{"id":46921,"date":"2023-12-02T16:43:46","date_gmt":"2023-12-02T08:43:46","guid":{"rendered":"https:\/\/swarma.org\/?p=46921"},"modified":"2023-12-02T16:43:46","modified_gmt":"2023-12-02T08:43:46","slug":"%e4%bc%97%e9%87%8c%e5%af%bb%e4%b8%80%ef%bc%9a%e4%bb%8e%e5%a4%8d%e6%9d%82%e6%80%a7%e4%b8%ad%e6%8e%a2%e7%b4%a2%e6%99%ae%e9%80%82%e8%a7%84%e5%be%8b","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=46921","title":{"rendered":"\u4f17\u91cc\u5bfb\u4e00\uff1a\u4ece\u590d\u6742\u6027\u4e2d\u63a2\u7d22\u666e\u9002\u89c4\u5f8b"},"content":{"rendered":"
\n
\n
\n
\n

<\/p>\n<\/section>\n

\n
\n
\n
\n
\n
\n

<\/section>\n<\/section>\n
\n
\n

\u5bfc\u8bed<\/strong><\/p>\n<\/section>\n<\/section>\n

\n

<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n
\n
\n
\u63a2\u7a76\u5b87\u5b99\u4e2d\u7684\u79e9\u5e8f\u548c\u6df7\u6c8c\u4e00\u76f4\u662f\u79d1\u5b66\u7814\u7a76\u7684\u6838\u5fc3\u547d\u9898\u3002\u9676\u54f2\u8f69\u6559\u6388\u7684\u8fd9\u7bc7\u6d1e\u5bdf\u6027\u6587\u7ae0\u5f15\u9886\u6211\u4eec\u8fdb\u5165\u666e\u904d\u6027\u7684\u4e16\u754c\u2014\u2014\u4e00\u4e2a\u5c55\u73b0\u4e86\u5982\u4f55\u4ece\u9519\u7efc\u590d\u6742\u7684\u5fae\u89c2\u52a8\u6001\u7cfb\u7edf\u4e2d\u62bd\u8c61\u51fa\u7b80\u660e\u7684\u5b8f\u89c2\u89c4\u5f8b\u7684\u5947\u5999\u9886\u57df\u3002\u4ece\u7edf\u8ba1\u5b66\u7684\u7ecf\u5178\u89c4\u5f8b\u5230\u7269\u7406\u5b66\u4e2d\u7684\u76f8\u53d8\u73b0\u8c61\uff0c\u4ece\u81ea\u7136\u6570\u5e8f\u5217\u7684\u795e\u79d8\u89c4\u5f8b\u5230\u91cf\u5b50\u529b\u5b66\u7684\u7cbe\u786e\u9884\u6d4b\uff0c\u666e\u9002\u6027\u4f5c\u4e3a\u4e00\u79cd\u88ab\u5e7f\u6cdb\u8bb0\u5f55\u548c\u9a8c\u8bc1\u7684\u6a21\u5f0f\u5728\u5404\u79cd\u4e0d\u540c\u5c3a\u5ea6\u548c\u9886\u57df\u4e2d\u5c55\u73b0\u4e86\u5176\u60ca\u4eba\u7684\u4e00\u81f4\u6027\u3002\u7136\u800c\uff0c\u5c3d\u7ba1\u8fd9\u4e9b\u89c4\u5f8b\u5df2\u88ab\u5b9e\u8bc1\u5b66\u79d1\u53cd\u590d\u786e\u8ba4\uff0c\u4f46\u5bf9\u4e8e\u666e\u9002\u6027\u7684\u4e25\u683c\u6570\u5b66\u57fa\u7840\u4ecd\u5b58\u5728\u7740\u8bf8\u591a\u672a\u77e5\u4e4b\u8c1c\u3002\u672c\u6587\u901a\u8fc7\u7efc\u5408\u4e0d\u540c\u9886\u57df\u4e2d\u7684\u5177\u4f53\u6848\u4f8b\u548c\u7814\u7a76\u6210\u679c\uff0c\u5c55\u793a\u4e86\u5f53\u524d\u79d1\u5b66\u754c\u5bf9\u8fd9\u4e9b\u5b8f\u89c2\u89c4\u5f8b\u6d8c\u73b0\u673a\u7406\u7684\u7406\u89e3\uff0c\u5e76\u6307\u51fa\u4e86\u8fd9\u4e00\u7814\u7a76\u9886\u57df\u6240\u9762\u4e34\u7684\u6311\u6218\u4e0e\u524d\u6cbf\u95ee\u9898\u3002<\/span><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/section>\n
<\/span><\/strong><\/section>\n<\/section>\n
\n
<\/span><\/strong><\/section>\n
<\/span><\/strong><\/section>\n<\/section>\n
\n
<\/span><\/section>\n

<\/section>\n
\u7814\u7a76\u9886\u57df\uff1a\u590d\u6742\u7cfb\u7edf\uff0c\u666e\u9002\u6027\uff0c\u6d8c\u73b0\uff0c\u91cd\u6574\u5316\u7fa4\uff0c\u9ece\u66fc\u731c\u60f3<\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/section>\n<\/section>\n
\n
<\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/section>\n<\/section>\n
\n
<\/span><\/strong><\/section>\n<\/section>\n
\n
<\/span><\/strong><\/strong><\/strong><\/span><\/strong><\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/strong><\/strong><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n
\n
\n
\n
<\/svg><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n
\n
<\/section>\n<\/section>\n
\n
<\/span><\/strong><\/section>\n
\u9676\u54f2\u8f69<\/span><\/span><\/span><\/span> <\/span>| \u4f5c\u8005<\/span><\/strong><\/span><\/strong><\/section>\n
\u7c73\u51ef<\/span><\/span><\/span> <\/span>| \u8bd1\u8005<\/span><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/section>\n
\u738b\u81f3\u5b8f\u3001\u82d1\u660e\u7406<\/span><\/span><\/span> <\/span>| \u5ba1\u6821<\/span><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/section>\n
\u6881\u91d1<\/span> <\/span>| \u7f16\u8f91<\/span><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/section>\n

<\/section>\n

<\/section>\n<\/section>\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
<\/section>\n
\n
\n
\n
\u8bba\u6587\u9898\u76ee\uff1a<\/span><\/section>\n
E pluribus unum: From Complexity, Universality<\/span><\/section>\n
\u8bba\u6587\u94fe\u63a5\uff1a<\/span><\/section>\n
https:\/\/www.stat.berkeley.edu\/~aldous\/157\/Papers\/tao_universality.pdf<\/span><\/section>\n<\/section>\n<\/section>\n<\/blockquote>\n

<\/section>\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\u76ee\u5f55<\/strong><\/section>\n
0. \u590d\u6742\u7cfb\u7edf\u4e0e\u7b80\u5355\u6cd5\u5219<\/span><\/strong><\/section>\n
1. \u5927\u6570\u5b9a\u5f8b<\/span><\/strong><\/section>\n
2. \u4e2d\u5fc3\u6781\u9650\u5b9a\u7406<\/span><\/strong><\/section>\n
3. \u76f8\u53d8\u4e0e\u91cd\u6574\u5316\u7fa4<\/span><\/strong><\/section>\n
4. \u79bb\u6563\u8c31\u3001\u968f\u673a\u77e9\u9635\u6a21\u578b\u3001\u9ece\u66fc\u731c\u60f3<\/span><\/strong><\/section>\n
5. \u666e\u9002\u6027\u7684\u5931\u6548\u4e0e\u590d\u6742\u6027\u7684\u51fa\u73b0<\/span><\/strong><\/section>\n
<\/strong><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

<\/section>\n

<\/section>\n
\u6458\u8981<\/strong>\uff1a<\/span>\u5728\u8fd9\u7bc7\u7b80\u77ed\u7684\u62a5\u544a\u4e2d\uff0c\u6211\u8ba8\u8bba\u4e86\u5173\u4e8e\u590d\u6742\u7cfb\u7edf\u4e2d\u666e\u9002\u6027\u8fd9\u4e00\u8ff7\u4eba\u73b0\u8c61\u7684\u4e00\u4e9b\u4f8b\u5b50\uff0c\u666e\u9002\u6027\u73b0\u8c61\u6307\u7684\u662f<\/span>\u4ece\u591a\u79cd\u4e0d\u540c\u7684\u5fae\u89c2\u52a8\u529b\u5b66\u884c\u4e3a\u4e2d\u6d8c\u73b0\u51fa\u6765\u7684\u3001\u666e\u904d\u7684\u5b8f\u89c2\u81ea\u7136\u89c4\u5f8b<\/strong>\u3002\u8fd9\u4e9b\u73b0\u8c61\u5728\u5b9e\u8bc1\u4e0a\u88ab\u5e7f\u6cdb\u89c2\u5bdf\u5230\uff0c\u7136\u800c\u5728\u4e00\u822c\u60c5\u5f62\u4e0b\uff0c\u666e\u9002\u6027\u7684\u4e25\u8c28\u6570\u5b66\u57fa\u7840\u4ecd\u672a\u80fd\u4ee4\u4eba\u6ee1\u610f\u3002<\/span><\/span><\/section>\n

<\/span><\/section>\n
\n
\n
\n
<\/section>\n<\/section>\n
\n
\n
\n
\u81ea\u7136\u662f\u4e00\u6735\u53d8\u5e7b\u83ab\u6d4b\u7684\u4e91\uff0c\u6c38\u8fdc\u5982\u4e00\uff0c\u53c8\u4ece\u4e0d\u76f8\u540c\u3002<\/span><\/section>\n

\u2014\u2014 Ralph Waldo Emerson\uff0c\u300a\u5386\u53f2\u300b(1841\u5e74)<\/span><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


<\/p>\n


<\/span><\/section>\n

\n
\n
\n
\n
\n

<\/section>\n

<\/section>\n
\n
<\/svg><\/section>\n<\/section>\n<\/section>\n
\n

0. \u590d\u6742\u7cfb\u7edf\u4e0e\u7b80\u5355\u6cd5\u5219<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


<\/p>\n

\u73b0\u4ee3\u6570\u5b66\u662f\u4e00\u79cd\u5f3a\u5927\u7684\u5de5\u5177\uff0c\u5b83\u80fd\u591f\u6a21\u62df\u65e0\u6570\u7684\u73b0\u5b9e\u4e16\u754c\u60c5\u666f\uff0c\u4e0d\u8bba\u662f\u81ea\u7136\u754c\u4e2d\u7684\u2014\u2014\u4f8b\u5982\u5929\u4f53\u8fd0\u52a8\uff0c\u6216\u6750\u6599\u7684\u7269\u7406\u53ca\u5316\u5b66\u5c5e\u6027\u2014\u2014\u8fd8\u662f\u4eba\u4e3a\u521b\u9020\u7684\u60c5\u666f\uff1a\u6bd4\u5982\u80a1\u7968\u5e02\u573a\u6216\u9009\u6c11\u7684\u6295\u7968\u503e\u5411[1]\u3002\u539f\u5219\u4e0a\uff0c\u5373\u4f7f\u662f\u5305\u542b\u8bf8\u591a\u76f8\u4e92\u4f5c\u7528\u7ec4\u4ef6\u7684\u6781\u7aef\u590d\u6742\u7cfb\u7edf\uff0c\u4e5f\u80fd\u901a\u8fc7\u6570\u5b66\u6a21\u578b\u8fdb\u884c\u7814\u7a76\u3002<\/span><\/section>\n

<\/section>\n
\u7136\u800c\uff0c\u5728\u5b9e\u8df5\u4e2d\uff0c\u6211\u4eec\u53ea\u80fd\u7cbe\u786e\u6c42\u89e3\u975e\u5e38\u7b80\u5355\u7684\u7cfb\u7edf<\/span>\uff08\u90a3\u4e9b\u4ec5\u5305\u542b\u4e24\u5230\u4e09\u4e2a\u76f8\u4e92\u4f5c\u7528\u4e3b\u4f53\u7684\u7cfb\u7edf\uff09<\/span>\u3002\u4f8b\u5982\uff0c\u5728\u672c\u79d1\u7684\u7269\u7406\u8bfe\u7a0b\u4e2d\uff0c\u6211\u4eec\u80fd\u7ed9\u51fa\u6c22\u539f\u5b50\u5149\u8c31\u7ebf\u7684\u6570\u5b66\u63a8\u5bfc\uff0c\u8fd9\u662f\u56e0\u4e3a\u6c22\u539f\u5b50\u4e2d\u53ea\u6709\u4e00\u4e2a\u7535\u5b50\u7ed5\u6838\u8fd0\u52a8\uff1b\u4f46\u662f\uff0c\u5373\u4fbf\u4f7f\u7528\u6700\u5148\u8fdb\u7684\u8ba1\u7b97\u673a\uff0c\u6211\u4eec\u4e5f\u65e0\u6cd5\u5b8c\u6210\u5bf9\u94a0\u539f\u5b50\u5149\u8c31\u7ebf\u7684\u6570\u5b66\u63a8\u5bfc\uff0c\u94a0\u539f\u5b50\u6709\u5341\u4e00\u4e2a\u7535\u5b50\uff0c\u8fd9\u4e9b\u7535\u5b50\u4e4b\u95f4\u4ee5\u53ca\u5b83\u4eec\u4e0e\u539f\u5b50\u6838\u4e4b\u95f4\u90fd\u5b58\u5728\u76f8\u4e92\u4f5c\u7528\u3002<\/span><\/section>\n

<\/section>\n
\u4e09\u4f53\u95ee\u9898\u662f\u6307\u6839\u636e\u725b\u987f\u7684\u4e07\u6709\u5f15\u529b\u5b9a\u5f8b\u9884\u6d4b\u4e09\u4e2a\u7269\u4f53\u7684\u8fd0\u52a8\uff0c\u636e\u8bf4\u8fd9\u662f\u552f\u4e00\u4ee4\u725b\u987f\u611f\u5230\u5934\u75bc\u7684\u95ee\u9898\u3002\u4e0d\u540c\u4e8e\u6709\u7740\u7b80\u5355\u6570\u5b66\u89e3\u7b54\u7684\u4e24\u4f53\u95ee\u9898\uff0c\u4eba\u4eec\u666e\u904d\u8ba4\u4e3a\u4e09\u4f53\u95ee\u9898\u6ca1\u6709\u7b80\u6d01\u7684\u6570\u5b66\u516c\u5f0f\u53ef\u4ee5\u89e3\u51b3\uff0c\u5b83\u53ea\u80fd\u901a\u8fc7\u6570\u503c\u7b97\u6cd5\u8fdb\u884c\u8fd1\u4f3c\u6c42\u89e3\u3002\u5728\u4e00\u4e2a\u5305\u542b\u8bb8\u591a\u76f8\u4e92\u4f5c\u7528\u7ec4\u4ef6\u7684\u7cfb\u7edf\u4e0a\u65e0\u6cd5\u6267\u884c\u5207\u5b9e\u53ef\u884c\u7684\u8ba1\u7b97\uff0c\u8fd9\u4e00\u73b0\u8c61\u88ab\u79f0\u4e3a\u201c\u7ef4\u6570\u8bc5\u5492\u201d\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u5c3d\u7ba1\u5b58\u5728\u8fd9\u4e2a\u8bc5\u5492\uff0c\u4f46\u662f\u5f53\u7ec4\u4ef6\u6570\u91cf\u8db3\u591f\u5927\u65f6\uff0c\u901a\u5e38\u4f1a\u51fa\u73b0\u4e00\u4e2a\u4ee4\u4eba\u60ca\u5947\u7684\u73b0\u8c61\uff1a\u590d\u6742\u7cfb\u7edf\u7684<\/strong>\u805a\u5408\u5c5e\u6027<\/strong>\u53ef\u4ee5<\/strong>\u4e0d\u53ef\u601d\u8bae<\/strong>\u5730\u518d\u6b21\u53d8\u5f97\u53ef\u9884\u6d4b\uff0c<\/strong>\u5e76<\/strong>\u7531\u7b80\u5355\u7684\u81ea\u7136\u6cd5\u5219\u652f\u914d\u3002<\/strong><\/span><\/section>\n

<\/strong><\/span><\/section>\n
\n
\u8bd1\u6ce8\uff1a<\/span><\/section>\n
\u805a\u5408\u5c5e\u6027\uff08aggregate properties\uff09\u6307\u7684\u662f\u590d\u6742\u7cfb\u7edf\u7684\u6574\u4f53\u6027\u8d28\u6216\u603b\u4f53\u7279\u5f81\u3002\u5f53\u4e00\u4e2a\u7cfb\u7edf\u7531\u8bb8\u591a\u76f8\u4e92\u4f5c\u7528\u7684\u7ec4\u4ef6\u7ec4\u6210\u65f6\uff0c\u8fd9\u4e9b\u7ec4\u4ef6\u7684\u96c6\u5408\u4f1a\u8868\u73b0\u51fa\u4e00\u4e9b\u5171\u540c\u7684\u7279\u5f81\uff0c\u8fd9\u4e9b\u7279\u5f81\u53ef\u4ee5\u88ab\u79f0\u4e3a\u201caggregate properties\u201d\u3002\u8fd9\u4e9b\u7279\u5f81\u53ef\u80fd\u662f\u7cfb\u7edf\u7684\u5e73\u5747\u503c\u3001\u603b\u548c\u3001\u5206\u5e03\u6216\u5176\u4ed6\u7edf\u8ba1\u91cf\uff0c\u5b83\u4eec\u63cf\u8ff0\u4e86\u7cfb\u7edf\u4f5c\u4e3a\u4e00\u4e2a\u6574\u4f53\u7684\u884c\u4e3a\u6216\u6027\u8d28\u3002\u8fd9\u4e9b\u7279\u5f81\u4e0d\u4ec5\u53d6\u51b3\u4e8e\u7cfb\u7edf\u4e2d\u5404\u4e2a\u7ec4\u4ef6\u7684\u6027\u8d28\uff0c\u8fd8\u53d7\u5230\u5b83\u4eec\u4e4b\u95f4\u76f8\u4e92\u4f5c\u7528\u7684\u5f71\u54cd\u3002\u901a\u8fc7\u7814\u7a76\u548c\u7406\u89e3\u8fd9\u4e9b\u201caggregate properties\u201d\uff0c\u6211\u4eec\u53ef\u4ee5\u66f4\u597d\u5730\u4e86\u89e3\u548c\u9884\u6d4b\u590d\u6742\u7cfb\u7edf\u7684\u884c\u4e3a\u3002<\/span><\/section>\n<\/blockquote>\n

<\/section>\n
\u66f4\u4ee4\u4eba\u60ca\u8bb6\u7684\u662f\uff0c\u6574\u4e2a\u7cfb\u7edf\u7684\u5b8f\u89c2<\/strong>\u89c4\u5f8b<\/strong>\u5e38\u5e38\u5728\u5f88\u5927\u7a0b\u5ea6\u4e0a\u4e0e\u63a7\u5236\u7cfb\u7edf\u5185\u90e8\u5355\u4e2a\u7ec4\u4ef6\u7684\u5fae\u89c2<\/strong>\u89c4\u5f8b<\/strong>\u65e0\u5173<\/strong>\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u4eba\u4eec\u53ef\u4ee5\u7528\u5b8c\u5168\u4e0d\u540c\u7c7b\u578b\u7684\u5bf9\u8c61\u66ff\u6362\u5fae\u89c2\u7ec4\u4ef6\uff0c\u5e76\u5728<\/span>\u5b8f\u89c2\u5c42\u9762\u4e0a\u83b7\u5f97\u76f8\u540c\u7684\u63a7\u5236\u89c4\u5f8b\u3002\u8fd9\u610f\u5473\u7740\uff0c\u65e0\u8bba\u7cfb\u7edf\u7684\u5fae\u89c2\u7ec4\u6210\u5982\u4f55\uff0c\u53ea\u8981\u7cfb\u7edf\u7684\u7ec4\u4ef6\u6570\u91cf\u8db3\u591f\u591a\uff0c\u5b8f\u89c2\u89c4\u5f8b\u5c31\u4f1a\u51fa\u73b0\uff0c\u5e76\u4e14\u8fd9\u4e9b\u89c4\u5f8b\u53ef\u4ee5\u72ec\u7acb\u4e8e\u5fae\u89c2\u7ec4\u4ef6\u7684\u7279\u6027\u800c\u5b58\u5728\u3002\u6211\u4eec\u5c31\u8bf4\u5b8f\u89c2\u89c4\u5f8b\u662f\u666e\u9002\u7684\u3002<\/span><\/section>\n

<\/section>\n
\u666e\u9002\u6027\u73b0\u8c61\u5728\u8bb8\u591a\u4e0d\u540c\u7684\u60c5\u5883\u4e2d\u90fd\u5df2\u7ecf\u5b9e\u8bc1\u5730\u548c\u5728\u6570\u5b66\u4e0a\u88ab\u89c2\u5bdf\u5230\uff0c\u5176\u4e2d\u51e0\u4e2a\u4f8b\u5b50\u6211\u5c06\u5728\u4e0b\u6587\u4e2d\u8fdb\u884c\u8ba8\u8bba\u3002\u5728\u4e00\u4e9b\u6848\u4f8b\u4e2d\uff0c\u6211\u4eec\u5df2\u7ecf\u5bf9\u8fd9\u79cd\u73b0\u8c61\u6709\u4e86\u5f88\u597d\u7684\u7406\u89e3\uff0c\u4f46\u5728\u8bb8\u591a\u60c5\u51b5\u4e0b\uff0c\u5b83\u7684\u6f5c\u5728\u6765\u6e90\u4ecd\u7136\u9887\u5177\u795e\u79d8\u8272\u5f69\uff0c\u5e76\u4e14\u4ecd\u7136\u662f\u6570\u5b66\u7814\u7a76\u4e2d\u7684\u4e00\u4e2a\u6d3b\u8dc3\u9886\u57df\u3002<\/span><\/section>\n

<\/span><\/section>\n

<\/span><\/section>\n

\n
\n
\n
\n
\n

<\/section>\n

<\/section>\n
\n
<\/svg><\/section>\n<\/section>\n<\/section>\n
\n

1. \u5927\u6570\u5b9a\u5f8b<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


