{"id":57533,"date":"2025-03-13T18:51:53","date_gmt":"2025-03-13T10:51:53","guid":{"rendered":"https:\/\/swarma.org\/?p=57533"},"modified":"2025-03-13T18:51:53","modified_gmt":"2025-03-13T10:51:53","slug":"%e8%b6%85%e8%b6%8a%e6%b7%b7%e6%b2%8c%ef%bc%9a%e4%bb%8e%e6%8b%89%e6%99%ae%e6%8b%89%e6%96%af%e5%a6%96%e5%88%b0%e4%b8%8d%e5%8f%af%e5%88%a4%e5%ae%9a%e6%80%a7","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=57533","title":{"rendered":"\u8d85\u8d8a\u6df7\u6c8c\uff1a\u4ece\u62c9\u666e\u62c9\u65af\u5996\u5230\u4e0d\u53ef\u5224\u5b9a\u6027"},"content":{"rendered":"
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\u5728\u6570\u5b66\u548c\u8ba1\u7b97\u673a\u79d1\u5b66\u9886\u57df\uff0c\u7814\u7a76\u4eba\u5458\u65e9\u5df2\u660e\u767d\uff0c\u6709\u4e9b\u95ee\u9898\u4ece\u6839\u672c\u4e0a\u5c31\u65e0\u89e3\u3002\u5982\u4eca\uff0c\u7269\u7406\u5b66\u5bb6\u6b63\u5728\u63a2\u7d22\uff0c\u5373\u4f7f\u662f\u666e\u901a\u7684\u7269\u7406\u7cfb\u7edf\uff0c\u4e5f\u4f1a\u5bf9\u6211\u4eec\u80fd\u591f\u9884\u6d4b\u7684\u5185\u5bb9\u8bbe\u7f6e\u4e25\u683c\u7684\u9650\u5236\uff0c\u751a\u81f3\u5728\u7406\u8bba\u4e0a\u4e5f\u662f\u5982\u6b64\u3002<\/span><\/strong><\/span><\/strong><\/p>\n

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Quantamagazine<\/span> <\/span>| \u6765\u6e90<\/span><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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\u6cd5\u56fd\u5b66\u8005\u76ae\u57c3\u5c14-\u897f\u8499\u00b7\u62c9\u666e\u62c9\u65af<\/span>\uff08Pierre-Simon Laplace\uff09<\/span>\u57281814\u5e74\u63d0\u51fa\u4e00\u4e2a\u8457\u540d\u7684\u8bba\u65ad\uff1a\u5018\u82e5\u5b58\u5728\u4e00\u4f4d\u201c\u5168\u77e5\u5996\u7cbe<\/span>\uff08demon\uff09<\/span>\u201d\uff0c\u80fd\u591f\u5b8c\u5168\u638c\u63e1\u5b87\u5b99\u5f53\u524d\u7684\u72b6\u6001\uff0c\u90a3\u4e48\u57fa\u4e8e\u6b64\u53ef\u4ee5\u51c6\u786e\u63a8\u6f14\u51fa\u672a\u6765\uff0c\u8fd9\u5c31\u662f\u88ab\u540e\u4eba\u79f0\u4e3a\u7269\u7406\u5b66\u4e0a\u7684\u56db\u5927\u795e\u517d\u4e4b\u4e00\u7684\u201c\u62c9\u666e\u62c9\u65af\u5996\uff08D\u00e9mon de Laplace\uff09<\/strong>\u201d\u3002\u8fd9\u4e00\u601d\u60f3\u5b9e\u9a8c\u5c06\u7269\u7406\u5b66\u5bb6\u5bf9\u9884\u6d4b\u7684\u4e50\u89c2\u60c5\u7eea\u63a8\u5411\u9876\u5cf0\u3002\u7136\u800c\uff0c\u73b0\u5b9e\u5374\u4e0d\u65ad\u51fb\u788e\u8fd9\u79cd\u5b8f\u4f1f\u7684\u96c4\u5fc3\u3002<\/span><\/section>\n

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\u62c9\u666e\u62c9\u65af\u00b7\u76ae\u57c3\u5c14\u00b7\u897f\u8499<\/strong>\uff08Pierre-Simon Laplace\uff09\uff0c\u662f\u6cd5\u56fd\u5929\u6587\u5b66\u5bb6\u3001\u5206\u6790\u5b66\u5bb6\u3001\u6982\u7387\u8bba\u5b66\u5bb6\u3001\u7269\u7406\u5b66\u5bb6\u3002\u4ed6\u4e5f\u662f\u5929\u4f53\u529b\u5b66\u7684\u4e3b\u8981\u5960\u57fa\u4eba<\/strong>\u3001\u5929\u4f53\u6f14\u5316\u5b66\u7684\u521b\u7acb\u8005<\/strong>\u4e4b\u4e00\uff0c\u4ed6\u8fd8\u662f\u5206\u6790\u6982\u7387\u8bba\u7684\u521b\u59cb\u4eba<\/strong>\uff0c\u56e0\u6b64\u53ef\u4ee5\u8bf4\u4ed6\u662f\u5e94\u7528\u6570\u5b66\u7684\u5148\u9a71\u3002\u4ed6\u662f\u79d1\u5b66\u53f2\u4e0a\u4e00\u4f4d\u7f55\u89c1\u7684\u5168\u624d\u3002<\/span><\/p>\n


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\u7b2c\u4e00\u6b21\u51b2\u51fb\u6765\u81ea20\u4e16\u7eaa\u521d\u91cf\u5b50\u529b\u5b66\u7684\u53d1\u73b0\u3002\u7814\u7a76\u8868\u660e\uff0c\u5f53\u91cf\u5b50\u7c92\u5b50\u672a\u88ab\u6d4b\u91cf\u65f6\uff0c\u5b83\u4eec\u5904\u4e8e\u4e00\u79cd\u4e0d\u786e\u5b9a\u72b6\u6001\u2014\u2014\u6ca1\u6709\u786e\u5b9a\u7684\u4f4d\u7f6e\uff0c\u5373\u4fbf\u662f\u65e0\u6240\u4e0d\u77e5\u7684\u201c\u5996\u7cbe\u201d\u4e5f\u96be\u4ee5\u638c\u63e1\u5176\u786e\u5207\u4fe1\u606f\u3002<\/span><\/section>\n

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\u7b2c\u4e8c\u6b21\u51b2\u51fb\u51fa\u73b0\u572820\u4e16\u7eaa\u540e\u671f\uff0c\u5f53\u65f6\u7269\u7406\u5b66\u5bb6\u4eec\u53d1\u73b0\u6240\u8c13\u7684\u201c\u6df7\u6c8c\u7cfb\u7edf<\/span>\uff08chaotic systems\uff09<\/span>\u201d\u4f1a\u653e\u5927\u4efb\u4f55\u5fae\u5c0f\u7684\u4e0d\u786e\u5b9a\u6027\u3002\u201c\u5996\u7cbe\u201d\u6216\u8bb8\u80fd\u591f\u9884\u6d4b\u672a\u6765\u4e94\u5341\u5e74\u7684\u5929\u6c14\uff0c\u4f46\u524d\u63d0\u662f\u5fc5\u987b\u65e0\u9650\u7cbe\u786e\u5730\u638c\u63e1\u5f53\u524d\u7684\u72b6\u6001\u2014\u2014\u7cbe\u786e\u5230\u6bcf\u4e00\u53ea\u8774\u8776\u7fc5\u8180\u7684\u6bcf\u4e00\u6b21\u632f\u52a8\u3002\u8fd9\u79cd\u9ad8\u5ea6\u654f\u611f\u6027\u4f7f\u5f97\u957f\u671f\u7cbe\u786e\u9884\u6d4b\u53d8\u5f97\u6781\u5176\u56f0\u96be\u3002<\/span><\/section>\n

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\u8fd1\u5e74\u6765\uff0c\u7269\u7406\u5b66\u754c\u9010\u6e10\u6d6e\u73b0\u51fa\u7b2c\u4e09\u91cd\u5c40\u9650\u2014\u2014\u4ece\u67d0\u4e9b\u65b9\u9762\u770b\uff0c\u8fd9\u53ef\u80fd\u662f\u8fc4\u4eca\u4e3a\u6b62\u6700\u60ca\u4eba\u7684\u53d1\u73b0\u3002\u7269\u7406\u5b66\u5bb6\u5728\u91cf\u5b50\u7cfb\u7edf\u548c\u7ecf\u5178\u7cfb\u7edf<\/span>\uff08\u5982\u6da1\u65cb\u6d0b\u6d41\uff09<\/span>\u4e2d\u5747\u89c2\u6d4b\u5230\u8be5\u73b0\u8c61\u3002\u79d1\u5b66\u5bb6\u5c06\u8fd9\u79cd\u73b0\u8c61\u79f0\u4e3a\u4e0d\u53ef\u5224\u5b9a\u6027\uff08undecidability\uff09<\/strong>\uff0c\u8d85\u8d8a\u4e86\u6df7\u6c8c\u7406\u8bba\u7684\u8303\u7574\u3002\u4e0d\u53ef\u5224\u5b9a\u6027\u8868\u660e\uff1a\u5373\u4f7f\u5b8c\u5168\u4e86\u89e3\u7cfb\u7edf\u5f53\u524d\u72b6\u6001<\/strong>\uff0c<\/strong>\u4e5f\u65e0\u6cd5\u5b8c\u5168\u9884\u6d4b\u6216\u638c\u63a7\u7cfb\u7edf\u672a\u6765\u7684\u53d8\u5316<\/strong>\u3002<\/strong><\/span><\/section>\n

