{"id":40303,"date":"2023-01-29T21:25:58","date_gmt":"2023-01-29T13:25:58","guid":{"rendered":"https:\/\/swarma.org\/?p=40303"},"modified":"2023-01-29T21:25:58","modified_gmt":"2023-01-29T13:25:58","slug":"stephan-wolfram%ef%bc%9a%e4%bd%9c%e4%b8%ba%e5%a4%9a%e9%87%8d%e8%ae%a1%e7%ae%97%e7%b3%bb%e7%bb%9f%e7%9a%84%e6%b8%b8%e6%88%8f%e5%92%8c%e8%b0%9c%e9%a2%98","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=40303","title":{"rendered":"Stephan Wolfram\uff1a\u4f5c\u4e3a\u591a\u91cd\u8ba1\u7b97\u7cfb\u7edf\u7684\u6e38\u620f\u548c\u8c1c\u9898"},"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
\n

2022\u5e746\u6708\uff0cStephan Wolfram \u53d1\u8868\u6587\u7ae0 \u201c\u4f5c\u4e3a\u591a\u91cd\u8ba1\u7b97\u7cfb\u7edf\u7684\u6e38\u620f\u548c\u8c1c\u9898\u201d\uff0c\u63d0\u51fa\u4e00\u79cd\u53ef\u89c6\u5316\u548c\u5177\u4f53\u63a2\u8ba8\u6d8c\u73b0\u884c\u4e3a\u7684\u4e30\u5bcc\u7a0b\u5ea6\u7684\u601d\u8def\u2014\u2014\u591a\u91cd\u8ba1\u7b97\u8fc7\u7a0b\uff08Multicomputational Process\uff09\u3002\u4f5c\u8005\u4ee5\u51e0\u4e2a\u4f20\u7edf\u7684\u6e38\u620f\u6216\u8c1c\u9898\u4e3a\u4f8b\uff0c\u7528\u56fe\uff08Graph\uff09\u7684\u65b9\u5f0f\u53ef\u89c6\u5316\u8fd9\u4e9b\u6e38\u620f\u89c4\u5219\u4e0b\u7684\u53ef\u80fd\u6e38\u73a9\u8def\u7ebf\uff0c\u4ece\u56fe\u4e2d\u6211\u4eec\u53ef\u4ee5\u76f4\u63a5\u770b\u5230\u8fd9\u4e2a\u6e38\u620f\u89c4\u5219\u6240\u6784\u5efa\u7684\u7cfb\u7edf\u6709\u591a\u590d\u6742\u3002Wolfram \u8fd8\u8fdb\u4e00\u6b65\u63a2\u8ba8\u4e86\u5c06\u6e38\u620f\u548c\u8c1c\u9898\u4e0e\u7269\u7406\u5b66\u8054\u7cfb\u8d77\u6765\u7684\u53ef\u80fd\u6027\u3002<\/span><\/strong><\/p>\n


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

\u7814\u7a76\u9886\u57df\uff1a\u590d\u6742\u7cfb\u7edf\uff0c\u591a\u91cd\u8ba1\u7b97\u7cfb\u7edf\uff0c\u6e38\u620f
<\/span><\/strong><\/p>\n<\/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
<\/strong><\/section>\n<\/section>\n
\n

Stephan Wolfram<\/span><\/strong><\/span><\/strong> <\/span>| \u4f5c\u8005<\/strong><\/span><\/strong><\/span><\/strong><\/p>\n

\u53f6\u6893\u6d9b<\/span><\/strong><\/span><\/strong> <\/span>| \u8bd1<\/strong><\/span><\/strong>\u8005<\/strong><\/span><\/strong><\/strong><\/span><\/strong><\/span><\/p>\n

\u538c\u6c27\u83cc<\/span> <\/span>| \u5ba1\u6821<\/strong><\/span><\/strong><\/p>\n


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


<\/p>\n

\n

\n
\n
\n
\n
\n

<\/section>\n

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

\u8bd1\u6309<\/span><\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

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

\u6211\u4eec\u77e5\u9053\uff0c\u590d\u6742\u7cfb\u7edf\u6700\u91cd\u8981\u7684\u7279\u5f81\u5c31\u662f\u5177\u6709\u6d8c\u73b0\u884c\u4e3a<\/strong>\uff0c\u7b80\u5355\u89c4\u5219\u7684\u8fd0\u7528\u8bde\u751f\u51fa\u590d\u6742\u800c\u96be\u4ee5\u9884\u6d4b\u7684\u884c\u4e3a\u2014\u2014\u4e5f\u5c31\u662f\u8bf4\uff0c\u5728\u7cfb\u7edf\u7684\u89c4\u5219\u548c\u884c\u4e3a\u4e4b\u95f4\u5b58\u5728\u4e00\u79cd\u8ba4\u77e5\u9e3f\u6c9f<\/span>\uff08Epistemic gap\uff09<\/span>\u3002<\/span><\/p>\n


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

\u8fd9\u79cd\u8ba4\u77e5\u9e3f\u6c9f\u80fd\u6709\u591a\u5927\uff1f\u9e3f\u6c9f\u5bf9\u9762\u7684\u90a3\u4e2a\u4e16\u754c\u7a76\u7adf\u6709\u591a\u590d\u6742\uff1f\u6211\u4eec\u80fd\u591f\u5728\u8fd9\u4e9b\u95ee\u9898\u4e0a\u4f5c\u51fa\u67d0\u79cd\u7a0b\u5ea6\u4e0a\u7684\u6bd4\u8f83\uff0c\u751a\u81f3\u91cf\u5316\u7684\u8ba1\u7b97\u5417\uff1f<\/span><\/p>\n


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

\u9664\u4e86\u4e00\u79cd\u5355\u7eaf\u7684\u597d\u5947\u5fc3\u5728\u4fc3\u4f7f\u6211\u4eec\u4f5c\u51fa\u8fd9\u6837\u7684\u53d1\u95ee\uff0c\u8fd9\u4e2a\u95ee\u9898\u8fd8\u6709\u66f4\u52a0\u73b0\u5b9e\u7684\u610f\u4e49\u3002\u590d\u6742\u7cfb\u7edf\u6709\u5f88\u591a\u5b9e\u9645\u5e94\u7528\u3002\u5728\u6e38\u620f\u8bbe\u8ba1\u4e2d\uff0c<\/span>\u6e38\u620f\u89c4\u5219\u7684\u6d8c\u73b0\u884c\u4e3a\u4f7f\u5f97\u4e00\u4e2a\u6e38\u620f\u5177\u6709\u6df1\u5ea6\u548c\u8da3\u5473\u6027<\/span><\/strong><\/a>\uff1b\u5728\u8ba1\u7b97\u521b\u610f\u5b66\u4e2d\uff0c<\/span>\u521b\u4f5c\u673a\u5236\u7684\u6d8c\u73b0\u884c\u4e3a\u51b3\u5b9a\u4e86\u6211\u4eec\u5728\u591a\u5927\u7a0b\u5ea6\u4e0a\u53ef\u4ee5\u5c06\u8fd9\u4e2a\u7cfb\u7edf\u770b\u4f5c\u662f\u5177\u6709\u60f3\u8c61\u529b\u7684<\/span><\/strong><\/a>\u3002\u6211\u4eec\u6709\u529e\u6cd5\u53bb\u6bd4\u8f83\u4e24\u4e2a\u6e38\u620f\u8c01\u66f4\u6709\u6df1\u5ea6\uff0c\u6216\u8005\u4e24\u4e2a\u81ea\u52a8\u521b\u4f5c\u7cfb\u7edf\u8c01\u66f4\u5177\u60f3\u8c61\u529b\u5417\uff1f<\/span><\/p>\n


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

Wolfram\u7684\u8fd9\u7bc7\u6587\u7ae0\uff0c\u63d0\u51fa\u4e86\u4e00\u79cd\u53ef\u89c6\u5316\u548c\u5177\u4f53\u63a2\u8ba8\u6d8c\u73b0\u884c\u4e3a\u7684\u4e30\u5bcc\u7a0b\u5ea6\u7684\u601d\u8def\u2014\u2014\u4e5f\u5c31\u662f\u591a\u91cd\u8ba1\u7b97\u8fc7\u7a0b<\/span>\uff08Multicomputational Process\uff09<\/span>\u7684\u6982\u5ff5\u3002\u4f5c\u8005\u4ee5\u51e0\u4e2a\u4f20\u7edf\u7684\u6e38\u620f\u6216\u8005\u8bf4\u8c1c\u9898\u4e3a\u4f8b\uff0c\u5728\u8ba1\u7b97\u673a\u7684\u5f3a\u5927\u7b97\u529b\u4e0b\u5f97\u4ee5\u7528\u56fe<\/span>\uff08Graph\uff09<\/span>\u7684\u65b9\u5f0f\u53bb\u53ef\u89c6\u5316\u8fd9\u4e9b\u6e38\u620f\u89c4\u5219\u4e0b\u7684\u53ef\u80fd\u6e38\u73a9\u8def\u7ebf\u3002\u80fd\u591f\u5c06\u6e38\u620f\u89c4\u5219\u7684\u6df1\u5ea6\u4e0e\u8fd9\u4e9b\u56fe\u7684\u8bb8\u591a\u76f4\u89c2\u7279\u5f81\u6302\u94a9\uff0c\u4e5f\u5f97\u4ee5\u5c06\u4e00\u4e9b\u56fe\u8bba\u4e2d\u65e9\u5df2\u5efa\u7acb\u7684\u7406\u8bba\u8fc1\u79fb\u5230\u5bf9\u6e38\u620f\u8da3\u5473\u6027\u7684\u8ba8\u8bba\u8bed\u5883\u4e0b\u3002\u6211\u4eec\u80fd\u5728\u8fd9\u4e9b\u56fe\u4e0a\u76f4\u63a5\u300c\u770b\u5230\u300d\u4e00\u4e2a\u6e38\u620f\u6709\u591a\u6709\u8da3\u3001\u6709\u591a\u96be\u3001\u5bf9\u54ea\u4e2a\u73a9\u5bb6\u66f4\u6709\u5229\u2014\u2014\u66f4\u91cd\u8981\u7684\u662f\uff0c\u8fd9\u4e2a\u6e38\u620f\u89c4\u5219\u6240\u6784\u5efa\u7684\u7cfb\u7edf\u6709\u591a\u590d\u6742\u3002<\/span><\/p>\n


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

\u5728\u6211\u4eec\u5df2\u7ecf\u611f\u53d7\u5230\u8bb8\u591a\u770b\u4f3c\u7b80\u5355\u7684\u6e38\u620f\u7adf\u6709\u7740\u5982\u6b64\u4ee4\u4eba\u53f9\u4e3a\u89c2\u6b62\u7684\u590d\u6742\u6027\u4e4b\u540e\uff0c\u4f5c\u8005\u53c8\u5f15\u51fa Rulial space<\/span>\uff08\u6240\u6709\u53ef\u80fd\u7684\u89c4\u5219\u4ee5\u53ca\u8fd9\u4e9b\u89c4\u5219\u7684\u6240\u6709\u5e94\u7528\u65b9\u5f0f\u6240\u7ec4\u6210\u7684\u7a7a\u95f4\uff09<\/span>\u7684\u6982\u5ff5\uff0c\u8ba9\u6211\u4eec\u53bb\u60f3\u8c61\u53ef\u8ba1\u7b97\u7684\u5b87\u5b99\u8fd9\u4e2a\u590d\u6742\u7cfb\u7edf\uff0c\u5176\u590d\u6742\u7a0b\u5ea6\u53c8\u5f62\u6210\u4e86\u600e\u6837\u7684\u4e00\u79cd\u7ef4\u5ea6\u78be\u538b\u3002\u8fd9\u8db3\u4ee5\u8ba9\u4e00\u4e2a\u5e76\u6ca1\u6709\u5728\u4ef0\u671b\u661f\u7a7a\u7684\u4eba\uff0c\u4e5f\u5728\u300c\u5b87\u5b99\u7684\u6d69\u701a\u300d\u4e4b\u4e0b\u54d1\u53e3\u5931\u8a00\u3002<\/span><\/p>\n


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

\u6211\u4f5c\u4e3a\u4e00\u4e2aAI\u7814\u7a76\u8005\uff0c\u867d\u7136\u5f88\u65e9\u5c31\u63a5\u89e6\u5230\u8bf8\u5982\u57fa\u4e8e\u8499\u7279\u5361\u6d1b\u6811\u641c\u7d22\u548c\u52a0\u5f3a\u5b66\u4e60\u7684\u6e38\u620fAI\uff0c\u4ee5\u53ca\u795e\u7ecf\u7f51\u7edc\u6216\u9057\u4f20\u7b97\u6cd5\u751f\u6210\u6e38\u620f\u89c4\u5219\u4e4b\u7c7b\u7684\u8ba1\u7b97\u673a\u6280\u672f\uff0c\u4f46\u8fd9\u7bc7\u6587\u7ae0\u8ba9\u6211\u7b2c\u4e00\u6b21\u611f\u53f9\uff0c\u6211\u4eec\u505a\u7684\u662f\u4e00\u4e9b\u591a\u4e48\u5927\u80c6\u7684\u300c\u8bd5\u56fe\u4e0e\u5b87\u5b99\u901a\u7075\u300d\u7684\u4e8b\u60c5\u3002<\/span><\/p>\n


<\/p>\n


<\/p>\n

\u538c\u6c27\u83cc<\/span><\/p>\n


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


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

\n
\n
\n
\n
\n

<\/section>\n

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

\u6821\u6309<\/span><\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

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

\u6211\u662f\u5728\u5c1d\u8bd5\u4f7f\u7528 Wolfram \u8bed\u8a00\u548c\u7406\u89e3\u5176\u521b\u59cb\u4eba\u5e9e\u5927\uff0c\u4e14\u4e1a\u5df2\u8fdb\u5165\u5de5\u4e1a\u5316\u548c\u5546\u4e1a\u53ef\u6301\u7eed\u9053\u8def\u7684\u613f\u666f\u4e2d\u53d1\u73b0\u4e86\u8fd9\u7bc7\u6587\u7ae0\u7684\uff0c\u6211\u7acb\u523b\u610f\u8bc6\u5230\u8fd9\u662f\u975e\u5e38\u6709\u8da3\u7684\u548c\u7a00\u6709\u7684\u7814\u7a76\u5c1d\u8bd5\uff0c\u5c31\u5982\u540c\u590d\u6742\u79d1\u5b66\u7684\u51fa\u73b0\uff0c\u5f00\u59cb\u5c06\u76ee\u5149\u4ece\u8fc7\u5927\u7684\u5929\u4f53\u3001\u8fc7\u5c0f\u7684\u539f\u5b50\u800c\u8f6c\u5411\u65e5\u5e38\u751f\u6d3b\u4e2d\u5982\u6c34\u9f99\u5934\u7684\u6c34\u6ef4\uff0c\u6e4d\u6d41\uff0c\u6c14\u4f53\uff0c\u6d77\u5cb8\u7ebf\u8fd9\u6837\u7684\u96be\u4ee5\u8ba1\u7b97\u7684\u4e8b\u7269\uff1b\u6216\u8bb8\u5c31\u5982\u75f4\u8ff7\u4e8e\u56fd\u9645\u8c61\u68cb\u7684\u514b\u52b3\u5fb7\u00b7\u9999\u519c\u4e00\u6837\uff0c\u6211\u4eec\u662f\u4e0d\u662f\u4e5f\u53ef\u4ee5\u7528\u79d1\u5b66\u7684\u89c6\u89d2\u6765\u4e25\u8083\u4e14\u6df1\u5165\u5730\u7814\u7a76\u4e00\u4e9b\u300c\u5f88\u7b80\u5355\u300d\u7684\u6e38\u620f\uff0c\u5c31\u50cf\u8fd9\u7bc7\u6587\u7ae0\u4e00\u6837\uff1f<\/span><\/p>\n


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

\u8fd9\u4e0d\u662f\u4e00\u4ef6\u5bb9\u6613\u7684\u4e8b\uff0c\u5c31\u50cf Wolfram \u8bd5\u56fe\u8fdb\u884c\u7684\uff0c\u5b9e\u9645\u4e0a\u662f\u901a\u8fc7\u4eba\u7c7b\u5c42\u9762\u5bf9\u6e38\u620f\u7684\u601d\u8003\u6765\u7c7b\u6bd4\u5bf9\u7167\u91cf\u5b50\u529b\u5b66\u4e00\u6837\uff0c\u5728\u8fd9\u7bc7\u6587\u7ae0\u7684\u4f8b\u5b50\u4e2d\uff0c\u5373\u4fbf\u6709\u5f3a\u5927\uff0c\u80fd\u5c06\u5927\u91cf\u8ba1\u7b97\u53ef\u89c6\u5316\u7684 Wolfram \u8bed\u8a00\u548c\u6846\u67b6\u7684\u5e2e\u52a9\uff0c\u6e38\u620f\u7684\u7b80\u5355\u89c4\u5219\u4e2d\u8574\u542b\u7740\u7684\u4eba\u7c7b\u8bed\u8a00\u548c\u601d\u7ef4\u96be\u4ee5\u6355\u6349\u7684\u53ef\u80fd\u6027\uff0c\u4ee5\u53ca\u300c\u591a\u91cd\u8ba1\u7b97\u7684\u4e0d\u53ef\u8fd8\u539f\u6027\u300d\u4e5f\u8fdc\u8fdc\u8db3\u4ee5\u8ba9\u4eba\u610f\u8bc6\u5230\u6e38\u620f\u4e2d\u5b58\u5728\u7684\u67d0\u4e9b\u60ca\u4eba\u7684\u4e8b\u7269\u3002<\/span><\/p>\n


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

\u6e38\u620f\u8bbe\u8ba1\u8005\u5230\u5e95\u521b\u9020\u51fa\u6765\u7684\u662f\u4ec0\u4e48\uff1f<\/span><\/p>\n


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

\u5b58\u5728\u4e8e\u65f6\u95f4\u4e2d\u7684\u6211\u4eec\u300c\u53ea\u80fd\u300d\u5728\u4e00\u6b21\u6b21\u7684\u91cd\u590d\u4e2d\u7a7f\u8fc7\u8fd9\u4e9b\u590d\u6742\u5206\u652f\u7684\u591a\u8def\u56fe\uff0c\u7528\u76f4\u89c9\uff0c\u7075\u611f\uff0c\u79ef\u7d2f\u53bb\u6355\u6349\uff0c\u53bb\u505a\u51fa\u67d0\u4e9b\u68cb\u5b50\u7684\u51b3\u5b9a\uff0c\u90a3\u56db\u7ef4\u751f\u7269\u662f\u5426\u80fd\u591f\u4e00\u77ac\u95f4\u540c\u65f6\u770b\u5230\u6240\u6709\u9b54\u65b9\u8f6c\u52a8\u7684\u53ef\u80fd\u6027\u5462\uff1f\u5f53\u6211\u4eec\u54c0\u53f9\u4eba\u7c7b\u68cb\u624b\u8d25\u4e8eAI\uff0c\u4f46\u6211\u5374\u89c9\u5f97\uff0c\u4eba\u7c7b\u4f5c\u4e3a\u5982\u6b64\u4e0d\u64c5\u957f\u8ba1\u7b97\u7684\u751f\u7269<\/span>\uff08\u6240\u8c13\u8ba1\u7b97\u53d7\u9650\u7684\u5b9e\u4f53 computationally bounded entities\uff09<\/span>\uff0c\u5c45\u7136\u80fd\u591f\u5728\u8fd9\u6837\u79bb\u6563\u548c\u8ba1\u7b97\u5316\u7684\u535a\u5f08\u4e2d\u6297\u8861\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u591a\u5c11\u4ebf\u4e07\u6b21\uff0c\u548c\u591a\u5c11\u53c2\u6570\u7684\u8ba1\u7b97\uff0c\u8fd9\u5df2\u8db3\u4ee5\u4ee4\u4eba\u60ca\u5947\u4e86\u3002<\/span><\/p>\n


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

\u90a3\u4e48\uff0c\u5f53\u7269\u7406\u5b66\u5bb6\u548c\u6570\u5b66\u5bb6\u53d6\u9053\u4e8e\u6e38\u620f\u6765\u9610\u8ff0\u4e9b\u4ec0\u4e48\u4e8b\u65f6\uff0c\u6211\u4eec\u6216\u8bb8\u5e94\u8be5\u95ee\uff1a\u4e3a\u4f55\u6e38\u620f\u603b\u662f\u88ab\u53d6\u9053\uff0c\u6e38\u620f\u4e3a\u4f55\u6709\u80fd\u529b\uff0c\u53bb\u6210\u4e3a\u8fd9\u4e9b\u6700\u6df1\u5965\u77e5\u8bc6\u7684\u4e2d\u4ecb\u5462\uff1f\u6e38\u620f\u548c\u5b83\u4eec\uff0c\u548c\u4e16\u754c\u7684\u89c4\u5219\uff0c\u79d8\u5bc6\u4e4b\u95f4\u662f\u4ec0\u4e48\u5173\u7cfb\uff1f\u5728\u8fd9\u4e2a\u610f\u4e49\u4e0a\uff0c\u5c31\u50cf\u662f\u6570\u5b66\u662f\u5bf9\u4e16\u754c\u7684\u62bd\u8c61\uff0c\u800c\u63ed\u793a\u51fa\u67d0\u4e9b\u9762\u5411\uff0c\u800c\u6e38\u620f\u4e5f\u603b\u662f\u67d0\u79cd\u300c\u63ed\u793a\u300d\uff0c\u5c55\u9732\u51fa\u4e86\u67d0\u79cd\u73b0\u5b9e\uff0c\u5e76\u4e14\u6210\u4e3a\u6b63\u5728\u53d1\u751f\u7684\u73b0\u5b9e\u3002<\/span><\/p>\n


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

\u5f88\u591a\u5bf9\u4e8e\u8ba1\u7b97\u673a\u7684\u54f2\u5b66\u8ba8\u8bba\u6709\u7740\u79bb\u6563\u548c\u8fde\u7eed\/\u6a21\u62df\u548c\u6570\u5b57\u7684\u5bf9\u7167\uff0c\u4f46\u5728\u7269\u7406\u5b66\u7684\u89c6\u89d2\u4e0b\uff0c\u4e0b\u964d\u5230\u8db3\u591f\u4f4e\u7684\u5c42\u7ea7<\/span>\uff08\u751a\u81f3\u662f\u666e\u6717\u514b\u65f6\u95f4\uff09<\/span>\uff0c\u5c31\u50cfWolfram\u5728\u6587\u7ae0\u5f00\u5934\u6240\u8bf4\u7684\u300c\u7269\u7406\u4e16\u754c\u5728\u6700\u4f4e\u5c42\u6b21\u4e0a\u662f\u79bb\u6563\u7684\u2014\u2014\u5c31\u50cf\u6e38\u620f\u548c\u8c1c\u9898\u4e00\u6837\u300d\uff0c\u800c\u5bf9\u4e8e\u6e38\u620f\u6765\u8bf4\uff0c\u81ea\u7136\u6700\u7ec8\u662f\u79bb\u6563\u4ea6\u6216\u662f\u8fde\u7eed\u7684\u5e76\u975e\u91cd\u70b9\uff0c\u91cd\u8981\u7684\u662f\u6e38\u620f\u5236\u4f5c\u8005\u5982\u4f55\u6709\u80fd\u529b\u5728\u4e0d\u540c\u7684\u5c42\u9762\u6784\u5efa\u79bb\u6563\u548c\u8054\u7cfb\u7684\u5173\u8054\uff0c\u5e76\u4e14\u4ee5\u4eba\u7c7b\u89c6\u89d2<\/span>\uff08Humanizing\uff09<\/span>\uff0c\u5c06\u8fd9\u4e9b\u8bed\u8a00\u96be\u4ee5\u6355\u6349\uff0c\u8ba1\u7b97\u4e0d\u53ef\u8fd8\u539f\u7684\u591a\u8def\u8fc7\u7a0b\u5c55\u5f00\u3002<\/span><\/p>\n


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

\u8fd9\u7bc7\u6587\u7ae0\u6240\u5c55\u793a\u7684\u8ba1\u7b97\u5206\u6790\u65b9\u6cd5\uff0c\u4ee5\u53ca\u5bf9\u73b0\u6709\u6e38\u620f\u7684\u8ba1\u7b97\u6027\u89e3\u6784\uff0c\u6216\u8bb8\u4e5f\u80fd\u76f4\u63a5\u5730\u7ed9\u6e38\u620f\u8bbe\u8ba1\u7684\u601d\u8003\u5e26\u6765\u7684\u542f\u53d1\uff0c\u300c\u5f53\u6211\u4eec\u53d1\u73b0\u591a\u8def\u56fe\u5728\u67d0\u79cd\u7a0b\u5ea6\u4e0a\u300c\u96be\u4ee5\u89e3\u7801<\/span>\uff08decode\uff09<\/span>\u300d\u65f6\uff0c\u6211\u4eec\u5c31\u4f1a\u5f97\u5230\u4e00\u4e2a\u4e30\u5bcc\u7684\u3001\u5438\u5f15\u4eba\u7684\u6e38\u620f\u6216\u8c1c\u9898\u300d\uff0c\u800c\u4e5f\u6b63\u662f\u4e00\u79cd\u5bf9\u4e8e\u6e38\u620f\u8bbe\u8ba1\u6240\u5728\u7740\u624b\u5904\u7406\u7684\u4e8b\u7269\u7684\u4e00\u6b21\u6b63\u9762\u4e14\u76f4\u63a5\u7684\u8ba1\u7b97\u5448\u73b0\uff0c\u6e38\u620f\u8bbe\u8ba1\u5728\u505a\u4ec0\u4e48\uff1f\u5728\u67d0\u79cd\u610f\u4e49\u4e0a\u6765\u8bf4\uff0c\u4fbf\u6b63\u662f\u5728\u8c03\u6821\uff0c\u8bd5\u9a8c\u8fd9\u4e9b\u4e0d\u53ef\u8fd8\u539f\u7684\u591a\u8def\u548c\u5206\u652f\u56fe\u7684\u5f62\u6001\u3002<\/span><\/p>\n


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

\u672c\u6587\u5f97\u76ca\u4e8e Wolfram \u8bed\u8a00\u7684\u5f3a\u5927\u8ba1\u7b97\u80fd\u529b\uff0c\u800c\u5374\u4e5f\u53ea\u80fd\u4ece\u6781\u7b80\u7684\u4f8b\u5b50\u51fa\u53d1\uff0c\u66f4\u65e0\u6d89\u7535\u5b50\u6e38\u620f\uff0c\u52a8\u4f5c\u6e38\u620f\u7b49\uff0c\u4e0d\u7981\u4ee4\u4eba\u597d\u5947\uff0c\u5982 MOBA \u6e38\u620f\u662f\u5426\u80fd\u4ee5\u8fd9\u79cd\u65b9\u5f0f\u5206\u6790\uff1f\u4eba\u5de5\u667a\u80fd\u89c6\u89d2\u4e0b\u7684\u8fd9\u4e9b\u591a\u8def\u56fe\u7684\u7a7a\u95f4\u662f\u600e\u6837\u7684\uff1f\u6e38\u620f\u662f\u4ec0\u4e48\u4e1c\u897f\u300c\u7406\u60f3\u6a21\u578b\u300d\uff1f\u79cd\u79cd\u8fd9\u4e9b\u95ee\u9898\u4f9d\u65e7\u5f15\u8d77\u6211\u4eec\u7684\u597d\u5947\uff0c\u800c\u4ece\u6b64\u6587\u5176\u4e2d\u5f97\u4ee5\u4e00\u7aa5\u7684\u9519\u7efc\u590d\u6742\uff0c\u5927\u6982\u4e5f\u6b63\u662f\u6e38\u620f\u4e4b\u96be\u4ee5\u8a00\u8bf4\u7684\u7f18\u6545\u5427\u3002<\/span><\/p>\n


<\/p>\n

*\u975e\u5e38\u5f00\u5fc3\u80fd\u591f\u4e0e\u538c\u6c27\u83cc\u518d\u6b21\u5408\u4f5c\uff0c\u672c\u7bc7\u8d85\u957f\u6587\u7ae0\u7684\u7ffb\u8bd1\u8981\u4ef0\u4ed7\u4e8e\u5979\u7684\u8010\u5fc3\u4e0e\u7ec6\u81f4\u4e0e\u5b66\u8bc6\uff0c\u6b22\u8fce\u66f4\u591a\u4eba\u5173\u6ce8\u5979\u5173\u4e8e\u8ba1\u7b97\u673a\u521b\u610f\u5b66\uff0c\u8d5b\u535a\u6587\u672c\uff0c\u6d8c\u73b0\u53d9\u4e8b\u7684\u5b9d\u85cf<\/span>\u83cc\u7fa4\u53cd\u5e94\u5668<\/span><\/strong><\/a>\u3002<\/p>\n


<\/p>\n


<\/p>\n

\u53f6\u6893\u6d9b
\u843d\u65e5\u95f4<\/span><\/p>\n


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

\n

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


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

\n
\n
\n
\n
\n

<\/section>\n

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

\u4f5c\u8005\uff1aStephen Wolfram<\/span><\/strong><\/span><\/h2>\n<\/section>\n
\n

<\/section>\n

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

<\/h2>\n
<\/section>\n


<\/p>\n

\u65af\u8482\u82ac \u00b7 \u6c83\u5c14\u592b\u62c9\u59c6<\/span>\uff08Stephen Wolfram\uff09<\/span>\u662f Mathematica\uff0cWolfram | Alpha \u548c Wolfram \u8bed\u8a00\u7684\u521b\u59cb\u4eba\uff0c\u300a\u4e00\u79cd\u65b0\u79d1\u5b66\u300b<\/span>\uff08A New Kind of Science\uff09<\/span>\u7684\u4f5c\u8005\uff0cWolfram \u7269\u7406\u8ba1\u5212\u7684\u53d1\u8d77\u4eba\uff0c\u4ee5\u53caWolfram Research \u516c\u53f8\u7684\u521b\u59cb\u4eba\u548c\u9996\u5e2d\u6267\u884c\u5b98\u3002\u5728\u56db\u5341\u591a\u5e74\u7684\u65f6\u95f4\u91cc\uff0c\u4ed6\u4e00\u76f4\u662f\u8ba1\u7b97\u601d\u7ef4\u53d1\u5c55\u548c\u5e94\u7528\u7684\u5148\u9a71\u30fc\u30fc\u5e76\u5728\u79d1\u5b66\u3001\u6280\u672f\u548c\u5546\u4e1a\u9886\u57df\u505a\u51fa\u8bb8\u591a\u53d1\u73b0\u3001\u53d1\u660e\u548c\u521b\u65b0\u3002<\/span><\/p>\n


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

\u6c83\u5c14\u592b\u62c9\u59c61959\u5e74\u51fa\u751f\u4e8e\u4f26\u6566\uff0c\u66fe\u5c31\u8bfb\u4e8e\u4f0a\u987f\u516c\u5b66\u3001\u725b\u6d25\u5927\u5b66\u548c\u52a0\u5dde\u7406\u5de5\u5b66\u9662\u3002\u4ed6\u572815\u5c81\u65f6\u53d1\u8868\u4e86\u7b2c\u4e00\u7bc7\u79d1\u5b66\u8bba\u6587\uff0c\u5e76\u572820\u5c81\u65f6\u83b7\u5f97\u4e86\u52a0\u5dde\u7406\u5de5\u5b66\u9662\u7684\u7406\u8bba\u7269\u7406\u5b66\u535a\u58eb\u5b66\u4f4d\u3002\u6c83\u5c14\u592b\u62c9\u59c6\u65e9\u671f\u7684\u79d1\u5b66\u5de5\u4f5c\u4e3b\u8981\u662f\u5728\u9ad8\u80fd\u7269\u7406\u5b66\u3001\u91cf\u5b50\u573a\u8bba\u548c\u5b87\u5b99\u5b66\u65b9\u9762\uff0c\u5176\u4e2d\u5305\u62ec\u4e00\u4e9b\u73b0\u5728\u5df2\u7ecf\u6210\u4e3a\u7ecf\u5178\u7684\u7ed3\u679c\u3002\u4ed6\u4ece1973\u5e74\u5f00\u59cb\u4f7f\u7528\u8ba1\u7b97\u673a\uff0c\u8fc5\u901f\u6210\u4e3a\u65b0\u5174\u79d1\u5b66\u8ba1\u7b97\u9886\u57df\u7684\u9886\u5bfc\u8005\u30021979\u5e74\uff0c\u4ed6\u5f00\u59cb\u6784\u5efasmp – \u7b2c\u4e00\u4e2a\u73b0\u4ee3\u8ba1\u7b97\u673a\u4ee3\u6570\u7cfb\u7edf\uff0c\u5e76\u4e8e1981\u5e74\u5546\u4e1a\u5316\u53d1\u5e03\u3002<\/span><\/p>\n


