ï»? 00:00:05,670 --> 00:00:07,860 剑桥的新巧构æ€? Another Good Idea from Cambridge 2 00:00:10,430 --> 00:00:12,860 辑ְ”文学院系列课½E? Darwin College Lecture Series Professor Lord Robert May 3 00:00:25,250 --> 00:00:28,550 再次热烈‹Æ¢è¿Žå„位参加 Well, once again a very warm welcome to this um 4 00:00:28,810 --> 00:00:32,230 ½W?6‹Æ¡è¾¾ž®”文学院的系列课½E? 26th, um, series of Darwin College lectures 5 00:00:33,420 --> 00:00:34,920 ˜q™æ¬¡çš„主题是 ¾Ÿ? Our theme this year as you know is beauty 6 00:00:36,140 --> 00:00:39,660 ˜q™å¥—评¡¨‹ and this series has been conceived and organized by um 7 00:00:40,740 --> 00:00:41,400 由Lorry Arriton Lorry Arrington, 8 00:00:42,470 --> 00:00:44,900 Sophie Lanyard,Fled David Sophie Lanyard, and, Fled David, 9 00:00:45,280 --> 00:00:46,610 å’?Jessie Holman设计¾l„织 and Jessie Holman 10 00:00:47,420 --> 00:00:51,650 他们同时 and they also have an expo of the arranged beauty work 11 00:00:52,720 --> 00:00:54,030 在Feats William¾ŸŽæœ¯é¦†ç»„¾l? at the Feats William Museum 12 00:00:55,210 --> 00:00:56,390 一场有点DIY意味的美学作品展è§? that is sort of do-it-yourself and such experince. 13 00:00:57,510 --> 00:01:00,810 所以在此也感谢¾ŸŽæœ¯é¦†çš„支持 And many thanks to the Feats William Museum for that. 14 00:01:03,790 --> 00:01:06,060 另外感谢Richard Nan King Well, I'm all thanks that he could be here tonight 15 00:01:06,380 --> 00:01:08,030 很高兴它今晚能出å¸? but many thanks to Richard Nan King 16 00:01:08,940 --> 00:01:12,190 正是他的æ…äh…¨æ‰è®©˜q™æ¬¡è¯„¡¨‹™åºåˆ©å¼€è®? His generosity enables us to run these lectures 17 00:01:14,440 --> 00:01:16,030 评¡¨‹¾l„委会对讲授内容的编åˆ? The team who put this together 18 00:01:17,000 --> 00:01:19,470 我想是以貌似对立矛盾çš? I think your choice of talking has been guided 19 00:01:19,850 --> 00:01:24,080 自然¾ŸŽäؓä¸Èº¿ by the essentially Paradoxical Nature of Beauty 20 00:01:24,680 --> 00:01:26,650 在接下来çš?周课½E‹é‡Œ So during the course of the next 8 weeks 21 00:01:26,910 --> 00:01:29,980 我们ž®†äº†è§£äh¾cȝš„探烦 we're going to be hearing about, the grope task and the sublime, 22 00:01:31,360 --> 00:01:33,170 自然的雄伟和宇宙的壮¾Ÿ? about the beauty and beauty of the cosmos 23 00:01:34,090 --> 00:01:36,950 来学习我们如何感受美 How we perceive beauty 24 00:01:37,530 --> 00:01:38,410 ¾ŸŽå¦‚何媄响我ä»? and how it affects us 25 00:01:39,170 --> 00:01:40,990 及美在愉悦或恐惧的体验中 and beauty in the service of happiness 26 00:01:41,240 --> 00:01:43,300 所扮演的角è‰? and the beauty in the service of terror 27 00:01:44,020 --> 00:01:48,730 ˜q™å°†æ˜¯éžå¸¸æœ‰­‘£çš„一套课½E? so it should be really interesting range of talks 28 00:01:49,420 --> 00:01:51,480 我们的课名是¾ŸŽä¸ŽçœŸç† And we're starting with beauty and scientific thinking 29 00:01:52,830 --> 00:01:55,890 首先ž®†ä»Ž¾ŸŽå’Œ¿U‘学思维讲è“v and this subject, the title is beauty and truth 30 00:01:58,210 --> 00:02:01,950 今天的讲师是教授 Lord Robert May As for the speaker we are very honored to have Professor Lord Robert May 31 00:02:02,450 --> 00:02:04,850 他目前ä“Q职于牛æÓ|大学和帝国理工学é™? he's currently in Oxford and Imperial College 32 00:02:05,310 --> 00:02:06,660 同时å…ÆDŒäºŽå“ˆä½? he is helping at Harvard 33 00:02:06,910 --> 00:02:09,210 他曾ž®Þp¯»äºŽæ‚‰ž®¼å¤§å­¦å’Œæ™®æž—斯顿大学 his native Sydney and Princeton 34 00:02:10,750 --> 00:02:12,070 他是一ä½? He is as you know a scientist 35 00:02:12,500 --> 00:02:15,070 有着杰出贡献的科学家 of quite remarkable brilliant achievements 36 00:02:15,620 --> 00:02:18,830 在不½E›_®šåŠ¨æ€ç³»¾lŸé¢†åŸŸæ¨¡åž‹ä¸Šæˆç‡W卓越 in his modeling of unstable dynamic system 37 00:02:19,290 --> 00:02:22,280 他的模型在多个学¿U‘都有极大的影响 which has been enormously influential across ranges of subjects 38 00:02:22,940 --> 00:02:27,660 比如理论生态学生物多样性学¿U‘ç­‰ in theoretical ecology and in biodiversity 39 00:02:29,200 --> 00:02:30,690 ˜q™ä¸ªæœˆçš„《自然》杂志上 And in this month's Nature I think 40 00:02:31,160 --> 00:02:36,750 他因一½‹‡æœ‰å…³é“¶è¡Œä¸š¾pȝ»Ÿé£Žé™©çš„论文而获å¥? he wins prizes by having a paper on systematic risk in banking 41 00:02:37,330 --> 00:02:39,630 昨天他还停留在金融时æŠ? Yesterday he had even remained in Financial Times 42 00:02:40,090 --> 00:02:45,420 因äؓ一场即ž®†ä‹D行的会议 for an engineering conference which is about going 43 00:02:46,000 --> 00:02:48,070 May教授˜q˜æ˜¯¿U‘学协会的一å‘? Professor May has been in the presence of the Science society 44 00:02:48,540 --> 00:02:51,970 òq¶ä¸”是政府的首席¿U‘å­¦™åùN—® and he's been the chief scientific advisor to government 45 00:02:52,810 --> 00:02:55,140 ˜q™ä¸ªèŒä½¾l™äº†ä»–å……­‘³çš„æœÞZ¼š a role which must have given him ample opportunities 46 00:02:55,700 --> 00:03:00,180 来思考真理的使用和误ç”? to reflect on the use and the misuse of truth 47 00:03:01,140 --> 00:03:02,210 我们评¡¨‹çš„标题是 ¾ŸŽä¸ŽçœŸç† The title is Beauty and Truth 48 00:03:02,730 --> 00:03:05,840 下面‹Æ¢è¿ŽMay It's a pleasure to introduce Professor May 49 00:03:21,980 --> 00:03:23,690 先让我打个广å‘? First a piece of self-advertisement 50 00:03:24,250 --> 00:03:27,510 《自然》的ž®é¢å›„¡‰‡¾l™äº†é›äh›¼å…„弟一个略昑֤¸å¼ çš„描述 The cover illustration of nature has fussed of Lemmon Brothers 51 00:03:28,390 --> 00:03:31,580 从左上角一直蜿èœ? with a jagged line, like a graph, 52 00:03:32,240 --> 00:03:34,450 到右下角的一条折¾U? going down from top left to bottom right. 53 00:03:36,900 --> 00:03:38,160 你们å»ø™®®å¤§å®¶çœ‹ä¸€çœ? And I recommend it to you 54 00:03:38,820 --> 00:03:42,140 我想评¡¨‹å‘è“v人的本意 I think what the organizer's intent is that 55 00:03:42,450 --> 00:03:44,090 是想叫我说一说美和数å­? I should talk about beauty and mathematics. 56 00:03:45,620 --> 00:03:48,580 某种½E‹åº¦ä¸Šè¯´ 我正要这样做 And I'm to a degree going to do this 57 00:03:48,940 --> 00:03:52,440 但我更愿意把它阐释成 but I have more generously interpreted 58 00:03:53,110 --> 00:03:57,590 ¾ŸŽä¸Žè®¤è¯†ä¸–界的运行规å¾? as beauty and understanding how the world works. 59 00:04:00,290 --> 00:04:03,790 我们对世界运作的求知‹Æ? Our attempts to understand how the world around us works 60 00:04:05,040 --> 00:04:06,410 我想可以˜q½æº¯åˆ? I believe go back 61 00:04:07,400 --> 00:04:11,320 史前的千万年 tens hundreds of thousands of years before recorded history began 62 00:04:12,710 --> 00:04:14,670 它们被刻在石½‹×ƒ¸Š They're written in Stone Hedge 63 00:04:15,180 --> 00:04:17,650 ˜q˜æœ‰Wuntemiro的岩‹zžé‡Œ ½{‰ç­‰ and the caves at the Wuntemiro and other places. 64 00:04:18,570 --> 00:04:22,740 在我看来对这些最合理的解释大概是 Well it seems to me the most plausible interpretation of what you see is 65 00:04:23,200 --> 00:04:26,930 ¾ŸŽçš„创造的集合 a mixture of artistic creativity, 66 00:04:27,510 --> 00:04:30,350 同时天然地带æœ? but seamlessly blended with an attempt 67 00:04:30,900 --> 00:04:35,000 åŽÀLŽ¢ç´¢åŽ»ç†è§£˜q™ä¸ªå¥‡å¦™ä¸–界的æÍæœ? to understand an influence the otherwise bewitching the world around 68 00:04:37,170 --> 00:04:41,060 接下来我ž®†æœ‰æ¡ç†åœ°å±•å¼€æˆ‘的讲授 Now I'm going further that actually impose upon a talk 69 00:04:41,450 --> 00:04:43,880 用我觉得比较舒服的结æž? more of the structure that I find congenial 70 00:04:44,860 --> 00:04:48,890 先不è®?¾ŸŽä¸ŽçœŸç† I'm going to begin by talking not so much about beauty and truth 71 00:04:49,160 --> 00:04:50,670 来讲è®?真理与美 but about truth and beauty, 72 00:04:50,990 --> 00:04:54,480 我将区分几种不同的真ç? and I'm going to distinguish several different kinds of truths 73 00:04:55,590 --> 00:04:58,770 首先是数å­? I'm going to begin indeed by talking about mathematics 74 00:04:59,050 --> 00:05:00,820 ¾lå¯¹çš„真ç? about truths which are absolute 75 00:05:01,740 --> 00:05:04,940 假设然后证明 When you make certain assumptions, and you prove things 76 00:05:05,870 --> 00:05:08,070 它们可能与现实世界有所兌™” And they may have relevant to the real world 77 00:05:08,540 --> 00:05:10,870 但其本èín是封闭的逻辑¾pȝ»Ÿ but they are close logical systems 78 00:05:12,280 --> 00:05:17,590 一般地如果我说¾Ÿ?希望你们明白它们各有特点 Often I hope to convince you with their own peculiar if I say beauty 79 00:05:20,120 --> 00:05:21,280 但数学是¾lå¯¹çœŸç† But they are absolute truths 80 00:05:21,840 --> 00:05:27,530 ˜q™çœŸç†é€æ¸è½¬åŒ–为我们认识世界的ž®è¯• and they shade into our attempts to understand the world around us 81 00:05:27,840 --> 00:05:32,320 ž®½ç®¡å®ƒå¯èƒ½æœ¬íw«åƈ不一定真实成ç«? with the truth we strive for unnecessarily always contingen 82 00:05:33,770 --> 00:05:38,430 比如我们可以证明三角形中两边相等 because we try whereas we can prove it two sides of a triangular are equal 83 00:05:39,000 --> 00:05:40,090 那么两角相等 the two angles are equal 84 00:05:41,110 --> 00:05:44,610 但不能用同样的逻辑去证明太é˜Ïx˜Žå¤©å‡èµ? we can't in the same sense prove the sun's gonna rise tomorrow 85 00:05:46,220 --> 00:05:48,140 它确实是极好的假è®? cuz it's extremely good working hypothesis 86 00:05:49,710 --> 00:05:51,530 但åƈ不包含同æ ïLš„真理 But it doesn't have the same kind of truth 87 00:05:51,880 --> 00:05:53,250 以后我可能会讲到一äº? that I'm going to talk a little bit about that 88 00:05:54,110 --> 00:05:55,820 æ€ÖM¹‹ and in short 89 00:05:57,710 --> 00:06:02,390 ˜q™èŠ‚译ְ†ä»¥æ­¤˜q™æ ·çš„线索展开 the organization of this talk is going to run along the line 90 00:06:03,140 --> 00:06:04,970 先是数学 where I'm getting to talk about mathematics 91 00:06:05,910 --> 00:06:09,230 和美 and beauty, in a quite real sense 92 00:06:09,750 --> 00:06:15,480 然后是现实世ç•? and then more I'm going to talk a little bit about moving to the real world 93 00:06:16,080 --> 00:06:17,000 说说自然¿U‘å­¦ natural sciences 94 00:06:17,690 --> 00:06:22,010 以及˜q™ä¹‹ä¸­çš„优雅与美æ„? and the role that elegance and beauty play sometimes. 95 00:06:22,450 --> 00:06:23,830 充分说明了以上内容后 It has played in adequates 96 00:06:24,470 --> 00:06:27,450 我会更广义地概括说一说今天的主题 and then I'm going to run and end up with some more general remarks 97 00:06:30,600 --> 00:06:34,500 那么先是å¯ÒŽ•°å­¦çœŸç†çš„˜q½æ±‚ So to begin with the quest for mathematical truth 98 00:06:39,030 --> 00:06:40,180 我最早看到这个图å½? My first acquaintance with this 99 00:06:40,590 --> 00:06:43,380 可能跟你们当中年¾Uªç¨å¤§çš„äºÞZ¸€æ ? might be similar to some of the elder people in the audience 100 00:06:44,260 --> 00:06:45,710 是学‹Æ§å‡ é‡Œå¯d几何的时å€? was the Euclid in geometry 101 00:06:46,180 --> 00:06:47,130 我记得是12å²? and I remember at the age of 12 102 00:06:48,430 --> 00:06:50,840 接触˜q™ä¸ªåŸºæœ¬å®šç† I have been presented with one of those basic theorems 103 00:06:51,110 --> 00:06:53,110 最早出现的几何命题之一 one of the first propositions in Euclid 104 00:06:53,670 --> 00:06:55,580 三角形的两边相等 You've two sides of a triangular equal 105 00:06:56,340 --> 00:06:58,180 然后其对应两角就相等 and then the two angles are equal 106 00:06:59,390 --> 00:07:00,610 其实我还记得 And I remember actually 107 00:07:00,870 --> 00:07:03,010 12岁的我因此和老师有过一åœÞZº‰æ‰? the age of 12 having an argument with the teacher 108 00:07:04,690 --> 00:07:06,160 我说 in which I said in effect 109 00:07:06,890 --> 00:07:09,010 天知道这有多明显 对称å•? this is obvious by symmetry for God's sake 110 00:07:09,240 --> 00:07:10,460 瞎忙什么呢 why fuss around. 111 00:07:12,810 --> 00:07:15,070 于是我理所当然地被批评äº? And I was rightly admonished for this 112 00:07:15,980 --> 00:07:17,710 因äؓ‹Æ§å‡ é‡Œå¯d because what Euclid did 113 00:07:18,480 --> 00:07:23,840 他在底边上作了一条垂¾U? was draw a perpendicular to the base 114 00:07:24,690 --> 00:07:26,570 两三角åŞ全等 and then two triangles are congruent 115 00:07:27,110 --> 00:07:31,670 如果两个三角形的三边长分别相½{? if either all three sides are the same 116 00:07:32,220 --> 00:07:36,510 或者三角åŞ有两条边两个角相½{? or two angles are the same two sides are the same, 117 00:07:37,070 --> 00:07:40,240 如果其中一个角是直è§? and the included angle or, if it's so, one of them are right angle 118 00:07:40,690 --> 00:07:42,600 那么另外的角也相½{? leaning angle is the same, 119 00:07:43,360 --> 00:07:47,900 或至ž®‘有一对相½{‰çš„角不应对于相½{‰çš„è¾? or if one side is the same and the angles are on the either side, 120 00:07:48,550 --> 00:07:49,560 所以欧几里德就è¯? so Euclid simply said 121 00:07:50,510 --> 00:07:57,970 在三角åŞABD和三角åŞACDä¸? in the triangle ABD and the triangle ACD 122 00:07:58,930 --> 00:08:00,720 已知ABåQAC AB equals AC, that you're given 123 00:08:01,770 --> 00:08:04,810 AD=AD 共同è¾? 