<time>3006_01:25:17,760 --> 01:25:19,920</time>
<s>它是聪明人聪明的意思</s>
<time>3007_01:25:20,280 --> 01:25:20,640</time>
<s>聪明</s>
<time>3008_01:25:21,000 --> 01:25:21,720</time>
<s>聪明人干的事</s>
<time>3009_01:25:23,160 --> 01:25:23,520</time>
<s>或者是聪明</s>
<time>3010_01:25:23,880 --> 01:25:25,680</time>
<s>或者说一个人如果什么都会的话</s>
<time>3011_01:25:26,040 --> 01:25:27,480</time>
<s>我们说他叫polymath（博学家）</s>
<time>3012_01:25:27,840 --> 01:25:30,360</time>
<s>就是各个方面你都是跟算数似的</s>
<time>3013_01:25:32,160 --> 01:25:34,680</time>
<s>那么数学的这个描述对象</s>
<time>3014_01:25:35,040 --> 01:25:35,400</time>
<s>包括什么呢</s>
<time>3015_01:25:35,760 --> 01:25:37,920</time>
<s>包括数包括形</s>
<time>3016_01:25:38,280 --> 01:25:39,000</time>
<s>包括形式</s>
<time>3017_01:25:41,160 --> 01:25:42,240</time>
<s>集合这些东西都是它的</s>
<time>3018_01:25:42,600 --> 01:25:43,680</time>
<s>图形都是它的研究对象</s>
<time>3019_01:25:44,040 --> 01:25:44,400</time>
<s>不是光是数</s>
<time>3020_01:25:45,840 --> 01:25:46,200</time>
<s>那么</s>
<time>3021_01:25:47,280 --> 01:25:49,080</time>
<s>有一种说法</s>
<time>3022_01:25:49,440 --> 01:25:51,240</time>
<s>是把数学是mathematics</s>
<time>3023_01:25:51,600 --> 01:25:52,680</time>
<s>就是单独作为学科</s>
<time>3024_01:25:53,040 --> 01:25:54,120</time>
<s>不算科学家里</s>
<time>3025_01:25:54,480 --> 01:25:56,280</time>
<s>我们就说人家是数学家</s>
<time>3026_01:25:56,640 --> 01:25:57,360</time>
<s>但是也很多场合</s>
<time>3027_01:25:57,720 --> 01:25:59,160</time>
<s>也会说mathematicscience（数学科学）</s>
<time>3028_01:25:59,520 --> 01:26:00,240</time>
<s>比方说相对论就算</s>
<time>3029_01:26:00,600 --> 01:26:01,320</time>
<s>mathematicscience</s>
<time>3030_01:26:02,760 --> 01:26:04,200</time>
<s>那是相当于应用数学了</s>
<time>3031_01:26:06,000 --> 01:26:06,720</time>
<s>有时候说科学家的时候</s>
<time>3032_01:26:07,080 --> 01:26:08,880</time>
<s>也把数学家包括在里面</s>
<time>3033_01:26:09,240 --> 01:26:11,400</time>
<s>但是我个人觉得数学家还是</s>
<time>3034_01:26:11,760 --> 01:26:13,560</time>
<s>他是相当独特的</s>
<time>3035_01:26:13,920 --> 01:26:14,280</time>
<s>因为什么呢</s>
<time>3036_01:26:14,640 --> 01:26:16,800</time>
<s>物理学的一个正确与否的问题</s>
<time>3037_01:26:18,600 --> 01:26:20,040</time>
<s>一定是现实要有就是说</s>
<time>3038_01:26:20,400 --> 01:26:20,760</time>
<s>证据嘛</s>
<time>3039_01:26:21,120 --> 01:26:21,840</time>
<s>当我在现实证实的时候</s>
<time>3040_01:26:22,200 --> 01:26:24,000</time>
<s>它才是一个合理的理论</s>
<time>3041_01:26:24,360 --> 01:26:24,720</time>
