《渺小一生》:“跟一般的數(shù)學(xué)有什么不一樣？”

　 Harold was quiet. “But I’ll bet they were proud of you,” he said, finally.

哈羅德沉默了?！翱墒俏腋艺f(shuō)，他們以你為榮?！弊詈笏K于說(shuō)。

　 Whenever Harold asked him questions about himself, he always felt something cold move across him, as if he were being iced from the inside, his organs and nerves being protected by a sheath of frost. In that moment, though, he thought he might break, that if he said anything the ice would shatter and he would splinter and crack. So he waited until he knew he would sound normal before he asked Harold if he needed him to find the rest of the articles now or if he should do it in the morning. He didn’t look at Harold, though, and spoke only to his notebook.

每回哈羅德問(wèn)起有關(guān)他個(gè)人的問(wèn)題時(shí)，他總覺(jué)得一股寒意襲來(lái)，仿佛從體內(nèi)開始結(jié)冰，器官和神經(jīng)罩上一層寒霜。那一刻，他覺(jué)得自己可能要崩潰了，如果他開口說(shuō)話，那些冰就會(huì)破碎，讓他整個(gè)人碎裂開來(lái)。所以他等了一會(huì)兒，直到確定自己能用正常的聲音說(shuō)話，才詢問(wèn)哈羅德剩下的文章要他現(xiàn)在找，還是等到明天早上?？墒撬麤](méi)看哈羅德，只是低頭對(duì)著自己的筆記本講話。

　 Harold took a long time to reply. “Tomorrow,” Harold said, quietly, and he nodded, and gathered his things to go home for the night, aware of Harold’s eyes following his lurching progress to the door.

哈羅德沉默了好一會(huì)兒才回答，“明天吧?！惫_德低聲說(shuō)。于是他點(diǎn)點(diǎn)頭，收拾東西回家，知道哈羅德的雙眼一路跟著他一跛一跛地走到門口。

　 Harold wanted to know how he had been raised, and if he had any siblings, and who his friends were, and what he did with them: he was greedy for information. At least he could answer the last questions, and he told him about his friends, and how they had met, and where they were: Malcolm in graduate school at Columbia, JB and Willem at Yale. He liked answering Harold’s questions about them, liked talking about them, liked hearing Harold laugh when he told him stories about them. He told him about CM, and how Santosh and Federico were in some sort of fight with the engineering undergrads who lived in the frat house next door, and how he had awoken one morning to a fleet of motorized dirigibles handmade from condoms floating noisily up past his window, up toward the fourth floor, each dangling signs that read SANTOSH JAIN AND FEDERICO DE LUCA HAVE MICRO-PENISES.

哈羅德想知道他是怎么長(zhǎng)大的、是否有兄弟姐妹，還想知道他有些什么朋友，跟朋友們一起做些什么，他渴望信息。至少他可以回答最后一題，所以就告訴哈羅德朋友們的事情，他們?cè)趺凑J(rèn)識(shí)的、現(xiàn)在他們?cè)谀睦铮厚R爾科姆在哥倫比亞大學(xué)讀研究生，杰比和威廉在耶魯。他喜歡回答哈羅德關(guān)于這些朋友的問(wèn)題，喜歡談起他們，喜歡聽到哈羅德為這些朋友的故事開心大笑的聲音。他告訴他CM的事情，還有桑托什和費(fèi)德里科如何跟隔壁棟兄弟會(huì)會(huì)館的計(jì)算機(jī)系大學(xué)生鬧不和，有天早上他醒來(lái)，看到一串用避孕套做成的機(jī)動(dòng)飛船嘈雜地飄過(guò)他的窗前，向上飄往四樓，每架飛船底下都有個(gè)標(biāo)語(yǔ)，上頭寫著：桑托什·賈殷和費(fèi)德里科·德盧卡有超袖珍老二。

　 But when Harold was asking the other questions, he felt smothered by their weight and frequency and inevitability. And sometimes the air grew so hot with the questions Harold wasn’t asking him that it was as oppressive as if he actually had. People wanted to know so much, they wanted so many answers. And he understood it, he did—he wanted answers, too; he too wanted to know everything. He was grateful, then, for his friends, and for how relatively little they had mined from him, how they had left him to himself, a blank, faceless prairie under whose yellow surface earthworms and beetles wriggled through the black soil, and chips of bone calcified slowly into stone.

