想起遙遠(yuǎn)的1954年，一切都如夢(mèng)似幻。那一年，我即將成為一名高中生，我的父親訂閱了一本叫《大眾電子》的雜志，送給我作禮物。他之所以這樣做，是因?yàn)樗旧硎且幻茖W(xué)家，而他的大兒子貌似在科學(xué)和數(shù)學(xué)上有點(diǎn)天賦，但這個(gè)孩子正在被可惡的科幻小說帶壞。事實(shí)上，我的確有足夠理由讓他這樣想。那時(shí)，我如饑似渴地看科幻小說，我會(huì)晚上十一點(diǎn)坐在廚房里，一邊吃著巨型三文治，一邊讀著關(guān)于百萬年后移居火星的小說。而我的父親，當(dāng)然希望我讀的是代數(shù)或者物理的書籍。
Long ago,in a year so far in the past (1954) that my life then as a high school freshman now seems like a dream, my father gave me the gift of a subscription to a new magazine called Popular Electronics. He did this because he was a scientist, and his oldest son seemed to have talents in science and mathematics that were in danger of being subverted by the evil of science fiction. I had, in fact, given him plenty of reason for such concern. I devoured science fiction in those days, you see, often sitting in the kitchen at eleven at night eating a huge sandwich and reading a novel set on Mars a million years in the future. Dad, of course, would have preferred that I be reading a book on algebra or physics.
作為一個(gè)聰明人，我的父親當(dāng)然不會(huì)明令禁止我讀科幻小說，而是通過一些技術(shù)類故事，比如每月《大眾電子》里面“卡爾和杰瑞”的故事，間接地讓我放棄科幻小說?？柡徒苋鹗莾擅咧须娮悠娌牛媒裉斓脑捳f，就是極客或書呆子。他們每個(gè)月，都會(huì)經(jīng)歷一場(chǎng)刺激的冒險(xiǎn)之旅，而每一次，他們都能憑借著專業(yè)知識(shí)化險(xiǎn)為夷。他們是“哈迪男孩”和“湯姆斯威夫特”的結(jié)合體（兩部均為美國(guó)少兒冒險(xiǎn)小說）。父親的計(jì)劃，就是讓我與卡爾和杰瑞一起，探索求真，而不是與羅伯特·海因萊因小說中那些神經(jīng)質(zhì)的時(shí)間旅行者廝混。
Being a clever man, he decided not to simply forbid the science fiction, but rather to outflank the science fiction stories by getting me to read technical stories, like the “Carl and Jerry” tales that appeared each month in Popular Electronics. Carl and Jerry were two high school electronics whiz kids, geeks or nerds, in today’s unattractive terms who managed each month to get involved in some exciting adventure in which their technical knowledge saved the day. They were a 1950s amalgamation of the Hardy Boys and Tom Swift. My father’s plan was to get me to identify with Carl and Jerry, instead of with Robert Heinlein’s neurotic time travelers.
當(dāng)然，父親的迂回策略真的奏效（盡管我從未真正放棄過科幻小說）。我不單對(duì)卡爾和杰瑞的故事著了迷，而且還被每期雜志的電子制作項(xiàng)目深深吸引。我從雜志中學(xué)會(huì)了如何讀電子原理圖。雜志編輯們使用了流行的分解圖進(jìn)行講解，生動(dòng)有趣。這些圖對(duì)于曾玩過郵購(gòu)電子工具套件的人來說一定不會(huì)陌生。我在家后面的車庫(kù)里，建起了一個(gè)工作坊，制作了許多有趣的小電器。
Well, Dad’s devious plan worked (although I never completely gave up the science fiction), and I got hooked not only on Carl and Jerry but also on the electronic construction projects the magazine featured in each issue. I learned how to read electrical schematics from the magazine, whose editors used the same exploded-view, pictorial wiring diagrams that became so well known to all who ever built an electronic, mail-order kit. I constructed a home workshop in the garage behind the house, and a lot of amazing gadgets were built.
我最大的成就，是造出了一臺(tái)“掌計(jì)器”（用于測(cè)量觀眾掌聲音量），在一年學(xué)校的達(dá)人秀中，評(píng)委們就用上了這臺(tái)儀器。這個(gè)儀器無非就是一個(gè)拾音器，一個(gè)音頻功放，和一個(gè)連接到功放輸出接口的500毫安計(jì)。但對(duì)我影響最大的，既不是這個(gè)儀器，也不是我在高中期間制造的其他儀器，而是一臺(tái)根本不可能造出來的儀器。當(dāng)時(shí)我根本沒想到這一點(diǎn)。我的年少輕狂背后，是對(duì)理論的巨大無知。
My greatest success was an “applause meter” that was used by the judges at the high school talent show one year —— a loudspeaker pick-up,? an audio amplifier, and a 500 microampere meter wired into the amplifier output was all it really was. But what really had the greatest impact on me wasn’t that gadget, or any of the others that I built during my high school years. It was one that, in a burst of youthful enthusiasm exceeded only by my enormous ignorance of theory, I didn’t realize is impossible to build.