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

\u4e3a\u4e86\u8868\u5f70\u4ed6\u5728\u7269\u7406\u5b66\u548c\u8ba1\u7b97\u673a\u65b9\u9762\u7684\u65e9\u671f\u5de5\u4f5c\uff0c\u6c83\u5c14\u592b\u62c9\u59c6\u57281981\u5e74\u6210\u4e3a\u9ea6\u514b\u963f\u745f\u5956\u5b66\u91d1<\/span>\uff08MacArthur Fellowship\uff09<\/span>\u6700\u5e74\u8f7b\u7684\u83b7\u5f97\u8005\u30021981\u5e74\u5e95\uff0c\u4ed6\u5f00\u59cb\u4e86\u4e00\u4e2a\u96c4\u5fc3\u52c3\u52c3\u7684\u79d1\u5b66\u65b0\u65b9\u5411\uff0c\u65e8\u5728\u7406\u89e3\u81ea\u7136\u754c\u590d\u6742\u6027\u7684\u8d77\u6e90\u3002\u4ed6\u7b2c\u4e00\u4e2a\u5173\u952e\u60f3\u6cd5\u662f\u4f7f\u7528\u8ba1\u7b97\u673a\u5b9e\u9a8c\u6765\u7814\u7a76\u88ab\u79f0\u4e3a\u5143\u80de\u81ea\u52a8\u673a<\/span>\uff08cellular automata\uff09<\/span>\u7684\u7b80\u5355\u8ba1\u7b97\u673a\u7a0b\u5e8f\u7684\u884c\u4e3a\u3002\u8fd9\u8ba9\u4ed6\u5bf9\u590d\u6742\u6027\u7684\u8d77\u6e90\u6709\u4e86\u4e00\u7cfb\u5217\u60ca\u4eba\u7684\u53d1\u73b0\u3002\u6c83\u5c14\u592b\u62c9\u59c6\u53d1\u8868\u7684\u8bba\u6587\u8fc5\u901f\u4ea7\u751f\u4e86\u91cd\u5927\u5f71\u54cd\uff0c\u4e3a\u4ed6\u79f0\u4e3a\u590d\u6742\u7cfb\u7edf\u7814\u7a76\u7684\u65b0\u5174\u9886\u57df\u5960\u5b9a\u4e86\u57fa\u7840\u3002<\/span><\/p>\n


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

20\u4e16\u7eaa80\u5e74\u4ee3\u4e2d\u671f\uff0c\u6c83\u5c14\u592b\u62c9\u59c6\u7ee7\u7eed\u4ed6\u5728\u590d\u6742\u6027\u65b9\u9762\u7684\u5de5\u4f5c\uff0c\u53d1\u73b0\u4e86\u8ba1\u7b97\u548c\u81ea\u7136\u4e4b\u95f4\u7684\u4e00\u4e9b\u57fa\u672c\u8054\u7cfb\uff0c\u5e76\u521b\u9020\u4e86\u8bf8\u5982\u8ba1\u7b97\u4e0d\u53ef\u8fd8\u539f\u6027<\/span>\uff08\u672c\u7bc7\u4e2d\u63d0\u53ca\uff09<\/span>\u7b49\u6982\u5ff5\u3002\u6c83\u5c14\u592b\u62c9\u59c6\u7684\u5de5\u4f5c\u5e26\u6765\u4e86\u5e7f\u6cdb\u7684\u5e94\u7528\uff0c\u5e76\u4e3a\u590d\u6742\u6027\u7406\u8bba\u548c\u4eba\u5de5\u751f\u547d\u7b49\u8ba1\u5212\u63d0\u4f9b\u4e86\u4e3b\u8981\u7684\u79d1\u5b66\u57fa\u7840\u3002\u6c83\u5c14\u592b\u62c9\u59c6\u672c\u4eba\u7528\u4ed6\u7684\u60f3\u6cd5\u5f00\u53d1\u4e86\u4e00\u79cd\u65b0\u7684\u968f\u673a\u751f\u6210\u7cfb\u7edf\u548c\u4e00\u79cd\u8ba1\u7b97\u6d41\u4f53\u52a8\u529b\u5b66\u7684\u65b0\u65b9\u6cd5\u2014\u2014\u8fd9\u4e24\u79cd\u65b9\u6cd5\u73b0\u5728\u90fd\u88ab\u5e7f\u6cdb\u4f7f\u7528\u3002<\/span><\/p>\n


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

\u968f\u7740\u4ed6\u5728\u590d\u6742\u7cfb\u7edf\u7814\u7a76\u65b9\u9762\u7684\u79d1\u5b66\u5de5\u4f5c\uff0c\u6c83\u5c14\u592b\u62c9\u59c6\u4e8e1986\u5e74\u521b\u529e\u4e86\u8be5\u9886\u57df\u7684\u7b2c\u4e00\u672c\u6742\u5fd7\u300a\u590d\u6742\u7cfb\u7edf\u300b<\/span>\uff08Complex Systems\uff09<\/span>\uff0c\u5e76\u5efa\u7acb\u4e86\u5176\u7b2c\u4e00\u4e2a\u7814\u7a76\u4e2d\u5fc3\u3002\u5728\u7ecf\u5386\u4e86\u4e00\u6bb5\u975e\u5e38\u6210\u529f\u7684\u5b66\u672f\u751f\u6daf\u540e\u2014\u2014\u5148\u662f\u5728\u52a0\u5dde\u7406\u5de5\u5b66\u9662\uff0c\u7136\u540e\u5728\u666e\u6797\u65af\u987f\u9ad8\u7ea7\u7814\u7a76\u9662\uff0c\u6700\u540e\u5728\u4f0a\u5229\u8bfa\u65af\u5dde\u5927\u5b66\u62c5\u4efb\u7269\u7406\u3001\u6570\u5b66\u548c\u8ba1\u7b97\u673a\u79d1\u5b66\u6559\u6388\u2014\u2014\u6c83\u5c14\u592b\u62c9\u59c6\u521b\u7acb\u4e86 Wolfram Research, Inc.\u3002<\/span><\/p>\n


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

\u6c83\u5c14\u592b\u62c9\u59c6\u57281986\u5e74\u5e95\u5f00\u59cb\u5f00\u53d1Mathematica\u3002Mathematica\u7684\u7b2c\u4e00\u4e2a\u7248\u672c\u4e8e1988\u5e746\u670823\u65e5\u53d1\u5e03\uff0c\u7acb\u5373\u88ab\u8a89\u4e3a\u8ba1\u7b97\u9886\u57df\u7684\u91cd\u5927\u8fdb\u6b65\u3002\u5728\u968f\u540e\u7684\u51e0\u5e74\u91cc\uff0cMathematica\u7684\u53d7\u6b22\u8fce\u7a0b\u5ea6\u8fc5\u901f\u589e\u957f\uff0cWolfram Research \u6210\u4e3a\u8f6f\u4ef6\u884c\u4e1a\u7684\u4e16\u754c\u9886\u5bfc\u8005\uff0c\u5728\u6280\u672f\u548c\u5546\u4e1a\u65b9\u9762\u7684\u5353\u8d8a\u88ab\u5e7f\u6cdb\u8ba4\u53ef\u3002\u4ece\u5b83\u6700\u521d\u4f5c\u4e3a\u4e00\u4e2a\u6280\u672f\u8ba1\u7b97\u7cfb\u7edf\u5f00\u59cb\uff0cMathematica\u5728\u8fc7\u53bb\u7684\u51e0\u5e74\u91cc\u5728\u8303\u56f4\u4e0a\u6025\u5267\u589e\u957f\u2014\u2014\u5728\u8d85\u8fc730\u5e74\u7684\u8fc7\u7a0b\u4e2d\uff0c\u5b83\u5728\u8bb8\u591a\u9886\u57df\u548c\u884c\u4e1a\u4e2d\u8d1f\u8d23\u8bb8\u591a\u91cd\u8981\u7684\u53d1\u660e\u548c\u53d1\u73b0\uff0c\u4ee5\u53ca\u6210\u4e3a\u4e00\u4ee3\u53c8\u4e00\u4ee3\u5b66\u751f\u6559\u80b2\u7684\u4e2d\u5fc3\u5de5\u5177\u3002<\/span><\/p>\n


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

1991\u5e74\uff0c\u6c83\u5c14\u592b\u62c9\u59c6\u5f00\u59cb\u628a\u4ed6\u7684\u65f6\u95f4\u5206\u914d\u5728Mathematica\u5f00\u53d1\u548c\u79d1\u5b66\u7814\u7a76\u4e4b\u95f4\u3002\u572820\u4e16\u7eaa80\u5e74\u4ee3\u4e2d\u671f\u5de5\u4f5c\u7684\u57fa\u7840\u4e0a\uff0c\u73b0\u5728\u53c8\u6709\u4e86Mathematica\u4f5c\u4e3a\u5de5\u5177\uff0c\u8fc5\u901f\u53d6\u5f97\u4e86\u4e00\u7cfb\u5217\u91cd\u5927\u7684\u65b0\u53d1\u73b0\u3002\u5230\u4e8620\u4e16\u7eaa90\u5e74\u4ee3\u4e2d\u671f\uff0c\u4ed6\u7684\u53d1\u73b0\u4f7f\u4ed6\u53d1\u5c55\u51fa\u4e86\u4e00\u4e2a\u5168\u65b0\u7684\u6982\u5ff5\u6846\u67b6\uff0c\u7136\u540e\u572890\u5e74\u4ee3\u5269\u4e0b\u7684\u65f6\u95f4\u91cc\uff0c\u4ed6\u4e0d\u4ec5\u5c06\u8fd9\u4e2a\u6846\u67b6\u5e94\u7528\u4e8e\u65b0\u7684\u95ee\u9898\uff0c\u800c\u4e14\u8fd8\u5e94\u7528\u4e8e\u7269\u7406\u5b66\u3001\u751f\u7269\u5b66\u3001\u8ba1\u7b97\u673a\u79d1\u5b66\u3001\u6570\u5b66\u548c\u5176\u4ed6\u51e0\u4e2a\u9886\u57df\u4e2d\u8bb8\u591a\u73b0\u5b58\u7684\u57fa\u7840\u95ee\u9898\u3002<\/span><\/p>\n


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

\u7ecf\u8fc7\u5341\u591a\u5e74\u9ad8\u5ea6\u96c6\u4e2d\u7684\u5de5\u4f5c\uff0c\u6c83\u5c14\u592b\u62c9\u59c6\u7ec8\u4e8e\u5728\u4ed61200\u9875\u7684\u300a\u4e00\u79cd\u65b0\u79d1\u5b66\u300b\u4e00\u4e66\u4e2d\u63cf\u8ff0\u4e86\u4ed6\u7684\u6210\u5c31\u3002\u8fd9\u672c\u4e66\u4e8e2002\u5e745\u670814\u65e5\u53d1\u884c\uff0c\u5e7f\u53d7\u597d\u8bc4\uff0c\u5e76\u7acb\u5373\u6210\u4e3a\u7545\u9500\u4e66\u3002\u5b83\u7684\u51fa\u7248\u88ab\u89c6\u4e3a\u5f00\u542f\u4e86\u79d1\u5b66\u9886\u57df\u5177\u6709\u5386\u53f2\u91cd\u8981\u6027\u7684\u8303\u5f0f\u8f6c\u53d8\uff0c\u6bcf\u5e74\u90fd\u6709\u65b0\u7684\u542b\u4e49\u51fa\u73b0\u3002\u300a\u4e00\u79cd\u65b0\u79d1\u5b66\u300b\u5305\u542b\u6216\u6fc0\u53d1\u4e86\u8bb8\u591a\u5177\u4f53\u7684\u53d1\u73b0\uff0c\u5305\u62ec\u6700\u7b80\u5355\u7684\u903b\u8f91\u516c\u7406\u7cfb\u7edf\u548c\u6700\u7b80\u5355\u7684\u901a\u7528\u56fe\u7075\u673a\u3002<\/span><\/p>\n


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

\u57fa\u4e8eMathematica\u548c\u300a\u4e00\u79cd\u65b0\u79d1\u5b66\u300b\u7684\u601d\u60f3\uff0c\u6c83\u5c14\u592b\u62c9\u59c6\u5f00\u59cb\u4e86\u4e00\u4e2a\u66f4\u96c4\u5fc3\u52c3\u52c3\u7684\u9879\u76ee\uff1a\u6784\u5efa\u4e00\u4e2a\u7cfb\u7edf\uff0c\u4f7f\u4e16\u754c\u4e0a\u5c3d\u53ef\u80fd\u591a\u7684\u77e5\u8bc6\u53ef\u4ee5\u7acb\u5373\u8ba1\u7b97\uff0c\u5e76\u8ba9\u6bcf\u4e2a\u4eba\u90fd\u53ef\u4ee5\u8bbf\u95ee\u3002Wolfram | Alpha \u57282009\u5e745\u6708\u7684\u53d1\u5e03\u88ab\u5e7f\u6cdb\u8ba4\u4e3a\u662f\u5386\u53f2\u6027\u7684\u4e00\u6b65\uff0c\u5b83\u4e3a\u8ba1\u7b97\u548c\u4eba\u5de5\u667a\u80fd\u5b9a\u4e49\u4e86\u4e00\u4e2a\u65b0\u7684\u7ef4\u5ea6\u2014\u2014\u73b0\u5728\u6570\u767e\u4e07\u4eba\u6bcf\u5929\u90fd\u4f9d\u8d56\u5b83\u76f4\u63a5\u6216\u901a\u8fc7\u667a\u80fd\u52a9\u624b<\/span>\uff08\u5982Siri\u548cAlexa\uff09<\/span>\u8ba1\u7b97\u7b54\u6848\u3002<\/span><\/p>\n


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

2014\u5e74\uff0c\u6c83\u5c14\u592b\u62c9\u59c6\u53d6\u5f97\u4e86\u53e6\u4e00\u4e2a\u7a81\u7834\uff0c\u5728 Mathematica \u548c Wolfram|Alpha \u7684\u57fa\u7840\u4e0a\u521b\u5efa\u4e86Wolfram \u8bed\u8a00\u3002\u57fa\u4e8e\u6c83\u5c14\u592b\u62c9\u59c6\u5728\u8fc7\u53bb\u4e09\u5341\u5e74\u4e2d\u5f00\u53d1\u7684\u524d\u6240\u672a\u6709\u7684\u6df1\u5ea6\u6280\u672f\u6808\uff0cWolfram\u8bed\u8a00\u5f15\u5165\u4e86\u5168\u5c3a\u5ea6\u8ba1\u7b97\u8bed\u8a00<\/span>\uff08full-scale computational language\uff09<\/span>\u7684\u65b0\u6982\u5ff5\uff0c\u5b83\u96c6\u6210\u4e86\u5927\u91cf\u5173\u4e8e\u8ba1\u7b97\u548c\u4e16\u754c\u7684\u77e5\u8bc6\uff0c\u4ece\u800c\u5b9e\u73b0\u8ba1\u7b97\u6027\u63cf\u8ff0\u548c\u81ea\u52a8\u5316\u7684\u65b0\u6c34\u5e73\uff0c\u8fd9\u53ef\u4ee5\u4f5c\u4e3a\u5927\u91cf\u57fa\u4e8e\u8ba1\u7b97\u7684\u65b0\u9886\u57df\u7684\u57fa\u7840\u3002<\/span><\/p>\n


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

2020\u5e74\uff0c\u5728\u8fd130\u5e74\u53d1\u5c55\u7684\u601d\u60f3\u57fa\u7840\u4e0a\uff0c\u6c83\u5c14\u592b\u62c9\u59c6\u5ba3\u5e03\u5728\u53d1\u73b0\u7269\u7406\u5b66\u57fa\u672c\u7406\u8bba\u65b9\u9762\u53d6\u5f97\u7a81\u7834\uff0c\u5e76\u542f\u52a8\u4e86Wolfram\u7269\u7406\u5b66\u8ba1\u5212\uff0c\u4ee5\u9f13\u52b1\u5e7f\u6cdb\u53c2\u4e0e\u8fd9\u4e00\u96c4\u5fc3\u52c3\u52c3\u7684\u5386\u53f2\u6027\u9879\u76ee\u3002<\/span><\/p>\n


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

https:\/\/www.stephenwolfram.com\/about\/<\/span><\/p>\n


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

\u300c\u7136\u540e\u5f53\u4ed6\u5f00\u59cb\u7814\u7a76\u6e38\u620f\u2026\u2026\u300d<\/span><\/p>\n

\n
\n
\n

\u539f\u6587\u94fe\u63a5\uff1a<\/span><\/p>\n

https:\/\/writings.stephenwolfram.com\/2022\/06\/games-and-puzzles-as-multicomputational-systems\/<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


<\/p>\n

\u672c\u6587\u7ffb\u8bd1\u5df2\u7ecf\u83b7\u5f97\u6388\u6743<\/span><\/p>\n


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

<\/section>\n


<\/p>\n

\u6821\u6ce8\uff1a\u6b64\u5916\uff0c\u672c\u6587\u7684\u539f\u6587\u94fe\u63a5\u4e2d\u7684\u6bcf\u4e00\u5f20\u56fe\u90fd\u662f\u7528 Wolfram \u8bed\u8a00\u8fdb\u884c\u7f16\u7a0b\u5e76\u53ef\u4ee5\u76f4\u63a5\u590d\u5236\u51fa\u6e90\u7801\uff0c\u4f60\u53ef\u4ee5\u5728 Wolfram Mathematica \u6216\u8005\u662f Wolfram  Cloud \u8fd9\u6837\u7684\u7f16\u8f91\u5668\u4e2d\u5c55\u5f00\uff0c\u5e76\u4e14\u8fdb\u884c\u8ba1\u7b97\u548c\u751f\u6210\u9a8c\u8bc1\u7684\uff0c\u751a\u81f3\u8fdb\u884c\u4ea4\u4e92\uff0c\u5982\u4e0b\uff1a<\/span><\/p>\n


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

<\/section>\n

<\/section>\n

<\/section>\n
\n

<\/section>\n

<\/section>\n

<\/h1>\n

\n
\n
\n
\n
\n

<\/section>\n

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

Games and Puzzles as <\/span><\/strong><\/span><\/h1>\n

Multicomputational Systems<\/span><\/strong><\/span><\/h1>\n<\/section>\n
\n

<\/section>\n

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

<\/h1>\n

June 8, 2022<\/span><\/p>\n


<\/p>\n

<\/section>\n

<\/section>\n

<\/section>\n

<\/section>\n

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

\n
\n
\n
\n
\n

<\/section>\n

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

\u65e5\u5e38\u89c6\u89d2\u4e0b\u7684\u591a\u91cd\u8ba1\u7b97\u8fc7\u7a0b <\/span><\/strong><\/span><\/h3>\n

Humanizing Multicomputational <\/span><\/strong><\/span><\/h3>\n

Processes<\/span><\/strong><\/span><\/h3>\n<\/section>\n
\n

<\/section>\n

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

<\/h3>\n

\u591a\u91cd\u8ba1\u7b97<\/span>\uff08Multicomputational\uff09<\/span>\u662f\u300cWolfram \u7269\u7406\u9879\u76ee\u300d<\/span>\uff08 Wolfram Physics Project\uff09<\/span>\u7684\u6838\u5fc3\u6982\u5ff5\u4e4b\u4e00\uff0c\u5c24\u5176\u662f\u6211\u4eec\u5bf9\u91cf\u5b50\u529b\u5b66\u7684\u65b0\u5174\u7406\u89e3\u7684\u6838\u5fc3\u3002\u4f46\u662f\uff0c\u5982\u4f55\u624d\u80fd\u5bf9\u4ece\u4e00\u5f00\u59cb\u5c31\u5f88\u62bd\u8c61\u7684\u591a\u91cd\u8ba1\u7b97\u7684\u6982\u5ff5\u6709\u4e00\u4e2a\u76f4\u89c2\u7684\u8ba4\u8bc6\u5462\uff1f<\/span><\/p>\n


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

\u6211\u76f8\u4fe1\uff0c\u4e00\u4e2a\u597d\u7684\u65b9\u6cd5\u662f\u5728\u719f\u6089\u7684\u7cfb\u7edf\u548c\u60c5\u51b5\u4e2d\u770b\u5230\u5b83\u8d77\u4f5c\u7528\u3002<\/span><\/p>\n


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

\u6211\u5728\u8fd9\u91cc\u63a2\u8ba8\u4e00\u4e2a\u4f3c\u4e4e\u7279\u522b\u597d\u7684\u4f8b\u5b50\uff1a\u6e38\u620f\u548c\u8c1c\u9898\u3002<\/span><\/p>\n


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

\u4eba\u4eec\u53ef\u80fd\u4e0d\u4f1a\u60f3\u5230\uff0c\u50cf\u4f17\u6240\u5468\u77e5\u7684\u6e38\u620f\u548c\u8c1c\u9898\u8fd9\u6837\u7684\u65e5\u5e38\u4e8b\u7269\u4f1a\u4e0e\u91cf\u5b50\u529b\u5b66\u8fd9\u6837\u7684\u5f62\u5f0f\u5316\u7406\u8bba\u6709\u4efb\u4f55\u8054\u7cfb\u3002\u4f46\u662f\u591a\u91cd\u8ba1\u7b97\u7684\u89c2\u70b9\u63d0\u4f9b\u4e86\u4e00\u4e2a\u5173\u8054\u3002\u4e8b\u5b9e\u4e0a\uff0c\u6211\u4eec\u53ef\u4ee5\u628a\u5b58\u5728\u300c\u6709\u8da3\u7684\u300d\u6e38\u620f\u548c\u8c1c\u9898\u7684\u8fd9\u79cd\u6070\u597d\u7684\u53ef\u80fd\u6027\u672c\u8eab\uff0c\u4e0e\u591a\u91cd\u8ba1\u7b97\u7684\u4e00\u4e2a\u6838\u5fc3\u73b0\u8c61\u8054\u7cfb\u8d77\u6765\uff0c\u5373\u591a\u91cd\u8ba1\u7b97\u7684\u4e0d\u53ef\u8fd8\u539f\u6027<\/span>\uff08multicomputational irreducibility\uff09<\/span>\u3002<\/span><\/p>\n


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

\uff08\u8bd1\u6ce8\uff1a\u300c\u591a\u91cd\u8ba1\u7b97\u7684\u4e0d\u53ef\u8fd8\u539f\u6027\u300d\u8fd9\u4e2a\u7ffb\u8bd1\u4e2d\u7684\u300c\u8fd8\u539f\u300d\u542b\u4e49\u7c7b\u4f3c\u4e0e\u300c\u8fd8\u539f\u8bba\u300d\u4e2d\u7684\u300c\u8fd8\u539f\u300d\uff0c\u6709\u5c06\u590d\u6742\u7684\u4e8b\u7269\u5f52\u7ed3\u5230\u7b80\u5355\u4e8b\u7269\u7684\u542b\u4e49\uff09<\/span><\/p>\n


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

\u5728\u4e00\u4e2a\u666e\u901a\u7684\u8ba1\u7b97\u7cfb\u7edf\u4e2d\uff0c\u7cfb\u7edf\u7684\u6bcf\u4e2a\u72b6\u6001\u90fd\u6709\u4e00\u4e2a\u552f\u4e00\u7684\u540e\u7eed\u72b6\u6001<\/span>\uff08successor\uff09<\/span>\uff0c\u800c\u4e14\u6700\u7ec8\u6709\u4e00\u4e2a\u5355\u4e00\u7684\u65f6\u95f4\u7ebf\u6765\u5b9a\u4e49\u4e00\u4e2a\u8ba1\u7b97\u8fc7\u7a0b\u3002\u4f46\u5728\u591a\u91cd\u8ba1\u7b97\u7cfb\u7edf\u4e2d\uff0c\u5173\u952e\u5c31\u5728\u4e8e\u6bcf\u4e2a\u72b6\u6001\u53ef\u4ee5\u6709\u591a\u4e2a\u540e\u7eed\u72b6\u6001\u2014\u2014\u8ffd\u8e2a\u5b83\u4eec\u7684\u884c\u4e3a\u5b9a\u4e49\u4e86\u4e00\u4e2a\u7531\u65f6\u95f4\u7ebf\u7a0b\u7684\u5206\u652f\u548c\u5408\u5e76\u7ec4\u6210\u7684\u4e00\u4e2a\u5b8c\u6574\u7684\u591a\u8def\u56fe<\/span>\uff08multiway graph\uff09<\/span>\u3002\u800c\u5173\u952e\u5c31\u5728\u4e8e\uff0c\u8fd9\u4e0e\u4eba\u4eec\u5982\u4f55\u601d\u8003\u5178\u578b\u7684\u6e38\u620f\u548c\u8c1c\u9898\u76f4\u63a5\u76f8\u5173\u3002<\/span><\/p>\n


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

<\/section>\n


<\/p>\n

\u7ed9\u5b9a\u67d0\u4e2a\u6e38\u620f\u6216\u8c1c\u9898\u7684\u4e00\u4e2a\u7279\u5b9a\u72b6\u6001\uff0c\u73a9\u5bb6\u901a\u5e38\u5fc5\u987b\u51b3\u5b9a\u4e0b\u4e00\u6b65\u8be5\u505a\u4ec0\u4e48\u3002\u4ed6\u4eec\u901a\u5e38\u6709\u5f88\u591a\u9009\u62e9\u53ef\u4ee5\u505a\uff0c\u8fd9\u4e2a\u65f6\u5019\u591a\u91cd\u8ba1\u7b97\u7684\u6982\u5ff5\u5c31\u51fa\u73b0\u4e86\u3002\u5728\u4e00\u6b21\u7279\u5b9a\u7684\u6e38\u620f\u8fc7\u7a0b<\/span>\uff08\u5b9e\u4f8b instance\uff09<\/span>\u4e2d\uff0c\u4ed6\u4eec\u4f1a\u505a\u51fa\u4e00\u4e2a\u7279\u5b9a\u7684\u9009\u62e9\u3002\u800c\u591a\u91cd\u8ba1\u7b97\u8303\u5f0f<\/span>\uff08paradigm\uff09<\/span>\u7684\u5173\u952e\uff0c\u662f\u5168\u5c40\u5730\u770b\u5f85\u6240\u6709\u53ef\u80fd\u9009\u62e9\u7684\u7ed3\u679c\u2014\u2014\u5e76\u4ea7\u751f\u4e00\u4e2a\u4ee3\u8868\u8fd9\u4e9b\u9009\u62e9\u7684\u591a\u8def\u56fe<\/span>\uff08Multiway Graph\uff09<\/span>\u3002<\/span><\/p>\n


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

\u4e3a\u6e38\u620f\u548c\u8c1c\u9898\u6784\u9020\u8fd9\u6837\u7684\u591a\u8def\u56fe\u7684\u505a\u6cd5\u5b9e\u9645\u4e0a\u5df2\u7ecf\u5b58\u5728\u4e86100\u591a\u5e74\u4e86\u2014\u2014\u901a\u5e38\u88ab\u53eb\u505a\u300c\u6e38\u620f\u56fe<\/span>\uff08game graphs\uff09<\/span>\u300d \u3002\u4f46\u968f\u7740\u591a\u91cd\u8ba1\u7b97\u8303\u5f0f\u7684\u51fa\u73b0\uff0c\u73b0\u5728\u6709\u4e00\u4e9b\u66f4\u4e00\u822c\u7684\u6982\u5ff5\u53ef\u4ee5\u5e94\u7528\u4e8e\u8fd9\u4e9b\u7ed3\u6784\u3002\u53cd\u8fc7\u6765\uff0c\u7406\u89e3\u8fd9\u4e9b\u7ed3\u6784\u4e0e\u6e38\u620f\u548c\u8c1c\u9898\u7684\u5173\u7cfb\u53ef\u4ee5\u63d0\u4f9b\u5173\u4e8e\u591a\u8def\u56fe\u65b0\u5c42\u6b21\u7684\u76f4\u89c2\u548c\u719f\u6089\u7684\u7406\u89e3\u3002<\/span><\/p>\n


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

\u6211\u5728\u8fd9\u91cc\u7684\u5177\u4f53\u76ee\u6807\u662f\uff0c\u4f7f\u7528\u6211\u4eec\u4e00\u76f4\u5728\u53d1\u5c55\u7684\u7814\u7a76\u591a\u91cd\u8ba1\u7b97\u7cfb\u7edf\u7684\u4e00\u822c\u65b9\u6cd5\uff0c\u6765\u8db3\u591f\u7cfb\u7edf\u6027\u5730\u7814\u7a76\u4e00\u7cfb\u5217\u4f17\u6240\u5468\u77e5\u7684\u6e38\u620f\u548c\u8c1c\u9898\u3002\u5c31\u50cf\u662f\u5728\u4e0e\u65e5\u5e38\u4e8b\u7269\u76f8\u5173\u7684\u7814\u7a76\u4e2d\u901a\u5e38\u4f1a\u51fa\u73b0\u7684\u90a3\u6837\uff0c\u6211\u4eec\u4f1a\u906d\u9047\u5404\u79cd\u5177\u4f53\u7ec6\u8282\u3002\u867d\u7136\u8fd9\u4e9b\u7ec6\u8282\u53ef\u80fd\u4e0d\u4f1a\u7acb\u5373\u88ab\u5173\u8054\u5230\u66f4\u5927\u5c3a\u5ea6\u7684\u8ba8\u8bba\uff0c\u4f46\u5bf9\u4e8e\u4e3a\u6211\u4eec\u63d0\u4f9b\u5b9e\u9645\u6e38\u620f\u548c\u8c1c\u9898\u7684\u73b0\u5b9e\u4e14\u53ef\u8054\u7cfb\u7684\u753b\u9762\u6765\u8bf4\uff0c\u5b83\u4eec\u662f\u5f88\u91cd\u8981\u7684\uff0c\u8fd9\u4e5f\u80fd\u4f7f\u6211\u4eec\u4e0e\u591a\u91cd\u8ba1\u7b97\u7684\u8054\u7cfb\u6709\u4e86\u4e00\u4e2a\u575a\u5b9e\u7684\u57fa\u7840\u3002<\/span><\/p>\n


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

\u503c\u5f97\u4e00\u63d0\u7684\u662f\uff0c\u5c06\u6e38\u620f\u548c\u8c1c\u9898\u4e0e\u7269\u7406\u5b66\u8054\u7cfb\u8d77\u6765\u7684\u53ef\u80fd\u6027\uff0c\u5982\u679c\u6ca1\u6709\u6211\u4eec\u7684\u300c\u7269\u7406\u5b66\u8ba1\u5212\u300d<\/span>\uff08Wolfram Physics Project\uff0c\u6821\u6ce8\uff1a\u9879\u76ee\u7684\u5b98\u65b9\u6587\u7ae0\u4e2d\u7684\u63cf\u8ff0\uff1a\u300c\u6211\u8ba4\u4e3a\u6211\u4eec\u5df2\u7ecf\u627e\u5230\u4e86\u4e00\u6761\u901a\u5f80\u7269\u7406\u5b66\u57fa\u7840\u7406\u8bba\u7684\u9053\u8def\u300d\uff09<\/span>\uff0c\u5c31\u57fa\u672c\u4e0a\u5f88\u96be\u7406\u89e3\u3002<\/span><\/p>\n


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

\u56e0\u4e3a\u6e38\u620f\u548c\u8c1c\u9898\u901a\u5e38\u5728\u67d0\u79cd\u6700\u6839\u672c\u5c42\u9762\u4e0a\u662f\u79bb\u6563\u7684\u2014\u2014\u7279\u522b\u662f\u5728\u5b83\u4eec\u6d89\u53ca\u79bb\u6563\u7684\u53ef\u80fd\u6027\u5206\u652f\u7684\u65b9\u9762\u3002\u800c\u5982\u679c\u6211\u4eec\u5047\u8bbe\u7269\u7406\u5b66\u4ece\u6839\u672c\u4e0a\u662f\u8fde\u7eed\u7684\uff0c\u90a3\u4e48\u5c31\u6ca1\u6709\u7406\u7531\u671f\u5f85\u5b83\u4e0e\u6e38\u620f\u548c\u8c1c\u9898\u4f1a\u6709\u8054\u7cfb\u3002\u4f46\u6211\u4eec\u7684\u300c\u7269\u7406\u5b66\u8ba1\u5212\u300d\u7684\u4e00\u4e2a\u5173\u952e\u60f3\u6cd5\u662f\uff0c\u7269\u7406\u4e16\u754c\u5728\u6700\u4f4e\u5c42\u6b21\u4e0a\u662f\u79bb\u6563\u7684\u2014\u2014\u5c31\u50cf\u6e38\u620f\u548c\u8c1c\u9898\u4e00\u6837\u3002\u5e76\u4e14\u66f4\u91cd\u8981\u7684\u662f\uff0c\u6211\u4eec\u7684\u300c\u7269\u7406\u5b66\u8ba1\u5212\u300d\u8ba4\u4e3a\uff0c\u7269\u7406\u5b66\u5c31\u50cf\u6e38\u620f\u548c\u8c1c\u9898\u4e00\u6837\uff0c\u6709\u79bb\u6563\u7684\u53ef\u80fd\u6027\u53ef\u63a2\u7d22\u3002<\/span><\/p>\n