但是當(dāng)哈羅德問(wèn)起其他問(wèn)題時(shí)，他就覺(jué)得那些問(wèn)題的重量、出現(xiàn)的頻率和必然性簡(jiǎn)直壓得他喘不過(guò)氣。有時(shí)他覺(jué)得，哈羅德那些沒(méi)有問(wèn)出口的問(wèn)題把空氣變得好熱好悶，簡(jiǎn)直跟問(wèn)了沒(méi)兩樣。人們想知道那么多，想得到那么多答案。他了解，他真的了解，他自己也很想得到答案，他也很想知道一切。然后他就會(huì)很慶幸自己有那些朋友，慶幸他們相較之下很少試圖從他身上挖出什么，慶幸他們不打擾他，讓他像一片空曠無(wú)名的大草原，黃色的表面之下有蚯蚓和甲蟲在黑色土壤中鉆動(dòng)，讓一片片碎骨緩緩鈣化為巖石。

　 “You’re really interested in this,” he snapped at Harold once, frustrated, when Harold had asked him whether he was dating anyone, and then, hearing his tone, stopped and apologized. They had known each other for almost a year by then.

“你真的對(duì)這個(gè)很感興趣?！彼写螣┑眠@么回哈羅德。哈羅德問(wèn)他有沒(méi)有在跟誰(shuí)交往，然后他聽到了自己的口氣，就停下來(lái)道歉。當(dāng)時(shí)他們認(rèn)識(shí)快一年了。

　 “This?” said Harold, ignoring the apology. “I’m interested in you. I don’t see what’s strange about that. This is the kind of stuff friends talk about with each other.”

“為了這個(gè)？”哈羅德說(shuō)，沒(méi)理會(huì)他的道歉，“我是對(duì)你有興趣，這沒(méi)什么好奇怪的，朋友間本來(lái)就會(huì)聊這類事情?！?

　 And yet despite his discomfort, he kept coming back to Harold, kept accepting his dinner invitations, even though at some point in every encounter there would be a moment in which he wished he could disappear, or in which he worried he might have disappointed.

盡管他覺(jué)得不自在，還是持續(xù)回到哈羅德身邊，持續(xù)接受他的晚餐邀約。盡管每回碰面，總有那么一刻他希望自己消失，或者擔(dān)心他會(huì)讓哈羅德失望。

　 One night he went to dinner at Harold’s and was introduced to Harold’s best friend, Laurence, whom he had met in law school and who was now an appellate court judge in Boston, and his wife, Gillian, who taught English at Simmons. “Jude,” said Laurence, whose voice was even lower than Harold’s, “Harold tells me you’re also getting your master’s at MIT. What in?”

某天晚上，他去哈羅德家吃晚餐，認(rèn)識(shí)了哈羅德最要好的朋友勞倫斯，還有他太太吉莉安。勞倫斯是哈羅德讀法學(xué)院時(shí)認(rèn)識(shí)的，現(xiàn)在是波士頓上訴法庭的法官，吉莉安則在西蒙斯女子學(xué)院教英文?！棒玫?，”勞倫斯說(shuō)，他的聲音比哈羅德還低沉，“哈羅德跟我說(shuō)，你同時(shí)也在麻省理工學(xué)院念碩士，是什么碩士？”

　 “Pure math,” he replied.

“純數(shù)學(xué)?！彼卮?。

　 “How is that different from”—she laughed—“regular math?” Gillian asked.

“純數(shù)學(xué)跟……”吉莉安笑了一聲，“跟一般的數(shù)學(xué)有什么不一樣？”她問(wèn)。

　 “Well, regular math, or applied math, is what I suppose you could call practical math,” he said. “It’s used to solve problems, to provide solutions, whether it’s in the realm of economics, or engineering, or accounting, or what have you. But pure math doesn’t exist to provide immediate, or necessarily obvious, practical applications. It’s purely an expression of form, if you will—the only thing it proves is the almost infinite elasticity of mathematics itself, within the accepted set of assumptions by which we define it, of course.”