1955年4月，《大眾電子》如期來到我的郵箱，里面有這么一張神奇的照片——一盞臺(tái)燈，發(fā)出的不是光錐，而是暗錐！我當(dāng)時(shí)看傻了眼，驚嘆道，科學(xué)是多么的神奇?。。ㄎ腋艺f，在你所知的14歲少年里，除了情景喜劇里的那些，誰會(huì)說出這樣的話）。根據(jù)該照片配文，其中的奧秘在于這盞臺(tái)燈并不是連接到一個(gè)普通的電源，而是連接到一個(gè)產(chǎn)生“反極電”電源上。另一張照片中，一根電烙鐵插到反極電源上。它的表面被冰覆蓋著！還有一張照片，一塊電熱板上面是一個(gè)已被凍成冰塊的托盤！這塊電熱板，因?yàn)榻拥搅朔礃O電源上，現(xiàn)在已變成了電冰板。我還記得，我目不轉(zhuǎn)睛地看著這三張照片，產(chǎn)生了一陣陣暈眩。這實(shí)在太神奇了！
When the April 1955 issue of Popular Electronics arrived in the mail, one of the inside photographs displayed an incredible sight —— a desk lamp emitting not a cone of light, but, instead, a cone of darkness! My eyes bugged out when I saw that. What wondrous science was at work here, I gasped (metaphorically speaking, of course, because what fourteen-year-old kid do you know, other than in a TV sitcom, who actually talks like that?). The secret, according to the accompanying article, was that the lamp was not plugged into a normal power outlet, but rather into an outlet delivering contra-polar power.Another photograph showed? a soldering iron plugged into the contra-polar power outlet -- it was covered with ice! And another displayed a frozen ice tray on a hot plate, except it was now a cold plate because it was plugged into contra-polar power. I looked at those three photographs, and I remember my pulse rate elevated and I felt a momentary spell of faintness. This was simply wonderful.
當(dāng)然，這只是編輯們開的一個(gè)大玩笑，他們通過精湛的修圖技巧，達(dá)到了這種效果。當(dāng)我把這篇文章拿給我父親看時(shí)，他暼了一眼后，轉(zhuǎn)頭看著我，覺得我既可憐又可笑，這是我后來才意識(shí)到的。我的父親不是一名電氣工程師，也不是一名物理學(xué)家，但他擁有一個(gè)化學(xué)博士學(xué)位，因此，對(duì)于苯環(huán)和分子鍵以外的技術(shù)知識(shí)，他也不至于一無所知。他馬上就對(duì)反極電產(chǎn)生懷疑，因?yàn)檫@有可能違背了已知的七個(gè)基本物理定律。但是他并沒有嘲笑我，而是簡(jiǎn)單地說，“孩子，看看日期吧”。之前，我根本沒有留意到封面上的“四月”，也沒有留意到下面一行字，“致四月的第一天”，這時(shí)我才恍然大悟。那種被完全愚弄的強(qiáng)烈尷尬，我依然記得清清楚楚。這個(gè)惡搞，其實(shí)在文末的腳注4，已暗示得十分明顯。那是一段虛構(gòu)的引用：“反極性能源委員會(huì)實(shí)務(wù)，第46卷，1324-1346頁(yè)（編者著：來自一艘不明飛行物的文件重印件）”
Well, of course it was all just a huge editorial joke, aided by some nifty photographic retouching. When I showed the article to my father, he glanced at it and then looked at me with what I now know was a mixture of pity and amusement. Dad wasn’t an electrical engineer or a physicist, but with a Ph.D. in chemistry he wasn’t totally ignorant of technical matters that fell outside the realm of benzene rings and molecular bonds. He immediately suspected that “contra-polar power” probably violated perhaps seven different fundamental principles of physics. Rather than laughing at me, however, he simply said, “Son, look at the date on the cover.” I had not noticed the “April” before, or even the subtitle, “In keeping with the first day of April,” but I quickly understood the significance. I still remember my enormous embarrassment at having been so completely taken in. Even I could recognize the “spoofiness” of contra-polar power once I got to the end of the article and read its footnote 4. It listed a phony citation, as follows: “Transactions of the Contra-Polar Energy Commission, Vol. 45, pp. 1324 1346 (Ed. Note A reprint of a document found in a flying saucer).”