且有一对等角äؓ直角 and AD equals AD that common , and this is the right angle 124 00:08:05,070 --> 00:08:06,230 所以全½{?两角相等 therefore the angles are equal 125 00:08:07,030 --> 00:08:08,150 åœ?0òq´ä»£æ—©æœŸ And in the early 60s, 126 00:08:08,810 --> 00:08:10,220 äºÞZ»¬å¼€å§‹åˆ¶é€? when people were first beginning to build 127 00:08:10,550 --> 00:08:13,240 复杂¾_‘Ö¯†çš„计½Ž—机 complicated sophisticated computers 128 00:08:13,850 --> 00:08:17,990 那时人工æ™ø™ƒ½˜q˜å¤„于萌芽期 and when artificial intelligence was in its infancy 129 00:08:18,690 --> 00:08:20,580 äºÞZ»¬çš„其中一™å¹å°è¯? one of the things that somebody sought to do 130 00:08:20,930 --> 00:08:22,560 ž®±æ˜¯è®©è®¡½Ž—机去运è¡? they'd say let's build a computer to go through 131 00:08:23,130 --> 00:08:25,570 看它ž®†å¦‚何高明地证明‹Æ§å‡ é‡Œå¯d定理 and see how good they are proving Euclid theorems 132 00:08:26,330 --> 00:08:27,300 先试想一ä¸? And let's begin with this one 133 00:08:28,430 --> 00:08:32,260 既然认äؓ电脑能做聪明äº? Because the computer's gonna have to do something clever 134 00:08:32,870 --> 00:08:34,970 那么它大概会先作一条垂¾U? it's gonna have to draw a perpendicular 135 00:08:35,260 --> 00:08:37,880 好吧 我们来看看它是不是聪明到了这¿Uåœ°æ­? let's see if it's up to then, and what'll the computer do? 136 00:08:39,580 --> 00:08:40,720 计算机是˜q™æ ·è¯´çš„ The computer said 137 00:08:41,040 --> 00:08:46,300 考查三角形ABC和三角åŞACB consider the triangle ABC and the triangle ACB 138 00:08:47,590 --> 00:08:53,120 ABåQAC AC=AB BC是共同边 AB equals AC, AC equals AB, BC is common 139 00:08:53,760 --> 00:08:54,500 所以它们全½{? therefore they are congruent 140 00:08:54,780 --> 00:08:55,990 所以两角相½{? therefore the angles are equal 141 00:08:56,540 --> 00:08:59,330 ˜q™ç®€ç›´å°±æ˜¯æˆ‘12岁所想的犀利版å•? which was a vigorous version of what I had done at 12 142 00:09:04,610 --> 00:09:08,170 数学学科发展到牛™å¿ä¹‹å‰çš„æ°´åã^ As mathematics developed pre-Newton 143 00:09:10,360 --> 00:09:13,240 各种事物以纯数字来表½C? various things just in purely numerical things 144 00:09:13,560 --> 00:09:15,860 ˜q™å¾ˆç†æ‰€å½“然 that we tend often not even to think about. 145 00:09:16,330 --> 00:09:18,170 0 的发æ˜? The invention of the concept of zero 146 00:09:19,830 --> 00:09:24,940 它由阿拉伯或者说伊斯å…îC¸–界发æ˜? which belongs to the Arab, sometimes call this Islamic world 147 00:09:25,700 --> 00:09:27,760 ¾lä¸æ˜¯äšgž®äº‹ is a non-trivial discovery 148 00:09:28,650 --> 00:09:29,950 事实ä¸? and in fact if you 149 00:09:30,220 --> 00:09:34,000 如果你观察北¾ŸŽçš„甉|¢¯ look at the way lifts or say call them elevators work in North America 150 00:09:35,110 --> 00:09:37,240 ž®×ƒ¼šå‘现 0 的概念还没有发展到那个领åŸ? the concept of zero hasn't made of that far 151 00:09:38,810 --> 00:09:41,880 因äؓ他们不理解会有第0层这¿Uä¸œè¥? because they don't understand that the ground floor was the zero floor 152 00:09:42,980 --> 00:09:43,920 ½W?层之所以被¿UîC½œ½W?å±? It's called the first floor 153 00:09:44,290 --> 00:09:48,440 仅仅是因为在¾læµŽå‘展早期 simply because of a genuine lack of sophistication 154 00:09:48,830 --> 00:09:49,330 他们真心地没æœ?0å±?˜q™ç§è§‰æ‚Ÿ in the earlier base of economy. 155 00:09:50,190 --> 00:09:51,610 真心没有 That didn't really, haven't really 156 00:09:52,530 --> 00:09:53,760 不过我离题了 but I digress. 157 00:09:56,980 --> 00:09:58,710 然后我们来看看复æ•? Then came negative numbers 158 00:09:59,770 --> 00:10:00,620 ˜q™æ˜¯ä¸ªæ›´å¤æ‚的概念了 so that's a more sophisticated concept 159 00:10:01,800 --> 00:10:05,110 å¯ÒŽ­¤æˆ‘不可能è½ÀLæ·¡å†™åœ°åŽ»è®? But I'm not going to talk for a little bit about something 160 00:10:06,130 --> 00:10:09,650 它实在很有趣 that I find particularly engaging 161 00:10:10,310 --> 00:10:13,120 而且它äؓ我们指了一个有意思的方向 and which may lead us in some amusing directions 162 00:10:13,720 --> 00:10:14,660 复数 complex numbers 163 00:10:15,850 --> 00:10:16,870 å¥?回到低年¾U§æ—¶å€? So, back to school 164 00:10:17,780 --> 00:10:19,000 ˜q™æ˜¯ä¸ªç®€å•çš„½{‰å¼ simple equations 165 00:10:19,540 --> 00:10:20,800 单变量的方程 and equations with one variable 166 00:10:21,120 --> 00:10:22,500 变量的åã^æ–? think of a number squared 167 00:10:23,570 --> 00:10:24,520 加上它的2å€? now multiplied by two 168 00:10:24,770 --> 00:10:26,170 加上2½{‰äºŽ0 that's two that's the zero 169 00:10:26,500 --> 00:10:27,670 求这个变é‡? so what's the number? 170 00:10:27,930 --> 00:10:29,530 求解的过½E‹ä¼šæ˜¯å¾’åŠ? You can usually fiddle around with that 171 00:10:29,970 --> 00:10:32,410 可以看到x的åã^方加ä¸?倍的X加上1 You can say x squared plus two x plus one 172 00:10:32,620 --> 00:10:33,680 刚好æ˜?x+1)的åã^æ–? is x plus one square 173 00:10:34,430 --> 00:10:35,720 æ ÒŽ®æ–¹ç¨‹å®ƒç­‰äº? and that's gonna be equal to minus one 174 00:10:36,010 --> 00:10:39,300 所以xæ˜?1加减-1的åã^æ–ÒŽ ¹ therefore it's minus one plus or minus the square root of minus one 175 00:10:40,380 --> 00:10:41,620 -1的åã^æ–ÒŽ ¹ The square root of minus one 176 00:10:41,910 --> 00:10:43,960 你可能会说这是什么鬼东西 you may say what the hell is that? 177 00:10:44,940 --> 00:10:45,470 它没有意ä¹? That's a nonsense. 178 00:10:47,990 --> 00:10:51,460 假设我们定义它äؓ真实存在的数 Let's define it to be a number or an entity 179 00:10:51,730 --> 00:10:54,280 ¿U°å®ƒä¸ºi -1的åã^æ–ÒŽ ¹ Let's call that i the square root of minus one 180 00:10:55,790 --> 00:10:59,310 那么x æ˜?1加减-1的åã^æ–ÒŽ ¹ And now x would be minus one plus or minus the square root of minus one 181 00:10:59,780 --> 00:11:00,910 也就是加减i as that plus minus i 182 00:11:03,000 --> 00:11:07,080 于是我们构造一个复òq³é¢ and we can think of the complex plane 183 00:11:07,630 --> 00:11:10,910 来表½Cø™¿™äº›å•å˜é‡æ–¹ç¨‹çš„解 for solutions of equations with one variable 184 00:11:13,230 --> 00:11:14,880 它们通常为实æ•? with solutions usually may be real numbers 185 00:11:15,590 --> 00:11:17,660 也有可能是复æ•? or say maybe complex numbers 186 00:11:18,440 --> 00:11:21,960 我们可以把它惌™±¡æˆäºŒ¾l´åã^é? We may think of them as being some sort of being two-dimensional plane 187 00:11:22,440 --> 00:11:25,960 横èáu是实数单ä½? in which the horizontal axis is real bits 188 00:11:26,450 --> 00:11:29,690 ¾Uµèáu是虚数单ä½? and you imagine vertical axis is imaginary bits 189 00:11:30,820 --> 00:11:35,310 ˜q™ä¸ªåæ ‡é‡Œæ¯ä¸ªå¤æ•°ç”±å®žæ•°å•ä½å’Œè™šæ•°å•ä½æž„æˆ? and in that space a complex number have a real bit and a imaginary bit 190 00:11:35,530 --> 00:11:36,820 我们ä¸ÞZ»€ä¹ˆè¦˜q™æ ·å? Why would we do this? (PPT 8) 191 00:11:38,260 --> 00:11:41,030 其中一ç‚ÒŽˆ‘不会详细解释 One of the things that I'm not going to lead you all the way through this 192 00:11:41,470 --> 00:11:42,070 我只¾l™ä½ ä»¬è¿™ä¸? I just give you this 193 00:11:42,640 --> 00:11:49,020 我想从理性思维的角度上 which I think is as beautiful an object in the intellectual sense 194 00:11:49,660 --> 00:11:50,880 来讲它非常美 as you are likely to find 195 00:11:54,070 --> 00:11:56,420 如果我再ç”?0分钟的话 If I took another ten minutes to go through it 196 00:11:56,600 --> 00:11:57,770 我能让你们明白它 I could take you all the way there 197 00:11:58,080 --> 00:11:58,950 不过我不会那么做 I'm just going to announce it 198 00:11:59,390 --> 00:12:01,200 我想你们中的半数äº? I'm sure about half of the people in the audience 199 00:12:01,450 --> 00:12:02,650 都熟悉这个公å¼? will be familiar with this formula 200 00:12:03,140 --> 00:12:07,660 它的奇妙之处在于 but I think it really has a genuine magic in that 201 00:12:08,330 --> 00:12:10,710 它的底是自然å¯ÒŽ•° It says, you take the base of natural logarithms 202 00:12:11,350 --> 00:12:15,630 ­‘…越数e 2.718 this transcendental number e, which is 2.718 203 00:12:17,620 --> 00:12:19,880 正是你解方程x'=x能得到的æ•? which is a number you get by solving the equation 204 00:12:20,700 --> 00:12:25,840 x随时间变化而变åŒ? How do something behave if the rate which is changing over time 205 00:12:26,510 --> 00:12:30,120 其变化率卛_¯¼æ•°æ°å¥½ä¸Žæœ¬èín成比ä¾? is exactly proportional to the magnitude of the object 206 00:12:30,940 --> 00:12:33,630 或者说 ˜q™ä¸ªå˜é‡å¯ÒŽ—¶é—´t求导½{‰äºŽæœ¬èín is that, the changing x is equal to x. 207 00:12:34,960 --> 00:12:37,190 ž®†æ—¶é—´å˜å¤§é—´éš”无限细åˆ? Time up, second up, second up, and second up. 208 00:12:37,480 --> 00:12:39,910 ¼œžå¥‡çš„是它在t时的瞬时增大é‡? It would increase exceptionally by x 209 00:12:40,330 --> 00:12:44,550 恰是其本íw? ž®±æ˜¯e的t‹Æ¡å¹‚ that after time t will be this funny number that raised to the power of t 210 00:12:44,940 --> 00:12:47,240 ˜q™ä¸ªež®±æ˜¯è‡ªç„¶å¯ÒŽ•° So this is just a natural number 211 00:12:48,560 --> 00:12:50,520 你在宇宙中随处可见它ä»? You see them everywhere in the universe. 212 00:12:51,380 --> 00:12:53,020 现在假设得到 You raise it to a power, 213 00:12:53,580 --> 00:12:57,080 其i‹Æ¡å¹‚ -1的åã^æ–ÒŽ ¹ this nonsense object, i, the square root of minus 1, 214 00:12:58,890 --> 00:12:59,670 ä¼ég¹Žæ²¡æœ‰æ„ä¹‰ seeming meaningless 215 00:13:00,220 --> 00:13:02,040 再自乘圆周率的数值次 Another multiplied by the ratio of 216 00:13:02,400 --> 00:13:04,000 卛_–Ï€‹Æ¡å¹‚ the other circle's circumference to its diameter 217 00:13:05,400 --> 00:13:07,230 然后你就得到äº?1 And then you get minus one 218 00:13:08,810 --> 00:13:09,950 ˜q™å¾ˆ¼œžå¥‡ That's some magical thing. 219 00:13:11,510 --> 00:13:14,260 对基本常æ•îC»€ä¹ˆçš„来说它毫无意ä¹? To fundamental constant things this is nonsense number 220 00:13:14,860 --> 00:13:16,340 但它¼‹®å®žéžå¸¸æœ‰ç”¨ and it's really useful 221 00:13:16,850 --> 00:13:19,000 它äؓ我们接下来要讲的东西铺åã^了道è·? And it paves the way for what I'm gonna do next 222 00:13:19,420 --> 00:13:20,750 不过像我提到˜q‡çš„那样 But I just mentioned in passing 223 00:13:21,750 --> 00:13:23,540 òq¶ä¸æ˜¯æ¯ä¸ªäh都发çŽîCº†å…¶å¦™å¤? not everybody finds this magic 224 00:13:24,170 --> 00:13:26,360 有些äºø™§‰å¾—它很不方便 there are people who just found it inconvenient 225 00:13:26,960 --> 00:13:29,140 比如πž®±å¾ˆç•¸åŞ for example, the π is not something 226 00:13:29,530 --> 00:13:31,390 它是个太复杂的数å­? it's just some complicated number 227 00:13:32,320 --> 00:13:34,490 ˜q™é‡Œæœ‰ä¸ªå¥½ç¬‘çš„æ•…äº? Then one of the more amusing expressions of that is 228 00:13:35,150 --> 00:13:36,430 大概50òq´å‰ about 50 years ago 229 00:13:37,240 --> 00:13:40,970 åºäh–¯å¨æ˜Ÿå·žç«‹æ³•æœºå…³é€šè¿‡äº†ä¸€æ¡è®®æ¡? the Wisconsin legislature actually passed a bill 230 00:13:41,740 --> 00:13:46,550 说在康州π被定义äؓ3.2 that said π we will define it in Wisconsin as 3.2 231 00:13:46,880 --> 00:13:48,520 ä¸ÞZº†å»ºç­‘业的操作便利 for the convenience of building industry 232 00:13:50,690 --> 00:13:54,320 不过我觉得更好笑更惊讶的æ˜? and the thing I find particularly amusing and amazing about that is 233 00:13:54,660 --> 00:13:56,120 如果你要重新定义π if you gonna redefine π 234 00:13:56,480 --> 00:13:58,390 ä¸ÞZ»€ä¹ˆæ˜¯3.2 why make it 3.2 235 00:13:58,570 --> 00:13:59,510 而不æ˜? why not 3? 236 00:14:01,740 --> 00:14:05,120 它没有最¾lˆæˆç«‹å› ä¸ºå·žé•¿åå¯? Never got into being passed because the governor rejected it 237 00:14:09,230 --> 00:14:10,640 现在½Eé€€ä¸€æ­? Now I'm gonna take a step back 238 00:14:11,430 --> 00:14:15,320 我来讲讲更晚时期我们所学的东西 and I'm going to talk about some more recent things that we've learned 239 00:14:16,150 --> 00:14:17,710 它最¾lˆå¼•é¢†æˆ‘ä»? and which will take us eventually 240 00:14:18,310 --> 00:14:20,120 åŽÀLŽ¢ç´¢å¤òq³é¢çš„美 in the quest of beauty in the complex plane 241 00:14:21,750 --> 00:14:25,440 大概100òq´å‰æœ‰äh提出了这个问é¢? This more recent question foreshadowed about a hundred years ago 242 00:14:26,370 --> 00:14:29,130 我记不清那个国王的名å­? when I've forgot the name of the king 243 00:14:31,110 --> 00:14:33,960 一个斯堪的¾U³ç»´äºšçš„国王讄¡«‹äº†ä¸€ä¸ªå¥–™å? one of the Scandinavian of the king offered the prize 244 00:14:35,750 --> 00:14:36,930 那是19世纪晚期 it's late in 1800s 245 00:14:38,370 --> 00:14:45,170 希望得证整个太阳¾pÕdŽŸæ˜¯ä¸€ä¸ªå°é—­ç³»¾l? to prove that the solar system as a whole was a close system 246 00:14:46,180 --> 00:14:49,380 为此有外行的证明说明 And in the quest for this quackery show 247 00:14:50,320 --> 00:14:54,840 假设你构造一个三体结æž? that if you started off simply with a three-body problem 248 00:14:55,500 --> 00:14:57,560 比如地月æ—? like the earth, the sun and the moon 249 00:14:58,630 --> 00:15:00,290 它就会很æ€? it did really weird things 250 00:15:00,810 --> 00:15:04,390 你几乎不可能扑ֈ°ä¸€ä¸ªç®€æ˜Žçš„证明æ–ÒŽ³• that really rather preclude any crisps solution to the problem 251 00:15:04,980 --> 00:15:08,430 待会å„?