irish Otherworld feast was the cauldron, which never ran out of food. One Irish cauldron-myth was associated with sacral kingship, where the new king of Ulster had to bathe in one, while consuming the meat and broth of a white mare he had ritually ‘married’. 29

$\S$ Ceridwen’s Cauldron: A Welsh mythic tale, preserved in a 13th-century text, The Book of Taliesin (塔列辛之书), contains a rich story of an enchanted cauldron, whose contents endowed those who ate or drank from it with knowledge and inspiration. The cauldron’s keeper was Ceridwen. She bore two children, Crearwy (‘the light or beautiful one’) and Afagddu (‘black’ or ‘ugly’). Wanting to compensate her son for his ill-favoured appearance, his mother mixed a special brew in the cauldron, designed to give him absolute wisdom. Because the potion needed to boil for a year, Ceridwen appointed a young boy, Gwion, to watch over it. As he was tending the cauldron, three drops of scalding liquid splashed onto his hand and, without thinking, he licked his fingers, thus inadvertently acquiring the wisdom intended for Afagddu. Gwion’s flight and pursuit by the angry Ceridwen eventually caused Gwion’s rebirth as the great visionary poet Taliesin. 30

Words are powerful things, the more so if they are spoken aloud, so that sound and meaning blend into a single powerful message that can be shared simultaneously by many people. Keepers of oral tradition had to have prodigiously long and accurate memories and the ability to learn long tales by heart, while adding embellishments along the way. Listeners, too, would remember stories they had heard all their lives, and would not have hesitated to point out errors or inconsistencies. 43

怀着深切的悲痛, 我们谨此告知, 著名数学家 William Lawvere 博士于 2023 年 1 月 23 日与世长辞. Lawvere 教授是加拿大共产党 (马列主义) 的好友, 一位始终秉持人类文明崇高道路的同路人, 致力于对抗并改变社会上的陈旧道德观念, 扫除阻碍进步与启蒙的障碍.

从 1970 年代初开始, 他与 CPC (M-L) [译注: 即 Communist Party of Canada (Marxist-Leninist), 加拿大共产党 (马列主义)] 的创始人和领导人 Hardial Bains 在 “变革的必然性” 与辩证法等哲学及其他项目上展开合作, Hardial Bains 本身就是一位科学家和哲学家. 从 1969 年到 1971 年, 作为 Killam 学者任职于 Halifax Dalhousie 大学, 领导一支享有国际声誉的数学家团队. 但在 1971 年, 当 Lawvere 教授抗议 Pierre Trudeau 颁布《战争措施法》[War Measures Act] 并暂停公民自由、实施种种暴行时, Dalhousie 大学拒绝续聘用他. 尽管其本人领导的数学家团队强烈抗议. 时逾千名学生齐聚 Dalhousie 大学学生会大楼大厅声援劳威尔教授, 反对校方这一专横解雇决定.

多年来, Lawvere 教授多次在加拿大与我们一起讨论重要议题, 并以他深厚广博的学识作出卓越贡献. 1996 年 2 月, 他在温莎大学举行的主题为 “意识起源和社会变革” [The Origin of Consciousness and Social Change] 的跨学科会议上发表了演讲. 该次会议所提交的论文, 对 “独立于人类之外的意识存在” “冷战史学” “现代民主人格的兴起” 等议题提出了深刻洞见. Lawvere 教授提交的论文为《数学改革的历史和哲学》[The History and Philosophy of Mathematic Reform], 该论文剖析了当时一种限制数学科学知识传播的教学趋势, 并指出除其他关切外, 这种趋势如何有效地助长了神秘主义与对权威的盲目服从.

1997 年, 他与来自世界各地的学者一起参加了 Bains 同志的葬礼. 他还参加了 1998 年的 CPC (M-L) 第七次代表大会, 会上他对 Hardial Bains 的工作表示赞赏, 并对大会讨论的论纲作出了贡献. 2005 年, 他参加了党的 35 周年庆典, 再次表达了对党在理论和现代定义方面的工作的赞赏. 他后来写道, 35 周年纪念日 “是一个非常有意义的时刻. […] 特别是, 这一场合使我的工作取得了进一步的进展, 特别是为纪念列宁哲学著作一百周年的项目, 详细介绍了它们如何从自然科学的角度以及从为启蒙而进行的阶级斗争的角度, 成为研究 19 世纪和 20 世纪哲学发展的有用指南. 自从 35 年前 Hardial 指出这些书的重要性以来, 它们一直是我的伴侣. […]”