<\/p>\n

2008\u5e7411\u67084\u65e5\u7684\u7f8e\u56fd\u603b\u7edf\u9009\u4e3e\u662f\u4e00\u573a\u6781\u5176\u590d\u6742\u7684\u4e8b\u4ef6\u3002\u6765\u81ea50\u4e2a\u5dde\u7684\u8d85\u8fc7\u4e00\u4ebf\u9009\u6c11\u6295\u4e0b\u4e86\u4ed6\u4eec\u7684\u9009\u7968\uff0c\u6bcf\u4e2a\u9009\u6c11\u7684\u51b3\u5b9a\u90fd\u53d7\u5230\u7ade\u9009\u8a00\u8bba\u3001\u5a92\u4f53\u62a5\u9053\u3001\u8c23\u8a00\u3001\u9009\u6c11\u5bf9\u5019\u9009\u4eba\u7684\u4e2a\u4eba\u5370\u8c61\u4ee5\u53ca\u670b\u53cb\u548c\u540c\u4e8b\u7684\u653f\u6cbb\u8ba8\u8bba\u7b49\u65e0\u6570\u65b9\u5f0f\u7684\u5f71\u54cd\u3002\u6709\u6570\u767e\u4e07\u7684\u201c\u6447\u6446\u9009\u6c11\u201d\u5e76\u4e0d\u575a\u5b9a\u5730\u652f\u6301\u4e24\u4f4d\u4e3b\u8981\u5019\u9009\u4eba\u4e2d\u7684\u4efb\u4f55\u4e00\u4f4d\uff0c\u4ed6\u4eec\u7684\u6700\u7ec8\u51b3\u5b9a\u53ef\u80fd\u65e0\u6cd5\u9884\u6599\uff0c\u751a\u81f3\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\u53ef\u80fd\u662f\u968f\u673a\u7684\u3002\u5728\u5dde\u4e00\u7ea7\uff0c\u540c\u6837\u5b58\u5728\u7740\u4e0d\u786e\u5b9a\u6027\uff1a\u867d\u7136\u8bb8\u591a\u5dde\u88ab\u8ba4\u4e3a\u5bf9\u67d0\u4e00\u4f4d\u5019\u9009\u4eba\u6765\u8bf4\u662f\u5b89\u5168\u7684\uff0c\u4f46\u81f3\u5c11\u6709\u5341\u51e0\u4e2a\u5dde\u88ab\u8ba4\u4e3a\u662f”\u6447\u6446\u5dde”\uff0c\u53ef\u80fd\u4f1a\u5012\u5411\u4efb\u4f55\u4e00\u65b9\u3002<\/span><\/section>\n

<\/section>\n
\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u51c6\u786e\u9884\u6d4b\u9009\u4e3e\u7ed3\u679c\u4f3c\u4e4e\u662f\u4e0d\u53ef\u80fd\u7684\u3002\u5f53\u7136\uff0c\u5b58\u5728\u7740\u6210\u767e\u4e0a\u5343\u6b21\u7684\u9009\u4e3e\u6c11\u8c03\uff0c\u4f46\u6bcf\u6b21\u6c11\u8c03\u53ea\u9488\u5bf9\u6570\u767e\u6216\u6570\u5343\u540d\u6f5c\u5728\u9009\u6c11\uff0c\u4ec5\u4ec5\u5360\u9009\u6c11\u7fa4\u4f53\u4e2d\u7684\u4e00\u5c0f\u90e8\u5206\u3002\u800c\u4e14\u6c11\u610f\u8c03\u67e5\u7ecf\u5e38\u6ce2\u52a8\u5f88\u5927\uff0c\u5f7c\u6b64\u76f8\u5de6\uff1b\u5e76\u975e\u6240\u6709\u7684\u6c11\u610f\u8c03\u67e5\u90fd\u540c\u6837\u53ef\u9760\u6216\u65e0\u504f\u89c1\uff0c\u6ca1\u6709\u4e24\u4e2a\u6c11\u610f\u8c03\u67e5\u673a\u6784\u4f7f\u7528\u5b8c\u5168\u76f8\u540c\u7684\u65b9\u6cd5\u3002<\/span><\/section>\n

<\/section>\n
\u5c3d\u7ba1\u5982\u6b64\uff0c\u5728\u9009\u4e3e\u4e4b\u591c\u7ed3\u675f\u4e4b\u524d\uff0c\u6c11\u610f\u8c03\u67e5\u5df2\u7ecf\u76f8\u5f53\u51c6\u786e\u5730\u9884\u6d4b\u4e86\u603b\u7edf\u9009\u4e3e<\/span>\uff08\u4ee5\u53ca\u5f53\u665a\u4e3e\u884c\u7684\u5927\u591a\u6570\u5176\u4ed6\u9009\u4e3e\uff09<\/span>\u7684\u7ed3\u679c\u3002\u4e5f\u8bb8\u6700\u5f15\u4eba\u6ce8\u76ee\u7684\u662f\u7edf\u8ba1\u5b66\u5bb6\u5185\u7279\u00b7\u897f\u5c14\u5f17<\/span>\uff08Nate Silver\uff09<\/span>\u7684\u9884\u6d4b\uff0c\u4ed6\u4f7f\u7528\u4e86\u6240\u6709\u73b0\u6709\u6c11\u610f\u8c03\u67e5\u7684\u52a0\u6743\u5206\u6790\u6765\u6b63\u786e\u9884\u6d4b\u4e8649\u4e2a\u5dde\u7684\u603b\u7edf\u9009\u4e3e\u7ed3\u679c\uff0c\u4ee5\u53ca\u6240\u670935\u573a\u7f8e\u56fd\u53c2\u8bae\u9662\u9009\u4e3e\u3002<\/span>\uff08\u552f\u4e00\u7684\u4f8b\u5916\u662f\u5370\u7b2c\u5b89\u7eb3\u5dde\u7684\u603b\u7edf\u9009\u4e3e\uff0c\u897f\u5c14\u5f17\u5c06\u5176\u5224\u5b9a\u4e3a\u9ea6\u51ef\u6069\u83b7\u80dc\uff0c\u4f46\u6700\u7ec8\u5965\u5df4\u9a6c\u4ee5\u4ec50.9%\u7684\u5fae\u5f31\u4f18\u52bf\u83b7\u80dc\u3002\uff09<\/span><\/section>\n

<\/section>\n
\u6c11\u8c03\u7684\u51c6\u786e\u6027\u53ef\u4ee5\u901a\u8fc7\u4e00\u4e2a\u79f0\u4e3a\u201c\u5927\u6570\u5b9a\u5f8b<\/strong>\u201d<\/span>\u7684\u6570\u5b66\u539f\u7406\u6765\u89e3\u91ca\u3002\u8fd9\u4e00\u6cd5\u5219\u544a\u8bc9\u6211\u4eec\uff0c\u53ea\u8981\u968f\u673a\u6837\u672c\u7684\u89c4\u6a21\u8db3\u591f\u5927\uff0c\u6c11\u8c03\u7684\u6f5c\u5728\u7ed3\u679c\u5c31\u4f1a\u8d8b\u8fd1\u4e8e\u5b9e\u9645\u4e0a\u613f\u610f\u6295\u7968\u7ed9\u7279\u5b9a\u5019\u9009\u4eba\u7684\u9009\u6c11\u6bd4\u4f8b\uff0c\u76f4\u5230\u8fbe\u5230\u4e00\u5b9a\u7684\u7cbe\u5ea6\u6c34\u5e73\uff0c\u4e5f\u5c31\u662f\u6211\u4eec\u6240\u8bf4\u7684\u8bef\u5dee\u8303\u56f4<\/span>\uff08margin of error\uff09<\/span>\u3002\u4f8b\u5982\uff0c\u5728\u5bf9\u4e00\u5343\u540d\u9009\u6c11\u8fdb\u884c\u7684\u968f\u673a\u6c11\u8c03\u4e2d\uff0c\u8bef\u5dee\u8303\u56f4\u5927\u7ea6\u4e3a3%\u3002<\/span><\/section>\n

<\/span><\/section>\n
<\/span><\/section>\n
\n
\u8bd1\u6ce8\uff1a<\/span><\/section>\n
\u5927\u6570\u5b9a\u5f8b\uff08Law of large numbers\uff09\uff1a\u5728\u6570\u5b66\u4e0e\u7edf\u8ba1\u5b66\u4e2d\uff0c\u5927\u6570\u5b9a\u5f8b\uff08Law of large numbers\uff09\u53c8\u79f0\u4e3a\u5927\u6570\u6cd5\u5219\u3001\u5927\u6570\u5f8b\uff0c\u662f\u63cf\u8ff0\u76f8\u5f53\u591a\u6b21\u6570\u91cd\u590d\u5b9e\u9a8c\u540e\u7684\u7ed3\u679c\u7684\u5b9a\u5f8b\u3002\u6839\u636e\u8fd9\u4e2a\u5b9a\u5f8b\uff0c\u968f\u7740\u6837\u672c\u6570\u91cf\u7684\u589e\u52a0\uff0c\u5176\u7b97\u672f\u5e73\u5747\u503c\u8d8a\u6765\u8d8a\u6709\u9ad8\u7684\u51e0\u7387\u63a5\u8fd1\u671f\u671b\u503c\u3002<\/span><\/section>\n
\u5927\u6570\u5b9a\u5f8b\u975e\u5e38\u91cd\u8981\uff0c\u56e0\u4e3a\u5b83\u201c\u8bf4\u660e\u201d\u4e86\u4e00\u4e9b\u968f\u673a\u4e8b\u4ef6\u5747\u503c\u7684\u957f\u671f\u7a33\u5b9a\u6027\u3002\u4eba\u4eec\u53d1\u73b0\uff0c\u5728\u91cd\u590d\u8bd5\u9a8c\u4e2d\uff0c\u968f\u7740\u8bd5\u9a8c\u6b21\u6570\u7684\u589e\u52a0\uff0c\u4e8b\u4ef6\u53d1\u751f\u7684\u9891\u7387\u8d8b\u5411\u4e8e\u4e00\u4e2a\u7a33\u5b9a\u503c\uff1b\u4eba\u4eec\u540c\u65f6\u4e5f\u53d1\u73b0\uff0c\u5728\u5bf9\u7269\u7406\u91cf\u7684\u6d4b\u91cf\u5b9e\u8df5\u4e2d\uff0c\u6d4b\u5b9a\u503c\u7684\u7b97\u672f\u5e73\u5747\u4e5f\u5177\u5907\u7a33\u5b9a\u6027\u3002\u6bd4\u5982\uff0c\u6211\u4eec\u5411\u4e0a\u629b\u63b7\u4e00\u679a\u786c\u5e01\uff0c\u786c\u5e01\u843d\u4e0b\u540e\u54ea\u4e00\u9762\u671d\u4e0a\u662f\u5076\u7136\u7684\uff0c\u4f46\u5f53\u6211\u4eec\u629b\u786c\u5e01\u7684\u6b21\u6570\u8db3\u591f\u591a\u540e\uff0c\u8fbe\u5230\u4e0a\u4e07\u6b21\u751a\u81f3\u51e0\u5341\u4e07\u3001\u51e0\u767e\u4e07\u6b21\u4e4b\u540e\uff0c\u6211\u4eec\u4f1a\u53d1\u73b0\u786c\u5e01\u6bcf\u4e00\u9762\u5411\u4e0a\u7684\u6b21\u6570\u7ea6\u5360\u603b\u6b21\u6570\u7684\u4e8c\u5206\u4e4b\u4e00\uff0c\u4ea6\u5373\u5076\u7136\u4e2d\u5305\u542b\u7740\u5fc5\u7136\u3002\u53c2\u89c1\u7ef4\u57fa\u767e\u79d1\uff1a<\/span><\/section>\n
https:\/\/zh.wikipedia.org\/zh-cn\/%E5%A4%A7%E6%95%B8%E6%B3%95%E5%89%87<\/span><\/section>\n<\/blockquote>\n

<\/section>\n
\u5927\u6570\u5b9a\u5f8b\u7684\u4e00\u4e2a\u663e\u8457\u7279\u70b9\u662f\u5b83\u7684\u666e\u9002\u6027\u3002\u9009\u4e3e\u6d89\u53ca10\u4e07\u9009\u6c11\u8fd8\u662f1\u4ebf\u9009\u6c11\u5e76\u4e0d\u91cd\u8981\uff1a\u6c11\u610f\u8c03\u67e5\u7684\u8bef\u5dee\u8303\u56f4\u4ecd\u7136\u662f3%\u3002\u540c\u6837\uff0c\u8fd9\u4e2a\u5dde55%\u5bf945%\u652f\u6301\u9ea6\u51ef\u6069\uff0c\u8fd8\u662f60%\u5bf940%\u652f\u6301\u5965\u5df4\u9a6c\uff0c\u8fd9\u4e2a\u5dde\u662f\u4e00\u4e2a\u7531\u5bcc\u88d5\u7684\u767d\u4eba\u57ce\u5e02\u9009\u6c11\u7ec4\u6210\u7684\u540c\u8d28\u5316\u96c6\u56e2\uff0c\u8fd8\u662f\u4e00\u4e2a\u7531\u5404\u79cd\u6536\u5165\u3001\u79cd\u65cf\u548c\u80cc\u666f\u7684\u9009\u6c11\u6df7\u5408\u800c\u6210\u7684\u5dde\uff0c\u8fd9\u65e0\u5173\u7d27\u8981\uff1a\u8c03\u67e5\u7684\u8bef\u5dee\u8303\u56f4\u4ecd\u7136\u662f3%\u3002\u552f\u4e00\u663e\u8457\u5f71\u54cd\u8bef\u5dee\u8303\u56f4\u7684\u56e0\u7d20\u662f\u6c11\u8c03\u7684\u89c4\u6a21\uff1b\u6c11\u8c03\u89c4\u6a21\u8d8a\u5927\uff0c\u8bef\u5dee\u8303\u56f4\u8d8a\u5c0f\u30021\u4ebf\u9009\u6c11\u5728\u51b3\u5b9a\u603b\u7edf\u5019\u9009\u4eba\u65f6\u6240\u9762\u4e34\u7684\u5de8\u5927\u590d\u6742\u6027\u6700\u7ec8\u53ef\u4ee5\u7b80\u5316\u4e3a\u53ea\u6709\u51e0\u4e2a\u6570\u5b57\u3002<\/span><\/section>\n

<\/section>\n
\u5927\u6570\u5b9a\u5f8b\u662f\u6570\u5b66\u548c\u81ea\u7136\u754c\u4e2d\u6700\u7b80\u5355\u3001\u6700\u5bb9\u6613\u7406\u89e3\u7684\u666e\u9002\u6027\u89c4\u5f8b\u4e4b\u4e00\uff0c\u4f46\u5b83\u7edd\u4e0d\u662f\u552f\u4e00\u7684\u4e00\u4e2a\u3002\u51e0\u5341\u5e74\u6765\uff0c\u4eba\u4eec\u53d1\u73b0\u4e86\u8bb8\u591a\u7c7b\u4f3c\u7684\u666e\u9002\u6027\u89c4\u5f8b\uff0c\u5b83\u4eec\u9002\u7528\u4e8e\u63a7\u5236\u5e7f\u6cdb\u7c7b\u578b\u7684\u590d\u6742\u7cfb\u7edf\u7684\u884c\u4e3a\uff0c\u65e0\u8bba\u7cfb\u7edf\u7684\u7ec4\u6210\u90e8\u5206\u662f\u4ec0\u4e48\uff0c\u5b83\u4eec\u5982\u4f55\u76f8\u4e92\u4f5c\u7528\u3002<\/span><\/section>\n

<\/section>\n
\u5bf9\u4e8e\u5927\u6570\u5b9a\u5f8b\uff0c\u8fd9\u4e00\u666e\u9002\u6027\u73b0\u8c61\u7684\u6570\u5b66\u57fa\u7840\u662f\u5f88\u597d\u7406\u89e3\u7684\uff0c\u5e76\u4e14\u5728\u6982\u7387\u548c\u7edf\u8ba1\u5b66\u7684\u672c\u79d1\u8bfe\u7a0b\u4e2d\u7ecf\u5e38\u6559\u6388\u3002\u7136\u800c\uff0c\u5bf9\u4e8e\u8bb8\u591a\u5176\u4ed6\u666e\u9002\u6027\u89c4\u5f8b\uff0c\u6211\u4eec\u7684\u6570\u5b66\u7406\u89e3\u8fd8\u4e0d\u591f\u5b8c\u5584\u3002\u63a2\u5bfb\u590d\u6742\u7cfb\u7edf\u4e2d\u9891\u7e41\u51fa\u73b0<\/strong>\u666e\u9002\u6027\u89c4\u5f8b<\/strong>\u7684\u539f\u56e0<\/strong>\uff0c<\/strong>\u662f\u6570\u5b66\u7814\u7a76\u4e2d\u4e00\u4e2a\u975e\u5e38\u6d3b\u8dc3\u7684\u65b9\u5411<\/strong>\u3002\u5728\u5927\u591a\u6570\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u79bb\u8fd9\u4e2a\u95ee\u9898\u7684\u6ee1\u610f\u7b54\u6848\u8fd8\u5f88\u8fdc\uff0c\u4f46\u6b63\u5982\u6211\u4e0b\u9762\u6240\u8ba8\u8bba\u7684\uff0c\u6211\u4eec\u5df2\u7ecf\u53d6\u5f97\u4e86\u4e00\u4e9b\u4ee4\u4eba\u9f13\u821e\u7684\u8fdb\u5c55\u3002<\/span><\/section>\n

<\/span><\/section>\n

<\/span><\/section>\n

\n
\n
\n
\n
\n

<\/section>\n

<\/section>\n
\n
<\/svg><\/section>\n<\/section>\n<\/section>\n
\n

2. \u4e2d\u5fc3\u6781\u9650\u5b9a\u7406<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


<\/p>\n

\u5728\u5927\u6570\u5b9a\u5f8b\u4e4b\u540e\uff0c\u4e5f\u8bb8\u53e6\u4e00\u4e2a\u6700\u57fa\u672c\u7684\u666e\u9002\u6027\u89c4\u5f8b\u7684\u4f8b\u5b50\u662f\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406<\/strong><\/span>\uff08<\/strong>Central Limit Theorem\uff09<\/span>\u3002\u7c97\u7565\u5730\u8bf4\uff0c\u8fd9\u4e2a\u5b9a\u7406\u65ad\u8a00\uff0c\u5982\u679c\u4e00\u4e2a\u7edf\u8ba1\u91cf\u662f\u7531\u8bb8\u591a\u72ec\u7acb\u4e14\u968f\u673a\u6ce2\u52a8\u7684\u7ec4\u6210\u90e8\u5206\u7ec4\u5408\u800c\u6210\uff0c\u4e14\u6ca1\u6709\u4e00\u4e2a\u7ec4\u6210\u90e8\u5206\u5bf9\u6574\u4f53\u6709\u51b3\u5b9a\u6027\u5f71\u54cd\uff0c\u90a3\u4e48\u8fd9\u4e2a\u7edf\u8ba1\u91cf\u5c06\u8fd1\u4f3c\u5730\u6309\u7167\u4e00\u79cd\u79f0\u4e3a\u6b63\u6001\u5206\u5e03<\/span>\uff08\u6216\u9ad8\u65af\u5206\u5e03\uff09<\/span>\u7684\u89c4\u5f8b\u5206\u5e03\uff0c\u6216\u8005\u66f4\u901a\u4fd7\u5730\u79f0\u4e3a\u949f\u5f62\u66f2\u7ebf\u3002\u8fd9\u4e2a\u89c4\u5f8b\u662f\u666e\u904d\u7684\uff0c\u56e0\u4e3a\u65e0\u8bba\u4e2a\u522b\u6210\u5206\u5982\u4f55\u6ce2\u52a8\uff0c\u6216\u8005\u6210\u5206\u6709\u591a\u5c11\u4e2a\uff0c\u5b83\u90fd\u6210\u7acb<\/span>\uff08\u5c3d\u7ba1\u6210\u5206\u6570\u91cf\u8d8a\u591a\uff0c\u89c4\u5f8b\u7684\u51c6\u786e\u5ea6\u8d8a\u9ad8\uff09<\/span>\u3002<\/span><\/section>\n

<\/span><\/section>\n
\n
\u8bd1\u6ce8\uff1a<\/span><\/section>\n
\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\uff08Central Limit Theorem\uff0cCLT\uff09\u662f\u6982\u7387\u8bba\u4e2d\u7684\u4e00\u7ec4\u5b9a\u7406\u3002\u5728\u6982\u7387\u8bba\u4e2d\uff0c\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\u8868\u660e\uff0c\u5728\u8bb8\u591a\u60c5\u51b5\u4e0b\uff0c\u5bf9\u4e8e\u72ec\u7acb\u4e14\u540c\u5206\u5e03\u7684\u968f\u673a\u53d8\u91cf\uff0c\u5373\u4f7f\u539f\u59cb\u53d8\u91cf\u672c\u8eab\u4e0d\u662f\u6b63\u6001\u5206\u5e03\uff0c\u6807\u51c6\u5316\u6837\u672c\u5747\u503c\u7684\u62bd\u6837\u5206\u5e03\u4e5f\u8d8b\u5411\u4e8e\u6807\u51c6\u6b63\u6001\u5206\u5e03\u3002\u8fd9\u7ec4\u5b9a\u7406\u662f\u6570\u7406\u7edf\u8ba1\u5b66\u548c\u8bef\u5dee\u5206\u6790\u7684\u7406\u8bba\u57fa\u7840\uff0c\u5b83\u6307\u51fa\u4e86\u5927\u91cf\u968f\u673a\u53d8\u91cf\u4e4b\u548c\u8fd1\u4f3c\u670d\u4ece\u6b63\u6001\u5206\u5e03\u7684\u6761\u4ef6\u3002\u53c2\u89c1\u7ef4\u57fa\u767e\u79d1\uff1a<\/span><\/section>\n
https:\/\/zh.wikipedia.org\/zh-cn\/%E4%B8%AD%E5%BF%83%E6%9E%81%E9%99%90%E5%AE%9A%E7%90%86<\/span><\/section>\n<\/blockquote>\n