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

\u6211\u5728\u8fd9\u91cc\u8ba8\u8bba\u7684\u6bcf\u4e00\u4e2a\u6e38\u620f\u548c\u8c1c\u9898\uff0c\u5728\u7ed3\u6784\u548c\u64cd\u4f5c<\/span>\uff08operation\uff09<\/span>\u4e0a\uff0c\u4e00\u5f00\u59cb\u90fd\u53ef\u80fd\u663e\u5f97\u76f8\u5f53\u4e0d\u540c\u3002\u4f46\u6211\u4eec\u5c06\u770b\u5230\u7684\u662f\uff0c\u5f53\u4ee5\u4e00\u79cd\u591a\u91cd\u8ba1\u7b97\u7684\u89c6\u89d2\u6765\u770b\u65f6\uff0c\u5728\u6211\u4eec\u4e0d\u540c\u7684\u4f8b\u5b50\u4e2d\uff0c\u5b58\u5728\u7740\u663e\u8457\u7684\u3001\u51e0\u4e4e\u662f\u5343\u7bc7\u4e00\u5f8b\u7684\u7edf\u4e00\u6027<\/span>\uff08uniformity\uff09<\/span>\u3002\u5728\u6587\u672c\u7ed3\u5c3e\u7684\u90e8\u5206\uff0c\u6211\u4f1a\u5f00\u59cb\u8ba8\u8bba\u5404\u79cd\u91cd\u8981\u7684\u591a\u91cd\u8ba1\u7b97\u73b0\u8c61\u5982\u4f55\u5728\u6e38\u620f\u548c\u8c1c\u9898\u7684\u80cc\u666f\u4e2d\u8d77\u4f5c\u7528\uff0c\u5728\u6b64\u4e4b\u524d\u6211\u4e0d\u4f1a\u8fc7\u591a\u5730\u8bc4\u8bba\u8fd9\u4e9b\u73b0\u8c61\u7684\u610f\u4e49\u3002\u6211\u4e5f\u4f1a\u5728\u6700\u540e\u8ba8\u8bba\u7528\u7b80\u5355\u76f4\u63a5\u7684\u4eba\u7c7b\u8bed\u8a00\u5bf9\u591a\u91cd\u8ba1\u7b97\u8fdb\u884c\u6982\u5ff5\u5316\u662f\u4f55\u7b49\u56f0\u96be\u2014\u2014\u800c\u6b63\u662f\u5b83\u4ece\u6839\u672c\u4e0a\u5bfc\u81f4\u4e86\u6e38\u620f\u548c\u8c1c\u9898\u7684\u8ff7\u4eba\u7279\u6027\u3002<\/span><\/p>\n


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


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

\n
\n
\n
\n
\n

<\/section>\n

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

Tic-Tac-Toe \u4e95\u5b57\u68cb<\/span><\/strong><\/h3>\n<\/section>\n
\n

<\/section>\n

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

<\/h3>\n

\u8003\u8651\u5728\u4e00\u4e2a2\u00d72\u7684\u68cb\u76d8\u4e0a\u73a9\u4e00\u4e2a\u7b80\u5316\u7248\u7684\u4e95\u5b57\u68cb<\/span>\uff08tic-tac-toe\uff09\uff08\u53c8\u79f0\u300c\u5708\u53c9\u6e38\u620f (noughts and crosses)\u300d\uff09<\/span>\u3002<\/span><\/p>\n


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

\u5047\u8bbe X \u5148\u4e0b\u3002\u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u4e0b\u7528\u56fe\u6765\u8868\u793a\u53ef\u80fd\u7684\u68cb\u6b65\uff1a<\/span><\/p>\n


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

<\/section>\n


<\/p>\n

\u518d\u8003\u8651\u4e0b\u4e00\u56de\u5408\u7684\u68cb\u6b65\uff0c\u5c31\u5f97\u5230\uff1a<\/span><\/p>\n


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

<\/section>\n


<\/p>\n

\u5230\u76ee\u524d\u4e3a\u6b62\uff0c\u8fd9\u4e2a\u56fe\u662f\u4e00\u4e2a\u7b80\u5355\u7684\u6811\u7ed3\u6784\u3002\u4f46\u5982\u679c\u6211\u4eec\u518d\u73a9\u4e00\u4e2a\u56de\u5408\uff0c\u6211\u4eec\u4f1a\u53d1\u73b0\u4e0d\u540c\u7684\u5206\u652f\u53ef\u4ee5\u5408\u5e76\uff0c\u300c\u73a9\u5230\u68cb\u76d8\u586b\u6ee1\u4e86\u4e3a\u6b62\u300d\uff0c\u6211\u4eec\u4f1a\u5f97\u5230\u4e00\u4e2a\u4e0b\u56fe\u8fd9\u6837\u7684\u591a\u8def\u56fe\uff0c\u6216\u300c\u6e38\u620f\u56fe\u300d\uff1a<\/span><\/p>\n


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

<\/section>\n


<\/p>\n


<\/p>\n

\u8fd9\u4e2a\u56fe\u4e2d\u7684\u6bcf\u4e00\u6761\u8def\u5f84\u90fd\u8868\u793a\u4e00\u4e2a\u53ef\u80fd\u7684\u5b8c\u6574\u6e38\u620f\uff1a<\/span><\/p>\n


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

<\/section>\n


<\/p>\n

\u6839\u636e\u76ee\u524d\u7684\u6e38\u620f\u8bbe\u5b9a\uff0c\u5728\u4efb\u4f55\u6e38\u620f\u4e2d\u53ef\u4ee5\u8fbe\u5230\u7684\u68cb\u76d8\u5c40\u9762\u914d\u7f6e\u7684\u603b\u6570<\/span>\uff08\u5373\u56fe\u4e2d\u7684\u8282\u70b9\u603b\u6570\uff09<\/span>\u4e3a35\uff0c\u800c\u53ef\u80fd\u7684\u5b8c\u6574\u6e38\u620f\u603b\u6570<\/span>\uff08\u5373\u4ece\u56fe\u7684\u6839\u90e8\u5f00\u59cb\u7684\u53ef\u80fd\u8def\u5f84\u6570\uff09<\/span>\u4e3a24\u3002<\/span><\/p>\n


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

\u5982\u679c\u5c06\u8be5\u56fe\u6e32\u67d3\u62103\u7ef4\uff0c\u53ef\u4ee5\u770b\u5230\u5b83\u6709\u4e00\u4e2a\u975e\u5e38\u89c4\u5219\u7684\u7ed3\u6784\uff1a<\/span><\/p>\n


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

<\/section>\n

<\/span><\/section>\n
\u800c\u73b0\u5728\uff0c\u5982\u679c\u6211\u4eec\u628a\u300c\u83b7\u80dc\u300d\u7684 2\u00d72 \u4e95\u5b57\u6e38\u620f\u5c40\u9762\u5b9a\u4e49\u4e3a\u5728\u4e00\u6a2a\u884c\u4e2d\u6709\u4e24\u4e2a\u76f8\u540c\u7684\u5143\u7d20\uff0c\u90a3\u4e48\u6211\u4eec\u5c31\u53ef\u4ee5\u5728\u8fd9\u4e2a\u591a\u8def\u56fe\u4e0a\u6807\u6ce8\u83b7\u80dc\u5c40\u9762\u2014\u2014\u4e5f\u5c31\u662f\u53bb\u6389\u90a3\u4e9b\u300c\u6e38\u620f\u5df2\u7ecf\u7ed3\u675f\u300d\u7684\u60c5\u51b5\u3002<\/span><\/section>\n

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


<\/p>\n

\u591a\u8def\u56fe\u7684\u5927\u90e8\u5206\u6838\u5fc3\u7ed3\u6784\u5b9e\u9645\u4e0a\u5df2\u7ecf\u5f88\u660e\u663e\u4e86\uff0c\u5373\u4f7f\u8fd9\u5728\u300c\u5355\u4eba\u4e95\u5b57\u68cb\u300d\u8fd9\u79cd\u770b\u4f3c\u4e0d\u8d77\u773c\u7684\u60c5\u51b5\u4e0b\uff0c\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u4eba\u4eec\u53ea\u662f\u5728\u9010\u6b65\u586b\u6ee1\u68cb\u76d8\u4e0a\u7684\u683c\u5b50\uff1a<\/span><\/p>\n


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

<\/section>\n

<\/section>\n

\u4f46\u662f\uff0c\u5e76\u4e0d\u90a3\u4e48\u4e0d\u8d77\u773c\u7684\u662f\uff0c\u5b58\u5728\u7740\u5f15\u5411\u540c\u6837\u68cb\u76d8\u5c40\u9762<\/span>\uff08state\uff09<\/span>\u7684\u4e0d\u540c\u8def\u5f84\u3002<\/span><\/p>\n


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

\u4ee5\u4e0d\u540c\u7684\u65b9\u5f0f\u5c55\u793a\u540e\u7684\u8fd9\u4e2a\u56fe<\/span>\uff08\u67092^4 = 16 \u4e2a\u8282\u70b9\u548c 4! = 24 \u6761\u300c\u6e38\u620f\u8def\u5f84\u300d\uff09<\/span>\u5177\u6709\u660e\u663e\u76844\u7ef4\u8d85\u7acb\u65b9\u4f53\u5f62\u5f0f<\/span>\uff08\u73b0\u5728\u6211\u4eec\u6ca1\u6709\u5199\u51fa\u4e86\u6bcf\u4e2a\u5404\u81ea\u4e2d\u7684\u660e\u786eX\u7b26\u53f7\uff09<\/span>\uff1a<\/span><\/p>\n


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

<\/section>\n

<\/section>\n

\u5bf9\u4e8e\u4e00\u4e2a3\u00d73\u7684\u68cb\u76d8\uff0c\u8fd9\u4e2a\u56fe\u4f1a\u662f\u4e00\u4e2a9\u7ef4\u7684\u8d85\u7acb\u65b9\u4f53\uff0c\u67092^9=512\u4e2a\u8282\u70b9\u548c 9!=362880 \u6761\u300c\u6e38\u620f\u8def\u5f84\u300d\uff0c\u4ee5\u300c\u68cb\u6b65\u5206\u5c42\u300d\u7684\u5f62\u5f0f\u8868\u793a\u5982\u4e0b\uff1a<\/span><\/p>\n


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

<\/section>\n

<\/span><\/section>\n
\u8fd9\u79cd\u57fa\u672c\u7ed3\u6784\u5728\u300c\u5355\u4eba1\u7ef4\u4e95\u5b57\u68cb\u300d\u4e2d\u5df2\u7ecf\u53ef\u89c1\uff0c\u5176\u4e2d\u300c\u957f\u5ea6\u4e3a n\u300d\u7684\u68cb\u76d8\u7684\u591a\u8def\u56fe\u6b63\u597d\u5bf9\u5e94\u4e8e\u4e00\u4e2an\u7ef4\u7684\u8d85\u7acb\u65b9\u4f53\u3002<\/span><\/section>\n

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

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

<\/section>\n

\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u4e0d\u540c\u7684\u68cb\u76d8\u5c40\u9762\u7684\u603b\u6570\u5c31\u662f2n\uff0c\u800c\u4e0d\u540c\u7684\u300c\u6e38\u620f\u300d\u8fc7\u7a0b\u7684\u6570\u91cf\u662fn!\u3002\u5728\u7b2ct\u6b65\uff0c\u4e0d\u540c\u68cb\u76d8\u5c40\u9762<\/span>\uff08\u5373\u72b6\u6001\uff09<\/span>\u7684\u6570\u91cf\u662f\u4e8c\u9879\u5f0f\u7cfb\u6570[n, t]<\/span>\uff08Binomial[n, t]\uff09 <\/span>\u3002<\/span><\/p>\n

\u5982\u679c\u662f2\u4e2a\u73a9\u5bb6\uff0c\u56fe\u4f1a\u53d8\u5f97\u7a0d\u5fae\u590d\u6742\u4e00\u4e9b\u3002<\/span><\/p>\n


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

<\/section>\n

<\/section>\n

\u8fd9\u4e9b\u56fe\u4e2d\u7684\u72b6\u6001\u603b\u6570\u662f<\/span><\/p>\n


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

<\/section>\n


<\/p>\n

\u5f53n\u503c\u8d8b\u8fd1\u65e0\u7a77\u65f6\uff0c\u56fe\u4e2d\u7684\u72b6\u6001\u603b\u6570\u8fbe\u5230 <\/span><\/p>\n


<\/p>\n

\uff08\u8bd1\u6ce8\uff1a\u5982\u679c\u628a\u4e0a\u5f0f\u4e2d\u7684n\u6362\u6210n+1\uff0c\u4f1a\u53d1\u73b0\u4ee3\u5165\u540e\u5f97\u5230\u7684\u7ed3\u679c\u5f88\u63a5\u8fd1\u957f\u5ea6\u4e3an\u65f6\u7684\u72b6\u6001\u6570\uff0c\u4f46\u5c06n\u63a8\u5411\u65e0\u7a77\u65f6\uff0cn+1\u53ef\u4ee5\u7b49\u540c\u4e8en\u3002\uff09<\/span><\/p>\n

\uff08\u6ce8\u610f\uff0c\u5bf9\u4e8en=4\uff0c\u5176\u7ed3\u679c\u4e0e\u4e0a\u9762\u8ba8\u8bba\u76842\u00d72\u68cb\u76d8\u76f8\u540c\u3002\uff09<\/span>\u5f53\u6e38\u620f\u8fdb\u884c\u5230\u7b2ct\u6b65\u65f6\uff0c\u4e0d\u540c\u72b6\u6001\u7684\u6570\u91cf\u7531\u4ee5\u4e0b\u516c\u5f0f\u7ed9\u51fa<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\uff08\u8bd1\u6ce8\uff1a\u4e0a\u9762\u4e24\u4e2a\u4e8c\u9879\u5f0f\u7cfb\u6570\u76f8\u4e58\uff09<\/span><\/p>\n


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

<\/section>\n

<\/section>\n

\u597d\u7684\uff0c\u90a3\u4e48\u6807\u51c6\u76842\u4eba3\u00d73\u4e95\u5b57\u68cb\u6e38\u620f\u5462\uff1f
<\/span><\/p>\n


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

\u5b83\u7684\u591a\u8def\u56fe\u5728\u6700\u5f00\u59cb\u662f\uff1a<\/span><\/p>\n


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

<\/section>\n


<\/p>\n

\u7ecf\u8fc7\u4e24\u6b65<\/span>\uff08\u5373X\u548cO\u5404\u8d70\u4e00\u6b65\uff09<\/span>\uff0c\u56fe\u4ecd\u7136\u662f\u4e00\u68f5\u6811<\/span>\uff08\u521d\u59cb\u72b6\u6001\u73b0\u5728\u5728\u4e2d\u5fc3\uff09<\/span>\uff1a<\/span><\/p>\n


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

<\/section>\n

<\/section>\n

\u4e09\u6b65\u4e4b\u540e\uff0c\u72b6\u6001\u5f00\u59cb\u53ef\u4ee5\u5408\u5e76\u4e86\u3002<\/span><\/p>\n


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

<\/section>\n


<\/p>\n

\u800c\u7ee7\u7eed\u8fdb\u884c\u5168\u90e8\u4e5d\u6b65\uff0c\u5b8c\u6574\u7684\u3001\u67096046\u4e2a\u72b6\u6001\u7684\u5206\u5c42\u56fe\u662f\uff1a<\/span><\/p>\n


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

<\/section>\n

<\/section>\n

\u4e00\u822c\u6765\u8bf4\uff0c \u5728\u5404\u4e2a\u6b65\u9aa4\u65f6\u7684\u8fde\u901a\u5b50\u56fe<\/span>\uff08connected components\uff09<\/span>\u7684\u90e8\u5206\u7684\u6570\u91cf\u5982\u4e0b\uff1a<\/span><\/p>\n


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

\u5728\u8fd9\u4e2a\u56fe\u7684\u5c42\u9762\u4e0a\uff0c\u5176\u7ed3\u679c\u4e0e\u603b\u5171\u67099\u65b9\u683c\u76842\u4eba1\u7ef4\u7248\u672c\u5b8c\u5168\u76f8\u540c\u3002\u4f46\u662f\u5bf9\u4e8e\u5b9e\u9645\u76842\u7ef43\u00d73\u4e95\u5b57\u68cb\u6765\u8bf4\uff0c\u8fd8\u6709\u4e00\u4e2a\u989d\u5916\u7684\u6982\u5ff5\uff1a\u8d62\u5f97\u6e38\u620f\uff0c\u4ece\u800c\u7ec8\u6b62\u6e38\u620f\u3002\u5728\u901a\u5e38\u7684\u89c4\u5219\u4e0b\uff0c\u5f53\u4e00\u4e2a\u73a9\u5bb6\u5728\u4e00\u4e2a\u6c34\u5e73\u3001\u5782\u76f4\u6216\u5bf9\u89d2\u7ebf\u7684\u4e09\u4e2a\u683c\u5b50\u4e0a\u4e0b\u4e86\u68cb\u5b50\u65f6\uff0c\u5c31\u88ab\u8ba4\u4e3a\u662f\u8d62\u4e86\u6e38\u620f\uff0c\u6bd4\u5982\u8bf4\uff1a<\/span><\/p>\n


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

<\/section>\n


<\/p>\n

\u6bcf\u5f53\u8fbe\u5230\u50cf\u8fd9\u6837\u7684\u300c\u83b7\u80dc\u72b6\u6001\u300d\u65f6\uff0c\u6e38\u620f\u5c31\u88ab\u8ba4\u4e3a\u662f\u7ed3\u675f\u4e86\uff0c\u56e0\u6b64\u591a\u8def\u56fe\u4e2d\u7684\u540e\u7eed\u72b6\u6001\u5c31\u53ef\u4ee5\u88ab\u5220\u51cf\uff0c\u800c\u4e4b\u524d\u76846046\u4e2a\u8282\u70b9\u56fe\u5c31\u4f1a\u53d8\u62105478\u4e2a\u8282\u70b9\u56fe\u3002<\/span><\/p>\n


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

<\/section>\n

<\/section>\n

\u4e0b\u9762\u662f\u8fd9568\u4e2a\u88ab\u4fee\u526a\u6389\u7684\u72b6\u6001\u7684\u4f8b\u5b50<\/span>\uff08\u5176\u4e2d\u6807\u8bb0\u4e86\u7ec8\u6b62\u6e38\u620f\u7684\u300c\u80dc\u5229 \u300d\uff09<\/span>\u3002<\/span><\/p>\n


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

<\/section>\n

<\/section>\n

\u6e38\u620f\u80dc\u5229\u53ef\u4ee5\u53d1\u751f\u5728\u4e0d\u540c\u7684\u6b65\u6570\uff1a\u4ece\u7b2c5\u6b65\u5230\u7b2c9\u6b65\u95f4\u90fd\u53ef\u80fd\u6709\u73a9\u5bb6\u83b7\u80dc\u3002\u4e0d\u540c\u7684\u80dc\u5229\u72b6\u6001\u603b\u6570\u5982\u4e0b<\/span><\/p>\n


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

<\/section>\n

<\/section>\n

\uff08\u4efb\u610f\u6b65\u9aa4\u4e2d\uff0cX\u6709626\u79cd\u53ef\u80fd\u7684\u80dc\u5229\u72b6\u6001\uff0cO\u6709316\u79cd\u53ef\u80fd\u7684\u80dc\u5229\u72b6\u6001\uff09<\/span>\u3002<\/span><\/p>\n


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

\u5728\u6bcf\u4e00\u4e2a\u65b9\u683c\u90fd\u88ab\u586b\u6ee1\u4e4b\u524d\uff0c\u4eba\u4eec\u65e0\u6cd5\u660e\u786e\u5224\u65ad\u4e00\u76d8\u68cb\u662f\u5426\u5df2\u7ecf\u4ee5\u5e73\u5c40\u7ed3\u675f\u2014\u2014\u53ea\u670916\u79cd\u6700\u7ec8\u7684\u300c\u5e73\u5c40\u72b6\u6001\u300d\u53ef\u4ee5\u8fbe\u6210\u3002<\/span><\/p>\n


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

<\/section>\n

<\/section>\n

\u6211\u4eec\u53ef\u4ee5\u5728\u5b8c\u6574\u7684\u4fee\u526a\u8fc7<\/span>\uff08game-over-pruned\uff09<\/span>\u7684\u591a\u8def\u56fe\u4e0a\u6807\u6ce8\u51fa\u80dc\u5229\u548c\u5e73\u5c40\u7684\u72b6\u6001\u3002<\/span><\/p>\n


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

<\/section>\n

<\/section>\n

\u4e3a\u4e86\u8fdb\u4e00\u6b65\u7814\u7a76\u8fd9\u4e2a\u95ee\u9898\uff0c\u8ba9\u6211\u4eec\u5148\u770b\u770b\u4e00\u4e2a\u53ea\u5305\u62ec\u300c\u7ec8\u5c40\u300d\u7684\u5b50\u56fe\uff0c\u8fd9\u4e2a\u5b50\u56fe\u4ece\u4e00\u4e2a\u5df2\u7ecf\u586b\u6ee1\u4e864\u4e2a\u683c\u5b50\u7684\u68cb\u76d8\u5f00\u59cb\u3002<\/span><\/p>\n


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

<\/section>\n


<\/p>\n

\u6211\u4eec\u5728\u8fd9\u91cc\u770b\u5230\uff0c\u4ece\u6211\u4eec\u6700\u521d\u7684\u68cb\u76d8\u72b6\u6001\u5f00\u59cb\uff0c
<\/span><\/p>\n


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

<\/section>\n

<\/section>\n

X\u548cO\u90fd\u6709\u53ef\u80fd\u6700\u540e\u83b7\u80dc<\/span><\/p>\n


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

<\/section>\n

<\/section>\n

\u4f46\u5728\u8bb8\u591a\u8fd9\u6837\u7684\u60c5\u51b5\u4e0b\uff0c\u7ed3\u679c\u5728\u5b9e\u9645\u80dc\u5229\u53d1\u751f\u524d\u4e00\u6b65\u6216\u66f4\u65e9\u7684\u65f6\u5019\u5c31\u5df2\u57fa\u672c\u786e\u5b9a\u4e86\u2014\u2014\u4ece\u8fd9\u4e2a\u610f\u4e49\u4e0a\u8bf4\uff0c\u9664\u975e\u67d0\u4e2a\u73a9\u5bb6\u300c\u72af\u9519\u300d\uff0c\u5426\u5219\u4ed6\u4eec\u662f\u6709\u5fc5\u80dc\u7b56\u7565\u7684<\/span>\uff08force a win\uff09<\/span>\u3002<\/span><\/p>\n


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

\u56e0\u6b64\uff0c\u4e3e\u4f8b\u6765\u8bf4\uff0c\u5047\u8bbe\u73b0\u5728\u8f6e\u5230X\u4e86\uff0c\u5e76\u4e14\u72b6\u6001\u662f\uff1a<\/span><\/p>\n


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

<\/section>\n


<\/p>\n

\u90a3\u4e48\uff0c\u53ea\u8981X\u6309\u4ee5\u4e0b\u65b9\u5f0f\u843d\u5b50\uff0c\u5c31\u80fd\u4fdd\u8bc1\u83b7\u80dc\uff1a<\/span><\/p>\n


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

<\/section>\n

<\/section>\n

\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u7ed9\u591a\u8def\u56fe\u4e2d\u7684\u5b50\u56fe<\/span>\uff08\u6216\u5b9e\u9645\u4e0a\u7684\u300c\u5149\u9525\u300d\uff09<\/span>\u7740\u8272\u6765\u6807\u8bb0\u8fd9\u79cd\u5df2\u7ecf\u6ce8\u5b9a\u7684\u80dc\u5229\u5c40\u9762\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5728\u6e38\u620f\u6700\u5f00\u59cb\uff0c\u5f53X\u4e0b\u7b2c\u4e00\u6b65\u68cb\u65f6\uff0c\u8fd8\u6ca1\u6709\u4efb\u4f55\u4e00\u65b9\u7684\u80dc\u5229\u662f\u5df2\u7ecf\u786e\u5b9a\u7684\u3002\u4f46\u53ea\u4e0b\u4e86\u4e00\u6b65\u68cb\uff0c\u5c31\u5df2\u7ecf\u6709\u53ef\u80fd\u8fbe\u5230X\u6709\u5fc5\u80dc\u7b56\u7565\u7684\u5c40\u9762\uff1a<\/span><\/p>\n


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

<\/section>\n


<\/p>\n

\u4ece\u7b2c\u4e00\u6b65\u540e\u5f97\u5230\u7684\u72b6\u6001\u5f00\u59cb\uff0c\u6211\u4eec\u53ef\u4ee5\u770b\u5230\uff0c\u4e24\u6b65\u540e\u6709\u4e00\u4e9b\u68cb\u76d8\u72b6\u6001\uff0c\u5176\u4e2dO\u6709\u5fc5\u80dc\u7b56\u7565\uff1a
<\/span><\/p>\n


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

<\/section>\n

<\/section>\n

\u8d70\u66f4\u591a\u6b65\uff0c\u5c31\u4f1a\u4ea7\u751f\u66f4\u591a\u7684\u8fd9\u79cd\u67d0\u4e00\u65b9\u6709\u5fc5\u80dc\u7b56\u7565\u7684\u68cb\u76d8\u72b6\u6001\uff1a<\/span><\/p>\n


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

<\/section>\n

<\/section>\n

\u6807\u6ce8\u6574\u4e2a\u591a\u8def\u56fe\uff0c\u6211\u4eec\u5c31\u80fd\u5f97\u5230\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u6211\u4eec\u53ef\u4ee5\u628a\u8fd9\u4e2a\u56fe\u770b\u4f5c\u662f\u5728\u8868\u793a\u8fd9\u4e2a\u6e38\u620f\u7684\u300c\u89e3<\/span>\uff08solution\uff09<\/span>\u300d\uff1a\u7ed9\u5b9a\u4efb\u4f55\u72b6\u6001\uff0c\u56fe\u4e2d\u7684\u7740\u8272\u544a\u8bc9\u6211\u4eec\u54ea\u4e2a\u68cb\u624b\u53ef\u4ee5\u4ece\u8be5\u72b6\u6001\u4e2d\u786e\u4fdd\u80dc\u5229\uff0c\u4e14\u56fe\u4e2d\u7ed9\u5b9a\u4e86\u4ed6\u4eec\u53ef\u4ee5\u600e\u4e48\u4e0b\u6765\u8fbe\u5230\u8fd9\u6837\u7684\u72b6\u6001\u3002<\/span><\/p>\n


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

\u4e0b\u56fe\u603b\u7ed3\u4e86\u6bcf\u4e00\u6b65\u68cb\u7684\u53ef\u80fd\u68cb\u76d8\u72b6\u6001\uff1a<\/span><\/p>\n


<\/p>\n

<\/section>\n

<\/section>\n

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

<\/section>\n

\u8fd9\u91cc\u6211\u4eec\u53ea\u662f\u5728\u8ba1\u7b97\u6bcf\u4e00\u6b65\u7684\u5404\u79cd\u53ef\u80fd\u72b6\u6001\u7684\u6570\u91cf\u3002\u4f46\u662f\uff0c\u80fd\u5426\u628a\u8fd9\u4e9b\u72b6\u6001\u770b\u4f5c\u662f\u4ee5\u67d0\u79cd\u65b9\u5f0f\u5206\u5e03\u5728\u300c\u6e38\u620f\u72b6\u6001\u7a7a\u95f4\u300d<\/span>\uff08game state space\uff09<\/span>\u4e2d\u7684\u67d0\u79cd\u4e1c\u897f\uff1f<\/span><\/p>\n


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

\u5206\u652f\u56fe<\/span>\uff08Branchial Graph\uff09<\/span>\u63d0\u4f9b\u4e86\u4e00\u79cd\u53ef\u80fd\u7684\u65b9\u6cd5\u6765\u505a\u5230\u8fd9\u4e00\u70b9\u3002\u67d0\u4e00\u7279\u5b9a\u6b65\u9aa4\u7684\u57fa\u672c\u5206\u652f\u56fe\u662f\u901a\u8fc7\u8fde\u63a5\u5728\u524d\u4e00\u6b65\u9aa4\u4e2d\u5177\u6709\u5171\u540c\u524d\u7f6e\u72b6\u6001\u7684\u72b6\u6001\u5bf9\u800c\u5f97\u5230\u7684\u3002\u5bf9\u4e8e2\u4eba2\u00d72\u4e95\u5b57\u68cb\u7684\u60c5\u51b5\uff0c\u6211\u4eec\u5728\u8fde\u7eed\u7684\u6b65\u9aa4\u4e2d\u5f97\u5230\u7684\u5206\u652f\u56fe\u5982\u4e0b\uff1a<\/span><\/p>\n


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

<\/section>\n


<\/p>\n

\u5bf9\u4e8e\u666e\u901a\u76843\u00d73\u4e95\u5b57\u68cb\u6765\u8bf4\uff0c\u8fd9\u4e2a\u5206\u652f\u56fe\u66f4\u52a0\u590d\u6742\u3002\u4f46\u7531\u4e8e\u524d\u4e24\u6b65\u7684\u591a\u8def\u56fe\u7eaf\u7cb9\u662f\u4e00\u68f5\u6811\uff0c\u8fd9\u4e9b\u6b65\u9aa4\u7684\u5206\u652f\u56fe\u4ecd\u6709\u4e00\u4e2a\u76f8\u5f53\u663e\u800c\u6613\u89c1\u7684\u7ed3\u6784\u3002<\/span>\uff08\u6821\u6ce8\uff1a\u6211\u7684\u901a\u4fd7\u7406\u89e3\u5f97\u5230\u4e86\u538c\u6c27\u83cc\u7684\u9f13\u52b1\uff0c\u5c31\u662f\u7b49\u4e8e\u662f\u628a\u539f\u6765\u7684\u591a\u8def\u56fe\u505a\u5782\u76f4\u5256\u9762\uff0c\u7c7b\u4f3c\u4f60\u628a\u591a\u7c07\u7684\u82b1\u83dc\u5256\u5f00\uff0c\u770b\u5230\u6bcf\u4e00\u4e2a\u6bb5\u843d\u4e0a\u7684\u5171\u65f6\u7684\u9762\uff09<\/span><\/p>\n


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

<\/section>\n

<\/section>\n

\u4e00\u822c\u60c5\u51b5\u4e0b\uff0c\u8fde\u7eed\u6b65\u9aa4\u4e0b\u7684\u5f3a\u8fde\u901a\u5b50\u56fe\u6570\u91cf\u5982\u4e0b\u8868\uff1a<\/span><\/p>\n


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

<\/section>\n


<\/p>\n

\u4ee5\u53ca\u8fd9\u4e9b\u901a\u8fc7\u4e0d\u540c\u56fe\u7684\u7ed3\u6784\u5f62\u6001\u5206\u89e3\u5982\u4e0b\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u4e0b\u9762\u662f\u5176\u4e2d\u4e00\u4e9b\u6b65\u9aa4\u7684\u5178\u578b\u5206\u652f\u56fe\u4e2d\u5b50\u56fe\u7684\u66f4\u5177\u4f53\u7684\u5f62\u6001\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5728\u67d0\u4e00\u7279\u5b9a\u6b65\u9aa4\u7684\u5206\u652f\u56fe\u5185\uff0c\u4e0d\u540c\u7684\u7ec4\u6210\u90e8\u5206\u4e2d\u53ef\u80fd\u6709\u4e0d\u540c\u6570\u91cf\u7684\u8d62\u5c40\u3002<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u8d62\u5c40\u5728\u5404\u5206\u652f\u56fe\u4e2d\u7684\u5206\u5e03\u76f8\u5f53\u5e7f\u6cdb\u3002\u800c\u8fd9\u5728\u67d0\u79cd\u610f\u4e49\u4e0a\u4e5f\u662f\u4e95\u5b57\u5f62\u6e38\u620f\u4e0d<\/span>\uff08\u90a3\u4e48\uff09<\/span>\u7b80\u5355\u7684\u539f\u56e0\u3002\u5982\u679c\u53ea\u9700\u77e5\u9053\u81ea\u5df1\u5904\u4e8e\u5206\u652f\u56fe\u7684\u54ea\u4e2a\u90e8\u5206\uff0c\u800c\u5c31\u80fd\u7acb\u5373\u77e5\u9053\u7ed3\u679c\uff0c\u90a3\u4e48\u6e38\u620f\u4e2d\u7684\u300c\u60ac\u5ff5\u300d\u5c31\u4f1a\u66f4\u5c11\u3002\u4f46\u662f\u5728\u6574\u4e2a\u5206\u652f\u7a7a\u95f4\u7684\u5e7f\u6cdb\u5206\u5e03\u4e0b\uff0c\u300c\u5927\u81f4\u77e5\u9053\u4f60\u5728\u54ea\u91cc\u300d\u5bf9\u786e\u5b9a\u4f60\u662f\u5426\u4f1a\u8d62\u6ca1\u6709\u4ec0\u4e48\u5e2e\u52a9\u3002<\/span><\/p>\n