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\u201c\u5373\u4fbf\u662f\u8ba9\u4f60\u7ad9\u5728\u4e0a\u5e1d\u89c6\u89d2\uff0c\u4ecd\u65e0\u6cd5\u9884\u5224\u5b83\u7684\u8f68\u8ff9\u3002\u201d\u4f26\u6566\u5927\u5b66\u5b66\u9662\u7269\u7406\u8f6c\u884c\u8ba1\u7b97\u673a\u7684\u79d1\u5b66\u5bb6Toby Cubitt[1]\u8bf4\u9053\uff0c\u4ed6\u6b63\u5f15\u9886\u63a2\u7d22\u4e0d\u53ef\u77e5\u9886\u57df\u7684\u524d\u6cbf\u3002\u897f\u73ed\u7259\u52a0\u6cf0\u7f57\u5c3c\u4e9a\u7406\u5de5\u5927\u5b66\u6570\u5b66\u5bb6Eva Miranda[2]\u5219\u5c06\u4e0d\u53ef\u5224\u5b9a\u6027\u79f0\u4e3a\u201c\u8d85\u8d8a\u6df7\u6c8c\u73b0\u8c61<\/span>\uff08next-level chaotic thing\uff09<\/span>\u201d\u3002<\/span><\/section>\n

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\u76ae\u57c3\u5c14-\u897f\u8499\u00b7\u62c9\u666e\u62c9\u65af\uff08Pierre-Simon Laplace\uff09\u66fe\u63d0\u51fa\u5047\u8bf4\uff1a\u4e00\u4e2a\u201c\u5168\u77e5\u5996\u7cbe\uff08demon\uff09\u201d\u80fd\u591f\u5b8c\u7f8e\u9884\u6d4b\u4efb\u4f55\u7269\u7406\u7cfb\u7edf\u7684\u672a\u6765\u3002\u7136\u800c\uff0c\u8fd9\u4e00\u5047\u8bf4\u88ab\u8bc1\u660e\u662f\u9519\u8bef\u7684\u3002\u4e28\u56fe\u7247\u6765\u6e90\uff1aJohann Ernst Heinsius\uff0c\u7ef4\u57fa\u5171\u4eab\u8d44\u6e90<\/span><\/span><\/p>\n


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\u4e0d\u53ef\u5224\u5b9a\u6027\u610f\u5473\u7740\u67d0\u4e9b\u95ee\u9898\u4ece\u6839\u672c\u4e0a\u65e0\u6cd5\u89e3\u7b54\uff0c\u8fd9\u5bf9\u7269\u7406\u5b66\u5bb6\u6765\u8bf4\u8f83\u4e3a\u964c\u751f\uff0c\u4f46\u5bf9\u6570\u5b66\u5bb6\u548c\u8ba1\u7b97\u673a\u79d1\u5b66\u5bb6\u800c\u8a00\u662f\u5e38\u8bc6\u3002\u4e00\u4e2a\u591a\u4e16\u7eaa\u524d\uff0c\u6570\u5b66\u5bb6\u4eec\u901a\u8fc7\u4e25\u683c\u7684\u6570\u5b66\u8bc1\u660e\u6307\u51fa\uff1a\u6709\u4e9b\u6570\u5b66\u95ee\u9898\u6c38\u8fdc\u65e0\u89e3\uff0c\u6709\u4e9b\u771f\u547d\u9898\u6c38\u8fdc\u65e0\u6cd5\u88ab\u8bc1\u660e\u3002\u5982\u4eca\uff0c\u7269\u7406\u5b66\u5bb6\u6b63\u5c06\u8fd9\u7c7b\u4e0d\u53ef\u5224\u5b9a\u7684\u6570\u5b66\u4f53\u7cfb\u4e0e\u8d8a\u6765\u8d8a\u591a\u7684\u7269\u7406\u7cfb\u7edf\u5efa\u7acb\u8054\u7cfb\uff0c\u4ece\u800c\u5f00\u59cb\u7ed8\u5236\u51fa\u7269\u7406\u5b66\u9886\u57df\u4e2d\u201c\u53ef\u77e5\u6027\u201d\u7684\u786c\u8fb9\u754c\u3002<\/span><\/section>\n

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\u201c\u8fd9\u4e9b\u4f8b\u5b50\u5bf9\u4eba\u7c7b\u8ba4\u77e5\u80fd\u529b\u65bd\u52a0\u4e86\u6839\u672c\u6027\u9650\u5236\uff0c\u5e76\u4e14\u8fd9\u4e9b\u9650\u5236\u662f\u4e0d\u53ef\u903e\u8d8a\u7684\u3002\u201d\u5723\u5854\u83f2\u7814\u7a76\u6240<\/span>\uff08Santa Fe Institute\uff09<\/span>\u7814\u7a76\u5458David Wolpert[3]\u8868\u793a\u3002\u4ed6\u957f\u671f\u7814\u7a76\u8ba4\u77e5\u8fb9\u754c\uff0c\u4f46\u5e76\u672a\u53c2\u4e0e\u8fd1\u671f\u7814\u7a76\u3002<\/span><\/section>\n

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1990\u5e74\uff0c\u7269\u7406\u5b66\u754c\u8fce\u6765\u4e86\u4e00\u4e2a\u5173\u4e8e\u201c\u4e0d\u53ef\u77e5\u6027\u201d\u7684\u60ca\u4eba\u6848\u4f8b\u3002\u5eb7\u5948\u5c14\u5927\u5b66\u7684\u7814\u7a76\u751fCris Moore[4]\u8bbe\u8ba1\u4e86\u4e00\u53f0\u4ec5\u6709\u4e00\u4e2a\u6d3b\u52a8\u90e8\u4ef6\u7684\u4e0d\u53ef\u5224\u5b9a\u673a\u5668<\/span>\uff08undecidable machine\uff09<\/span>\u3002\u4ed6\u7684\u88c5\u7f6e\u7406\u8bba\u4e0a\u7c7b\u4f3c\u4e8e\u4e00\u4e2a\u9ad8\u5ea6\u53ef\u5b9a\u5236\u7684\u5f39\u7403\u673a\uff1a\u60f3\u8c61\u4e00\u4e2a\u5e95\u90e8\u5f00\u53e3\u7684\u76d2\u5b50\uff0c\u73a9\u5bb6\u53ef\u4ee5\u653e\u7f6e\u969c\u788d\u7269\u5e76\u5c06\u53d1\u5c04\u5668\u79fb\u52a8\u5230\u4efb\u610f\u4f4d\u7f6e\uff0c\u7136\u540e\u53d1\u5c04\u4e00\u9897\u5f39\u7403\u8fdb\u5165\u76d2\u5185\u3002\u867d\u7136\u88c5\u7f6e\u770b\u4f3c\u7b80\u5355\uff0c\u4f46\u968f\u7740\u5f39\u7403\u5728\u76d2\u5185\u53cd\u5f39\uff0c\u5b83\u5b9e\u9645\u4e0a\u5728\u8fdb\u884c\u67d0\u79cd\u8ba1\u7b97\u3002\u8fd9\u4e2a\u8bbe\u8ba1\u5c55\u793a\u4e86\u4e00\u4e2a\u6df1\u523b\u7684\u79d1\u5b66\u95ee\u9898\uff1a\u5373\u4f7f\u5728\u4e00\u4e2a\u770b\u4f3c\u7b80\u5355\u7684\u7269\u7406\u7cfb\u7edf\u4e2d\uff0c\u4e5f\u53ef\u80fd\u5b58\u5728\u65e0\u6cd5\u89e3\u7b54\u7684\u95ee\u9898\u3002\u8fd9\u79cd\u4e0d\u53ef\u9884\u6d4b\u6027\u63ed\u793a\u4e86\u4e0d\u53ef\u5224\u5b9a\u6027\u5728\u7269\u7406\u5b66\u4e2d\u7684\u91cd\u8981\u6027\u3002<\/span><\/section>\n