<\/section>\n
\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\u5728\u8303\u56f4\u6781\u5e7f\u7684\u7edf\u8ba1\u6570\u636e\u4e2d\u5f97\u5230\u4f53\u73b0\uff0c\u4ece\u4e8b\u6545\u53d1\u751f\u7387\u5230\u4e0d\u540c\u7269\u79cd\u4e2a\u4f53\u7684\u8eab\u9ad8\u3001\u4f53\u91cd\u6216\u5176\u4ed6\u5173\u952e\u7edf\u8ba1\u6570\u636e\u7684\u53d8\u5316\uff0c\u518d\u5230\u7531\u5076\u7136\u4e8b\u4ef6\u5bfc\u81f4\u7684\u8d22\u52a1\u76c8\u4e8f\uff0c\u4ee5\u53ca\u7269\u7406\u7cfb\u7edf\u4e2d\u5404\u7ec4\u6210\u7c92\u5b50\u7684\u901f\u5ea6\uff0c\u90fd\u80fd\u627e\u5230\u5b83\u7684\u8e2a\u8ff9\u3002\u8fd9\u4e9b\u5206\u5e03\u7684\u5927\u5c0f\u3001\u5bbd\u5ea6\u3001\u4f4d\u7f6e\u4e43\u81f3\u6d4b\u91cf\u5355\u4f4d\u968f\u7740\u4e0d\u540c\u7684\u7edf\u8ba1\u800c\u6709\u6240\u4e0d\u540c\uff0c\u4f46\u949f\u5f62\u66f2\u7ebf\u7684\u5f62\u72b6\u5374\u80fd\u5728\u6240\u6709\u5b9e\u4f8b\u4e2d\u88ab\u8bc6\u522b\u51fa\u6765\u3002\u8fd9\u79cd\u8d8b\u540c\u5e76\u975e\u56e0\u4e3a\u8f66\u7978\u3001\u4eba\u7c7b\u8eab\u9ad8\u3001\u4ea4\u6613\u5229\u6da6\u6216\u661f\u4f53\u901f\u5ea6\u7b49\u591a\u6837\u5316\u73b0\u8c61\u4e4b\u95f4\u5b58\u5728\u7684\u201c\u4f4e\u7ea7\u201d\u6216\u201c\u5fae\u89c2\u201d\u5c42\u9762\u7684\u8054\u7cfb\uff0c\u800c\u662f\u56e0\u4e3a\u5728\u6240\u6709\u8fd9\u4e9b\u60c5\u51b5\u4e0b\uff0c\u5176\u201c\u9ad8\u7ea7\u201d\u6216\u201c\u5b8f\u89c2\u201d\u7ed3\u6784\u76f8\u540c\uff1a\u5373\u7531\u8bb8\u591a\u72ec\u7acb\u56e0\u7d20\u7684\u5c0f\u5f71\u54cd\u7ec4\u5408\u6210\u7684\u590d\u5408\u7edf\u8ba1\u91cf\u3002\u4e00\u4e2a\u5927\u578b\u590d\u6742\u7cfb\u7edf\u7684\u5b8f\u89c2\u884c\u4e3a\u51e0\u4e4e\u5b8c\u5168\u4e0e\u5176\u5fae\u89c2\u6784\u9020\u65e0\u5173\uff0c\u8fd9\u6b63\u662f<\/strong>\u666e\u9002\u6027<\/strong>\u7684\u8981\u4e49\u3002<\/strong><\/span><\/section>\n

<\/section>\n
\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\u7684\u666e\u9002\u6027\u5728\u8bb8\u591a\u884c\u4e1a\u4e2d\u975e\u5e38\u6709\u7528\uff0c\u5b83\u5141\u8bb8\u8fd9\u4e9b\u884c\u4e1a\u7ba1\u7406\u672c\u6765\u96be\u4ee5\u5904\u7406\u7684\u590d\u6742\u548c\u6df7\u4e71\u7684\u7cfb\u7edf\u3002\u6709\u4e86\u8fd9\u4e2a\u5b9a\u7406\uff0c\u4fdd\u9669\u516c\u53f8\u53ef\u4ee5\u7ba1\u7406\u4ed6\u4eec\u7684\u6c7d\u8f66\u4fdd\u9669\u653f\u7b56\u7684\u98ce\u9669\uff0c\u800c\u4e0d\u5fc5\u77e5\u9053\u8f66\u7978\u53d1\u751f\u7684\u6240\u6709\u590d\u6742\u7ec6\u8282\uff1b\u5929\u6587\u5b66\u5bb6\u53ef\u4ee5\u6d4b\u91cf\u9065\u8fdc\u661f\u7cfb\u7684\u5927\u5c0f\u548c\u4f4d\u7f6e\uff0c\u800c\u4e0d\u5fc5\u89e3\u51b3\u5929\u4f53\u529b\u5b66\u7684\u590d\u6742\u65b9\u7a0b\uff1b\u7535\u6c14\u5de5\u7a0b\u5e08\u53ef\u4ee5\u9884\u6d4b\u566a\u58f0\u548c\u5e72\u6270\u5bf9\u7535\u5b50\u901a\u4fe1\u7684\u5f71\u54cd\uff0c\u800c\u4e0d\u5fc5\u77e5\u9053\u8fd9\u79cd\u566a\u58f0\u662f\u5982\u4f55\u4ea7\u751f\u7684\uff1b\u7b49\u7b49\u3002\u7136\u800c\uff0c\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\u5e76\u4e0d\u662f\u5b8c\u5168\u666e\u904d\u7684\uff1b\u4e00\u4e9b\u91cd\u8981\u60c5\u51b5\u4e0b\u5b9a\u7406\u4e0d\u9002\u7528\uff0c\u5176\u7ed9\u51fa\u4e0e\u949f\u5f62\u66f2\u7ebf\u5b8c\u5168\u4e0d\u540c\u7684\u5206\u5e03\u7edf\u8ba1\u6570\u636e\u3002<\/span>\uff08\u6211\u7a0d\u540e\u4f1a\u56de\u5230\u8fd9\u4e00\u70b9\u3002\uff09<\/span><\/section>\n

<\/section>\n
\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\u5b58\u5728\u7740\u4e00\u4e9b\u6269\u5c55\uff0c\u5b83\u4eec\u662f\u9488\u5bf9\u67d0\u4e9b\u7565\u6709\u4e0d\u540c\u7684\u7edf\u8ba1\u6570\u636e\u7c7b\u578b\u7684\u666e\u9002\u6027\u89c4\u5f8b\u3002\u672c\u798f\u5fb7\u5b9a\u5f8b<\/strong><\/span>\uff08Benford’s Law\uff09<\/span>\u5c31\u662f\u4e00\u4e2a\u4f8b\u5b50\uff0c\u5b83\u662f\u5173\u4e8e\u5927\u91cf\u7ea7\u7edf\u8ba1\u6570\u636e\u7684\u524d\u51e0\u4f4d\u6570\u5b57\u7684\u4e00\u4e2a\u666e\u9002\u6027\u89c4\u5f8b\uff0c\u5982\u4e00\u4e2a\u56fd\u5bb6\u7684\u4eba\u53e3\u6570\u91cf\u6216\u8d26\u6237\u7684\u91d1\u989d\u5927\u5c0f\uff1b\u8fd9\u4e2a\u6cd5\u5219\u7ed9\u51fa\u4e86\u4e00\u4e9b\u53cd\u76f4\u89c9\u7684\u9884\u6d4b\uff0c\u6bd4\u5982\uff0c\u5728\u81ea\u7136\u754c\u4e2d\u51fa\u73b0\u7684\u4efb\u4f55\u7ed9\u5b9a\u7edf\u8ba1\u6570\u636e\u90fd\u66f4\u53ef\u80fd\u4ee5\u6570\u5b571\u5f00\u5934\uff0c\u800c\u4e0d\u662f\u6570\u5b579\u5f00\u5934<\/strong>\u2014\u2014\u5b9e\u9645\u4e0a\u4ee51\u5f00\u5934\u7684\u6982\u7387\u662f\u4ee59\u5f00\u5934\u7684\u516d\u500d\u591a\u3002\u9664\u6b64\u4e4b\u5916\uff0c\u672c\u798f\u5fb7\u5b9a\u5f8b<\/span>\uff08\u53ef\u4ee5\u901a\u8fc7\u7ed3\u5408\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\u548c\u5bf9\u6570\u7684\u6570\u5b66\u7406\u8bba\u6765\u89e3\u91ca\uff09<\/span>\u8fd8\u88ab\u7528\u4e8e\u68c0\u6d4b\u4f1a\u8ba1\u6b3a\u8bc8\uff0c\u56e0\u4e3a\u4e0e\u81ea\u7136\u4ea7\u751f\u7684\u6570\u5b57\u76f8\u6bd4\uff0c\u88ab\u4eba\u4e3a\u7f16\u9020\u7684\u6570\u5b57\u5f80\u5f80\u4e0d\u7b26\u5408\u672c\u798f\u5fb7\u5b9a\u5f8b\u3002<\/span><\/section>\n

<\/section>\n
<\/section>\n

\u56fe1. 2010\u5e74\u4e16\u754c237\u4e2a\u56fd\u5bb6\u4eba\u53e3\u7684\u9996\u4f4d\u6570\u5b57\u7684\u76f4\u65b9\u56fe\u3002\u9ed1\u8272\u7684\u70b9\u8868\u793a Benford \u5b9a\u5f8b\u7684\u9884\u6d4b\u3002\uff5c\u56fe\u6e90\uff1a\u7ef4\u57fa\u767e\u79d1\uff0chttps:\/\/en.wikipedia.org\/wiki\/File:Benfords_law_illustrated_by_world%27s_countries_population.png<\/span><\/p>\n


<\/span><\/p>\n

\n
\u8bd1\u6ce8\uff08\u6765\u6e90\u4e8e\u7ef4\u57fa\u767e\u79d1\uff09\uff1a<\/span><\/section>\n
\u672c\u56fe\u8868\u4f7f\u7528\u4e16\u754c\u5404\u56fd\u7684\u4eba\u53e3\u4e3a\u4f8b\uff0c\u8bf4\u660e\u672c\u798f\u5fb7\u5b9a\u5f8b\uff08Benford’s law\uff09\u3002\u56fe\u8868\u663e\u793a\u4e86\u5404\u56fd\u4eba\u53e3\u7b2c1\u4f4d\u6570\u5b57\u6240\u5360\u7684\u767e\u5206\u6bd4\uff08\u7070\u8272\u67f1\u72b6\u56fe\uff09\u3002\u4f8b\u5982\uff0c237\u4e2a\u56fd\u5bb6\u4e2d\u670964\u4e2a\uff08\u536027%\uff09\u7684\u4eba\u53e3\u4ee51\u4e3a\u9996\u4f4d\u6570\u5b57\u3002\u9ed1\u8272\u70b9\u8868\u793a\u672c\u798f\u5fb7\u5b9a\u5f8b\u7684\u9884\u6d4b\u7ed3\u679c\u3002\u6570\u636e\u6765\u81eaCIA\u4e16\u754c\u624b\u518c https:\/\/www.cia.gov\/library\/publications\/the-world-factbook\/rankorder\/2119rank.html\uff0c\u8bbf\u95ee\u65f6\u95f4\u4e3a2010\u5e748\u67087\u65e5\u3002<\/span><\/section>\n<\/blockquote>\n

<\/section>\n
\u7c7b\u4f3c\u5730\uff0cZipf \u5b9a\u5f8b\u662f\u63cf\u8ff0\u7279\u5b9a\u7c7b\u522b\u4e2d\u6700\u5927\u7edf\u8ba1\u91cf\u7684\u666e\u9002\u6027\u89c4\u5f8b\uff0c\u4f8b\u5982\u4e16\u754c\u4e0a\u4eba\u53e3\u6700\u591a\u7684\u56fd\u5bb6\u6216\u82f1\u6587\u4e2d\u4f7f\u7528\u9891\u7387\u6700\u9ad8\u7684\u5355\u8bcd\u3002\u5b83\u6307\u51fa\uff0c\u7edf\u8ba1\u6570\u636e\u7684\u5927\u5c0f\u901a\u5e38\u4e0e\u5176\u6392\u540d\u6210\u53cd\u6bd4<\/strong>\uff1b\u56e0\u6b64\uff0c\u4f8b\u5982\uff0c\u7b2c\u5341\u5927\u7684\u6570\u636e\u5927\u7ea6\u662f\u7b2c\u4e94\u5927\u6570\u636e\u7684\u4e00\u534a\u5927\u5c0f\u3002\u8fd9\u4e2a\u6cd5\u5219\u5bf9\u4e8e\u6700\u9876\u7aef\u7684\u4e24\u4e09\u4e2a\u6570\u636e\u53ef\u80fd\u4e0d\u592a\u7cbe\u786e\uff0c\u4f46\u5728\u4e4b\u540e\u7684\u6570\u636e\u4e2d\u51c6\u786e\u6027\u63d0\u9ad8\u3002\u4e0e\u6570\u5b66\u4e0a\u8f83\u5bb9\u6613\u7406\u89e3\u7684\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\u548c\u672c\u798f\u5fb7\u5b9a\u5f8b\u4e0d\u540c\uff0cZipf \u5b9a\u5f8b\u662f\u57fa\u4e8e\u7ecf\u9a8c\u7684\u3002\u5b83\u662f\u901a\u8fc7\u5b9e\u8df5\u89c2\u5bdf\u800c\u786e\u5b9a\u7684\uff0c\u4f46\u6570\u5b66\u5bb6\u4eec\u5c1a\u672a\u7ed9\u51fa\u4e00\u4e2a\u5b8c\u5168\u6ee1\u610f\u548c\u6709\u8bf4\u670d\u529b\u7684\u89e3\u91ca\uff0c\u6765\u8bf4\u660e\u8fd9\u4e2a\u5b9a\u5f8b\u600e\u6837\u4ea7\u751f\u4ee5\u53ca\u4e3a\u4ec0\u4e48\u5177\u6709\u666e\u9002\u6027\u3002<\/span><\/section>\n

<\/span><\/section>\n
\n
\u8bd1\u6ce8\uff1a<\/span><\/section>\n
Zipf\u5b9a\u5f8b\u662f\u4e00\u79cd\u7ecf\u9a8c\u89c4\u5f8b\uff0c\u5f53\u4e00\u4e2a\u6d4b\u91cf\u503c\u5217\u8868\u6309\u964d\u5e8f\u6392\u5e8f\u65f6\uff0c\u5b83\u901a\u5e38\u5927\u81f4\u6210\u7acb\u3002\u5b83\u6307\u51fa\uff0c\u7b2cn\u4e2a\u6761\u76ee\u7684\u503c\u4e0en\u6210\u53cd\u6bd4\u3002Zipf\u5b9a\u5f8b\u6700\u8457\u540d\u7684\u5b9e\u4f8b\u9002\u7528\u4e8e\u81ea\u7136\u8bed\u8a00\u6587\u672c\u6216\u8bed\u6599\u5e93\u4e2d\u5355\u8bcd\u7684\u9891\u7387\u8868\u3002\u901a\u5e38\u60c5\u51b5\u4e0b\uff0c\u6700\u5e38\u89c1\u7684\u8bcd\u51fa\u73b0\u7684\u9891\u7387\u5927\u7ea6\u662f\u6b21\u5e38\u89c1\u8bcd\u7684\u4e24\u500d\uff0c\u662f\u7b2c\u4e09\u5e38\u89c1\u8bcd\u7684\u4e09\u500d\uff0c\u4f9d\u6b64\u7c7b\u63a8\u3002<\/span><\/section>\n
\u6765\u6e90\u4e8e\u7ef4\u57fa\u767e\u79d1\uff1ahttps:\/\/en.wikipedia.org\/wiki\/Zipf%27s_law<\/span><\/span><\/section>\n<\/blockquote>\n


<\/h2>\n


<\/span><\/p>\n

\n
\n
\n
\n
\n

<\/section>\n

<\/section>\n
\n
<\/svg><\/section>\n<\/section>\n<\/section>\n
\n

3. \u76f8\u53d8\u4e0e\u91cd\u6574\u5316\u7fa4<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


<\/p>\n

\u76ee\u524d\u4e3a\u6b62\uff0c\u6211\u8ba8\u8bba\u4e86\u4e2a\u4f53\u7edf\u8ba1\u91cf\u7684\u666e\u9002\u6027\u89c4\u5f8b\uff1a\u5f53\u591a\u4e2a\u5c0f\u7684\u72ec\u7acb\u56e0\u7d20\u590d\u5408\u65f6\uff0c\u5c31\u4f1a\u4ea7\u751f\u8fd9\u4e9b\u590d\u6742\u7684\u6570\u503c\u91cf\u3002\u7136\u800c\uff0c\u9664\u4e86\u6570\u503c\u7edf\u8ba1\u4e4b\u5916\uff0c\u66f4\u52a0\u590d\u6742\u7684\u5bf9\u8c61\u4e5f\u9075\u5faa\u666e\u9002\u6027\u89c4\u5f8b\u3002\u4ee5\u7269\u7406\u548c\u5316\u5b66\u4e2d\u76f8\u53d8\u5f15\u8d77\u7684\u590d\u6742\u5f62\u72b6\u548c\u7ed3\u6784\u4e3a\u4f8b\u3002\u6b63\u5982\u6211\u4eec\u5728\u9ad8\u4e2d\u79d1\u5b66\u8bfe\u4e0a\u6240\u5b66\u7684\uff0c\u7269\u8d28\u5b58\u5728\u4e0d\u540c\u72b6\u6001\uff0c\u5305\u62ec\u4e09\u79cd\u7ecf\u5178\u72b6\u6001\u2014\u2014\u56fa\u6001\u3001\u6db2\u6001\u548c\u6c14\u6001\uff0c\u8fd8\u6709\u4e00\u4e9b\u5947\u5f02\u72b6\u6001\uff0c\u6bd4\u5982\u7b49\u79bb\u5b50\u4f53\u6216\u8d85\u6d41\u4f53\u3002\u4f8b\u5982\u94c1\u8fd9\u6837\u7684\u94c1\u78c1\u6027\u6750\u6599\uff0c\u4e5f\u5b58\u5728\u78c1\u5316\u548c\u975e\u78c1\u5316\u7684\u72b6\u6001\uff1b\u5176\u4ed6\u6750\u6599\u53ef\u80fd\u5728\u67d0\u4e9b\u6e29\u5ea6\u4e0b\u662f\u5bfc\u4f53\uff0c\u5728\u53e6\u4e00\u4e9b\u6e29\u5ea6\u4e0b\u5219\u662f\u7edd\u7f18\u4f53\u3002\u6750\u6599\u7684\u72b6\u6001\u53d6\u51b3\u4e8e\u8bb8\u591a\u56e0\u7d20\uff0c\u5c24\u5176\u662f\u6e29\u5ea6\uff0c\u6709\u65f6\u8fd8\u5305\u62ec\u538b\u529b\u3002<\/span>\uff08\u5bf9\u67d0\u4e9b\u6750\u6599\u800c\u8a00\uff0c\u6742\u8d28\u6c34\u5e73\u4e5f\u662f\u91cd\u8981\u56e0\u7d20\u3002\uff09<\/span>\u5728\u56fa\u5b9a\u538b\u529b\u4e0b\uff0c\u5927\u90e8\u5206\u6750\u6599\u503e\u5411\u4e8e\u5728\u4e00\u4e2a\u6e29\u5ea6\u533a\u95f4\u5185\u5448\u73b0\u67d0\u79cd\u72b6\u6001\uff0c\u5728\u53e6\u4e00\u4e2a\u533a\u95f4\u5185\u5448\u73b0\u53e6\u4e00\u79cd\u72b6\u6001\u3002\u4f46\u5f53\u6750\u6599\u7684\u6e29\u5ea6\u8fbe\u5230\u6216\u975e\u5e38\u63a5\u8fd1\u8fd9\u4e24\u4e2a\u533a\u95f4\u7684\u5206\u754c\u7ebf\u65f6\uff0c\u4fbf\u4f1a\u53d1\u751f\u6709\u8da3\u7684\u76f8\u53d8\u73b0\u8c61\u3002\u6b64\u65f6\u7684\u6750\u6599\u5e76\u672a\u5b8c\u5168\u5904\u4e8e\u5176\u4e2d\u4e00\u79cd\u72b6\u6001\uff0c\u5f80\u5f80\u4f1a\u5206\u88c2\u6210\u4e3a\u7f8e\u4e3d\u7684\u5206\u5f62\u5f62\u72b6\uff0c\u79f0\u4e3a\u7c07<\/span>\uff08clusters\uff09<\/span>\uff0c\u6bcf\u4e2a\u7c07\u4ee3\u8868\u4e24\u79cd\u72b6\u6001\u4e2d\u7684\u4e00\u79cd\u3002<\/span>
<\/section>\n

<\/span><\/section>\n
\n
\u8bd1\u6ce8\uff1a<\/span><\/section>\n
\u5206\u5f62<\/strong>\uff08\u82f1\u8bed\uff1afractal\uff0c\u6709\u201c\u96f6\u788e\u201d\u3001\u201c\u7834\u88c2\u201d\u4e4b\u610f\uff09\uff0c\u53c8\u79f0\u788e\u5f62<\/strong>\u3001\u6b8b\u5f62<\/strong>\uff0c\u901a\u5e38\u88ab\u5b9a\u4e49\u4e3a\u201c\u4e00\u4e2a\u7c97\u7cd9\u6216\u96f6\u788e\u7684\u51e0\u4f55\u5f62\u72b6\uff0c\u53ef\u4ee5\u5206\u6210\u6570\u4e2a\u90e8\u5206\uff0c\u4e14\u6bcf\u4e00\u90e8\u5206\u90fd\uff08\u81f3\u5c11\u8fd1\u4f3c\u5730\uff09\u662f\u6574\u4f53\u7f29\u5c0f\u540e\u7684\u5f62\u72b6\u201d\uff0c\u5373\u5177\u6709\u81ea\u76f8\u4f3c\u7684\u6027\u8d28\u3002\u5206\u5f62\u5728\u6570\u5b66\u4e2d\u662f\u4e00\u79cd\u62bd\u8c61\u7684\u7269\u4f53\uff0c\u7528\u4e8e\u63cf\u8ff0\u81ea\u7136\u754c\u4e2d\u5b58\u5728\u7684\u4e8b\u7269\u3002\u4eba\u5de5\u5206\u5f62\u901a\u5e38\u5728\u653e\u5927\u540e\u80fd\u5c55\u73b0\u51fa\u76f8\u4f3c\u7684\u5f62\u72b6\u3002\u5206\u5f62\u4e5f\u88ab\u79f0\u4e3a\u6269\u5c55\u5bf9\u79f0<\/strong>\u6216\u5c55\u5f00\u5bf9\u79f0<\/strong>\u3002\u5982\u679c\u5728\u6bcf\u6b21\u653e\u5927\u540e\uff0c\u5f62\u72b6\u7684\u91cd\u590d\u662f\u5b8c\u5168\u76f8\u540c\u7684\uff0c\u8fd9\u88ab\u79f0\u4e3a\u81ea\u76f8\u4f3c\u3002<\/span><\/section>\n
\u53c2\u8003\u94fe\u63a5\uff1ahttps:\/\/zh.wikipedia.org\/zh-cn\/%E5%88%86%E5%BD%A2<\/span><\/section>\n<\/blockquote>\n

