This is Roger Penrose. Certainly one of the great scientists of our time, winner of the 2020 Nobel Prize in Physics for his work reconciling black holes with Einstein's general theory of relativity. But back in the 1970s, Roger Penrose made a contribution to the world of mathematics and that part of mathematics known as tiling. You know, tiling, the process of putting tiles together so that they form a particular pattern.
这位是罗杰·彭罗斯 (Roger Penrose), 当代最杰出的科学家之一, 2020 年诺贝尔物理学奖得主, 因证明黑洞遵循 爱因斯坦广义相对论获奖。 但回到 20 世纪 70 年代, 罗杰·彭罗斯也为数学界 做出了一个贡献, 所在数学领域被称为“铺砌”。 所谓“铺砌”,就是铺上瓷砖, 形成某种图案。
The thing that was remarkable about the pattern that Roger Penrose developed is that by using only two shapes, he constructed a pattern that could be expanded infinitely in any direction without ever repeating. Much like the number pi has a decimal that isn’t random, but it will go on forever without repeating. In mathematics, this is a property known as aperiodicity and the notion of an aperiodic tile set using only two tiles was such a sensation, it was given the name Penrose tiling. Here's Roger Penrose, now Sir Roger Penrose, standing on a field of Penrose tiles.
罗杰·彭罗斯想出的图案 之所以非比寻常, 是因为仅仅使用两种图形, 就能组成一个向任意方向无限延展, 却不会重复的图案。 很像 π 有个不是随机的小数一样, 可以在不重复的情况下无限延续。 在数学中,该属性被称为“非周期性”, 仅由两种瓷砖组成的 非周期性瓷砖组合轰动一时, 以至于被命名为“彭罗斯铺砌”。 如图是罗杰·彭罗斯, 现在该称他为罗杰·彭罗斯爵士, 站在由彭罗斯瓷砖铺成的地面上。
Then in 2007, this man, Peter Lu, who was then a graduate student in physics at Princeton, while on vacation with his cousin in Uzbekistan, discovered this pattern on a 14th century madrassa. And after some analysis, concluded that this was, in fact, Penrose tiling 500 years before Penrose.
2007 年,彼得·陆(Peter Lu), 当时是普林斯顿大学物理学研究生, 与亲戚在乌兹别克斯坦度假时, 在一所 14 世纪的伊斯兰学校中 发现了这个图案。 经过一些分析后, 发现这其实是早于彭罗斯 500 年的彭罗斯铺砌。
(Laughter)
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That information took the scientific world by storm and prompted headlines everywhere, including “Discover” magazine, which proclaimed this the 59th most important scientific discovery of the year 2007.
这条信息震惊了科学界, 相关头条层出不穷, 包括《发现》(Discover)杂志, 称其为 2007 年度 第 59 项最重要科学发现。
So now we've heard about this amazing pattern from the point of view of mathematics and from physics and now art and archeology. So that leads us to the question what was there about this pattern that this ancient culture found so important that they put it on their most important building? So for that, we look to the world of anthropology and ask the question, What was the worldview of the culture that made this? And this is what we learn.
我们从数学、物理、艺术、考古的角度 了解了这个惊艳的图案, 这就引出了一个问题: 这个图案有什么特别之处, 让这个古文明都认为它重要到 要被放在最重要的建筑物上面呢? 就此, 我们研究了人类学界,问出了这个问题: 创造出这些的文化拥有什么世界观呢? 以下是我们的收获。
This pattern is life. And as you can see, life's complicated. It's complicated. But not only is life complicated, life is also aperiodic in the sense that every event, every happening, every decision will make the future unfold differently, often in ways that are impossible to predict. Yet, in spite of the complexity and in spite of a future that's impossible to predict, there remains an underlying unity that holds everything together and gives rise to everything. Let's see how that works in a design much like the one Peter Lu found in Uzbekistan.