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\u5f39\u7403\u673a\u88c5\u7f6e\u7684\u7075\u611f\u6765\u6e90\u4e8e\uff0cMoore\u9605\u8bfb\u4e86\u666e\u5229\u7b56\u5956\u83b7\u5956\u8457\u4f5c\u300a\u54e5\u5fb7\u5c14\u3001\u827e\u820d\u5c14\u3001\u5df4\u8d6b\u300b\uff08G\u00f6del, Escher, Bach\uff09<\/strong>\uff0c\u5bf9\u5176\u4e2d\u81ea\u6307\u7cfb\u7edf<\/span>\uff08self-referential systems\uff09<\/span>\u7684\u8ba1\u7b97\u7406\u8bba\u4ea7\u751f\u4e86\u6d53\u539a\u5174\u8da3\u3002\u6700\u4ee4\u4ed6\u7740\u8ff7\u7684\uff0c\u662f\u8ba1\u7b97\u673a\u79d1\u5b66\u9886\u57df\u7684\u5960\u57fa\u6027\u6784\u60f3\u2014\u2014\u56fe\u7075\u673a<\/span>\uff08Turing machine\uff09<\/span>\u3002<\/span><\/section>\n
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\u300a\u54e5\u5fb7\u5c14\u3001\u827e\u820d\u5c14\u3001\u5df4\u8d6b\u300b\u7684\u539f\u8457(\u5de6\uff0c20 \u5468\u5e74)\u548c\u4e2d\u8bd1\u672c(\u53f3)<\/span><\/section>\n

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\u96c6\u667a\u4ff1\u4e50\u90e8\u66fe\u4e8e2018\u5e744\u670818\u65e5\u9080\u8bf7\u4faf\u4e16\u8fbe\uff08DouglasRichard Hofstadter\uff09\u6765\u5230\u5317\u4eac\u7ebf\u4e0b\u548c\u676d\u5dde\u7ebf\u4e0b\u505a\u5206\u4eab\u4ea4\u6d41\uff1a\u4faf\u4e16\u8fbe\uff1a\u673a\u5668\u53ef\u4ee5\u201c\u7ffb\u8bd1\u201d\u4f46\u4e0d\u80fd\u771f\u6b63\u7406\u89e3 | AI&Society<\/a><\/span><\/section>\n
\u539f\u8457\u548c\u4e2d\u8bd1\u672c\u90fd\u767b\u5cf0\u9020\u6781\u7684\u79d1\u666e\u795e\u4f5c \u2014\u2014\u4faf\u4e16\u8fbe\u7684\u300a\u54e5\u5fb7\u5c14\u3001\u827e\u820d\u5c14\u3001\u5df4\u8d6b\uff1a\u96c6\u5f02\u74a7\u4e4b\u5927\u6210\u300b<\/a>\u6df1\u523b\u7684\u5f71\u54cd\u4e86\u5f88\u591a\u96c6\u667a\u793e\u533a\u7684\u6210\u5458\uff0c\u5305\u62ec\u96c6\u667a\u4ff1\u4e50\u90e8\u7684\u521b\u59cb\u4eba\uff0c\u5317\u4eac\u5e08\u8303\u5927\u5b66\u7684\u6559\u6388\u5f20\u6c5f\uff0c\u63a8\u8350\u5f20\u6c5f\u6559\u6388\u5bf9\u300aGEB\u300b\u7684\u89e3\u8bfb\u89c6\u9891\uff1ahttps:\/\/campus.swarma.org\/course\/51 \uff0c\u4ee5\u53ca\u5f20\u6c5f\u6559\u6388\u64b0\u5199\u7684\u56fe\u7075\u673a\u7684\u8bcd\u6761<\/a>\u548c\u5173\u4e8e\u300a\u81ea\u6307\u300b\u7684\u79d1\u666e\u6587\u7ae0\uff1a\u300a\u81ea\u6307\u2014\u2014\u8fde\u63a5\u56fe\u5f62\u4e0e\u886c\u5e95\u7684\u91d1\u5e26<\/a>\u300b<\/span><\/section>\n<\/blockquote>\n
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\u57281936\u5e74\u7684\u4e00\u9879\u91cc\u7a0b\u7891\u5f0f\u5de5\u4f5c\u4e2d\uff0c\u827e\u4f26\u00b7\u56fe\u7075\u901a\u8fc7\u63cf\u8ff0\u4e00\u79cd\u901a\u7528\u8ba1\u7b97\u8bbe\u5907\u7684\u5173\u952e\u7279\u6027\uff0c\u5b9a\u4e49\u4e86\u8ba1\u7b97\u7684\u8fb9\u754c\u3002\u8fd9\u79cd\u8bbe\u5907\u5982\u4eca\u88ab\u79f0\u4e3a\u56fe\u7075\u673a\uff08Turing machine\uff09\u3002<\/span>\u4e28GL Archive\/Alamy Stock \u62cd\u6444<\/span><\/p>\n


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\u6570\u5b66\u5bb6\u827e\u4f26\u00b7\u56fe\u7075<\/span>\uff08Alan Turing\uff09<\/span>\u5728\u51761936\u5e74\u53d1\u8868\u7684\u91cc\u7a0b\u7891\u5f0f\u8bba\u6587\u4e2d\u5b9a\u4e49\u4e86\u56fe\u7075\u673a<\/span>\uff08Turing machine\uff09<\/span>[5]<\/span><\/section>\n
\uff08https:\/\/www.cs.virginia.edu\/~robins\/Turing_Paper_1936.pdf\uff09<\/span>\u3002\u5b83\u7531\u4e00\u4e2a\u53ef\u6cbf\u65e0\u9650\u957f\u7eb8\u5e26\u4e0a\u4e0b\u79fb\u52a8\u7684\u8bfb\u5199\u5934\u7ec4\u6210\uff0c\u6839\u636e\u4e00\u7ec4\u7b80\u5355\u89c4\u5219\uff0c\u9010\u6b65\u8bfb\u53d6\u548c\u5199\u51650\u548c1\u3002\u4e00\u53f0\u56fe\u7075\u673a\u9075\u5faa\u4e00\u7ec4\u89c4\u5219\uff0c\u53ef\u4ee5\u8bfb\u53d6\u4e24\u4e2a\u6570\u5b57\u5e76\u8f93\u51fa\u5b83\u4eec\u7684\u4e58\u79ef\uff1b\u53e6\u4e00\u53f0\u56fe\u7075\u673a\u9075\u5faa\u4e0d\u540c\u7684\u89c4\u5219\uff0c\u53ef\u4ee5\u8bfb\u53d6\u4e00\u4e2a\u6570\u5b57\u5e76\u8f93\u51fa\u5176\u5e73\u65b9\u6839\u3002\u901a\u8fc7\u8fd9\u79cd\u65b9\u5f0f\uff0c\u56fe\u7075\u673a\u53ef\u4ee5\u88ab\u8bbe\u8ba1\u4e3a\u6267\u884c\u4efb\u4f55\u6570\u5b66\u548c\u903b\u8f91\u8fd0\u7b97\u7684\u5e8f\u5217\u3002\u5982\u4eca\uff0c\u6211\u4eec\u4f1a\u8bf4\u56fe\u7075\u673a\u6267\u884c\u7684\u662f\u201c\u7b97\u6cd5\u201d<\/span>\uff08algorithm\uff09<\/span>\uff0c\u800c\u8bb8\u591a\u7269\u7406\u5b66\u5bb6\u8ba4\u4e3a\uff0c\u56fe\u7075\u673a\u5b9a\u4e49\u4e86\u8ba1\u7b97\u672c\u8eab\u7684\u6781\u9650\uff0c\u65e0\u8bba\u662f\u8ba1\u7b97\u673a\u3001\u4eba\u7c7b\u8fd8\u662f\u201c\u5168\u77e5\u5996\u7cbe\u201d\u6267\u884c\u7684\u8ba1\u7b97\u3002<\/span><\/section>\n

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Kristina Armitage\/Quanta Magazine<\/em><\/span><\/section>\n