<\/section>\n
\u73b0\u5b9e\u4e16\u754c\u5b58\u5728\u65e0\u6570\u79cd\u6750\u6599\uff0c\u6bcf\u4e00\u79cd\u90fd\u6709\u4e00\u7ec4\u5173\u952e\u7279\u6027\u53c2\u6570<\/span>\uff08\u4f8b\u5982\uff0c\u5728\u7ed9\u5b9a\u538b\u529b\u4e0b\u7684\u6cb8\u70b9\uff09<\/span>\u3002\u7269\u7406\u5b66\u5bb6\u548c\u5316\u5b66\u5bb6\u4eec\u91c7\u7528\u4e86\u8bb8\u8bb8\u591a\u591a\u6570\u5b66\u6a21\u578b\u6765\u6a21\u62df\u8fd9\u4e9b\u6750\u6599\u53ca\u5176\u76f8\u53d8\u3002\u5728\u8fd9\u4e9b\u6a21\u578b\u4e2d\uff0c\u901a\u5e38\u4f1a\u5047\u8bbe\u5355\u4e2a\u539f\u5b50\u6216\u5206\u5b50\u901a\u8fc7\u968f\u673a\u6570\u91cf\u7684\u952e\u4e0e\u4e00\u4e9b\u5468\u56f4\u90bb\u5c45\u8fde\u63a5\uff0c\u4e14\u8fd9\u4e9b\u8fde\u63a5\u6309\u67d0\u79cd\u6982\u7387\u89c4\u5f8b\u6765\u5206\u914d\u3002\u5728\u5fae\u89c2\u5c3a\u5ea6\u4e0a\uff0c\u8fd9\u4e9b\u6a21\u578b\u4e4b\u95f4\u53ef\u80fd\u5dee\u5f02\u663e\u8457\u3002\u4f8b\u5982\uff0c\u4e0b\u9762\u7684\u63d2\u56fe\u5c55\u793a\u4e86\u4e24\u79cd\u5178\u578b\u6a21\u578b\u7684\u5c0f\u5c3a\u5ea6\u7ed3\u6784\uff1a<\/span><\/section>\n

<\/span><\/section>\n
\u56fe2\u6240\u793a\u4e3a\u516d\u89d2\u5f62\u6676\u683c\u4e0a\u7684\u70b9\u6e17\u6d41\u6a21\u578b<\/span>\uff08site percolation model\uff09<\/span>\uff0c\u6bcf\u4e2a\u516d\u8fb9\u5f62<\/span>\uff08\u6216\u4f4d\u70b9\uff09<\/span>\u4e3a\u539f\u5b50\u6216\u5206\u5b50\u7684\u62bd\u8c61\u5316\uff0c\u5b83\u4eec\u88ab\u968f\u673a\u8d4b\u4e88\u4e24\u79cd\u72b6\u6001\u4e4b\u4e00\uff0c\u76f8\u540c\u72b6\u6001\u7684\u8fde\u63a5\u533a\u57df\u7ec4\u6210\u7c07\uff1b<\/span><\/section>\n

<\/section>\n
<\/section>\n

\u56fe2 \u4e34\u754c\u9608\u503c\u4e0b\u7684\u516d\u8fb9\u5f62\u6676\u683c\u70b9\u6e17\u6d41\u6a21\u578b\u3002<\/span>\u56fe\u6e90\uff1a<\/span>Michael Kozdron\uff0chttp:\/\/stat.math.uregina.ca\/~kozdron\/Simulations\/Percolation\/percolation.htm<\/span><\/p>\n


<\/span><\/section>\n
\u56fe3\u6240\u793a\u4e3a\u6b63\u65b9\u5f62\u6676\u683c\u4e0a\u7684\u952e\u6e17\u6d41\u6a21\u578b\uff0c\u5176\u4e2d\u6676\u683c\u7684\u8fb9\u7f18\u4e3a\u5206\u5b50\u952e\u7684\u62bd\u8c61\u5316\uff0c\u6bcf\u4e2a\u952e\u6709\u4e00\u5b9a\u51e0\u7387\u88ab\u6fc0\u6d3b\uff0c\u7531\u6fc0\u6d3b\u952e\u8fde\u63a5\u6210\u7684\u533a\u57df\u5f62\u6210\u7c07\u3002<\/span><\/section>\n

<\/section>\n
<\/section>\n

\u56fe3 \u65b9\u683c\u6e17\u6d41\u6a21\u578b\u5728\u4e34\u754c\u9608\u503c\u4e0b\u7684\u952e\u6e17\u6d41\u6a21\u578b\u3002\u6ce8\u610f\u8fd9\u91cc\u65e2\u6709\u975e\u5e38\u5c0f\u7684\u7c07\uff0c\u4e5f\u6709\u6781\u5927\u7684\u7c07\u3002<\/span>\u56fe\u6e90\uff1a\u7ef4\u57fa\u767e\u79d1\uff0chttp:\/\/en.wikipedia.org\/wiki\/File:Bondpercolationp_51.png<\/span><\/p>\n


<\/section>\n
\u5f53\u6211\u4eec\u4ece\u5b8f\u89c2\u89d2\u5ea6\u5ba1\u89c6\u7c07\u7684\u5927\u5c3a\u5ea6\u7ed3\u6784\u65f6\uff0c\u7279\u522b\u662f\u5728\u63a5\u8fd1\u4e34\u754c\u53c2\u6570\u503c<\/span>\uff08\u4f8b\u5982\uff0c\u6e29\u5ea6\uff09<\/span>\u7684\u60c5\u51b5\u4e0b\uff0c\u5fae\u89c2\u7ed3\u6784\u4e0a\u7684\u5dee\u5f02\u5f00\u59cb\u53d8\u5f97\u6a21\u7cca\u4e0d\u6e05\uff0c\u4e00\u4e9b\u666e\u9002\u6027\u89c4\u5f8b\u4e5f\u968f\u4e4b\u6d8c\u73b0\u3002\u5c3d\u7ba1\u7c07\u7684\u5927\u5c0f\u548c\u5f62\u72b6\u662f\u968f\u673a\u51fa\u73b0\u7684\uff0c\u4f46\u5b83\u4eec\u51e0\u4e4e\u603b\u4f1a\u5448\u73b0\u51fa\u5206\u5f62\u7ed3\u6784\uff1b\u8fd9\u610f\u5473\u7740\u5982\u679c\u4f60\u653e\u5927\u89c2\u5bdf\u7c07\u7684\u4efb\u4f55\u4e00\u4e2a\u90e8\u5206\uff0c\u5176\u663e\u793a\u7684\u56fe\u50cf\u90fd\u4f1a\u6216\u591a\u6216\u5c11\u5730\u7c7b\u4f3c\u4e8e\u6574\u4e2a\u7c07\u3002\u57fa\u672c\u7edf\u8ba1\u91cf\uff0c\u6bd4\u5982\u7c07\u7684\u6570\u91cf\u3001\u7c07\u7684\u5e73\u5747\u5927\u5c0f\u6216\u7c07\u8fde\u63a5\u4e24\u4e2a\u7279\u5b9a\u7a7a\u95f4\u533a\u57df\u7684\u9891\u7387\u7b49\uff0c\u90fd\u9075\u5faa\u4e00\u4e9b\u7279\u6709\u7684\u666e\u9002\u6027\u89c4\u5f8b\uff0c\u88ab\u79f0\u4f5c\u5e42\u5f8b<\/span>\uff08\u8fd9\u4e9b\u4e0eZipf\u5b9a\u5f8b\u7c7b\u4f3c\uff0c\u4f46\u5e76\u975e\u5b8c\u5168\u4e00\u6837\uff09<\/span>\u3002\u8fd9\u4e9b\u89c4\u5f8b\u51e0\u4e4e\u5b58\u5728\u4e8e\u6bcf\u4e00\u4e2a\u7528\u6765\u89e3\u91ca<\/span>\uff08\u8fde\u7eed\uff09<\/span>\u76f8\u53d8\u73b0\u8c61\u7684\u6570\u5b66\u6a21\u578b\u4e2d\uff0c\u5e76\u4e14\u5728\u81ea\u7136\u754c\u4e2d\u88ab\u53cd\u590d\u89c2\u5bdf\u5230\u3002\u5c31\u50cf\u5176\u4ed6\u666e\u9002\u6027\u89c4\u5f8b\u4e00\u6837\uff0c\u6a21\u578b\u6216\u6750\u6599\u7684\u786e\u5207\u5fae\u89c2\u7ed3\u6784\u53ef\u80fd\u5f71\u54cd\u4e00\u4e9b\u57fa\u7840\u53c2\u6570\uff0c\u6bd4\u5982\u76f8\u53d8\u6e29\u5ea6\uff0c\u4f46\u65e0\u8bba\u5728\u54ea\u4e2a\u6a21\u578b\u6216\u6750\u6599\u4e2d\uff0c\u8fd9\u4e9b<\/strong>\u89c4\u5f8b<\/strong>\u7684\u57fa\u7840\u7ed3\u6784\u90fd\u662f\u4e00\u81f4\u7684<\/strong>\u3002<\/span><\/section>\n

<\/section>\n
\u4e0e\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\u7b49\u66f4\u7ecf\u5178\u7684\u666e\u9002\u6027\u5b9a\u5f8b\u4e0d\u540c\uff0c\u6211\u4eec\u5bf9\u76f8\u53d8\u7684\u666e\u9002\u6027\u89c4\u5f8b\u7684\u7406\u89e3\u8fd8\u4e0d\u5b8c\u5168\u3002\u7269\u7406\u5b66\u5bb6\u63d0\u51fa\u4e86\u4e00\u4e9b\u4ee4\u4eba\u4fe1\u670d\u7684\u542f\u53d1\u6027\u8bba\u8bc1\uff0c\u89e3\u91ca\u6216\u652f\u6301\u4e86\u8bb8\u591a\u8fd9\u4e9b\u89c4\u5f8b<\/span>\uff08\u8fd9\u4e9b\u8bba\u70b9\u57fa\u4e8e\u4e00\u79cd\u5f3a\u5927\u4f46\u4e0d\u5b8c\u5168\u4e25\u8c28\u7684\u5de5\u5177\uff0c\u79f0\u4e3a\u91cd\u6574\u5316\u7fa4\u65b9\u6cd5 \uff08renormalization group\uff09\uff09<\/span>\uff0c\u4f46\u5728\u4e00\u822c\u60c5\u5f62\u4e0b\u8fd8\u6ca1\u6709\u5f97\u5230\u8fd9\u4e9b\u89c4\u5f8b\u7684\u5b8c\u5168\u4e25\u683c\u8bc1\u660e\u3002\u8fd9\u662f\u4e00\u4e2a\u975e\u5e38\u6d3b\u8dc3\u7684\u7814\u7a76\u9886\u57df\uff1b\u4f8b\u5982\uff0c\u57282010\u5e748\u6708\uff0c\u83f2\u5c14\u5179\u5956<\/span>\uff08\u6570\u5b66\u754c\u6700\u8d1f\u76db\u540d\u7684\u5956\u9879\u4e4b\u4e00\uff09<\/span>\u6388\u4e88\u65af\u5766\u5c3c\u65af\u62c9\u592b\u00b7\u65af\u7c73\u5c14\u8bfa\u592b<\/span>\uff08Stanislav Smirrnov)<\/span>\uff0c\u4ee5\u8868\u5f70\u4ed6\u5728\u4e25\u683c\u5efa\u7acb\u4e00\u4e9b\u5173\u952e\u6a21\u578b<\/span>\uff08\u5982\u4e09\u89d2\u6676\u683c\u4e0a\u7684\u6e17\u6d41\u6a21\u578b\uff09<\/span>\u7684\u666e\u9002\u6027\u89c4\u5f8b\u7684\u6709\u6548\u6027\u65b9\u9762\u53d6\u5f97\u7684\u7a81\u7834\u3002<\/span><\/section>\n

<\/span><\/section>\n
\n
\u8bd1\u6ce81\uff1a<\/span><\/section>\n
\u91cd\u6574\u5316\u7fa4\u65b9\u6cd5\uff1a\u5728\u7406\u8bba\u7269\u7406\u4e2d\uff0c\u91cd\u6574\u5316\u7fa4\uff08renormalization group\uff0c\u7b80\u79f0RG\uff09\u662f\u4e00\u4e2a\u5728\u4e0d\u540c\u957f\u5ea6\u6807\u5ea6\u4e0b\u8003\u5bdf\u7269\u7406\u7cfb\u7edf\u53d8\u5316\u7684\u6570\u5b66\u5de5\u5177\u3002\u6807\u5ea6\u4e0a\u7684\u53d8\u5316\u79f0\u4e3a\u201c\u6807\u5ea6\u53d8\u6362\u201d\u3002\u91cd\u6574\u5316\u7fa4\u4e0e\u201c\u6807\u5ea6\u4e0d\u53d8\u6027\u201d\u548c\u201c\u5171\u5f62\u4e0d\u53d8\u6027\u201d\u7684\u5173\u7cfb\u8f83\u4e3a\u7d27\u5bc6\u3002\u5171\u5f62\u4e0d\u53d8\u6027\u5305\u542b\u4e86\u6807\u5ea6\u53d8\u6362\uff0c\u5b83\u4eec\u90fd\u4e0e\u81ea\u76f8\u4f3c\u6709\u5173\u3002\u5728\u91cd\u6574\u5316\u7406\u8bba\u4e2d\uff0c\u7cfb\u7edf\u5728\u67d0\u4e00\u4e2a\u6807\u5ea6\u4e0a\u81ea\u76f8\u4f3c\u4e8e\u4e00\u4e2a\u66f4\u5c0f\u7684\u6807\u5ea6\uff0c\u4f46\u63cf\u8ff0\u5b83\u4eec\u7ec4\u6210\u7684\u53c2\u91cf\u503c\u4e0d\u76f8\u540c\u3002\u7cfb\u7edf\u7684\u7ec4\u6210\u53ef\u4ee5\u662f\u539f\u5b50\uff0c\u57fa\u672c\u7c92\u5b50\uff0c\u81ea\u65cb\u7b49\u3002\u7cfb\u7edf\u7684\u53d8\u91cf\u662f\u4ee5\u7cfb\u7edf\u7ec4\u6210\u4e4b\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\u6765\u63cf\u8ff0\u3002<\/span><\/section>\n
\u8d44\u6599\u6765\u6e90\uff1a<\/span><\/section>\n
https:\/\/zh.wikipedia.org\/wiki\/%E9%87%8D%E6%95%B4%E5%8C%96%E7%BE%A4<\/span><\/span><\/section>\n<\/blockquote>\n
\n
\u8bd1\u6ce82\uff1a<\/span><\/section>\n
\u4e09\u89d2\u6676\u683c\u4e0a\u7684\u6e17\u6d41\u6a21\u578b\uff08percolation models on a triangular lattice\uff09\uff1a\u4e09\u89d2\u683c\u70b9\u4e0a\u7684\u70b9\u6e17\u6d41\u662f\u5c11\u6570\u51e0\u4e2a\u7cbe\u786e\u89e3\u7684\u7edf\u8ba1\u7cfb\u7edf\u4e4b\u4e00\u3002\u4ece\u968f\u673a\u653e\u7f6e\u7684\u4e34\u754c\u6e17\u6d41\u96c6\u7fa4\u7684\u9ed1\u8272\u6216\u767d\u8272\u4f4d\u70b9\u5f00\u59cb\uff0c\u6211\u4eec\u968f\u673a\u91cd\u65b0\u5206\u914d\u6bcf\u4e2a\u6e17\u6d41\u96c6\u7fa4\u7684\u989c\u8272\uff0c\u5e76\u901a\u8fc7\u5408\u5e76\u76f8\u540c\u989c\u8272\u7684\u96c6\u7fa4\u83b7\u5f97\u7c97\u7c92\u5316\u6784\u578b\u3002\u7814\u7a76\u8868\u660e\uff0c\u5728\u70ed\u529b\u5b66\u6781\u9650\u4e0b\uff0c\u8fd9\u4e2a\u8fc7\u7a0b\u53ef\u4ee5\u65e0\u9650\u8fed\u4ee3\uff0c\u4ece\u800c\u5f97\u5230\u4e00\u4e2a\u8fed\u4ee3\u6e17\u6d41\u6a21\u578b\u3002\u6b64\u5916\uff0c\u6839\u636e\u81ea\u5339\u914d\u8bba\u8bc1\uff0c\u731c\u60f3\u6e17\u6d41\u96c6\u7fa4\u5728\u4efb\u4f55\u6709\u9650\u7684\u4ee3\u6570\u4e2d\u4ecd\u7136\u662f\u5206\u5f62\u7684\uff0c\u751a\u81f3\u53ef\u4ee5\u901a\u8fc7\u5e7f\u4e49\u8fc7\u7a0b\u53d6\u4efb\u610f\u5b9e\u6570\u3002\u8fdb\u884c\u4e86\u5927\u91cf\u7684\u6a21\u62df\uff0c\u5e76\u4ece\u4ee3\u6570\u76f8\u5173\u7684\u5206\u5f62\u7ef4\u5ea6\u4e2d\u63ed\u793a\u4e86\u4e00\u4e2a\u8fde\u7eed\u7684\u4ee5\u524d\u672a\u77e5\u7684\u666e\u9002\u6027\u3002\u6700\u540e\uff0c\u901a\u8fc7\u7c7b\u4f3c\u7684\u8fc7\u7a0b\uff0c\u5b9a\u4e49\u4e86\u4e34\u754c\u952e\u6e17\u6d41\u96c6\u7fa4\u7684\u8fed\u4ee3\u6e17\u6d41\u3002\u53c2\u89c1\uff1a<\/span><\/section>\n
Iterative Percolation on Triangular Lattice – arXiv.org. https:\/\/arxiv.org\/pdf\/2305.14021.pdf.<\/span><\/span><\/section>\n<\/blockquote>\n


<\/h2>\n


<\/p>\n

\n
\n
\n
\n
\n

<\/section>\n

<\/section>\n
\n
<\/svg><\/section>\n<\/section>\n<\/section>\n
\n

4. \u79bb\u6563\u8c31\u3001\u968f\u673a\u77e9\u9635\u6a21\u578b\u3001\u9ece\u66fc\u731c\u60f3<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


<\/p>\n

\u5728\u6211\u4eec\u5bf9\u666e\u9002\u6027\u89c4\u5f8b\u7684\u63a2\u7d22\u5373\u5c06\u7ed3\u675f\u4e4b\u9645\uff0c\u6211\u60f3\u8003\u8651\u4e00\u4e2a\u66f4\u8d34\u8fd1\u6211\u7814\u7a76\u9886\u57df\u7684\u73b0\u8c61\u793a\u4f8b\u3002\u5728\u6b64\uff0c\u6211\u4eec\u5173\u6ce8\u7684\u4e0d\u662f\u5355\u4e00\u7684\u6570\u503c\u7edf\u8ba1<\/span>\uff08\u5982\u5728\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\u4e2d\u7684\u60c5\u51b5\uff09<\/span>\uff0c\u4e5f\u4e0d\u662f\u5f62\u72b6<\/span>\uff08\u5982\u5728\u76f8\u53d8\u4e2d\u7684\u60c5\u51b5\uff09<\/span>\uff0c\u800c\u662f\u4e00\u4e2a\u79bb\u6563\u8c31\uff1a\u8fd9\u662f\u6cbf\u76f4\u7ebf\u5206\u5e03\u7684\u4e00\u7cfb\u5217\u70b9<\/span>\uff08\u6216\u6570\u503c\u3001\u9891\u7387\u3001\u80fd\u7ea7\uff09<\/span>\u3002<\/span><\/section>\n

<\/section>\n
\u6700\u5e38\u89c1\u7684\u79bb\u6563\u8c31\u4f8b\u5b50\u6216\u8bb8\u662f\u5f53\u5730\u5e7f\u64ad\u7535\u53f0\u53d1\u5c04\u7684\u65e0\u7ebf\u7535\u9891\u7387\uff1b\u5b83\u4eec\u6784\u6210\u4e86\u7535\u78c1\u5149\u8c31\u4e2d\u65e0\u7ebf\u7535\u8303\u56f4\u5185\u7684\u4e00\u4e2a\u9891\u7387\u5e8f\u5217\uff0c\u4eba\u4eec\u53ef\u4ee5\u901a\u8fc7\u65cb\u8f6c\u6536\u97f3\u673a\u7684\u8c03\u9891\u94ae\u6765\u9009\u62e9\u63a5\u6536\u3002\u8fd9\u4e9b\u9891\u7387\u4e0d\u662f\u7b49\u8ddd\u6392\u5217\u7684\uff0c\u4f46\u4e3a\u4e86\u51cf\u5c11\u76f8\u4e92\u5e72\u6270\uff0c\u901a\u5e38\u4f1a\u52aa\u529b\u786e\u4fdd\u5404\u4e2a\u5e7f\u64ad\u7535\u53f0\u7684\u9891\u7387\u4e4b\u95f4\u6709\u4e00\u5b9a\u7684\u5206\u9694\u3002<\/span><\/section>\n