<s>但是数学不用</s>
<time>3042_01:26:25,080 --> 01:26:27,960</time>
<s>数学本身我逻辑自洽地构成体系</s>
<time>3043_01:26:28,320 --> 01:26:29,040</time>
<s>这就是一个好的数学家</s>
<time>3044_01:26:30,120 --> 01:26:34,800</time>
<s>数学难道放之全宇宙而皆准吗</s>
<time>3045_01:26:35,520 --> 01:26:36,960</time>
<s>7月30号</s>
<time>3046_01:26:37,320 --> 01:26:39,480</time>
<s>我在今年的中国数学学会上</s>
<time>3047_01:26:39,840 --> 01:26:42,000</time>
<s>有一个45分钟报告</s>
<time>3048_01:26:42,360 --> 01:26:43,800</time>
<s>那个题目就是用这个谁</s>
<time>3049_01:26:44,160 --> 01:26:45,240</time>
<s>刚才这个狄拉克的大舅哥</s>
<time>3050_01:26:45,600 --> 01:26:47,040</time>
<s>叫尤金·保罗·维格纳的</s>
<time>3051_01:26:47,400 --> 01:26:49,200</time>
<s>一篇文章的题目叫</s>
<time>3052_01:26:49,560 --> 01:26:52,440</time>
<s>《数学在物理学中不可思议的有效性》</s>
<time>3053_01:26:54,600 --> 01:26:56,040</time>
<s>数学如果你的东西</s>
<time>3054_01:26:56,400 --> 01:26:56,760</time>
<s>数学对的</s>
<time>3055_01:26:57,120 --> 01:26:58,200</time>
<s>十有八九它物理是对的</s>
<time>3056_01:27:00,000 --> 01:27:01,440</time>
<s>就是数学是这样的</s>
<time>3057_01:27:01,800 --> 01:27:02,880</time>
<s>我们刚开始时候</s>
<time>3058_01:27:03,240 --> 01:27:04,320</time>
<s>人类去研究数学</s>
<time>3059_01:27:04,680 --> 01:27:05,760</time>
<s>就是去探究本质</s>
<time>3060_01:27:06,120 --> 01:27:06,840</time>
<s>什么叫本质呢</s>
<time>3061_01:27:07,200 --> 01:27:08,280</time>
<s>比如说你有三个苹果</s>
<time>3062_01:27:08,640 --> 01:27:09,360</time>
<s>加两个苹果</s>
<time>3063_01:27:09,720 --> 01:27:10,080</time>
<s>是五个苹果</s>
<time>3064_01:27:10,440 --> 01:27:11,520</time>
<s>三个桃加两个桃</s>
<time>3065_01:27:11,880 --> 01:27:12,600</time>
<s>等于五个桃</s>
<time>3066_01:27:12,960 --> 01:27:13,680</time>
<s>然后人们就觉得说</s>
<time>3067_01:27:14,040 --> 01:27:16,200</time>
<s>这个苹果和桃本身不是本质</s>
<time>3068_01:27:16,560 --> 01:27:18,720</time>
<s>你不能被它这个是甜的还是酸的</s>
<time>3069_01:27:19,080 --> 01:27:20,880</time>
<s>是大的还是小的是红的青的</s>
<time>3070_01:27:21,240 --> 01:27:22,320</time>
<s>这些东西你不能干扰</s>
<time>3071_01:27:22,680 --> 01:27:23,400</time>
<s>你得知道说</s>
<time>3072_01:27:23,760 --> 01:27:25,200</time>
<s>这三个加两个就是五个</s>
<time>3073_01:27:25,560 --> 01:27:26,280</time>
<s>这个才是本质</s>
<time>3074_01:27:26,640 --> 01:27:28,440</time>
<s>所以这是数学最开始诞生的</s>
<time>3075_01:27:28,800 --> 01:27:30,600</time>
<s>它就是去探究本质是什么</s>
<time>3076_01:27:30,960 --> 01:27:32,760</time>
<s>然后但是后来就会发现</s>
<time>3077_01:27:33,120 --> 01:27:33,840</time>