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Moore\u5728\u5176\u7814\u7a76\u751f\u9636\u6bb5\u7684\u7814\u7a76\u8bfe\u9898\u2014\u2014\u6df7\u6c8c<\/span>\uff08chaos\uff09<\/span>\u4e2d\uff0c\u53d1\u73b0\u4e86\u56fe\u7075\u673a\u884c\u4e3a\u7684\u96cf\u5f62\u3002\u5728\u6df7\u6c8c\u7cfb\u7edf\u4e2d\uff0c\u6bcf\u4e00\u4e2a\u7ec6\u8282\u90fd\u81f3\u5173\u91cd\u8981\u3002\u7528\u4e00\u53e5\u8457\u540d\u7684\u6bd4\u55bb\u6765\u8bf4\uff1a\u5c06\u5df4\u897f\u7684\u4e00\u53ea\u8774\u8776\u7684\u4f4d\u7f6e\u8c03\u6574\u4e00\u6beb\u7c73\uff0c\u53ef\u80fd\u5e26\u6765\u662f\u4e1c\u4eac\u906d\u9047\u53f0\u98ce\uff0c\u8fd8\u662f\u7530\u7eb3\u897f\u5dde\u88ab\u9f99\u5377\u98ce\u5e2d\u5377\u5982\u6b64\u5929\u58e4\u4e4b\u522b\u7684\u5f71\u54cd\u3002\u8d77\u521d\u5fae\u5c0f\u7684\u820d\u5165\u8bef\u5dee\u4f1a\u9010\u6e10\u6269\u5927\uff0c\u6700\u7ec8\u5f71\u54cd\u6574\u4e2a\u8ba1\u7b97\u3002\u5728\u6df7\u6c8c\u7cfb\u7edf\u4e2d\uff0c\u8fd9\u79cd\u589e\u957f\u53ef\u4ee5\u8868\u73b0\u4e3a\u5728\u6570\u5b57\u4e0a\u7684\u4f4d\u79fb\uff1a\u5341\u5206\u4f4d\u7684\u8bef\u5dee\uff080.1\uff09\u4f1a\u5411\u5de6\u6269\u6563\uff0c\u6700\u7ec8\u7a7f\u8fc7\u5c0f\u6570\u70b9\uff0c\u53d8\u6210\u5341\u4f4d\u4e0a\u7684\u8bef\u5dee\uff0810\uff09\u3002<\/span><\/section>\n

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Moore\u8bbe\u8ba1\u7684\u5f39\u73e0\u673a\u5b8c\u7f8e\u5bf9\u5e94\u4e86\u56fe\u7075\u673a\u7684\u7ed3\u6784\uff0c\u5f39\u7403\u7684\u8d77\u59cb\u4f4d\u7f6e\u4ee3\u8868\u8f93\u5165\u56fe\u7075\u673a\u7eb8\u5e26\u7684\u6570\u636e\u3002\u5173\u952e<\/span>\uff08\u4f46\u4e0d\u5207\u5b9e\u9645\uff09<\/span>\u7684\u662f\uff0c\u73a9\u5bb6\u5fc5\u987b\u80fd\u591f\u4ee5\u65e0\u9650\u7cbe\u5ea6\u8c03\u6574\u5f39\u7403\u7684\u8d77\u59cb\u4f4d\u7f6e\uff0c\u610f\u5473\u7740\u7528\u5e26\u6709\u65e0\u9650\u957f\u5c0f\u6570\u4f4d\u7684\u6570\u5b57\u6765\u63cf\u8ff0\u5f39\u73e0\u7684\u4f4d\u7f6e\uff0c\u53ea\u6709\u5728\u8fd9\u6837\u7684\u6570\u5b57\u4e2d\uff0cMoore\u624d\u80fd\u7f16\u7801\u65e0\u9650\u957f\u56fe\u7075\u7eb8\u5e26\u7684\u6570\u636e\u3002\u968f\u540e\uff0c\u969c\u788d\u7269\u7684\u6392\u5217\u5f15\u5bfc\u5f39\u7403\u79fb\u52a8\u5230\u65b0\u4f4d\u7f6e\uff0c\u8fd9\u4e00\u8fc7\u7a0b\u5bf9\u5e94\u4e8e\u56fe\u7075\u673a\u7eb8\u5e26\u4e0a\u7684\u8bfb\u5199\u64cd\u4f5c\u3002\u67d0\u4e9b\u5f2f\u66f2\u7684\u969c\u788d\u7269\u5c06\u7eb8\u5e26\u5411\u4e00\u4e2a\u65b9\u5411\u79fb\u52a8\uff0c\u4f7f\u5f97\u5b58\u50a8\u5728\u9065\u8fdc\u6570\u4f4d\u7684\u6570\u636e\u53d8\u5f97\u66f4\u52a0\u91cd\u8981\uff0c\u8fd9\u4e00\u73b0\u8c61\u8ba9\u4eba\u8054\u60f3\u5230\u6df7\u6c8c\u7cfb\u7edf\uff1b\u800c\u53cd\u65b9\u5411\u5f2f\u66f2\u7684\u969c\u788d\u7269\u5219\u4ea7\u751f\u76f8\u53cd\u7684\u6548\u679c\u3002\u5f39\u73e0\u4ece\u76d2\u5e95\u5f39\u51fa\u65f6\uff0c\u8ba1\u7b97\u7ec8\u6b62\uff0c\u6700\u7ec8\u843d\u70b9\u5373\u4e3a\u8fd0\u7b97\u7ed3\u679c\u3002<\/span><\/section>\n

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\u6469\u5c14\u4e3a\u4ed6\u7684\u5f39\u7403\u673a\u88c5\u7f6e\u8d4b\u4e88\u4e86\u8ba1\u7b97\u673a\u7684\u7075\u6d3b\u6027\uff0c\u6bd4\u5982\u8bbe\u8ba1\u4e00\u79cd\u969c\u788d\u7269\u6392\u5217\u65b9\u5f0f\u53ef\u4ee5\u8ba1\u7b97\u5706\u5468\u7387\u7684\u524d\u4e00\u5343\u4f4d\u6570\u5b57\uff0c\u800c\u53e6\u4e00\u79cd\u6392\u5217\u65b9\u5f0f\u5219\u53ef\u80fd\u8ba1\u7b97\u56fd\u9645\u8c61\u68cb\u6e38\u620f\u4e2d\u7684\u6700\u4f73\u4e0b\u4e00\u6b65\u3002\u4f46\u5b83\u4e5f\u6709\u4e00\u4e2a\u6211\u4eec\u5f88\u96be\u4e0e\u8ba1\u7b97\u673a\u8054\u7cfb\u8d77\u6765\u7684\u7279\u6027\uff1a\u4e0d\u53ef\u9884\u6d4b\u6027<\/span>\uff08unpredictability\uff09<\/span>\u3002<\/span><\/section>\n

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\u67d0\u4e9b\u7b97\u6cd5\u4f1a\u505c\u6b62\u8fd0\u884c\u5e76\u8f93\u51fa\u7ed3\u679c\uff0c\u800c\u53e6\u4e00\u4e9b\u5219\u4f1a\u65e0\u9650\u8fd0\u884c\uff0c\u4f8b\u5982\uff0c\u6253\u5370\u5706\u5468\u7387\u6700\u540e\u4e00\u4f4d\u6570\u5b57\u7684\u7a0b\u5e8f\u3002\u56fe\u7075\u63d0\u51fa\u4e86\u4e00\u4e2a\u6839\u672c\u6027\u7684\u8ffd\u95ee\uff1a\u662f\u5426\u5b58\u5728\u4e00\u79cd\u901a\u7528\u7a0b\u5e8f\uff0c\u80fd\u5224\u65ad\u4efb\u610f\u4e00\u4e2a\u7a0b\u5e8f\u662f\u4f1a\u81ea\u884c\u7ec8\u6b62\uff0c\u8fd8\u662f\u65e0\u9650\u8fd0\u884c\uff1f\u8fd9\u4e2a\u95ee\u9898\u88ab\u79f0\u4e3a\u201c\u56fe\u7075\u505c\u673a\u95ee\u9898\u201d\uff08halting problem\uff09<\/strong>\u3002<\/span><\/section>\n

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\u56fe\u7075\u901a\u8fc7\u5047\u8bbe\u8fd9\u79cd\u7a0b\u5e8f\u5b58\u5728\u5e76\u8fdb\u884c\u63a8\u7406\uff0c\u6700\u7ec8\u8bc1\u660e\u4e86\u8fd9\u79cd\u7a0b\u5e8f\u4e0d\u53ef\u80fd\u5b58\u5728\u3002\u5982\u679c\u4e00\u53f0\u673a\u5668\u80fd\u591f\u9884\u6d4b\u53e6\u4e00\u53f0\u673a\u5668\u7684\u884c\u4e3a\uff0c\u90a3\u4e48\u4f60\u53ef\u4ee5\u8f7b\u677e\u5730\u4fee\u6539\u8fd9\u53f0\u9884\u6d4b\u673a\u5668\uff0c\u4f7f\u5f97\u5f53\u53e6\u4e00\u53f0\u673a\u5668\u505c\u6b62\u65f6\uff0c\u5b83\u65e0\u9650\u8fd0\u884c\uff1b\u53cd\u4e4b\uff0c\u5f53\u53e6\u4e00\u53f0\u673a\u5668\u4f1a\u65e0\u9650\u8fd0\u884c\u65f6\uff0c\u5b83\u505c\u6b62\u3002\u63a5\u7740\uff0c\u56fe\u7075\u8fdb\u884c\u4e86\u4e00\u4e2a\u7cbe\u5999\u7684\u63a8\u6f14\uff1a\u5c06\u7ecf\u8fc7\u8c03\u6574\u7684\u9884\u6d4b\u673a\u5668\u7684\u63cf\u8ff0\u8f93\u5165\u5230\u5b83\u81ea\u8eab\u4e2d\uff1a\u5982\u679c\u8fd9\u53f0\u673a\u5668\u505c\u6b62\u8fd0\u884c\uff0c\u5b83\u4e5f\u5fc5\u987b\u65e0\u9650\u8fd0\u884c\uff1b\u5982\u679c\u5b83\u65e0\u9650\u8fd0\u884c\uff0c\u5b83\u4e5f\u5fc5\u987b\u505c\u6b62\u3002\u8fd9\u4e24\u79cd\u60c5\u51b5<\/span>\uff08\u505c\u6b62\u548c\u65e0\u9650\u8fd0\u884c\uff09<\/span>\u4e92\u76f8\u77db\u76fe\uff0c\u65e0\u6cd5\u540c\u65f6\u6210\u7acb\u3002\u56e0\u6b64\uff0c\u8fd9\u79cd\u9884\u6d4b\u7a0b\u5e8f\u4e0d\u53ef\u80fd\u5b58\u5728\u3002<\/span><\/section>\n