<\/section>\n
\u53e6\u4e00\u4e2a\u719f\u77e5\u7684\u79bb\u6563\u8c31\u4f8b\u5b50\u662f\u539f\u5b50\u5143\u7d20\u7684\u5149\u8c31\u7ebf\uff0c\u6839\u636e\u91cf\u5b50\u529b\u5b66\u5b9a\u5f8b<\/span> (laws of quantum mechanics)<\/span>\uff0c\u5b83\u6765\u81ea\u4e8e\u539f\u5b50\u58f3\u5c42\u4e2d\u7684\u7535\u5b50\u80fd\u591f\u5438\u6536\u548c\u53d1\u5c04\u7684\u9891\u7387\u3002\u5f53\u8fd9\u4e9b\u9891\u7387\u4f4d\u4e8e\u7535\u78c1\u8c31\u7684\u53ef\u89c1\u5149\u90e8\u5206\u65f6\uff0c\u5b83\u4eec\u8d4b\u4e88\u5404\u4e2a\u5143\u7d20\u72ec\u7279\u7684\u989c\u8272\uff0c\u4ece\u6c29\u6c14\u7684\u84dd\u5149<\/span>\uff08\u4ee4\u4eba\u56f0\u60d1\u7684\u662f\uff0c\u6c29\u6c14\u901a\u5e38\u7528\u4e8e\u9713\u8679\u706f\uff0c\u56e0\u4e3a\u7eaf\u6c16\u53d1\u51fa\u6a59\u7ea2\u8272\u5149\uff09<\/span>\u5230\u94a0\u7684\u9ec4\u5149\u3002\u5bf9\u4e8e\u8bf8\u5982\u6c22\u8fd9\u6837\u7684\u7b80\u5355\u5143\u7d20\uff0c\u91cf\u5b50\u529b\u5b66\u65b9\u7a0b\u53ef\u4ee5\u76f8\u5bf9\u5bb9\u6613\u5730\u89e3\u51b3\uff0c\u5149\u8c31\u7ebf\u9075\u5faa\u4e00\u79cd\u89c4\u5f8b\u7684\u6a21\u5f0f\uff1b\u4f46\u5bf9\u4e8e\u8f83\u91cd\u7684\u5143\u7d20\uff0c\u5149\u8c31\u7ebf\u53d8\u5f97\u76f8\u5f53\u590d\u6742\uff0c\u4ec5\u4ec5\u4f9d\u9760\u57fa\u7840\u539f\u7406\u5e76\u4e0d\u5bb9\u6613\u63a8\u5bfc\u51fa\u6765\u3002<\/span><\/section>\n

<\/span><\/section>\n
\n
\u8bd1\u6ce8\uff1a<\/span><\/section>\n
\u5149\u8c31\u7ebf\u662f\u5f53\u539f\u5b50\u4e2d\u7684\u7535\u5b50\u5438\u6536\u6216\u53d1\u5c04\u80fd\u91cf\u65f6\u5f62\u6210\u7684\uff0c\u5bfc\u81f4\u5b83\u4eec\u5728\u4e0d\u540c\u80fd\u7ea7\u6216\u8f68\u9053\u4e4b\u95f4\u79fb\u52a8\u3002\u539f\u5b50\u7684\u80fd\u7ea7\u662f\u91cf\u5b50\u5316\u7684\uff0c\u610f\u5473\u7740\u53ea\u6709\u7279\u5b9a\u7684\u79bb\u6563\u80fd\u7ea7\u662f\u5141\u8bb8\u7684\u3002\u8fd9\u5bfc\u81f4\u5728\u4e0e\u5141\u8bb8\u80fd\u7ea7\u4e4b\u95f4\u7684\u80fd\u91cf\u5dee\u5bf9\u5e94\u7684\u7279\u5b9a\u6ce2\u957f\u5904\u5f62\u6210\u5149\u8c31\u7ebf\u3002\u4f8b\u5982\uff0c\u5728\u6c22\u7684\u60c5\u51b5\u4e0b\uff0c\u5f53\u4e00\u675f\u767d\u5149\uff08\u7531\u6240\u6709\u53ef\u89c1\u6ce2\u957f\u7684\u5149\u5b50\u7ec4\u6210\uff09\u901a\u8fc7\u6c22\u539f\u5b50\u7684\u6c14\u4f53\u65f6\uff0c\u53ea\u6709\u5177\u6709\u7279\u5b9a\u80fd\u91cf\u7684\u5149\u5b50\u53ef\u4ee5\u88ab\u6c22\u539f\u5b50\u5438\u6536\u3002\u8fd9\u4e9b\u5149\u5b50\u5bf9\u5e94\u4e8e\u6c22\u539f\u5b50\u7684\u5141\u8bb8\u80fd\u7ea7\u4e4b\u95f4\u7684\u80fd\u91cf\u5dee\u3002\u56e0\u6b64\uff0c\u6c22\u539f\u5b50\u53ea\u5728\u7279\u5b9a\u6ce2\u957f\u5904\u5438\u6536\u5149\uff0c\u5e76\u5728\u5149\u8c31\u4e2d\u4ea7\u751f\u76f8\u5e94\u7684\u6697\u7ebf\u3002\u7c7b\u4f3c\u5730\uff0c\u5f53\u6c22\u539f\u5b50\u4e2d\u7684\u7535\u5b50\u4ece\u8f83\u9ad8\u80fd\u7ea7\u5411\u8f83\u4f4e\u80fd\u7ea7\u79fb\u52a8\u65f6\uff0c\u5b83\u4eec\u4f1a\u53d1\u5c04\u80fd\u91cf\u4e0e\u4e24\u4e2a\u80fd\u7ea7\u4e4b\u95f4\u7684\u80fd\u91cf\u5dee\u76f8\u5bf9\u5e94\u7684\u5149\u5b50\u3002\u8fd9\u5bfc\u81f4\u5728\u7279\u5b9a\u6ce2\u957f\u5904\u5f62\u6210\u660e\u4eae\u7684\u53d1\u5c04\u7ebf\u3002\u5149\u8c31\u7ebf\u4e2d\u89c2\u5bdf\u5230\u7684\u89c4\u5f8b\u6a21\u5f0f\u662f\u7531\u4e8e\u539f\u5b50\u80fd\u7ea7\u7684\u91cf\u5b50\u5316\u3002\u80fd\u7ea7\u9075\u5faa\u4e00\u79cd\u89c4\u5f8b\u6a21\u5f0f\uff0c\u56e0\u6b64\u7531\u8fd9\u4e9b\u80fd\u7ea7\u4e4b\u95f4\u7684\u8dc3\u8fc1\u5f62\u6210\u7684\u5149\u8c31\u7ebf\u4e5f\u9075\u5faa\u4e00\u79cd\u89c4\u5f8b\u6a21\u5f0f\u3002\u8fd9\u79cd\u89c4\u5f8b\u6a21\u5f0f\u53ef\u4ee5\u7528\u4e8e\u8bc6\u522b\u5143\u7d20\u5e76\u786e\u5b9a\u5b83\u4eec\u7684\u6027\u8d28\u3002\u4f8b\u5982\uff0c\u5929\u6587\u5b66\u5bb6\u4f7f\u7528\u5149\u8c31\u7ebf\u6765\u786e\u5b9a\u6052\u661f\u548c\u5176\u4ed6\u5929\u4f53\u7684\u7ec4\u6210\u3002<\/span><\/section>\n
\u53c2\u8003\u6765\u6e90\uff1a<\/span><\/section>\n
\uff081\uff09Formation of Spectral Lines  <\/span>https:\/\/openstax.org\/books\/astronomy-2e\/pages\/5-5-formation-of-spectral-lines<\/span><\/section>\n
\uff082\uff09Absorption spectrum (emission spectrum lines) <\/span> https:\/\/www.khanacademy.org\/science\/physical-chemistry-essentials\/x98cdf762ed888601:structure-of-atom\/x98cdf762ed888601:bohr-s-model-of-hydrogen-atom\/a\/absorptionemission-lines<\/span><\/section>\n<\/blockquote>\n

<\/section>\n
\u4e00\u4e2a\u7c7b\u4f3c\u4f46\u4e0d\u5e38\u89c1\u7684\u8c31\u7684\u4f8b\u5b50\u6765\u81ea\u539f\u5b50\u6838<\/span>\uff08\u5982\u94c0-238\u6838\uff09<\/span>\u5bf9\u4e2d\u5b50\u7684\u6563\u5c04\u3002\u7ed3\u5408\u91cf\u5b50\u529b\u5b66\u5b9a\u5f8b\u4ee5\u53ca\u539f\u5b50\u6838\u7684\u7535\u78c1\u529b\u548c\u6838\u529b\u4f5c\u7528\uff0c\u9884\u6d4b\u5728\u67d0\u4e9b\u80fd\u91cf\u4e0b\u4e2d\u5b50\u53ef\u4ee5\u51e0\u4e4e\u65e0\u963b\u788d\u5730\u7a7f\u900f\u539f\u5b50\u6838\uff0c\u5728\u5176\u4ed6\u80fd\u91cf\u4e0b\u5219\u88ab\u539f\u5b50\u6838\u53cd\u5f39\uff0c\u8fd9\u4e9b\u7279\u6b8a\u7684\u80fd\u91cf\u70b9\u79f0\u4e3a\u6563\u5c04\u5171\u632f\u70b9<\/strong>\u3002\u56e0\u4e3a\u8fd9\u4e9b\u5927\u578b\u539f\u5b50\u6838\u7684\u5185\u90e8\u7ed3\u6784\u590d\u6742\u5230\u65e0\u6cd5\u4ece\u7406\u8bba\u4e0a\u6216\u901a\u8fc7\u6570\u503c\u8ba1\u7b97\u6765\u9884\u6d4b\u8fd9\u4e9b\u5171\u632f\u70b9\uff0c\u6211\u4eec\u53ea\u80fd\u4f9d\u9760\u5b9e\u9a8c\u6570\u636e\u6765\u8fdb\u884c\u7814\u7a76\u3002<\/span><\/section>\n

<\/section>\n
\u8fd9\u4e9b\u5171\u632f\u5177\u6709\u6709\u8da3\u7684\u5206\u5e03\u7279\u5f81\uff1b\u5b83\u4eec\u5e76\u4e0d\u5f7c\u6b64\u72ec\u7acb\uff0c\u800c\u662f\u4f3c\u4e4e\u9075\u5faa\u4e00\u79cd\u7cbe\u786e\u7684\u6392\u65a5\u89c4\u5f8b\uff0c\u4f7f\u5f97\u4e24\u4e2a\u76f8\u90bb\u7684\u5171\u632f\u4e0d\u592a\u53ef\u80fd\u5f7c\u6b64\u9760\u8fd1\uff0c\u6709\u70b9\u7c7b\u4f3c\u4e8e\u65e0\u7ebf\u7535\u53f0\u9891\u7387\u503e\u5411\u4e8e\u907f\u514d\u5f7c\u6b64\u9760\u8fd1\uff0c\u53ea\u662f\u524d\u8005\u73b0\u8c61\u6e90\u81ea\u81ea\u7136\u5b9a\u5f8b\uff0c\u800c\u975e\u653f\u5e9c\u5bf9\u9891\u8c31\u7684\u8c03\u63a7\u3002\u572820\u4e16\u7eaa50\u5e74\u4ee3\uff0c\u8457\u540d\u7269\u7406\u5b66\u5bb6\u548c\u8bfa\u8d1d\u5c14\u5956\u5f97\u4e3b\u5c24\u91d1\u00b7\u7ef4\u683c\u7eb3<\/span>\uff08Eugene Wigner\uff09<\/span>\u7814\u7a76\u4e86\u8fd9\u4e9b\u5171\u632f\u7edf\u8ba1\u6570\u636e\uff0c\u5e76\u63d0\u51fa\u4e86\u4e00\u4e2a\u975e\u51e1\u7684\u6570\u5b66\u6a21\u578b\u6765\u89e3\u91ca\u5b83\u4eec\uff0c\u5c31\u662f\u6211\u4eec\u73b0\u5728\u6240\u79f0\u7684\u968f\u673a\u77e9\u9635\u6a21\u578b<\/strong><\/span>\uff08random matrix model\uff09<\/span>\u3002\u8fd9\u4e9b\u6a21\u578b\u7cbe\u786e\u7684\u6570\u5b66\u7ec6\u8282\u592a\u8fc7\u6280\u672f\u6027\uff0c\u5728\u6b64\u4e0d\u4fbf\u63cf\u8ff0\u3002\u4f46\u603b\u7684\u6765\u8bf4\uff0c\u53ef\u4ee5\u5c06\u8fd9\u6837\u7684\u6a21\u578b\u770b\u4f5c\u662f\u4e00\u4e2a\u5927\u91cf<\/strong>\u8d28\u91cf<\/strong>\u7684\u96c6\u5408\uff0c\u6240\u6709<\/strong>\u8d28\u91cf<\/strong>\u90fd\u901a\u8fc7\u5404\u79cd\u968f\u673a\u9009\u62e9\u7684\u3001\u4e0d\u540c\u5f3a\u5ea6\u7684\u5f39\u7c27\u8fde\u63a5\u5728\u4e00\u8d77\u3002<\/strong>\u8fd9\u6837\u4e00\u4e2a\u673a\u68b0\u7cfb\u7edf\u5c06\u5728\u4e00\u5b9a\u7684\u9891\u7387\u4e0b\u632f\u8361\uff08\u6216\u5171\u632f\uff09<\/strong>\uff1b\u7ef4\u683c\u7eb3\u5047\u8bbe\u8ba4\u4e3a\uff0c\u5927\u578b\u539f\u5b50\u6838\u7684\u5171\u632f\u5e94\u8be5\u7c7b\u4f3c\u4e8e\u968f\u673a\u77e9\u9635\u6a21\u578b\u7684\u5171\u632f\u3002\u7279\u522b\u5730\uff0c\u5b83\u4eec\u5e94\u5448\u73b0\u76f8\u540c\u7684\u6392\u65a5\u6548\u5e94\u3002\u56e0\u4e3a\u53ef\u4ee5\u4e25\u683c\u8bc1\u660e\u968f\u673a\u77e9\u9635\u6a21\u578b\u7684\u9891\u7387\u6392\u65a5\uff0c\u6240\u4ee5\u53ef\u4ee5\u5bf9\u6838\u5171\u632f\u5b9e\u9a8c\u89c2\u5bdf\u5230\u7684\u76f8\u540c\u73b0\u8c61\u63d0\u4f9b\u542f\u53d1\u5f0f\u7684\u89e3\u91ca\u3002<\/span><\/section>\n

<\/span><\/section>\n
\n
\u8bd1\u6ce8\uff1a<\/span><\/section>\n
\u968f\u673a\u77e9\u9635\u7406\u8bba\uff08RMT\uff09\u5229\u7528\u7edf\u8ba1\u529b\u5b66\u7684\u539f\u7406\u6765\u6a21\u62df\u591a\u4e2a\u6570\u5b66\u9886\u57df\u4e2d\u590d\u6742\u7cfb\u7edf\u7684\u4ea4\u4e92\u4f5c\u7528\u3002\u5b83\u6700\u521d\u88ab\u7528\u4e8e\u6a21\u62df\u91cd\u539f\u5b50\u7684\u6838\uff0c\u540e\u6765\u88ab\u7528\u4e8e\u4f30\u8ba1\u5927\u91cf\u7edf\u8ba1\u6837\u672c\u4e2d\u7684\u534f\u65b9\u5dee\uff0c\u5e76\u9884\u6d4b\u8457\u540d\u7684\u9ece<\/span>\u66fc\u03b6<\/span>\u51fd\u6570<\/span>\u96f6\u70b9\u7684\u5206\u5e03\u3002\u66f4\u73b0\u4ee3\u7684\u5e94\u7528\u5305\u62ec\u7406\u8bba\u795e\u7ecf\u79d1\u5b66\u548c\u6700\u4f18\u63a7\u5236\u3002<\/span><\/section>\n
\u968f\u673a\u77e9\u9635\uff0c\u987e\u540d\u601d\u4e49\uff0c\u968f\u673a\u77e9\u9635\u662f\u4efb\u610f\u5177\u6709\u968f\u673a\u5143\u7d20\u7684\u77e9\u9635\uff0c\u5176\u5143\u7d20\u4e3a\u975e\u8d1f\u5b9e\u6570\uff0c\u4e14\u884c\u548c\u6216\u5217\u548c\u4e3a1\u3002\u5982\u679c\u884c\u548c\u4e3a1\uff0c\u5219\u79f0\u4e3a\u884c\u968f\u673a\u77e9\u9635\uff1b\u5982\u679c\u5217\u548c\u4e3a1\uff0c\u5219\u79f0\u4e3a\u5217\u968f\u673a\u77e9\u9635\uff1b\u5982\u679c\u884c\u548c\u548c\u5217\u548c\u90fd\u4e3a1\uff0c\u5219\u79f0\u4e3a\u53cc\u968f\u673a\u77e9\u9635\u3002\u521b\u5efa\u968f\u673a\u77e9\u9635\u7684\u4e00\u4e2a\u7b80\u5355\u65b9\u6cd5\u662f\u521b\u5efa\u4e00\u4e2aN \u00d7 N\u77e9\u9635\uff0c\u5176\u4e2d\u5143\u7d20\u6765\u81eaN(0,1)\u5206\u5e03\u3002\u7136\u800c\uff0c\u8fd9\u4e2a\u77e9\u9635\u4f1a\u6709\u590d\u6570\u548c\u91cd\u590d\u7684\u7279\u5f81\u503c\u3002\u4e00\u822c\u800c\u8a00\uff0c\u5b9e\u7279\u5f81\u503c\u624d\u4f1a\u6709\u610f\u4e49\uff0c\u7279\u522b\u662f\u5982\u679c\u6070\u597d\u6709N\u4e2a\u7279\u5f81\u503c\u3002\u56e0\u6b64\uff0c\u5982\u679c\u7814\u7a76\u9650\u5236\u5728\u5bf9\u79f0\u77e9\u9635\u7684\u60c5\u51b5\uff0c\u5c06\u4ea7\u751fN\u4e2a\u5b9e\u7279\u5f81\u503c\u3002\u8fd9\u4e9b\u77e9\u9635\u79f0\u4e3a\u9ad8\u65af\u6b63\u4ea4\uff08GOE\uff09\u4e2d\u7684\u6837\u672c\uff0c\u4e5f\u79f0\u4e3aGOE\u77e9\u9635\u3002<\/span><\/section>\n<\/blockquote>\n

<\/section>\n
\u5f53\u7136\uff0c\u539f\u5b50\u6838\u5b9e\u9645\u4e0a\u5e76\u4e0d\u50cf\u4e00\u4e2a\u5927\u578b\u7684\u8d28\u91cf\u548c\u5f39\u7c27\u7cfb\u7edf<\/span>\uff08\u9664\u4e86\u5176\u5b83\u56e0\u7d20\u5916\uff0c\u5b83\u53d7\u91cf\u5b50\u529b\u5b66\u800c\u975e\u7ecf\u5178\u529b\u5b66\u7684\u5b9a\u5f8b\u652f\u914d\uff09<\/span>\u3002\u76f8\u53cd\uff0c\u6b63\u5982\u6211\u4eec\u540e\u6765\u53d1\u73b0\u7684\uff0c\u7ef4\u683c\u7eb3\u7684\u5047\u8bbe\u662f\u4e00\u79cd\u666e\u9002\u6027\u89c4\u5f8b\u7684\u4f53\u73b0\uff0c\u5b83\u652f\u914d\u7740\u8bb8\u591a\u7c7b\u578b\u7684\u5149\u8c31\u7ebf\uff0c\u5305\u62ec\u90a3\u4e9b\u4e0e\u539f\u5b50\u6838\u6216\u968f\u673a\u77e9\u9635\u6a21\u578b\u770b\u4f3c\u6ca1\u6709\u592a\u591a\u5171\u540c\u70b9\u7684\u5149\u8c31\u7ebf\u3002\u4f8b\u5982\uff0c\u5728\u58a8\u897f\u54e5\u5e93\u57c3\u5c14\u7eb3\u74e6\u5361\u7684\u4e00\u4e2a\u516c\u4ea4\u8f66\u7ad9\uff0c\u4eba\u4eec\u53d1\u73b0\u516c\u4ea4\u8f66\u4e4b\u95f4\u7684\u7b49\u5f85\u65f6\u95f4\u5b58\u5728\u76f8\u540c\u7684\u95f4\u8ddd\u5206\u5e03<\/span>\uff08\u5c3d\u7ba1\u5bf9\u4e8e\u4e3a\u4ec0\u4e48\u8fd9\u79cd\u5206\u5e03\u4f1a\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\u4f1a\u51fa\u73b0\uff0c\u76ee\u524d\u5c1a\u65e0\u4ee4\u4eba\u4fe1\u670d\u7684\u89e3\u91ca\uff09<\/span>\u3002<\/span><\/section>\n

<\/section>\n
\u4e5f\u8bb8\u5bf9\u8fd9\u4e9b\u666e\u9002\u6027\u89c4\u5f8b\u6700\u51fa\u4eba\u610f\u6599\u7684\u8bc1\u660e\u6765\u81ea\u4e8e\u6570\u8bba\u8fd9\u4e00\u5b8c\u5168\u4e0d\u76f8\u5173\u7684\u9886\u57df\uff0c\u5c24\u5176\u662f\u8d28\u6570\u5206\u5e03\u2014\u2014\u59822\u30013\u30015\u30017\u300111\u7b49\uff0c\u5b83\u4eec\u662f\u5927\u4e8e1\u4e14\u4e0d\u80fd\u88ab\u5206\u89e3\u6210\u66f4\u5c0f\u56e0\u5b50\u7684\u81ea\u7136\u6570\u3002\u8d28\u6570\u5728\u6574\u6570\u4e2d\u7684\u5206\u5e03\u662f\u65e0\u89c4\u5219\u7684\uff1b\u7136\u800c\uff0c\u5982\u679c\u8fdb\u884c\u8fd9\u79cd\u5206\u5e03\u7684\u8c31\u5206\u6790\uff0c\u53ef\u4ee5\u53d1\u73b0\u5206\u5e03\u4e2d\u5b58\u5728\u67d0\u4e9b\u957f\u671f\u632f\u8361<\/span>\uff08\u6709\u65f6\u79f0\u4f5c\u8d28\u6570\u7684\u4e50\u66f2\uff09<\/span>\uff0c\u5176\u9891\u7387\u7531\u4e00\u4e32\u590d\u6570\u5e8f\u5217\u63cf\u8ff0\uff0c\u5373\u6240\u8c13\u7684\u9ece\u66fc \u03b6 \u51fd\u6570\u7684\u975e\u5e73\u51e1\u96f6\u70b9\uff0c\u5b83\u57281859\u5e74\u9996\u6b21\u7531\u4f2f\u6069\u54c8\u5fb7\u00b7\u9ece\u66fc<\/span>\uff08Bernhard Riemann\uff09<\/span>\u7814\u7a76\u3002<\/span>\uff08\u5bf9\u8fd9\u91cc\u7684\u8ba8\u8bba\uff0c\u9ece\u66fc \u03b6 \u51fd\u6570\u7a76\u7adf\u662f\u4ec0\u4e48\u5e76\u6ca1\u6709\u90a3\u4e48\u91cd\u8981\u3002\uff09<\/span><\/section>\n

