So let me start with an example. You all know the story of Newton's apple, right? OK. Is that true? Probably not. Still, it's difficult to think that no apple at all was there. I mean some stepping stone, some specific conditions that made universal gravitation not impossible to conceive. And definitely this was not impossible, at least for Newton. It was possible, and for some reason, it was also there, available at some point, easy to pick as an apple. Here is the apple.
And what about Einstein? Was relativity theory another big leap in the history of ideas no one else could even conceive? Or rather, was it again something adjacent and possible, to Einstein of course, and he got there by small steps and his very peculiar scientific path? Of course we cannot conceive this path, but this doesn't mean that the path was not there.
So all of this seems very evocative, but I would say hardly concrete if we really want to grasp the origin of great ideas and more generally the way in which the new enters our lives. As a physicist, as a scientist, I have learned that posing the right questions is half of the solution. But I think now we start having a great conceptual framework to conceive and address the right questions. So let me drive you to the edge of what is known, or at least, what I know, and let me show you that what is known could be a powerful and fascinating starting point to grasp the deep meaning of words like novelty, innovation, creativity perhaps.
So we are discussing the "new," and of course, the science behind it. The new can enter our lives in many different ways, can be very personal, like I meet a new person, I read a new book, or I listen to a new song. Or it could be global, I mean, something we call innovation. It could be a new theory, a new technology, but it could also be a new book if you're the writer, or it could be a new song if you're the composer. In all of these global cases, the new is for everyone, but experiencing the new can be also frightening, so the new can also frighten us. But still, experiencing the new means exploring a very peculiar space, the space of what could be, the space of the possible, the space of possibilities. It's a very weird space, so I'll try to get you through this space. So it could be a physical space. So in this case, for instance, novelty could be climbing Machu Picchu for the first time, as I did in 2016. It could be a conceptual space, so acquiring new information, making sense of it, in a word, learning. It could be a biological space. I mean, think about the never-ending fight of viruses and bacteria with our immune system.
And now comes the bad news. We are very, very bad at grasping this space. Think of it. Let's make an experiment. Try to think about all the possible things you could do in the next, say, 24 hours. Here the key word is "all." Of course you can conceive a few options, like having a drink, writing a letter, also sleeping during this boring talk, if you can. But not all of them. So think about an alien invasion, now, here, in Milan, or me -- I stopped thinking for 15 minutes.
So it's very difficult to conceive this space, but actually we have an excuse. So it's not so easy to conceive this space because we are trying to conceive the occurrence of something brand new, so something that never occurred before, so we don't have clues. A typical solution could be looking at the future with the eyes of the past, so relying on all the time series of past events and hoping that this is enough to predict the future. But we know this is not working. For instance, this was the first attempt for weather forecasts, and it failed. And it failed because of the great complexity of the underlying phenomenon. So now we know that predictions had to be based on modeling, which means creating a synthetic model of the system, simulating this model and then projecting the system into the future through this model. And now we can do this in a lot of cases with the help of a lot of data.
Looking at the future with the eye of the past could be misleading also for machines. Think about it. Now picture yourself for a second in the middle of the Australian Outback. You stand there under the sun. So you see something weird happening. The car suddenly stops very, very far from a kangaroo crossing the street. You look closer and you realize that the car has no driver. It is not restarting, even after the kangaroo is not there anymore. So for some reasons, the algorithms driving the car cannot make sense of this strange beast jumping here and there on the street. So it just stops. Now, I should tell you, this is a true story. It happened a few months ago to Volvo's self-driving cars in the middle of the Australian Outback.
So let me take a step back, five years back. Italy. Rome. Winter. So the winter of 2012 was very special in Rome. Rome witnessed one of the greatest snowfalls of its history. That winter was special also for me and my colleagues, because we had an insight about the possible mathematical scheme -- again, possible, possible mathematical scheme, to conceive the occurrence of the new. I remember that day because it was snowing, so due to the snowfall, we were blocked, stuck in my department, and we couldn't go home, so we got another coffee, we relaxed and we kept discussing. But at some point -- maybe not that date, precisely -- at some point we made the connection between the problem of the new and a beautiful concept proposed years before by Stuart Kauffman, the adjacent possible. So the adjacent possible consists of all those things. It could be ideas, it could be molecules, it could be technological products that are one step away from what actually exists, and you can achieve them through incremental modifications and recombinations of the existing material.