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

\u5230\u76ee\u524d\u4e3a\u6b62\uff0c\u6211\u4eec\u4e00\u76f4\u5728\u8ba8\u8bba\u53ef\u4ee5\u8fbe\u5230\u4ec0\u4e48\u72b6\u6001\uff0c\u4f46\u6ca1\u6709\u8ba8\u8bba\u300c\u591a\u7ecf\u5e38\u300d\u4f1a\u8fbe\u5230\u8fd9\u4e9b\u72b6\u6001\u7684\u3002\u60f3\u8c61\u4e00\u4e0b\uff0c\u6211\u4eec\u4e0d\u662f\u5728\u73a9\u4e00\u4e2a\u7279\u5b9a\u7684\u6e38\u620f\uff0c\u800c\u662f\u5728\u6bcf\u4e00\u6b65\u90fd\u4ee5\u76f8\u540c\u7684\u6982\u7387\u8fdb\u884c\u6bcf\u4e00\u79cd\u53ef\u80fd\u7684\u4e0b\u5b50\u3002\u4e95\u5b57\u68cb\u7684\u8bbe\u7f6e\u662f\u5bf9\u79f0\u7684\uff0c\u5728\u6e38\u620f\u7684\u5927\u90e8\u5206\u65f6\u95f4\u91cc\uff0c\u6bcf\u4e2a\u53ef\u80fd\u7684\u5c40\u9762\u5728\u7ed9\u5b9a\u7684\u6b65\u9aa4\u4e2d\u51fa\u73b0\u7684\u6982\u7387\u90fd\u662f\u76f8\u7b49\u7684\u3002\u4f46\u662f\u4e00\u65e6\u5f00\u59cb\u6709\u300c\u83b7\u80dc\u300d\uff0c\u5e76\u4e14\u6709\u4e00\u4e2a\u300c\u9525\u5f62\u300d\u7684\u300c\u6e38\u620f\u7ed3\u675f\u526a\u679d<\/span>\uff08game-over-pruned\uff09<\/span>\u300d\u7684\u72b6\u6001\uff0c\u90a3\u4e48\u5269\u4e0b\u7684\u72b6\u6001\u5c31\u4e0d\u518d\u6709\u76f8\u7b49\u7684\u6982\u7387\u3002<\/span><\/p>\n


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

\u5bf9\u4e8e\u6807\u51c6\u76843\u00d73\u4e95\u5b57\u68cb\u6765\u8bf4\uff0c\u8fd9\u79cd\u60c5\u51b5\u53d1\u751f\u57287\u6b65\u4e4b\u540e\uff0c\u5176\u4e2d\u6709\u4e24\u7c7b\u72b6\u6001\uff0c\u5176\u53d1\u751f\u7684\u6982\u7387\u7565\u6709\u4e0d\u540c\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5728\u6e38\u620f\u7ed3\u675f\u65f6\uff0c\u6709\u51e0\u7c7b\u5177\u6709\u4e0d\u540c\u6982\u7387\u7684\u6700\u7ec8\u72b6\u6001\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u800c\u4e0b\u56fe\u5c55\u793a\u4e86\u8fd9\u5bf9\u4e8e\u6e38\u620f\u7684\u4e0d\u540c\u7ed3\u679c\u7684\u6982\u7387\u610f\u5473\u7740\u4ec0\u4e48\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5e76\u4e0d\u51fa\u4e4e\u610f\u6599\u7684\u662f\uff0c\u5148\u4e0b\u7684\u68cb\u624b\u5728\u83b7\u80dc\u4e0a\u6709\u4f18\u52bf\u3002\u4e5f\u8bb8\u66f4\u4ee4\u4eba\u60ca\u8bb6\u7684\u662f\uff0c\u5728\u8fd9\u79cd\u300c\u65e0\u7b56\u7565\u300d\u7684\u6e38\u73a9\u4e2d\uff0c\u5e73\u5c40\u662f\u6bd4\u8f83\u5c11\u89c1\u7684\u2014\u2014\u5c3d\u7ba1\u5982\u679c\u4e00\u4e2a\u73a9\u5bb6\u79ef\u6781\u5730\u8bd5\u56fe\u963b\u6b62\u53e6\u4e00\u4e2a\u73a9\u5bb6\uff0c\u4ed6\u4eec\u5f80\u5f80\u4f1a\u8feb\u4f7f\u6e38\u620f\u8d70\u5411\u5e73\u5c40\u3002<\/span><\/p>\n


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

\u6211\u4eec\u5df2\u7ecf\u7814\u7a76\u4e86\u300c\u7ecf\u5178\u4e95\u5b57\u68cb\u300d\u548c\u4e00\u4e9b\u7279\u5b9a\u7684\u53d8\u4f53\u3002\u4f46\u6700\u7ec8\u8fd8\u6709\u5404\u79cd\u53ef\u80fd\u7684\u53d8\u4f53\u3002\u4e00\u79cd\u6765\u8868\u793a\u4efb\u4f55\u7c7b\u4f3c\u4e95\u5b57\u6e38\u620f\u7684\u300c\u68cb\u76d8\u300d\u7684\u65b9\u4fbf\u7684\u4e00\u822c\u65b9\u6cd5\u662f\uff0c\u7ed9\u51fa\u4e00\u4e2a\u300c\u6241\u5e73\u5316\u300d\u7684\u6570\u503c\u5217\u8868\u2014\u2014 0 \u4ee3\u8868\u7a7a\u767d\u4f4d\u7f6e\uff0ci \u4ee3\u8868\u73a9\u5bb6 i \u6dfb\u52a0\u7684\u4e00\u4e2a\u7b26\u53f7\u3002<\/span><\/p>\n


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

\u5728\u6807\u51c6\u7684\u300c\u4e8c\u7ef4\u8868\u793a\u6cd5\u300d\u4e2d\uff0c\u4eba\u4eec\u53ef\u80fd\u4f1a\u6709\u8fd9\u6837\u4e00\u4e2a\u68cb\u76d8<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5c06\u5b83\u6241\u5e73\u5316\u540e\u5f97\u5230\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u7136\u540e\u53ef\u4ee5\u8868\u793a\u51fa\u5178\u578b\u7684\u83b7\u80dc\u6a21\u5f0f\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5176\u4e2d\uff0c\u5728\u6bcf\u4e00\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u90fd\u6807\u51fa\u4e86\u8ddf\u83b7\u80dc\u76f8\u5173\u7684\u300c\u83b7\u80dc\u7b26\u53f7\u300d\uff0c\u7136\u540e\u7ed9\u51fa\u5b83\u4eec\u5728\u6241\u5e73\u5316\u5217\u8868\u4e2d\u7684\u4f4d\u7f6e\u3002\u5728\u666e\u901a\u7684\u4e95\u5b57\u68cb\u4e2d\uff0c\u5f88\u660e\u663e\uff0c\u300c\u83b7\u80dc\u7b26\u53f7\u300d\u7684\u4f4d\u7f6e\u5fc5\u987b\u603b\u662f\u5f62\u6210\u4e00\u4e2a\u7b49\u5dee\u6570\u5217\u3002\u800c\u6982\u62ec\u4e95\u5b57\u68cb\u7684\u4e00\u4e2a\u597d\u65b9\u6cd5\u4f3c\u4e4e\u662f\u5c06 i \u7684\u80dc\u5229\u5b9a\u4e49\u4e3a\u4e0e i \u7684\u7b26\u53f7\u51fa\u73b0\u5728\u5f62\u6210\u4e00\u5b9a\u957f\u5ea6s\u7684\u7b49\u5dee\u6570\u5217\u7684\u4f4d\u7f6e\u6709\u5173\u3002\u5bf9\u4e8e\u666e\u901a\u7684\u4e95\u5b57\u68cb\u6765\u8bf4\uff0cs=3\uff0c\u4f46\u4e00\u822c\u60c5\u51b5\u4e0b\uff0c\u5b83\u53ef\u4ee5\u6709\u5176\u4ed6\u503c\u3002<\/span><\/p>\n


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

\u73b0\u5728\u8003\u8651\u4e00\u4e2a\u957f\u5ea6\u4e3a5\u7684\u5217\u8868<\/span>\uff08\u53735\u4e2a\u4f4d\u7f6e\u7684\u300c1\u7ef4\u68cb\u76d8\u300d\uff09<\/span>\u7684\u60c5\u51b5\u3002\u5b8c\u6574\u7684\u591a\u8def\u56fe\u5982\u4e0b\uff0c\u5176\u4e2d\u957f\u5ea6\u4e3as=3\u7684\u7b49\u5dee\u6570\u5217\u7684\u300c\u83b7\u80dc\u72b6\u6001\u300d\u88ab\u6807\u51fa\u4e86\u3002<\/span><\/p>\n


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

<\/p>\n


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

\u4e0a\u56fe\u7684\u4e00\u4e2a\u66f4\u5177\u5bf9\u79f0\u6027\u7684\u53ef\u89c6\u5316\u662f\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u4e0b\u9762\u662f\u957f\u5ea6\u4e3a7\u76841\u7ef4\u68cb\u76d8\u548c2\u4e2a\u73a9\u5bb6\u7684\u60c5\u5f62\u7684\u7c7b\u4f3c\u7ed3\u679c\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5bf9\u4e8e\u6bcf\u4e2a\u5927\u5c0f\u7684\u68cb\u76d8n\uff0c\u6211\u4eec\u53ef\u4ee5\u8ba1\u7b97\u51fa\u4efb\u4f55\u7279\u5b9a\u73a9\u5bb6\u7684\u83b7\u80dc\u72b6\u6001\u603b\u6570\uff0c\u4ee5\u53ca\u603b\u7684\u72b6\u6001\u6570\u3002\u5f53\u83b7\u80dc\u662f\u57fa\u4e8e\u957f\u5ea6\u4e3a3\u7684\u7b97\u672f\u7ea7\u6570<\/span>\uff08\u5373s=3\uff09<\/span>\u65f6\uff0c\u5176\u7ed3\u679c\u662f\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u8fd9\u91cc\u7684\u4e24\u4e2a\u73a9\u5bb6\u3001n=9<\/span>\uff08=3\u00d73\uff09<\/span>\u7684\u60c5\u51b5\u4e0e\u666e\u901a\u4e95\u5b57\u68cb\u76f8\u4f3c\uff0c\u4f46\u4e0d\u662f\u5b8c\u5168\u4e00\u6837\u3002<\/span><\/p>\n

\u7279\u522b\u662f\uff0c\u50cf\u8fd9\u6837\u7684\u72b6\u6001<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5728\u6241\u5e73\u5316\u4e86\u4e4b\u540e\uff0c\u4e5f\u88ab\u8ba4\u4e3a\u662fX\u83b7\u80dc\u7684\u72b6\u6001\uff0c\u4f46\u5728\u666e\u901a\u4e95\u5b57\u6e38\u620f\u4e2d\u5374\u4e0d\u662f\u3002<\/span><\/p>\n


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

\u5982\u679c\u6211\u4eec\u589e\u52a0\u80dc\u5229\u6240\u9700\u7684\u7b49\u5dee\u6570\u5217\u957f\u5ea6\uff0c\u4f8b\u5982\u589e\u52a0\u5230s=4\uff0c\u6211\u4eec\u5c31\u4f1a\u5f97\u5230\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u6e38\u620f\u72b6\u6001\u7684\u603b\u6570\u6ca1\u6709\u53d8\u5316\uff0c\u4f46\u6b63\u5982\u9884\u671f\u7684\u90a3\u6837\uff0c\u300c\u83b7\u80dc\u7684\u65b9\u5f0f\u66f4\u5c11\u4e86\u300d\u3002<\/span><\/p>\n


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

\u4f46\u662f\uff0c\u5047\u8bbe\u6211\u4eec\u7684\u68cb\u76d8\u5b8c\u5168\u88ab\u586b\u6ee1\u4e86\u3002\u5bf9\u4e8e\u5c0f\u68cb\u76d8\u6765\u8bf4\uff0c\u4efb\u4f55\u68cb\u624b\u4e0d\u7ba1\u600e\u4e48\u4e0b\u5b50\u90fd\u53ef\u80fd\u8fbe\u4e0d\u5230\u7b49\u5dee\u6570\u5217\uff0c\u56e0\u6b64\u6e38\u620f\u5fc5\u987b\u88ab\u8ba4\u4e3a\u662f\u5e73\u5c40\u2014\u2014\u6b63\u5982\u6211\u4eec\u5728n=5\u7684\u60c5\u51b5\u4e0b\u770b\u5230\u7684\u90a3\u6837\u3002<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u4f46\u662f\uff0c\u6700\u540e\u53d1\u73b0\u8fd9\u662f\u4e00\u4e2a\u4e0e\u62c9\u59c6\u9f50\u7406\u8bba<\/span>\uff08Ramsey theory\uff09<\/span>\u76f8\u5173\u7684\u7ed3\u679c\uff1a\u5bf9\u4e8en\u22659\uff0c\u4e0d\u53ef\u907f\u514d\u7684\u662f\uff0c\u81f3\u5c11\u6709\u4e00\u4e2a\u73a9\u5bb6\u4f1a\u6709\u300c\u7b49\u5dee\u6570\u5217\u7684\u80dc\u5229\u300d\uff0c\u6240\u4ee5\u6c38\u8fdc\u4e0d\u4f1a\u51fa\u73b0\u5e73\u5c40\u2014\u2014\u6b63\u5982\u4e0b\u9762\u8fd9\u4e9b\u4f8b\u5b50\u6240\u8bf4\u660e\u7684\u90a3\u6837\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n


<\/p>\n

\n
\n
\n
\n
\n

<\/section>\n

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

\u884c\u8fdb\uff08Walk\uff09\u548c\u5b83\u4eec\u5bf9\u5e94\u7684\u591a\u8def\u56fe <\/span><\/strong><\/span><\/h3>\n

Walks and Their<\/span><\/strong><\/span> <\/span><\/strong>Multiway Graphs<\/span><\/strong><\/h3>\n<\/section>\n
\n

<\/section>\n

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

\uff08\u6821\u6ce8\uff1awalk \u7684\u7ffb\u8bd1\u4f5c\u4e3a\u540d\u8bcd\u4e0e\u52a8\u8bcd\uff0c\u56fd\u5185\u6709\u7ffb\u8bd1\u4e3a\u9014\u5f84\uff0c\u4f46\u4ece Wolfram \u5199\u4f5c\u51fa\u53d1\u70b9\u7684\u6784\u60f3\u53c8\u662f\u975e\u5e38\u7ecf\u5178\u7684 random-walk\uff0c\u5373\u968f\u673a\u6f2b\u6b65\u6216\u968f\u673a\u6e38\u8d70\u7684\u95ee\u9898\u6765\u6e90\uff0c\u4f46\u7528\u4e8e\u672c\u6587\u4e2d\u663e\u5f97\u6709\u4e9b\u8fc7\u4e8e\u6d6a\u6f2b\u5316\u8868\u8fbe\uff0c\u53d6\u6298\u4e2d\u7ffb\u8bd1\u505a\u300c\u884c\u8fdb\u300d\uff09<\/span><\/p>\n


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

\u50cf\u4e95\u5b57\u68cb\u8fd9\u6837\u7684\u6e38\u620f\uff0c\u5b9e\u9645\u4e0a\u5728\u6bcf\u4e00\u6b65\u90fd\u8981\u79fb\u52a8\u5230\u51e0\u4e2a\u53ef\u80fd\u7684\u65b0\u68cb\u76d8\u72b6\u6001\u4e2d\u7684\u4e00\u4e2a\u2014\u2014\u6211\u4eec\u53ef\u4ee5\u628a\u5b83\u770b\u4f5c\u662f\u5728\u300c\u6e38\u620f\u72b6\u6001\u7a7a\u95f4\u300d\u4e2d\u7684\u4e0d\u540c\u300c\u4f4d\u7f6e\u300d\u3002\u4f46\u662f\uff0c\u5982\u679c\u6211\u4eec\u4e0d\u8003\u8651\u68cb\u76d8\u72b6\u6001\uff0c\u800c\u53ea\u662f\u628a\u6211\u4eec\u7684\u72b6\u6001\u770b\u4f5c\u662f\u4e00\u4e2a\u6805\u683c<\/span>\uff08lattice\uff09<\/span>\u4e0a\u7684\u4f4d\u7f6e\uff0c\u5982\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u7136\u540e\u6211\u4eec\u770b\u4e00\u4e0b\u8fd9\u4e2a\u56fe\u4e2d\u53ef\u80fd\u7684\u884c\u8fdb\u8def\u7ebf<\/span>\uff08walks\uff09<\/span>\uff0c\u73b0\u5728\u8fd9\u4e2a\u60c5\u51b5\u4e0b\uff0c\u6bcf\u4e00\u6b65\u90fd\u53ef\u4ee5\u54114\u4e2a\u65b9\u5411\u4e2d\u7684\u4efb\u4f55\u4e00\u4e2a\u65b9\u5411\u8d70\u4e00\u4e2a\u5355\u4f4d\u5417\uff1f<\/span><\/p>\n


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

\u4ece\u56fe\u4e0a\u67d0\u4e00\u70b9\u5f00\u59cb\uff0c1\u6b65\u4e4b\u540e\u7684\u591a\u8def\u56fe\u5f88\u7b80\u5355\u5730\u5c31\u662f<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u8fd9\u91cc\u6211\u4eec\u7279\u5730\u5e03\u7f6e\u4e86\u8fd9\u4e2a\u56fe\u5f62\uff0c\u4f7f\u5f97\u300c\u72b6\u6001\u300d\u7684\u4f4d\u7f6e\u5bf9\u5e94\u4e8e\u5b83\u4eec\u5728\u6805\u683c\u4e0a\u7684\u51e0\u4f55\u4f4d\u7f6e\u3002
<\/span><\/p>\n


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

\u4e24\u6b65\u4e4b\u540e\u6211\u4eec\u5f97\u5230\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u800c\u66f4\u4e00\u822c\u7684\u60c5\u51b5\u4e0b\uff0c\u8fd9\u4e2a\u591a\u8def\u56fe\u7684\u7ed3\u6784\u53ea\u662f\u300c\u91cd\u8ff0\u300d<\/span>\uff08recapitulates\uff09<\/span>\u4e86\u6805\u683c\u7684\u7ed3\u6784\u3002<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u6211\u4eec\u53ef\u4ee5\u628a\u591a\u8def\u56fe\u4e2d\u7684\u8def\u5f84\uff0c\u770b\u4f5c\u662f\u4ee3\u8868\u6805\u683c\u4e2d\u6240\u6709\u53ef\u80fd\u7684\u4e00\u5b9a\u957f\u5ea6\u7684\u968f\u673a\u884c\u8fdb<\/span>\uff08Walk\uff09<\/span>\u8def\u7ebf\u3002\u6211\u4eec\u53ef\u4ee5\u5c06\u8be5\u56fe\u94fa\u62103D\uff0c\u5782\u76f4\u4f4d\u7f6e\u4ee3\u8868\u53ef\u4ee5\u5230\u8fbe\u67d0\u4e00\u70b9\u7684\u7b2c\u4e00\u6b65\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u6211\u4eec\u4e5f\u53ef\u4ee5\u50cf\u5e03\u7f6e\u4e95\u5b57\u56fe\u7684\u591a\u8def\u56fe\u90a3\u6837\u5e03\u7f6e\u8fd9\u4e2a\u56fe\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u8fd9\u4e9b\u300c\u968f\u673a\u884c\u8fdb<\/span>\uff08random-walk\uff09<\/span>\u300d\u7684\u591a\u8def\u56fe\u7684\u4e00\u4e2a\u7279\u70b9\u662f\uff0c\u5b83\u4eec\u5305\u542b\u5faa\u73af\uff0c\u8bb0\u5f55\u4e86\u300c\u8fd4\u56de\u5df2\u7ecf\u53bb\u8fc7\u7684\u5730\u65b9\u300d\u7684\u53ef\u80fd\u6027\u3002\u8fd9\u4e0e\u4e95\u5b57\u68cb\u4e2d\u7684\u60c5\u51b5\u4e0d\u540c\uff0c\u5728\u4e95\u5b57\u68cb\u4e2d\uff0c\u6bcf\u4e00\u6b65\u90fd\u662f\u5728\u68cb\u76d8\u4e0a\u589e\u52a0\u4e00\u4e2a\u5143\u7d20\uff0c\u800c\u4e0d\u53ef\u80fd\u518d\u56de\u5230\u4ee5\u524d\u7684\u72b6\u6001\u3002<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u4f46\u662f\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u8003\u8651\u300c\u81ea\u6211\u56de\u907f\u7684\u884c\u8fdb\u8def\u7ebf\u300d\uff0c\u4e3a\u884c\u8fdb\u5efa\u7acb\u4e00\u4e2a\u7c7b\u4f3c\u7684\u300c\u6c38\u4e0d\u56de\u5934\u7684\u89c4\u5219\u300d\uff0c\u5176\u4e2d\u4efb\u4f55\u88ab\u8bbf\u95ee\u8fc7\u7684\u70b9\u90fd\u4e0d\u4f1a\u88ab\u518d\u6b21\u8bbf\u95ee\u3002<\/span><\/p>\n


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

\u8ba9\u6211\u4eec\u9996\u5148\u8003\u8651\u975e\u5e38\u7b80\u5355\u7684\u6805\u683c\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u73b0\u5728\u7528\u7ea2\u70b9\u8868\u793a\u300c\u6211\u4eec\u76ee\u524d\u5230\u8fbe\u7684\u5730\u65b9\u300d\uff0c\u7528\u84dd\u70b9\u8868\u793a\u6211\u4eec\u4ee5\u524d\u53bb\u8fc7\u7684\u5730\u65b9\uff0c\u5e76\u4ece\u4e00\u4e2a\u89d2\u843d\u5f00\u59cb\uff1a<\/span><\/p>\n


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

<\/section>\n


<\/p>\n

\u8fd9\u91cc\u53ea\u6709\u4e24\u79cd\u53ef\u80fd\u7684\u8d70\u6cd5\uff0c\u4e00\u79cd\u662f\u987a\u65f6\u9488\u8d70\uff0c\u53e6\u4e00\u79cd\u662f\u9006\u65f6\u9488\u8d70\u3002\u5982\u679c\u5141\u8bb8\u4ece\u6bcf\u4e2a\u53ef\u80fd\u7684\u4f4d\u7f6e\u5f00\u59cb\uff0c\u5c31\u4f1a\u4ea7\u751f\u4e00\u4e2a\u7a0d\u5fae\u590d\u6742\u7684\u591a\u8def\u56fe\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5982\u679c\u662f\u4e00\u4e2a2\u00d73\u7684\u7f51\u683c\uff0c\u6211\u4eec\u5c31\u5f97\u5230\u4e0b\u56fe\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u800c 3×3 \u7684\u7f51\u683c\u5bf9\u5e94\u7684\u591a\u8def\u56fe\u662f\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u4ece\u4e2d\u95f4\u5f00\u59cb\uff0c\u7528\u4e0d\u540c\u7684\u5e03\u5c40\u6765\u753b\u591a\u8def\u56fe\uff0c\u53ef\u4ee5\u5f97\u5230\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u8bf7\u6ce8\u610f\u56fe\u4e2d\u7684\u51e0\u4e2a\u5927\u300c\u6d1e\u300d\u7684\u5b58\u5728\uff0c\u5176\u4e2d\u6bcf\u4e00\u8fb9\u7684\u8def\u5f84\u57fa\u672c\u4e0a\u662f\u4ee5\u300c\u76f8\u53cd\u7684\u65b9\u5f0f\u300d\u5230\u8fbe\u300c\u540c\u4e00\u4e2a\u5730\u65b9\u300d\u3002\u8bf7\u6ce8\u610f\uff0c\u5728\u67091\u4e2a\u84dd\u70b9\u548c\u6700\u591a8\u4e2a\u7ea2\u70b9\u76842304\u79cd\u53ef\u80fd\u65b9\u5f0f\u4e2d\uff0c\u8fd9\u4e2a\u591a\u8def\u56fe\u5b9e\u9645\u53ea\u8fbe\u5230\u4e8657\u79cd\u3002<\/span>\uff08\u4ece\u89d2\u843d\u5f00\u59cb\u53ef\u4ee5\u8fbe\u523075\u79cd\uff0c\u4ece\u6240\u6709\u53ef\u80fd\u7684\u521d\u59cb\u4f4d\u7f6e\u53ef\u4ee5\u8fbe\u5230438\u79cd\uff09<\/span>\u3002<\/span><\/p>\n


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

\u57284\u00d74\u7684\u6805\u683c\u91cc\uff08\u4ece\u89d2\u843d\u91cc\u5f00\u59cb\u8d70\uff09\uff0c\u591a\u8def\u56fe\u6709\u8fd9\u6837\u7684\u5f62\u6001\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u6216\u8005\u6362\u4e00\u79cd\u5e03\u5c40\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5176\u4e2d\uff0c\u5171\u8ba1524288\u4e2a\u72b6\u6001\u4e2d\uff0c\u67091677\u4e2a\u72b6\u6001\u6700\u7ec8\u88ab\u8bbf\u95ee\u5230\u4e86\uff0c\u6bcf\u4e00\u6b65\u8bbf\u95ee\uff08\u5373\u56fe\u4e2d\u8fde\u7eed\u51e0\u5c42\u7684\u8282\u70b9\u6570\u91cf\uff09\u7684\u65b0\u72b6\u6001\u7684\u6570\u91cf\u4e3a\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5bf9\u4e8e\u4e00\u4e2a5\u00d75\u7684\u7f51\u683c\u6765\u8bf4\uff0c\u670989,961\u4e2a\u72b6\u6001\u80fd\u591f\u8fbe\u5230\uff0c\u6839\u636e\u4ee5\u4e0b\u60c5\u51b5\u5206\u5e03\u5728\u5404\u4e2a\u6b65\u9aa4\u4e2d\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\uff08\u5bf9\u4e8e\u4e00\u4e2a\u6709n\u4e2a\u9876\u70b9\u7684\u7f51\u683c\uff0c\u603b\u5171\u6709n x 2^(n\u20131) \u4e2a\u53ef\u80fd\u7684\u72b6\u6001\uff0c\u4f46\u5b9e\u9645\u8fbe\u5230\u7684\u6570\u91cf\u603b\u662f\u5c0f\u5f97\u591a\uff09<\/span>\u3002<\/span><\/p>\n


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

\u5728\u8ba8\u8bba\u884c\u8fdb\u65f6\uff0c\u4e00\u4e2a\u660e\u663e\u7684\u95ee\u9898\u662f\u5173\u4e8e\u8ff7\u5bab\u7684\u3002<\/span><\/p>\n


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

\u8003\u8651\u4e0b\u9762\u8fd9\u4e2a\u8ff7\u5bab\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5c31\u7a7f\u8d8a\u8fd9\u4e2a\u8ff7\u5bab\u800c\u8a00\uff0c\u5b83\u7b49\u540c\u4e8e\u5728\u56fe\u4e0a\u300c\u884c\u8fdb\u300d<\/span>\uff08walking\uff09<\/span>\u3002<\/span><\/p>\n


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

<\/section>\n

<\/section>\n

\u800c\u53e6\u4e00\u79cd\u8868\u793a\u5373\u662f\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u4f46\u5c31\u50cf\u4ee5\u524d\u4e00\u6837\uff0c\u4ee3\u8868\u6240\u6709\u53ef\u80fd\u7684\u884c\u8fdb\u8def\u7ebf\u7684\u591a\u8def\u56fe\u672c\u8d28\u4e0a\u53ea\u662f\u300c\u91cd\u8ff0\u300d\u4e86\u8fd9\u4e2a\u56fe\u3002\u8fd9\u610f\u5473\u7740\uff0c\u300c\u89e3\u300d\u8fd9\u4e2a\u8ff7\u5bab\u5728\u67d0\u79cd\u610f\u4e49\u4e0a\u540c\u6837\u53ef\u4ee5\u88ab\u8ba4\u4e3a\u662f\u76f4\u63a5\u5728\u8ff7\u5bab\u56fe\u6216\u591a\u8def\u56fe\u4e2d\u627e\u5230\u4e00\u6761\u8def\u5f84\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n


<\/p>\n

\n
\n
\n
\n
\n

<\/section>\n

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

\u5341\u4e8c\u9762\u4f53\u6e38\u620f\u4e0e\u5176\u4ed6\u76f8\u5173\u6e38\u620f<\/strong><\/span><\/h3>\n

The Icosian Game <\/strong><\/span><\/h3>\n

& Some Relatives<\/strong><\/h3>\n<\/section>\n
\n

<\/section>\n

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

<\/h3>\n

\u6211\u4eec\u5bf9\u81ea\u6211\u56de\u907f\u7684\u884c\u8fdb\u8def\u7ebf\u7684\u8ba8\u8bba\uff0c\u5176\u5b9e\u4e0e\u5a01\u5ec9\u00b7\u7f57\u6587\u00b7\u6c49\u5bc6\u5c14\u987f<\/span>\uff08William Rowan Hamilton\uff09<\/span>\u57281857\u5e74\u63d0\u51fa\u7684\u5341\u4e8c\u9762\u4f53\u6e38\u620f<\/span>\uff08Icosian game\uff09\uff08\u8fd9\u4e0e\u65e9\u671f\u7684\u8ba1\u7b97\u673a\u6e38\u620f Hunt the Wumpus \u6709\u4e00\u5b9a\u7684\u5173\u7cfb\uff09<\/span>\u76f4\u63a5\u76f8\u5173\u3002<\/span><\/p>\n


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

<\/p>\n

<\/p>\n


<\/p>\n

\u8fd9\u4e2a\u300c\u6e38\u620f\u300d<\/span>\uff08\u6216\u8005\u66f4\u6070\u5f53\u5730\u8bf4\uff0c\u8c1c\u9898\uff09<\/span>\u7684\u76ee\u7684\u662f\u5728\u4e8c\u5341\u9762\u4f53\u56fe\u5f62\u7684\u8fb9\u4e0a\u627e\u5230\u4e00\u6761\u8def\u5f84<\/span>\uff08\u662f\u7684\uff0c\u4e00\u6761\u6c49\u5bc6\u5c14\u987f\u8def\u5f84\uff09<\/span>\uff0c\u8bbf\u95ee\u6bcf\u4e2a\u8282\u70b9<\/span>\uff08\u5e76\u8fd4\u56de\u5230\u5b83\u7684\u8d77\u70b9\uff09<\/span>\u3002\u6211\u4eec\u53ef\u4ee5\u518d\u6b21\u6784\u5efa\u4e00\u4e2a\u591a\u8def\u56fe\uff0c\u4ee3\u8868\u6e38\u620f\u4e2d\u6240\u6709\u53ef\u80fd\u7684\u300c\u79fb\u52a8\u300d\u5e8f\u5217\u3002<\/span><\/p>\n


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

\u8ba9\u6211\u4eec\u4ece\u5e95\u5c42\u56db\u9762\u4f53\u56fe\u5f62\u7684\u8f83\u7b80\u5355\u60c5\u51b5\u5f00\u59cb\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u7531\u6b64\u6211\u4eec\u5f97\u5230\u591a\u8def\u56fe\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u800c\u8003\u8651\u8fdb\u4e86\u56db\u9762\u4f53\u56fe\u5f62\u4e0a\u6240\u6709\u53ef\u80fd\u7684\u8d77\u59cb\u4f4d\u7f6e\u5f97\u51fa\u7684\u300c\u7ec4\u5408\u7684\u591a\u8def\u56fe\u300d\uff0c\u7ed9\u51fa\u4e86\u4e00\u4e2a\u5448\u622a\u65ad\u7684\u7acb\u65b9\u516b\u9762\u4f53\u5f62\u72b6<\/span>\uff08truncated cuboctahedron\uff09<\/span>\u7684\u591a\u8def\u56fe\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u6309\u7167\u8fd9\u4e2a\u56fe\u5f62\uff0c\u6211\u4eec\u53ef\u4ee5\u770b\u5230\uff0c\u4ece\u4efb\u4f55\u521d\u59cb\u72b6\u6001\u51fa\u53d1\uff0c\u90fd\u6709\u53ef\u80fd\u8fbe\u5230\u56db\u9762\u4f53\u56fe\u5f62\u4e2d\u7684\u6bcf\u4e2a\u8282\u70b9\u90fd\u88ab\u8bbf\u95ee\u8fc7\u7684\u72b6\u6001\u3002\u4e8b\u5b9e\u4e0a\uff0c\u7531\u4e8e\u56db\u9762\u4f53\u56fe\u662f\u4e00\u4e2a\u5b8c\u5168\u56fe<\/span>\uff08Complete graph\uff09<\/span>\uff0c\u5b83\u751a\u81f3\u53ef\u4ee5\u4fdd\u8bc1\u5e8f\u5217\u4e2d\u7684\u6700\u540e\u4e00\u4e2a\u8282\u70b9\u5c06\u4e0e\u8d77\u59cb\u8282\u70b9\u300c\u76f8\u90bb\u300d\u2014\u2014\u8fd9\u6837\u6211\u4eec\u5c31\u5f62\u6210\u4e86\u4e00\u4e2a\u6c49\u5bc6\u5c14\u987f\u73af<\/span>\uff08Hamiltonian Cycle\uff09<\/span>\u6765\u89e3\u51b3\u8fd9\u4e2a\u8c1c\u9898\u3002<\/span><\/p>\n