<\/span><\/section>\n
\n
\u8bd1\u6ce8\uff1a<\/span><\/section>\n
\u9ece\u66fc\u03b6\u51fd\u6570\u662f\u4e00\u4e2a\u6570\u5b66\u51fd\u6570\uff0c\u7531\u5fb7\u56fd\u6570\u5b66\u5bb6\u4f2f\u6069\u54c8\u5fb7\u00b7\u9ece\u66fc\u57281859\u5e74\u9996\u6b21\u7814\u7a76\u3002\u5b83\u662f\u4e00\u4e2a\u590d\u53d8\u51fd\u6570\uff0c\u5b9a\u4e49\u5728\u590d\u5e73\u9762\u4e0a\u7684\u6240\u6709\u590d\u6570\uff08\u9664\u4e861\u4ee5\u5916\u7684\u6b63\u6574\u6570\uff09\u3002\u9ece\u66fc\u03b6\u51fd\u6570\u5728\u6570\u8bba\u4e2d\u5177\u6709\u91cd\u8981\u7684\u4f5c\u7528\uff0c\u5b83\u4e0e\u8d28\u6570\u7684\u5206\u5e03\u548c\u7d20\u6570\u5b9a\u7406\u4e4b\u95f4\u6709\u5bc6\u5207\u7684\u5173\u8054\u3002\u9ece\u66fc\u731c\u60f3\u662f\u5173\u4e8e\u9ece\u66fc\u03b6\u51fd\u6570\u96f6\u70b9\u5206\u5e03\u7684\u4e00\u4e2a\u91cd\u8981\u5047\u8bbe\uff0c\u5b83\u8ba4\u4e3a\u8fd9\u4e9b\u96f6\u70b9\u90fd\u4f4d\u4e8e\u590d\u5e73\u9762\u4e0a\u7684\u4e00\u6761\u76f4\u7ebf\u4e0a\u3002\u5c3d\u7ba1\u9ece\u66fc\u731c\u60f3\u5c1a\u672a\u88ab\u8bc1\u660e\uff0c\u4f46\u5b83\u5bf9\u4e8e\u7406\u89e3\u8d28\u6570\u7684\u5206\u5e03\u548c\u6570\u8bba\u7684\u8bb8\u591a\u91cd\u8981\u7ed3\u679c\u5177\u6709\u91cd\u8981\u5f71\u54cd\u3002<\/span><\/section>\n<\/blockquote>\n

<\/section>\n
\u539f\u5219\u4e0a\uff0c\u8fd9\u4e9b\u6570\u5b57\u544a\u8bc9\u6211\u4eec\u5173\u4e8e\u8d28\u6570\u7684\u4e00\u5207\u6211\u4eec\u5e0c\u671b\u77e5\u9053\u7684\u4fe1\u606f\u3002\u6570\u8bba\u4e2d\u6700\u8457\u540d\u548c\u91cd\u8981\u7684\u95ee\u9898\u4e4b\u4e00\u662f\u9ece\u66fc\u5047\u8bbe\uff0c\u5b83\u65ad\u8a00\u8fd9\u4e9b\u6570\u5b57\u90fd\u4f4d\u4e8e\u590d\u5e73\u9762\u4e0a\u7684\u4e00\u6761\u76f4\u7ebf\u4e0a\u3002\u8be5\u731c\u60f3\u5728\u6570\u8bba\u9886\u57df\u6709\u7740\u5e7f\u6cdb\u7684\u5f71\u54cd\uff0c\u7279\u522b\u662f\u7ed9\u51fa\u4e86\u8bb8\u591a\u5173\u4e8e\u8d28\u6570\u7684\u91cd\u8981\u63a8\u8bba\u3002\u7136\u800c\uff0c\u5373\u4f7f\u662f\u5f3a\u5927\u7684\u9ece\u66fc\u5047\u8bbe\u4e5f\u6ca1\u6709\u89e3\u51b3\u8fd9\u4e2a\u4e3b\u9898\u7684\u4e00\u5207\u95ee\u9898\uff0c\u90e8\u5206\u539f\u56e0\u662f\u5b83\u5e76\u6ca1\u6709\u76f4\u63a5\u8bf4\u660e\u96f6\u70b9\u5728\u8fd9\u6761\u76f4\u7ebf\u4e0a\u7684\u5206\u5e03\u60c5\u51b5\u3002\u4f46\u662f\uff0c\u6709\u6781\u5f3a\u7684\u6570\u503c\u8bc1\u636e\u8868\u660e\uff0c\u8fd9\u4e9b\u96f6\u70b9\u9075\u5faa\u4e0e\u4e2d\u5b50\u6563\u5c04\u548c\u5176\u4ed6\u7cfb\u7edf\u4e2d\u89c2\u5bdf\u5230\u7684\u540c\u6837\u7684\u7cbe\u786e\u5b9a\u5f8b\uff1b\u7279\u522b\u5730\uff0c\u96f6\u70b9\u7684\u5206\u5e03\u65b9\u5f0f\u4f7f\u5f97\u76f8\u90bb\u7684\u4e24\u4e2a\u96f6\u70b9\u4e4b\u95f4\u4f3c\u4e4e\u5f7c\u6b64\u201c\u6392\u65a5\u201d\uff0c\u8fd9\u4e00\u73b0\u8c61\u5df2\u7ecf\u88ab\u89c2\u5bdf\u5230\uff0c\u4e0e\u968f\u673a\u77e9\u9635\u7406\u8bba\u9884\u6d4b\u60ca\u4eba\u5730\u76f8\u7b26\u3002\u8fd9\u4e2a\u5b9a\u5f8b\u7684\u6b63\u5f0f\u63cf\u8ff0\u79f0\u4e3a\u9ad8\u65af\u9149\u96c6<\/span>\uff08Gaussian Unitary Ensemble\uff0cGUE\uff09<\/span>\u5047\u8bbe\u3002<\/span>\uff08GUE\u662f\u968f\u673a\u77e9\u9635\u6a21\u578b\u7684\u4e00\u4e2a\u57fa\u672c\u4f8b\u5b50\u3002\uff09<\/span>\u50cf\u9ece\u66fc\u5047\u8bbe\u4e00\u6837\uff0c\u5b83\u76ee\u524d\u5c1a\u672a\u88ab\u8bc1\u660e\uff0c\u4f46\u5b83\u5bf9\u8d28\u6570\u5206\u5e03\u6709\u5f3a\u5927\u7684\u5f71\u54cd\u3002<\/span><\/section>\n
\n
\u8bd1\u6ce8\uff1a<\/span><\/section>\n
\u5728\u968f\u673a\u77e9\u9635\u7406\u8bba\u4e2d\uff0c\u5df2\u77e5\u9ece\u66fc\u03b6\u51fd\u6570\u7684\u96f6\u70b9\u5177\u6709\u4e00\u79cd\u88ab\u79f0\u4e3a\u8499\u54e5\u9a6c\u5229\u7684\u5bf9\u76f8\u5173\u731c\u60f3\u7684\u7279\u5b9a\u6027\u8d28\u3002\u8fd9\u4e2a\u731c\u60f3\u8868\u660e\uff0c\u8fd9\u4e9b\u96f6\u70b9\u5728\u76f8\u90bb\u7ea7\u522b\u4e4b\u95f4\u503e\u5411\u4e8e\u76f8\u4e92\u6392\u65a5\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u8fd9\u4e9b\u96f6\u70b9\u7684\u5206\u5e03\u65b9\u5f0f\u4f7f\u5f97\u76f8\u90bb\u7684\u4e24\u4e2a\u96f6\u70b9\u4e4b\u95f4\u5f88\u4e0d\u53ef\u80fd\u592a\u9760\u8fd1\u3002\u8fd9\u4e00\u73b0\u8c61\u5df2\u7ecf\u88ab\u89c2\u5bdf\u5230\u4e0e\u968f\u673a\u77e9\u9635\u7406\u8bba\u7684\u9884\u6d4b\u60ca\u4eba\u5730\u543b\u5408\u3002<\/span><\/section>\n
\u6765\u6e90\uff1a<\/span>https:\/\/www.ias.edu\/ideas\/2013\/primes-random-matrices<\/span><\/section>\n<\/blockquote>\n

<\/section>\n
1972\u5e74\u5728\u9ad8\u7b49\u7814\u7a76\u9662\uff0c\u9ad8\u65af\u9149\u96c6\u5408\u5047\u8bbe\u7684\u53d1\u73b0\u5efa\u7acb\u4e86\u8d28\u6570\u4e50\u66f2\u4e0e\u539f\u5b50\u6838\u80fd\u7ea7\u95f4\u7684\u8054\u7cfb\uff0c\u8fd9\u6210\u4e3a\u6570\u5b66\u754c\u7684\u4e00\u4e2a\u4f20\u5947\u6545\u4e8b\u3002\u6b64\u4f20\u5947\u6545\u4e8b\u6d89\u53ca\u6570\u5b66\u5bb6\u4f11\u00b7\u8499\u54e5\u9a6c\u5229<\/span>\uff08Hugh Montgomery\uff09<\/span>\u548c\u6770\u51fa\u7269\u7406\u5b66\u5bb6\u5f17\u91cc\u66fc\u00b7\u6234\u68ee<\/span>\uff08Freeman Dyson\uff09<\/span>\u4e4b\u95f4\u7684\u4e00\u6b21\u5076\u9047\u3002\u8499\u54e5\u9a6c\u5229\u5f53\u65f6\u6b63\u5728\u7814\u7a76\u9ece\u66fc\u03b6\u51fd\u6570\u96f6\u70b9\u7684\u5206\u5e03\u2014\u2014\u7279\u522b\u662f\u7814\u7a76\u8be5\u5206\u5e03\u76f8\u5173\u7684\u4e00\u79cd\u7edf\u8ba1\u91cf\uff0c\u5373\u6240\u8c13\u7684\u5bf9\u5173\u8054\u51fd\u6570<\/span>\uff08pair correlation function\uff09<\/span>\u3002\u6570\u5b66\u5bb6\u517c\u8ba1\u7b97\u673a\u79d1\u5b66\u5bb6\u4e39\u00b7\u6d1b\u514b\u83ab\u5c14<\/span>\uff08Dan Rockmore\uff09<\/span>\u5728\u4ed6\u7684\u8457\u4f5c\u300a\u8ffd\u8e2a\u9ece\u66fc\u5047\u8bbe\u300b\u4e2d\u63cf\u8ff0\u4e86\u8fd9\u6b21\u4f1a\u9762\uff1a<\/span><\/section>\n

<\/section>\n
\u636e\u6234\u68ee\u56de\u5fc6\uff0c\u4ed6\u4e0e\u8499\u54e5\u9a6c\u5229\u5728\u7814\u7a76\u6240\u7684\u6258\u513f\u6240\u63a5\u9001\u5b69\u5b50\u65f6\u5076\u5c14\u76f8\u9047\uff0c\u4f46\u4e24\u4eba\u5e76\u672a\u6b63\u5f0f\u88ab\u4ecb\u7ecd\u8fc7\u3002\u5c3d\u7ba1\u6234\u68ee\u540d\u58f0\u663e\u8d6b\uff0c\u8499\u54e5\u9a6c\u5229\u5e76\u4e0d\u8ba4\u4e3a\u6709\u5fc5\u8981\u53bb\u8ba4\u8bc6\u4ed6\u3002\u636e\u79f0\uff0c\u5f53\u88ab\u9080\u8bf7\u559d\u8336\u65f6\uff0c\u8499\u54e5\u9a6c\u5229\u8bf4\uff1a\u201c\u6211\u4eec\u8981\u8c08\u4ec0\u4e48\u5462\uff1f\u201d\u5c3d\u7ba1\u5982\u6b64\uff0c\u8499\u54e5\u9a6c\u5229\u6700\u7ec8\u8fd8\u662f\u540c\u610f\u89c1\u9762\uff0c\u5f53\u88ab\u4ecb\u7ecd\u540e\uff0c\u8fd9\u4f4d\u548c\u5584\u7684\u7269\u7406\u5b66\u5bb6\u8be2\u95ee\u4e86\u5e74\u8f7b\u6570\u8bba\u5b66\u5bb6\u5173\u4e8e\u4ed6\u7684\u5de5\u4f5c\u3002\u8499\u54e5\u9a6c\u5229\u5f00\u59cb\u9610\u8ff0\u4ed6\u8fd1\u671f\u5173\u4e8e\u5bf9\u76f8\u5173\u6027<\/span>\uff08pair correlation\uff09<\/span>\u7684\u7814\u7a76\u6210\u679c\uff0c\u6234\u68ee\u6253\u65ad\u4ed6\u7684\u8bdd\uff0c\u63d0\u51fa\u4e86\u4e00\u4e2a\u95ee\u9898\uff0c\u5e76\u5199\u4e0b\u4e86\u4e00\u4e2a\u5177\u4f53\u7684\u6570\u5b66\u516c\u5f0f\u3002\u201c\u4f60\u5f97\u5230\u4e86\u8fd9\u4e2a\u5417\uff1f\u201d\u4ed6\u95ee\u9053\u3002\u8499\u54e5\u9a6c\u5229\u60ca\u8bb6\u4e4b\u4f59\u51e0\u4e4e\u6454\u5012\uff1a\u6234\u68ee\u7adf\u7136\u5199\u4e0b\u4e86\u5e26\u6709sinc\u51fd\u6570\u7684\u5bf9\u5173\u8054\u51fd\u6570\u2026\u2026\u5c3d\u7ba1\u8499\u54e5\u9a6c\u5229\u662f\u901a\u8fc7\u6570\u8bba\u5bb6\u7684\u8def\u5f84\uff0c\u7814\u7a76\u5bf9\u5173\u8054\u51fd\u6570\u7684\u201c\u8d28\u6570\u753b\u50cf\u201d\uff0c\u800c\u6234\u68ee\u5374\u662f\u901a\u8fc7\u5bf9\u77e9\u9635\u6570\u5b66\u4e2d\u7684\u80fd\u7ea7\u7814\u7a76\u800c\u5f97\u51fa\u4e86\u8fd9\u4e00\u516c\u5f0f[2]\u3002<\/span><\/section>\n

<\/em><\/span><\/section>\n
\n
\u8bd1\u6ce8\uff1a<\/span><\/section>\n
\u4f11\u00b7\u8499\u54e5\u9a6c\u5229\uff08Hugh Montgomery\uff09\u662f\u4e00\u4f4d\u6570\u5b66\u5bb6\uff0c\u4ed6\u7814\u7a76\u4e86\u9ece\u66fc\u51fd\u6570\u7684\u96f6\u70b9\u5206\u5e03\uff0c\u7279\u522b\u662f\u4e0e\u8be5\u5206\u5e03\u76f8\u5173\u7684\u4e00\u9879\u7edf\u8ba1\u91cf\uff0c\u5373\u88ab\u79f0\u4e3a\u5bf9\u76f8\u5173\u51fd\u6570\u7684\u7edf\u8ba1\u91cf\u3002\u5f17\u91cc\u66fc\u00b7\u6234\u68ee\u662f\u4e00\u4f4d\u8457\u540d\u7684\u7269\u7406\u5b66\u5bb6\u548c\u6570\u5b66\u5bb6\uff0c\u4ee5\u4ed6\u5728\u91cf\u5b50\u573a\u8bba\u3001\u5929\u4f53\u7269\u7406\u5b66\u3001\u968f\u673a\u77e9\u9635\u3001\u91cf\u5b50\u529b\u5b66\u7684\u6570\u5b66\u5f62\u5f0f\u5316\u3001\u51dd\u805a\u6001\u7269\u7406\u5b66\u3001\u6838\u7269\u7406\u5b66\u548c\u5de5\u7a0b\u5b66\u65b9\u9762\u7684\u5de5\u4f5c\u800c\u95fb\u540d\u3002<\/span><\/section>\n
The History-Maker: Remembering Ambassador Montgomery – CIA. https:\/\/www.cia.gov\/stories\/story\/the-history-maker-remembering-ambassador-montgomery\/.<\/span><\/section>\n
Hugh Montgomery, 1st Viscount Montgomery – Wikipedia. https:\/\/en.wikipedia.org\/wiki\/HughMontgomery,1stViscountMontgomery.<\/span><\/section>\n

<\/section>\n
\u5bf9\u5173\u8054\u51fd\u6570\uff1a\u5206\u5e03\u51fd\u6570\u7684\u4e00\u4e2a\u91cd\u8981\u63a8\u5e7f\u662f\u5f84\u5411\u5206\u5e03\u51fd\u6570 (radial distribution function; RDF)\uff0c\u4e5f\u79f0\u4f5c\u6210\u5bf9\u5173\u8054\u51fd\u6570 (pair correlationfunction\uff09\uff0c\u662f\u7edf\u8ba1\u529b\u5b66\u4e2d\u7684\u4e00\u4e2a\u91cd\u8981\u6982\u5ff5\uff0c\u7528Q(r)\u8868\u793a\uff0c\u5176\u53cd\u6620\u7c92\u5b50\u5bc6\u5ea6\u5728\u7a7a\u95f4\u968f\u4e0e\u53c2\u8003\u7c92\u5b50\u8ddd\u79bb\u7684\u53d8\u5316\u800c\u53d8\u5316\u7684\u60c5\u51b5\uff0c\u901a\u5e38\u53ef\u4ee5\u7528\u6765\u7814\u7a76\u7269\u8d28\u7684\u6709\u5e8f\u6027\u6216\u8005\u7535\u5b50\u7684\u76f8\u5173\u6027\u3002\u901a\u4fd7\u6765\u8bb2\uff0c\u5f84\u5411\u5206\u5e03\u51fd\u6570\u6307\u5728\u67d0\u7ed9\u5b9a\u53c2\u8003\u7c92\u5b50\u5468\u56f4\u8ddd\u79bb\u5011\u5904\u627e\u5230\u53e6\u4e00\u4e2a\u7c92\u5b50\u7684\u6982\u7387\u9664\u4ee5\u6b64\u5904\u7c92\u5b50\u7684\u5bc6\u5ea6\u3002<\/span><\/section>\n
\u4e2d\u56fd\u767e\u79d1\u5168\u4e66: https:\/\/www.zgbk.com\/ecph\/words?SiteID=1&ID=228773<\/span><\/section>\n<\/blockquote>\n

<\/section>\n
\u8499\u54e5\u9a6c\u5229\u548c\u6234\u68ee\u7684\u5076\u7136\u53d1\u73b0\u2014\u2014\u5373\u63a7\u5236\u968f\u673a\u77e9\u9635\u548c\u539f\u5b50\u5149\u8c31\u7684\u540c\u4e00\u666e\u9002\u6027\u89c4\u5f8b\u4e5f\u9002\u7528\u4e8e\u03b6\u51fd\u6570\u2014\u2014\u5f97\u5230\u4e86\u5b89\u5fb7\u9c81\u00b7\u5965\u5fb7\u5229\u5179\u79d1<\/span>\uff08Andrew Odlyzko\uff09<\/span>\u81ea20\u4e16\u7eaa80\u5e74\u4ee3\u4ee5\u6765\u8ba1\u7b97\u5de5\u4f5c\u7684\u5927\u91cf\u6570\u503c\u652f\u6301\u3002\u4f46\u8fd9\u4e00\u53d1\u73b0\u5e76\u4e0d\u610f\u5473\u7740\u8d28\u6570\u672c\u8eab\u53d7\u6838\u80fd\u529b\u9a71\u52a8\uff0c\u4e5f\u4e0d\u8868\u660e\u539f\u5b50\u7269\u7406\u5b9e\u8d28\u4e0a\u7531\u8d28\u6570\u63a8\u52a8\uff1b\u76f8\u53cd\uff0c\u5b83\u8bc1\u660e\u4e86\u8c31\u7684<\/strong>\u8fd9\u4e00\u89c4\u5f8b<\/strong>\u975e\u5e38\u666e\u904d<\/strong>\uff0c\u5b83\u53ef\u80fd\u662f\u4f17\u591a\u4e0d\u540c\u8fc7\u7a0b\u7684\u81ea\u7136\u7ec8\u70b9\uff0c\u4e0d\u8bba\u8fd9\u4e9b\u8fc7\u7a0b\u6e90\u81ea\u6838\u7269\u7406\u5b66\u3001\u968f\u673a\u77e9\u9635\u6a21\u578b\u8fd8\u662f\u6570\u8bba\u3002<\/strong><\/span><\/section>\n

<\/section>\n

<\/p>\n

\u56fe4 . \u9ece\u66fc\u03b6\u51fd\u6570\u7684\u5341\u4ebf\u4e2a\u96f6\u70b9\u7684\u95f4\u8ddd\u5206\u5e03\uff0c\u4ee5\u53ca\u6765\u81ea\u968f\u673a\u77e9\u9635\u7406\u8bba\u7684\u76f8\u5e94\u9884\u6d4b\u3002\u56fe\u6e90\uff1aAndrew M. Odlyzko\uff0c\u300a\u9ece\u66fc\u03b6\u51fd\u6570\u7684\u7b2c1022\u4e2a\u96f6\u70b9\u300b\uff0c\u6536\u5f55\u4e8e\u300a\u52a8\u529b\u5b66\u3001\u8c31\u548c\u7b97\u672f\u03b6\u51fd\u6570\u300b\uff0c\u5f53\u4ee3\u6570\u5b66\u7cfb\u5217\uff0c\u7b2c290\u518c\uff0c\u7f16\u8f91Machiel van Frankenhuysen\u548cMichel L. Lapidus\uff08\u7f8e\u56fd\u6570\u5b66\u5b66\u4f1a\uff0c2001\u5e74\uff09\uff0c139-144\u9875\uff0chttp:\/\/www.dtc.umn.edu\/~odlyzko\/doc\/zeta.10to22.pdf\uff1b\u5728\u6b64\u83b7\u5f97Andrew Odlyzko\u7684\u8bb8\u53ef\u4f7f\u7528\u3002<\/span><\/section>\n