So for instance, if I speak about the space of my friends, my adjacent possible would be the set of all friends of my friends not already my friends. I hope that's clear. But now if I meet a new person, say Briar, all her friends would immediately enter my adjacent possible, pushing its boundaries further. So if you really want to look from the mathematical point of view -- I'm sure you want -- you can actually look at this picture. So suppose now this is your universe. I know I'm asking a lot. I mean, this is your universe. Now you are the red spot. And the green spot is the adjacent possible for you, so something you've never touched before. So you do your normal life. You move. You move in the space. You have a drink. You meet friends. You read a book. At some point, you end up on the green spot, so you meet Briar for the first time. And what happens? So what happens is there is a new part, a brand new part of the space, becoming possible for you in this very moment, even without any possibility for you to foresee this before touching that point. And behind this there will be a huge set of points that could become possible at some later stages. So you see the space of the possible is very peculiar, because it's not predefined. It's not something we can predefine. It's something that gets continuously shaped and reshaped by our actions and our choices.
So we were so fascinated by these connections we made -- scientists are like this. And based on this, we conceived our mathematical formulation for the adjacent possible, 20 years after the original Kauffman proposals. In our theory -- this is a key point -- I mean, it's crucially based on a complex interplay between the way in which this space of possibilities expands and gets restructured, and the way in which we explore it.
After the epiphany of 2012, we got back to work, real work, because we had to work out this theory, and we came up with a certain number of predictions to be tested in real life. Of course, we need a testable framework to study innovation. So let me drive you across a few predictions we made. The first one concerns the pace of innovation, so the rate at which you observe novelties in very different systems. So our theory predicts that the rate of innovation should follow a universal curve, like this one. This is the rate of innovation versus time in very different conditions. And somehow, we predict that the rate of innovation should decrease steadily over time. So somehow, innovation is predicted to become more difficult as your progress over time.
So we went back to reality and we collected a lot of data, terabytes of data, tracking innovation in Wikipedia, Twitter, the way in which we write free software, even the way we listen to music. I cannot tell you, we were so amazed and pleased and thrilled to discover that the same predictions we made in the theory were actually satisfied in real systems, many different real systems. We were so excited. Of course, apparently, we were on the right track, but of course, we couldn't stop, so we didn't stop. So we kept going on, and at some point we made another discovery that we dubbed "correlated novelties."
It's very simple. So I guess we all experience this. So you listen to "Suzanne" by Leonard Cohen, and this experience triggers your passion for Cohen so that you start frantically listening to his whole production. And then you realize that Fabrizio De André here recorded an Italian version of "Suzanne," and so on and so forth. So somehow for some reason, the very notion of adjacent possible is already encoding the common belief that one thing leads to another in many different systems. But the reason why we were thrilled is because actually we could give, for the first time, a scientific substance to this intuition and start making predictions about the way in which we experience the new.
But there is a third consequence of the existence of the adjacent possible that we named "waves of novelties." So just to make this simple, so in music, without waves of novelties, we would still be listening all the time to Mozart or Beethoven, which is great, but we don't do this all the time. We also listen to the Pet Shop Boys or Justin Bieber -- well, some of us do.
So we could see very clearly all of these patterns in the huge amounts of data we collected and analyzed. For instance, we discovered that popular hits in music are continuously born, you know that, and then they disappear, still leaving room for evergreens. So somehow waves of novelties ebb and flow while the tides always hold the classics. There is this coexistence between evergreens and new hits.
Not only our theory predicts these waves of novelties. This would be trivial. But it also explains why they are there, and they are there for a specific reason, because we as humans display different strategies in the space of the possible. So some of us tend to retrace already known paths. So we say they exploit. Some of us always launch into new adventures. We say they explore. And what we discovered is all the systems we investigated are right at the edge between these two strategies, something like 80 percent exploiting, 20 percent exploring, something like blade runners of innovation. So it seems that the wise balance, you could also say a conservative balance, between past and future, between exploitation and exploration, is already in place and perhaps needed in our system. But again the good news is now we have scientific tools to investigate this equilibrium, perhaps pushing it further in the near future.