我会¾l™ä½ ä»¬ä¸€ä¸?æ·äh²Œ 的简化版解释 I'm gonna give you a simpler version of what we now call Chaos 252 00:15:09,230 --> 00:15:10,810 再看˜q™ä¸ª 你们大概也不陌生 Again, many of you are familiar with this 253 00:15:11,280 --> 00:15:13,050 用一点简单的数学 use a simple piece of mathematics 254 00:15:15,150 --> 00:15:16,630 我画å‡ÞZ¸€ä¸ªçª—™å¶ä¼¼çš„拱å½? I stumbled crossette 255 00:15:17,180 --> 00:15:19,850 在大多数早期工作ä¸?一个世¾Uªå‰ in most of the earlier work, a century ago 256 00:15:20,750 --> 00:15:23,730 没有计算机情况下它很隑־—åˆ? was too hard to pursue before the advent of computers 257 00:15:24,120 --> 00:15:28,360 因äؓ它用到微分学的连¾l­ç³»¾l? because it dealt with continuous systems in differential calculus 258 00:15:29,160 --> 00:15:33,820 òq¶ä¸”你需要至ž®?¾l´çš„¾pȝ»Ÿ and you needed, in that case, at least three-dimensional systems 259 00:15:34,070 --> 00:15:36,400 来得到我们将要谈到的现象 before you can get the phenomenon I'm gonna talk about 260 00:15:39,210 --> 00:15:41,240 但如果你处理的是¼›ÀL•£¾pȝ»Ÿ but if you deal with discrete systems 261 00:15:41,790 --> 00:15:44,800 事物的变化都是离散åŞ式的 where things changing in discrete intervals 262 00:15:44,810 --> 00:15:47,310 我们得到的数字可能分布在 the number of that we got for in either in 263 00:15:48,410 --> 00:15:50,680 当年 ½W¬äºŒòq?½W¬ä¸‰òq? this year, next year, and the year after 264 00:15:52,120 --> 00:15:54,610 然后你会推测½W¬äºŒòq´çš„变量 and you will assume that the number next year 265 00:15:55,220 --> 00:15:58,040 ½W¬äºŒòq´çš„x是当òq´çš„x x of next year is the number this year x 266 00:15:59,080 --> 00:16:02,690 乘上一个内生的帔R‡ times some intrinsic multiplier constant 267 00:16:03,100 --> 00:16:05,320 乘上一个负反馈™å? time some negative feedback term 268 00:16:05,840 --> 00:16:09,490 比如说繁ŒD–扩张的能力 that says that the intrinsic capacity to reproduce 269 00:16:09,890 --> 00:16:14,990 随着¿Uç¾¤å¯†åº¦çš„增大而减å¼? is diminished as the population becomes more abundant compared 270 00:16:15,230 --> 00:16:19,520 我们定义扭è{­‘‹åŠ¿çš„è¿™™å¹äؓ1-m let's define ob-trendy rescale* to one minus x 271 00:16:21,240 --> 00:16:24,590 ˜q™ä¸€òq´çš„密度 t时的x The relation in between the population this year x of t 272 00:16:24,870 --> 00:16:26,550 和第二年的密åº?t+1时的密度的关¾p? and the population next year, x of t plus 1 273 00:16:27,230 --> 00:16:30,660 是一条实心抛物线 will be that solid parabolic curve 274 00:16:31,940 --> 00:16:35,260 然后你可以看åˆ? and you can then ask, you can then see from that 275 00:16:36,390 --> 00:16:43,480 如果密度在这条线上的å€ég»¥ä¸? that if the population is below this value here, line along here 276 00:16:46,630 --> 00:16:49,300 ž®±æ˜¯è¯´å¯†åº¦æ°´òq³ä½ŽäºŽå®ƒ that is to say, it is below the point 277 00:16:49,560 --> 00:16:54,720 能够保持不变的水òq? the way the line of unchanging population into x 278 00:16:55,570 --> 00:16:59,310 ˜q™ä¸ª½{‰å¼ž®±å‘Šè¯‰æˆ‘们代际间的密度关¾p? this equation then tells you the relation between generations 279 00:17:00,130 --> 00:17:04,700 密度低于˜q™æ¡¾U?有逐年上升­‘‹åŠ¿ The population below that it will tend to increase from year to year 280 00:17:06,390 --> 00:17:08,660 只要高于˜q™æ¡¾U? on the other hand if it is above that point a little 281 00:17:08,910 --> 00:17:10,270 ž®±é€å¹´é€’减 decrease from year to year 282 00:17:11,020 --> 00:17:12,170 然后你会é—? And you can then ask 283 00:17:12,860 --> 00:17:15,860 多长时期内种¾Ÿ¤å¯†åº¦ä¼šå†›_®šäºŽè¿™ä¸ªå†…在增长率 how long will this depend on the value of this intrinsic growth rate? 284 00:17:16,460 --> 00:17:19,420 然后不难发现如果a<1 Well you can easily see that if I use less than one 285 00:17:19,760 --> 00:17:22,020 那么¿Uç¾¤å¯†åº¦ä¸€å®šä¼šå‡å°åˆ°é›¶æ°´åã^以下 the population is just is gonna decline under zero 286 00:17:24,680 --> 00:17:29,490 直觉告诉我们a>1 The only intuition was the population value is bigger than one 287 00:17:30,360 --> 00:17:34,640 那么密度xæ€ÖM¼š­‘‹å‘均衡å€? that it will settle one way or another to this equilibrium point 288 00:17:35,910 --> 00:17:37,030 但它òq¶æ²¡é‚£ä¹ˆ½Ž€å? That's not so simple as that 289 00:17:38,500 --> 00:17:40,920 如果a>1但也不是太大 if a is bigger than one but not too big 290 00:17:41,570 --> 00:17:46,800 密度最¾lˆä¼šå›žå½’åˆîC¸€ä¸ªç¾Žå¥½çš„均衡ä¸? you get the population indeed settling to a nice happy equilibrium 291 00:17:48,530 --> 00:17:51,160 昄¡¤ºä¸ºçŽ¯å¢ƒæ‰°åŠ¨æœ€¾lˆä¸èƒ½é˜»æ­¢æ‡L动回å½? displaced by environmental fluctuations will come back 292 00:17:52,170 --> 00:17:55,910 但超˜q‡è¿™ä¸ªèŒƒå›´ä½ å¯èƒ½ä¼šè¿›å…¥æ›´å¤æ‚çš„æ‡LåŠ? But beyond that you begin into moving to a more complicated ratio 293 00:17:56,640 --> 00:17:58,610 ž®±æ˜¯½E›_®šçš„上下摇æ‘? in where it goes stably up and down 294 00:17:59,080 --> 00:18:03,830 由其自èín动态规律控制的上下波动 driven by its own dynamics, into going up and down 295 00:18:04,640 --> 00:18:08,780 然后如果a更大一äº? Then if you make it a bit bigger, it starts doing things that 296 00:18:09,320 --> 00:18:11,530 全世界都会认ä¸ø™¿™æ˜¯éšæœø™¿åŠ? for all the world to look like it's just random noise 297 00:18:14,950 --> 00:18:18,090 另一¿Uè§‚察它的方å¼? Another way of looking at it is to say 298 00:18:19,610 --> 00:18:22,840 是将方程解立体作å›? fort up the points on this equation 299 00:18:26,170 --> 00:18:28,760 ˜q™æ—¶è®¤äؓ体系是稳定的 where the system believe it will be steady 300 00:18:29,250 --> 00:18:33,630 所有点æ€ÖM¼šå›žåˆ°æŸäº›ç‰ÒŽ®Šçš„位¾|®ä¸Š or will return to where are points which if you put them exactly 301 00:18:33,930 --> 00:18:38,410 在那里这些点不受到向前或后的åŠ? on the points with no forward or backward trend set there 302 00:18:39,020 --> 00:18:39,640 ˜q™äº›ç‚ÒŽ˜¯ä»€ä¹? what are they? 303 00:18:40,580 --> 00:18:42,270 在第一¿Uæƒ…况下只有单个均衡ç‚? Well, first is just one stable point 304 00:18:43,110 --> 00:18:46,340 分叉图能¾l™å‡º2个稳定点 and then this Bifurcate gives you two such points in the system 305 00:18:46,610 --> 00:18:50,120 位于二叉之间 四次分叉 that also lays between them and Bifurcates again four times 306 00:18:51,550 --> 00:18:52,840 最后回归到某个ç‚? and then comes on to this point 307 00:18:53,320 --> 00:18:55,350 看è“v来太乱难以理è§? that it gets too messy really to understand. 308 00:18:56,060 --> 00:18:59,150 从这个窗口你大概可以看到一ç‚? There are bits you can see what's happening in the siddur window here 309 00:18:59,500 --> 00:19:01,120 ˜q™é‡Œæœ‰å‘¨æœŸäؓ3的åó@çŽ? there is a cycle of three that 310 00:19:01,990 --> 00:19:06,980 从A到B到C 再到A 如此重复 it goes from A to B to C back to A to B to C back to A to B to C 311 00:19:10,070 --> 00:19:13,870 ˜q™å¾ˆ½Ž€å? and, this particular thing in that simplest thing 312 00:19:14,860 --> 00:19:17,870 ž®å­©ç”¨æ‰‹æ‘‡è®¡½Ž—器ž®Þpƒ½çŸ¥é“ that a child could literate on a hand calculator 313 00:19:19,400 --> 00:19:20,770 然后来求a that one should get up to a around 314 00:19:21,080 --> 00:19:23,540 如果a>4 那么˜q™ä¸ªå¾ªçŽ¯ž®±æ­»äº? if a is bigger than 4 the whole thing goes extinct 315 00:19:23,850 --> 00:19:27,990 ž®±åƒåˆšæ‰çš„抛物线å›? because going back to this diagram you get out here 316 00:19:28,260 --> 00:19:30,410 你回åˆîCº†0 and so you've just gone back to zero 317 00:19:30,860 --> 00:19:33,990 所以我们考虑1åˆ?之间的å€? so we're looking at values between one and four 318 00:19:37,270 --> 00:19:38,600 假设½{‰äºŽ4 As you go it equals four 319 00:19:40,690 --> 00:19:45,110 它就会在­‘‹å‘ä»ÖM¸€æ— ç©·å¤„不停往复运åŠ? it can jigger around among any one of the infinite number points along here 320 00:19:49,300 --> 00:19:51,700 ˜q™ç§çŠ¶æ€?我们现在¿UîC¹‹ä¸?æ·äh²Œ The work on, we call it Chaos now 321 00:19:51,990 --> 00:19:53,940 因äؓ它实在太ä¹×ƒº† because it's such as a mess. 322 00:19:55,390 --> 00:19:57,520 我们˜q˜åœç•™åœ¨å·®åˆ†æ–¹ç¨‹ The work we're still on differentially equations 323 00:19:57,730 --> 00:19:59,420 它有臛_°‘3个维åº? this at least three dimensions 324 00:19:59,780 --> 00:20:01,770 很难让大家彻底理è§? much harder to get you truly understand it 325 00:20:03,290 --> 00:20:06,040 有两三个数学å®? Two or three different mathematicians have found this 326 00:20:06,530 --> 00:20:09,950 早在½W¬ä¸€æœ¬å®Œæˆå‘表的物理上发çŽîCº†˜q™ä¸ªçŽ°è±¡ earlier in the first published and finished journal in physics 327 00:20:10,250 --> 00:20:12,250 都没惌™¿‡é™¤äº†ä¼˜ç¾Žçš„数学外 without having a sense of this 328 00:20:12,770 --> 00:20:15,170 它还会是什ä¹? was anything other than some elegant mathematical theme 329 00:20:16,860 --> 00:20:21,830 我偶然发çŽîCº†˜q™éƒ¨åˆ?òq¶åœ¨é©¬é‡Œå…°å¤§å­¦å¼€äº†ç ”讨班 I have stumbled upon this bit of it and I got seminar in Maryland. 330 00:20:22,820 --> 00:20:25,350 但我òq¶ä¸çŸ¥é“˜q™ä»¥å¤–是什ä¹? And say I don't know what happens next beyond here 331 00:20:26,240 --> 00:20:27,330 然后Jim York知道 and Jim York, who 332 00:20:27,630 --> 00:20:30,710 当然我知道这之前部分是怎么一回事 and I understood what was happening here but never realized 333 00:20:31,120 --> 00:20:33,700 可从没想˜q‡åŠ å€åŽçš„时期里它会有怎样的信息表è¾? that come from a sort of cascade of a period of doublings 334 00:20:34,700 --> 00:20:36,040 但Jim York说他知道 said I know 335 00:20:37,010 --> 00:20:39,650 他发表了论文òq¶ç»™äº†è¿™ä¸ªåŒºåŸŸä¸€ä¸ªåå­? he had just published a paper that gave this a name 336 00:20:39,980 --> 00:20:40,650 æ·äh²Œ Chaos 337 00:20:40,890 --> 00:20:42,880 ½W?阶段意味着 æ·äh²Œ period three implies Chaos 338 00:20:43,240 --> 00:20:44,460 ˜q™å¾ˆé…? it's cool 339 00:20:46,070 --> 00:20:50,100 我们都发现数学家们好像早ž®ÞqŸ¥é“è¿™äº? We both discovered then the mathematicians has sort of known this 340 00:20:50,490 --> 00:20:52,130 但他们从没觉得有什么了不è“v but they never thought it was particular interesting 341 00:20:52,380 --> 00:20:54,060 然后Jim York喜欢è¯? that Jim York was fond of saying 342 00:20:54,590 --> 00:20:56,700 我们本想最先发现它 we want to first to find this 343 00:20:57,230 --> 00:20:58,730 但事实上是最后发现的 but we were the last 344 00:20:59,880 --> 00:21:02,970 因äؓ我们到处嚷嚷˜q™æœ‰å¤šæœ‰­‘? because we made a noise about how interesting it was 345 00:21:05,090 --> 00:21:06,300 而它的有­‘? And it's really interesting 346 00:21:06,510 --> 00:21:10,600 不只是因为有一个简单的军_®šæ€§è§„åˆ? not only do these things in a simple deterministic rule 347 00:21:10,810 --> 00:21:12,710 有一个参æ•?没什么神¿U˜çš„ that one parameter, nothing unknown 348 00:21:13,200 --> 00:21:16,300 而在于它对初始状态非常敏æ„? but it's so sensitive to the initial conditions 349 00:21:17,870 --> 00:21:20,450 以致于你无法作出长期的预‹¹? that you can't make long-term predictions 350 00:21:21,070 --> 00:21:22,660 你看在实¾U¿ä¸Š so here in the solid line 351 00:21:23,000 --> 00:21:25,700 把第3个点作äؓèµïL‚¹ I start with the first decades of the point 3 352 00:21:26,080 --> 00:21:31,320 我故意做错一些数æ? the dot of line I make a mistake about one par in 3 hundred 353 00:21:34,210 --> 00:21:37,380 用不着再看多少个数æ? And before I've gone about half a dozen or more literates out 354 00:21:38,600 --> 00:21:40,030 后面部分的图像已¾lå®Œå…¨å˜äº? the parts are entirely different 355 00:21:41,740 --> 00:21:45,050 ˜q™å¯ä¸æ­¢æ˜¯ä¼˜¾ŸŽçš„数学什么的äº? and that's much more than a piece of beautiful mathematics 356 00:21:45,720 --> 00:21:51,550 ˜q™å…¶å®žæ˜¯ç‰›é¡¿å­¦è¯´çš„终极理æƒ? That actually is the aim of the Newtonian dream 357 00:21:52,690 --> 00:21:53,560 ž®±æ˜¯˜q™ä¸ª¾pȝ»Ÿ Here is the system 358 00:21:53,820 --> 00:21:55,040 现在我们已经了解它的全部äº? where we've known everything about it 359 00:21:57,140 --> 00:22:00,760 我们可以为短期预‹¹‹æ‰“开新的局é? we can make it open to a new window on short-term predictions 360 00:22:01,290 --> 00:22:03,430 我有一个学生George Parley which one of my students Parley 361 00:22:03,890 --> 00:22:06,940 已经在å¯d意志保险的美国公司工作了四五òq? running for Deutsche Security USA for 4 or 5 years 362 00:22:07,390 --> 00:22:11,250 利用产生随机数的æ–ÒŽ³• as a way you can take what was annoying in the misuses 363 00:22:11,830 --> 00:22:16,150 åƒ?8òq´ç¬¬1台计½Ž—机的随机数发生å™? in random number generater for the first computer ENIAC in 48 364 00:22:16,940 --> 00:22:18,480 然后用常规试éª? and test it with conventional test 365 00:22:18,870 --> 00:22:20,940 åŽÀL£€éª? for random numbers in systematic random numbers 366 00:22:21,830 --> 00:22:25,080 事实上äh们今天用˜q™æ¥åšå…¶ä»–新的东è¥? it's actually that what they use with something new today 367 00:22:25,300 --> 00:22:27,250 地图着è‰? called a version of chromatic Map 368 00:22:27,740 --> 00:22:32,480 George和我˜q˜å‘çŽîCº†å®ƒåœ¨æ•°å­¦ä¸Šçš„应用 and George and I found a mathematic using of this 369 00:22:33,370 --> 00:22:35,310 我们可以用它来判断较˜q‘的之后几个 of saying what we can at least tell the next few 370 00:22:36,050 --> 00:22:39,950 随机æ•?