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\uff08\u4ed6\u7684\u53d1\u73b0\u4e0e1931\u5e74\u7684\u4e00\u9879\u5f00\u521b\u6027\u6210\u679c\u5bc6\u5207\u76f8\u5173\u3002\u5f53\u65f6\uff0c\u903b\u8f91\u5b66\u5bb6\u5e93\u5c14\u7279\u00b7\u54e5\u5fb7\u5c14\uff08Kurt G\u00f6del\uff09\u53d1\u660e\u4e86\u4e00\u79cd\u7c7b\u4f3c\u7684\u65b9\u6cd5\uff0c\u5c06<\/span>\u81ea\u6307\u6096\u8bba<\/a><\/span>[6]\uff08self-referential paradox\uff09\u5f15\u5165\u4e25\u683c\u7684\u6570\u5b66\u6846\u67b6\u4e2d\u3002\u54e5\u5fb7\u5c14\u8bc1\u660e\u4e86\u5b58\u5728\u4e00\u4e9b\u6570\u5b66\u547d\u9898\uff0c\u5176\u771f\u4f2a\u6c38\u8fdc\u65e0\u6cd5\u88ab\u786e\u5b9a\u3002\uff09<\/span><\/section>\n

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\u7b80\u8a00\u4e4b\uff0c\u56fe\u7075\u8bc1\u660e\u4e86\u505c\u673a\u95ee\u9898\u7684\u4e0d\u53ef\u89e3\u6027\u3002\u8981\u5224\u65ad\u4e00\u4e2a\u7b97\u6cd5\u662f\u5426\u4f1a\u505c\u6b62\uff0c\u552f\u4e00\u7684\u529e\u6cd5\u5c31\u662f\u8fd0\u884c\u5b83\uff0c\u6301\u7eed\u89c2\u5bdf\u4e0b\u53bb\u3002\u5982\u679c\u5b83\u505c\u6b62\u4e86\uff0c\u7b54\u6848\u81ea\u7136\u660e\u4e86\u3002\u4f46\u5982\u679c\u5b83\u6ca1\u6709\u505c\u6b62\uff0c\u4f60\u5c06\u6c38\u8fdc\u65e0\u6cd5\u786e\u5b9a\uff1a\u5b83\u4f1a\u4e00\u76f4\u8fd0\u8f6c\u4e0b\u53bb\uff1f\u8fd8\u662f\u53ea\u662f\u56e0\u4e3a\u4f60\u6ca1\u6709\u7b49\u5f85\u8db3\u591f\u957f\u7684\u65f6\u95f4\u3002\u201c\u6211\u4eec\u77e5\u9053\uff0c\u5b58\u5728\u8fd9\u6837\u4e00\u4e9b\u521d\u59cb\u72b6\u6001\uff0c\u6211\u4eec\u65e0\u6cd5\u63d0\u524d\u9884\u6d4b\u5b83\u4eec\u7684\u884c\u4e3a\uff0c\u201dWolpert\u8bf4\u9053\u3002<\/span><\/section>\n

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\u7531\u4e8eMoore\u8bbe\u8ba1\u7684\u5f39\u7403\u673a[7]<\/span>\uff08Moore\u4e8e1990\u5e74\u5728PRL\u4e0a\u53d1\u8868\u7684\u8bba\u6587\u300aUnpredictability and undecidability in dynamical systems\u300b\uff09<\/span>\u80fd\u591f\u6a21\u62df\u4efb\u4f55\u56fe\u7075\u673a\uff0c\u56e0\u6b64\u5b83\u4e5f\u53ef\u80fd\u8868\u73b0\u51fa\u4e0d\u53ef\u9884\u6d4b\u7684\u884c\u4e3a\u3002\u5f39\u7403\u7684\u79bb\u5f00\u6807\u5fd7\u7740\u8ba1\u7b97\u7684\u7ec8\u6b62\uff0c\u56e0\u6b64\uff0c\u4efb\u4f55\u7279\u5b9a\u969c\u788d\u7269\u6392\u5217\u662f\u5426\u4f1a\u56f0\u4f4f\u5f39\u7403\u6216\u5f15\u5bfc\u5176\u79bb\u5f00\u76d2\u5b50\u7684\u95ee\u9898\uff0c\u4e5f\u5fc5\u7136\u662f\u4e0d\u53ef\u5224\u5b9a\u7684\u3002\u201c\u4e8b\u5b9e\u4e0a\uff0c\u5173\u4e8e\u8fd9\u4e9b\u590d\u6742\u6620\u5c04\u7684\u957f\u671f\u52a8\u6001\u7684\u6240\u6709\u95ee\u9898\u90fd\u662f\u4e0d\u53ef\u5224\u5b9a\u7684\uff0c\u201dMoore\u8bf4\u9053\u3002<\/span><\/section>\n
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\u514b\u91cc\u65af\u00b7\u6469\u5c14\uff08Cris Moore\uff09\u5f00\u53d1\u4e86\u6700\u65e9\u4e14\u6700\u7b80\u5355\u7684\u4e0d\u53ef\u5224\u5b9a\u7684\u7269\u7406\u7cfb\u7edf\u3002\u4e28Cressandra Thibodeaux<\/span><\/span><\/p>\n


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Moore\u7684\u5f39\u7403\u673a\u8d85\u8d8a\u4e86\u666e\u901a\u7684\u6df7\u6c8c\u7cfb\u7edf\u3002\u9f99\u5377\u98ce\u9884\u62a5\u5458\u65e0\u6cd5\u51c6\u786e\u9884\u6d4b\u9f99\u5377\u98ce\u7684\u7740\u9646\u70b9\uff0c\u539f\u56e0\u6709\u4e8c\uff1a\u4e00\u662f\u9884\u62a5\u5458\u5bf9\u6bcf\u53ea\u201c\u5df4\u897f\u8774\u8776\u201d\u7684\u7cbe\u786e\u4f4d\u7f6e\u4e00\u65e0\u6240\u77e5\uff0c\u4e8c\u662f\u8ba1\u7b97\u80fd\u529b\u6709\u9650\u3002\u4f46\u6469\u5c14\u7684\u5f39\u7403\u673a\u5c55\u73b0\u4e86\u4e00\u79cd\u66f4\u6df1\u5c42\u7684\u4e0d\u53ef\u9884\u6d4b\u5f62\u5f0f\u3002\u5373\u4f7f\u5bf9\u8fd9\u53f0\u673a\u5668\u4e86\u5982\u6307\u638c\u4e14\u62e5\u6709\u65e0\u9650\u8ba1\u7b97\u80fd\u529b\uff0c\u5173\u4e8e\u5176\u547d\u8fd0\u7684\u67d0\u4e9b\u95ee\u9898\u4ecd\u7136\u65e0\u6cd5\u56de\u7b54\u3002\u201c\u8fd9\u66f4\u52a0\u620f\u5267\u5316\uff0c\u5373\u4f7f\u62e5\u6709\u65e0\u9650\u8d44\u6e90\uff0c\u4f60\u4e5f\u65e0\u6cd5\u7f16\u5199\u51fa\u89e3\u51b3\u8be5\u95ee\u9898\u7684\u7a0b\u5e8f\u3002\u201d\u9a6c\u5fb7\u91cc\u5eb7\u666e\u987f\u65af\u5927\u5b66\u6570\u5b66\u5bb6David P\u00e9rez-Garc\u00eda[8]\u8868\u793a\u3002<\/span><\/section>\n