So as you can imagine, I was really fascinated by all this. Our mathematical scheme is already providing cues and hints to investigate the space of possibilities and the way in which all of us create it and explore it. But there is more. This, I guess, is a starting point of something that has the potential to become a wonderful journey for a scientific investigation of the new, but also I would say a personal investigation of the new. And I guess this can have a lot of consequences and a huge impact in key activities like learning, education, research, business. So for instance, if you think about artificial intelligence, I am sure -- I mean, artificial intelligence, we need to rely in the near future more and more on the structure of the adjacent possible, to restructure it, to change it, but also to cope with the unknowns of the future. In parallel, we have a lot of tools, new tools now, to investigate how creativity works and what triggers innovation. And the aim of all this is to raise a generation of people able to come up with new ideas to face the challenges in front of us. We all know. I think it's a long way to go, but the questions, and the tools, are now there, adjacent and possible.
一些什么，卻又不具象， 尤其當(dāng)我們真的希望 找到變得更優(yōu)秀的源頭， 或通俗一點(diǎn)說，我們怎樣 在生活中發(fā)現(xiàn)新鮮事物的時候。 作為一個物理學(xué)家，科學(xué)家， 我知道，提出正確的問題， 問題就解決了一半。 而我想，我們現(xiàn)在已經(jīng)擁有了 很棒的概念性的框架 來發(fā)現(xiàn)和解決問題。 那么現(xiàn)在，讓我?guī)Т蠹?進(jìn)入身邊所熟悉的領(lǐng)域， 或至少，是我熟悉的。 讓我來說明一下，從熟悉的領(lǐng)域開始 去感知新奇，創(chuàng)新，或者創(chuàng)造 這類詞語更深層的含義， 是一個多么好的起點(diǎn)。
我們在討論“新”， 同時還有它背后的科學(xué)。 “新”可以由不同的方式 進(jìn)入我們的生活， 可以是很私人的， 比如，我認(rèn)識了一個新朋友， 讀了一本新書或者聽了一首新歌； 也可以是普遍化的， 比如，我們所說的創(chuàng)新， 可以是新理論，新技術(shù)， 同樣也可以是一本新書， 前提是你是個作家， 也可以是一首新歌， 如果你是個作曲家。 這所有的例子里的“新”， 是每個人都有機(jī)會接觸發(fā)現(xiàn)的。 但體驗(yàn)“新”卻也常常令人擔(dān)憂， 因?yàn)槲覀兠鎸Α靶隆?，會有畏懼感?/a> 同時，體驗(yàn)“新”意味著 我們在探索一段奇特的領(lǐng)域， 它具有任意性， 還有可能性。 這是個很神奇的領(lǐng)域， 不過我會嘗試帶大家領(lǐng)略一下。 它可以是某個物理空間。 比如， 我在2016年第一次爬上 馬丘比丘（古代印加城遺址， 在今秘魯中南部)。 也可以是理論上的空間， 如獲取新的信息， 簡而言之，就是學(xué)習(xí)。 它還可以是生物層次的。 想想我們的免疫系統(tǒng) 與病毒及細(xì)菌之間 永不停歇的對抗。