<s>我们很多数学</s>
<time>3078_01:27:34,200 --> 01:27:36,720</time>
<s>是从我们表面上看到的这些现象</s>
<time>3079_01:27:37,080 --> 01:27:38,520</time>
<s>我们去抽炼其中的本质</s>
<time>3080_01:27:38,880 --> 01:27:39,960</time>
<s>但是找到了这一些</s>
<time>3081_01:27:40,320 --> 01:27:41,760</time>
<s>合适的数学表达以后</s>
<time>3082_01:27:42,120 --> 01:27:44,280</time>
<s>它本身又能够去引发很多</s>
<time>3083_01:27:44,640 --> 01:27:46,440</time>
<s>关于数本身的这些思考</s>
<time>3084_01:27:46,800 --> 01:27:47,160</time>
<s>你像数论</s>
<time>3085_01:27:47,520 --> 01:27:48,240</time>
<s>它就是那个</s>
<time>3086_01:27:48,600 --> 01:27:51,480</time>
<s>这些自然数都有什么什么性质</s>
<time>3087_01:27:51,840 --> 01:27:52,560</time>
<s>那些很多理论</s>
<time>3088_01:27:52,920 --> 01:27:55,080</time>
<s>就是纯讨论这个数学本身了</s>
<time>3089_01:27:55,440 --> 01:27:57,240</time>
<s>那后来人们就会发现</s>
<time>3090_01:27:57,600 --> 01:27:59,400</time>
<s>当你开始纯讨论这个数学本身的</s>
<time>3091_01:27:59,760 --> 01:28:00,840</time>
<s>很多很多性质</s>
<time>3092_01:28:01,200 --> 01:28:03,360</time>
<s>讨论出来一些新的数学以后吧</s>
<time>3093_01:28:03,720 --> 01:28:05,880</time>
<s>它在我们自然界真的能找到对应</s>
<time>3094_01:28:06,240 --> 01:28:06,600</time>
<s>对</s>
<time>3095_01:28:06,960 --> 01:28:07,680</time>
<s>这个很神奇的</s>
<time>3096_01:28:08,040 --> 01:28:10,560</time>
<s>像刚才我们这个量子力学的</s>
<time>3097_01:28:10,920 --> 01:28:13,440</time>
<s>这个奠基人之一狄拉克</s>
<time>3098_01:28:14,160 --> 01:28:15,600</time>
<s>他本身应该说就是</s>
<time>3099_01:28:15,960 --> 01:28:16,680</time>
<s>英伦的数学传统</s>
<time>3100_01:28:17,040 --> 01:28:18,480</time>
<s>你可以认为他就是数学家</s>
<time>3101_01:28:18,840 --> 01:28:19,920</time>
<s>彭罗斯不也是数学家吗</s>
<time>3102_01:28:20,280 --> 01:28:21,720</time>
<s>彭罗斯是大数学家</s>
<time>3103_01:28:22,080 --> 01:28:24,600</time>
<s>那么他对数学的这个认识有一个</s>
<time>3104_01:28:24,960 --> 01:28:25,680</time>
<s>我给你讲一个轶事</s>
<time>3105_01:28:26,400 --> 01:28:27,120</time>
<s>就是1955年</s>
<time>3106_01:28:27,480 --> 01:28:29,280</time>
<s>他竟然去访问当年的前苏联</s>
<time>3107_01:28:29,640 --> 01:28:30,360</time>
<s>就说这个人很有意思</s>
<time>3108_01:28:30,720 --> 01:28:31,800</time>
<s>狄拉克</s>
<time>3109_01:28:32,160 --> 01:28:33,960</time>
<s>在莫斯科大学做讲座的时候</s>
<time>3110_01:28:34,320 --> 01:28:36,120</time>
<s>他在黑板上写下一句话</s>
<time>3111_01:28:36,840 --> 01:28:39,000</time>
<s>叫物理定律应该具有数学美</s>
<time>3112_01:28:40,440 --> 01:28:41,160</time>
<s>黑板上写一句话</s>
<time>3113_01:28:43,320 --> 01:28:44,040</time>