正如所有高水平惡搞，這個(gè)惡搞本身包含了很多淺顯易懂的常識(shí)，同時(shí)又用一種荒謬的手法呈現(xiàn)出來。這里我給你們模仿一下文中的句調(diào)，比如這一句就很典型：“當(dāng)普通臺(tái)燈使用反極性能源，臺(tái)燈不產(chǎn)生光，而是吸收光，原來臺(tái)燈照亮的地方，會(huì)變黑暗。（編者著：不要與所謂的“黑光”混淆，黑光只是一種沒有任何可視元素的光。對(duì)于人類的眼睛，“黑光”等價(jià)于沒有光。而由反極性能源產(chǎn)生的光，可以稱之為“負(fù)光”，因?yàn)樗鼫p去了現(xiàn)有的光）”。
Like any good spoof, it had lots of tantalizing truths in it, but presented in a slightly goofy way. To give you a sample of the tone of the article, here’s a typical passage: “When ‘contra-polar energy’ is applied to an ordinary table lamp, light is not produced, but taken away, and the area affected by the lamp becomes dark. (Editor’s Note:This phenomenon should not be confused with ‘black light,’ so-called, which actually is merely light without any visible elements. As far as the human eye is concerned, ‘black light’ is equivalent to zero light; the light produced by contra-polar energy might be designated ‘negative light,’ since it subtracts from light already present.)”
為了蒙騙讀者相信反極性能源的奇妙“特性”，配文下一句就馬上稱，“原子能之所以未能在（電子）愛好者之中普及，是因?yàn)橐靼追礃O性能源的產(chǎn)生原理，需要非常高深的數(shù)學(xué)知識(shí)”。幾十年后重新看這話，真是可笑至極，但當(dāng)我1955年第一次看到時(shí)，卻是非常合理。事實(shí)上，單單代數(shù)足以把反極性能源還有這篇所謂的科普文駁斥得體無原膚。反極電的工作原理，就是利用負(fù)平方根（而不是正平方根），在計(jì)算帶電感電容的電路諧振頻率時(shí)會(huì)用到。我本身對(duì)負(fù)頻率充滿興趣（電氣工程師們已經(jīng)通過使用虛數(shù)i使之具有實(shí)際意義），然而，編輯們還不滿足，并耍了一些聰明小手段，提出“負(fù)電阻”概念。
To set readers up for an “explanation” of the astounding properties of contra-polar energy, the very next sentence makes the following assertion, hilarious now, as I read it decades later, but quite logical to me in 1955: “One of the reasons why atomic energy has not yet become popular among home experimenters is that an understanding of its production requires a knowledge of very advanced mathematics.” Just algebra, however, would strip bare contra-polar energy, or so claimed the article. Contra-polar power “worked” by simply using the negative square root (instead of the positive root) in calculating the resonant frequency in a circuit containing both inductance and capacitance. The idea of negative frequency was intriguing to my mind (and electrical engineers have actually made sense out of it when combined with i), but then the editors played a few more clever tricks and came up with negative resistance.
夜里蜷縮在被窩，能感受到電熱毯的熱量；早上起床，吃一片香脆吐司，能感受到吐司的溫暖，人們都明白，當(dāng)電流通過電阻（正電阻）時(shí)，電阻會(huì)產(chǎn)生熱?！懊黠@地”，當(dāng)電流通過負(fù)電阻時(shí)，溫度會(huì)下降。因此，就有了前面提及的被冰覆蓋的電烙鐵和結(jié)冰了的托盤照片（但臺(tái)燈生成暗錐的邏輯，對(duì)我來說依然不成立）?，F(xiàn)在，負(fù)電阻真的出現(xiàn)了。電氣工程師們?cè)缫炎⒁獾皆谔囟l件下操作電弧，就能產(chǎn)生負(fù)電阻。比如，在電子元件出現(xiàn)之前，人們已經(jīng)懂得利用這種電弧去制造十分先進(jìn)的無線廣播發(fā)射機(jī)，能傳播音樂或者演說，不像赫茲發(fā)射機(jī)和馬可尼火花間隙發(fā)射機(jī)，只能傳播電報(bào)代碼開關(guān)信號(hào)。進(jìn)入大學(xué)之后，我才發(fā)現(xiàn)如果不了解虛數(shù)i的話，是無法從深層理論上了解到無線廣播工作原理的。
As everybody knows who likes to curl up in a warm bed at night under an electric blanket, or who likes a crunchy piece of toast in the morning, resistors (positive resistors) get hot when conducting an electric current. “Obviously,” then, a negative resistor should cool down when conducting a current hence the soldering iron and the ice cube tray photographs. (The logic, if you can call it that, behind the cone of darkness out of a desk lamp still eludes me, however.) Now, there really is such a thing as negative resistance, and it has long been known by electrical engineers to occur in the operation, under certain specific conditions, of electric arcs. Such arcs were used, for example, in the very early pre-electronic days of radio to build extremely powerful transmitters that were able to broadcast music and human speech, rather than just the on-off telegraph code signals that were all the Hertz and Marconi sparkgap transmitters could send. Later, in college, I would learn that the operation of radio is impossible to understand, at a deep theoretical level, without an understanding of i.