所以，要察覺到 所有可能發(fā)生的事情并不容易。 但這可以理解。 不容易實(shí)現(xiàn)的原因是 我們都嘗試著 去發(fā)現(xiàn)一些絕對的“新”， 一些以前從未發(fā)生的事情， 所以我們找不到任何線索。 那么有什么解決辦法嗎？ 用目睹了過去的眼睛看未來， 就是憑借著在過去發(fā)生的事， 這些經(jīng)歷能支持我們預(yù)測未來。 但實(shí)際上，這種方法的效果差強(qiáng)人意。 就跟首次播報天氣失敗了一樣。 因?yàn)槭虑槎喟l(fā)生在表面， 而內(nèi)部的復(fù)雜性卻被忽略了。 所以，我們會通過建模來幫助預(yù)測， 就是建立一個系統(tǒng)的綜合模型， 通過模型模擬，預(yù)測系統(tǒng)的 未來發(fā)展。 在很多情況下，基于大量數(shù)據(jù)， 我們都可以建模。
但用過去的眼睛（數(shù)據(jù)） 預(yù)測未來（系統(tǒng)）， 也可能會出錯， 對計算機(jī)來說也是一樣。 設(shè)想一個畫面， 你在澳大利亞內(nèi)陸地區(qū)， 站在太陽底下， 看到了一些奇怪的事情。 遠(yuǎn)遠(yuǎn)地，一輛車突然停住了， 在它前面很遠(yuǎn)處 有一只袋鼠在過馬路。 你仔細(xì)一看， 發(fā)現(xiàn)車?yán)锞箾]有司機(jī)。 袋鼠過完馬路后， 汽車也沒有重新啟動。 因?yàn)橐恍┰颍?/a> 這輛無人駕駛汽車內(nèi)置的算法 并不能理解這種現(xiàn)象， 一只奇怪的龐然大物 在街上蹦來蹦去。 于是它就停下了。 這是個真實(shí)的故事。 幾個月前，沃爾沃的 無人駕駛汽車就這樣 停在了澳洲內(nèi)陸中部地區(qū)。
讓我們暫時回到過去， 五年前， 意大利，羅馬，冬天。 2012的冬天， 對羅馬來說是很特別的， 因?yàn)橐粓鍪窡o前例， 美不勝收的飄雪。 這個冬天對我和我的同事們 來說也有著特殊的意義， 因?yàn)槲覀兝斫饬艘环N 近乎合理的數(shù)學(xué)模型—— 強(qiáng)調(diào)一下，只是可能， 用來幫助發(fā)現(xiàn)“新”。 我記得那天在下雪， 也正是因?yàn)檫@場雪， 我們被困在了辦公室， 無法回家， 所以我們決定喝杯咖啡，放松一下， 同時繼續(xù)討論我們的研究， 忽然之間——準(zhǔn)確地說， 可能并不在那段小憩的時間—— 在某個時間點(diǎn)，我們在 發(fā)現(xiàn)“新”，與斯圖亞特 · 考夫曼 曾經(jīng)提出的一個美妙的 理論之間建立起了一種聯(lián)系， 即臨界的可能性。 臨界的可能性可以包含很多東西， 比如新點(diǎn)子，新分子， 或者新科技產(chǎn)品。 我們距離這些實(shí)際存在的“新”， 只有一步之遙。 我們可以通過改變身邊存在的事物， 或?qū)ζ浼右灾亟M來發(fā)現(xiàn)“新”。
舉個例子，比如我身邊有一群朋友， 那么身邊可能的“新”， 可以是一群我朋友的朋友， 他們目前還不是我的朋友。 希望我說的夠清楚。 如果我現(xiàn)在認(rèn)識一個新朋友， 比如布萊爾， 那么她的朋友們就會 立即成為我的“新”朋友的備選人， 這樣我的人脈就會越來越多。 如果你們想用數(shù)學(xué)角度 來看待這件事—— 我確信你們有這個想法—— 我們可以來看一眼這張圖。 這就是你的世界。 我知道我要求有點(diǎn)多。 麻煩大家把自己置身于這張圖，這個 紅點(diǎn)，就是我們現(xiàn)在所處的位置。 綠點(diǎn)便是我們身邊可能的“新”， 即我們從未踏入的領(lǐng)域。 我們過著正常的生活， 在自己的世界中一步一步走， 喝杯水，見個朋友，讀本書， 在某個時間點(diǎn)， 我們就走到了這個綠點(diǎn)， 比如，我們在這里 第一次見到了布萊爾， 然后呢？ 在這個特殊時刻， 我們會涉足一個嶄新的領(lǐng)域， 我們從未投身的領(lǐng)域， 即使我們從未預(yù)想能走到 這片未知的領(lǐng)域。 在踏入這片新區(qū)域后， 會有更多新領(lǐng)域， 在未來的某個時段可能被我們開啟。 所以我們看到了， 身邊可能的未知領(lǐng)域是很神奇的， 因?yàn)樗牟豢深A(yù)知。 我們沒有辦法提前得知， 這片區(qū)域是隨著我們的行動和選擇 被隨時塑造的。