“這個(gè)嘛，一般數(shù)學(xué)或應(yīng)用數(shù)學(xué)，我認(rèn)為可以算是實(shí)用數(shù)學(xué)，”他說(shuō)，“是用來(lái)解決問(wèn)題、提供解答的，無(wú)論是在經(jīng)濟(jì)學(xué)、工程學(xué)、會(huì)計(jì)學(xué)，或任何方面。但純數(shù)學(xué)不是用來(lái)提供直接、明顯、能實(shí)際被應(yīng)用的解答的，那純粹是一種形式的表達(dá)。它唯一證明的，就是數(shù)學(xué)本身幾乎無(wú)窮無(wú)盡的彈性。當(dāng)然了，是在我們定義的那套假設(shè)里?！?

　 “Do you mean imaginary geometries, stuff like that?” Laurence asked.

“你是指，比如虛數(shù)幾何學(xué)那一類的？”勞倫斯問(wèn)。

　 “It can be, sure. But it’s not just that. Often, it’s merely proof of—of the impossible yet consistent internal logic of math itself. There’s all kinds of specialties within pure math: geometric pure math, like you said, but also algebraic math, algorithmic math, cryptography, information theory, and pure logic, which is what I study.”

“當(dāng)然，包括在內(nèi)，但不只是那些。純數(shù)學(xué)往往只是……只是證明了數(shù)學(xué)本身那種不可能存在、卻始終一致的內(nèi)在邏輯而已。純數(shù)學(xué)領(lǐng)域里還有各式各樣的專業(yè)，比如你剛剛提到的幾何純數(shù)學(xué)，但還有代數(shù)數(shù)學(xué)、程序化數(shù)學(xué)、密碼學(xué)、信息論，以及我在學(xué)的純邏輯。”

　 “Which is what?” Laurence asked.

“那是什么？”勞倫斯問(wèn)。

　 He thought. “Mathematical logic, or pure logic, is essentially a conversation between truths and falsehoods. So for example, I might say to you ‘All positive numbers are real. Two is a positive number. Therefore, two must be real.’ But this isn’t actually true, right? It’s a derivation, a supposition of truth. I haven’t actually proven that two is a real number, but it must logically be true. So you’d write a proof to, in essence, prove that the logic of those two statements is in fact real, and infinitely applicable.” He stopped. “Does that make sense?”

他思索著：“數(shù)學(xué)邏輯，或者純邏輯，基本上是真與假之間的對(duì)話。比方說(shuō)，我可能跟你說(shuō)‘所有正數(shù)都是實(shí)數(shù)。2是正數(shù)，因此2就一定是實(shí)數(shù)?！@不見(jiàn)得確實(shí)為真，對(duì)吧？這是從邏輯上去推演、去假設(shè)的。我其實(shí)沒(méi)有實(shí)際證明2是實(shí)數(shù)，但邏輯上這必然為真。所以你就會(huì)寫出一份證明，從本質(zhì)上去證明這兩種陳述的邏輯確實(shí)為真，而且適用于其他無(wú)窮盡的情況?！彼Ｏ聛?lái)，“你覺(jué)得這樣有道理嗎？”

　 “Video, ergo est,” said Laurence, suddenly. I see it, therefore it is.

“我看到，所以它存在?！眲趥愃购鋈挥美≌Z(yǔ)說(shuō)。

　 He smiled. “And that’s exactly what applied math is. But pure math is more”—he thought again—“Imaginor, ergo est.”

他微笑：“那正是應(yīng)用數(shù)學(xué)的意義。但純數(shù)學(xué)要更……”他又想了一下，然后用拉丁語(yǔ)說(shuō)，“我想象，所以它存在?！?

　 Laurence smiled back at him and nodded. “Very good,” he said.

勞倫斯也朝他微笑點(diǎn)頭?！胺浅：谩！彼f(shuō)。

　 “Well, I have a question,” said Harold, who’d been quiet, listening to them. “How and why on earth did you end up in law school?”

“唔，我有個(gè)問(wèn)題?！惫_德說(shuō)，之前他一直默默在旁邊聽，“你怎么會(huì)來(lái)讀法學(xué)院？到底是為什么？”