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

\u5bf9\u4e8e\u7acb\u65b9\u4f53\u56fe\u6765\u8bf4\uff0c\u4e8b\u60c5\u5c31\u4e0d\u90a3\u4e48\u7b80\u5355\u4e86\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u8fd9\u65f6\u4ece\u4e00\u4e2a\u7279\u5b9a\u7684\u72b6\u6001\u5f00\u59cb\u7684\u591a\u8def\u56fe\u662f\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u8fd9\u65f6\u5c31\u670913\u4e2a\u65e0\u6cd5\u4ea7\u751f\u8fdb\u4e00\u6b65\u884c\u52a8\u7684\u72b6\u6001\u3002<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5728\u5176\u4e2d\u4e00\u4e9b\u60c5\u51b5\u4e0b\uff0c\u73a9\u5bb6\u88ab\u300c\u5835\u4f4f\u300d<\/span>\uff08boxed in\uff09<\/span>\u4e86\uff0c\u6ca1\u6709\u76f8\u90bb\u7684\u8282\u70b9\u53ef\u4f9b\u8bbf\u95ee\u3002\u5728\u5176\u4ed6\u60c5\u51b5\u4e0b\uff0c\u6240\u6709\u7684\u8282\u70b9\u90fd\u88ab\u586b\u6ee1\u4e86\u3002\u4f46\u53ea\u67093\u4e2a\u6700\u7ec8\u5b9e\u73b0\u4e86\u771f\u6b63\u7684\u6c49\u5bc6\u5c14\u987f\u5faa\u73af\uff0c\u5373\u5176\u7ec8\u70b9\u4e0e\u8d77\u59cb\u8282\u70b9\u76f8\u90bb\u3002<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u4e8b\u5b9e\u8bc1\u660e\uff0c\u4eba\u4eec\u53ef\u4ee5\u901a\u8fc74\u6761\u4e0d\u540c\u7684\u8def\u5f84\u4ece\u591a\u8def\u56fe\u7684\u6839\u90e8\u5230\u8fbe\u8fd9\u4e9b\u72b6\u6001\u4e2d\u7684\u6bcf\u4e00\u4e2a\u3002\u8fd9\u79cd\u8def\u5f84\u7684\u4e00\u4e2a\u4f8b\u5b50\u662f\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u6211\u4eec\u53ef\u4ee5\u5c06\u8fd9\u4e00\u8def\u5f84\u6982\u62ec\u4e3a\u539f\u59cb\u7acb\u65b9\u4f53\u56fe\u7684\u6c49\u5bc6\u5c14\u987f\u73af\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5728\u591a\u8def\u56fe\u4e2d\uff0c12\u6761\u300c\u83b7\u80dc\u8def\u5f84\u300d\u662f<\/span><\/p>\n


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

<\/section>\n

<\/section>\n

\u8fd9\u8fd8\u53ef\u4ee5\u8868\u793a\u6210\u4e0b\u56fe\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5982\u679c\u53ea\u4fdd\u7559\u300c\u83b7\u80dc\u8def\u5f84\u300d\uff0c\u591a\u8def\u56fe\u7684\u5b50\u56fe\u5177\u6709\u5bf9\u79f0\u7684\u5f62\u5f0f\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5bf9\u5e94\u4e8e\u8fd9\u4e9b\u83b7\u80dc\u7684\u8def\u5f84\u7684\u5e95\u5c42\u7acb\u65b9\u4f53\u56fe\u7684\u6c49\u5bc6\u5c14\u987f\u73af\u5206\u522b\u662f\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5bf9\u4e8e\u5341\u4e8c\u9762\u4f53\u56fe<\/span>\uff08\u5373\u539f\u672c\u7684\u4e8c\u5341\u9762\u4f53\u6e38\u620f\uff09<\/span>\uff0c\u591a\u8def\u56fe\u66f4\u5927\u3001\u66f4\u590d\u6742\u3002\u5b83\u5f00\u59cb\u4e8e\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5e76\u572811\u6b65\u4e4b\u540e\u51fa\u73b0\u4e86\u7b2c\u4e00\u6b21\u5408\u5e76<\/span>\uff08\u603b\u5171529\u6b65\uff09<\/span>\uff0c\u6700\u540e\u603b\u5171\u670911093\u4e2a\u8282\u70b9\uff0c\u5176\u4e2d2446\u4e2a\u662f\u300c\u7ec8\u6b62\u72b6\u6001\u300d\uff0c\u4e0d\u53ef\u80fd\u518d\u6709\u8fdb\u4e00\u6b65\u7684\u79fb\u52a8\u3002\u4e0b\u56fe\u5c55\u793a\u4e86\u6bcf\u4e2a\u8fde\u7eed\u6b65\u9aa4\u4e2d\u7684\u7ec8\u6b62<\/span>\uff08\u9ec4\u8272\u67f1\u72b6\u56fe\uff09<\/span>\u548c\u975e\u7ec8\u6b62<\/span>\uff08\u84dd\u8272\u67f1\u72b6\u56fe\uff09<\/span>\u72b6\u6001\u7684\u6570\u91cf\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u8fde\u7eed\u7684\u300c\u8d70\u4e0a\u6210\u529f\u4e4b\u8def\u300d\u7684\u72b6\u6001\u6bd4\u4f8b\u5982\u4e0b\uff0c\u8868\u660e\u4ece\u67d0\u79cd\u610f\u4e49\u4e0a\u8bf4\uff0c\u8be5\u8c1c\u9898\u5728\u5f00\u59cb\u65f6\u6bd4\u7ed3\u675f\u65f6\u66f4\u96be\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u670913\u4e2a\u300c\u7ed3\u675f\u72b6\u6001\u300d\uff0c\u586b\u8865\u4e86\u5e95\u5c42\u5341\u4e8c\u9762\u4f53\u56fe\u7684\u6bcf\u4e00\u4e2a\u4f4d\u7f6e\uff0c\u5176\u4e2d3\u4e2a\u5bf9\u5e94\u4e8e\u6c49\u5bc6\u5c14\u987f\u73af\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u4ece\u591a\u8def\u56fe\u7684\u6839\u90e8\u901a\u5f80\u6700\u7ec8\u72b6\u6001\u7684\u8def\u5f84\u603b\u6570<\/span>\uff08\u5b9e\u9645\u4e0a\u662f\u4e5f\u5c31\u662f\u5c1d\u8bd5\u89e3\u8c1c\u7684\u603b\u6570\u91cf\uff09<\/span>\u4e3a3120\u6761\u3002\u5176\u4e2d\uff0c\u670960\u6761\u8def\u5f84\u901a\u54113\u4e2a\u6c49\u5bc6\u5c14\u987f\u73af\u7684\u6700\u7ec8\u72b6\u6001\u3002\u8fd9\u4e9b\u300c\u83b7\u80dc\u8def\u5f84\u300d\u7684\u4e00\u4e2a\u4f8b\u5b50\u662f\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u4e0e3\u4e2a\u6c49\u5bc6\u5c14\u987f\u73af\u7ed3\u675f\u72b6\u6001\u4e2d\u7684\u6bcf\u4e00\u4e2a\u5bf9\u5e94\u7684\u57fa\u672c\u6c49\u5bc6\u5c14\u987f\u73af\u7684\u4f8b\u5b50\u662f\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u800c\u8fd9\u5c55\u793a\u4e86\u901a\u8fc7\u591a\u8def\u56fe\u5230\u8fbe\u6c49\u5bc6\u5c14\u987f\u73af\u7ec8\u70b9\u72b6\u6001\u7684\u6240\u670960\u6761\u8def\u5f84\u2014\u2014\u4ece\u800c\u5bf9\u5e94\u4e8e\u8c1c\u9898\u7684\u89e3\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5b9e\u9645\u4e0a\uff0c\u89e3\u8c1c\u5c31\u662f\u5728\u591a\u8def\u56fe\u7684\u6240\u6709\u53ef\u80fd\u6027\u4e2d\u6210\u529f\u627e\u5230\u8fd9\u4e9b\u8def\u5f84\u3002\u4e0d\u8fc7\uff0c\u5728\u5b9e\u8df5\u4e2d\u2014\u2014\u4f8b\u5982\u5728\u5b9a\u7406\u8bc1\u660e\u4e2d\u2014\u2014\u6709\u6bd4\u76f4\u63a5\u67e5\u770b\u591a\u8def\u56fe\u4e2d\u7684\u6240\u6709\u53ef\u80fd\u6027\u66f4\u6709\u6548\u7684\u65b9\u6cd5\u6765\u5bfb\u627e\u300c\u83b7\u80dc\u8def\u5f84\u300d<\/span>\uff08\u4f8b\u5982Wolfram\u8bed\u8a00\u4e2d\u7684 FindHamiltonianCycle\uff09<\/span>\u3002\u4f46\u5bf9\u4e8e\u6211\u4eec\u5728\u591a\u91cd\u8ba1\u7b97\u6846\u67b6\u4e2d\u7406\u89e3\u6e38\u620f\u548c\u8c1c\u9898\u7684\u76ee\u6807\u6765\u8bf4\uff0c\u770b\u770b\u8fd9\u4e2a\u8c1c\u9898\u7684\u89e3\u51b3\u65b9\u6848\u5728\u591a\u8def\u56fe\u4e2d\u662f\u5982\u4f55\u5e03\u5c40\u7684\u662f\u5f88\u6709\u7528\u7684\u3002<\/span><\/p>\n


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

\u6c49\u5bc6\u5c14\u987f\u7684\u5341\u4e8c\u9762\u4f53\u6e38\u620f\u9996\u6b21\u5f15\u5165\u4e86\u56fe\u4e0a\u7684\u6c49\u5bc6\u5c14\u987f\u73af\u7684\u6982\u5ff5\u3002\u4f46\u65e9\u57281736\u5e74\uff0c\u83b1\u6602\u54c8\u5fb7\u00b7\u6b27\u62c9<\/span>\uff08Leonhard Euler\uff09<\/span>\u5c31\u5728\u67ef\u5c3c\u65af\u5821\u6865\u4e4b\u8c1c\u4e2d\u8ba8\u8bba\u4e86\u73b0\u5728\u6240\u8c13\u7684\u6b27\u62c9\u73af<\/span>\uff08Eulerian cycles\uff09<\/span>\u3002<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u7528\u73b0\u4ee3\u672f\u8bed\u6765\u8bf4\uff0c\u6211\u4eec\u53ef\u4ee5\u628a\u8fd9\u4e2a\u8c1c\u9898\u8868\u8ff0\u4e3a\u5bfb\u627e\u4e00\u6761\u80fd\u591f\u8bbf\u95ee\u4e00\u6b21\u4e14\u53ea\u8bbf\u95ee\u4e00\u6b21\u56fe\u4e2d\u6240\u6709\u8fb9\u7684\u8def\u5f84\u7684\u95ee\u9898<\/span>\uff08\u5176\u4e2d\u539f\u8c1c\u9898\u4e2d\u7684\u300c\u53cc\u6865\u300d\u5df2\u7ecf\u88ab\u989d\u5916\u7684\u8282\u70b9\u6240\u53d6\u4ee3\uff09<\/span>\u3002<\/span><\/p>\n

<\/p>\n

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

<\/p>\n


<\/p>\n

\u6211\u4eec\u53ef\u4ee5\u521b\u5efa\u4e00\u4e2a\u591a\u8def\u56fe\uff0c\u4ee3\u8868\u4ece\u67d0\u4e00\u7279\u5b9a\u9876\u70b9\u51fa\u53d1\u7684\u6240\u6709\u53ef\u80fd\u8def\u5f84\u3002<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u4f46\u73b0\u5728\u6211\u4eec\u770b\u5230\uff0c\u8fd9\u91cc\u7684\u6700\u7ec8\u72b6\u6001\u662f:<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u800c\u7531\u4e8e\u5b83\u4eec\u90fd\u6ca1\u6709\u8bbf\u95ee\u8fc7\u6240\u6709\u7684\u8fb9\uff0c\u6240\u4ee5\u8fd9\u91cc\u6ca1\u6709\u6b27\u62c9\u73af\u3002\u4e3a\u4e86\u5f7b\u5e95\u89e3\u51b3\u8fd9\u4e2a\u96be\u9898\uff0c\u6211\u4eec\u9700\u8981\u6784\u9020\u4e00\u4e2a\u591a\u8def\u56fe\uff0c\u4ece\u6240\u6709\u53ef\u80fd\u7684\u5e95\u5c42\u9876\u70b9\u5f00\u59cb\u3002\u5176\u7ed3\u679c\u662f\u4e00\u4e2a\u4e0d\u76f8\u8fde\u7684\u591a\u8def\u56fe\uff0c\u5176\u672b\u7aef\u72b6\u6001\u4e5f\u4ece\u672a\u8bbf\u95ee\u8fc7\u5e95\u5c42\u56fe\u4e2d\u7684\u6bcf\u4e00\u6761\u8fb9<\/span>\uff08\u4ece\u6bcf\u4e2a\u5b50\u56fe\u4e2d\u7684\u300c\u5c42\u6b21\u300d\u6570\u91cf\u5c11\u4e8e10\u8fd9\u4e00\u4e8b\u5b9e\u53ef\u4ee5\u770b\u51fa\uff09<\/span>\u3002<\/span><\/p>\n


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

<\/p>\n


<\/p>\n


<\/p>\n

\n
\n
\n
\n
\n

<\/section>\n

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

\u5730\u7406\u6e38\u620f <\/span><\/strong><\/h3>\n

The Geography Game<\/span><\/strong><\/h3>\n<\/section>\n
\n

<\/section>\n

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

<\/h3>\n

\u5728\u5730\u7406\u6e38\u620f\u4e2d\uff0c\u4eba\u4eec\u6709\u4e00\u7ec4\u8bcd<\/span>\uff08\u6bd4\u5982\u8bf4\u5730\u540d\uff09<\/span>\uff0c\u7136\u540e\u8bd5\u56fe\u5c06\u8fd9\u4e9b\u8bcd\u300c\u4e32\u8d77\u6765\u300d\uff0c\u4e00\u4e2a\u8bcd\u7684\u6700\u540e\u4e00\u4e2a\u5b57\u6bcd\u4e0e\u4e0b\u4e00\u4e2a\u8bcd\u7684\u7b2c\u4e00\u4e2a\u5b57\u6bcd\u76f8\u540c\u3002\u6e38\u620f\u901a\u5e38\u5728\u6ca1\u6709\u4eba\u80fd\u591f\u60f3\u51fa\u4e00\u4e2a\u7b26\u5408\u89c4\u5219\u7684\u3001\u4e14\u4e4b\u524d\u6ca1\u6709\u4f7f\u7528\u8fc7\u7684\u8bcd\u65f6\u7ed3\u675f\u3002<\/span><\/p>\n


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

\u901a\u5e38\u5728\u5b9e\u8df5\u4e2d\uff0c\u8fd9\u4e2a\u6e38\u620f\u662f\u7531\u591a\u4e2a\u73a9\u5bb6\u6e38\u73a9\u7684\u3002\u4f46\u6211\u4eec\u5b8c\u5168\u53ef\u4ee5\u8003\u8651\u53ea\u6709\u4e00\u4e2a\u73a9\u5bb6\u7684\u7248\u672c\u3002\u4f5c\u4e3a\u4e00\u4e2a\u4f8b\u5b50\uff0c\u8ba9\u6211\u4eec\u628a\u6211\u4eec\u7684\u300c\u8bcd\u300d\u4f5c\u4e3a\u7f8e\u56fd\u5404\u5dde\u7684\u7f29\u5199\u3002\u7136\u540e\u6211\u4eec\u5c31\u53ef\u4ee5\u6784\u9020\u4e00\u4e2a\u4ec0\u4e48\u8bcd\u53ef\u4ee5\u63a5\u4ec0\u4e48\u8bcd\u7684\u56fe\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u9996\u5148\uff0c\u8ba9\u6211\u4eec\u5ffd\u7565\u4e00\u4e2a\u5dde\u540d\u662f\u5426\u300c\u5df2\u7ecf\u88ab\u4f7f\u7528\u300d\u7684\u95ee\u9898\u3002\u7136\u540e\uff0c\u4ece\u9a6c\u8428\u8bf8\u585e\u5dde<\/span>\uff08Massachusetts\uff09<\/span>\u5f00\u59cb\uff0c\u6211\u4eec\u53ef\u4ee5\u6784\u5efa\u4e00\u4e2a\u591a\u8def\u56fe\u7684\u5f00\u5934\uff0c\u7ed9\u6211\u4eec\u6240\u6709\u53ef\u80fd\u7684\u5e8f\u5217\u3002<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5341\u6b65\u4ee5\u540e\u8fd9\u4e2a\u56fe\u53d8\u6210\u4e86\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u6216\u8005\u6362\u4e00\u79cd\u5e03\u5c40\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5047\u8bbe\u4e0d\u5141\u8bb8\u4efb\u4f55\u72b6\u6001\u91cd\u590d\uff0c\u4e0b\u9762\u7684\u56fe\u8868\u5c55\u793a\u4e86\u8be5\u56fe\u4e2d\u7684\u8def\u5f84\u603b\u6570\u4e0e\u8def\u5f84\u957f\u5ea6\u7684\u5173\u7cfb\u3002<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u8def\u5f84\u7684\u6700\u5927\u957f\u5ea6\u662f23\uff0c\u6709256\u6761\u8fd9\u6837\u7684\u8def\u5f84\uff0c88\u6761\u4ee5TX\u7ed3\u5c3e\uff0c168\u6761\u4ee5AZ\u7ed3\u5c3e\u3002\u51e0\u4e2a\u8fd9\u6837\u7684\u8def\u5f84\u7684\u4f8b\u5b50\u662f\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u800c\u6240\u6709\u8fd9\u4e9b\u8def\u5f84\u90fd\u53ef\u4ee5\u7528\u7b49\u540c\u4e8e\u6709\u9650\u72b6\u6001\u673a<\/span>\uff08finite state machine\uff09<\/span>\u7684\u5f62\u5f0f\u6765\u8868\u793a\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u987a\u4fbf\u8bf4\u4e00\u4e0b\uff0c\u5f15\u5411\u6700\u957f\u8def\u5f84\u7684\u8d77\u59cb\u72b6\u6001\u662fMN\u2014\u2014\u5b83\u4ee52336\u79cd\u4e0d\u540c\u7684\u65b9\u5f0f\u8fbe\u5230\u957f\u5ea624\uff0c\u53ef\u80fd\u7684\u7ed3\u5c3e\u662fAZ\u3001DE\u3001KY\u548cTX\u3002\u51e0\u4e2a\u4f8b\u5b50\u662f\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5728\u4eceMN\u5f00\u59cb\u7684\u591a\u8def\u56fe\u7684\u524d\u51e0\u6b65\u4e2d\u7ed8\u5236\u8fd9\u4e9b\u8def\u5f84\uff0c\u6211\u4eec\u5f97\u5230\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n


<\/p>\n

\n
\n
\n
\n
\n

<\/section>\n

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

\u7fa4\u548c\uff08\u7b80\u5316\u7684\uff09\u9b54\u65b9 <\/span><\/strong><\/span><\/h3>\n

Groups and (Simplified)<\/span><\/strong><\/span><\/h3>\n

Rubik\u2019s Cubes<\/span><\/strong><\/span><\/h3>\n<\/section>\n
\n

<\/section>\n

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

<\/h3>\n

\u6211\u4eec\u5df2\u7ecf\u8c08\u8bba\u8fc7\u90a3\u4e9b\u672c\u8d28\u4e0a\u6d89\u53ca\u56fe\u7ed3\u6784\u4e0a\u7684\u884c\u8fdb<\/span>\uff08Walk\uff09<\/span>\u7684\u8c1c\u9898\u3002\u4e00\u4e2a\u7279\u522b\u8457\u540d\u7684\u53ef\u4ee5\u7528\u8fd9\u79cd\u65b9\u5f0f\u601d\u8003\u7684\u8c1c\u9898\u7684\u4f8b\u5b50\u662f\u9b54\u65b9\u3002\u6709\u5173\u7684\u56fe\u662f\u7531\u53ef\u5e94\u7528\u4e8e\u9b54\u65b9\u7684\u53d8\u6362\u6240\u5f62\u6210\u7684\u7fa4<\/span>\uff08group\uff09<\/span>\u7684\u51ef\u83b1\u56fe<\/span>\uff08Cayley Graph\uff09<\/span>\u3002<\/span><\/p>\n

\uff08\u8bd1\u6ce8\uff1a\u7fa4\uff08group\uff09\u662f\u4e00\u4e2a\u6570\u5b66\u672f\u8bed\uff0c\u6307\u4e00\u4e2a\u96c6\u5408\u548c\u4e00\u4e2a\u4f5c\u7528\u5728\u8fd9\u4e2a\u96c6\u5408\u7684\u5143\u7d20\u4e0a\u7684\u4e8c\u5143\u8fd0\u7b97\u3002\u8fd9\u4e2a\u96c6\u5408\u9700\u8981\u6ee1\u8db3\u5176\u4e2d\u4efb\u610f\u5143\u7d20\u5b58\u5728\u4e00\u4e2a\u9006\u5143\u7d20\uff08inverse\uff09\uff0c\u4ee5\u53ca\u5b58\u5728\u4e00\u4e2a\u5355\u4f4d\u5143\u7d20\uff08identity<\/span>\uff09\u3002\u8fd9\u4e2a\u4e8c\u5143\u8fd0\u7b97\u9700\u8981\u7b26\u5408\u5c01\u95ed\u6027\uff08\u8fd0\u7b97\u7ed3\u679c\u4ecd\u7136\u662f\u96c6\u5408\u4e2d\u7684\u5143\u7d20\uff09\u3001\u7ed3\u5408\u5f8b\u3001\u5355\u4f4d\u5143\uff08\u5728\u5355\u4f4d\u5143\u7d20\u4e0a\u5e94\u7528\u8be5\u8fd0\u7b97\u5f97\u5230\u7684\u4ecd\u7136\u662f\u5355\u4f4d\u5143\u7d20\uff09\u7684\u6027\u8d28\u3002\u6bd4\u5982\u6240\u6709\u6574\u6570\u7ec4\u6210\u7684\u96c6\u5408\u548c\u52a0\u6cd5\u5c31\u6784\u6210\u4e00\u4e2a\u7fa4\u3002\u51ef\u83b1\u56fe\uff08Cayley Graph\uff09\u662f\u7fa4\u7684\u7ed3\u6784\u4e00\u79cd\u53ef\u89c6\u5316\u65b9\u6cd5\u3002\uff08\u63a8\u8350 3B1B\u89c6\u9891 \u7fa4\u8bba\u4e0e808017424794512875886459904961710757005\u200d754368000000000\uff09\uff09<\/span><\/p>\n


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

\u4f5c\u4e3a\u4e00\u4e2a\u975e\u5e38\u7b80\u5355\u7684\u7c7b\u6bd4\uff0c\u6211\u4eec\u53ef\u4ee5\u8003\u8651\u6b63\u65b9\u5f62\u7684\u5bf9\u79f0\u53d8\u6362\u7fa4<\/span>\uff08the symmetry group of the square\uff09\uff08D4\uff09<\/span>\uff0c\u57fa\u4e8e\u955c\u50cf\u53cd\u8f6c\u548c90\u00b0\u65cb\u8f6c\u7684\u64cd\u4f5c\u3002\u6211\u4eec\u751f\u6210\u7684\u51ef\u83b1\u56fe\u5c31\u50cf\u4e00\u4e2a\u591a\u5411\u56fe\uff1a\u901a\u8fc7\u5728\u6bcf\u4e00\u6b65\u5e94\u7528\u6bcf\u4e2a\u64cd\u4f5c\u3002\u800c\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u51ef\u83b1\u56fe\u662f\uff1a<\/span><\/p>\n

\uff08\u8bd1\u6ce8\uff1a\u84dd\u8272\u7bad\u5934\u8868\u793a90\u00b0\u65cb\u8f6c\uff0c\u7eff\u8272\u7bad\u5934\u8868\u793a\u955c\u50cf\u53cd\u8f6c\uff09<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u8fd9\u4e2a\u56fe\u8db3\u591f\u5c0f\uff0c\u53ef\u4ee5\u76f4\u63a5\u770b\u5230\u5982\u4f55\u4ece\u4efb\u4f55\u72b6\u6001\u5230\u4efb\u4f55\u5176\u4ed6\u72b6\u6001\u3002\u4f46\u662f\uff0c\u5c3d\u7ba1\u8fd9\u4e2a\u51ef\u83b1\u56fe\u67098\u4e2a\u8282\u70b9\uff0c\u4ece\u4efb\u4f55\u4e00\u4e2a\u8282\u70b9\u5230\u53e6\u4e00\u4e2a\u8282\u70b9\u7684\u6700\u5927\u8def\u5f84\u957f\u5ea6\u4e3a3\uff0c\u9b54\u65b9\u7684\u51ef\u83b1\u56fe\u7684\u8282\u70b9\u6570\u91cf\u5374\u6709
<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u6700\u5927\u6700\u77ed\u8def\u5f84\u957f\u5ea6\u4e3a20\u3002<\/span><\/p>\n


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

\u4e3a\u4e86\u4e86\u89e3\u8fd9\u6837\u4e00\u4e2a\u4e8b\u7269\u7684\u7ed3\u6784\uff0c\u6211\u4eec\u53ef\u4ee5\u8003\u8651\u975e\u5e38\u7b80\u5316\u7684\u300c2\u00d72\u00d72 \u7acb\u65b9\u4f53\u300d\u7684\u60c5\u51b5\u2014\u2014\u53ea\u5728\u5176\u89d2\u4e0a\u7740\u8272\u2014\u2014\u6bcf\u4e2a\u9762\u53ef\u4ee5\u65cb\u8f6c90\u00b0\u3002<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u4ece\u4e0a\u56fe\u4e2d\u7684\u72b6\u6001\u5f00\u59cb\uff0c\u591a\u8def\u56fe\u7684\u7b2c\u4e00\u6b65\u5c31\u662f\uff08\u6ce8\u610f\uff0c\u56fe\u4e2d\u7684\u8fb9\u4e0d\u662f\u6709\u5411\u7684\uff0c\u56e0\u4e3a\u5bf9\u5e94\u7684\u8f6c\u6362\u603b\u662f\u53ef\u9006\u7684\uff09\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u518d\u591a\u8d70\u4e00\u6b65\u5c31\u5f97\u5230\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5b8c\u6574\u7684\u591a\u8def\u56fe<\/span>\uff08\u4e5f\u662f\u7531\u53d8\u6362\u4ea7\u751f\u7684\u8fd9\u4e2a\u7fa4\u7684\u51ef\u83b1\u56fe\u2014\u2014\u5c31\u662fS8\uff09<\/span>\u67098\uff01=40320\u4e2a\u8282\u70b9<\/span>\uff08\u548c483840\u6761\u8fb9\uff09<\/span>\u3002\u4ece\u4e00\u4e2a\u72b6\u6001<\/span>\uff08\u5373\u51ef\u83b1\u56fe\u4e2d\u7684\u8282\u70b9\uff09<\/span>\u5f00\u59cb\uff0c\u5728\u8fde\u7eed\u7684\u6b65\u9aa4\u4e2d\u8fbe\u5230\u7684\u65b0\u72b6\u6001\u7684\u6570\u91cf\u662f\uff1a
<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u56fe\u4e2d\u7684\u6700\u5927\u6700\u77ed\u8def\u5f84<\/span>\uff08maximum shortest paths\uff09<\/span>\u75318\u4e2a\u6b65\u9aa4\u7ec4\u6210\uff0c\u4e00\u4e2a\u4f8b\u5b50\u662f\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\uff08\u8bd1\u6ce8\uff1amaximum shortest paths \u6307\u7684\u662f\u90a3\u4e9b\u4e0d\u662f\u4efb\u4f55\u5176\u4ed6\u6700\u77ed\u8def\u5f84\u7684\u5b50\u8def\u5f84\u7684\u6700\u77ed\u8def\u5f84\u3002\u6bd4\u5982\u5047\u8bbe A-B-C \u662fA\u70b9\u5230C\u70b9\u4e4b\u95f4\u7684\u6700\u77ed\u8def\u5f84\uff0cA-B-C-D\u662fA\u70b9\u5230D\u70b9\u7684\u6700\u77ed\u8def\u5f84\uff0c\u90a3\u4e48A-B-C\u5c31\u4e0d\u662f\u4e00\u4e2amaxumum shortest path\uff0c\u56e0\u4e3a\u53e6\u4e00\u6761\u6700\u77ed\u8def\u5f84A-B-C-D\u5305\u542b\u4e86A-B-C\uff09<\/span><\/p>\n


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

\u5728\u8fd9\u4e24\u4e2a\u7279\u5b9a\u7684\u7aef\u70b9\u4e4b\u95f4\uff0c\u5b9e\u9645\u4e0a\u67093216\u6761\u300c\u6d4b\u5730<\/span>\uff08geodesic\uff09<\/span>\u300d\u8def\u5f84\u2014\u2014\u8fd9\u4e9b\u8def\u5f84\u5728\u591a\u8def\u56fe\u4e2d\u5206\u5e03\u5f88\u5e7f\u3002<\/span>\uff08\u8bd1\u6ce8\uff1a\u300c\u6d4b\u5730\u300d\u8def\u5f84\u6307\u7403\u4f53\u7ed3\u6784\u4e0a\u4e24\u70b9\u4e4b\u95f4\u7684\u6700\u77ed\u8def\u5f84\u3002\uff09<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u53ea\u6311\u51fa\u6d4b\u5730\u8def\u5f84\uff0c\u6211\u4eec\u770b\u5230\u6709\u8bb8\u591a\u65b9\u6cd5\u53ef\u4ee5\u4ece\u7acb\u65b9\u4f53\u7684\u4e00\u4e2a\u72b6\u6001\u5230\u8fbe\u5b83\u7684\u4e00\u4e2a\u300c\u53cd\u8282\u70b9\u300d<\/span>\uff08antipodes\uff09<\/span>\u3002<\/span><\/p>\n


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

<\/p>\n


<\/p>\n


<\/p>\n

\n
\n
\n
\n
\n

<\/section>\n

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

\u5b54\u660e\u68cb <\/span><\/strong><\/span><\/h3>\n

Peg Solitaire<\/span><\/strong><\/span><\/h3>\n<\/section>\n
\n

<\/section>\n

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

\u50cf\u4e95\u5b57\u68cb\u8fd9\u6837\u7684\u8c1c\u9898\u6d89\u53ca\u5230\u9010\u6b65\u586b\u6ee1\u68cb\u76d8\uff0c\u800c\u81f3\u5c11\u4ece16\u4e16\u7eaa\u5f00\u59cb\u4f7f\u7528\u7684\u4e00\u5927\u7c7b\u8c1c\u9898\u5219\u6d89\u53ca\u5230\u4ece\u68cb\u76d8\u4e0a\u79fb\u8d70\u68cb\u5b50\u3002\u5178\u578b\u7684\u89c4\u5219\u662f\u68cb\u5b50\u80fd\u591f\u8df3\u8fc7\u4e00\u4e2a\u4e2d\u95f4\u7684\u68cb\u5b50\u8fdb\u5165\u4e00\u4e2a\u6d1e\uff0c\u7136\u540e\u4e2d\u95f4\u7684\u68cb\u5b50\u88ab\u79fb\u9664\u3002\u76ee\u6807\u662f\u6700\u7ec8\u5728\u68cb\u76d8\u4e0a\u53ea\u5269\u4e0b\u4e00\u4e2a\u68cb\u5b50\u3002<\/span><\/p>\n


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

\u8fd9\u91cc\u6709\u4e00\u4e2a\u975e\u5e38\u7b80\u5355\u7684\u4f8b\u5b50\uff0c\u57fa\u4e8e\u4e00\u4e2a\u68cb\u5b50\u7684T\u5b57\u5f62\u6392\u5217\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u53ea\u6709\u4e00\u79cd\u65b9\u6cd5\u53ef\u4ee5\u300c\u89e3\u5f00\u8c1c\u9898\u300d\u3002
<\/span><\/p>\n


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

\u4f46\u5728\u4e00\u822c\u60c5\u51b5\u4e0b\uff0c\u6709\u4e00\u4e2a\u591a\u8def\u56fe\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u4e00\u4e2a\u66f4\u590d\u6742\u7684\u4f8b\u5b50\u662f\u300c\u68d8\u624b\u7684\u4e09\u89d2\u5f62\u300d<\/span>\uff08\u53c8\u79f0\u300c\u997c\u5e72\u6876\u8c1c\u9898\uff08Cracker Barrel puzzle\uff09\u300d\uff09<\/span>\u3002\u5b83\u7684\u591a\u8def\u56fe\u8fd9\u6837\u5f00\u59cb\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u518d\u8d70\u51e0\u6b65\u540e\uff0c\u5c31\u53d8\u6210\u4e86\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5728\u6700\u7ec8\u7684\u591a\u8def\u56fe\u4e2d\u603b\u5171\u67093016\u4e2a\u72b6\u6001\uff0c\u5176\u4e2d118\u4e2a\u662f\u300c\u6b7b\u80e1\u540c\u300d\uff0c\u4ece\u90a3\u91cc\u4e0d\u53ef\u80fd\u6709\u8fdb\u4e00\u6b65\u7684\u884c\u52a8\u3002\u8fd9\u4e9b\u6b7b\u80e1\u540c\u72b6\u6001\u4e2d\u300c\u6700\u65e9\u80fd\u8fbe\u5230\u300d\u7684\u662f\uff1a<\/span><\/p>\n


<\/p>\n


<\/p>\n

<\/p>\n


<\/p>\n

\u53ef\u4ee5\u8fbe\u5230\u7684\u300c\u83b7\u80dc\u72b6\u6001\u300d\u53ea\u67094\u4e2a\uff0c\u800c\u5bfc\u81f4\u8fd9\u4e9b\u72b6\u6001\u7684\u300c\u7ec8\u5c40\u300d\u662f\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u4ece\u521d\u59cb\u72b6\u6001\u5f00\u59cb\uff0c\u6bcf\u4e00\u6b65\u8fbe\u5230\u7684\u53ef\u80fd\u72b6\u6001\u7684\u6570\u91cf\u5982\u4e0b\uff0c\u5176\u4e2d\u53ef\u4ee5\u5bfc\u81f4\u83b7\u80dc\u7684\u72b6\u6001\u663e\u793a\u4e3a\u9ec4\u8272\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u4e0b\u56fe\u5c55\u793a\u4e86\u5b8c\u6574\u7684\u591a\u8def\u56fe\uff0c\u5e76\u9ad8\u4eae\u663e\u793a\u4e86\u300c\u83b7\u80dc\u8def\u5f84\u300d\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5728\u8fde\u7eed\u7684\u6b65\u9aa4\u4e2d\uff0c\u80fd\u591f\u5bfc\u81f4\u83b7\u80dc\u72b6\u6001\u7684\u72b6\u6001\u7684\u6bd4\u4f8b\u5982\u4e0b\uff1a<\/span>
<\/p>\n


