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.
這是羅傑・潘若斯, 我們這時代最偉大的科學家之一。 他在 2020 獲得年諾貝爾物理獎, 因為他證明了黑洞與 愛因斯坦的廣義相對論有關。 但早在 1970 年代, 羅傑・潘若斯就已對數學界 做出了一項貢獻, 那就是數學中的密鋪。 密鋪指的是鋪磗形成 某種特定圖案的流程。 羅傑構思的密鋪圖案不凡的地方在於
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.
只需要兩種形狀, 就能建構一種能朝任何方向 無限擴展的圖案, 且永遠不重複。 很類似圓周率 π , 它的小數部分並非隨機, 但會無止盡延續下去,永不循環。 在數學領域,這個特性叫做無週期, 只用兩種形狀就能拼出無週期的密鋪, 這在當時數學界造成轟動, 這種密鋪就此被命名「潘若斯密鋪」。 這是羅傑・潘若斯, 現在要叫羅傑・潘若斯「爵士」, 站在潘若斯密鋪的地板上。
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 年時,陸述義(Peter Lu)博士 仍就讀於普林斯頓大學物理研究所, 他放假時跟親戚去烏茲別克旅遊, 偶然發現十四世紀建造的伊斯蘭學校 也有這樣的圖樣。 分析後發現, 這圖樣也是潘若斯密鋪, 但比潘若斯還早了五百年。
(Laughter)
(笑聲)
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.
這消息馬上震驚了整個科學界, 沒有頭條不提這件事, 連《探索》雜誌也不例外, 並宣布這項發現是 2007 年裡 重要度第 59 名的科學發現。
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.
我們已經從許多領域的視角 探討潘若斯密鋪, 比如數學、物理學, 甚至是藝術和考古學。 這不禁讓我們開始思考, 究竟是這圖樣的哪個特點, 讓活在幾千年前的人覺得至關重要, 還把潘若斯密鋪畫在最重要的建築上? 要回答這問題, 就得從人類學角度來看,並發問: 「打造這圖樣的文化, 它的世界觀是什麼樣子?」 之後我們得知
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.
這圖樣象徵著人生! 你想想,人生非常複雜, 真的複雜。 人生不只複雜,還沒有規律週期, 每件大事、每個偶然、每項決定 都會讓人生有不同的展開, 通常難以預測,出乎意料。 但,人生即使複雜, 即使未來難以預測, 卻還是隱約有種統整性 收束一切線索,觸發所有事件。 接下來我們來看看這種思路怎麼運用到 陸博士在烏茲別克找到的圖樣上吧。
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.
這是烏茲別克的密鋪。 其實這種圖樣源自這套潘若斯密鋪, 由這幾種圖形組成。 要畫出這些圖形, 負責繪製的中世紀工匠們 應該有畫這些輔助線來精準畫出圖形。 我補充一下, 這些輔助線不會出現在成品, 但,若把輔助線跟成品重疊, 會出現這樣的圖樣。 如果把輔助線交織起來,會得到這圖案。 現在把密鋪磚拿掉, 只看輔助線的話, 會得到這個圖樣。 很明顯有種潛藏的結構規律和統一性 藏在這看似無週期的複雜圖形當中。
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.”
「萬物皆有潛藏的統一性」 這樣的主張在古代時很普及, 出現在埃及, 希臘, 澳洲, 中美洲, 北美, 歐洲, 以及中東。 現代西方世界稱潛藏的統一性為「神」, 但自古以來, 就有其他詞彙可以形容這件事: 柏拉圖稱之為「第一因」, 中世紀時期 哲學家史賓諾沙稱之為「單一實體」, 20 世紀, 人們創造大量詞彙來形容這股統一性, 其中我最喜歡的說法是哲學家 阿爾弗雷德・諾斯・懷海德的 「同質美學連續體」 聽起來很有 20 世紀的感覺吧? 但以我這個科學愛好者來說, 我會採用 20 世紀物理學家 戴維・玻姆的說法, 他稱之為「隱序」。
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.
今天演講的重點是什麼呢? 這個,很簡單。 以後看到這些美麗的圖樣, 來自不同的文化、 來自千里之外、千年以前的圖樣, 要知道這些不只是裝飾, 這些圖樣都訴說該文化的基本價值, 他們覺得哪些事重要,如何看待自我、 看待世界,自己在其中的定位。 有人說建築是用石頭打造的書, 所以下次看見令人驚艷的設計時, 你就會知道那些不只是裝飾, 更是一種表態, 一則訊息。 仔細看,仔細聽, 且聽它們娓娓道來。
Thank you.
謝謝大家。
(Applause)
(鼓掌)