<\/section>\n
\u8fd9\u4e2a\u5b9a\u5f8b\u80cc\u540e\u7684\u786e\u5207\u673a\u5236\u5c1a\u672a\u5b8c\u5168\u63ed\u793a\u51fa\u6765\uff1b\u7279\u522b\u5730\uff0c\u6211\u4eec\u4ecd\u7136\u6ca1\u6709\u4e00\u4e2a\u4ee4\u4eba\u4fe1\u670d\u7684\u89e3\u91ca\uff0c\u66f4\u4e0d\u7528\u8bf4\u4e00\u4e2a\u4e25\u683c\u7684\u8bc1\u660e\u6765\u8bf4\u660e\u4e3a\u4ec0\u4e48 \u03b6 \u51fd\u6570\u7684\u96f6\u70b9\u7b26\u5408 GUE \u5047\u8bbe\u3002\u7136\u800c\uff0c\u73b0\u5728\u5df2\u7ecf\u6709\u4e86\u5927\u91cf\u7684\u4e25\u8c28\u7814\u7a76<\/span>\uff08\u5305\u62ec\u6211\u81ea\u5df1\u7684\u4e00\u4e9b\u5de5\u4f5c\uff0c\u4ee5\u53ca\u6700\u8fd1\u51e0\u5e74\u7684\u4e00\u4e9b\u91cd\u5927\u7a81\u7834\uff09<\/span>\uff0c\u5b83\u4eec\u663e\u793a\u4e86\u5404\u79cd\u5404\u6837\u7684\u968f\u673a\u77e9\u9635\u6a21\u578b<\/span>\uff08\u4e0d\u4ec5\u4ec5\u662f\u6700\u8457\u540d\u7684GUE\u6a21\u578b\uff09<\/span>\u90fd\u9075\u5b88\u76f8\u540c\u7684\u95f4\u8ddd\u5b9a\u5f8b\uff0c\u4e3a\u8fd9\u4e00\u5047\u8bbe\u7684\u666e\u9002\u6027\u63d0\u4f9b\u4e86\u652f\u6301\u3002\u76ee\u524d\uff0c\u8fd9\u4e9b\u5173\u4e8e\u666e\u9002\u6027\u7684\u8bba\u8bc1\u5c1a\u672a\u6269\u5c55\u5230\u6570\u8bba\u7684\u6216\u8005\u7269\u7406\u7684\u8bbe\u5b9a\u4e2d\uff0c\u4f46\u5b83\u4eec\u786e\u5b9e\u95f4\u63a5\u5730\u652f\u6301\u4e86\u8fd9\u4e00\u5b9a\u5f8b\u5728\u8fd9\u4e9b\u6848\u4f8b\u4e2d\u7684\u9002\u7528\u6027\u3002<\/span><\/section>\n

<\/section>\n
\u8fd9\u4e9b\u6700\u8fd1\u5de5\u4f5c\u4e2d\u4f7f\u7528\u7684\u8bba\u8bc1\u8fc7\u4e8e\u6280\u672f\u6027\uff0c\u4e0d\u4fbf\u5728\u6b64\u8be6\u8ff0\u3002\u4f46\u6211\u53ef\u4ee5\u63d0\u5230\u4e00\u4e2a\u5173\u952e\u601d\u60f3\uff0c\u5373\u6211\u548c\u540c\u4e8b Van Vu \u4ece Jarl Lindeberg 1922\u5e74\u5bf9\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\u7684\u8bc1\u660e\u4e2d\u6c72\u53d6\u4e86\u7075\u611f\u3002\u4ece\u8d28\u91cf\u548c\u5f39\u7c27\u7cfb\u7edf<\/span>\uff08\u4e0a\u6587\u63d0\u5230\uff09<\/span>\u7684\u673a\u68b0\u7c7b\u6bd4\u6765\u770b\uff0c\u6838\u5fc3\u7b56\u7565\u662f\u5c06\u7cfb\u7edf\u4e2d\u7684\u4e00\u4e2a\u5f39\u7c27\u66ff\u6362\u4e3a\u53e6\u4e00\u4e2a\u968f\u673a\u9009\u62e9\u7684\u5f39\u7c27\uff0c\u5e76\u8bc1\u660e\u8fd9\u6837\u505a\u65f6\u7cfb\u7edf\u9891\u7387\u7684\u5206\u5e03\u6ca1\u6709\u663e\u8457\u53d8\u5316<\/strong>\u3002\u63a5\u7740\u9010\u4e2a\u5bf9\u6bcf\u4e2a\u5f39\u7c27\u8fdb\u884c\u8fd9\u79cd\u66ff\u4ee3\u64cd\u4f5c\uff0c\u6700\u7ec8\u80fd\u591f\u7528\u4e00\u4e2a\u5b8c\u5168\u4e0d\u540c\u7684\u6a21\u578b\u6765\u66ff\u4ee3\u7279\u5b9a\u7684\u968f\u673a\u77e9\u9635\u6a21\u578b\uff0c\u5e76\u4e14\u4fdd\u6301\u5206\u5e03\u57fa\u672c\u4e0d\u53d8\u2014\u2014\u8fd9\u4e00\u65b9\u6cd5\u53ef\u4ee5\u7528\u6765\u8bc1\u660e\uff0c\u4e00\u5927\u7c7b\u968f\u673a\u77e9\u9635\u6a21\u578b\u6709\u7740\u672c\u8d28\u4e0a\u76f8\u540c\u7684\u5206\u5e03\u7279\u6027\u3002<\/span><\/section>\n

<\/section>\n
\u8fd9\u662f\u4e00\u4e2a\u975e\u5e38\u6d3b\u8dc3\u7684\u7814\u7a76\u9886\u57df\uff1b\u4f8b\u5982\uff0c\u4e0e\u53bb\u5e74Van Vu\u548c\u6211\u5de5\u4f5c\u540c\u65f6\uff0cL\u00e1szl\u00f3 Erd\u00f6s\u3001Benjamin Schlein\u548cHorng-Tzer Yau\u4e5f\u7ed9\u51fa\u4e86\u8bb8\u591a\u5176\u4ed6\u5173\u4e8e\u968f\u673a\u77e9\u9635\u6a21\u578b\u666e\u9002\u6027\u7684\u8bc1\u660e\u3002\u8fd9\u4e2a\u9886\u57df\u53d1\u5c55\u8fc5\u901f\uff0c\u672a\u6765\u51e0\u5e74\u6211\u4eec\u53ef\u80fd\u4f1a\u5bf9\u8fd9\u4e2a\u795e\u79d8\u7684\u666e\u9002\u6027\u89c4\u5f8b\u7684\u672c\u8d28\u6709\u66f4\u591a\u7684\u4e86\u89e3\u3002<\/span><\/section>\n

<\/span><\/section>\n

<\/span><\/section>\n

\n
\n
\n
\n
\n

<\/section>\n

<\/section>\n
\n
<\/svg><\/section>\n<\/section>\n<\/section>\n
\n

5. \u666e\u9002\u6027\u7684\u5931\u6548\u4e0e\u590d\u6742\u6027\u7684\u51fa\u73b0<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


<\/p>\n

\u6570\u5b66\u548c\u81ea\u7136\u754c\u8fd8\u6709\u8bb8\u591a\u5176\u4ed6\u666e\u9002\u6027\u89c4\u5f8b\uff1b\u6211\u6240\u63d0\u5230\u7684\u4ec5\u4ec5\u662f\u591a\u5e74\u6765\u4eba\u4eec\u5728\u52a8\u529b\u7cfb\u7edf\u3001\u91cf\u5b50\u573a\u8bba\u7b49\u4e0d\u540c\u9886\u57df\u53d1\u73b0\u7684\u4f8b\u5b50\u4e2d\u7684\u4e00\u5c0f\u90e8\u5206\u3002\u6bd4\u5982\uff0c\u5f88\u591a\u7269\u7406\u5b66\u4e2d\u7684\u5b8f\u89c2\u89c4\u5f8b\uff0c\u50cf\u70ed\u529b\u5b66\u5b9a\u5f8b\u6216\u6d41\u4f53\u8fd0\u52a8\u65b9\u7a0b\uff0c\u672c\u8d28\u4e0a\u662f\u975e\u5e38\u666e\u904d\u7684\uff0c\u8fd9\u4f7f\u5f97\u88ab\u7814\u7a76\u6750\u6599\u6216\u6d41\u4f53\u7684\u5fae\u89c2\u7ed3\u6784\u51e0\u4e4e\u65e0\u5173\u7d27\u8981\uff0c\u9664\u4e86\u901a\u8fc7\u4e00\u4e9b\u5173\u952e\u6027\u53c2\u6570\u6765\u63cf\u8ff0\uff0c\u4f8b\u5982\u7c98\u5ea6\u3001\u53ef\u538b\u7f29\u6027\u6216\u71b5\u3002<\/span><\/section>\n

<\/section>\n
\u7136\u800c\uff0c\u666e\u9002\u6027\u5b9a\u5f8b\u786e\u5b9e\u5b58\u5728\u4e00\u5b9a\u7684\u5c40\u9650\u3002\u4ee5\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\u4e3a\u4f8b\uff0c\u5b83\u9884\u6d4b\u4e86\u4efb\u4f55\u7531\u4f17\u591a\u5c0f\u7684\u3001\u72ec\u7acb\u56e0\u7d20\u7ec4\u5408\u800c\u6210\u7684\u6570\u91cf\u90fd\u5c06\u8d8b\u5411\u949f\u5f62\u66f2\u7ebf\u5206\u5e03\u3002\u4f46\u5982\u679c\u4e0d\u6ee1\u8db3\u8be5\u5b9a\u7406\u6240\u9700\u7684\u524d\u63d0\u5047\u8bbe\uff0c\u8fd9\u4e2a\u5b9a\u5f8b\u5c31\u53ef\u80fd\u4e0d\u9002\u7528\u3002\u6bd4\u5982\u8bf4\uff0c\u6240\u6709\u6210\u5e74\u4eba<\/span>\uff08\u7537\u6027\u548c\u5973\u6027\uff09<\/span>\u7684\u8eab\u9ad8\u5206\u5e03\u5e76\u4e0d\u7b26\u5408\u6807\u51c6\u7684\u949f\u5f62\u66f2\u7ebf\uff0c\u56e0\u4e3a\u6027\u522b\u8fd9\u4e00\u5355\u4e00\u56e0\u7d20\u5bf9\u8eab\u9ad8\u7684\u5f71\u54cd\u5de8\u5927\uff0c\u65e0\u6cd5\u88ab\u5176\u4ed6\u6240\u6709\u73af\u5883\u548c\u9057\u4f20\u56e0\u7d20\u5e73\u8861\u6389\u3002<\/span><\/section>\n

<\/section>\n
\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\u8fd8\u6709\u4e00\u4e2a\u91cd\u8981\u7684\u5931\u6548\u573a\u666f\uff0c\u90a3\u5c31\u662f\u6784\u6210\u67d0\u4e2a\u91cf\u7684\u72ec\u7acb\u56e0\u7d20\u5e76\u975e\u771f\u6b63\u72ec\u7acb\uff0c\u800c\u662f\u5b58\u5728\u76f8\u5173\u6027\uff0c\u5bfc\u81f4\u5b83\u4eec\u503e\u5411\u4e8e\u540c\u6da8\u540c\u8dcc\u3002\u5728\u8fd9\u6837\u7684\u60c5\u51b5\u4e0b\uff0c\u53ef\u80fd\u5f62\u6210\u201c\u80d6\u5c3e\u201d\u73b0\u8c61<\/span>\uff08\u4fd7\u79f0\u201c\u9ed1\u5929\u9e45\u201d\uff09<\/span>\uff0c\u5176\u6570\u503c\u4f1a\u6bd4\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\u6240\u9884\u6d4b\u7684\u5e73\u5747\u503c\u6ce2\u52a8\u8303\u56f4\u5927\u5f97\u591a\u3002\u8fd9\u4e00\u73b0\u8c61\u5728\u91d1\u878d\u6a21\u578b\u4e2d\u7279\u522b\u91cd\u8981\uff0c\u5728\u5904\u7406\u590d\u6742\u91d1\u878d\u5de5\u5177\u65f6\u5c24\u5176\u660e\u663e\uff0c\u6bd4\u5982\u901a\u8fc7\u6c47\u96c6\u62b5\u62bc\u8d37\u6b3e\u6240\u5f62\u6210\u7684\u62b5\u62bc\u503a\u52a1\u62c5\u4fdd\u8bc1\u5238<\/span>\uff08CDOs\uff09<\/span>\u3002\u53ea\u6709\u5728\u5047\u8bbe\u5404\u4e2a\u62b5\u62bc\u8d37\u6b3e\u76f8\u4e92\u72ec\u7acb\u65f6\uff0c\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\u624d\u80fd\u7528\u6765\u8bc4\u4f30\u8fd9\u4e9b\u5de5\u5177\u7684\u98ce\u9669\uff1b\u4f46\u5728\u8fd1\u671f\u91d1\u878d\u5371\u673a\u4e2d<\/span>\uff08\u5178\u578b\u7684\u201c\u9ed1\u5929\u9e45\u201d\u4e8b\u4ef6\uff09<\/span>\uff0c\u8fd9\u79cd\u72ec\u7acb\u6027\u5047\u8bbe\u620f\u5267\u6027\u5730\u5d29\u6e83\u4e86\uff0c\u5bfc\u81f4\u8bb8\u591a\u6301\u6709\u8fd9\u4e9b\u8bc1\u5238\u7684\u6295\u8d44\u8005\u548c\u5b83\u4eec\u7684\u4fdd\u9669\u516c\u53f8\u906d\u53d7\u5de8\u5927\u8d22\u52a1\u635f\u5931\u3002\u6570\u5b66\u6a21\u578b\u7684\u5f3a\u5927\u4ec5\u53d6\u51b3\u4e8e\u5176\u80cc\u540e\u7684\u5047\u8bbe\u662f\u5426\u575a\u5b9e<\/strong>\u3002<\/span><\/section>\n

<\/section>\n
\u666e\u9002\u6027\u89c4\u5f8b\u74e6\u89e3\u7684\u7b2c\u4e09\u79cd\u60c5\u5f62\u662f\u7cfb\u7edf\u6ca1\u6709\u8db3\u591f\u7684\u81ea\u7531\u5ea6\u6765\u4f7f\u5f97\u8fd9\u4e9b\u5b9a\u5f8b\u751f\u6548\u3002\u4e3e\u4f8b\u6765\u8bf4\uff0c\u5b87\u5b99\u5b66\u5bb6\u53ef\u4ee5\u4f9d\u636e\u6d41\u4f53\u529b\u5b66\u7684\u666e\u9002\u6027\u89c4\u5f8b\u6765\u63cf\u8ff0\u6574\u4e2a\u661f\u7cfb\u7684\u8fd0\u52a8\u6a21\u5f0f\uff0c\u7136\u800c\uff0c\u5728\u4ec5\u53d7\u5230\u4e09\u4e2a\u5929\u4f53\u5f15\u529b\u5f71\u54cd\u7684\u73af\u5883\u4e0b\uff0c\u5355\u4e2a\u536b\u661f\u7684\u8fd0\u52a8\u53ef\u80fd\u8981\u590d\u6742\u5f97\u591a\u2014\u2014\u8fd9\u5b9e\u9645\u4e0a\u5c31\u662f\u6240\u8c13\u7684\u706b\u7bad\u79d1\u5b66\u3002<\/span><\/section>\n

<\/section>\n
\u6d41\u4f53\u529b\u5b66\u7684\u666e\u9002\u6027\u89c4\u5f8b\u8fd8\u4f1a\u5728\u4ecb\u89c2\u5c3a\u5ea6\u4e0a\u5931\u6548\uff1a\u8fd9\u4e2a\u5c3a\u5ea6\u6bd4\u5355\u5206\u5b50\u7684\u5fae\u89c2\u5c3a\u5ea6\u8981\u5927\uff0c\u4f46\u53c8\u5c0f\u4e8e\u5b8f\u89c2\u5c3a\u5ea6\uff0c\u540e\u8005\u662f\u666e\u9002\u6027\u89c4\u5f8b\u9002\u7528\u7684\u8303\u56f4\u3002\u4e00\u4e2a\u5178\u578b\u7684\u4ecb\u89c2\u6d41\u4f53\u4f8b\u5b50\u662f\u6d41\u7ecf\u8840\u7ba1\u7684\u8840\u6db2\uff1b\u6784\u6210\u8fd9\u79cd\u6db2\u4f53\u7684\u8840\u7ec6\u80de\u975e\u5e38\u5927\uff0c\u4ee5\u81f3\u4e8e\u5b83\u4eec\u4e0d\u80fd\u7b80\u5355\u5730\u88ab\u89c6\u4f5c\u5fae\u89c2\u5206\u5b50\u7684\u96c6\u5408\u4f53\uff0c\u800c\u5e94\u8be5\u88ab\u8ba4\u4e3a\u662f\u5177\u6709\u590d\u6742\u884c\u4e3a\u7684\u4ecb\u89c2\u5b9e\u4f53\u3002\u5176\u4ed6\u4e00\u4e9b\u5177\u6709\u6709\u8da3\u4ecb\u89c2\u7279\u6027\u7684\u6750\u6599\u5305\u62ec\u80f6\u4f53\u6d41\u4f53<\/span>\uff08\u6bd4\u5982\u6ce5\u6d46\uff09<\/span>\u3001\u67d0\u4e9b\u7c7b\u578b\u7684\u7eb3\u7c73\u6750\u6599\u548c\u91cf\u5b50\u70b9\u7b49\uff1b\u4e3a\u8fd9\u7c7b\u6750\u6599\u5efa\u7acb\u51c6\u786e\u7684\u6570\u5b66\u6a21\u578b\u4ecd\u7136\u662f\u4e00\u4e2a\u6301\u7eed\u5b58\u5728\u7684\u6311\u6218\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u8fd8\u6709\u8bb8\u591a\u5b8f\u89c2\u60c5\u51b5\uff0c\u5176\u4e2d\u6ca1\u6709\u5df2\u77e5\u7684\u666e\u9002\u6027\u89c4\u5f8b\uff0c\u7279\u522b\u662f\u5728\u7cfb\u7edf\u4e2d\u5305\u542b\u4eba\u7c7b\u4e3b\u4f53\u7684\u60c5\u51b5\u4e0b\u3002\u80a1\u7968\u5e02\u573a\u5c31\u662f\u4e00\u4e2a\u5f88\u597d\u7684\u4f8b\u5b50\uff1a\u5c3d\u7ba1\u505a\u51fa\u4e86\u6781\u5927\u7684\u52aa\u529b\uff0c\u4f46\u5c1a\u672a\u53d1\u73b0\u80fd\u591f\u63cf\u8ff0\u80a1\u7968\u4ef7\u683c\u53d8\u52a8\u7684\u4ee4\u4eba\u6ee1\u610f\u7684\u666e\u9002\u6027\u89c4\u5f8b\u3002<\/span>\uff08\u4f8b\u5982\uff0c\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\u4f3c\u4e4e\u4e0d\u662f\u4e00\u4e2a\u597d\u7684\u6a21\u578b\uff0c\u5982\u524d\u6240\u8ff0\u3002\uff09<\/span>\u8fd9\u79cd\u7f3a\u9677\u7684\u4e00\u4e2a\u539f\u56e0\u662f\uff0c\u5e02\u573a\u4e2d\u53d1\u73b0\u7684\u4efb\u4f55\u89c4\u5f8b\u90fd\u5f88\u53ef\u80fd\u88ab\u5957\u5229\u8005\u5229\u7528\u76f4\u5230\u5b83\u6d88\u5931\u3002\u7531\u4e8e\u7c7b\u4f3c\u7684\u539f\u56e0\uff0c\u5bfb\u627e\u5b8f\u89c2\u7ecf\u6d4e\u5b66\u7684\u666e\u9002\u6027\u89c4\u5f8b\u4f3c\u4e4e\u662f\u4e00\u4e2a\u79fb\u52a8\u76ee\u6807\uff1b\u6839\u636e\u53e4\u5fb7\u54c8\u7279\u5b9a\u5f8b<\/span>\uff08Goodhart\u2019s law\uff09<\/span>\uff0c\u5982\u679c\u7ecf\u6d4e\u6570\u636e\u4e2d\u89c2\u5bdf\u5230\u7684\u7edf\u8ba1\u89c4\u5f8b\u88ab\u7528\u4e8e\u653f\u7b56\u76ee\u7684\uff0c\u5219\u5b83\u503e\u5411\u4e8e\u5d29\u6e83<\/strong>\u3002<\/span>\uff08\u5177\u6709\u8bbd\u523a\u610f\u5473\u7684\u662f\uff0c\u53e4\u5fb7\u54c8\u7279\u5b9a\u5f8b\u672c\u8eab\u53ef\u4ee5\u8bf4\u662f\u4e00\u4e2a\u666e\u9002\u6027\u89c4\u5f8b\u7684\u4f8b\u5b50\u3002\uff09<\/span><\/section>\n