只要走得不太˜q? so-called random numbers along not further down the road 371 00:22:40,610 --> 00:22:47,470 较低¾U§çš„传统‹‚€éªŒæ³•å¯èƒ½æ²¡æœ‰åŠžæ³• so a lower conventional test would say for*next few 372 00:22:47,910 --> 00:22:50,900 George用这做的是投资方面的东西 and George Parley back in running investment things 373 00:22:51,180 --> 00:22:54,380 ˜q™ä¹Ÿæ˜¯æˆ‘最初涉­‘ÏxŠ•èµ„的原因 which is how I got involved in the investment stuff in the first place 374 00:22:54,730 --> 00:22:56,510 我又¼›»é¢˜äº? that I digress again 375 00:23:00,220 --> 00:23:01,900 再往下讲 Let's however go on beyond that 376 00:23:04,120 --> 00:23:07,200 ˜q›å…¥äºŒç»´½Iºé—´ Let's go into two dimensions 377 00:23:08,490 --> 00:23:09,570 ˜q™æ˜¯ä¸ªç®€å•çš„方程å¼? with that simple equation 378 00:23:10,040 --> 00:23:11,910 在上面动ç‚ÒŽ‰‹è„? but let's do it by the trick 379 00:23:12,510 --> 00:23:17,440 ž®†å˜é‡æ”¾˜q›å¼å­é‡Œ or just saying let's put the variable in that simplest equation 380 00:23:17,770 --> 00:23:19,400 用一个复数变量替换它 and replace it with a complex variable 381 00:23:20,620 --> 00:23:21,870 当然事实ä¸? in an effect, of course 382 00:23:22,170 --> 00:23:24,530 ˜q™è®©˜q™ä¸ªä¸€¾l´çš„方程 that makes that one dimensional system 383 00:23:25,830 --> 00:23:30,400 下一个z½{‰äºŽå¸¸æ•°ä¹˜ä»¥z乘以1-z next z is a constant times z times one minus z 384 00:23:30,670 --> 00:23:31,500 有了两个½{‰å¼ two equations 385 00:23:31,700 --> 00:23:32,850 一个是实数部分 one for the real part 386 00:23:33,190 --> 00:23:35,090 另一个是虚数部分çš? and one for the imaginary part 387 00:23:35,410 --> 00:23:38,550 于是下一个x是x和y的复合äñ”ç‰? so tells us the next x is this mixture of x and y 388 00:23:38,790 --> 00:23:40,800 y同样是两者的复合产物 and the next y is mixture of x and y 389 00:23:41,660 --> 00:23:43,070 它们有些复杂 and they're a bit more complicated 390 00:23:43,830 --> 00:23:47,800 不过你们可以看到 but we can ask and more commonly you see that 391 00:23:48,230 --> 00:23:50,380 ˜q™æ ·å†™å‡ºæ¥çš„½{‰å¼ equation written that way 392 00:23:50,630 --> 00:23:52,530 是等ä»ïLš„ which is equivalent I skip past that 393 00:23:54,430 --> 00:23:57,190 我们来看看这æ ïLš„式子能做什ä¹? What that does and then now I'm going to show you some 394 00:23:57,430 --> 00:24:00,260 它的优美之处以后我会向大家揭½C? that will be others in the beauty exhibited later (PPT 13). 395 00:24:01,660 --> 00:24:02,380 由此å¼? From this 396 00:24:03,140 --> 00:24:07,100 你可以画出复杂又惊艳的图æ¡? you can generate pattern as complex and as bizarre 397 00:24:07,440 --> 00:24:10,540 只要你想得到 as you can imagine 398 00:24:10,780 --> 00:24:12,890 而且 你可以得到茹利亚集合 and more, the called Julia sets 399 00:24:13,300 --> 00:24:19,710 一位数学家åœ?00òq´å‰é¦–次阐释了它ä»? general from a mathematician who first noted them hundred years ago almost 400 00:24:21,140 --> 00:24:24,950 但大家更能联惛_ˆ°çš„是Benoit Mandelbrot˜q™ä¸ªåå­— but the more familiarly associated was the name of Benoit Mandelbrot 401 00:24:25,630 --> 00:24:28,200 它不仅是重发çŽîCº†èŒ¹åˆ©äºšé›†å? who again not only rediscovered them 402 00:24:28,560 --> 00:24:30,340 而且揭示了它们的奇妙 but so how interesting they were 403 00:24:30,670 --> 00:24:32,760 我会告诉你们我说奇妙是什么意æ€? and I'm going to show you what I mean by that 404 00:24:33,280 --> 00:24:37,290 ˜q™æ˜¯æˆ‘们˜q™èŠ‚评¡š„一个内å®? in the case of one particular member of this class 405 00:24:38,020 --> 00:24:39,920 曼å¯d勃罗集合 called the Mandelbrot set 406 00:24:43,310 --> 00:24:45,510 ˜q™æ˜¯ä¸€ä¸ªåã^面图å½? Here it is in the simplest flat form 407 00:24:45,850 --> 00:24:47,480 它如何得到的å‘? and how it has been obtained 408 00:24:48,050 --> 00:24:50,700 有一条X轴代表着虚数单位 this is really an x-axis along here 409 00:24:51,340 --> 00:24:53,570 ¾U늫‹åœ¨å›¾åƒé‡Œ and exactly imaginary x somewhere up here 410 00:24:54,700 --> 00:24:56,240 但到底怎么ç”Õd‡º˜q™å›¾çš„å‘¢ but how it's been down essentially? 411 00:24:56,710 --> 00:25:00,170 曼å¯d勃罗用了复åã^é? He's taken that simple complex plane 412 00:25:00,990 --> 00:25:04,910 ½Ž€å•äºŒ‹Æ¡æ–¹½E‹çš„二维òq³é¢å½¢å¼ two-dimensional version of the simple quadratic equation 413 00:25:05,170 --> 00:25:12,880 在复òq³é¢ä¸Šæ‰¾åˆ°æ‰€æœ‰ç‚¹ Trivial equation and looked for all the points in the complex plain 414 00:25:15,200 --> 00:25:22,440 使它们代表的z代入½{‰å¼ä¸­èƒ½å¤Ÿæˆç«? which correspond to points where the next z equals to z into the axis 415 00:25:23,550 --> 00:25:27,600 通过重复演算 你可以回到原ä½? the real z, he might have come back there for many iterates 416 00:25:27,910 --> 00:25:30,360 ˜q™æ˜¯ä¸€¿UæŽ¨òq¿çš„æƒ…åŞ Their points that's generalization 417 00:25:30,760 --> 00:25:34,060 分叉囄¡š„二维的推òq? this is the two-dimensional generalization of Bifurcation diagram 418 00:25:34,340 --> 00:25:35,220 之前说过çš? I showed a moment ago 419 00:25:36,080 --> 00:25:36,950 如果你不懂那ä¸? that if you don't understand that 420 00:25:37,220 --> 00:25:38,630 没关¾p?你不需要懂 don't worry about it because you don't have to 421 00:25:39,320 --> 00:25:42,740 我会来描˜q°è¿™ä¸œè¥¿æœ‰å¤šæ€? Let me just describe how weird this thing is 422 00:25:44,600 --> 00:25:48,260 ˜q™å—å›´è“v来的囑ÖŞ This thing, the area into closers 423 00:25:48,950 --> 00:25:50,210 你不可能在这òq…图上看åˆ? and you can't see 424 00:25:50,450 --> 00:25:53,570 所有大ž®çš„¾l†èŠ‚ all the details of the funny little bits big on this figure 425 00:25:53,850 --> 00:25:55,810 它只是给一个概å¿? which is just to give an idea of it 426 00:25:56,640 --> 00:25:58,870 ˜q™äº›å»¶äŽ×出去的细æž? The complicated details go out further 427 00:26:00,820 --> 00:26:02,370 我待会儿˜q˜ä¼šè®²åˆ°å®ƒä»¬ and I'll come back to that a moment 428 00:26:03,910 --> 00:26:04,950 但它æ€Èš„轮廓 but in broad outline 429 00:26:05,350 --> 00:26:07,570 圈è“v来的是一个有限的区域 this encompasses a finite area 430 00:26:10,200 --> 00:26:14,930 可以被一个半径äؓ2.5的圆圈住 it's all enclosed by a circle of radius 2.5 431 00:26:16,000 --> 00:26:17,470 如果攑֜¨å®ƒåŽŸæ¥çš„复åã^面上 set on the original complex plane 432 00:26:18,540 --> 00:26:19,610 所以这个区域是有限çš? so the area is finite 433 00:26:21,050 --> 00:26:22,350 边界是无限的 its boundary is infinite 434 00:26:24,970 --> 00:26:27,770 但边界理è®ÞZ¸Šè®²æ˜¯ä¸€æ¡çº¿ but its boundary is in principle a line 435 00:26:28,510 --> 00:26:29,500 ¾U¿æ˜¯å•ç»´çš? a line is one-dimensional 436 00:26:30,220 --> 00:26:31,800 除了˜q™æ¡¾U¿ä¸æ˜¯ä¸€¾l´çš„ except this line is not one-dimensional 437 00:26:32,070 --> 00:26:33,550 ˜q™æ¡¾U?是二¾l´çš„ this line is two-dimensional 438 00:26:34,240 --> 00:26:36,590 你越是观察它 ­‘Šæ˜¯èƒ½çœ‹åˆ°æ›´å¤šç»†èŠ? for more you look at it the more detail you see 439 00:26:38,080 --> 00:26:39,040 所以再¾l™ä½ ä»¬ä¸€ç‚¹ä½“ä¼? So let's give some idea 440 00:26:40,030 --> 00:26:41,990 你抽å‡ø™¾¹ç•Œç»†éƒ¨çš„一ž®éƒ¨åˆ? Here's, you pick out a little bitof it 441 00:26:42,340 --> 00:26:45,340 它们向外¾˜Õd·ç€ and you pick one of these bits here that's curling out 442 00:26:45,720 --> 00:26:50,470 攑֤§è§‚察更多¾l†èŠ‚ and you zoom in on it you look at more detail and you see more detail 443 00:26:52,550 --> 00:26:54,760 仔细看其中一ä¸? You look at one of these and find more details 444 00:26:55,000 --> 00:26:58,850 然后它又奇异地生å‡ø™®¸å¤šå°¾l†æž you can see them like funny little things coming off here in more detail 445 00:26:59,100 --> 00:27:01,780 像很多大象排除走着 and you see there a lot of elephants wandering on a line 446 00:27:02,040 --> 00:27:04,250 然后再抽å‡ÞZ“Q一个细éƒ? and you can pick out a little bit of the detail there 447 00:27:04,530 --> 00:27:06,010 ˜q˜æœ‰æ›´å¤š¾l†å¾®çš„东è¥? you see more detail 448 00:27:08,400 --> 00:27:09,480 太神奇了 astonishing 449 00:27:10,070 --> 00:27:11,890 真是个神奇的集合 Really an astonishing set of things 450 00:27:13,330 --> 00:27:19,460 ˜q™ä¸ªå¼å­¾l™æˆ‘们展çŽîCº†ä¸€ä¸ªæ–°çš„视é‡? The notion of going back to really sort of put you into perspective 451 00:27:19,700 --> 00:27:22,120 不只是画条赘余的垂线 not only draw an unnecessary perpendicular 452 00:27:23,390 --> 00:27:27,820 但大家现在正专注的几何图形是个少见的特例 but all of you clinging in geometry is a special case 453 00:27:28,700 --> 00:27:33,000 它åƈ不与现实世界中的许多物äšg都联¾pȝ´§å¯? which arguably is not very relevant to many objects in the real world 454 00:27:33,520 --> 00:27:34,980 比如‹¹·å²¸¾U? like coastlines 455 00:27:36,390 --> 00:27:37,750 又或è€? or maybe like 456 00:27:39,000 --> 00:27:40,210 树的表面 the surface of a tree 457 00:27:40,620 --> 00:27:42,390 在极ž®çš„虫子的眼é‡? as seen by small enough insects 458 00:27:46,420 --> 00:27:48,200 有关˜q™ä¸ªé›†åˆæ›´æœ‰­‘£çš„表达 One of the more amusing manifestations 459 00:27:48,800 --> 00:27:53,340 是äh们在户外做的麦田åœ? this is crop circles generated by the man abroad set 460 00:27:54,870 --> 00:27:59,470 一¾Ÿ¤æ¶ä½œå‰§çˆ±å¥½è€…在夜晚偷偷òq²çš„ set out over night by some group of pranksters down near*? 461 00:27:59,780 --> 00:28:02,570 当然如果ç›æ€¿¡‹¹è¨€ and there are if I'm to believe what I'm told 462 00:28:04,180 --> 00:28:06,140 有一¾Ÿ¤äh 他们是真心觉å¾? a set of people who genuinely believe 463 00:28:06,460 --> 00:28:09,160 ˜q™æ˜¯å¤–星人的æîC½œ that this is the manifestation from outer space 464 00:28:14,620 --> 00:28:18,410 现在我将把话题è{¿UÕdˆ°¾ŸŽä¸Žè‡ªç„¶¿U‘学的问题上 Now I'm going to move on to beauty and the natural science 465 00:28:18,650 --> 00:28:20,520 但在˜q™ä¹‹å‰æˆ‘惌™¦å¼ø™°ƒ before I do so, I want to emphasize 466 00:28:21,190 --> 00:28:23,280 òq¶ä¸æ˜¯æ‰€æœ‰çš„数学推理证明都是¾ŸŽçš„ not all mathematical proves are beautiful 467 00:28:25,800 --> 00:28:31,520 一个经典的数学问题å?四色理论 A classic mathematical quest has been proved so called four-color theory 468 00:28:32,200 --> 00:28:36,950 ˜q™ä¸ªç†è®ºè¯?ä»ÖM½•ä¸¤ç»´¾pȝ»Ÿä¸‹çš„地图 the theory as it says, any map, any two-dimensional map 469 00:28:40,700 --> 00:28:45,790 其中ä»ÖM½•è¢«åˆ’出的国家或大陆的边界 with any obituary arrangements of territory borders among countries 470 00:28:46,120 --> 00:28:48,370 或者ä“Q何你惛_ˆ’清的边界 or continents or whatever you want to distinguish, 471 00:28:49,750 --> 00:28:56,010 都可以由四种颜色清晰地标注区分开 can be meaningfully and clearly colored with only four colors 472 00:28:59,480 --> 00:29:01,240 很长旉™—´ä»¥æ¥˜q™ä¸€ç†è®ºéƒ½è¢«è®¤äؓ是错误的 that's probably seems to be wrong for a long time 473 00:29:02,580 --> 00:29:04,870 ¾lˆäºŽ 随着电脑技术越来越发达 finally as the computers become more sophisticated 474 00:29:05,750 --> 00:29:10,710 ˜q™ä¸€ç†è®ºæœ€¾lˆè¢«è¯æ˜Žäº? 因äؓ它最¾lˆå¯ä»¥è¢«éªŒè¯äº? it's been proved because you can examine it and say, 475 00:29:10,940 --> 00:29:14,410 ž®½ç®¡æˆ‘知道有成千上万的特例存åœ? set aside what I believe and I hope I'm in the number here, 476 00:29:15,120 --> 00:29:19,050 有成千上万的特例存在 something like several hundred, exceptional cases, 477 00:29:20,010 --> 00:29:21,170 一个证据åƈ不能证明一åˆ? one proof doesn't cover 478 00:29:21,640 --> 00:29:24,380 但你可以在电脑上验证每一个特ä¾? and then you can explore each of these on computer, 479 00:29:24,870 --> 00:29:29,800 òq¶å¯ä»¥æž¯ç‡¥ä¹å‘›_œ°è®°å½•òq¶å±•½Cºæ¯ä¸€ä¸ªç‰¹ä¾? and save and show each one of them very tediously can also be done 480 00:29:30,750 --> 00:29:33,210 但问题是 假如你是¾U¯æ•°å­¦å®¶ And the question is, if you are pure mathematician, 481 00:29:33,560 --> 00:29:34,940 你证明了˜q™ä¸ªç†è®ºä¹? have you proved the theory? 482 00:29:35,150 --> 00:29:38,250 你证明是正确çš?但你的证明方法很¾pŸç³• You are right but you proved them so ugly, 483 00:29:39,630 --> 00:29:41,660 òq¶ä¸”ä½ äؓ什么要去证明定理呢? and furthermore, why do you want to prove theorems? 