<s>那么接着讲</s>
<time>3114_01:28:45,840 --> 01:28:48,360</time>
<s>在黑板上接着写对不对</s>
<time>3115_01:28:48,720 --> 01:28:49,800</time>
<s>那么黑板上写完了又怎么着</s>
<time>3116_01:28:51,960 --> 01:28:53,400</time>
<s>擦黑板对不对</s>
<time>3117_01:28:54,120 --> 01:28:56,280</time>
<s>可是当他拿这个黑板擦</s>
<time>3118_01:28:56,640 --> 01:28:57,720</time>
<s>要擦这个黑板的时候</s>
<time>3119_01:28:58,080 --> 01:28:58,440</time>
<s>主持人我现在想不起来</s>
<time>3120_01:28:58,800 --> 01:28:59,520</time>
<s>是前苏联哪个科学家</s>
<time>3121_01:29:00,600 --> 01:29:02,040</time>
<s>突然认识到这句话的重要性</s>
<time>3122_01:29:02,400 --> 01:29:04,200</time>
<s>一把抱住说</s>
<time>3123_01:29:04,560 --> 01:29:05,640</time>
<s>不要擦我给你换黑板</s>
<time>3124_01:29:07,080 --> 01:29:08,520</time>
<s>这一块写着</s>
<time>3125_01:29:09,960 --> 01:29:11,040</time>
<s>就是狄拉克写的</s>
<time>3126_01:29:12,120 --> 01:29:13,920</time>
<s>物理定律应该具有数学美的</s>
<time>3127_01:29:14,280 --> 01:29:15,360</time>
<s>这一句话的黑板</s>
<time>3128_01:29:15,720 --> 01:29:17,880</time>
<s>是莫斯科大学的镇校之宝</s>
<time>3129_01:29:20,040 --> 01:29:21,120</time>
<s>你看他这个重要的认识</s>
<time>3130_01:29:21,480 --> 01:29:22,200</time>
<s>今天曹老师有两个词</s>
<time>3131_01:29:22,560 --> 01:29:24,360</time>
<s>丧心病狂和不可思议</s>
<time>3132_01:29:24,720 --> 01:29:25,080</time>
<s>不可思议</s>
<time>3133_01:29:25,440 --> 01:29:26,160</time>
<s>但你想这两个词是</s>
<time>3134_01:29:26,520 --> 01:29:27,960</time>
<s>“丧心病狂”的理工科教育</s>
<time>3135_01:29:28,320 --> 01:29:29,040</time>
<s>这点其实非常重要</s>
<time>3136_01:29:29,400 --> 01:29:30,120</time>
<s>还有不可思议的有效性</s>
<time>3137_01:29:30,480 --> 01:29:31,200</time>
<s>有效性对</s>
<time>3138_01:29:31,560 --> 01:29:32,280</time>
<s>这个其实不可思议</s>
<time>3139_01:29:32,640 --> 01:29:33,360</time>
<s>来源于哪儿呢</s>
<time>3140_01:29:33,720 --> 01:29:35,160</time>
<s>其实你仔细想一想的话</s>
<time>3141_01:29:35,520 --> 01:29:38,040</time>
<s>很有可能我们这个宇宙本身</s>
<time>3142_01:29:38,400 --> 01:29:39,480</time>
<s>它最根本最根本的</s>
<time>3143_01:29:39,840 --> 01:29:41,640</time>
<s>就是一些数学的规律</s>
<time>3144_01:29:42,000 --> 01:29:43,440</time>
<s>然后我们这个物质世界</s>
<time>3145_01:29:43,800 --> 01:29:45,600</time>
<s>本身就是按照那个数学规律</s>
<time>3146_01:29:45,960 --> 01:29:46,680</time>
<s>去组合起来的</s>
<time>3147_01:29:47,040 --> 01:29:48,480</time>
<s>然后组成了我们现在这个</s>
<time>3148_01:29:48,840 --> 01:29:49,560</time>
<s>千变万化的世界</s>
<time>3149_01:29:49,920 --> 01:29:50,640</time>