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\u6b64\u524d\uff0c\u5176\u4ed6\u7814\u7a76\u4eba\u5458\u5df2\u7ecf\u8bbe\u8ba1\u51fa\u4e86\u4e00\u4e9b\u7c7b\u4f3c\u4e8e\u56fe\u7075\u673a<\/span>\uff08Turing machine\uff09<\/span>\u7684\u7cfb\u7edf\u2014\u2014\u7279\u522b\u662f\u68cb\u76d8\u683c[9]<\/span>\uff08checkerboard grid\uff09<\/span>\uff0c\u5176\u4e2d\u7684\u65b9\u683c\u4f1a\u6839\u636e\u76f8\u90bb\u65b9\u683c\u7684\u989c\u8272\u4e0d\u65ad\u95ea\u70c1\u5f00\u5173[10]\u3002\u7136\u800c\uff0c\u8fd9\u4e9b\u7cfb\u7edf\u975e\u5e38\u62bd\u8c61\u4e14\u590d\u6742\u3002\u800cMoore\u5219\u7528\u4e00\u4e2a\u7b80\u5355\u7684\u88c5\u7f6e\u6784\u5efa\u4e86\u4e00\u53f0\u56fe\u7075\u673a\uff0c\u5c31\u50cf\u5728\u5b9e\u9a8c\u5ba4\u91cc\u5e38\u89c1\u7684\u90a3\u79cd\u3002\u8fd9\u4e00\u751f\u52a8\u7684\u5b9e\u9a8c\u8868\u660e\uff0c\u5373\u4f7f\u662f\u4e00\u4e2a\u4ec5\u9075\u5faa\u9ad8\u4e2d\u7269\u7406\u5b9a\u5f8b\u7684\u7cfb\u7edf\uff0c\u4e5f\u53ef\u80fd\u5177\u6709\u4e0d\u53ef\u9884\u6d4b\u7684\u672c\u8d28\u3002<\/span><\/section>\n

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\u201c\u5b83\u4e0d\u53ef\u5224\u5b9a\u8fd9\u4e00\u70b9\u6709\u4e9b\u4ee4\u4eba\u9707\u60ca\uff0c\u201dCubitt\u8bf4\u9053\uff0c\u4ed6\u5728\u7814\u7a76\u751f\u65f6\u671f\u88ab\u8be5\u673a\u5668\u6df1\u6df1\u5438\u5f15\uff0c\u540e\u6765\u8fd8\u4e3a\u6b64\u5f00\u8bbe\u4e86\u4e13\u9898\u8bb2\u5ea7\u3002\u201c\u672c\u8d28\u4e0a\uff0c\u8fd9\u4e0d\u8fc7\u662f\u5355\u4e2a\u7c92\u5b50\u5728\u76d2\u5185\u53cd\u590d\u78b0\u649e\u800c\u5df2\u3002\u201dCubitt\u83b7\u5f97\u7269\u7406\u5b66\u535a\u58eb\u540e\uff0c\u8f6c\u800c\u6295\u8eab\u6570\u5b66\u4e0e\u8ba1\u7b97\u673a\u79d1\u5b66\u9886\u57df\u3002\u7136\u800c\uff0c\u4ed6\u59cb\u7ec8\u65e0\u6cd5\u5fd8\u8bb0\u90a3\u53f0\u5f39\u7403\u673a\uff0c\u4ee5\u53ca\u8ba1\u7b97\u673a\u79d1\u5b66\u5bf9\u673a\u5668\u7269\u7406\u89c4\u5f8b\u7684\u9650\u5236\u3002\u4ed6\u4e0d\u65ad\u601d\u8003\uff1a\u4e0d\u53ef\u5224\u5b9a\u6027\u662f\u5426\u89e6\u53ca\u4e86\u771f\u6b63\u7684\u7269\u7406\u95ee\u9898\uff1f<\/strong>\u7ecf\u8fc7\u5341\u5e74\u7684\u63a2\u7d22\uff0c\u4ed6\u7ec8\u4e8e\u53d1\u73b0\uff0c\u7b54\u6848\u786e\u5b9e\u662f\u80af\u5b9a\u7684\u3002<\/span><\/section>\n

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2012\u5e74\uff0cCubitt\u5c06\u4e0d\u53ef\u5224\u5b9a\u6027\u4e0e\u5927\u578b\u91cf\u5b50\u7cfb\u7edf\u7684\u7814\u7a76\u7d27\u5bc6\u7ed3\u5408\u3002\u5728\u5965\u5730\u5229\u963f\u5c14\u5351\u65af\u5c71\u7684\u4e00\u6b21\u4f1a\u8bae\u4e0a\uff0c\u4ed6\u4e0eP\u00e9rez-Garc\u00eda\u53ca\u540c\u4e8bMichael Wolf[11]\u4e00\u8d77\u559d\u7740\u5496\u5561\uff0c\u8ba8\u8bba\u4e00\u4e2a\u51b7\u95e8\u95ee\u9898\u662f\u5426\u53ef\u80fd\u662f\u4e0d\u53ef\u5224\u5b9a\u7684\u3002\u5f53Wolf\u5efa\u8bae\u4ed6\u4eec\u6682\u65f6\u6401\u7f6e\u8be5\u95ee\u9898\uff0c\u8f6c\u800c\u89e3\u51b3\u91cf\u5b50\u7269\u7406\u5b66\u4e2d\u6700\u5927\u95ee\u9898\u4e4b\u4e00\u7684\u53ef\u5224\u5b9a\u6027\u65f6\uff0c\u4ed6\u751a\u81f3\u6ca1\u6709\u6599\u5230\u4ed6\u4eec\u53ef\u80fd\u4f1a\u6210\u529f\u3002\u201c\u5f00\u59cb\u53ea\u662f\u4e00\u53e5\u73a9\u7b11\uff0c\u6ca1\u60f3\u5230\u7075\u611f\u5374\u63a5\u4e8c\u8fde\u4e09\u5730\u8ff8\u53d1\uff0c\u201dP\u00e9rez-Garc\u00eda\u56de\u5fc6\u9053\u3002<\/span><\/section>\n

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Wolf\u63d0\u7784\u51c6\u91cf\u5b50\u7cfb\u7edf\u7684\u6838\u5fc3\u5c5e\u6027\u2014\u2014\u80fd\u9699\uff08spectral gap\uff09\uff0c\u5b83\u6307\u7684\u662f\u5c06\u7cfb\u7edf\u4ece\u6700\u4f4e\u80fd\u91cf\u72b6\u6001\u6fc0\u53d1\u6240\u9700\u7684\u80fd\u91cf<\/strong>\u3002\u5982\u679c\u6fc0\u53d1\u9700\u8981\u4e00\u5b9a\u7684\u80fd\u91cf\uff0c\u7cfb\u7edf\u5c31\u662f\u201c\u6709\u80fd\u9699\u7684\u201d\uff1b\u5982\u679c\u7cfb\u7edf\u53ef\u4ee5\u5728\u4efb\u4f55\u65f6\u523b\u65e0\u9700\u80fd\u91cf\u6ce8\u5165\u5c31\u88ab\u6fc0\u53d1\uff0c\u5b83\u5c31\u662f\u201c\u65e0\u80fd\u9699\u7684\u201d\u3002\u80fd\u9699\u51b3\u5b9a\u4e86\u9713\u8679\u706f\u53d1\u51fa\u7684\u989c\u8272\u3001\u6750\u6599\u5728\u79fb\u9664\u6240\u6709\u70ed\u91cf\u65f6\u7684\u884c\u4e3a\uff0c\u4ee5\u53ca\u5728\u4e0d\u540c\u80cc\u666f\u4e0b\u8d28\u5b50\u7684\u8d28\u91cf\u5e94\u8be5\u662f\u4ec0\u4e48\u3002\u5728\u8bb8\u591a\u60c5\u51b5\u4e0b\uff0c\u7269\u7406\u5b66\u5bb6\u53ef\u4ee5\u8ba1\u7b97\u51fa\u7279\u5b9a\u539f\u5b50\u6216\u6750\u6599\u7684\u80fd\u9699\uff1b\u4f46\u5728\u66f4\u591a\u5176\u4ed6\u60c5\u51b5\u4e0b\uff0c\u4ed6\u4eec\u4e5f\u65e0\u6cd5\u505a\u5230\u3002\u5982\u679c\u6709\u4eba\u80fd\u4ece\u7b2c\u4e00\u6027\u539f\u7406[12]\u4e25\u683c\u8bc1\u660e\u8d28\u5b50\u5e94\u5177\u6709\u6b63\u8d28\u91cf\uff0c\u5c06\u83b7\u5f97\u767e\u4e07\u7f8e\u5143\u7684\u5956\u91d1\u3002<\/span><\/section>\n