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

<\/p>\n


<\/p>\n

\u5206\u652f\u56fe\u662f\u9ad8\u5ea6\u8fde\u63a5\u7684\uff0c\u8fd9\u610f\u5473\u7740\u5728\u67d0\u79cd\u610f\u4e49\u4e0a\uff0c\u8fd9\u4e2a\u8c1c\u9898\u76f4\u5230\u6700\u540e\u4ecd\u7136\u662f\u300c\u5747\u5300\u6df7\u5408\u7684<\/span>\uff08well mixed\uff09<\/span>\u300d\u548c\u300c\u4e0d\u53ef\u9884\u77e5\u7684\u300d\uff1a<\/span><\/p>\n


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

<\/section>\n


<\/p>\n


<\/p>\n

\n
\n
\n
\n
\n

<\/section>\n

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

\u897f\u6d0b\u8df3\u68cb <\/span><\/strong><\/span><\/h3>\n

Checkers<\/span><\/strong><\/span><\/h3>\n<\/section>\n
\n

<\/section>\n

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

\u5b54\u660e\u68cb\u662f\u4e00\u79cd\u5355\u4eba\u300c\u6e38\u620f\u300d\u3002\u897f\u6d0b\u8df3\u68cb\u662f\u4e00\u79cd\u53cc\u4eba\u6e38\u620f\uff0c\u89c4\u5219\u6709\u70b9\u7c7b\u4f3c\u3002<\/span><\/p>\n


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

\u300c\u9ed1\u300d\u68cb\u548c\u300c\u7ea2\u300d\u68cb\u5728\u68cb\u76d8\u4e0a\u5411\u4e0d\u540c\u65b9\u5411\u659c\u5411\u79fb\u52a8\uff0c\u5f53\u5b83\u4eec\u76f8\u90bb\u65f6\uff0c\u901a\u8fc7\u8df3\u8fc7\u5bf9\u65b9\u68cb\u5b50\u6765\u300c\u5403\u6389 \u300d\u5bf9\u65b9\u7684\u68cb\u5b50\u3002<\/span><\/p>\n


<\/p>\n

\u8003\u8651\u4e00\u4e2a\u76f8\u5f53\u5c0f\u76844\u00d74\u68cb\u76d8\u7684\u4f8b\u5b50\u3002<\/span><\/p>\n


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

\u300c\u9ed1\u300d\u548c\u300c\u7ea2\u300d\u7684\u57fa\u672c\u8d70\u6cd5\u7531\u4e0b\u56fe<\/span>\uff08\u6ce8\u610f\uff0c4\u00d74\u68cb\u76d8\u592a\u5c0f\uff0c\u4e0d\u652f\u6301\u300c\u591a\u8df3\u300d\uff09<\/span>\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u6211\u4eec\u53ef\u4ee5\u7acb\u5373\u5f00\u59cb\u751f\u6210\u4e00\u4e2a\u8fd9\u4e2a\u60c5\u51b5\u4e0b\u7684\u591a\u8def\u56fe\uff0c\u57fa\u4e8e\u9ed1\u68cb\u548c\u7ea2\u68cb\u7684\u4ea4\u66ff\u8fdb\u884c\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u6309\u7167\u76ee\u524d\u5b9a\u4e49\u7684\u89c4\u5219\uff0c\u5b8c\u6574\u7684161\u4e2a\u8282\u70b9\u7684\u591a\u8def\u56fe\u662f\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5728\u8fd9\u79cd\u7b80\u5355\u76844\u00d74\u60c5\u51b5\u4e0b\uff0c\u300c\u8d62\u300d\u7684\u542b\u4e49\u5e76\u4e0d\u5b8c\u5168\u6e05\u695a\u3002\u4f46\u53ef\u4ee5\u8bf4\uff0c\u5f53\u5bf9\u65b9\u5728\u4e0b\u4e00\u6b65\u68cb\u4e2d\u4e0d\u80fd\u505a\u4efb\u4f55\u4e8b\u60c5\u65f6\u5c31\u8d62\u4e86\u3002\u8fd9\u4e0e\u591a\u8def\u56fe\u4e2d\u7684\u300c\u6b7b\u8def<\/span>\uff08dead ends\uff09<\/span>\u300d\u76f8\u5bf9\u5e94\u3002\u8fd9\u79cd\u60c5\u51b5\u670926\u4e2a\uff0c\u5176\u4e2d\u53ea\u67093\u4e2a\u53d1\u751f\u5728\u7ea2\u65b9\u4e0b\u4e00\u6b65\u68cb\u7684\u65f6\u5019\uff0c\u5176\u4f59\u7684\u90fd\u53d1\u751f\u5728\u9ed1\u65b9\u7684\u65f6\u5019\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5982\u524d\u6240\u8ff0\uff0c\u4efb\u4f55\u7279\u5b9a\u7684\u6e38\u620f\u8fc7\u7a0b\u90fd\u5bf9\u5e94\u4e8e\u591a\u8def\u56fe\u4e2d\u4ece\u6839\u72b6\u6001<\/span>\uff08root state\uff09<\/span>\u5230\u67d0\u4e2a\u7ec8\u6b62\u72b6\u6001\u7684\u8def\u5f84\u3002\u5982\u679c\u6211\u4eec\u770b\u4e00\u4e0b\u8fd9\u79cd\u60c5\u51b5\u4e0b\u7684\u5206\u652f\u56fe\uff0c\u6211\u4eec\u4f1a\u53d1\u73b0\u5b83\u4eec\u6709\u8bb8\u591a\u4e0d\u76f8\u8fde\u7684\u5b50\u56fe\uff0c\u8fd9\u8868\u660e\u5bf9\u4e8e\u8fd9\u4e2a\u7b80\u5355\u7684\u6e38\u620f\u6765\u8bf4\uff0c\u6709\u8bb8\u591a\u57fa\u672c\u72ec\u7acb\u7684\u300c\u6e38\u620f\u8def\u5f84\u300d\u2014\u2014\u6240\u4ee5\u6ca1\u6709\u591a\u5c11\u7ed3\u679c\u7684\u300c\u6df7\u5408\u300d\u3002<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

<\/p>\n


<\/p>\n

\u5230\u76ee\u524d\u4e3a\u6b62\uff0c\u6211\u4eec\u4f7f\u7528\u7684\u89c4\u5219\u6ca1\u6709\u8003\u8651\u5230\u8df3\u68cb\u7684\u7b2c\u4e8c\u5c42\u89c4\u5219\uff1a\u5f53\u4e00\u4e2a\u68cb\u5b50\u5230\u8fbe\u68cb\u76d8\u7684\u53e6\u4e00\u8fb9\u65f6\uff0c\u5b83\u5c31\u6210\u4e3a\u4e00\u4e2a\u300c\u56fd\u738b\u300d\uff0c\u5141\u8bb8\u5411\u540e\u548c\u5411\u524d\u79fb\u52a8\u3002\u5373\u4f7f\u53ea\u6709\u4e00\u4e2a\u68cb\u5b50\u548c\u4e00\u4e2a\u68cb\u624b\uff0c\u8fd9\u4e5f\u5df2\u7ecf\u4ea7\u751f\u4e86\u4e00\u4e2a\u591a\u8def\u56fe\u2014\u2014\u5c24\u5176\u73b0\u5728\u56fe\u4e2d\u6709\u4e86\u5faa\u73af\uff1a
<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u6216\u8005\u6362\u4e00\u79cd\u5e03\u5c40<\/span>\uff08\u6709\u660e\u786e\u7684\u65e0\u5411\u8fb9\uff09<\/span>\uff1a<\/span><\/p>\n


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

<\/section>\n

<\/section>\n

\u6709\u4e86\u4e24\u9897\u68cb\u5b50<\/span>\uff08\u4e24\u4e2a\u73a9\u5bb6\u8f6e\u6d41\uff09<\/span>\uff0c\u300c\u56fd\u738b\u300d\u591a\u8def\u56fe\u662f\u8fd9\u6837\u5f00\u59cb\u7684\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5728\u8fd9\u4e2a\u521d\u59cb\u68cb\u5c40\u4e0b\uff0c\u4f46\u4e0d\u8003\u8651\u540e\u9000\u7684\u52a8\u4f5c\uff0c\u6574\u4e2a\u591a\u8def\u56fe\u5c31\u53ef\u4ee5\u7b80\u5316\u4e3a\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5b8c\u6574\u7684\u300c\u56fd\u738b\u300d\u591a\u8def\u56fe\u5728\u4e0a\u8ff0\u6761\u4ef6\u4e0b\u4e5f\u53ea\u670962\u4e2a\u8282\u70b9\u2014\u2014\u4f46\u5305\u62ec\u5404\u79cd\u5faa\u73af<\/span>\uff08\u5c3d\u7ba1\u6709\u8fd9\u4e48\u5c11\u7684\u68cb\u5b50\u5e76\u4e14\u8ba9\u9ed1\u68cb\u5148\u4e0b\uff0c\u4e14\u4efb\u4f55\u80dc\u5229\u90fd\u4e0d\u53ef\u907f\u514d\u5730\u4f1a\u662f\u9ed1\u68cb\u7684\uff09<\/span>\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5728\u6211\u4eec\u6700\u521d\u7684\u521d\u59cb\u6761\u4ef6\u4e0b\u7684\u666e\u901a+\u56fd\u738b\u7684\u591a\u8def\u56fe\u53c8\u5982\u4f55\u5462\uff1f\u7ec4\u5408\u56fe\u6709161\u4e2a\u8282\u70b9\u6765\u81ea\u300c\u524d\u56fd\u738b\u300d\u9636\u6bb5\uff0c4302\u4e2a\u6765\u81ea\u300c\u540e\u56fd\u738b\u300d\u9636\u6bb5\u2014\u2014\u4e0b\u56fe\u7ed9\u51fa\u4e86\u6700\u7ec8\u5f62\u5f0f:<\/span><\/p>\n


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

<\/p>\n


<\/p>\n


<\/p>\n

\n
\n
\n
\n
\n

<\/section>\n

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

\uff08\u6781\u5176\u7b80\u5316\u7684\uff09\u56f4\u68cb <\/span><\/strong><\/span><\/h3>\n

\uff08Very Simplified\uff09Go<\/span><\/strong><\/span><\/h3>\n<\/section>\n
\n

<\/section>\n

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

\u5b8c\u6574\u7684\u56f4\u68cb\u6e38\u620f\u662f\u9519\u7efc\u590d\u6742\u7684\uff0c\u5728\u4efb\u4f55\u73b0\u5b9e\u60c5\u51b5\u4e0b\uff0c\u5b83\u7684\u591a\u8def\u56fe\u90fd\u592a\u5927\u4e86\uff0c\u6211\u4eec\u6839\u672c\u65e0\u6cd5\u660e\u786e\u5730\u751f\u6210<\/span>\uff08\u5c3d\u7ba1\u4eba\u4eec\u5f53\u7136\u53ef\u4ee5\u60f3\u4e00\u60f3\u662f\u5426\u6709\u6709\u610f\u4e49\u7684\u300c\u8fde\u7eed\u6781\u9650\uff08continuum limit\uff09\u300d\u7ed3\u679c\uff09<\/span>\u3002\u7136\u800c\uff0c\u4e3a\u4e86\u80fd\u5bf9\u56f4\u68cb\u6709\u70b9\u6982\u5ff5\uff0c\u6211\u4eec\u53ef\u4ee5\u8003\u8651\u4e00\u4e2a\u975e\u5e38\u7b80\u5316\u7684\u7248\u672c\uff0c\u5728\u8fd9\u4e2a\u7248\u672c\u4e2d\uff0c\u9ed1\u8272\u548c\u767d\u8272\u7684 \u300c\u68cb\u5b50\u300d\u88ab\u9010\u6b65\u653e\u5728\u56fe\u7684\u8282\u70b9\u4e0a\uff0c\u5982\u679c\u4e00\u65b9\u6210\u529f\u5730\u5305\u56f4\u4e86\u8fde\u6210\u4e00\u7247\u7684\u53e6\u4e00\u65b9\u7684\u68cb\u5b50\uff0c\u6e38\u620f\u5c31\u88ab\u89c6\u4f5c\u300c\u80dc\u5229\u300d\u3002<\/span><\/p>\n


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

\u60f3\u8c61\u4e00\u4e0b\uff0c\u6211\u4eec\u4ece\u4e00\u4e2a\u75312\u00d72\u7f51\u683c\u7ec4\u6210\u7684\u7a7a\u767d\u300c\u68cb\u76d8\u300d\u5f00\u59cb\uff0c\u7136\u540e\u5728\u4e00\u8fde\u4e32\u7684\u300c\u56de\u5408\u300d\u4e2d\u4ee5\u6240\u6709\u53ef\u80fd\u7684\u65b9\u5f0f\u6dfb\u52a0\u9ed1\u767d\u68cb\u5b50\u3002\u7531\u6b64\u4ea7\u751f\u7684\u591a\u8def\u56fe\u662f\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u6bcf\u4e00\u4e2a\u5728\u8fd9\u91cc\u6ca1\u6709\u540e\u7ee7\u60c5\u5f62\u7684\u72b6\u6001\u90fd\u662f\u9ed1\u6216\u767d\u65b9\u7684\u80dc\u5229\u3002<\/span><\/p>\n


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

\u300c\u9ed1\u80dc\u300d<\/span>\uff08\u9ad8\u4eae\u663e\u793a\u4e86\u88ab\u5305\u56f4\u7684\u68cb\u5b50\uff09<\/span>\u662f\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u800c\u300c\u767d\u80dc\u300d\u5219\u6709\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5728\u8fd9\u4e2a\u5c42\u9762\u4e0a\uff0c\u6211\u4eec\u6240\u62e5\u6709\u7684\u57fa\u672c\u4e0a\u76f8\u5f53\u4e8e2\u00d72\u7684\u4e95\u5b57\u68cb\u2014\u2014\u9664\u4e86\u540e\u8005\u6709\u4e00\u4e2a\u300c\u5bf9\u89d2\u7ebf\u300d\u7684\u80dc\u5229\u6761\u4ef6\u3002<\/span><\/p>\n


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

\u5728\u4e00\u4e2a3\u00d72\u7684\u300c\u68cb\u76d8\u300d\u4e0a\uff0c\u591a\u8def\u56fe\u7684\u524d\u4e24\u6b65\u662f\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5b8c\u6574\u7684\u591a\u8def\u56fe\u662f\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u8be5\u56fe\u6709235\u4e2a\u8282\u70b9\uff0c\u5176\u4e2d24\u4e2a\u662f\u767d\u65b9\u7684\u80dc\u5229\uff0c34\u4e2a\u662f\u9ed1\u65b9\u7684\u80dc\u5229\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u8fde\u7eed\u7684\u5206\u652f\u56fe\u662f<\/span>\uff08\u56fe\u4e2d\u6807\u660e\u4e86\u662f\u54ea\u65b9\u80dc\u5229\uff09<\/span>\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5bf9\u4e8e\u4e00\u4e2a3\u00d73\u7684\u300c\u68cb\u76d8\u300d\u6765\u8bf4\uff0c\u591a\u8def\u56fe\u67095172\u4e2a\u72b6\u6001\uff0c\u5176\u4e2d604\u4e2a\u662f\u767d\u65b9\u7684\u80dc\u5229\uff0c684\u4e2a\u662f\u9ed1\u65b9\u7684\u80dc\u5229\u3002<\/span><\/p>\n


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


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

\n
\n
\n
\n
\n

<\/section>\n

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

\u5c3c\u59c6\u6e38\u620f<\/span><\/strong><\/span><\/h3>\n

Nim<\/span><\/strong><\/span><\/h3>\n<\/section>\n
\n

<\/section>\n

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

\u4f5c\u4e3a\u53e6\u4e00\u4e2a\u7b80\u5355\u6e38\u620f\u7684\u4f8b\u5b50\uff0c\u6211\u4eec\u73b0\u5728\u8003\u8651\u5c3c\u59c6\u6e38\u620f<\/span>\uff08Nim\uff09<\/span>\u3002<\/span><\/p>\n


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

\u5728\u5c3c\u59c6\u6e38\u620f\u4e2d\uff0c\u6709k\u5806\u7269\u4f53\uff0c\u6bcf\u4e00\u6b65\u4e2d\uff0cp\u4e2a\u73a9\u5bb6\u4ea4\u66ff\u4ece\u4ed6\u4eec\u9009\u62e9\u7684\u4efb\u4f55\u4e00\u4e2a\u7269\u4f53\u5806\u4e2d\u53bb\u9664\u4efb\u610f\u6570\u91cf\u7684\u7269\u4f53\u3002\u6e38\u620f\u7684\u5931\u8d25\u8005\u662f\u88ab\u8feb\u5904\u5728\u6240\u6709\u5806\u4e2d\u90fd\u6ca1\u6709\u7269\u4f53\u7684\u73a9\u5bb6\u3002<\/span><\/p>\n


<\/p>\n

\u4ece\u4e24\u5806\u5404\u542b2\u4e2a\u7269\u4f53\u5f00\u59cb\uff0c\u6211\u4eec\u53ef\u4ee5\u4e3a\u8fd9\u4e2a\u6e38\u620f\u6784\u5efa\u4e00\u4e2a\u591a\u8def\u56fe\uff1a<\/span><\/p>\n


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

<\/section>\n

<\/section>\n

\u5982\u679c\u6709\u4e09\u5806\u7684\u7269\u4f53\uff0c\u8fd9\u4e2a\u591a\u8def\u56fe\u5c31\u53d8\u6210\u4e86\uff1a
<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u8fd9\u4e9b\u56fe\u663e\u793a\u4e86\u5c06\u7269\u4f53\u5806\u7684\u4e0d\u540c\u72b6\u6001\u76f8\u8054\u7cfb\u7684\u6240\u6709\u4e0d\u540c\u7684\u53ef\u80fd\u68cb\u6b65\u3002\u7136\u800c\uff0c\u5b83\u4eec\u5e76\u6ca1\u6709\u6307\u51fa\u54ea\u4f4d\u68cb\u624b\u5728\u4ec0\u4e48\u65f6\u5019\u79fb\u52a8\u3002\u52a0\u4e0a\u8fd9\u70b9\uff0c\u6211\u4eec\u57282-2\u60c5\u51b5\u4e0b\u5f97\u5230\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u800c\u5728\u4e09\u4e2a\u7269\u4f53\u5806\u3001\u6bcf\u5806\u67092\u4e2a\u7269\u4f53<\/span>\uff082-2-2\uff09<\/span>\u7684\u60c5\u51b5\u4e0b\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5c3d\u7ba1\u8fd9\u4e9b\u56fe\u770b\u8d77\u6765\u6709\u4e9b\u590d\u6742\uff0c\u4f46\u4e8b\u5b9e\u8bc1\u660e\uff0c\u5bf9\u4e8e\u4e00\u4e2a\u7279\u5b9a\u7684\u72b6\u6001\u4f55\u65f6\u5177\u6709\u53ef\u4ee5\u4fdd\u8bc1\u300c\u5bf9\u624b\u300d\u8f93\u6389\u7684\u5c5e\u6027\uff0c\u6709\u4e00\u4e2a\u975e\u5e38\u76f4\u63a5\u7684\u6807\u51c6\uff1a\u53ea\u8981\u62ff\u7740\u6570\u5b57\u5217\u8868\uff0c\u770b\u770b\u8fd9\u4e2a\u5217\u8868\u4e2d\u7684\u6570\u5b57\u6309\u6bd4\u7279\u4f4d\u53d6\u5f02\u6216<\/span>\uff08bitwise XOR \uff09<\/span>\u4e4b\u540e\u662f\u5426\u4e3a0\u3002<\/span><\/p>\n


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

\uff08\u8bd1\u6ce8\uff1a\u6309\u6bd4\u7279\u4f4d\u53d6\u5f02\u6216\u6307\u5c06\u4e24\u4e2a\u6570\u5b57\u8f6c\u6362\u6210\u4e8c\u8fdb\u5236\u4e4b\u540e\uff0c\u6bd4\u8f83\u6bcf\u4e00\u4e2a\u4f4d\u662f\u5426\u76f8\u540c\uff0c\u540c\u4e3a0\uff0c\u5f02\u4e3a1\uff0c\u6700\u540e\u5f97\u5230\u53e6\u4e00\u4e2a\u4e8c\u8fdb\u5236\u6570\u3002\u7ed3\u679c\u53ef\u4ee5\u518d\u4e0e\u7b2c\u4e09\u4e2a\u6570\u8fdb\u884c\u5f02\u6216\u64cd\u4f5c\uff08\u540c\u4e3a0\uff0c\u5f02\u4e3a1\uff09\uff0c\u4ee51\u6b64\u7c7b\u63a8\u3002\u6bd4\u5982 BitXor[2,2,2] = 11 ^ 11 ^ 11 = 00 ^ 11 = 11 = 2\uff0c\u5176\u4e2d\u7c97\u4f53\u8868\u793a\u4e8c\u8fdb\u5236\u6570\u3002\uff09<\/span><\/p>\n


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

\u6807\u8bb0\u8fd9\u4e9b\u72b6\u6001\uff0c\u6211\u4eec\u5f97\u5230<\/span>\uff08\u8bd1\u6ce8\uff1a\u4e0b\u56fe\u4e2d\u7528\u6df1\u7ea2\u8272\u505a\u6807\u8bb0\uff09<\/span>:<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u4e8b\u5b9e\u8bc1\u660e\uff0c\u5bf9\u4e8e\u5c3c\u59c6\u6e38\u620f\u6765\u8bf4\uff0c\u6211\u4eec\u5f97\u5230\u7684\u5206\u652f\u56fe\u5e8f\u5217\u6709\u4e00\u4e2a\u76f8\u5f53\u89c4\u5f8b\u7684\u7ed3\u6784\u3002\u5728\u4e24\u5806\u5404\u6709\u4e24\u4e2a\u7269\u4f53<\/span>\uff082-2\uff09<\/span>\u7684\u60c5\u51b5\u4e0b\uff0c\u91c7\u7528\u4e0e\u4e4b\u524d\u76f8\u540c\u7684\u6807\u8bb0\uff0c\u6211\u4eec\u5f97\u5230\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5728\u4e09\u4e2a\u7269\u4f53\u5806\u3001\u6bcf\u5806\u67092\u4e2a\u7269\u4f53<\/span>\uff082-2-2\uff09<\/span>\u7684\u60c5\u51b5\u4e0b\uff0c\u8fd9\u4e2a\u5206\u652f\u56fe\u5e8f\u5217\u53d8\u6210\u4e86\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u4e0b\u56fe\u5c55\u793a\u4e86\u4e00\u4e9b\u5176\u4ed6\u60c5\u51b5\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n


<\/p>\n

\n
\n
\n
\n
\n

<\/section>\n

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

\u6ed1\u5757\u8c1c\u9898 <\/span><\/strong><\/span><\/h3>\n

Sliding Block Puzzles<\/span><\/strong><\/span><\/h3>\n<\/section>\n
\n

<\/section>\n

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

<\/section>\n

\u8fd9\u7c7b\u6e38\u620f\u6709\u5f88\u591a\u540d\u5b57\uff0c\u6709\u5f88\u591a\u4e0d\u540c\u7684\u4e3b\u9898\u3002<\/span><\/p>\n


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

\u4f46\u8bb8\u591a\u8c1c\u9898\u672c\u8d28\u4e0a\u90fd\u662f\u6ed1\u5757\u8c1c\u9898\u3002<\/span><\/p>\n


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

\u4e00\u4e2a\u7b80\u5355\u7684\u4f8b\u5b50\u53ef\u80fd\u662f\u8981\u6c42\u4ece\u4e0b\u9762\u7684\u5de6\u56fe\u53d8\u6362\u6210\u53f3\u56fe\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u53d8\u6362\u662f\u901a\u8fc7\u5c06\u79ef\u6728\u6ed1\u5165\u7a7a<\/span>\uff08\u8f83\u6697\uff09<\/span>\u7684\u65b9\u5757\u5b8c\u6210\u7684\u3002
<\/span><\/p>\n


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

\u8fd9\u4e2a\u8c1c\u9898\u7684\u4e00\u4e2a\u89e3\u662f\uff1a<\/span><\/p>\n


<\/p>\n

<\/p>\n


<\/p>\n

\u53ef\u4ee5\u7528\u4e00\u4e2a\u591a\u8def\u56fe\u6765\u8868\u793a\u6240\u6709\u53ef\u80fd\u7684\u53d8\u6362\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\uff08\u6ce8\u610f\u8fd94\uff01= 24\u4e2a\u53ef\u80fd\u7684\u72b6\u6001\u4e2d\u53ea\u670912\u4e2a\u51fa\u73b0\u5728\u4e86\u4e0a\u56fe\u4e2d\uff1b\u50cf\u4e0b\u9762\u8fd9\u6837\u7684\u72b6\u6001<\/span><\/p>\n

\u662f\u4e0d\u53ef\u80fd\u8fbe\u5230\u7684\u3002\uff09<\/span><\/p>\n


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

\u7531\u4e8e\u6ed1\u5757\u603b\u662f\u53ef\u4ee5\u300c\u53cc\u5411\u6ed1\u52a8\u300d\uff0c\u6240\u4ee5\u6ed1\u52a8\u79ef\u6728\u8c1c\u9898\u7684\u591a\u8def\u56fe\u4e2d\u7684\u6bcf\u6761\u8fb9\u90fd\u6709\u4e00\u4e2a\u9006\u5411<\/span>\uff08inverse\uff09<\/span>\uff0c\u56e0\u6b64\uff0c\u6211\u4eec\u5c31\u628a\u8fd9\u4e9b\u591a\u8def\u56fe\u753b\u6210\u65e0\u5411\u56fe\u3002<\/span><\/p>\n


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

\u4e0b\u9762\u662f\u51e0\u79cd\u7b80\u5355\u7684\u60c5\u51b5\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

<\/p>\n


<\/p>\n

\u5f53\u6211\u4eec\u8003\u86513×2\u89c4\u6a21\u7684\u7f51\u683c\u65f6\uff0c\u60c5\u51b5\u4e00\u4e0b\u5b50\u5c31\u590d\u6742\u8d77\u6765\u4e86\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u57283\u7ef4\u7684\u8868\u793a\u4e0b\u8fd9\u4e2a\u591a\u8def\u56fe\u662f\uff1a
<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5f53\u6240\u6709\u7684\u79ef\u6728\u90fd\u4e0d\u540c\u7684\u65f6\u5019\uff0c\u4eba\u4eec\u503e\u5411\u4e8e\u5f97\u5230\u5177\u6709\u67d0\u79cd\u7403\u5f62\u7ed3\u6784\u7684\u591a\u8def\u56fe\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

(\u8bf7\u6ce8\u610f\uff0c\u5728\u524d\u4e09\u79cd\u60c5\u51b5\u4e0b\uff0c\u6709\u53ef\u80fd\u8fbe\u5230\u6240\u670930\u3001120\u3001360\u4e2a\u53ef\u60f3\u8c61\u7684\u79ef\u6728\u6392\u5217\uff0c\u800c\u5728\u6700\u540e\u4e00\u79cd\u60c5\u51b5\u4e0b\uff0c\u53ea\u80fd\u8fbe\u5230\u79ef\u6728\u7684\u300c\u5076\u6570\u6392\u5217\u300d\uff0c\u6216720\u4e2a\u53ef\u60f3\u8c61\u7684\u6392\u5217\u4e2d\u7684360\u4e2a\uff09<\/span>\u3002<\/span><\/p>\n

\u4ee5\u53ca\u8fd9\u5f20\u56fe\u7684\u6807\u8bb0\u90e8\u5206\u5c55\u793a\u4e86\u4ece <\/span> \u5230\u8fbe <\/span><\/p>\n

\u7684\u8def\u7ebf\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5982\u679c\u6709\u8bb8\u591a\u76f8\u540c\u7684\u79ef\u6728\uff0c\u901a\u5e38\u4f1a\u5f62\u6210\u7b80\u5355\u7684\u7f51\u683c\u72b6\u7ed3\u6784\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u800c\u5982\u679c\u53ea\u662f\u8ba9\u4e00\u4e2a\u79ef\u6728\u4e0d\u540c\uff0c\u57fa\u672c\u4e0a\u53ea\u662f\u5728\u8fd9\u4e2a\u7f51\u683c\u56fe\u4e2d\u300c\u589e\u52a0\u88c5\u9970\u300d\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u968f\u7740\u300c1\u300d\u548c\u300c2\u300d\u7684\u79ef\u6728\u7684\u6570\u91cf\u8d8a\u6765\u8d8a\u63a5\u8fd1\u4e8e\u76f8\u7b49\uff0c\u7ed3\u6784\u5c31\u4f1a\u88ab\u586b\u6ee1\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u6dfb\u52a0\u7b2c\u4e09\u79cd\u7c7b\u578b\u7684\u79ef\u6728\u4f1a\u8fc5\u901f\u5bfc\u81f4\u4e00\u4e2a\u975e\u5e38\u590d\u6742\u7684\u7ed3\u6784\uff1a
<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u4e0b\u56fe\u603b\u7ed3\u4e86\u4e00\u4e9b\u591a\u8def\u56fe\u7684\u60c5\u51b5\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

<\/p>\n


<\/p>\n


<\/p>\n

\n
\n
\n
\n
\n

<\/section>\n

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

\u6c49\u8bfa\u5854\uff0c\u7b49\u7b49 <\/strong><\/span><\/h3>\n

Towers of Hanoi, etc.<\/strong><\/span><\/h3>\n<\/section>\n
\n

<\/section>\n

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

\u53e6\u4e00\u4e2a\u8457\u540d\u7684\u8c1c\u9898\u662f\u6c49\u8bfa\u5854<\/span>\uff08Towers of Hanoi\uff09<\/span>\u3002<\/span><\/p>\n


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

\u6211\u4eec\u53ef\u4ee5\u4e3a\u5b83\u4e5f\u6784\u5efa\u4e00\u4e2a\u591a\u8def\u56fe\u3002\u4ece\u5de6\u8fb9\u7684\u6240\u6709\u76d8\u5b50\u5f00\u59cb\uff0c\u591a\u8def\u56fe\u7684\u7b2c\u4e00\u6b65\u662f\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u524d\u8fdb\u4e24\u6b65\u5c31\u5f97\u5230\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u4ece\u800c\u5b8c\u6574\u7684\u591a\u8def\u56fe\u5c31\u662f<\/span>\uff08\u5c55\u793a\u7684\u662f\u65e0\u5411\u8fb9\uff0c\u4ee5\u4ee3\u66ff\u6210\u5bf9\u7684\u6709\u5411\u8fb9\uff09<\/span>\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5f88\u5bb9\u6613\u770b\u51fa\u8fd9\u4e2a\u591a\u8def\u56fe\u7684\u9012\u5f52\u7ed3\u6784\u662f\u5982\u4f55\u5efa\u7acb\u8d77\u6765\u7684\u3002<\/span><\/p>\n


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

\u4e0b\u56fe\u662f2\u4e2a\u5706\u76d8<\/span>\uff08\u548c3\u6839\u67f1\u5b50\uff09<\/span>\u7684\u300c\u57fa\u7840\u60c5\u5f62\u300d\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u6bcf\u589e\u52a0\u4e00\u4e2a\u5706\u76d8\uff0c\u591a\u8def\u56fe\u4e2d\u7684\u8282\u70b9\u6570\u91cf\u5c31\u589e\u52a03\u500d\uff0c\u4f8b\u5982\uff0c\u67094\u4e2a\u5706\u76d8<\/span>\uff08\u4ecd\u67093\u6839\u67f1\u5b50\uff09<\/span>\u3002<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5982\u679c\u67094\u6839\u67f1\u5b50\uff0c\u4e8b\u60c5\u8d77\u521d\u770b\u8d77\u6765\u66f4\u590d\u6742\uff0c\u5373\u4f7f\u53ea\u6709\u4e24\u4e2a\u5706\u76d8\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5728\u4e09\u7ef4\u7684\u53ef\u89c6\u5316\u4e0b\u80fd\u770b\u51fa\u66f4\u660e\u663e\u7684\u7ed3\u6784\uff1a<\/span><\/p>\n

<\/p>\n


<\/p>\n

\u4e0b\u9762\u5206\u522b\u662f3\u4e2a\u30014\u4e2a\u548c5\u4e2a\u5706\u76d8\u7684\u7ed3\u679c\u2014\u2014\u300c\u8033\u6735\u4e0a\u7684\u70b9\u300d\u5bf9\u5e94\u4e8e\u6240\u6709\u5706\u76d8\u90fd\u5728\u4e00\u4e2a\u67f1\u5b50\u4e0a\u7684\u72b6\u6001\u3002<\/span><\/p>\n