484 00:29:42,240 --> 00:29:45,760 你证明定理是ä¸ÞZº†æ›´å¥½åœ°ç†è§£äº‹ç‰? You usually want to prove theorems to understand things better, 485 00:29:46,700 --> 00:29:48,450 但äؓ了得出定理更好地理解事物 and if you really understood things better, 486 00:29:48,680 --> 00:29:50,550 你将会失åŽÈ‰¹ä¾? you got to lose exceptional cases 487 00:29:50,810 --> 00:29:53,610 òq¶ç¹ççš„排除他们中的每一ä¸? and tediously went through all them, 488 00:29:53,970 --> 00:29:55,080 å¯ÒŽ­¤ä¸åŒçš„äh可能会有不同的观ç‚? well, different people will have different views, 489 00:29:55,470 --> 00:29:56,950 但我ç›æ€¿¡è¯æ˜Žäº†è¿™äº›å®šç†çš„äº? now I'm sure that people who proved the theorem 490 00:29:57,360 --> 00:30:00,590 会和其他人有所不同çš? have a different view from the one that I, perhaps,just expressed, 491 00:30:02,140 --> 00:30:03,710 所以这正是一ä¸? so I felt this is one of these things 492 00:30:04,340 --> 00:30:06,890 很好支持我观点的例子 that I contain to say all of these, anyway 493 00:30:08,790 --> 00:30:15,910 除此以外 ˜q˜æœ‰åˆ«çš„一些例å­? And then quite a few things like that and I, I mean another one, recently, 494 00:30:18,500 --> 00:30:20,780 你们中的一些äh也许注意åˆîCº† and many of you, the audience may be unaware 495 00:30:22,330 --> 00:30:26,020 划艇比赛的胜利队伍æ€ÀL˜¯èƒ½æŠŠå¥½é€‰æ‰‹åœ¨ä¸¤ä¾§éƒ½æœ‰æ‰€å®‰æŽ’ that the game of draft with best player on both sides win, 496 00:30:26,400 --> 00:30:28,830 有时½W¬ä¸€å’Œç¬¬äºŒåòq¶ä¸èƒ½åŒºåˆ†ä¼šå½¢æˆòq›_±€ the first player, the second player was the draw 497 00:30:30,960 --> 00:30:31,730 划艇是很½Ž€å•çš„˜qåŠ¨ Draft is a simple game 498 00:30:32,890 --> 00:30:36,880 最˜q‘的很多数据表明 It's only very recently that a huge number of crunch of exercises show 499 00:30:37,090 --> 00:30:39,470 在划艇运动中 双方都常处在òq›_±€çš„僵持中 in drafts display both sides as a draw 500 00:30:41,850 --> 00:30:43,610 下棋问题最复杂 Chess is vastly more complicated 501 00:30:44,410 --> 00:30:48,000 我很难想象一个äh在下‹‚‹ä¸­è¦å¦‚何预‹¹‹è¾“èµ? I found it hard to imagine that an adult, if been an answer to a question 502 00:30:50,230 --> 00:30:51,930 白棋莯‚ƒœæˆ–黑‹‚‹èŽ·èƒ? in chess win for white, win for black, 503 00:30:52,940 --> 00:30:54,970 或双方åã^局½I¶ç«Ÿå“ªè€…将发生 or the draw is best played on both sides 504 00:30:55,200 --> 00:30:57,360 我不ç›æ€¿¡˜q™ä¸‰è€…的概率是无法计½Ž—çš„ I find it hardly to believe that there will never be the answer 505 00:30:57,990 --> 00:30:59,100 但即使能计算 But even if it was, 506 00:30:59,290 --> 00:31:02,090 我不ç›æ€¿¡å›žç­”˜q™ä¸ªé—®é¢˜æ˜¯æœ‰æ„ä¹‰çš? I don't think it would be interesting the way we have to the answer 507 00:31:02,920 --> 00:31:05,100 所以即使有½{”案 我觉得回½{”这问题的方式一定是无聊çš? Be a pity like a shambo of the guy 508 00:31:06,570 --> 00:31:09,350 让我们再回到¾ŸŽä¸Žè‡ªç„¶¿U‘学问题ä¸? OK, beauty and natural sciences, and again, 509 00:31:09,550 --> 00:31:12,960 人类试图åŽÈ†è§£èín边世界的˜q½å¯» wegonnaremind ourselves the quest to understand the world around us, 510 00:31:13,940 --> 00:31:16,710 可以˜q½æº¯åˆ°æœ‰è®°è¿°çš„历史以å‰? goes back well before recorded history, 511 00:31:18,650 --> 00:31:21,680 在格拉斯哥发现的‹zžç©´é‡Œå°±æœ‰æ‰€è®°è² it's written there in the caves of Glasgow and 512 00:31:22,690 --> 00:31:25,360 ˜q™ä¸€åº”用的è“v源是非常实际çš? its beginnings were pretty practical, 513 00:31:26,140 --> 00:31:27,180 òq‰™žç†è®ºåŒ–çš„ not very theoretical, 514 00:31:28,020 --> 00:31:31,130 òq¶åœ¨å·´æ¯”伦第三时期开始应ç”? and begin more or less in the third accretion in Babylon and 515 00:31:31,430 --> 00:31:34,150 他们一直在使用60˜q›åˆ¶ they've been quit number 60 516 00:31:35,170 --> 00:31:36,100 一个十分实际的计数æ³? Be very pragmatic 517 00:31:36,690 --> 00:31:40,550 他们做一切的事情都以60为基¼‹€çš„计数系¾lŸåšåŸºç¡€ It struck calendars and do staffs with the counting systems based on 60 518 00:31:41,850 --> 00:31:44,740 虽然他们没有个世界留下什么其他的¿U‘学成果 and alone they have not left much else to the world of science 519 00:31:45,070 --> 00:31:46,700 但他们留下了¾U¯çÑa的计数方æ³? but they have left the pure counting thing, 520 00:31:46,940 --> 00:31:49,180 如今我们仍在使用˜q™ç§è®¡æ•°åšè§’度测量等工作 which is still a way we measure angles and so on 521 00:31:50,220 --> 00:31:56,280 希腊人有个观å¿? ¾ŸŽæŸ¿Uç¨‹åº¦ä¸Šæ˜¯å‘å¯? The Greeks have a notion that beauty was a guide somehow, 522 00:31:58,230 --> 00:32:00,910 ˜q™æ˜¯ä¸ªä¸é”™çš„ 有时很有帮助的想æ³? and that was both a nice idea and helpful idea 523 00:32:01,320 --> 00:32:03,250 有时却稍有些误导äº? and at the same time it is slightly a misleading one 524 00:32:04,850 --> 00:32:08,220 托勒密和哥白ž®¼çš„传统观点 The conventional view of Ptolemy and Copernicus, 525 00:32:08,730 --> 00:32:13,020 ½Ž€å•è¯´æ¥å°±æ˜? the thing in simplified texts is that 526 00:32:14,030 --> 00:32:16,600 当你仔细观察 when you actually started looking in detail 527 00:32:17,020 --> 00:32:19,320 太阳¾pÕd†…的行星运动时 of the motions of the planets passing around the sun, 528 00:32:20,620 --> 00:32:22,290 你会发现它们的轨道åƈ不是åœ? it didn't actually fit circles, 529 00:32:23,210 --> 00:32:27,220 于是äºÞZ»¬åªèƒ½ç”¨æœ¬è½®ä½“¾p»é™„ä¼? so people have to fudge it by doing all the stuff with epicycles, 530 00:32:28,150 --> 00:32:31,240 然后哥白ž®ÆD·‘æ? 说太é˜Ïx‰æ˜¯ä¸­å¿? and then along came Copernicus said the sun was in the middle, 531 00:32:31,510 --> 00:32:32,480 ˜q™æ ·é—®é¢˜ž®Þp§£å†³äº† and everything was OK 532 00:32:33,910 --> 00:32:34,710 但实际上完全没有 It was not like that at all, 533 00:32:34,940 --> 00:32:36,730 哥白ž®¼åšçš„主要改é€? the main thing Copernicus did, 534 00:32:38,750 --> 00:32:42,220 地球在自å·Þqš„本轮上è{ Ptolemy's construction of the earth going around the sun, 535 00:32:42,890 --> 00:32:44,280 同时˜q™ä¸ªæœ¬è½®åœ¨ä»¥å¤ªé˜³ä¸ÞZ¸­å¿ƒçš„均轮上è{的模å¼? for example, with an epicycle, 536 00:32:46,010 --> 00:32:51,640 关键的错误在于接受了希腊人的 认äؓ圆是完美çš? is in fact, it takes the Greek fixation on the perfection of the circle, 537 00:32:53,940 --> 00:32:55,610 天体˜qåŠ¨éƒ½åº”当走圆åŞ轨道的观å¿? the heavens are got to be all circle 538 00:32:56,560 --> 00:33:00,810 但如果你调整椭圆的离心率的话 But it gives you to second order in the eccentricity of the ellipse 539 00:33:01,080 --> 00:33:01,860 我们现在知道轨道是椭圆的 we now know it is, 540 00:33:02,810 --> 00:33:04,490 ˜q™å°†æ˜¯å¯¹å¤©ä½“˜qåŠ¨çš„æ­£¼‹®æ˜q? it gives you a correct description 541 00:33:05,990 --> 00:33:08,250 如果哥白ž®¼æŠŠå¤ªé˜³æ”‘Öœ¨åœ†å¿ƒçš„话 What Copernicus did would make a big thing 542 00:33:08,500 --> 00:33:09,690 ˜q™å°±ä¼šå˜æˆä¸€ä¸ªé‡å¤§çš„改变 if he put the sun in the center 543 00:33:09,940 --> 00:33:11,350 但他没有把太é˜Ïx”¾åœ¨åœ†å¿? but he didn't put the sun in the center, 544 00:33:12,410 --> 00:33:16,510 他没有把太阳攑֜¨åœ°çƒè½¨é“的中å¿? he put the sun not at the center of the earth going round, 545 00:33:16,750 --> 00:33:18,480 他把太阳攑֜¨äº†åœ†å¿ƒæ—è¾? he put the sun off the center, 546 00:33:19,060 --> 00:33:21,030 一个圆的圆心旁è¾? in off center of a circle, 547 00:33:22,120 --> 00:33:26,290 和托勒密的本轮体¾pÖM¸€æ ? in the construction which also was to exactly the same approximation 548 00:33:26,580 --> 00:33:27,570 当然得到的近似å€ég¹Ÿä¸€æ ? as Ptolemy's epicycles, 549 00:33:30,570 --> 00:33:33,620 如果修正为椭圆的¼›Õd¿ƒçŽ‡çš„è¯? correct to second order in the eccentricity of the ellipse 550 00:33:35,720 --> 00:33:38,110 很多人关å¿? 地球˜q˜æ˜¯å¤ªé˜³æ˜¯ä½“¾pȝš„中心˜q™ä¸ªå‚»é—®é¢? The big fuss about, which was the centre was so silly 551 00:33:38,480 --> 00:33:41,660 被拿来测试一个äh是否了解¿U‘学的测试也æ˜? and indeed the thing that tests people's knowledge of science is 552 00:33:41,990 --> 00:33:42,990 是地球绕着太阳è½? the earth goes around the sun, 553 00:33:43,210 --> 00:33:43,900 ˜q˜æ˜¯å¤ªé˜³¾l•ç€åœ°çƒè½? the sun goes around the earth 554 00:33:44,170 --> 00:33:47,810 正确的答案是 都行 ˜q™é—®é¢˜å¤ªè ¢äº† The right answer is, both, it's a silly question 555 00:33:48,690 --> 00:33:51,260 但答GRE的时å€? But if you want to get the right answer on the GREs 556 00:33:51,540 --> 00:33:53,700 你最好说地球¾l•å¤ªé˜Œ™{ you'd better say that the earth goes around the sun 557 00:33:56,180 --> 00:33:57,030 ˜q™ç§åšæŒ ½Ž€å•æ¥è¯? That fixation, in short, 558 00:33:57,300 --> 00:34:00,070 轨道为正圆的坚持 òq¶ä¸èƒ½å¸®åŠ©è§£å†³é—®é¢? on circles, wasn't necessarily helpful 559 00:34:00,440 --> 00:34:01,980 你可以坚持这¿Uè§‚ç‚? because you could argue it hind it 560 00:34:02,830 --> 00:34:06,340 但开普勒在深入研½I¶äº†è§‚测数据以后¾léªŒåœ°æ€È»“ but Kepler noticed empirically when he got really into the data that 561 00:34:06,810 --> 00:34:12,150 起作用的其实是在相等旉™—´å†…扫˜q‡ç›¸½{‰é¢¿U¯çš„椭圆 is was an ellipse in effect by sweeping out equal areas during equal times 562 00:34:12,500 --> 00:34:14,980 ˜q™äؓ牛顿奠定了基¼‹€ And that paved the way for Newton 563 00:34:18,750 --> 00:34:22,890 可能是最鲜明çš? The perhaps the clearest articulation of 564 00:34:23,140 --> 00:34:27,740 应保持对作äؓ向导的美的追å¯Èš„声称是伽利略发出çš? the notion of a quest for beauty as a guide is Galileo 565 00:34:28,800 --> 00:34:32,040 有趣的是 与此同时到来的是 and this comes interestingly at the same time 566 00:34:34,210 --> 00:34:36,500 äºÞZ»¬å¼€å§‹å°†åˆ¤æ–­é—®é¢˜çš„æ ‡å‡? as people are beginning to shift the focus 567 00:34:36,800 --> 00:34:40,480 从脱¼›ÈŽ°å®žåœ°æ€è€? from thinking you decide how the world works by thinking about it, 568 00:34:41,120 --> 00:34:45,200 求助于前代的权威 被抽象观å¿? appealing to older the authorities, and being guided by abstractions 569 00:34:45,720 --> 00:34:47,070 比如它一定是¾ŸŽçš„引导 like it must be beautiful, 570 00:34:47,640 --> 00:34:50,350 也就是说如果你想¼‹®å®šé‡ç‰©ä¸‹è½å¾—æ›´å¿? so if you want to decide the heavy bodies fall faster, 571 00:34:51,230 --> 00:34:54,240 当然不是那么重的重物 你会求助于权å¨? not so heavy bodies, you appeal to the authorities, 572 00:34:57,410 --> 00:34:59,690 而不是真的拿个重ç‰?拿个è½È‰© don't actually think of taking a heavy body and a light body 573 00:34:59,930 --> 00:35:01,580 然后跑到比萨斜塔上面把它们扔下来 and walk to the top of the tower of Pizza and drop it 574 00:35:01,800 --> 00:35:03,270 或者做些类似的äº?而是求助于权å¨? or something, to the authorities 575 00:35:03,600 --> 00:35:06,020 ž®±æ˜¯è¯´åˆ°é‚£æ—¶ä¸ºæ­¢ Just it is basically up to that point 576 00:35:07,140 --> 00:35:09,710 自然¿U‘学都还处在 the natural sciences were pretty much in the same state 577 00:35:09,980 --> 00:35:11,220 现在的经‹¹Žå­¦æ‰€å¤„的状æ€? that economics still is 578 00:35:16,130 --> 00:35:19,770 有趣的是 我们看到 或者说现在我们意识åˆ? Interestingly, we observe, what we realize today is that 579 00:35:20,280 --> 00:35:23,670 ˜q™ç§è§‚点基本上和伽利略说的一è‡? well that may have been a basically sound point to what Galileo said, 580 00:35:25,520 --> 00:35:28,530 伽利略感觉到了是数学在其中è“v作用 Galileo sense that it was mathematics doing it, 581 00:35:29,020 --> 00:35:32,220 òq¶è®¤ä¸ºæ˜¯ä¸‰è§’ åœ? 几何囑ÖŞ 在è“v作用 and therefore was triangles and circles and geometrical objects, 582 00:35:33,240 --> 00:35:34,270 后半个观点不å¯? that bit was wrong 583 00:35:35,420 --> 00:35:36,790 出现的不æ€ÀL˜¯åœ? It's not always cycles, 584 00:35:37,250 --> 00:35:41,220 不是所有事情表面上看è“v来都很好 it's not always in the face playing nice things, 585 00:35:41,580 --> 00:35:44,150 不æ€ÀL˜¯å…‰æ»‘的圆 it's not always smooth cycles, 586 00:35:44,940 --> 00:35:49,960 而经常是æ·äh²Œ 分åŞ 和奇怪的引äh注意的东è¥? it's very often chaos, fractals and strange attractors, 587 00:35:50,610 --> 00:35:52,420 世界要复杂得å¤? that's a more complicated world, 588 00:35:53,140 --> 00:35:56,430 但数å­? 仍然是很强的因素 but it still has strong elements with mathematics being 589 00:35:56,880 --> 00:35:58,140 在Jean Vegnar的话é‡? in the words of Jean Vegnar 590 00:35:59,270 --> 00:36:02,390 在对世界的描˜qîC¸­éžå¸¸æœ‰æ•ˆ unusually effective in describing the world 591 00:36:08,070 --> 00:36:10,940 到此 我已¾lå¯ä»¥è½»æ‘Öœ°¼›Õd¼€è®²å° è¯? At this point, it would be easy to sort of go off and say, 592 00:36:11,700 --> 00:36:16,320 基本ä¸?¾ŸŽå°±æ˜¯çœŸå®? 真实ž®±æ˜¯¾Ÿ? essentially Beauty is truth, and truth is beauty 593 00:36:16,570 --> 00:36:18,280 ˜q™å½“然也是我选择˜q™ä¸ªä¸»é¢˜çš„原å›? and that is why of course I pick the topic 594 00:36:21,120 --> 00:36:24,590 但是 说这ž®±æ˜¯ä½ ä»¬çŸ¥é“çš„å…¨éƒ? However, to complete it by saying that's all you know 595 00:36:24,990 --> 00:36:30,420 你们知道˜q™äº›ž®Þp¡Œ òq¶ä¸åˆé€? and all you need to know is really ah, not really true, 596 00:36:31,840 --> 00:36:35,480 因äؓ与伽利略有关的另一个决定性事实是 because the crucial thing that Galileo was also associated with was 597 00:36:36,130 --> 00:36:39,430 以实验äؓæ? 