获悉 Lawvere 教授逝世的消息后, 他的长期伙伴 Eric Hoffman 在感谢 Hardial Bains 和 Bill Lawvere [译注: 即 William Lawvere] 对他自己的生活和工作产生的深远影响时说:

“他们各自在1960年代早期所开展的开创性工作, 如今交汇出一种崭新而令人惊讶的关联, 其最强有力的证据已然显现. 这种关联是人类与自然之间复杂关系网络的一个组成部分. Bill 说, 这一复杂整体所具有的客观性, 迫使我们必须坚定不移地关注对空间与数量的研究.

“在他博客上的一次采访中, Bill 说, ‘数学理论的核心, 在于空间中数量的变化, 以及在这种变化中质的飞跃.’ 无论考虑的是几何学、范畴、逻辑、政治形态的转变、亲属关系亦或其他领域, Bill 始终印证着对立面的统一与同一, 即辩证法的真实存在.

“Bill 的工作将作为扩大启蒙空间的贡献而经久不衰.”

在 CPC (M-L) 中央第一书记发给 Lawvere 教授家人的哀悼信中, 她写道:

“Bill 在他的一生中做出了如此多的贡献, 我们非常感激. 他对发现新事物的热情和奉献精神总是令人鼓舞. 他的方法总是充满活力、专注、在许多方面都很新鲜. 他作为教师的耐心、他的论点的智慧和连贯性、他对年轻一代和教化他们的热情, 以及他对文明崇高道路的勇敢坚持, 都非常出色.

“与 Bill 会面总是非常高兴. 我们将永远珍惜他的友谊、慷慨的精神和对我们共同事业的奉献精神, 他为此毫不畏惧地大声疾呼. 这正彰显了他非凡的品格.

为展示 Lawvere 教授作为数学教育者的风范, 其对问题直截了当的阐释方式, 以及对所有对其工作感兴趣者开放坦诚的讨论态度, 我们谨举一例: 他曾应请求就 “为何范畴论可能如此有用” 提供一个宽泛的论证. 以下是比尔的回答:

人类的日常活动, 如在溪流旁的山上建造房屋、铺设电话管道网络、在太阳系中航行, 都需要可行的计划. 规划任何此类工作都需要发展对空间的思考. 每个发展都涉及许多思考步骤和许多相关的空间几何结构. 由于思考空间的必要多步骤性质, 必须采取独特的数学措施来使其可靠. 只有明确的思维原则 (逻辑) 和明确的空间原则 (几何) 才能保证可靠性. Eilenberg 和 Mac Lane 60 年前发明的理论所取得的巨大进步使逻辑和几何学的原则变得明确; 他们通过发现逻辑与几何的共同形式, 使得二者之间的关系原则也变得清晰可见. 他们解决了亚里士多德在 2300 年前提出的一个问题, 即初步尝试将 “概念的范畴” 显式化. 在 21 世纪, 他们的解决方案不仅适用于平面几何和中世纪三段论, 还适用于无穷维变换空间、数据 “空间” 以及其他每日被成千上万次应用的概念工具. 范畴学家发现, 逻辑与几何原则的形式, 根植于空间之间变换以及空间内部变换的 “自然性” 之中.

下文附上 Lawvere 教授逝世时发表的讣告 [译注: 讣告和后文的传真件等内容请前往原文查看.]. 我们添加了 1971 年 1 月 22 日《达尔豪斯公报》[Dalhousie Gazette] 上关于他被 Dalhousie 大学开除的文章的传真件. 我们还提供了 Lawvere 博士在 1996 年 2 月 9 日至 11 日在温莎大学举行的关于意识起源和社会变革的跨学科会议上发表的题为 “数学教育改革的历史与哲学” [The History and Philosophy of Mathematic Reform] 的论文. 最后, 我们还提供一段 Lawvere 博士的访谈, 其中他亲自阐释了自己的学术工作.

我们向 Bill 的终身伴侣与合作者、他的子女、孙辈、兄弟姊妹, 以及无数朋友与同事致以最深切的哀悼. 愿他们从共同创造的美好回忆中获得慰藉.