<\/p>\n

<\/p>\n


<\/p>\n

\u57283\u6839\u67f1\u5b50\u7684\u60c5\u51b5\u4e0b\uff0c\u6700\u77ed\u6b65\u9aa4\u6570\u7684\u300c\u8c1c\u9898\u89e3\u51b3\u65b9\u6848\u300d\u2014\u2014\u5c06\u6240\u6709\u5706\u76d8\u4ece\u4e00\u6839\u67f1\u5b50\u79fb\u52a8\u5230\u53e6\u4e00\u6839\u67f1\u5b50\u2014\u2014\u6cbf\u7740\u591a\u8def\u56fe\u7684\u300c\u8fb9\u300d\u8d70\uff0c\u5bf9\u4e8en\u6839\u67f1\u5b50\u6765\u8bf4\uff0c\u957f\u5ea6\u4e3a2n – 1\uff1a<\/span><\/p>\n


<\/p>\n

<\/p>\n


<\/p>\n

4\u6839\u67f1\u5b50\u7684\u60c5\u51b5\u4e0b\uff0c\u5c31\u4e0d\u518d\u6709\u552f\u4e00\u7684\u300c\u6d4b\u5730\u8def\u5f84<\/span>\uff08geodesic path\uff09<\/span>\u300d\u4e86\u3002<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5e76\u4e14\u8fde\u7eed\u7684\u67f1\u5b50\u6570\u91cf\u4e0b\u8def\u5f84\u957f\u5ea6\u7ec4\u6210\u7684\u5e8f\u5217\u662f  <\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u6216\u8005\u5bf9\u4e8e\u5f88\u5927\u7684\u67f1\u5b50\u6570\u91cfn\u6765\u8bf4\uff0c\u8def\u5f84\u957f\u5ea6\u7565\u4f4e\u4e8e<\/span><\/p>\n


<\/p>\n

\u90a3\u4e48\u5206\u652f\u56fe\u5462\uff1f<\/span><\/p>\n


<\/p>\n

\u5bf9\u4e8e\u6807\u51c6\u76843\u4e2a\u5706\u76d8\u548c3\u6839\u67f1\u5b50\u7684\u60c5\u51b5\uff0c\u6211\u4eec\u6709\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5176\u4e2d\uff0c\u8fde\u7eed\u7684\u300c\u65f6\u95f4\u5207\u7247<\/span>\uff08time slices\uff09<\/span>\u300d\u88ab\u8ba4\u4e3a\u662f\u901a\u8fc7\u89c2\u5bdf\u4e0a\u8ff0\u591a\u8def\u56fe\u7684\u8fde\u7eed\u5782\u76f4\u5c42\u6b21\u800c\u83b7\u5f97\u7684\u3002<\/span><\/p>\n


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

\u5bf9\u4e8e4\u4e2a\u5706\u76d8\u7684\u60c5\u51b5\uff0c\u6211\u4eec\u5b9e\u8d28\u4e0a\u5f97\u5230\u7684\u300c\u57fa\u672c\u4e0a\u662f\u540c\u6837\u7684\u4e1c\u897f\u300d\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u800c4\u6839\u67f1\u5b50\u5c31\u8ba9\u95ee\u9898\u53d8\u5f97\u7a0d\u5fae\u590d\u6742\u4e86\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

5\u6839\u67f1\u5b50\u7684\u60c5\u51b5\u4e5f\u5ef6\u7eed\u4e86\u8fd9\u4e2a\u8d8b\u52bf\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n


<\/p>\n

\n
\n
\n
\n
\n

<\/section>\n

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

\u591a\u91cd\u8ba1\u7b97\u89c6\u89d2\u4e0b\u7684\u63a8\u8bba\u548c\u9610\u91ca <\/span><\/strong><\/span><\/h3>\n

Multicomputational Implications <\/span><\/strong><\/span><\/h3>\n

& Interpretation<\/span><\/strong><\/span><\/h3>\n<\/section>\n
\n

<\/section>\n

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

\u6211\u4eec\u5df2\u7ecf\u8003\u5bdf\u4e86\u8bb8\u591a\u6e38\u620f\u548c\u8c1c\u9898\u7684\u4f8b\u5b50\u3002\u5728\u6bcf\u4e00\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u90fd\u63a2\u7d22\u4e86\u56ca\u62ec\u4e86\u6574\u4e2a\u53ef\u80fd\u884c\u4e3a\u8c31\u7cfb\u7684\u591a\u8def\u56fe\u3002\u90a3\u4e48\uff0c\u6211\u4eec\u7684\u7ed3\u8bba\u662f\u4ec0\u4e48\u5462\uff1f<\/span><\/p>\n


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

\u6700\u660e\u663e\u7684\u4e00\u70b9\u662f\uff0c\u5982\u679c\u6e38\u620f\u548c\u8c1c\u9898\u5728\u6211\u4eec\u770b\u6765\u662f\u56f0\u96be\u7684\u2014\u2014\u6216\u8005\u8bf4\u662f\u300c\u6709\u8da3\u7684\u300d\u2014\u2014\u5b83\u5728\u67d0\u79cd\u7a0b\u5ea6\u4e0a\u4e3a\u591a\u8def\u56fe\u7684\u663e\u8457\u590d\u6742\u6027\u6240\u53cd\u6620\u3002\u6216\u8005\uff0c\u6362\u53e5\u8bdd\u8bf4\uff0c\u5f53\u6211\u4eec\u53d1\u73b0\u591a\u8def\u56fe\u5728\u67d0\u79cd\u7a0b\u5ea6\u4e0a\u300c\u96be\u4ee5\u89e3\u7801<\/span>\uff08decode\uff09<\/span>\u300d\u65f6\uff0c\u6211\u4eec\u5c31\u4f1a\u5f97\u5230\u4e00\u4e2a\u4e30\u5bcc\u7684\u3001\u5438\u5f15\u4eba\u7684\u6e38\u620f\u6216\u8c1c\u9898\u3002<\/span><\/p>\n


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

\u5728\u73a9\u4e00\u4e2a\u6e38\u620f\u7684\u4efb\u4f55\u7279\u5b9a\u5b9e\u4f8b\u4e2d\uff0c\u6211\u4eec\u57fa\u672c\u4e0a\u662f\u6cbf\u7740\u4e00\u6761\u7279\u5b9a\u7684\u8def\u5f84<\/span>\uff08\u4e0e\u7269\u7406\u5b66\u76f8\u7c7b\u4f3c\uff0c\u6211\u4eec\u53ef\u4ee5\u79f0\u4e4b\u4e3a\u300c\u65f6\u95f4\u8def\u5f84\uff08timelike path\uff09\u300d\uff09<\/span>\u7a7f\u8fc7\u6e38\u620f\u7684\u591a\u8def\u56fe<\/span>\uff08\u6216\u300c\u6e38\u620f\u56fe\u300d\uff09<\/span>\u3002\u5e76\u4e14\u5728\u67d0\u79cd\u7a0b\u5ea6\u4e0a\uff0c\u6211\u4eec\u53ef\u80fd\u53ea\u662f\u505a\u4e86\u4e00\u4e2a\u5168\u5c40\u6027\u7684\u58f0\u660e\uff0c\u5373\u6e38\u620f\u56fe\u4ee3\u8868\u4e86\u6240\u6709\u8fd9\u6837\u7684\u8def\u5f84\u3002<\/span><\/p>\n


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

\u4f46\u591a\u91cd\u8ba1\u7b97\u8303\u5f0f<\/span>\uff08Multicomputational paradigm\uff09<\/span>\u6240\u5efa\u8bae\u7684\u662f\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u6709\u6548\u5730\u505a\u51fa\u66f4\u591a\u7684\u5c40\u90e8\u58f0\u660e\u3002\u7279\u522b\u662f\uff0c\u5728\u6cbf\u7740\u4e00\u6761\u65f6\u95f4\u8def\u5f84\u7684\u6bcf\u4e00\u6b65\uff0c\u6211\u4eec\u53ef\u4ee5\u5728\u591a\u8def\u56fe\u4e2d\u300c\u6a2a\u65ad\u5730<\/span>\uff08transversally\uff09<\/span>\u300d\u89c2\u5bdf\uff0c\u5e76\u770b\u5230\u300c\u77ac\u65f6\u5206\u652f\u56fe\u300d\uff0c\u5b83\u4ee3\u8868\u4e86\u6211\u4eec\u7684\u8def\u5f84\u4e0e\u300c\u90bb\u8fd1\u8def\u5f84\u300d\u7684\u300c\u7ea0\u7f20<\/span>\uff08entanglement\uff09<\/span>\u300d\u3002<\/span><\/p>\n


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

\u4ece\u800c\uff0c\u67d0\u79cd\u610f\u4e49\u4e0a\u8bf4\uff0c\u5f04\u6e05\u300c\u4e0b\u4e00\u6b65\u8be5\u505a\u4ec0\u4e48\u300d\u5c31\u662f\u51b3\u5b9a\u5728\u5206\u652f\u7a7a\u95f4\u4e2d\u300c\u671d\u4ec0\u4e48\u65b9\u5411\u300d\u8d70\u3002\u800c\u6e38\u620f\u7684\u56f0\u96be\u4e4b\u5904\u5728\u4e8e\uff0c\u6211\u4eec\u65e0\u6cd5\u8f7b\u6613\u9884\u77e5\u6211\u4eec\u300c\u7a7f\u8d8a\u5206\u652f\u7a7a\u95f4\u300d\u65f6\u53d1\u751f\u4e86\u4ec0\u4e48\u3002\u8fd9\u91cc\u6709\u4e00\u4e2a\u4e0e\u8ba1\u7b97\u7684\u4e0d\u53ef\u8fd8\u539f\u6027<\/span>\uff08computational Irreducibility\uff09<\/span>\u6982\u5ff5\u7684\u67d0\u79cd\u7c7b\u6bd4\u3002\u6cbf\u7740\u4e00\u4e9b\u65f6\u95f4\u8def\u5f84\u4ece\u4e00\u4e2a\u72b6\u6001\u5230\u53e6\u4e00\u4e2a\u72b6\u6001\uff0c\u8ba1\u7b97\u7684\u4e0d\u53ef\u8fd8\u539f\u6027\u610f\u5473\u7740\uff0c\u5373\u4f7f\u6211\u4eec\u53ef\u80fd\u77e5\u9053\u6839\u672c\u7684\u89c4\u5219\uff0c\u6211\u4eec\u4e5f\u4e0d\u80fd\u8f7b\u6613\u5730\u9884\u6d4b\u5176\u7ed3\u679c\u2014\u2014\u56e0\u4e3a\u8fd9\u53ef\u80fd\u9700\u8981\u4e0d\u53ef\u51cf\u5c11\u7684\u8ba1\u7b97\u91cf\u6765\u8ba1\u7b97\u51fa\u8bb8\u591a\u6b65\u9aa4\u4e4b\u540e\u7684\u7ed3\u679c\u3002<\/span><\/p>\n


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

\u9884\u6d4b\u300c\u7a7f\u8d8a\u5206\u652f\u7a7a\u95f4\u300d\u662f\u4e00\u4e2a\u76f8\u5173\u7684\u3001\u4f46\u7a0d\u6709\u4e0d\u540c\u7684\u73b0\u8c61\uff0c\u4eba\u4eec\u53ef\u4ee5\u5c06\u5176\u63cf\u8ff0\u4e3a\u300c\u591a\u91cd\u8ba1\u7b97\u7684\u4e0d\u53ef\u8fd8\u539f\u6027<\/span>\uff08multicomputational irreducibility\uff09<\/span>\u300d\u3002\u8fd9\u4e0d\u662f\u5173\u4e8e\u8ba1\u7b97\u51fa\u4e00\u4e2a\u7279\u5b9a\u8def\u5f84\u7684\u56f0\u96be\uff0c\u800c\u662f\u5173\u4e8e\u770b\u5230\u8bb8\u591a\u7ea0\u7f20\u7684\u8def\u5f84\u5982\u4f55\u76f8\u4e92\u4f5c\u7528\u7684\u56f0\u96be\u3002<\/span><\/p>\n


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

\u5f53\u4e00\u4e2a\u4eba\u5728\u73a9\u6e38\u620f\u65f6\uff0c\u901a\u5e38\u4f1a\u8c08\u8bba\u300c\u80fd\u5f80\u524d\u770b\u5230\u591a\u5c11\u6b65\u300d\u3002\u800c\u5728\u6211\u4eec\u8fd9\u91cc\uff0c\u8fd9\u57fa\u672c\u4e0a\u662f\u5728\u95ee\u6211\u4eec\u53ef\u4ee5\u8f7b\u6613\u83b7\u77e5\u80fd\u5728\u5206\u652f\u7a7a\u95f4\u91cc\u8d70\u591a\u8fdc\u3002\u4f5c\u4e3a\u8ba1\u7b97\u4e0a\u53d7\u7ea6\u675f\u7684\u5b9e\u4f53<\/span>\uff08computationally bounded entities\uff09<\/span>\uff0c\u6211\u4eec\u5728\u5206\u652f\u7a7a\u95f4\u6709\u4e00\u5b9a\u7684\u300c\u89e6\u8fbe\u8303\u56f4\u300d\u3002\u5982\u679c\u8fd9\u4e2a\u8303\u56f4\u4e0d\u8db3\u4ee5\u8fbe\u5230\u7c7b\u4f3c\u300c\u83b7\u80dc\u70b9\u300d\u7684\u5730\u65b9\uff0c\u90a3\u4e48\u8fd9\u4e2a\u6e38\u620f\u5bf9\u6211\u4eec\u6765\u8bf4\u5c31\u662f\u300c\u56f0\u96be\u7684\u300d\u3002<\/span><\/p>\n


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

\u4e0d\u8fc7\uff0c\u8fd9\u91cc\u8fd8\u6709\u4e00\u4e2a\u95ee\u9898\u3002\u5728\u4e00\u4e2a\u6e38\u620f\u4e2d\u300c\u83b7\u80dc\u300d\u7684\u56e0\u7d20\u901a\u5e38\u662f\u5728\u591a\u8def\u56fe\u4e2d\u8fbe\u5230\u4e00\u4e9b\u7279\u5b9a\u7684\u5730\u65b9\u6216\u533a\u57df\u3002\u4f46\u8fd9\u4e9b\u5730\u65b9\u6216\u533a\u57df\u7684\u5b9a\u4e49\u901a\u5e38\u662f\u4e00\u4e9b\u8ba1\u7b97\u4e0a\u5728\u7ea6\u675f\u8303\u56f4\u5185\u7684\u4e1c\u897f<\/span>\uff08\u300c\u53ea\u8981\u770b\u770b\u662f\u5426\u6709\u4e00\u884cX\u300d\uff0c\u7b49\u7b49\uff09<\/span>\u3002\u8fd9\u662f\u5bf9\u7cfb\u7edf\u7684\u67d0\u79cd\u300c\u89c2\u5bdf\u300d\uff0c\u5b83\u53ea\u662f\u63d0\u53d6\u4e86\u5b8c\u6574\u72b6\u6001\u7684\u4e00\u4e2a\u7279\u5b9a\u7684<\/span>\uff08\u8ba1\u7b97\u7ea6\u675f\u5185\uff09<\/span>\u91c7\u6837\u3002\u7136\u540e\uff0c\u5173\u952e\u5728\u4e8e\uff0c\u8fd9\u4e2a\u91c7\u6837\u5e76\u6ca1\u6709\u8bbe\u6cd5\u53bb\u300c\u89e3\u7801\u591a\u91cd\u8ba1\u7b97\u7684\u4e0d\u53ef\u8fd8\u539f\u6027\u300d\u3002<\/span><\/p>\n


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

\u8fd9\u91cc\u6709\u4e00\u4e2a\u4e0e\u70ed\u529b\u5b66\u7684\u7c7b\u6bd4\u3002\u5728\u70ed\u529b\u5b66\u4e2d\uff0c\u6211\u4eec\u611f\u77e5\u5230\u300c\u70ed\u300d\u548c\u300c\u71b5\u589e\u52a0\u300d\u7684\u4e8b\u5b9e\u662f\u8fd9\u6837\u7684\uff1a\u6211\u4eec\u7684<\/span>\uff08\u7c97\u7c92\u5ea6\u7684\uff09<\/span>\u5ea6\u91cf\u4e0d\u80fd\u300c\u89e3\u7801\u300d\u5bfc\u81f4\u7cfb\u7edf\u4e2d\u4ea7\u751f\u7684\u7279\u5b9a\u72b6\u6001\u7684\u4e0d\u53ef\u8fd8\u539f\u7684\u8fc7\u7a0b\u3002\u540c\u6837\uff0c\u6211\u4eec\u8ba4\u4e3a\u300c\u5f88\u96be\u5f04\u6e05\u695a\u5982\u4f55\u8d62\u5f97\u4e00\u573a\u6e38\u620f\u300d\u7684\u4e8b\u5b9e\u662f\u8fd9\u6837\u4e00\u4e2a\u7ed3\u679c\uff0c\u5373\u6211\u4eec\u7684\u83b7\u80dc\u5224\u65ad\u6807\u51c6\u4e0d\u80fd\u53bb\u300c\u89c2\u5bdf\u6e38\u620f\u7684\u5185\u90e8\u300d\u548c\u300c\u89e3\u7801\u6b63\u5728\u53d1\u751f\u7684\u4e8b\u300d\uff0c\u76f4\u5230\u8bf4\u5b83\u5b9e\u9645\u4e0a\u6210\u4e3a\u53ea\u662f\u9009\u62e9\u4e00\u4e2a\u7279\u5b9a\u7684\u3001\u7b80\u5355\u5f84\u76f4\u7684\u8def\u5f84\u3002\u76f8\u53cd\uff0c\u5b83\u662f\u4e00\u4e2a\u53bb\u7ecf\u5386\u73a9\u6e38\u620f\u7684\u591a\u91cd\u8ba1\u7b97\u4e0d\u53ef\u8fd8\u539f\u7684\u8fc7\u7a0b\u7684\u95ee\u9898\uff0c\u5e76\u4e14\u76f8\u5bf9\u4e8e\u5bf9\u80dc\u5229\u7684\u89c2\u5bdf\uff0c\u5b9e\u9645\u4e0a\u662f\u300c\u770b\u770b\u5b83\u4f1a\u843d\u5728\u4ec0\u4e48\u4f4d\u7f6e<\/span>\uff08seeing where it lands\uff09<\/span>\u300d\u3002<\/span><\/p>\n


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

\u8fd9\u91cc\u4e5f\u6709\u4e00\u4e2a\u4e0e\u91cf\u5b50\u529b\u5b66\u7684\u7c7b\u6bd4\u3002\u8ffd\u6eaf\u73a9\u4e00\u4e2a\u6e38\u620f\u7684\u8bb8\u591a\u53ef\u80fd\u8def\u5f84\uff0c\u5c31\u50cf\u8ffd\u5bfb\u91cf\u5b50\u529b\u5b66\u4e2d\u7684\u8bb8\u591a\u5386\u53f2\u7ebf\u7a0b<\/span>\uff08threads\uff09<\/span>\uff0c\u800c\u83b7\u80dc\u7684\u6807\u51c6\u5c31\u50cf\u4e00\u4e2a\u9009\u62e9\u67d0\u4e9b\u7ebf\u7a0b\u7684\u91cf\u5b50\u5ea6\u91cf\u3002\u5728\u6211\u4eec\u7684\u300c\u7269\u7406\u5b66\u8ba1\u5212\u300d\u4e2d\uff0c\u6211\u4eec\u60f3\u8c61\u6211\u4eec\u4f5c\u4e3a\u89c2\u5bdf\u8005\u662f\u5728\u5206\u652f\u7a7a\u95f4\u4e2d\u5ef6\u4f38\u7684\uff0c\u901a\u8fc7\u6211\u4eec\u5bf9\u81ea\u5df1\u7684\u5355\u4e00\u7ecf\u9a8c\u7ebf\u7a0b\u7684\u4fe1\u5ff5\uff0c\u5c06\u4e0d\u540c\u7684\u5386\u53f2\u7ebf\u7a0b\u300c\u7f16\u7ec7\u5728\u4e00\u8d77\u300d\u3002\u5728\u6e38\u620f\u4e2d\uff0c\u6211\u4eec\u5bf9\u5355\u4e00\u7ecf\u9a8c\u7ebf\u7684\u4fe1\u5ff5\u7684\u7c7b\u6bd4\uff0c\u5927\u6982\u5c31\u662f\u300c\u91cd\u8981\u7684\u662f\u8c01\u8d62\u8c01\u8f93\uff1b\u6e38\u620f\u5177\u4f53\u662f\u600e\u4e48\u73a9\u7684\u5e76\u4e0d\u91cd\u8981\u300d\u3002<\/span><\/p>\n


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

\u4e3a\u4e86\u4e0e\u91cf\u5b50\u529b\u5b66\u505a\u4e00\u4e2a\u66f4\u63a5\u8fd1\u7684\u7c7b\u6bd4\uff0c\u6211\u4eec\u53ef\u4ee5\u5f00\u59cb\u8003\u8651\u5c06\u300c\u591a\u8def\u6e38\u73a9\u300d\u7684\u4e0d\u540c\u90e8\u5206\u7ed3\u5408\u8d77\u6765\uff0c\u5e76\u8bd5\u56fe\u4e3a\u8fd9\u4e9b\u90e8\u5206\u5982\u4f55\u7ed3\u5408\u8d77\u6765\u5236\u5b9a\u4e00\u5957\u300c\u5fae\u79ef\u5206\u5b66\u300d\u3002<\/span><\/p>\n


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

\u6211\u4eec\u5728\u8fd9\u91cc\u8ba8\u8bba\u7684\u6e38\u620f\u5728\u67d0\u79cd\u610f\u4e49\u4e0a\u90fd\u662f\u7eaf\u7cb9\u7684\u300c\u6280\u5de7\u6e38\u620f\u300d\u3002\u4f46\u5728\u4e5f\u6709\u8fd0\u6c14\u56e0\u7d20\u7684\u6e38\u620f\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u8ba4\u4e3a\u8fd9\u5bfc\u81f4\u4e86\u591a\u8def\u56fe\u4e2d\u7684\u5355\u4e00\u8def\u5f84\u300c\u6a21\u7cca\u5316<\/span>\uff08fuzz out\uff09<\/span>\u300d\u4e3a\u4e00\u675f\u8def\u5f84\uff0c\u4ee5\u53ca\u672c\u6765\u662f\u5206\u652f\u7a7a\u95f4\u4e2d\u7684\u4e00\u4e2a\u70b9\u53d8\u6210\u4e86\u6574\u4e2a\u6269\u5c55\u533a\u57df\u3002<\/span><\/p>\n


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

\u5728\u7814\u7a76\u4e0d\u540c\u7684\u5177\u4f53\u6e38\u620f\u548c\u8c1c\u9898\u65f6\uff0c\u6211\u4eec\u7ecf\u5e38\u4e0d\u5f97\u4e0d\u53bb\u7814\u7a76\u4e00\u4e9b\u76f8\u5f53\u7b80\u5316\u7684\u6848\u4f8b\uff0c\u4ee5\u4fbf\u5f97\u5230\u89c4\u6a21\u53ef\u63a7\u7684\u591a\u8def\u56fe\u3002\u4f46\u662f\uff0c\u5982\u679c\u6211\u4eec\u7814\u7a76\u975e\u5e38\u5927\u7684\u591a\u8def\u56fe\uff0c\u662f\u5426\u4f1a\u6709\u6574\u4f53\u7684\u89c4\u5f8b\u6027\u6d8c\u73b0\uff1f\u5bf9\u4e8e\u6e38\u620f\u56fe\u6765\u8bf4\uff0c\u662f\u5426\u5b58\u5728\u67d0\u79cd\u6f5c\u5728\u7684\u300c\u8fde\u7eed\u6781\u9650<\/span>\uff08continuum limit\uff09<\/span>\u300d\uff1f<\/span><\/p>\n


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

\u51e0\u4e4e\u4e0d\u53ef\u907f\u514d\u7684\u662f\uff0c\u5982\u679c\u6211\u4eec\u770b\u5f97\u300c\u8db3\u591f\u8be6\u7ec6\u300d\uff0c\u6211\u4eec\u5c31\u4f1a\u770b\u5230\u5404\u79cd\u591a\u91cd\u8ba1\u7b97\u7684\u4e0d\u53ef\u8fd8\u539f\u6027\u5728\u53d1\u6325\u4f5c\u7528\u3002\u4f46\u5728\u6211\u4eec\u7684\u300c\u7269\u7406\u5b66\u8ba1\u5212\u300d\u4e2d\uff0c\u751a\u81f3\u5728\u4e00\u822c\u7684\u591a\u91cd\u8ba1\u7b97\u8303\u5f0f\u4e2d\uff0c\u4e00\u4e2a\u5173\u952e\u7684\u95ee\u9898\u662f\uff0c\u76f8\u5173\u7684\u89c2\u5bdf\u8005\u5e76\u6ca1\u6709\u770b\u5230\u90a3\u4e2a\u5c42\u6b21\u7684\u7ec6\u8282\u3002\u5c31\u50cf\u70ed\u529b\u5b66\u6216\u6c14\u4f53\u5b9a\u5f8b\u4ece\u5e95\u5c42\u5206\u5b50\u52a8\u529b\u5b66\u4e2d\u7684\u300c\u6d8c\u73b0<\/span>\uff08emergence \uff09<\/span>\u300d\u4e00\u6837\uff0c\u5e95\u5c42\u8ba1\u7b97\u7684\u4e0d\u53ef\u8fd8\u539f\u6027\u7684\u5b58\u5728\uff0c\u4e0d\u53ef\u907f\u514d\u5730\u5bfc\u81f4\u89c2\u5bdf\u8005\u6240\u80fd\u611f\u77e5\u7684\u7b80\u5355\u5b9a\u5f8b\u3002<\/span><\/p>\n


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

\u90a3\u4e48\uff0c\u5bf9\u4e8e\u4e00\u4e2a\u6e38\u620f\u6765\u8bf4\uff0c\u300c\u89c2\u5bdf\u8005\u300d\u7684\u7c7b\u6bd4\u662f\u4ec0\u4e48\u5462\uff1f\u81f3\u5c11\u5728\u67d0\u4e9b\u65b9\u9762\uff0c\u5b83\u53ef\u4ee5\u88ab\u8ba4\u4e3a\u662f\u300c\u83b7\u80dc\u300d\u7684\u5224\u65ad\u6807\u51c6\u3002\u90a3\u4e48\u73b0\u5728\u95ee\u9898\u6765\u4e86\uff1a\u5982\u679c\u6211\u4eec\u53ea\u770b\u8fd9\u4e9b\u6807\u51c6\uff0c\u6211\u4eec\u80fd\u4e0d\u80fd\u63a8\u5bfc\u51fa\u300c\u7269\u7406\u5b9a\u5f8b\u300d\u7684\u7c7b\u4f3c\u7269\uff0c\u800c\u4e0d\u654f\u611f\u4e8e\u5176\u4e0b\u7684\u6240\u6709\u591a\u91cd\u8ba1\u7b97\u7684\u4e0d\u53ef\u8fd8\u539f\u7684\u7ec6\u8282\uff1f<\/span><\/p>\n


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

\u5173\u4e8e\u8fd9\u4e00\u70b9\uff0c\u8fd8\u6709\u5f88\u591a\u4e1c\u897f\u9700\u8981\u5f04\u6e05\u695a\uff0c\u4f46\u4e5f\u8bb8\u53ef\u4ee5\u4ece\u4e00\u4e2a\u5730\u65b9\u5f00\u59cb\uff0c\u770b\u770b\u5404\u79cd\u6e38\u620f\u4e2d\u7684\u5206\u652f\u7a7a\u95f4\u548c\u591a\u8def\u56fe\u7684\u5927\u89c4\u6a21\u7ed3\u6784\u3002\u5728\u8bb8\u591a\u4e0d\u540c\u7684\u6e38\u620f\u4e2d\uff0c\u4e00\u4e2a\u57fa\u672c\u7684\u5370\u8c61\u662f\uff0c\u867d\u7136\u5206\u652f\u56fe\u7684\u7279\u5f81\u53ef\u80fd\u5728\u6e38\u620f\u7684\u300c\u4e0d\u540c\u9636\u6bb5\u300d\u4e4b\u95f4\u53d1\u751f\u53d8\u5316\uff0c\u4f46\u5728\u5355\u4e2a\u5206\u652f\u56fe\u4e2d\uff0c\u5f80\u5f80\u6709\u67d0\u79cd\u7edf\u4e00\u6027\u3002\u5982\u679c\u6211\u4eec\u770b\u4e00\u4e0b\u7ec6\u8282\uff0c\u53ef\u80fd\u6709\u5f88\u591a\u591a\u91cd\u8ba1\u7b97\u7684\u4e0d\u53ef\u8fd8\u539f\u6027\u3002\u4f46\u5728\u67d0\u79cd\u300c\u53ef\u611f\u77e5\u7684\u6c34\u5e73\u300d\u4e0a\uff0c\u56fe\u7684\u4e0d\u540c\u90e8\u5206\u53ef\u80fd\u770b\u8d77\u6765\u5f88\u76f8\u4f3c\u3002\u8fd9\u8868\u660e\uff0c\u5373\u4f7f\u5df2\u7ecf\u91c7\u53d6\u4e86\u76f8\u5f53\u4e0d\u540c\u7684\u884c\u52a8\uff0c\u5c06\u4eba\u4eec\u5e26\u5230\u7531\u5206\u652f\u56fe\u5b9a\u4e49\u7684\u300c\u6e38\u620f\u7a7a\u95f4\u300d\u7684\u76f8\u5f53\u4e0d\u540c\u90e8\u5206\uff0c\u300c\u6e38\u620f\u7684\u5c40\u90e8\u5370\u8c61\u300d\u5728\u67d0\u4e00\u7279\u5b9a\u9636\u6bb5\u5f80\u5f80\u662f\u76f8\u4f3c\u7684\uff0c\u3002<\/span><\/p>\n


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

\u4f46\u662f\uff0c\u867d\u7136\u5206\u652f\u56fe\u7684\u4e0d\u540c\u90e8\u5206\u4e4b\u95f4\u53ef\u80fd\u5b58\u5728\u76f8\u4f3c\u6027\uff0c\u4f46\u6211\u4eec\u770b\u5230\u7684\u662f\uff0c\u5728\u4e00\u4e9b\u6e38\u620f\u548c\u8c1c\u9898\u4e2d\uff0c\u5206\u652f\u56fe\u4f1a\u5206\u6210\u591a\u4e2a\u4e0d\u76f8\u8fde\u7684\u533a\u57df\u3002\u8fd9\u53cd\u6620\u4e86\u6e38\u620f\u4e2d\u5b58\u5728\u7740\u4e0d\u540c\u7684\u300c\u5b88\u6052\u533a<\/span>\uff08conserved sectors\uff09<\/span>\u300d\u2014\u2014\u73a9\u5bb6\u53ef\u4ee5\u8fdb\u5165\u7684\u6e38\u620f\u7a7a\u95f4\u533a\u57df\uff0c\u4f46\u968f\u540e\u4f1a\u88ab\u5361\u4f4f\uff08\u81f3\u5c11\u5728\u4e00\u5b9a\u65f6\u95f4\u5185\uff09\uff0c\u5c31\u50cf\u5728\u65f6\u7a7a\u4e2d\u4e8b\u4ef6\u89c6\u754c<\/span>\uff08event horizons\uff0c\u6821\u6ce8\uff1a\u5fb7\u56fd\u5929\u6587\u5b66\u5bb6\u5361\u5c14\u00b7\u53f2\u74e6\u897f\u63d0\u51fa\u7684\u6d89\u53ca\u9ed1\u6d1e\u7684\u6982\u5ff5\uff0c\u4e00\u65e6\u5149\u7ebf\u6216\u7269\u8d28\u8d8a\u8fc7\u4e8b\u4ef6\u89c6\u754c\uff0c\u5c31\u6c38\u8fdc\u65e0\u6cd5\u9003\u8131\u4e86\uff09<\/span>\u53ef\u4ee5\u963b\u6b62\u7269\u7406\u7a7a\u95f4\u7684\u4e0d\u540c\u533a\u57df\u4e4b\u95f4\u7684\u4f20\u9001\u3002<\/span><\/p>\n


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

\u6211\u4eec\u5728\u4e00\u4e9b\u6e38\u620f\u548c\u8c1c\u9898\u4e2d\u6ce8\u610f\u5230\u7684\u53e6\u4e00\u4e2a<\/span>\uff08\u76f8\u5173\u7684\uff09<\/span>\u73b0\u8c61\u662f\u591a\u8def\u56fe\u4e2d\u7684\u5927\u300c\u6d1e\u300d\uff1a\u5728\u56fe\u4e2d\u4e24\u70b9\u4e4b\u95f4\u6709\u591a\u6761\u300c\u9065\u8fdc\u300d\u7684\u8def\u5f84\u3002\u5f53\u591a\u8def\u56fe\u662f\u5bc6\u96c6\u8fde\u63a5\u7684\u65f6\u5019\uff0c\u901a\u5e38\u603b\u662f\u6709\u529e\u6cd5\u901a\u8fc7\u9644\u8fd1\u7684\u8def\u5f84\u6539\u9053\u6765 \u300c\u4fee\u590d\u4efb\u4f55\u9519\u8bef\u300d\u3002\u4f46\u662f\uff0c\u5f53\u6709\u4e00\u4e2a\u6d1e\u65f6\uff0c\u8fd9\u5c31\u8868\u660e\u4eba\u4eec\u6700\u7ec8\u4f1a\u300c\u81f4\u529b\u4e8e<\/span>\uff08committed\uff09<\/span>\u300d\u67d0\u4e2a\u884c\u52a8\u7684\u8fdb\u7a0b\u800c\u4e0d\u662f\u53e6\u4e00\u4e2a\uff0c\u800c\u4e14\u8981\u7ecf\u8fc7\u8bb8\u591a\u6b65\u9aa4\u624d\u6709\u53ef\u80fd\u5230\u8fbe\u4e0e\u53e6\u4e00\u4e2a\u884c\u52a8\u8fdb\u7a0b\u6240\u80fd\u5230\u8fbe\u7684\u76f8\u540c\u7684\u5730\u65b9\u3002<\/span><\/p>\n