不依赖权威的观念的发æ˜? the invention of experimental message, don't appealed to authorities, 598 00:36:39,890 --> 00:36:41,080 他è{向实éª? he go into experiments, 599 00:36:41,490 --> 00:36:43,300 当然˜q™ä»–之前ž®±æœ‰äººé¢„½CÞZº†˜q™ä¸€è§‚念的到æ? that of course was foreshadowed by other people 600 00:36:43,580 --> 00:36:45,040 比如我最喜欢的äh之一 格罗斯泰斯特ä¸ÀL•™ one of my favorites is Bishop Grosseteste 601 00:36:46,690 --> 00:36:50,050 亚里士多德遗留下çš? One of the things that Aristotle bequeathed to solve enough 602 00:36:50,610 --> 00:36:55,480 被阿奎那¾lå…¸åŒ–的说法之一æ˜? and was made canonical by Aquinas, was that, 603 00:36:56,650 --> 00:36:59,360 信不信由ä½? 獄¡š„双™…¿ believe it or not, badgers have the legs on the right side, 604 00:36:59,700 --> 00:37:02,030 ˜q˜æ˜¯å·¦è…¿ 比另一边的腿短 or maybe the left side shorter than the other side, 605 00:37:02,410 --> 00:37:04,410 因äؓ他们æ€ÀL˜¯ä»Žå·¦å‘右爬山 because they always go up hills from right to left, 606 00:37:04,680 --> 00:37:06,120 可能反过æ?我记不清äº? or left to right, I forgot which 607 00:37:06,750 --> 00:37:08,470 多奇妙的¾ŸŽä¸½ç†è®º Wonderful piece of beautiful theory! 608 00:37:09,200 --> 00:37:10,650 格罗斯泰斯特ä¸ÀL•™ Um, Bishop Grosseteste, 609 00:37:11,220 --> 00:37:15,110 感到不得不质疑这一¾lå…¸è¯´æ³• was sufficiently bowed to question this canonical letterings. 610 00:37:16,260 --> 00:37:18,860 当时只有教宗在场 Just one present pontiff was around at the time 611 00:37:19,190 --> 00:37:23,390 他真的去看了一下獾 然后发现它们òq¶ä¸å¦‚æ­¤ Um, and, and he actually looked at the badgers and found they didn't 612 00:37:23,730 --> 00:37:25,020 所ä»? 那时变化ž®±å¼€å§‹äº† So, it was beginning 613 00:37:25,400 --> 00:37:28,750 但真的直到最˜q‘几癑ֹ´ But it really is only the last few hundred years 614 00:37:29,210 --> 00:37:31,750 我们才真的开始完全信ä»ÖMº‹å®? that we have come to the fully embrace of the fact, 615 00:37:32,170 --> 00:37:35,420 战胜了美丽的命题的丑陋的事实 that an ugly fact, trumps the beautiful theorem, 616 00:37:36,760 --> 00:37:38,730 而伽利略正是˜q™ä¸€åˆ‡çš„èµïL‚¹ and that is what is setting chain 617 00:37:40,080 --> 00:37:44,670 ˜q™ç§è‡³ä»Šä»åœ¨åŠ é€Ÿå‘展的对世界的理解 The still accelerating, understanding of the world 618 00:37:45,210 --> 00:37:49,230 被我们持¾l­åœ°å¸¦ç€¾ŸŽå¥½çš„目的ä‹Éç”? which we've used unremittingly with good intentions, 619 00:37:50,740 --> 00:37:54,490 愿äh们健åº? 愿äh们长å¯? 愿能源充­‘? may people healthier, live longer lives, more energy subsidies, 620 00:37:55,050 --> 00:37:58,410 而今也不得不处理一些未被期待的后果 and ah now, having to deal with the unintended consequences 621 00:38:00,920 --> 00:38:03,820 但即便如æ­? ¾ŸŽä»å¤ÒŽ‚其中 But even in that, beauty is still entrained, 622 00:38:04,110 --> 00:38:06,970 让我们以另外两个例子走向¾l“束 let me move toward the end with two more examples 623 00:38:08,490 --> 00:38:12,100 狭义相对论就是这样一个美丽的例子 And special relativity is a beautiful such example, 624 00:38:12,340 --> 00:38:15,560 再一‹Æ? 我只½Ž€å•åœ°è¯´ä¸€ä¸‹å®ƒ and again, I'm going to do this in a rather superficial way 625 00:38:15,960 --> 00:38:17,350 ¾l™ä½ ä¸€äº›ç›´è§‚æ„Ÿå? but I just give a feel for it 626 00:38:21,230 --> 00:38:24,860 十九世纪æœ? Towards the end of the 1800s, 627 00:38:26,440 --> 00:38:29,360 äºÞZ»¬æŽ¥å—的对ç”?¼‚? the accepted understanding of electricity and magnets 628 00:38:29,640 --> 00:38:31,080 和另一些东西的理解æ˜? and a lot of other things was 629 00:38:31,320 --> 00:38:35,360 它们的场靠一些有­‘£çš„ that there were some curious ether there propagate the fields 630 00:38:35,600 --> 00:38:36,970 叫以太的东西传导 such the sort as it were 631 00:38:37,320 --> 00:38:39,510 äºÞZ»¬è¯•ç€‹¹‹é‡ and people set out to try and measure, 632 00:38:39,990 --> 00:38:43,430 相对于这个背景我们如何运åŠ? to what extent we were moving relevant to this background 633 00:38:44,270 --> 00:38:47,970 用这个发现看实物 by looking at things 634 00:38:48,600 --> 00:38:53,690 但实验的¾l“果却明¼‹®åœ°æŒ‡å‘ and the experiment seemed unambiguously to point to the fact that 635 00:38:54,290 --> 00:38:55,680 无论你向什么方向看 it didn't matter which way you looked 636 00:38:55,750 --> 00:38:57,970 你移动得多快或多æ…? or how fast you moved or how slow you moved, 637 00:39:00,200 --> 00:39:03,220 光速绝对不å? the speed of light was absolute invariable 638 00:39:05,980 --> 00:39:08,190 无论你在是朝着光子è·? Didn't matter whether you are running towards the photons 639 00:39:08,430 --> 00:39:09,210 ˜q˜æ˜¯èƒŒæœå…‰å­è·? or away from the photons, 640 00:39:09,510 --> 00:39:11,190 ä»ÖM½•åœ°æ–¹çš„光速都是一æ ïLš„ the speed of the light is the same everywhere, 641 00:39:13,200 --> 00:39:17,360 ˜q™ä¸Žç›´è§‚感受完全不符 which is entirely inconsistent with the feeling 642 00:39:17,860 --> 00:39:23,490 如果旉™—´å’Œç©ºé—´æ˜¯¾lå¯¹çš„çš„è¯? that if anything's absolute, its motions of space, and time 643 00:39:24,670 --> 00:39:26,130 十分钟就是十分钟 Ten minutes is ten minutes 644 00:39:27,500 --> 00:39:29,060 一码就是一ç ? One yard is one yard 645 00:39:29,720 --> 00:39:31,720 无论动得多快或多æ…?òq¶æ²¡æœ‰å…³¾p? Doesn't matter with gone too fast, or slow 646 00:39:32,560 --> 00:39:35,440 而爱因斯坦的伟大发现æ˜? And Einstein's great observation was, 647 00:39:36,530 --> 00:39:39,660 如果光速确实是个绝对的常数 That if indeed the speed of light is an absolute constant, 648 00:39:40,880 --> 00:39:43,610 òq¶ä¸”物理规律 and it is true also that the laws of physics 649 00:39:43,840 --> 00:39:45,990 不随时空位置的改变而改å? are the same at all places and all times, 650 00:39:48,900 --> 00:39:50,400 现有的理论有的可能会坚持 well there are theories around today would stay 651 00:39:51,330 --> 00:39:53,920 当然如果很久的话 说不定会被推¾˜? maybe if you mean really long times, maybe not, 652 00:39:54,280 --> 00:39:56,120 我们˜q˜æ˜¯å…ˆåšæŒ? but, just stick with this, 653 00:39:57,130 --> 00:40:00,210 物理规律不随时空位置的改变而改å? laws of physics are the same in all places and all times, 654 00:40:00,470 --> 00:40:01,690 光速是个常æ•? speed of light is a constant 655 00:40:02,380 --> 00:40:04,530 ˜q™æ„å‘³ç€æ—‰™—´çš„概å¿? That means notions of time, 656 00:40:05,490 --> 00:40:08,830 以及长度 ¾l§è€Œé€Ÿåº¦å’ŒåŠ¨é‡? and length and thus, velocity and momentum, 657 00:40:09,320 --> 00:40:10,530 必须被修æ­? have to be modified 658 00:40:11,020 --> 00:40:14,710 爱因斯坦开始寻找一个自‹z½çš„构架 And Einstein set out to find a consistent framework, 659 00:40:16,490 --> 00:40:21,130 ž®†å››ä¸ªå˜é‡?三个½Iºé—´å˜é‡ treating the four variables of the three dimensions of space, 660 00:40:21,420 --> 00:40:22,540 和一个时间变é‡? and the dimension of time 661 00:40:22,890 --> 00:40:23,960 对称地处ç? in a symmetrical way, 662 00:40:24,650 --> 00:40:28,670 òq¶ä»Žé€»è¾‘上得å‡? and pursuit that to its logical conclusion, which was 663 00:40:29,110 --> 00:40:32,180 物体动量的测é‡? that the measuring of momentum of an object, for example, 664 00:40:32,480 --> 00:40:34,380 它的质量 旉™—´ 和速度 its mass, time and its velocity, 665 00:40:34,640 --> 00:40:39,560 必须è¢?减去速度与光速比的åã^方的òqÏx–¹æ ¹çš„倒数 has to be modified by the inverse square root of one minus the ratio of 666 00:40:39,820 --> 00:40:42,610 修正的结è®? that velocity, the velocity of light squared 667 00:40:45,320 --> 00:40:48,320 而äؓ了引入ä‹É旉™—´ä¸Žç©ºé—´è¢«òq¶ç½®æˆäؓ可能的对¿U? And in order to bring in the symmetry of putting space and time together, 668 00:40:49,580 --> 00:40:51,050 你不得不得到˜q™æ ·ä¸€ä¸ªç»“è®? you force to the conclusion 669 00:40:51,650 --> 00:40:54,100 与三¾l´ç©ºé—´ä¸­çš„动量一èµ? that accompanying the three dimensions of momentum, 670 00:40:55,800 --> 00:40:59,320 三维½Iºé—´ä¸­çš„速度带来能量 velocity of the three-dimensional space, comes energy, 671 00:41:00,300 --> 00:41:04,160 你必™åÕd¾—承认一个可能ä×o人感到奇怪的 and you're going to assign what you might have seen peculiar 672 00:41:04,640 --> 00:41:09,830 物体的静止能é‡?数å€ég¸Š a rest energy of objects, that should own, 673 00:41:10,150 --> 00:41:11,730 ½{‰äºŽå…‰™™æ­¢è´¨é‡ä¸Žå…‰é€Ÿåã^方之¿U? physically measures and matches m c squared 674 00:41:12,200 --> 00:41:17,250 ˜q™æ„å‘³ç€ 如果物体 in the sense that if, something happens to the object 675 00:41:17,490 --> 00:41:18,980 因某¿UåŽŸå› è€Œå¤±åŽÖM¸€éƒ¨åˆ†é™æ­¢è´¨é‡ in such a way that it does lose mass, 676 00:41:19,580 --> 00:41:21,060 ž®±åƒåœ¨æ ¸è£‚变反应中会发生的那æ ? as happens in nuclear fission, 677 00:41:22,990 --> 00:41:26,000 那么守恒的能量肯定有一部分åŽÖMº†åˆ«å¤„ then that energy which is conserved must appear somewhere else 678 00:41:27,300 --> 00:41:29,140 物体å…ähœ‰é™æ­¢èƒ½é‡˜q™äšgäº? But it does have that rest energy, 679 00:41:29,570 --> 00:41:32,820 最初看èµäh¥åƒæ˜¯èƒ¡è¨€ä¹Þp¯­ and at first it seemed maybe nonsense 680 00:41:33,100 --> 00:41:34,600 或是½Iºæƒ³ or it's certainly an abstraction, 681 00:41:35,420 --> 00:41:40,010 没äh 我想是一个小学生 nobody asks him as I think was a primary student 682 00:41:40,410 --> 00:41:43,910 问法拉第 你做的这些有什么用 asked Faraday, what's the use of what you are doing 683 00:41:44,130 --> 00:41:45,360 法拉½W¬å›ž½{”说 我不知道 and Faraday said, I don't know, 684 00:41:45,640 --> 00:41:47,350 但我ç›æ€¿¡ä½ å¾—学会怎么表述å®? but I'm sure you will learn to text it 685 00:41:50,690 --> 00:41:53,870 当时ž®±æ˜¯˜q™æ · 现在˜q™ä¸ªä¹Ÿæ˜¯˜q™æ · It's just as true then, that's true then today. 686 00:41:56,100 --> 00:41:59,240 ½Ž€å•æ¥è¯? um, in short, 687 00:41:59,470 --> 00:42:02,850 在这¿Uå¯¹¿U°åœ°å¤„理旉™—´å’Œç©ºé—´çš„¾lå…¸å½¢å¼ä¸? in this canonical format of treating the thing symmetrically, 688 00:42:03,360 --> 00:42:08,840 你必™åÖM»¥ä¸€¿Uæœ‰­‘£çš„方式重新定义能量 最¾lˆå¾—åˆ? you have to redefine energy, in a curious way that ends up giving you 689 00:42:09,330 --> 00:42:13,530 能量½{‰äºŽé™æ­¢è´¨é‡ä¹˜ä»¥å…‰é€Ÿçš„òqÏx–¹ the energy is mc squared over the one minus v over c 690 00:42:13,830 --> 00:42:15,550 除以一减去速度与光速比的åã^方的开æ–? the whole squared, square rooted 691 00:42:15,890 --> 00:42:19,140 但因为在一般的¾léªŒä¸? And then ordinarily, in any usual experience 692 00:42:19,560 --> 00:42:23,530 我们需要处理的速度都远比光速小 the velocities we are dealing with are vastly less than the velocity of light 693 00:42:23,780 --> 00:42:25,830 它又会被½Ž€åŒ–成用速度òqÏx–¹çš„二分之一表示的åŞå¼? so this come back to give you half in v squared, 694 00:42:26,100 --> 00:42:30,390 ž®±æ˜¯ä½ åˆä¸?不是ž®å­¦ 学的那些. that what you learned in secondary school, not in primary school 695 00:42:34,090 --> 00:42:38,500 但扩展这些要说的æ˜? But extending this, that is an example, 696 00:42:39,070 --> 00:42:43,530 ˜q™æ˜¯¾ŸŽä¸½çš„理论带来非å¸æ€¸¥é‡çš„后果的一个例å­? of something that turned out to be extraordinarily consequential, 697 00:42:45,600 --> 00:42:48,130 äºÞZ»¬å¯¹è¿™ä¸ªå‘现的表述 it's not so much the people learned to text the discovery 698 00:42:48,440 --> 00:42:52,210 与用它制造大规模杀伤性武器相比不½Ž—什ä¹? as they learned to build weapons of mass destruction from it 699 00:42:55,820 --> 00:42:57,360 ¾l§ç®‹æˆ‘们的追å¯? Continuing the quest, 700 00:42:58,430 --> 00:43:01,240 很多äº?包括æˆ? the person that many people including myself, 701 00:43:01,610 --> 00:43:03,890 都认ä¸ø™¿™ä¸ªäh能和爱因斯坦òq¶è‚© would rank right there with Einstein, 702 00:43:05,780 --> 00:43:09,780 但他的名声实际上ž®å¾—å¤? but a less publicity, which, 703 00:43:10,640 --> 00:43:12,590 某种意义上你可以认äؓ˜q™æ˜¯å› äؓ in some sense, you could say that, 704 00:43:12,960 --> 00:43:14,550 爱因斯坦òq¶ä¸æŽ’斥公众场合 Einstein was not adverse the publicity, 705 00:43:15,130 --> 00:43:17,840 而狄拉克肯定排斥 whereas Dirac certainly was, 706 00:43:18,780 --> 00:43:21,430 我认ä¸ÞZ»–完全不必爱因斯坦å·? I would rate him fully Einstein's equal 707 00:43:22,810 --> 00:43:25,950 ˜q™æ˜¯ä»–在威斯敏斯特修道院的纪å¿ëŠ¢‘ This is his memorial stone in Westminster Abbey, 708 00:43:26,720 --> 00:43:30,380 ¾Uªå¿µç€ä»–超凡的方程 and it commemorate his extraordinary equation 709 00:43:30,620 --> 00:43:33,200 ˜q™é‡Œç”¨ç®€åŒ–的方式呈现 which is written in deliberately simplified terms there 710 00:43:34,840 --> 00:43:35,620 又写在这äº? It is written again here 711 00:43:36,960 --> 00:43:42,910 ˜q™ä¸ªæ–¹ç¨‹è¯•å›¾ž®†é‡å­åŠ›å­¦çš„基本方程 It is an equation that seeks to take the basic equation of quantum mechanics 712 00:43:43,180 --> 00:43:44,320 薛定谔方½E? the Schrodinger equation, 713 00:43:44,690 --> 00:43:52,110 变得在相对论意义上成ç«? and turn it into something that is relativistically sympathetic, 714 00:43:52,410 --> 00:43:57,700 òq¶åŒæ—¶å¤„理三个空间变量和一个时间变é‡? and handles the three variables of space and the variable of time together 715 00:43:58,090 --> 00:44:00,570 希腊字母Ψ So the Greek letter Ψ, 716 00:44:00,880 --> 00:44:04,770 像被一条竖¾U¿ç©¿˜q‡çš„U的那ä¸? the thing like a U with a vertical line through it, 717 00:44:05,090 --> 00:44:08,050 代表着描述量子¾pȝ»Ÿçš„æ—¶é—? is the wave function that describes the state in space 718 00:44:08,300 --> 00:44:10,360 ½Iºé—´çŠ¶æ€çš„波函æ•? and time of the system you talking about 719 00:44:11,120 --> 00:44:13,840 那个delta意味着 The delta thing eveard means derivatives with respective 720 00:44:14,630 --> 00:44:15,400 对三个空间维åº? to the three space dimensions 721 00:44:15,790 --> 00:44:16,740 和时间维度分别取导数 the time dimension 722 00:44:18,360 --> 00:44:19,420 i是我们的老朋å? i is our old friend, 723 00:44:19,710 --> 00:44:20,770 负一的åã^æ–ÒŽ ¹ the square root of -1, 724 00:44:21,120 --> 00:44:22,100 它在˜q™å¹²å˜? what's it doing there? 