这个图案代表着人生。 我们都知道,人生是复杂的。 它是复杂的。 但人生不仅仅是复杂的, 它还是非周期性的,每一个事件、 每一个决定都会改变未来的走向, 而通常我们都无法预测。 但是,虽然复杂, 虽然前途未卜, 潜在的统一性仍将凝聚一切、孕育一切。 我们来看看这是怎么运用在设计上的, 那个在乌兹别克斯坦发现的设计。
This is that design. Now, it turns out this is actually based on this set of Penrose tiles, which are reducible to these shapes. And in order to draw these shapes, the medieval craftsmen who did this would have done them by using these construction lines. And I add here that the construction lines don't appear in the final work. But if we add them back, we have this. And now if we weave them together, we will have this. And now if we hide the tiles and just look at the construction lines, we see this. Clearly there's an underlying structure and unity to things that seem to be complex and aperiodic.
这就是那个设计。 它其实是基于这组彭罗斯砌块, 最终可以简化为这些图形。 要画出这些图形, 中世纪的匠人会借助这些辅助线。 我在这里添加了辅助线, 但它们不会出现在最终成品中。 但若在成品中还原辅助线,就会是这样。 若把它们交织在一起,就会得到这个。 如果我们隐去瓷砖, 只看辅助线, 就会看到这个。 显然有一个潜在的结构和统一性, 藏在看似复杂、 非周期性的事物之下。
This notion of a hidden underlying unity was common throughout the ancient world, and one sees it in Egypt, in Greece, in Australia, in Mesoamerica, in North America, in Europe and in the Middle East. Now in the modern West, we might call this underlying unity “God,” but throughout the ages, other terms have been used to describe the same thing. This is what Plato called “first cause.” In the medieval period, philosopher Spinoza called this the “singular substance.” In the 20th century, a number of terms were coined to describe this, one of my favorites being from philosopher Alfred North Whitehead, who called this the “undifferentiated aesthetic continuum.” Doesn't that have a 20th century sound to it? But for me, a lover of science that I am, I will take the term coined by the great 20th century physicist David Bohm, who called this the “implicate order.”
这种隐藏的潜在统一性的概念 在古代世界屡见不鲜, 埃及出现过, 希腊出现过, 澳大利亚出现过, 中美洲出现过, 北美出现过, 欧洲出现过, 中东也出现过。 在当代西方,我们会将 这一隐含的统一称为“上帝”, 但长久以来, 它也有过其它名称。 柏拉图称之为“第一因”。 中世纪, 哲学家斯宾诺莎(Spinoza) 称之为“单一物质”。 20 世纪, 出现了很多描述它的词语, 我最喜欢的一个来自哲学家 阿弗烈·诺夫·怀特海 (Alfred North Whitehead), 他称之为“同质美学连续体”。 听起来是不是很 20 世纪? 但对我这位科学爱好者来说, 我会选取 20 世纪的伟大物理学家 戴维·玻姆(David Bohm)创造的术语, 称之为“隐序”。
So what's the takeaway here? Very simply, this. When we see these wonderful designs created by cultures that are separated from our own by thousands of miles or thousands of years, we can know these aren't decorations. These are statements about the fundamental values that culture had, what they found important, how they saw themselves, the world and themselves in the world. It has been said that architecture is a book written in stone. So when we see these amazing designs, we can know they're not decorations. They're a statement. They're a message. Look, listen. You can hear their voices.
那么今天的要点是什么呢? 很简单。 当看到与我们相距千里、相距千年的文化 创造出的精美设计时, 我们就知道它们并非只是装饰, 它们呈现了那个文明的基本价值、 珍视之物、自我映射、 眼里的世界和身处其中的自己。 有人说,建筑物是用石头撰写的书。 当看到这些美丽的设计时, 我们就知道它们并不是装饰, 它们是一种声明, 传递一个信息。 看一看,听一听, 你能听到他们的声音。
Thank you.
谢谢。
(Applause)
(掌声)