<s>所以你在</s>
<time>3150_01:29:51,000 --> 01:29:52,080</time>
<s>那物质载体呢</s>
<time>3151_01:29:52,440 --> 01:29:53,160</time>
<s>就物质载体</s>
<time>3152_01:29:53,520 --> 01:29:54,240</time>
<s>物质材料是什么</s>
<time>3153_01:29:54,600 --> 01:29:55,680</time>
<s>就是苹果或者是桃子而已</s>
<time>3154_01:29:56,040 --> 01:29:57,120</time>
<s>对它其实</s>
<time>3155_01:29:57,480 --> 01:29:58,920</time>
<s>就这个是不同层次的表象</s>
<time>3156_01:29:59,280 --> 01:30:00,360</time>
<s>不同层次的表象</s>
<time>3157_01:30:01,080 --> 01:30:01,440</time>
<s>最小的呢</s>
<time>3158_01:30:02,160 --> 01:30:03,600</time>
<s>难道真的是数字</s>
<time>3159_01:30:04,320 --> 01:30:05,760</time>
<s>就是你认为它是某种信息</s>
<time>3160_01:30:06,120 --> 01:30:07,200</time>
<s>有空我给你好好讲讲</s>
<time>3161_01:30:07,560 --> 01:30:11,160</time>
<s>逻辑链条的极端</s>
<time>3162_01:30:11,520 --> 01:30:13,680</time>
<s>就是说你现在在讨论问题的时候</s>
<time>3163_01:30:14,040 --> 01:30:15,480</time>
<s>你始终在用的是一个什么呢</s>
<time>3164_01:30:15,840 --> 01:30:16,920</time>
<s>就是逻辑链条</s>
<time>3165_01:30:17,280 --> 01:30:18,360</time>
<s>AA下面有个B</s>
<time>3166_01:30:18,720 --> 01:30:19,080</time>
<s>B下面有个C</s>
<time>3167_01:30:19,440 --> 01:30:20,520</time>
<s>C下面一定要往下</s>
<time>3168_01:30:20,880 --> 01:30:23,040</time>
<s>你的逻辑链条永远是无穷往下想的</s>
<time>3169_01:30:23,400 --> 01:30:24,480</time>
<s>逻辑链条是有限的</s>
<time>3170_01:30:25,560 --> 01:30:26,640</time>
<s>逻辑链条走到极端的时候</s>
<time>3171_01:30:27,000 --> 01:30:28,080</time>
<s>那个地方一定会出现事情</s>
<time>3172_01:30:28,440 --> 01:30:29,880</time>
<s>我给你举个简单的例子</s>
<time>3173_01:30:30,240 --> 01:30:31,680</time>
<s>逻辑链条是不可以推的</s>
<time>3174_01:30:32,040 --> 01:30:32,400</time>
<s>我是天子</s>
<time>3175_01:30:32,760 --> 01:30:33,480</time>
<s>我爸就是皇帝</s>
<time>3176_01:30:34,560 --> 01:30:34,920</time>
<s>对不对</s>
<time>3177_01:30:35,280 --> 01:30:36,000</time>
<s>爸爸那一辈呢</s>
<time>3178_01:30:36,360 --> 01:30:37,080</time>
<s>他的爷爷是皇帝</s>
<time>3179_01:30:37,440 --> 01:30:38,160</time>
<s>他是天经地义的</s>
<time>3180_01:30:38,520 --> 01:30:39,960</time>
<s>但是那个王朝第一个皇帝怎么办</s>
<time>3181_01:30:42,480 --> 01:30:42,840</time>
<s>会推到头儿</s>
<time>3182_01:30:43,200 --> 01:30:43,920</time>
<s>王朝第一个皇帝</s>
<time>3183_01:30:44,280 --> 01:30:45,000</time>
<s>一定是否认自己</s>
<time>3184_01:30:45,360 --> 01:30:48,240</time>
<s>那个特别不成器的父亲的地位</s>
<time>3185_01:30:48,600 --> 01:30:49,320</time>
<s>刘邦的父亲</s>