725 00:44:22,360 --> 00:44:26,300 ¾•æ˜¯ä¸€¾pÕdˆ—四乘四的矩阵 And ¾• is a set of four by four matrices that 726 00:44:27,790 --> 00:44:31,900 它们与涉及的¾_’子有某¿Uç›¸ä¼? have some kind of correspondence to the particles you are talking about 727 00:44:33,140 --> 00:44:35,110 ˜q™é‡Œæ¯”较古怪的æ˜? And the bizarre thing about this is, 728 00:44:36,880 --> 00:44:38,800 旉™—´åœ¨ä½•å¤„ä×oäºÞZ¸å®? which is the time was really disconcerting, 729 00:44:39,020 --> 00:44:42,840 我觉得这是物理中最¼œžå¥‡çš„事之一 and I think it's one of the most magical things in all the physics 730 00:44:44,960 --> 00:44:47,110 如果它们能感觉到˜q™é‡Œå‘生的事æƒ? If they are sensing what is done here, 731 00:44:49,070 --> 00:44:50,790 我们说到的四个基本粒å­? of the four particles you are talking about, 732 00:44:51,080 --> 00:44:53,120 我们开始讲电子 to start talking about electrons, 733 00:44:53,390 --> 00:44:56,510 其中两个是电å­?上下自旋 two of them are electrons which spins up or the spins down 734 00:44:57,730 --> 00:44:58,580 另两个是什ä¹? What are the other two? 735 00:44:58,960 --> 00:45:01,570 狄拉克希望它们是质子 Dirac hope they would turn out to be protons, 736 00:45:02,130 --> 00:45:04,370 比电子重得多的一¿Uç²’å­? the things that are much heavier than the electrons, 737 00:45:04,750 --> 00:45:09,750 他们当时被看作是电子的兄弟姐å¦? but really ought to be thought ofat that time as their cousins or siblings 738 00:45:10,280 --> 00:45:13,310 有äh认äؓ是测质量的时候弄混了 And it maybe someone screwed up on measuring the mass, 739 00:45:13,700 --> 00:45:15,880 或者应该有重新定义它的æ–ÒŽ³• or, there was some way of redefining it 740 00:45:16,150 --> 00:45:18,930 但实际上 当然 另一¿Ué€‰æ‹©æ˜¯å‡è®? It turns out, of course, the alternative was to assume 741 00:45:19,370 --> 00:45:23,740 存在着一个我们从未观‹¹‹åˆ°˜q‡çš„ there is a background sea of particles that we never see 742 00:45:25,800 --> 00:45:27,710 反电子æ“v that are anti-electrons, 743 00:45:28,180 --> 00:45:30,210 除带正电之外它们与电子完全相å? that are like electrons except that they got positive charge 744 00:45:31,200 --> 00:45:36,060 ˜q™è¶…å‡ÞZº†äººç±»æœ€ç‹‚野的想è±? This seems beyond the wildest shores of man's, 745 00:45:37,140 --> 00:45:38,740 äºÞZ»¬ä¹Ÿç¡®å®žä¸èƒ½æŽ¥å?直到它们真的被找åˆ? And so it did until they were found 746 00:45:41,440 --> 00:45:45,570 ½Ž€è€Œè¨€ä¹?我们对真理的˜q½æ±‚ There are examples in short, where our pursuit of truth 747 00:45:46,760 --> 00:45:52,370 曄¡»è¢«å¯¹ä¼˜é›…和美的求助指å¼? has been guided by appeal to elegance and beauty, 748 00:45:53,870 --> 00:45:55,340 以我不认为â€? in ways that I don't thinkâ€? 749 00:45:55,610 --> 00:45:57,230 我不认äؓ我会ç›æ€¿¡˜q™äº› I know I wouldn't have believed, 750 00:45:57,840 --> 00:46:00,280 如果你用抽象概念解释的话 if you'd explain it to be as an abstract concept 751 00:46:01,460 --> 00:46:04,340 我很¼‹®å®š 如果狄拉克选择了写下了˜q™ä¸ªå…¬å¼ I'm quite sure if then Dirac would have written that equation down, 752 00:46:04,660 --> 00:46:07,120 而是用质子或带负ç”늚„背景 rather than conjectured it with the things were protons 753 00:46:07,440 --> 00:46:10,350 ¾_’子‹¹ïLš„存在推出å®? or some background sea of negative particles, 754 00:46:10,800 --> 00:46:13,440 我会说求å¯ÆD¿‡½E‹æœ‰é—®é¢˜ I would have said there's something wrong with the derivation 755 00:46:15,500 --> 00:46:16,570 我很¼‹®ä¿¡˜q™ä¸€ç‚? I am quite convinced to that 756 00:46:21,820 --> 00:46:23,970 我还可以举更多的例子 但我不再多说äº? I could have gone on and I am not going to, 757 00:46:24,410 --> 00:46:27,140 我本来还惌™¯´ä¸€äº›åˆ«çš? I had conjectured telling you some other things, 758 00:46:27,390 --> 00:46:29,040 但我惌™¯´åˆ°è¿™å·®ä¸å¤šäº† I think it probably have enough by this time, 759 00:46:29,460 --> 00:46:33,160 但还有很多真的很漂亮的东è¥? but there are also some really beautiful things you can do 760 00:46:34,420 --> 00:46:37,200 在生命科学和物理学中都有 in both life sciences and physical sciences, 761 00:46:38,680 --> 00:46:40,670 不需要对体系做深入的了解 without knowing very much about the system, 762 00:46:41,030 --> 00:46:42,880 只要看看标定律就è¡? just ask in what are the scaling laws 763 00:46:43,630 --> 00:46:47,630 物体å…ähœ‰çš„三个最基本的量æ˜? There are three quantities, basic quantities things have 764 00:46:48,060 --> 00:46:52,910 质量 长度和时é—? they have mass, they have length and there is time in this 765 00:46:53,920 --> 00:46:55,880 只要写下˜q™äº›æ ‡å®šå¾? If you just write down those scaling laws 766 00:46:56,150 --> 00:46:58,260 你就会发çŽîC»–们能展现的东西ä×o人惊å¥? it is amazing what things you can show 767 00:46:59,510 --> 00:47:00,660 有一个生物学中的½Ž€å•ä¾‹å­? Very simple one in biology, 768 00:47:00,940 --> 00:47:03,760 三百多年以前的äh发现çš? that was done by someone three hundred years ago, 769 00:47:04,280 --> 00:47:08,710 现在被印在了¾U¦ç¿° 梅纳å¾?史密æ–? and it's the cover of the wonderful book John Meynard Smith 770 00:47:09,000 --> 00:47:10,000 关于生物模型的书的封面上 wrote on models in biology 771 00:47:10,300 --> 00:47:12,900 ˜q™æ˜¯ä¸€ä¸ªéžå¸¸ç®€å•çš„关于标定律的论点 It is a very simple scaling law argument, 772 00:47:13,590 --> 00:47:19,080 要求个头不同的会跳的生物 that asks for organisms of different sizes that have ways of jumping up, 773 00:47:20,240 --> 00:47:22,940 无论是马˜q˜æ˜¯è·Œ™š¤ whether they are horses or whether they are fleas 774 00:47:26,010 --> 00:47:27,470 考虑它们跳的方式 Thinking about how they do it, 775 00:47:27,790 --> 00:47:31,530 涉及的势能大ž®å’Œå¼¹åŠ›å¤§å° what's the potential energy involved, what's the springiness involved 776 00:47:33,620 --> 00:47:35,350 有一个关于尺寸的论点æ˜? There is a dimensional argument that says, 777 00:47:35,670 --> 00:47:39,750 实际上生物的赯‚Ÿ©é«˜åº¦ä¸Žå®ƒçš„个头无å…? in fact it's going to be independent of the size of the organisms, 778 00:47:40,660 --> 00:47:43,550 你可以粗略估è®?如果会蟩的话 and you can make a rough estimate, all organisms, if they fit, 779 00:47:45,230 --> 00:47:46,930 他们差不多都跳一¾c³é«˜ all to be able to jump about a meter 780 00:47:47,680 --> 00:47:50,290 把它们的重心抬高一¾c? elevate their center of gravity about a meter 781 00:47:50,710 --> 00:47:54,640 我们如此 马如æ­?跌™š¤ä¹Ÿå¦‚æ­? That's what we do, horses do or fleas do 782 00:47:54,940 --> 00:47:56,590 当然有的跛_¾—高些或低äº? There are things that jump higher or lower 783 00:47:56,950 --> 00:48:00,500 因äؓ˜q›åŒ–把它们锻造成了特别会跳的或不太会跳的 because evolutions forged them to be particularly jumpy or not very jumpy 784 00:48:00,920 --> 00:48:03,590 ˜q™å¾ˆå¥‡å¦™ 而与此相关的最优美的事情是 It is a wonderful thing and the really elegant thing about it, 785 00:48:03,920 --> 00:48:05,460 ¾U¦ç¿° 梅纳å¾?史密斯的 the cover illustration of John Meynard Smith's 786 00:48:05,890 --> 00:48:07,420 关于生物模型的书的封面插图上 little book on models in biology 787 00:48:08,040 --> 00:48:10,500 有一只老鼠 has a little representation of a mouse 788 00:48:10,730 --> 00:48:13,500 我该把它攑֜¨òqȝ¯ç‰‡é‡Œçš?但我没来得及扑ֈ°é‚£æœ¬ä¹? I should have had it on the slide but I couldn't find the book in time, 789 00:48:14,320 --> 00:48:16,990 那是一只有着会蟩的腿的小老鼠 And it's generally a squared little mouse with springy legs 790 00:48:18,670 --> 00:48:20,350 让约¾˜°æ„Ÿåˆ°å¾ˆè‹¦æ¼çš„是 Was very distressful for John, 791 00:48:20,750 --> 00:48:25,510 有时我不太友好地把他当成一个伊™å¿å‡ºíw«çš„马克思主义è€? who was what I sometimes did unkindly think of as an Etonian Marxist, 792 00:48:26,080 --> 00:48:29,790 他肯定是 他肯定同情马克思主ä¹? that he was a, definitely he had Marxist sympathies, 793 00:48:30,360 --> 00:48:32,160 真的使他非常苦恼的一件事æ˜? and it was a matter of real distress to him 794 00:48:32,430 --> 00:48:34,130 当他的书被译成俄语时 when the book was translated into Russian, 795 00:48:35,120 --> 00:48:40,800 ž®é¢ä¸?完全不同åœ?是一只社会主义现实主义老鼠 and on the cover, completely changed, was a socialist realist mouse 796 00:48:44,810 --> 00:48:48,100 后果更严重的 又是一个很好的故事 More consequential, again, a great story, 797 00:48:48,300 --> 00:48:50,030 ¾l™å¾ˆå¤šäh带来了欢ä¹? brought great joy to many people, 798 00:48:50,850 --> 00:48:54,630 ½W¬ä¸€‹Æ¡åŽŸå­å¼¹è¯•éªŒåœ¨é˜¿æ‹‰èŽ«æˆˆå¤š˜q›è¡Œçš„æ—¶å€? when the first atom bomb test was conducted in Alamogordo, 799 00:48:55,900 --> 00:48:59,930 涉及到的首席‹¹ä½“动力学家之一 one of the chief fluid dynamicists involved in that 800 00:49:00,180 --> 00:49:01,690 是一个叫G I 泰勒的家ä¼? was a chap called G I Taylor, 801 00:49:02,150 --> 00:49:05,340 一个你们中的很多äh都会è®îC½çš„剑桥äh a Cambridge person that many of you will remember 802 00:49:07,550 --> 00:49:10,860 当他在涂ç”ÖMº›è°çŸ¥é“是什么东西的东西的时å€? And as this guy was sort of scribbling what nobody really knows, 803 00:49:11,250 --> 00:49:16,380 他随着蘑菇云的展开记录的是 what he was taking note of was, as the mushroom cloud expanded, 804 00:49:17,200 --> 00:49:18,880 它以怎样的过½E‹å±•å¼€ how was it expanding, 805 00:49:19,130 --> 00:49:23,720 他测量的东西大致上给å‡ÞZ¸€ä¸ªç¡®å®šæ—¶åˆÈš„半径 what was he measuring, giving an idea of what was the radius at a given time 806 00:49:24,860 --> 00:49:25,900 以及˜q™äº›æ—¶åˆ»åˆ†åˆ«éƒ½æ˜¯ä»€ä¹? and keep in track of the time 807 00:49:27,080 --> 00:49:29,360 他之前想 事都做完äº? He had thought before that anything was done, 808 00:49:29,820 --> 00:49:31,990 接下来会发生的事æ˜? what's going to go on here is that 809 00:49:32,270 --> 00:49:33,730 有很多能量会被释攑ևºæ? there is going to be a lot of energy released 810 00:49:34,420 --> 00:49:36,380 当裂变反应发生的时å€? when the fission effect occurs 811 00:49:38,290 --> 00:49:40,330 ˜q™äº›èƒ½é‡ž®†ä¼šå½¢æˆè˜‘菇äº? And that energy is going to drive this cloud out, 812 00:49:41,110 --> 00:49:44,130 且必焉™¡¶ç€½Iºæ°”密度向外扩张 and it's going to have to go out against the density of air 813 00:49:45,310 --> 00:49:48,260 所以涉及到的两个变量是能量 So the two variables involved are the energy, 814 00:49:49,770 --> 00:49:52,910 质量乘以长度的åã^方乘以时间的负二‹Æ? mass length squared time to the minus two, 815 00:49:53,710 --> 00:49:58,680 和空气密åº? 质量除以长度的三‹Æ¡æ–¹ and the density of the air, mass divided by length cube 816 00:50:00,370 --> 00:50:02,510 你可以消去质é‡?òq¶æ®æ­¤é¢„‹¹? You can cancel out the masses and you get the prediction, 817 00:50:03,000 --> 00:50:06,110 半径ž®? that the radius is going to expand 818 00:50:06,580 --> 00:50:08,170 球面半径和时间的òqÏx–¹ç›¸å…³ radius to the sphere is going to go like t square 819 00:50:09,140 --> 00:50:10,910 然后你以可以ç”Õd‡ºåŠå¾„和时间的 So you are going to plot the logarithm of the radius 820 00:50:11,170 --> 00:50:12,440 å¯ÒŽ•°ä¹‹é—´çš„å…³¾p? against the logarithm of the time 821 00:50:12,650 --> 00:50:14,880 囑փå¤§çº¦æ˜¯ç¼“慢上升的直线 and you can get something that slow point forward 822 00:50:15,620 --> 00:50:19,530 然后囑փåœ¨åæ ‡èáu上的截距会告诉你释放的能量的é‡? And where it intercepts the axis will tells you the energy released 823 00:50:20,200 --> 00:50:22,980 他觉得这æŒÞZ¸é”? 于是他写了一½‹‡ä¸¤™å늺¸çš„小论文 He thought this is pretty nice so he wrote a little two-page paper, 824 00:50:23,230 --> 00:50:26,870 把它寄给了一个真把它发表了的‹¹ä½“力学杂志 he send it out to the journal of fluid mechanics that truly published it 825 00:50:27,230 --> 00:50:30,350 格雷夫斯ž®†å†›å’Œæ›¼å“ˆé¡¿è®¡åˆ’那些äº? And the General Groves and the people of the Manhattan Project 826 00:50:30,790 --> 00:50:31,810 完全陷入了狂æ€? went absolutely apeshit 827 00:50:32,800 --> 00:50:35,460 因äؓ˜q™åœ¨ä¿å¯†ä¸Šè¢«å½’入最高çñ” because this was classified as the highest level 828 00:50:36,430 --> 00:50:38,950 ˜q™å¤ªå¯çˆ±äº? 