<\/span><\/section>\n
\n
\u8bd1\u6ce8\uff1a<\/span><\/section>\n
\u53e4\u5fb7\u54c8\u7279\u5b9a\u5f8b\uff08Goodhart’s law\uff09\u8868\u660e\uff0c\u5f53\u4e00\u4e2a\u5ea6\u91cf\u6307\u6807\u6210\u4e3a\u76ee\u6807\u65f6\uff0c\u5b83\u5c31\u4e0d\u518d\u662f\u4e00\u4e2a\u597d\u7684\u5ea6\u91cf\u6307\u6807\u3002\u5b83\u4ee5\u82f1\u56fd\u7ecf\u6d4e\u5b66\u5bb6\u67e5\u5c14\u65af\u00b7\u53e4\u5fb7\u54c8\u7279\uff08Charles Goodhart\uff09\u7684\u540d\u5b57\u547d\u540d\uff0c\u4ed6\u57281975\u5e74\u7684\u4e00\u7bc7\u5173\u4e8e\u82f1\u56fd\u8d27\u5e01\u653f\u7b56\u7684\u6587\u7ae0\u4e2d\u8868\u8fbe\u4e86\u8fd9\u4e2a\u683c\u8a00\u7684\u6838\u5fc3\u601d\u60f3\u3002\u8be5\u5b9a\u5f8b\u53cd\u6620\u4e86\u8fd9\u6837\u4e00\u4e2a\u89c2\u70b9\uff0c\u5373\u5f53\u4e00\u4e2a\u6307\u6807\u88ab\u7528\u4f5c\u653f\u7b56\u5236\u5b9a\u7684\u76ee\u6807\u65f6\uff0c\u5b83\u5f88\u53ef\u80fd\u5931\u53bb\u4f5c\u4e3a\u5ea6\u91cf\u6307\u6807\u7684\u6709\u6548\u6027\u3002\u8fd9\u662f\u56e0\u4e3a\u4eba\u4eec\u4f1a\u5f00\u59cb\u64cd\u7eb5\u6216\u201c\u64cd\u5f04\u201d\u7cfb\u7edf\u4ee5\u8fbe\u5230\u76ee\u6807\uff0c\u5373\u4f7f\u8fd9\u610f\u5473\u7740\u727a\u7272\u4e86\u5176\u4ed6\u91cd\u8981\u65b9\u9762\u7684\u60c5\u51b5\u3002<\/span><\/section>\n
https:\/\/zh.wikipedia.org\/wiki\/%E5%8F%A4%E5%BE%B7%E5%93%88%E7%89%B9%E5%AE%9A%E5%BE%8B<\/span><\/section>\n<\/blockquote>\n

<\/section>\n
\u5373\u4f7f\u5b58\u5728\u666e\u9002\u6027\u89c4\u5f8b\uff0c\u4e5f\u53ef\u80fd\u5b9e\u9645\u4e0a\u65e0\u6cd5\u4f7f\u7528\u5b83\u4eec\u8fdb\u884c\u9884\u6d4b\u3002\u4f8b\u5982\uff0c\u6211\u4eec\u6709\u6d41\u4f53\u8fd0\u52a8\u7684\u666e\u9002\u6027\u89c4\u5f8b\uff0c\u5982\u7eb3\u7ef4-\u65af\u6258\u514b\u65af\u65b9\u7a0b\uff0c\u8fd9\u4e9b\u5b9a\u5f8b\u4e00\u76f4\u7528\u4e8e\u8bf8\u5982\u5728\u5929\u6c14\u9884\u62a5\u4e4b\u7c7b\u7684\u4efb\u52a1\u3002\u4f46\u8fd9\u4e9b\u65b9\u7a0b\u975e\u5e38\u590d\u6742\u548c\u4e0d\u7a33\u5b9a\uff0c\u5373\u4f7f\u4f7f\u7528\u6700\u5f3a\u5927\u7684\u8ba1\u7b97\u673a\uff0c\u6211\u4eec\u4ecd\u7136\u65e0\u6cd5\u51c6\u786e\u9884\u6d4b\u672a\u6765\u4e00\u4e24\u5468\u7684\u5929\u6c14\u3002<\/span>\uff08\u6240\u8c13\u7684\u201c\u4e0d\u7a33\u5b9a\u201d\uff0c\u610f\u5473\u7740\u5373\u4f7f\u662f\u975e\u5e38\u5c0f\u7684\u6d4b\u91cf\u6570\u636e\u8bef\u5dee\u6216\u6570\u503c\u8ba1\u7b97\u504f\u5dee\uff0c\u90fd\u53ef\u80fd\u5bfc\u81f4\u65b9\u7a0b\u9884\u6d4b\u89e3\u51fa\u73b0\u5de8\u5927\u504f\u5dee\u3002\uff09<\/span> <\/span><\/span><\/section>\n

<\/span><\/section>\n
\u56e0\u6b64\uff0c\u5728\u90a3\u4e9b\u53d7\u666e\u904d\u89c4\u5f8b\u4e3b\u5bfc\u7684\u5e9e\u5927\u5b8f\u89c2\u7cfb\u7edf\u548c\u80fd\u591f\u901a\u8fc7\u81ea\u7136\u754c\u57fa\u672c\u6cd5\u5219\u6765\u5206\u6790\u7684\u7b80\u5355\u7cfb\u7edf\u4e4b\u95f4\uff0c\u8fd8\u5b58\u5728\u4e00\u4e2a\u5e9e\u5927\u7684\u4e2d\u95f4\u9886\u57df\u3002\u8fd9\u4e9b\u7cfb\u7edf\u5bf9\u4e8e\u57fa\u7840\u6027\u5206\u6790\u6765\u8bf4\u8fc7\u4e8e\u590d\u6742\uff0c\u4f46\u53c8\u4e0d\u8db3\u4ee5\u8fbe\u5230\u666e\u9002\u6027\u7684\u6c34\u5e73\u2014\u2014\u7b80\u800c\u8a00\u4e4b\uff0c\u8fd9\u4e3a\u6211\u4eec\u6240\u719f\u6089\u7684\u751f\u6d3b\u4e2d\u7684\u5404\u79cd\u590d\u6742\u6027\u63d0\u4f9b\u4e86\u5e7f\u9614\u7684\u7a7a\u95f4\u3002<\/span><\/section>\n

<\/span><\/section>\n

<\/span><\/section>\n
\u5c3e\u6ce8<\/strong><\/span><\/section>\n
1 This essay benefited from the feedback of many readers of my blog. They commented on a draft version that (together with additional figures and links) can be read at http:\/\/terrytao.wordpress.com\/2010\/09\/14\/a-second-draft-of-a-non-technical-article-on-universality\/ .<\/span><\/section>\n
2 Dan Rockmore, Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime Numbers (New York: Pantheon Books, 2005).<\/span><\/section>\n


<\/p>\n


<\/section>\n
\n
\n
\n
\n

<\/section>\n
\n
\n
\n
\n
\n

<\/section>\n<\/section>\n<\/section>\n<\/section>\n
\n
\n
\n

<\/section>\n<\/section>\n<\/section>\n<\/section>\n
\n
\n
\n

<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

\u6d3b\u52a8\u9884\u544a<\/span><\/strong><\/p>\n


<\/span><\/strong><\/p>\n

<\/p>\n

<\/span><\/section>\n

<\/section>\n


<\/p>\n

\n
\n
\n
\n

\u65b0\u4fe1\u606f\u8bba\uff1a\u4ece\u5206\u89e3\u5230\u6574\u5408<\/strong><\/p>\n

\u56e0\u679c\u6d8c\u73b0\u8bfb\u4e66\u4f1a\u7b2c\u56db\u5b63\u62db\u52df\u4e2d<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


<\/section>\n

\u4ec0\u4e48\u662f\u610f\u8bc6\uff1f\u610f\u8bc6\u80fd\u5426\u5ea6\u91cf\uff1f\u673a\u5668\u80fd\u5426\u4ea7\u751f\u610f\u8bc6\uff1f\u5bf9\u4e8e\u610f\u8bc6\u95ee\u9898\uff0c\u4eba\u4eec\u53ef\u80fd\u5373\u5c06\u8fce\u6765\u4e00\u4e2a\u5927\u7684\u7a81\u7834\uff0c\u5404\u79cd\u6709\u5173\u610f\u8bc6\u7684\u7406\u8bba\u6b63\u5982\u96e8\u540e\u6625\u7b0b\u822c\u5c55\u73b0\u51fa\u52c3\u52c3\u751f\u673a\u3002\u5176\u4e2d\u795e\u7ecf\u79d1\u5b66\u5bb6 Giulio Tononi \u7684\u6574\u5408\u4fe1\u606f\u8bba\uff08IID\uff09\u88ab\u8ba4\u4e3a\u662f\u6700\u6709\u524d\u666f\u7684\u610f\u8bc6\u7406\u8bba\u4e4b\u4e00\u3002\u5982\u679c\u8bf4\u610f\u8bc6\u662f\u5927\u8111\u795e\u7ecf\u6d3b\u52a8\u7684\u4e00\u79cd\u6d8c\u73b0\u7ed3\u679c\uff0c\u90a3\u4e48\u523b\u753b\u6d8c\u73b0\u4fbf\u6210\u4e3a\u7406\u89e3\u610f\u8bc6\u8fc7\u7a0b\u4e2d\u4e00\u4e2a\u91cd\u8981\u73af\u8282\u3002\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\u76ee\u524d\u53d1\u5c55\u51fa\u4e24\u4e2a\u6d3e\u522b\uff0c\u9664\u4e86 Erik Hoel \u7684\u6709\u6548\u4fe1\u606f\u56e0\u679c\u6d8c\u73b0\u6846\u67b6\uff0c\u8fd8\u6709\u4e00\u4e2a\u662f Rosas \u7684\u4fe1\u606f\u5206\u89e3\uff08PID\uff09\u6846\u67b6\uff0c\u6b64\u540e Rosas \u57fa\u4e8e\u6b64\u8fdb\u4e00\u6b65\u63d0\u51fa\u878d\u5408\u6574\u5408\u4fe1\u606f\u8bba\u7684\u4fe1\u606f\u5206\u89e3\u6846\u67b6 \u03a6ID\uff0c\u5c1d\u8bd5\u6784\u5efa\u65b0\u7684\u610f\u8bc6\u7406\u8bba\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u4e00\u8fb9\u662f\u4fe1\u606f\u6574\u5408\uff08IIT\uff09\uff0c\u4e00\u8fb9\u662f\u4fe1\u606f\u5206\u89e3\uff08PID\uff09\uff0c\u770b\u4f3c\u5206\u88c2\uff0c\u5b9e\u9645\u4e0a\u90fd\u662f\u5bf9\u9999\u519c\u7ecf\u5178\u4fe1\u606f\u8bba\u7684\u8fdb\u4e00\u6b65\u53d1\u5c55\u3002\u56e0\u679c\u6d8c\u73b0\u8bfb\u4e66\u4f1a\u7b2c\u56db\u5b63\u300c\u65b0\u4fe1\u606f\u8bba\uff1a\u4ece\u5206\u89e3\u5230\u6574\u5408<\/a>\u300d\u7531\u5317\u4eac\u5e08\u8303\u5927\u5b66\u7cfb\u7edf\u79d1\u5b66\u5b66\u9662\u6559\u6388\u3001\u96c6\u667a\u4ff1\u4e50\u90e8\u521b\u59cb\u4eba\u5f20\u6c5f\u8001\u5e08\u9886\u8854\u53d1\u8d77\uff0c\u65e8\u5728\u68b3\u7406\u4fe1\u606f\u8bba\u9886\u57df\u7684\u53d1\u5c55\u8109\u7edc\uff0c\u4ece\u9999\u519c\u7684\u7ecf\u5178\u4fe1\u606f\u8bba\u5f00\u59cb\uff0c\u91cd\u70b9\u5173\u6ce8\u6574\u5408\u4fe1\u606f\u8bba\u548c\u4fe1\u606f\u5206\u89e3\u8fd9\u4e24\u4e2a\u524d\u6cbf\u8bdd\u9898\uff0c\u53ca\u5176\u5728\u4ea4\u53c9\u9886\u57df\u7684\u5e94\u7528\u3002\u5e0c\u671b\u901a\u8fc7\u5bf9\u8fd9\u4e9b\u201c\u65b0\u4fe1\u606f\u8bba\u201d\u5ea6\u91cf\u6307\u6807\u7684\u6df1\u5165\u63a2\u8ba8\uff0c\u5e2e\u52a9\u6211\u4eec\u7406\u89e3\u4ec0\u4e48\u662f\u610f\u8bc6\uff0c\u4ec0\u4e48\u662f\u6d8c\u73b0\uff0c\u5e76\u627e\u5230\u4e0d\u540c\u5b66\u79d1\uff0c\u4e0d\u540c\u95ee\u9898\u80cc\u540e\u7684\u7edf\u4e00\u6027\u539f\u7406\u3002\u8bfb\u4e66\u4f1a\u4ece2023\u5e7411\u670819\u65e5\u5f00\u59cb\uff0c\u6bcf\u5468\u65e5\u4e0a\u5348 9:00-11:00\uff0c\u6301\u7eed\u65f6\u95f4\u9884\u8ba1 8\uff5e10 \u5468\uff0c\u6b22\u8fce\u611f\u5174\u8da3\u7684\u670b\u53cb\u62a5\u540d\u53c2\u4e0e\uff01<\/span><\/p>\n


<\/span><\/section>\n
<\/span><\/a><\/section>\n

<\/section>\n
\u8be6\u60c5\u8bf7\u89c1\uff1a<\/span><\/section>\n
\u65b0\u4fe1\u606f\u8bba\uff1a\u4ece\u5206\u89e3\u5230\u6574\u5408\uff5c\u56e0\u679c\u6d8c\u73b0\u8bfb\u4e66\u4f1a\u7b2c\u56db\u5b63\u542f\u52a8<\/a><\/span><\/section>\n


<\/p>\n

\n
\n
\n
\n

\u4eba\u5de5\u667a\u80fd\u4e0e\u6570\u5b66\u8bfb\u4e66\u4f1a<\/strong>
<\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


<\/section>\n

\u6570\u5341\u5e74\u6765\uff0c\u4eba\u5de5\u667a\u80fd\u7684\u7406\u8bba\u53d1\u5c55\u548c\u6280\u672f\u5b9e\u8df5\u4e00\u76f4\u4e0e\u79d1\u5b66\u63a2\u7d22\u76f8\u4f34\u800c\u751f\uff0c\u5c24\u5176\u5728\u4ee5\u5927\u6a21\u578b\u4e3a\u4ee3\u8868\u7684\u4eba\u5de5\u667a\u80fd\u6280\u672f\u5e94\u7528\u96c6\u4e2d\u7206\u53d1\u7684\u5f53\u4e0b\uff0c\u4eba\u5de5\u667a\u80fd\u6b63\u5728\u52a0\u901f\u7269\u7406\u3001\u5316\u5b66\u3001\u751f\u7269\u7b49\u57fa\u7840\u79d1\u5b66\u7684\u9769\u65b0\uff0c\u800c\u8fd9\u4e9b\u5b66\u79d1\u4e5f\u5728\u53cd\u8fc7\u6765\u542f\u53d1\u4eba\u5de5\u667a\u80fd\u6280\u672f\u521b\u65b0\u3002\u5728\u6b64\u8fc7\u7a0b\u4e2d\uff0c\u6570\u5b66\u4f5c\u4e3a\u517c\u5177\u7406\u8bba\u5c5e\u6027\u4e0e\u5de5\u5177\u5c5e\u6027\u7684\u91cd\u8981\u57fa\u7840\u5b66\u79d1\uff0c\u4e0e\u4eba\u5de5\u667a\u80fd\u5173\u7cfb\u751a\u5bc6\uff0c\u76f8\u8f85\u76f8\u6210\u3002\u4e00\u65b9\u9762\uff0c\u4eba\u5de5\u667a\u80fd\u5728\u89e3\u51b3\u6570\u5b66\u9886\u57df\u7684\u8bf8\u591a\u5de5\u7a0b\u95ee\u9898\u3001\u7406\u8bba\u95ee\u9898\u4e43\u81f3\u5723\u676f\u96be\u9898\u4e0a\u5c61\u521b\u8bb0\u5f55\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u6570\u5b66\u6301\u7eed\u4e3a\u4eba\u5de5\u667a\u80fd\u6784\u7b51\u7406\u8bba\u57fa\u77f3\u5e76\u62d3\u5c55\u5176\u672a\u6765\u7a7a\u95f4\u3002\u8fd9\u4e24\u4e2a\u5173\u952e\u9886\u57df\u7684\u4ea4\u53c9\u878d\u5408\uff0c\u6b63\u5728\u63ed\u5f00\u4e0b\u4e2a\u65f6\u4ee3\u7684\u79d1\u5b66\u4e4b\u5e55\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u4e3a\u4e86\u63a2\u7d22\u6570\u5b66\u4e0e\u4eba\u5de5\u667a\u80fd\u6df1\u5ea6\u878d\u5408\u7684\u53ef\u80fd\u6027\uff0c\u96c6\u667a\u4ff1\u4e50\u90e8\u8054\u5408\u540c\u6d4e\u5927\u5b66\u7279\u8058\u7814\u7a76\u5458\u9648\u5c0f\u6768\u3001\u6e05\u534e\u5927\u5b66\u4ea4\u53c9\u4fe1\u606f\u5b66\u9662\u52a9\u7406\u6559\u6388\u8881\u6d0b\u3001\u5357\u6d0b\u7406\u5de5\u5927\u5b66\u526f\u6559\u6388\u590f\u514b\u6797\u4e09\u4f4d\u8001\u5e08\uff0c\u5171\u540c\u53d1\u8d77\u201c\u4eba\u5de5\u667a\u80fd\u4e0e\u6570\u5b66\u201d\u8bfb\u4e66\u4f1a\uff0c\u5e0c\u671b\u4ece AI\u3000for\u3000Math\uff0cMath\u3000for\u3000AI \u4e24\u4e2a\u65b9\u9762\u6df1\u5165\u63a2\u8ba8\u4eba\u5de5\u667a\u80fd\u4e0e\u6570\u5b66\u7684\u5bc6\u5207\u8054\u7cfb\u3002\u672c\u8bfb\u4e66\u4f1a\u662f\u201cAI+Science\u201d\u4e3b\u9898\u8bfb\u4e66\u4f1a\u7684\u7b2c\u4e09\u5b63\u3002\u6b22\u8fce\u611f\u5174\u8da3\u7684\u670b\u53cb\u62a5\u540d\u53c2\u4e0e\uff01<\/span><\/p>\n


<\/span><\/section>\n
<\/span><\/a><\/span><\/section>\n
\u8be6\u60c5\u8bf7\u89c1\uff1a<\/span>
<\/section>\n

\u4eba\u5de5\u667a\u80fd\u4e0e\u6570\u5b66\u8bfb\u4e66\u4f1a\u542f\u52a8\uff1aAI for Math\uff0cMath for AI<\/a><\/span><\/p>\n


<\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


<\/section>\n<\/section>\n<\/section>\n<\/section>\n
\n

\u63a8\u8350\u9605\u8bfb<\/span><\/strong><\/strong><\/p>\n

<\/strong><\/span><\/section>\n
1. <\/strong>\u5b89\u5fb7\u68ee\u56db\u539f\u5219\uff1a\u4ece\u5bf9\u79f0\u6027\u7834\u7f3a\u5230\u590d\u6742\u6027\u6d8c\u73b0<\/a><\/strong><\/span><\/strong><\/strong><\/section>\n
2.<\/strong>\u591a\u8005\u5f02\u4e5f\uff1a\u7834\u7f3a\u7684\u5bf9\u79f0\u6027\u4e0e\u79d1\u5b66\u5c42\u7ea7\u7ed3\u6784\u7684\u672c\u8d28 | \u7ecf\u5178\u56de\u987e<\/a><\/strong><\/span><\/strong><\/section>\n
3.<\/strong> \u673a\u5668\u7ffb\u8bd1\u4e4b\u7236\u97e6\u5f17\uff1a\u79d1\u5b66\u4e0e\u590d\u6742\u6027<\/a><\/strong><\/strong><\/span><\/section>\n
4. <\/strong><\/strong><\/span>\u5f20\u6c5f\uff1a\u7b2c\u4e09\u4ee3\u4eba\u5de5\u667a\u80fd\u6280\u672f\u57fa\u7840\u2014\u2014\u4ece\u53ef\u5fae\u5206\u7f16\u7a0b\u5230\u56e0\u679c\u63a8\u7406 | \u96c6\u667a\u5b66\u56ed\u5168\u65b0\u8bfe\u7a0b<\/a><\/strong><\/strong><\/span><\/section>\n
5. \u6210\u4e3a\u96c6\u667aVIP\uff0c\u89e3\u9501\u5168\u7ad9\u8bfe\u7a0b\uff0f\u8bfb\u4e66\u4f1a<\/a><\/span><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/span><\/section>\n
6. <\/strong>\u52a0\u5165\u96c6\u667a\uff0c\u4e00\u8d77\u590d\u6742\uff01<\/strong><\/span><\/a><\/section>\n


<\/p>\n


<\/p>\n<\/section>\n

\u70b9\u51fb\u201c\u9605\u8bfb\u539f\u6587\u201d\uff0c\u62a5\u540d\u8bfb\u4e66\u4f1a<\/span><\/strong><\/section>\n

<\/mp-style-type><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

\u5bfc\u8bed \u63a2\u7a76\u5b87\u5b99\u4e2d\u7684\u79e9\u5e8f\u548c\u6df7\u6c8c\u4e00\u76f4\u662f\u79d1\u5b66\u7814\u7a76\u7684\u6838\u5fc3\u547d\u9898\u3002\u9676\u54f2\u8f69\u6559\u6388\u7684\u8fd9\u7bc7\u6d1e\u5bdf\u6027\u6587\u7ae0\u5f15\u9886\u6211\u4eec\u8fdb\u5165\u666e\u904d\u6027\u7684\u4e16\u754c\u2014\u2014\u4e00\u4e2a\u5c55\u73b0\u4e86\u5982\u4f55\u4ece\u9519\u7efc\u590d\u6742\u7684\u5fae\u89c2\u52a8\u6001\u7cfb\u7edf\u4e2d\u62bd\u8c61\u51fa\u7b80\u660e\u7684\u5b8f\u89c2\u89c4\u5f8b\u7684\u5947\u5999\u9886\u57df\u3002\u4ece\u7edf\u8ba1\u5b66\u7684\u7ecf\u5178\u89c4\u5f8b\u5230\u7269\u7406\u5b66\u4e2d\u7684\u76f8\u53d8\u73b0\u8c61\uff0c\u4ece\u81ea\u7136\u6570\u5e8f\u5217\u7684\u795e\u79d8\u89c4\u5f8b\u5230\u91cf\u5b50\u529b\u5b66\u7684\u7cbe\u786e\u9884\u6d4b\uff0c\u666e\u9002\u6027\u4f5c\u4e3a\u4e00\u79cd\u88ab\u5e7f\u6cdb\u8bb0\u5f55\u548c\u9a8c\u8bc1\u7684\u6a21\u5f0f…<\/p>\n","protected":false},"author":0,"featured_media":46910,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"special":[],"_links":{"self":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/46921"}],"collection":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"replies":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=46921"}],"version-history":[{"count":0,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/46921\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/media\/46910"}],"wp:attachment":[{"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=46921"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=46921"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=46921"},{"taxonomy":"special","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fspecial&post=46921"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}