<time>3186_01:30:49,680 --> 01:30:50,040</time>
<s>当你有一个</s>
<time>3187_01:30:50,400 --> 01:30:51,480</time>
<s>特别成器的儿子的时候</s>
<time>3188_01:30:52,560 --> 01:30:54,720</time>
<s>首先就要否定你这样的一个</s>
<time>3189_01:30:55,080 --> 01:30:55,800</time>
<s>不成器的父亲的地位</s>
<time>3190_01:30:57,960 --> 01:30:58,680</time>
<s>这说明什么</s>
<time>3191_01:30:59,040 --> 01:30:59,760</time>
<s>逻辑链条</s>
<time>3192_01:31:00,120 --> 01:31:01,920</time>
<s>有限逻辑链条就会出现跳变</s>
<time>3193_01:31:03,360 --> 01:31:04,440</time>
<s>只是你刚才习惯的都是什么</s>
<time>3194_01:31:04,800 --> 01:31:05,880</time>
<s>你刚才习惯的都是逻辑链条</s>
<time>3195_01:31:06,240 --> 01:31:06,960</time>
<s>A能追到B</s>
<time>3196_01:31:07,320 --> 01:31:08,040</time>
<s>B能追到C一定</s>
<time>3197_01:31:08,760 --> 01:31:09,840</time>
<s>他希望有个完美证明</s>
<time>3198_01:31:10,200 --> 01:31:10,920</time>
<s>不是就是这种</s>
<time>3199_01:31:11,280 --> 01:31:11,640</time>
<s>就是老说的</s>
<time>3200_01:31:12,720 --> 01:31:13,440</time>
<s>日取一半</s>
<time>3201_01:31:14,520 --> 01:31:14,880</time>
<s>无尽</s>
<time>3202_01:31:15,240 --> 01:31:16,320</time>
<s>有这事吗</s>
<time>3203_01:31:19,200 --> 01:31:20,640</time>
<s>我忍不住像曹老师一样说你一句</s>
<time>3204_01:31:21,000 --> 01:31:21,360</time>
<s>不是这样的</s>
<time>3205_01:31:22,800 --> 01:31:23,160</time>
<s>对对对</s>
<time>3206_01:31:23,520 --> 01:31:23,880</time>
<s>总结到位</s>
<time>3207_01:31:24,240 --> 01:31:24,960</time>
<s>对说得太好了</s>
<time>3208_01:31:25,680 --> 01:31:28,560</time>
<s>这就是最后我们的态度</s>
<time>3209_01:31:28,920 --> 01:31:29,280</time>
<s>学习的态度</s>
<time>3210_01:31:29,640 --> 01:31:31,080</time>
<s>你会发现不真是这样</s>
<time>3211_01:31:31,800 --> 01:31:33,600</time>
<s>就是说当我们对这个世界</s>
<time>3212_01:31:33,960 --> 01:31:34,680</time>
<s>慢慢认识的时候</s>
<time>3213_01:31:35,040 --> 01:31:36,120</time>
<s>你会发现真的</s>
<time>3214_01:31:36,480 --> 01:31:37,200</time>
<s>每那么两个层次的时候</s>
<time>3215_01:31:37,560 --> 01:31:38,640</time>
<s>它会给你一惊喜</s>
<time>3216_01:31:39,360 --> 01:31:40,080</time>
<s>不是那么回事儿</s>
<time>3217_01:31:40,440 --> 01:31:41,880</time>
<s>但是我们还是要问下去</s>
<time>3218_01:31:42,240 --> 01:31:43,320</time>
<s>问下去对是</s>
<time>3219_01:31:43,680 --> 01:31:44,040</time>
<s>对吧</s>
<time>3220_01:31:45,120 --> 01:31:46,920</time>
<s>这还应该拉曹老师再录二十季</s>
<time>3221_01:31:47,280 --> 01:31:47,640</time>
<s>对对对</s>
<time>3222_01:31:48,000 --> 01:31:49,440</time>
<s>这家伙聊不完这个</s>