盡管四十多年過去了，我的詞匯量也似乎增加了，但是我依然不能向你描述，上述這一切對(duì)年輕的我?guī)淼恼鸷?。它使我意識(shí)到，電子世界有著太多宏大且激動(dòng)人心的內(nèi)容，遠(yuǎn)遠(yuǎn)比我還在車庫(kù)搗鼓小電器時(shí)所想的多。后來，我從高中數(shù)學(xué)課里學(xué)到，有一些二次方程的解是復(fù)數(shù)，我意識(shí)到（不像我那些滿臉困惑的同學(xué)）它不僅僅是枯燥的智力游戲。我已經(jīng)明白到，虛數(shù)i不僅對(duì)電氣工程師來說非常重要，而且它可以用于構(gòu)建真正了不起的設(shè)備。
All of this was more fascinating to my young mind than I can tell you, even forty years later, even with a somewhat increased vocabulary. It showed me that there were big, exciting ideas in the world of electronics, bigger than I had ever imagined while out in the garage tinkering with my gadgets. And later, when in my high school algebra classes I was introduced to complex numbers as the solutions to certain quadratic equations, I knew (unlike my mostly perplexed classmates) that they were not just part of a sterile intellectual game. I already knew that i was important to electrical engineers, and to their ability to construct truly amazing devices.
1958年的一個(gè)清晨，也就是我讀到負(fù)極性能源的三年半后，我坐上一列火車，從洛杉磯聯(lián)合車站出發(fā)，向北開往帕洛阿爾托，到斯坦福大學(xué)開始大學(xué)生活。多年來，卡爾和杰瑞每期都出現(xiàn)在《大眾電子》里，故事也隨著他們也從高中新生，一直講到他們成為虛構(gòu)的袙沃大學(xué)的電氣工程學(xué)生。像他們一樣，我也正式開始了我奉獻(xiàn)終生的事業(yè)，電氣工程師。一到斯坦福，閱讀即占據(jù)了我所有時(shí)間，很快地，我就放下了《大眾電子》，但這本雜志，正好出現(xiàn)合適的時(shí)間。父親的計(jì)劃進(jìn)行得比他想象中還要好。某程度上，我的整個(gè)職業(yè)生涯，都是年輕時(shí)對(duì)虛數(shù)i著迷的結(jié)果，而這也正是我寫這本書的原因。
Three and a half years after reading about contra-polar power, I was sitting in an early morning train out of Los Angeles’ Union Station, heading north to Palo Alto on my way to join the Stanford University freshman class of 1958. Over the years that Carl and Jerry appeared in Popular Electronics,the tales chronicled their progression from high school freshmen to electrical engineering students at the fictional “Parvoo University” and, like them, I was taking the first step on the career path I’ve trodden ever since, as an electrical engineer. Once at Stanford I had more than enough to fill my days with reading and so I quickly drifted away from Popular Electronics,but it had been there at just the right time for me; Dad’s plan had worked better than he could have possibly hoped. In a certain sense, then, my whole professional life has been the result of my youthful fascination with the mystery of i and that is why I have written this book.
1852年1月13日，愛爾蘭數(shù)學(xué)家威廉 漢密爾頓在一封寫給好友，英格蘭數(shù)學(xué)家奧古斯都 摩根的信中提到：“我想，要么是你，要么是我，但我希望是你，必須在某個(gè)時(shí)刻，寫一本關(guān)于虛數(shù)i的歷史書”。五天之后，摩根回信道：“虛數(shù)的歷史，就像印度教歷史，要梳理起來十分困難”。事實(shí)上，他們倆都沒有寫這段歷史。據(jù)我所知，沒有一個(gè)人做過這件事。這也是我寫這本書的另一個(gè)原因。我純粹想了解更多。
In a letter (dated January 13, 1852) to his English friend Augustus De Morgan, the Irish mathematician William Rowan Hamilton wrote, “I see that either you or I but I hope it will be you must write, some time or other,? a history of i .” Five days later De Morgan replied, “As to a history of i , it would be no small job to do it well from the Hindoos downwards.” Well, neither Hamilton or De Morgan ever wrote that history and, as far as I know, nobody else has either. And so that’s another reason why I wrote this book. I simply wanted to learn more.
我的一大遺憾，就是我的父親未能看到這本書。如果他能看到，我希望他會(huì)因?yàn)榘雮€(gè)世紀(jì)前投資訂閱了一本雜志，而倍感欣喜。
My one great regret is that Dad isn’t here to read it. But if he were, I hope he would be pleased at the result of his investment in a magazine subscription nearly a half century ago.