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

\u5982\u679c\u6211\u4eec\u5047\u8bbe\u5728\u67d0\u4e2a\u5c42\u9762\u4e0a\uff0c\u6211\u4eec\u5728\u591a\u8def\u56fe\u4e2d\u6700\u7ec8\u300c\u89c2\u5bdf\u300d\u5230\u7684\u662f\u4e0e\u8bc4\u4f30\u8f93\u8d62\u76f8\u5bf9\u5e94\u7684\u90a3\u79cd\u7c97\u7c92\u5ea6\uff0c\u90a3\u4e48\u6211\u4eec\u5c06\u4e0d\u53ef\u907f\u514d\u5730\u5904\u7406\u4e00\u4e2a\u53ef\u80fd\u8def\u5f84\u7684\u5206\u5e03\u60c5\u51b5\u3002\u5728\u6ca1\u6709\u300c\u6d1e\u300d\u7684\u60c5\u51b5\u4e0b\uff0c\u8fd9\u4e9b\u8def\u5f84\u53ef\u80fd\u5f88\u63a5\u8fd1\uff0c\u800c\u4e14\u770b\u8d77\u6765\u5f88\u76f8\u4f3c\u3002\u4f46\u662f\u5f53\u6709\u6d1e\u7684\u65f6\u5019\uff0c\u53ef\u80fd\u4f1a\u6709\u76f8\u8ddd\u751a\u8fdc\u7684\u4e0d\u540c\u7684\u8def\u5f84\u3002\u800c\u300c\u5c5e\u4e8e\u76f8\u540c\u5206\u5e03\u90e8\u5206\u300d\u7684\u9065\u8fdc\u8def\u5f84\u53ef\u80fd\u88ab\u8ba4\u4e3a\u662f\u7c7b\u4f3c\u4e8e\u91cf\u5b50\u53e0\u52a0\u6548\u5e94\u7684\u4e8b\u5b9e\u3002<\/span><\/p>\n


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

\u6e38\u620f\u4e2d\u662f\u5426\u6709\u7c7b\u4f3c\u4e8e\u5e7f\u4e49\u76f8\u5bf9\u8bba\u548c\u8def\u5f84\u79ef\u5206<\/span>\uff08path integral\uff09<\/span>\u7684\u6982\u5ff5\uff1f\u4e3a\u4e86\u6e05\u695a\u5730\u8868\u8ff0\u8fd9\u4e2a\u95ee\u9898\uff0c\u6211\u4eec\u5fc5\u987b\u66f4\u4ed4\u7ec6\u5730\u5b9a\u4e49\u300c\u6e38\u620f\u7a7a\u95f4\u300d\u7684\u7279\u5f81\u3002\u5f88\u53ef\u80fd\u4f1a\u6709\u56e0\u679c\u56fe<\/span>\uff08causal graph\uff09<\/span>\u7684\u7c7b\u4f3c\u7269\u3002\u4e5f\u5f88\u53ef\u80fd\u6e38\u620f\u7a7a\u95f4\u4e2d\u4e5f\u4f1a\u6709\u4e00\u4e2a\u7c7b\u4f3c\u80fd\u91cf\u7684\u6982\u5ff5\uff0c\u4e0e\u6e38\u620f\u7a7a\u95f4\u4e2d\u4e0d\u540c\u5730\u65b9\u7684\u300c\u6d3b\u52a8\u5bc6\u5ea6\u300d\u76f8\u5173\u3002<\/span><\/p>\n


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

\u90a3\u4e48\uff0c\u5f15\u529b\u73b0\u8c61\u7684\u7c7b\u4f3c\u7269\u5c06\u662f\u8fd9\u6837\u7684\uff1a\u6700\u597d\u7684\u6e38\u620f\u7684\u6e38\u73a9\u65b9\u5f0f<\/span>\uff08\u5373\u901a\u8fc7\u6e38\u620f\u56fe\u7684\u6d4b\u5730\u8def\u5f84\uff09<\/span>\u5c06\u503e\u5411\u4e8e\u88ab\u9ad8\u6d3b\u52a8\u5bc6\u5ea6\u7684\u5b58\u5728\u6240\u504f\u8f6c\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u5982\u679c\u4e00\u4e2a\u6e38\u620f\u5904\u4e8e\u67d0\u79cd\u72b6\u6001\u65f6\u6709\u5f88\u591a\u4e8b\u8981\u505a\uff0c\u90a3\u4e48\u597d\u7684\u6e38\u620f\u6e38\u73a9\u5c06\u503e\u5411\u4e8e\u300c\u88ab\u62c9\u5411\u90a3\u4e2a\u72b6\u6001\u300d\u3002\u5728\u67d0\u79cd\u7a0b\u5ea6\u4e0a\uff0c\u8fd9\u5e76\u4e0d\u4ee4\u4eba\u60ca\u8bb6\uff1a\u5f53\u6e38\u620f\u56fe\u4e2d\u5b58\u5728\u9ad8\u5bc6\u5ea6\u7684\u6d3b\u52a8\u65f6\uff0c\u5f80\u5f80\u4f1a\u6709\u66f4\u591a\u5173\u4e8e\u505a\u4ec0\u4e48\u7684\u9009\u62e9\uff0c\u56e0\u6b64\uff0c\u5982\u679c\u4e00\u4e2a\u73a9\u5bb6\u7ecf\u8fc7\u90a3\u91cc\uff0c\u5c31\u66f4\u6709\u53ef\u80fd \u300c\u73a9\u51fa\u4e00\u573a\u7cbe\u5f69\u7684\u6e38\u620f\u300d\u3002<\/span><\/p>\n


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

\u5230\u76ee\u524d\u4e3a\u6b62\uff0c\u6211\u4eec\u8fd8\u6ca1\u6709\u660e\u786e\u5730\u8c08\u8bba\u6e38\u620f\u7684\u7b56\u7565\u3002\u4f46\u5728\u6211\u4eec\u7684\u591a\u91cd\u8ba1\u7b97\u6846\u67b6\u4e2d\uff0c\u7b56\u7565\u6709\u4e00\u4e2a\u76f8\u5f53\u660e\u786e\u7684\u89e3\u91ca\uff1a\u5b83\u662f\u53ef\u80fd\u89c4\u5219\u7a7a\u95f4<\/span>\uff08rulial space\uff09<\/span>\u4e2d\u7684\u4e00\u4e2a\u5730\u65b9\uff0c\u5728\u90a3\u91cc\uff0c\u4eba\u4eec\u5b9e\u9645\u4e0a\u662f\u5047\u8bbe\u4e86\u4e00\u5957\u5173\u4e8e\u5982\u4f55\u6784\u5efa\u591a\u8def\u56fe\u7684\u89c4\u5219\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u7ed9\u5b9a\u4e00\u4e2a\u7b56\u7565\uff0c\u4eba\u4eec\u5c31\u4f1a\u5728\u591a\u8def\u56fe\u4e2d\u9009\u62e9\u4e00\u4e9b\u8fb9<\/span>\uff08\u6216\u8005\u5728\u76f8\u5173\u7684\u591a\u8def\u56e0\u679c\u56fe\u4e2d\u9009\u62e9\u4e00\u4e9b\u53ef\u80fd\u7684\u4e8b\u4ef6\uff09<\/span>\uff0c\u800c\u653e\u5f03\u5176\u4ed6\u7684\u8fb9\u3002<\/span><\/p>\n


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

\u4e00\u822c\u6765\u8bf4\uff0c\u8c08\u8bba\u300c\u53ef\u80fd\u7b56\u7565\u7684\u7a7a\u95f4\u300d\u53ef\u80fd\u5f88\u56f0\u96be\uff0c\u56e0\u4e3a\u8fd9\u5c31\u50cf\u8c08\u8bba\u300c\u53ef\u80fd\u7a0b\u5e8f\u7684\u7a7a\u95f4\u300d\u3002\u4f46\u8fd9\u6070\u6070\u662f\u53ef\u80fd\u89c4\u5219\u7a7a\u95f4<\/span>\uff08rulial space\uff09<\/span>\u8ba9\u6211\u4eec\u8c08\u8bba\u7684\u4e1c\u897f\u3002\u300c\u7b56\u7565\u7a7a\u95f4\u300d\u5230\u5e95\u6709\u4ec0\u4e48\u6837\u7684\u300c\u51e0\u4f55\u7ed3\u6784\u300d\uff0c\u5c06\u53d6\u51b3\u4e8e\u6211\u4eec\u5982\u4f55\u9009\u62e9\u534f\u8c03\u53ef\u80fd\u89c4\u5219\u7a7a\u95f4\u3002\u4f46\u662f\uff0c\u518d\u4e00\u6b21\uff0c\u901a\u8fc7\u4ec5\u4ec5\u53ea\u770b\u7c7b\u4f3c\u4e8e\u535a\u5f08\u8bba\u4e2d\u8ba8\u8bba\u7684\u90a3\u79cd\u4e1c\u897f\uff0c\u5c06\u503e\u5411\u4e8e\u5b9e\u73b0\u67d0\u79cd\u7a0b\u5ea6\u7684\u7c97\u653e<\/span>(coarse-graining)<\/span>\u2014\u2014\u5728\u8fd9\u79cd\u7a0b\u5ea6\u4e0a\uff0c\u6211\u4eec\u53ef\u4ee5\u9884\u671f\u6240\u6709\u5404\u79cd\u6807\u51c6\u7684\u300c\u7ed3\u6784\u5316\u300d\u7684\u535a\u5f08\u8bba\u7ed3\u679c\u5c06\u666e\u904d\u6210\u7acb\u3002<\/span><\/p>\n


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

\uff08\u8bd1\u6ce8\uff1aRulial space\u662f Wolfram \u81ea\u521b\u7684\u4e00\u4e2a\u672f\u8bed\uff0c\u610f\u6307\u6240\u6709\u53ef\u80fd\u7684\u89c4\u5219\u4ee5\u53ca\u8fd9\u4e9b\u89c4\u5219\u7684\u6240\u6709\u5e94\u7528\u65b9\u5f0f\u6240\u7ec4\u6210\u7684\u7a7a\u95f4\u3002\u6bd4\u5982\uff0c\u4ece\u7b26\u53f7A\u5f00\u59cb\u5e94\u7528\u7b26\u53f7\u66ff\u6362\u89c4\u5219{A \u2192 AB, BB \u2192 A}\uff0c\u53ef\u4ee5\u7528\u4e0b\u9762\u7684\u591a\u8def\u56fe\u8868\u793a\u8fd9\u4e2a\u89c4\u5219\u6240\u6709\u53ef\u80fd\u7684\u5e94\u7528\u65b9\u5f0f\uff1a<\/span><\/p>\n

<\/p>\n


<\/p>\n

\uff08\u8fd9\u4e2a\u56fe\u53ea\u753b\u51fa\u4e86\u524d\u51e0\u6b65\uff0c\u5b8c\u6574\u7684\u56fe\u5e94\u8be5\u662f\u65e0\u9650\u7684\uff09<\/span><\/p>\n


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

\u5047\u8bbe\u53ea\u6709A\u3001B\u4e24\u4e2a\u7b26\u53f7\uff0c\u53ea\u8003\u8651\u957f\u5ea6\u6700\u591a\u4e3a2\u7684\u7b26\u53f7\u4e32\uff0c\u90a3\u4e48\u6240\u6709\u8fd9\u6837\u7684\u53ef\u80fd\u7684\u66ff\u6362\u89c4\u5219\u6709<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u6309\u7167\u4e0a\u9762\u7684\u65b9\u5f0f\u753b\u51fa\u6240\u6709\u8fd9\u4e9b\u66ff\u6362\u89c4\u5219\u5bf9\u5e94\u7684\u591a\u8def\u56fe\uff0c\u5e76\u628a\u8fd9\u4e9b\u591a\u8def\u56fe\u5408\u5e76\u6210\u4e00\u4e2a\u56fe\uff0c\u5c31\u6784\u6210\u4e86\u8fd9\u4e2a\u6709\u9650\u8bed\u5883\u4e0b\u7684 Rulial space\u3002<\/span><\/p>\n


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

\u73b0\u5728\u60f3\u8c61\u6211\u4eec\u8003\u8651\u7684\u4e0d\u4ec5\u4ec5\u662f\u4e0a\u9762\u8fd9\u4e9b\u7b26\u53f7\u66ff\u6362\u89c4\u5219\uff0c\u800c\u662f\u5b87\u5b99\u4e2d\u6240\u6709\u53ef\u80fd\u7684\u89c4\u5219\uff0c\u8fd9\u4e2a\u5de8\u5927\u7684Rulial Space\u53ef\u4ee5\u8ba4\u4e3a\u5305\u542b\u4e86\u4e00\u5207\u201c\u53ef\u8ba1\u7b97\u7684\u4e8b\u7269\uff08everything that is computationally possible.\uff09\u201d\u3002<\/span><\/p>\n

\u63a8\u8350\u9605\u8bfb\uff1ahttps:\/\/writings.stephenwolfram.com\/2021\/11\/the-concept-of-the-ruliad\/ \uff09<\/span><\/p>\n


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


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

\n
\n
\n
\n
\n

<\/section>\n

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

\u4e2a\u4eba\u7b14\u8bb0 <\/span><\/strong><\/span><\/h3>\n

Personal Notes<\/span><\/strong><\/span><\/h3>\n<\/section>\n
\n

<\/section>\n

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

\u5373\u4f7f\u5728\u5c0f\u65f6\u5019\uff0c\u6211\u4e5f\u4ece\u672a\u7279\u522b\u559c\u6b22\u73a9\u6e38\u620f\u6216\u505a\u62fc\u56fe\u3002\u800c\u8fd9\u4e5f\u8bb8\u662f\u6211\u592a\u50cf\u4e2a\u79d1\u5b66\u5bb6\u7684\u4e00\u4e2a\u6807\u5fd7\u3002\u56e0\u4e3a\u53ea\u662f\u9009\u51fa\u7279\u5b9a\u7684\u68cb\u6b65\u5bf9\u6211\u6765\u8bf4\u603b\u662f\u663e\u5f97\u592a\u6b66\u65ad\u4efb\u610f\u4e86\u3002\u4e3a\u4e86\u5f15\u8d77\u6211\u7684\u5174\u8da3\uff0c\u6211\u9700\u8981\u4e00\u4e2a\u66f4\u5927\u7684\u56fe\u666f\uff0c\u66f4\u52a0\u524d\u540e\u4e00\u81f4\u7684\u8ba4\u77e5\u53d9\u4e8b\u3002<\/span><\/p>\n


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

\u800c\u73b0\u5728\uff0c\u4ece\u67d0\u79cd\u610f\u4e49\u4e0a\u8bf4\uff0c\u8fd9\u6b63\u662f\u6211\u5728\u8fd9\u91cc\u8ba8\u8bba\u7684\u5bf9\u6e38\u620f\u548c\u8c1c\u9898\u7684\u591a\u91cd\u8ba1\u7b97\u65b9\u6cd5\u5e26\u7ed9\u6211\u4eec\u7684\u4e1c\u897f\u3002\u662f\u7684\uff0c\u80fd\u591f\u601d\u8003\u505a\u51fa\u7279\u5b9a\u7684\u52a8\u4f5c\u662f\u975e\u5e38\u300c\u4eba\u7c7b\u89c6\u89d2\u5316<\/span>\uff08humanizing\uff09<\/span>\u300d\u7684\u3002\u4f46\u662f\uff0c\u591a\u91cd\u8ba1\u7b97\u65b9\u6cd5\u7acb\u5373\u7ed9\u4eba\u4e86\u4e00\u79cd\u8fde\u8d2f\u7684\u5168\u5c40\u89c2\uff0c\u81f3\u5c11\u5bf9\u6211\u6765\u8bf4\uff0c\u7406\u667a\u4e0a\u66f4\u4ee4\u4eba\u6ee1\u610f\u3002<\/span><\/p>\n


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

\u6211\u5728\u8fd9\u91cc\u8ba8\u8bba\u7684\u63a2\u7d22\u53ef\u4ee5\u88ab\u8ba4\u4e3a\u662f\u6e90\u4e8e\u300a\u4e00\u79cd\u65b0\u79d1\u5b66\u300b\u4e2d\u7684\u4e00\u4e2a\u6ce8\u91ca\u3002\u5728\u300a\u4e00\u79cd\u65b0\u79d1\u5b66\u300b\u7684\u7b2c\u4e94\u7ae0\u4e2d\uff0c\u6211\u6709\u4e00\u8282\u9996\u6b21\u4ecb\u7ecd\u4e86\u591a\u8def\u7cfb\u7edf\u3002\u5728\u90a3\u4e00\u8282\u7684\u6700\u540e\u4e00\u4e2a\u6ce8\u91ca\u4e2d\uff0c\u6211\u8ba8\u8bba\u4e86\u300c\u6e38\u620f\u7cfb\u7edf\u300d\u3002<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u6211\u572820\u4e16\u7eaa90\u5e74\u4ee3\u505a\u4e86\u8fd9\u65b9\u9762\u7684\u7814\u7a76\u2014\u2014\u4e8b\u5b9e\u4e0a\uff0c\u6211\u73b0\u5728\u53d1\u73b01998\u5e74\u7684\u4e00\u672c\u5173\u4e8e\u4e95\u5b57\u68cb\u7684\u6587\u4ef6\uff0c\u5176\u4e2d\u5f97\u51fa\u4e86\u4e00\u4e9b\u76f8\u540c\u7684\u7ed3\u679c<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5176\u4e2d\u8fd8\u6709\u4e00\u4e2a\u770b\u8d77\u6765\u5f88\u8010\u4eba\u5bfb\u5473\u7684\u5173\u4e8e\u4e95\u5b57\u68cb\u7684\u56fe\u8868\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u4f46\u5728\u90a3\u4e2a\u65f6\u5019\uff0c\u6211\u5e76\u6ca1\u6709\u4ece\u6211\u751f\u6210\u7684\u8fd9\u4e9b\u6e38\u620f\u76f8\u5173\u7684\u56fe\u4e2d\u5f97\u51fa\u4ec0\u4e48\u7ed3\u8bba\uff1b\u5b83\u4eec\u53ea\u662f\u663e\u5f97\u5e9e\u5927\u800c\u590d\u6742\u300220\u5e74\u8fc7\u53bb\u4e86\uff0c\u6211\u6ca1\u6709\u518d\u591a\u60f3\u8fd9\u4e2a\u95ee\u9898\u3002\u4f46\u540e\u6765\u57282017\u5e74\uff0c\u6211\u7684\u513f\u5b50\u514b\u91cc\u65af\u6258\u5f17<\/span>\uff08https:\/\/christopherwolfram.com\/\uff09<\/span>\u5728\u73a9\u4e00\u4e2a\u53eb\u300aRush Hour\u300b\u7684\u684c\u6e38\u3002<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u4e5f\u8bb8\u662f\u5bb6\u65cf\u503e\u5411\u7684\u8868\u73b0\uff0c\u4ed6\u51b3\u5b9a\u6784\u5efa\u5176\u6e38\u620f\u56fe\u2014\u2014\u5f97\u51fa\u4e86\u5bf9\u6211\u6765\u8bf4\u4f3c\u4e4e\u662f\u975e\u5e38\u4ee4\u4eba\u60ca\u8bb6\u7684\u7ed3\u679c\u3002<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5f53\u65f6\u6211\u5e76\u6ca1\u6709\u8bd5\u56fe\u53bb\u7406\u89e3\u8fd9\u91cc\u7684\u7ed3\u6784\uff0c\u4f46\u6211\u8fd8\u662f\u628a\u5b83\u300c\u5f52\u6863\u300d\u4e86\uff0c\u4f5c\u4e3a\u6e38\u620f\u56fe\u53ef\u4ee5\u6709\u300c\u53ef\u89c1\u7684\u5927\u89c4\u6a21\u7ed3\u6784\u300d\u7684\u8bc1\u636e\u3002<\/span><\/p>\n


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

\u51e0\u5e74\u540e\u2014\u20142019\u5e74\u5e95\u2014\u2014\u6211\u4eec\u7684\u7269\u7406\u9879\u76ee\u6b63\u5728\u8fdb\u884c\u4e2d\uff0c\u6211\u4eec\u5df2\u7ecf\u610f\u8bc6\u5230\uff0c\u91cf\u5b50\u529b\u5b66\u548c\u591a\u8def\u56fe\u4e4b\u95f4\u5b58\u5728\u7740\u6df1\u523b\u7684\u5173\u7cfb\u3002\u91cf\u5b50\u529b\u5b66\u4e00\u76f4\u770b\u8d77\u6765\u662f\u795e\u79d8\u7684\u4e1c\u897f\u2014\u2014\u7eaf\u6570\u5b66\u5f62\u5f0f\u4e3b\u4e49\u7684\u62bd\u8c61\u7ed3\u679c\u3002\u4f46\u662f\uff0c\u770b\u5230\u4e0e\u591a\u8def\u7cfb\u7edf\u7684\u8054\u7cfb\uff0c\u5f00\u59cb\u6697\u793a\u4eba\u4eec\u5b9e\u9645\u4e0a\u80fd\u591f\u300c\u7406\u89e3\u91cf\u5b50\u529b\u5b66\u300d\uff0c\u56e0\u4e3a\u5b83\u53ef\u4ee5\u4ece\u4e00\u4e9b\u5177\u4f53\u7684\u57fa\u7840\u7ed3\u6784\u4e2d\u300c\u673a\u5236\u5730\u4ea7\u751f\u300d\u3002<\/span><\/p>\n


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

\u6211\u5f00\u59cb\u601d\u8003\u5982\u4f55\u5728\u4e00\u4e2a\u76f4\u89c2\u7684\u5c42\u9762\u4e0a\u89e3\u91ca\u91cf\u5b50\u529b\u5b66\u3002\u4e3a\u6b64\uff0c\u6211\u9700\u8981\u4e00\u4e2a\u719f\u6089\u7684\u7c7b\u6bd4\uff1a\u53ef\u4ee5\u4e0e\u591a\u8def\u7cfb\u7edf\u8054\u7cfb\u8d77\u6765\u7684\u65e5\u5e38\u4e8b\u7269\u3002\u6211\u7acb\u5373\u60f3\u5230\u4e86\u6e38\u620f\u30022020\u5e749\u6708\uff0c\u6211\u51b3\u5b9a\u8003\u5bdf\u4e00\u4e0b\u6e38\u620f\uff0c\u4ee5\u66f4\u8be6\u7ec6\u5730\u63a2\u7d22\u8fd9\u4e2a\u7c7b\u6bd4\u3002\u6211\u5f88\u5feb\u5c31\u5206\u6790\u4e86\u4e95\u5b57\u6e38\u620f\u548c\u5c3c\u59c6\u6e38\u620f\uff0c\u4ee5\u53ca\u7b80\u5355\u7684\u6ed1\u52a8\u5757\u8c1c\u9898\u548c\u6c49\u8bfa\u5854\u3002\u4f46\u6211\u60f3\u63a2\u7d22\u66f4\u591a\u7684\u6e38\u620f\u548c\u8c1c\u9898\u3002\u800c\u4e14\u6211\u8fd8\u6709\u5176\u4ed6\u9879\u76ee\u8981\u505a\uff0c\u6240\u4ee5\u6e38\u620f\u548c\u8c1c\u9898\u7684\u591a\u91cd\u8ba1\u7b97\u5206\u6790\u88ab\u6401\u7f6e\u4e86\u3002<\/span><\/p>\n


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

\u4eca\u5e74\u65e9\u4e9b\u65f6\u5019\uff0c\u6c49\u8bfa\u5854\u53c8\u51fa\u73b0\u4e86\uff0c\u5f53\u65f6\u6211\u628a\u5b83\u4f5c\u4e3a\u4e00\u4e2a\u751f\u6210\u7c7b\u4f3c\u8bc1\u660e\u7684\u591a\u8def\u56fe\u7684\u4f8b\u5b50\uff0c\u4e0e\u6211\u5bf9\u5143\u6570\u5b66\u7684\u7269\u7406\u5316\u7814\u7a76\u6709\u5173\u3002\u6700\u540e\uff0c\u51e0\u5468\u524d\u6211\u51b3\u5b9a\u662f\u65f6\u5019\u5199\u4e0b\u6211\u5230\u76ee\u524d\u4e3a\u6b62\u6240\u77e5\u9053\u7684\u5173\u4e8e\u6e38\u620f\u548c\u8c1c\u9898\u7684\u4e1c\u897f\u4e86\u2014\u2014\u5e76\u4ea7\u751f\u4e86\u8fd9\u91cc\u7684\u4e1c\u897f\u3002<\/span><\/p>\n


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


<\/h3>\n

\n
\n
\n
\n
\n

<\/section>\n

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

\u81f4\u8c22 <\/strong><\/span><\/h3>\n

Thanks<\/strong><\/span><\/h3>\n<\/section>\n
\n

<\/section>\n

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

\u611f\u8c22 Brad Klee \u548c Ed Pegg \u5728\u672c\u6587\u7ed9\u51fa\u7684\u5206\u6790\u7684\u6700\u540e\u9636\u6bb5\u63d0\u4f9b\u7684\u5404\u79cd\u5e2e\u52a9\u2014\u2014\u4ee5\u53ca Christopher Wolfram \u57282017\u5e74\u7684\u7075\u611f\u548c2020\u5e74\u7684\u5e2e\u52a9\u3002<\/span><\/p>\n


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


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

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

\u25ba\u25ba\u25ba<\/p>\n<\/section>\n<\/section>\n

\n
\n

\u590d\u6742\u79d1\u5b66\u00d7\u827a\u672f\u7cfb\u5217\u7814\u8ba8\u4f1a\u516c\u5f00\u62a5\u540d\u4e2d<\/span><\/strong><\/span><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

20\u4e16\u7eaa\u4e0b\u534a\u53f6\u4ee5\u6765\uff0c\u53d7\u5230\u590d\u6742\u6027\u7814\u7a76\u542f\u53d1\u7684\u201c\u601d\u7ef4\u65b9\u5f0f\u201d\u5df2\u8fc5\u901f\u4f20\u64ad\u5230\u8ba4\u77e5\u6d3b\u52a8\u7684\u591a\u4e2a\u9886\u57df\u3002\u6df7\u6c8c\u3001\u81ea\u7ec4\u7ec7\u3001\u4e34\u754c\u3001\u81ea\u521b\u751f\u3001\u6d8c\u73b0 \u2026\u2026\u5176\u6982\u5ff5\u5c42\u6b21\u7684\u4e30\u5bcc\u6027\u4e3a\u6211\u4eec\u63d0\u4f9b\u4e86\u7814\u7a76\u4e16\u754c\u7684\u7075\u6d3b\u5de5\u5177\u3002\u4ece\u8fd9\u4e2a\u610f\u4e49\u4e0a\u8bf4\uff0c\u6211\u4eec\u6709\u7406\u7531\u5c06\u590d\u6742\u6027\u7406\u8bba\u89c6\u4e3a\u4e00\u4e2a\u6269\u5145\u827a\u672f\u4e0e\u79d1\u5b66\u4e4b\u95f4\u4ea4\u53c9\u9886\u57df\u7684\u91cd\u8981\u8bfe\u9898\u3002\u827a\u672f\u5bf9\u590d\u6742\u6027\u505a\u51fa\u53cd\u5e94\u7684\u4e00\u79cd\u57fa\u672c\u65b9\u5f0f\u662f\u521b\u9020\u51fa\u663e\u793a\u201c\u6d8c\u73b0\u884c\u4e3a\u201d\u7684\u7cfb\u7edf\u3002\u5c31\u672c\u4f53\u8bba\u800c\u8a00\uff0c\u6211\u4eec\u4e0d\u518d\u5c06\u827a\u672f\u54c1\u89c6\u4e3a\u9759\u6001\u4e4b\u7269\uff0c\u800c\u662f\u5c06\u5176\u770b\u4f5c\u4e0d\u65ad\u53d1\u5c55\u7684\u521b\u9020\u6027\u8fc7\u7a0b\u7684\u4e00\u4e2a\u5b9e\u4f8b\u3002\u540c\u65f6\uff0c\u65b0\u5174\u7684\u590d\u6742\u79d1\u5b66\uff08Complexity Science\uff09\u4e5f\u5411\u5f53\u4ee3\u827a\u672f\u5b9e\u8df5\u8005\u63d0\u4f9b\u4e86\u4e00\u4e2a\u655e\u5f00\u7684\u5de5\u5177\u7bb1\uff0c\u8fd9\u4e9b\u5de5\u5177\u5305\u62ec\u6df7\u6c8c\u3001\u5206\u5f62\u3001\u5143\u80de\u81ea\u52a8\u673a\u3001\u9057\u4f20\u7b97\u6cd5\u3001\u8681\u7fa4\u7b97\u6cd5\u3001\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u3001L-System\u3001\u4eba\u5de5\u751f\u547d\u7b49\uff0c\u5b83\u4eec\u8fdb\u4e00\u6b65\u63a8\u52a8\u4e86\u6570\u5b57\u7f8e\u5b66\u3001\u751f\u7269\u827a\u672f\u4e0e\u4eba\u5de5\u667a\u80fd\u827a\u672f\u7b49\u9886\u57df\u7684\u53d1\u5c55\u3002\u590d\u6742\u79d1\u5b66\u4e0d\u4ec5\u5e2e\u52a9\u6211\u4eec\u6df1\u5165\u4e86\u89e3\u610f\u8bc6\u548c\u751f\u547d\u7cfb\u7edf\u7684\u751f\u6210\u673a\u5236\uff0c\u800c\u4e14\u6709\u5229\u4e8e\u6fc0\u53d1\u5404\u5b66\u79d1\u7684\u7814\u7a76\u8005\u548c\u5b9e\u8df5\u8005\u534f\u540c\u53d1\u6398\u540e\u4eba\u7c7b\u521b\u9020\u529b\u548c\u65b0\u7f8e\u5b66\u7684\u6f5c\u529b\uff0c\u4ee5\u671f\u6253\u5f00\u66f4\u8d8b\u5411\u4e8e\u7efc\u5408\u6027\u7684\u521b\u610f\u7a7a\u95f4\u3002<\/span><\/section>\n
\u7531\u96c6\u667a\u4ff1\u4e50\u90e8\u4e3b\u529e\uff0c\u5fc3\u8bc6\u5b87\u5b99\u7814\u7a76\u9662\u9662\u957f\u3001\u79d1\u666e\u4f5c\u5bb6\u5341\u4e09\u7ef4\uff0c\u827a\u672f\u8bc4\u8bba\u4eba\u6c6a\u5ae3\u7136\u548c\u7b56\u5c55\u4eba\u9f99\u661f\u5982\u8054\u5408\u53d1\u8d77\u7684\u201c\u590d\u6742\u79d1\u5b66\u4e0e\u827a\u672f\u201d\u7814\u8ba8\u4f1a\uff0c\u65e8\u5728\u6c47\u805a\u5404\u9886\u57df\u5185\u7684\u884c\u52a8\u8005\u4e0e\u601d\u60f3\u8005\u2014\u2014\u5305\u62ec\u79d1\u5b66\u5bb6\u3001\u827a\u672f\u5bb6\u3001\u5b66\u8005\u53ca\u76f8\u5173\u4ece\u4e1a\u8005\u2014\u2014\u5c55\u5f00\u8d85\u8d8a\u5355\u4e00\u5b66\u79d1\u7684\u8de8\u754c\u77e5\u8bc6\u8ba8\u8bba\uff0c\u63a2\u7d22\u590d\u6742\u6027\u7814\u7a76\u4e0e\u4eba\u6587\u827a\u672f\u6f5c\u5728\u7684\u4ea4\u53c9\u5730\u5e26<\/span><\/strong>\u3002\u672c\u7814\u8ba8\u4f1a\u4ece2022\u5e747\u6708\u5f00\u59cb\uff0c\u6bcf\u6708\u4e3e\u529e\u4e00\u6b21\uff0c\u5171\u8ba1\u5341\u4e8c\u671f\u3002\u6b22\u8fce\u611f\u5174\u8da3\u7684\u670b\u53cb\u62a5\u540d\u53c2\u4e0e\uff0c\u53ef\u52a0\u5165\u793e\u7fa4\u5e76\u83b7\u5f97\u89c6\u9891\u56de\u653e\u3002<\/span><\/section>\n
<\/span><\/a><\/section>\n


<\/p>\n

\u7814\u8ba8\u4f1a\u8be6\u60c5\u4e0e\u6846\u67b6\uff1a<\/span><\/p>\n

Chaos & Muses\uff1a\u590d\u6742\u79d1\u5b66\u00d7\u827a\u672f\u7cfb\u5217\u7814\u8ba8\u4f1a<\/a>
<\/span><\/strong><\/span><\/p>\n


<\/p>\n

\n


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

\n

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