它以自己的方å¼? That is a really lover, I mean it in its own way 829 00:50:39,350 --> 00:50:43,100 ­‘…越了费曼对˜q™å¸®äººå¼€çš„所有玩½W? it's better than those jokes Feynman played on this bunch of people 830 00:50:43,680 --> 00:50:47,040 ™åÞZ¾¿ ˜q™æ ·çš„æ•™è®? And incidentally, those, this, it's the received wisdom, 831 00:50:47,620 --> 00:50:50,570 当然只是我感觉到çš? 在我接触到的范围é‡? as I understand it, certainly in the circles in which I moved, 832 00:50:50,800 --> 00:50:54,540 格雷夫斯在曼哈顿计划中要求的 that the tight security Groves imposed on the Manhattan Project 833 00:50:54,820 --> 00:50:56,390 那些没äh提è“v的保密措施的落实 that nobody told anybody else to start, 834 00:50:56,690 --> 00:50:59,930 ˜qŸé’åœ?òq¶æ²¡æœ‰å› æ­¤åŠ é€? actually retarded, didn't go faster by virtue at all, 835 00:51:00,310 --> 00:51:01,680 反而减¾~“了 但这是另一个问é¢? went slower, but that is another point 836 00:51:02,280 --> 00:51:04,590 我的最后一个例子对于那些航‹¹ïLš„人来说很½Ž€å? And my last example of these things is a very simple one 837 00:51:04,900 --> 00:51:07,450 但这其中不包括我 particularly for those who sail but not including me 838 00:51:08,060 --> 00:51:10,070 ¾l™æˆ‘五分é’? I can again five minutes 839 00:51:10,860 --> 00:51:13,610 我将解释˜q™ä¸€çŽ°è±¡ or so I can give you a very very simple dimensional of 840 00:51:14,270 --> 00:51:17,770 ˜q™ä¸€çŽ°è±¡å…¶å®žå¾ˆç®€å?涉及船的bell waves argument that would tell you the bell waves the common waves of ships, 841 00:51:18,490 --> 00:51:21,540 无论是补鲸轮˜q˜æ˜¯åˆ’艇的引èµïLš„æ°´æ‡L whether they are a whale tanker or whether they are a rowing boat , 842 00:51:22,440 --> 00:51:24,600 都是ä»?3度出现的 all coming out at the angle about 23 degrees 843 00:51:27,660 --> 00:51:34,590 ˜q™ä¸ªå¼§åº¦çš„正切值是 1/2.2 一个优¾ŸŽçš„弧度 An angle whose tan is 1 over 2.2, all sorts of elegant thing you can do 844 00:51:37,010 --> 00:51:41,500 我自己們֐‘于科学中最¾ŸŽçš„事物 My own prejudice is that the nicest thing in science is the things 845 00:51:41,820 --> 00:51:42,560 是那些你可以完全ç›æ€¿¡çš? that you can really trust 846 00:51:43,150 --> 00:51:44,280 现在 often these days, 847 00:51:44,520 --> 00:51:51,650 一个äh需要巨大的计算é‡? the things you have to have a huge computations exercise 848 00:51:52,000 --> 00:51:53,590 和细节来展示自己的理è®? where you put in all the details, 849 00:51:54,730 --> 00:51:56,370 因äؓäºÞZ»¬æƒŒ™¦çœ‹åˆ°˜q™äº› because there are people who want to see that 850 00:51:57,190 --> 00:52:01,240 但假如这些细èŠ? But I am not going to trust that if it is not backed 851 00:52:01,500 --> 00:52:03,010 不能指向一个本è´? by something that strips the things 852 00:52:03,300 --> 00:52:06,850 或者什么背后的现象的话 to its essentials and can show me 853 00:52:07,200 --> 00:52:08,100 òq¶ä¸èƒ½è¯´æœæˆ‘ more or less on the back of an envelope 854 00:52:08,460 --> 00:52:09,650 那么怎么åŠ? What's going on? 855 00:52:10,650 --> 00:52:14,550 仅以一些金融方面的事情ä¸ÞZ¾‹ And just for instance, some financial things, 856 00:52:15,980 --> 00:52:18,080 如果我被ä»Õd‘½ä¸ºæ•´ä¸ªå®‡å®™çš„指导è€? if I was supremed to be the dictator of the universe, 857 00:52:19,410 --> 00:52:21,730 我将做的½W¬ä¸€ä»¶å…³äºŽé“¶è¡Œç®¡ç†çš„äº? the first thing I would do for banking regulations 858 00:52:22,970 --> 00:52:25,960 是禁止在高复æ? would forbid the trading in instruments 859 00:52:26,300 --> 00:52:31,520 ˜qç®—下的交易合作 which are very computationally collaborate 860 00:52:32,040 --> 00:52:35,110 一些事æƒ?假如你以一个勘探者的角度来写 Some of the things that if you write them as prospectors 861 00:52:36,620 --> 00:52:38,400 能写出无数的½‹‡å¹… would be in the size equivalent of millions of pages, 862 00:52:40,550 --> 00:52:45,710 包括英国银行的很多事ç‰? including the Bank of England on that I would forbid the trading on 863 00:52:46,180 --> 00:52:47,610 äºÞZ»¬å‚与在这些交易中 something like that on grounds 864 00:52:48,470 --> 00:52:49,700 却åƈ不知道他们在做什ä¹? that people doing it don's know what they are doing 865 00:52:51,680 --> 00:52:53,710 一个不知道自己在做什么的äº? and you shouldn't be allowed to do what you don't know you are doing 866 00:52:54,140 --> 00:52:55,470 或有˜q™ç§å€‘֐‘çš„äh应当被禁止做˜q™äº›äº‹æƒ… and has such implications 867 00:52:56,620 --> 00:52:58,500 因此 在某些层面上我åƈ不想è¯?却不得不è¯? So in some sense I don' t want to, 868 00:53:00,540 --> 00:53:04,420 我不会说ä»ÖM½•æˆ‘不了解的事æƒ? I am not going to say something that I do not know what I am saying, 869 00:53:04,810 --> 00:53:08,880 比如¾ŸŽåœ¨æ•°å­¦ä¸? which is beauty is there everywhere in mathematics, 870 00:53:10,140 --> 00:53:12,830 随处可见 almost everywhere in math 871 00:53:15,050 --> 00:53:21,450 在科学中˜q™ä¸€ç‚¹å¾ˆé‡è¦ In the sciences, it can often be quite magically important 872 00:53:22,290 --> 00:53:23,600 我讲¾l™ä½ ä»¬ä‹D一些列å­? And I will give you some examples 873 00:53:23,910 --> 00:53:28,840 通常äºÞZ»¬ä¼šè®¤ä¸ºå¾ç«‹åœ¨¿U‘学基础上的一些解é‡? More commonly it's that things then build on that and their elaboration 874 00:53:29,110 --> 00:53:32,680 或由人强加的解释 or that they are importuned by the people or they seem to be humdrum than 875 00:53:33,430 --> 00:53:37,670 会比äºÞZ»¬ç›´è§‚åœ?真正地所了解的事物无è? they are based on things that are really good and you really understand 876 00:53:40,520 --> 00:53:41,420 我只想以一个真诚的 And I want to conclude 877 00:53:42,700 --> 00:53:47,950 关于如换¿Uæ–¹å¼ä½•ç†è§£ by saying just a word a genuine reflecting in the direction of 878 00:53:53,050 --> 00:53:56,210 我们周围˜q™ä¸ªä¸–ç•Œ 的思考作为æ€È»“ an alternative way of understanding the world around us 879 00:53:57,460 --> 00:54:02,800 我们已和世界一起存在至ž®‘十万年äº? which has been with us again for at least 100 thousand years, 880 00:54:03,470 --> 00:54:11,060 在这之中我们形成了信ä»îC¸Žä»·å€ÆD§‚ which is just how it all began, beliefs, values 881 00:54:11,580 --> 00:54:13,470 我åƈ不想¾l“束˜q™ä¸ªè¯é¢˜ And I am not wanting to put it down 882 00:54:13,970 --> 00:54:18,190 我只是想说ä“Q何永恒存在于˜q™ä¸ª½C¾ä¼šä¸­çš„事物 but I am just saying any of the things that abiding the society together 883 00:54:18,390 --> 00:54:19,980 都有一¾pÕdˆ—的特å¾? have a set of characteristics, 884 00:54:20,390 --> 00:54:23,670 有所有我们需要依靠的价å€? all the values we need to adhere to 885 00:54:24,020 --> 00:54:26,970 ˜q™åƈ不在我所说的那个框架之外 And they are out of the framework that I want to talk about 886 00:54:27,240 --> 00:54:28,880 因此他们òq¶ä¸æ˜¯åçš? so that they are not necessarily bad 887 00:54:29,160 --> 00:54:37,220 ˜q™äº›è§‚念只有在企囑ֈºç ´åƈòq²æ‰°¿U‘学所涉的领域 They are only bad when they take the form of transpiercing into a domain 888 00:54:37,570 --> 00:54:39,860 òq¶å¼ºåŠ ç»™äººç­”案时才是坏的 where science has come and told you an answer, 889 00:54:40,190 --> 00:54:43,970 ˜q™äº›ç†å¿µòq¶ä¸èƒ½çŸ¥é“ä½ çš„è¡Œä¸? it hasn't told you an answer about how to conduct yourself personally 890 00:54:44,730 --> 00:54:47,620 但却告诉你如何避免危险的½{”案 but it has told you the answer to avoid danger 891 00:54:48,000 --> 00:54:50,920 如果你想知道我们存在的世界äؓ什么如此丰富多æ ? If you want to know how the diversity of the world around us occurs, 892 00:54:51,340 --> 00:54:53,190 ˜q›åŒ–论就会告诉你½{”案 evolution tells you that now 893 00:54:54,100 --> 00:54:55,790 如果你愿æ„? And you are entitled if you wish, 894 00:55:01,590 --> 00:55:07,790 你也可以被告知机械的存在是由某种¼œžåœ£çš„力量赋予的 that to believe the machinery was set in place by something divine 895 00:55:08,890 --> 00:55:10,660 ˜q™ç§è®¾æƒ³æœ‰æ—¶æ˜¯æœ‰å®³çš„ I think that is an unnecessary assumption 896 00:55:11,100 --> 00:55:12,990 有时是无害的 but if you wish to, it does no harm 897 00:55:13,670 --> 00:55:16,530 但当你开始教孩子ä»? On the other hand it does do harm if you start teaching kids 898 00:55:16,920 --> 00:55:19,380 世界是公å…?004òq´åˆ›é€ çš„ž®±æ˜¯æœ‰å®³çš? that the world was created in the year 4004 899 00:55:21,180 --> 00:55:24,710 很多事情正像世界的è“v源一æ ? And there are many things like that and it is not at all clear 900 00:55:25,210 --> 00:55:28,950 我们òq¶ä¸çŸ¥é“˜q™æ˜ŸçƒåŽ†å²ä¸­æ—‰™—´çš„准¼‹®æ—¶é—´ç‚¹ that at the time of particularly difficulty in the history of this planet 901 00:55:33,110 --> 00:55:34,930 对于惌™¦ The indication of the attempt to 902 00:55:35,270 --> 00:55:42,350 真正了解事物 really understand things in favor or embracing some set of answers 903 00:55:44,450 --> 00:55:47,670 們֐‘于固定的½{”案的方å¼? which more very often is built around assumptions 904 00:55:49,640 --> 00:55:51,660 无异于相信女性的åœîC½åº”该比男äºÞZ½Ž that women states should be lower than men's 905 00:55:54,340 --> 00:55:56,720 ˜q™å¯¹æˆ‘们毫无用处 It's unhelpful to us and 906 00:55:57,010 --> 00:55:58,420 我们íw«å¤„一个一èˆ? we are living in the time we tend to 907 00:55:58,630 --> 00:56:00,390 集中兛_¿ƒä¸€ä¸ªé—®é¢˜çš„时代 focus on one problem at the time of the moment 908 00:56:00,890 --> 00:56:02,300 比如我们现在集中注意在气候变化问题上 we tend to focus on climate change 909 00:56:02,600 --> 00:56:05,580 30òq´å‰æˆ‘们更关注äh口增镉K—®é¢? If we go back 30 years, we focused on population growth 910 00:56:06,050 --> 00:56:10,340 10òq´åŽæˆ‘认ä¸ÞZh们会å…Ïx³¨é£Ÿç‰©çš„ä¾›¾l™é—®é¢? If you look ahead 10 years, my prediction will be focusing on food supply 911 00:56:11,180 --> 00:56:14,190 20òq´åŽž®†æ˜¯ä¸–界性æÙEæ°´ç´§¾~ºé—®é¢? and 20 years will focus on fresh water globally 912 00:56:14,660 --> 00:56:17,800 其实˜q™äº›é—®é¢˜çš„根本都是一æ ïLš„ and they are all part of the same thing and what we really need 913 00:56:18,500 --> 00:56:19,700 都与人相å…? is coming together with people 914 00:56:20,980 --> 00:56:24,070 每个人都有关于这个世界究竟如何äñ”生运作的æƒÏx³• people all hold beliefs about how the world ultimately happen, 915 00:56:25,180 --> 00:56:26,620 但除了这些笼¾lŸçš„æƒÏx³• but other than the trunk, 916 00:56:28,290 --> 00:56:31,870 我们也需要细节的理解 detailed understanding or particularly aspects 917 00:56:32,480 --> 00:56:33,850 和一些需要特ŒDŠå…³æ³¨çš„æ–šw¢ that we need to come together to address 918 00:56:35,670 --> 00:56:38,950 å¯ÒŽˆ‘来说˜q™äº›òq¶ä¸æ˜¯éƒ½æ˜? and it's not all together clear to me 919 00:56:39,960 --> 00:56:42,100 关于真理与美的问é¢? that this has been a long talk on truth and beauty 920 00:56:42,890 --> 00:56:46,220 也许òq¶ä¸æ˜¯ç¾Žçš?但一定是˜q™ä¸–界的真相 but it certainly is a part of truth if not beauty 921 00:57:09,760 --> 00:57:11,490 听众们好 Hello all the people in this hall 922 00:57:12,270 --> 00:57:15,500 那些每日挣扎于调查报å‘? who have to struggle through their daily life in researches assignment 923 00:57:15,840 --> 00:57:19,120 ¾lƒä¹ é¢?论文的ähä»? and exercises and research checks and impacts 924 00:57:19,360 --> 00:57:23,630 我希望你们都能很好地è®îC¸‹½W”è®° I hope you all have taken notes and you know the importance of, 925 00:57:24,980 --> 00:57:28,340 òq¶ä¸”希望你们能意识到最重要的是你们要保持探索的心æ€? the most important is to at last being able to discover something 926 00:57:30,290 --> 00:57:32,620 你们的反思也ž®†æˆä¸ø™¯¾½E‹çš„一部分 Those who assess impacts have taken into account 927 00:57:34,540 --> 00:57:36,380 May教授已经为我们做了一‹Æ¡å¾ˆæœ‰ä­h值的报告 Professor May has given us the first lovely lecture 928 00:57:36,840 --> 00:57:40,740 关于¾ŸŽä¸Žå¯¹è‡ªç„¶çš„理解和探ç´? about the quests into love and beauty as a guide to understanding nature 929 00:57:43,680 --> 00:57:45,870 他带我们由Euclidto Dirac开始探ç´? He took us from Euclidto Dirac, 930 00:57:47,380 --> 00:57:52,810 但我认äؓ那个说我们当å¯ÀL‰¾½Ž€‹z? but I think it is the philosopher who said seek simplicity 931 00:57:53,200 --> 00:57:54,460 但åƈ不相信它的那个哲学家 and mistrust it 932 00:57:54,870 --> 00:58:01,280 和课上的一些其他反例是丑陋çš? and the other things the professor mentioned were about ugly facts 933 00:58:04,370 --> 00:58:08,960 但May教授讲的最最核心的是¿U‘学是好çš? but the really nice thing he said was, of course, is the science is good 934 00:58:09,760 --> 00:58:12,910 那些é˜È¢¾ŸŽå¥½çš„理论的丑陋的事å®? Those ugly facts and the trumping of the beautiful theory 935 00:58:13,320 --> 00:58:15,910 其实最¾lˆå°†ä¼šå°†æˆ‘们指导向更¾ŸŽçš„理论 lead us into more beautiful theories 936 00:58:16,190 --> 00:58:17,900 今天的课为我们日后的讲åñ”开了个好头 A lovely start to our lecture series 937 00:58:18,120 --> 00:58:19,300 谢谢大家的到æ? Thank you very much indeed ÍøÇò±È·ÖÍøÖ±²¥