在2012年的頓悟后， 我們回到工作中，進(jìn)行實(shí)地考察， 因?yàn)橐獙⒗碚搼?yīng)用于實(shí)踐。 我們提出了幾個需要用實(shí)際生活 來檢驗(yàn)的預(yù)測。 當(dāng)然，我們需要一個測試體系， 來研究這個新方法。 讓我簡單介紹一下 我們所做的預(yù)測。 第一個是創(chuàng)新的步調(diào)， 即不同的體系中 發(fā)現(xiàn)“新”的速度。 我們的理論預(yù)測出這種速度 應(yīng)該遵循通用曲線， 比如這張圖。 這是不同條件下新方法的 速率與時間的比值。 通常，我們預(yù)測發(fā)現(xiàn)“新”的速率 隨著時間變長穩(wěn)定降低， 由于某些限制，隨著我們行動的增加 發(fā)現(xiàn)“新”會變得更加困難。
所以我們回到現(xiàn)實(shí)中來， 收集了很多數(shù)據(jù)，多達(dá)萬億字節(jié)。 從維基百科，到推特記錄， 記錄我們寫新程序的方式， 甚至聽音樂的方式。 我絕對不會跟你們說， 我們是多么激動，雀躍地發(fā)現(xiàn)， 在許多不同實(shí)際的體系中， 我們的預(yù)測與真實(shí)情況 幾乎沒有差別。 我們太激動了。 很明顯，我們走在一條正確的路上， 當(dāng)然，我們不愿意就此停下， 也沒有停下。 我們一直努力著， 直到某個時候， 我們發(fā)現(xiàn)了另外的新理論， 我們把它叫做“關(guān)聯(lián)性創(chuàng)新”。
很簡單， 我想我們都經(jīng)歷過。 當(dāng)我們聽到萊昂納德 · 科恩的 《蘇珊》（歌曲）時， 這會激起你對科恩的熱情， 然后你就會迫不及待地 去聽他所有的作品， 然后你會看到一個名字， 法布里奇奧 · 德 · 安德雷， 翻唱了蘇珊的意大利語版本， 等等類似的例子。 不知怎么的， 這個臨界可能性的概念就會 根植于我們的信念中， 即在很多不同的體系中， “新”的發(fā)現(xiàn)具有連續(xù)性。 那么我們?yōu)槭裁茨敲锤吲d呢， 因?yàn)榈谝淮危覀兛梢园堰@種直覺 科學(xué)地實(shí)體化， 并且開始對 體驗(yàn)“新”的方式進(jìn)行預(yù)測。
不僅僅是我們的理論預(yù)測到了 創(chuàng)新浪潮的存在， 這不重要。 重要的是，為什它們在那里， 基于某種特殊的原因， 因?yàn)槲覀兪侨祟悾?會在充滿可能性空間中 展現(xiàn)不同的策略。 我們中的有些人傾向 去走已經(jīng)走過的路， 我們稱之為開拓。 有的人愿意去做新的探險， 這是探索。 我們發(fā)現(xiàn)的自己探究的東西， 就在開拓和探索的邊緣， 就像80%是開發(fā)，20%是探索。 像是葉片式螺旋的創(chuàng)新。 看上去，保持在過去和未來之間， 開發(fā)與探索之間的 智慧的平衡， 或稱為保守的平衡， 已經(jīng)就位，并且被 我們的自身所需要。 好消息是，現(xiàn)在我們有科學(xué)工具 來研究這種均衡， 或許在不久的將來 可以推廣這種平衡。
你們能想象到， 我是多么的深陷其中。 我們的數(shù)學(xué)模型已經(jīng) 提供了線索和暗示， 去尋找可能行的空間， 以及我們所有人創(chuàng)造并探索的方式。 不僅如此， 這是一段關(guān)于“新”的 奇妙科學(xué)探索之路的起點(diǎn)， 同樣也是個人自我發(fā)現(xiàn)的起點(diǎn)。 我猜這個過程會卓有成效， 并對主要活動產(chǎn)生巨大影響， 比如學(xué)習(xí)，教育，研究，商務(wù)。 比如，想一下人工智能， 我確信——在不久的將來， 我們會越來越依附 發(fā)現(xiàn)臨界可能性的這樣一種結(jié)構(gòu)， 人工智能會去幫助重建這個結(jié)構(gòu)， 去改變，去應(yīng)對未知。 同時，我們也有很多工具， 嶄新的現(xiàn)代工具， 去探究創(chuàng)新力是怎樣產(chǎn)生， 是什么使創(chuàng)新應(yīng)運(yùn)而生。 這所有一切的目的 便是去扶持一代人， 一代能有新想法， 有能力面對挑戰(zhàn)的人 我們都知道。 還有很長的路要走， 但現(xiàn)在已有的問題，工具， 就在身邊，甚至唾手可得。
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