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\u5927\u536b\u00b7\u4f69\u96f7\u65af-\u52a0\u897f\u4e9a\uff08David P\u00e9rez-Garc\u00eda\uff0c\u5de6\uff09\u548c\u6258\u6bd4\u00b7\u5e93\u6bd4\u7279\uff08Toby Cubitt\uff09\u8bbe\u8ba1\u4e86\u4e00\u79cd\u91cf\u5b50\u6750\u6599\uff0c\u5176\u72b6\u6001\u53ef\u4ee5\u6355\u6349\u56fe\u7075\u673a\u53ef\u80fd\u8fdb\u884c\u7684\u4efb\u4f55\u8ba1\u7b97\u3002\u4e28<\/span>\u4ece\u5de6\u81f3\u53f3\uff1aDavid P\u00e9rez-Garc\u00eda; Johnny Millar\uff1bJohnny Millar\u62cd\u6444<\/span><\/p>\n


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Cubitt\u3001Wolf\u3001P\u00e9rez-Garc\u00eda\u4ed6\u4eec\u8bbe\u5b9a\u4e86\u975e\u5e38\u9ad8\u8fdc\u7684\u76ee\u6807\u3002\u4ed6\u4eec\u8bd5\u56fe\u8bc1\u660e\u6216\u8bc1\u4f2a\u4e00\u79cd\u5355\u4e00\u7b56\u7565\u2014\u2014\u662f\u5426\u5b58\u5728\u4e00\u79cd\u901a\u7528\u7b97\u6cd5\uff0c\u80fd\u591f\u5224\u5b9a\u6240\u6709\u7269\u8d28\u662f\u5426\u5177\u6709\u80fd\u9699\uff0c\u8303\u56f4\u4ece\u8d28\u5b50\u5230\u94dd\u7b94\u65e0\u6240\u4e0d\u5305\u3002\u4e3a\u6b64\uff0c\u4ed6\u4eec\u501f\u9274\u4e86\u6469\u5c14\u7814\u7a76\u5f39\u7403\u673a\u7684\u65b9\u6cd5\uff1a\u8bbe\u8ba1\u51fa\u4e00\u79cd\u865a\u62df\u7684\u91cf\u5b50\u6750\u6599\uff0c\u8fd9\u79cd\u6750\u6599\u80fd\u591f\u6a21\u62df\u4efb\u4f55\u56fe\u7075\u673a\u7684\u8fd0\u4f5c\u3002\u4ed6\u4eec\u5c06\u80fd\u9699\u95ee\u9898\u91cd\u65b0\u5305\u88c5\u4e3a\u505c\u673a\u95ee\u9898\uff0c\u8bd5\u56fe\u901a\u8fc7\u8fd9\u4e00\u9014\u5f84\u627e\u5230\u7b54\u6848\u3002<\/strong><\/span><\/section>\n

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\u7ecf\u8fc7\u4e09\u5e74\u7684\u52aa\u529b\uff0c\u4ed6\u4eec\u5b8c\u6210\u4e86\u4e00\u7bc7\u957f\u8fbe144\u9875\u7684\u590d\u6742\u6570\u5b66\u8bba\u6587[13]<\/span>\uff08\u300aUndecidability of the Spectral Gap (full version)\uff09<\/span>\u3002\u8fd9\u7bc7\u8bba\u6587\u878d\u5408\u4e86\u8fc7\u53bb\u4e94\u5341\u5e74\u6570\u5b66\u4e0e\u7269\u7406\u5b66\u7684\u91cd\u8981\u6210\u679c\u3002\u8bba\u6587\u7684\u6838\u5fc3\u601d\u60f3\u662f\uff1a\u5229\u7528\u5e73\u9762\u6750\u6599\u7684\u91cf\u5b50\u7c92\u5b50\u6765\u6a21\u62df\u56fe\u7075\u673a\u7684\u7eb8\u5e26\uff0c\u8fd9\u7c7b\u5e73\u9762\u6750\u6599\u5b9e\u9645\u4e0a\u662f\u7531\u539f\u5b50\u6784\u6210\u7684\u6676\u683c\u3002<\/span><\/section>\n

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\u7531\u4e8e\u8fd9\u662f\u4e00\u79cd\u91cf\u5b50\u6750\u6599\uff0c\u7c92\u5b50\u53ef\u4ee5\u540c\u65f6\u5904\u4e8e\u591a\u4e2a\u72b6\u6001\u7684\u53e0\u52a0\u6001\u2014\u2014\u5373\u6750\u6599\u7684\u4e0d\u540c\u6784\u578b\u7684\u91cf\u5b50\u53e0\u52a0\u6001\u3002\u7814\u7a76\u8005\u4eec\u5229\u7528\u8fd9\u4e00\u7279\u6027\uff0c\u8bb0\u5f55\u4e0b\u8ba1\u7b97\u7684\u6bcf\u4e00\u4e2a\u9636\u6bb5\u3002\u4ed6\u4eec\u5728\u914d\u7f6e\u53e0\u52a0\u6001\u65f6\uff0c\u4f7f\u5f97\u67d0\u4e00\u79cd\u6784\u578b\u5bf9\u5e94\u56fe\u7075\u673a\u7684\u521d\u59cb\u6001\uff0c\u53e6\u4e00\u79cd\u6784\u578b\u5bf9\u5e94\u8ba1\u7b97\u7684\u7b2c\u4e00\u6b65\uff0c\u518d\u4e00\u79cd\u6784\u578b\u5bf9\u5e94\u7b2c\u4e8c\u6b65\uff0c\u4f9d\u6b64\u7c7b\u63a8\u3002<\/span><\/section>\n

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\u6700\u7ec8\uff0c\u4ed6\u4eec\u5229\u7528\u91cf\u5b50\u8ba1\u7b97\u6280\u672f\u8c03\u6574\u4e86\u7c92\u5b50\u4e4b\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\uff0c\u4f7f\u5f97\u5982\u679c\u53e0\u52a0\u6001\u4ee3\u8868\u7684\u8ba1\u7b97\u505c\u673a\uff0c\u6750\u6599\u5c31\u4f1a\u5177\u6709\u80fd\u9699\uff1b\u5982\u679c\u8ba1\u7b97\u65e0\u9650\u8fdb\u884c\uff0c\u6750\u6599\u5c31\u6ca1\u6709\u80fd\u9699\u3002\u57282015\u5e74\u53d1\u8868\u4e8e\u300a\u81ea\u7136\u300b<\/span>\uff08Nature<\/em>\uff09<\/span>\u7684\u8fd9\u7bc7\u8bba\u6587\u300aUndecidability of the spectral gap\u300b[14]\u4e2d\uff0c\u4ed6\u4eec\u8bc1\u660e\u4e86\u80fd\u9699\u95ee\u9898\u7b49\u4ef7\u4e8e\u505c\u673a\u95ee\u9898\u2014\u2014\u56e0\u6b64\u662f\u4e0d\u53ef\u5224\u5b9a\u7684\u3002<\/strong>\u5982\u679c\u6709\u4eba\u7ed9\u4f60\u4e00\u4efd\u5173\u4e8e\u6750\u6599\u7c92\u5b50\u7684\u5b8c\u6574\u63cf\u8ff0\uff0c\u5b83\u8981\u4e48\u6709\u80fd\u9699\uff0c\u8981\u4e48\u6ca1\u6709\u3002\u4f46\u4ece\u7c92\u5b50\u76f8\u4e92\u4f5c\u7528\u7684\u65b9\u5f0f\u51fa\u53d1\uff0c\u6570\u5b66\u4e0a\u65e0\u6cd5\u8ba1\u7b97\u51fa\u8fd9\u4e00\u7279\u6027\uff0c\u5373\u4fbf\u662f\u4f7f\u75283000\u5e74\u7684\u91cf\u5b50\u8d85\u7b97\uff0c\u4e5f\u65e0\u6cd5\u4ece\u7c92\u5b50\u4f5c\u7528\u63a8\u5bfc\u51fa\u8be5\u5c5e\u6027\u3002<\/span><\/section>\n

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2020\u5e74\uff0cP\u00e9rez-Garc\u00eda\u3001Cubitt\u548c\u5176\u4ed6\u5408\u4f5c\u8005\u5728\u4e00\u7ef4\u7c92\u5b50\u94fe[15]<\/span>\uff08\u800c\u975e\u7f51\u683c\uff09<\/span>\u4e0a\u91cd\u590d\u4e86\u8fd9\u4e00\u8bc1\u660e\u3002\u53bb\u5e74\uff0cCubitt\u3001James Purcell\u548cZhi Li\u8fdb\u4e00\u6b65\u6269\u5c55\u4e86\u8fd9\u4e00\u6846\u67b6\uff0c\u7814\u5236\u51fa\u4e00\u79cd\u7279\u6b8a\u6750\u6599\u3002\u5f53\u78c1\u573a\u6301\u7eed\u589e\u5f3a\u65f6\uff0c\u6750\u6599\u4f1a\u5728\u4e0d\u53ef\u9884\u6d4b\u7684\u77ac\u95f4\u53d1\u751f\u76f8\u53d8[16]\u3002<\/span><\/section>\n

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\u8fd9\u9879\u7814\u7a76\u6fc0\u53d1\u4e86\u5176\u4ed6\u56e2\u961f\u7684\u7075\u611f\u30022021\u5e74\uff0c\u5f53\u65f6\u5728\u65e5\u672c\u5b66\u4e60\u9662\u5927\u5b66Naoto Shiraishi\u548c\u65e5\u672c\u56fd\u7acb\u4fe1\u606f\u5b66\u7814\u7a76\u6240Keiji Matsumoto\u5408\u4f5c\uff0c\u6784\u60f3\u51fa\u4e86\u4e00\u79cd\u540c\u6837\u5947\u7279\u7684\u6750\u6599[17]\uff0c\u5728\u8fd9\u79cd\u6750\u6599\u4e2d\uff0c\u65e0\u6cd5\u9884\u6d4b\u80fd\u91cf\u662f\u5426\u4f1a\u201c\u70ed\u5316\u201d<\/span>\uff08thermalize\uff09<\/span>\uff0c\u5373\u5747\u5300\u5206\u5e03\u5728\u6574\u4e2a\u7269\u8d28\u4e2d\u3002<\/span><\/section>\n

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\u8fd9\u4e9b\u7ed3\u679c\u5e76\u4e0d\u610f\u5473\u7740\u6211\u4eec\u65e0\u6cd5\u9884\u6d4b\u7279\u5b9a\u6750\u6599\u7684\u7279\u5b9a\u6027\u8d28\u3002\u4f8b\u5982\uff0c\u7406\u8bba\u5bb6\u6216\u8bb8\u80fd\u591f\u8ba1\u7b97\u94dc\u7684\u80fd\u9699\uff0c\u751a\u81f3\u5224\u65ad\u6240\u6709\u91d1\u5c5e\u5728\u7279\u5b9a\u6761\u4ef6\u4e0b\u662f\u5426\u4f1a\u70ed\u5316\u3002\u4f46\u8fd9\u9879\u7814\u7a76\u786e\u5b9e\u8bc1\u660e\uff1a\u4e0d\u5b58\u5728\u4e00\u79cd\u901a\u7528\u65b9\u6cd5\u9002\u7528\u4e8e\u6240\u6709\u6750\u6599\u3002<\/span><\/section>\n

<\/span><\/section>\n
Naoto Shiraishi\u8bf4\u9053\uff1a\u201c\u5982\u679c\u4f60\u8ffd\u6c42\u901a\u7528\uff0c\u5c31\u4f1a\u5931\u8d25\u3002\u201d<\/span><\/section>\n

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\u6700\u8fd1\uff0c\u7814\u7a76\u4eba\u5458\u5728\u91cf\u5b50\u7269\u7406\u4e4b\u5916\u7684\u9886\u57df\u4e5f\u53d1\u73b0\u4e86\u4e00\u7cfb\u5217\u65b0\u7684\u53ef\u9884\u6d4b\u6027\u9650\u5236\u3002<\/span><\/section>\n

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\u52a0\u6cf0\u7f57\u5c3c\u4e9a\u7406\u5de5\u5927\u5b66\u7684Miranda\u5728\u8fc7\u53bb\u51e0\u5e74\u4e2d\u4e00\u76f4\u5728\u7814\u7a76\u6db2\u4f53\u662f\u5426\u53ef\u4ee5\u4f5c\u4e3a\u8ba1\u7b97\u673a\u4f7f\u7528\u30022014\u5e74\uff0c\u6570\u5b66\u5bb6\u9676\u54f2\u8f69<\/span>\uff08Terence Tao\uff09<\/span>\u6307\u51fa\uff1a\u5982\u679c\u6db2\u4f53\u53ef\u4ee5\u5145\u5f53\u8ba1\u7b97\u673a\uff0c\u6216\u8bb8\u53ef\u4ee5\u901a\u8fc7\u7f16\u7a0b\u4f7f\u6db2\u4f53\u4ee5\u67d0\u79cd\u7279\u5b9a\u7684\u65b9\u5f0f\u6ce2\u52a8[18]\uff0c\u4ece\u800c\u5f15\u53d1\u4e00\u573a\u65e0\u9650\u66b4\u529b\u7684\u6d77\u5578\u3002\u8fd9\u6837\u7684\u6d77\u5578\u5728\u7269\u7406\u4e0a\u662f\u4e0d\u53ef\u80fd\u7684\uff0c\u56e0\u4e3a\u5728\u73b0\u5b9e\u4e16\u754c\u4e2d\u6ca1\u6709\u4efb\u4f55\u6ce2\u6d6a\u80fd\u591f\u5bb9\u7eb3\u65e0\u9650\u7684\u80fd\u91cf\u3002\u56e0\u6b64\uff0c\u4efb\u4f55\u53d1\u73b0\u8be5\u7b97\u6cd5\u8005\u90fd\u5c06\u8bc1\u660e\u6d41\u4f53\u7406\u8bba\uff0c\u5373\u7eb3\u7ef4-\u65af\u6258\u514b\u65af\u65b9\u7a0b<\/span>\uff08Navier-Stokes equations\uff09<\/span>\uff0c\u53ef\u9884\u6d4b\u4e0d\u53ef\u80fd\u73b0\u8c61\u3002\u8fd9\u6210\u4e3a\u53c8\u4e00\u9879\u767e\u4e07\u7f8e\u5143\u96be\u9898[19]\u3002<\/span><\/section>\n
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\uff08Eva Miranda\u8bc1\u5b9e\uff1a\u6d41\u4f53\u7684\u6d41\u52a8\u590d\u6742\u5230\u8f68\u8ff9\u4e0d\u53ef\u5224\u5b9a\u3002\u2014\u2014Jordi Cortada\uff09<\/span><\/section>\n

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Miranda\u4e0eRobert Cardona\u3001Daniel Peralta-Salas\u3001Francisco Presas\u5408\u4f5c\u3002\u4ed6\u4eec\u4ece\u4e00\u79cd\u9075\u5faa\u66f4\u7b80\u5355\u65b9\u7a0b\u7684\u6d41\u4f53\u5f00\u59cb\u3002\u4ed6\u4eec\u5c06\u56fe\u7075\u673a\u7684\u7eb8\u5e26\u8f6c\u6362\u4e3a\u5e73\u9762\u4e0a\u7684\u4e00\u4e2a\u4f4d\u7f6e<\/span>\uff08\u7c7b\u4f3c\u4e8e\u6469\u5c14\u5f39\u7403\u7bb1\u7684\u5e95\u90e8\uff09<\/span>\u3002\u968f\u7740\u56fe\u7075\u673a\u7684\u8fd0\u884c\uff0c\u5e73\u9762\u4e0a\u7684\u8fd9\u4e2a\u70b9\u4f1a\u4e0d\u65ad\u8df3\u8dc3\u3002\u7136\u540e\uff0c\u901a\u8fc7\u4e00\u7cfb\u5217\u51e0\u4f55\u53d8\u6362\uff0c\u4ed6\u4eec\u80fd\u591f\u5c06\u8fd9\u4e2a\u70b9\u7684\u8df3\u8dc3\u8f6c\u5316\u4e3a\u6d41\u4f53\u5728\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u6d41\u52a8\u7684\u5e73\u6ed1\u7535\u6d41<\/span>\uff08\u5c3d\u7ba1\u8fd9\u662f\u4e00\u4e2a\u4e2d\u5fc3\u5377\u66f2\u6210\u751c\u751c\u5708\u5f62\u72b6\u7684\u5947\u602a\u6d41\u4f53\uff09<\/span>\u3002\u4e3a\u4e86\u5728Zoom\u4e0a\u6f14\u793a\u8fd9\u4e00\u6982\u5ff5\uff0cMiranda\u4ece\u7535\u8111\u540e\u9762\u62ff\u51fa\u4e86\u4e00\u53ea\u6a61\u76ae\u9e2d\u6765\u8fdb\u884c\u6f14\u793a\u3002<\/span><\/section>\n

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\u201c\u5f53\u6c34\u4e2d\u7684\u70b9<\/span>\uff08\u53ef\u80fd\u662f\u4e00\u53ea\u9e2d\u5b50\uff09<\/span>\u7684\u8f68\u8ff9\u79fb\u52a8\u65f6\uff0c\u8fd9\u4e0e\u56fe\u7075\u673a\u7684\u7eb8\u5e26\u4ee5\u67d0\u79cd\u65b9\u5f0f\u524d\u8fdb\u662f\u76f8\u540c\u7684\uff0c\u201d\u5979\u89e3\u91ca\u9053\u3002<\/span><\/section>\n

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\u800c\u56fe\u7075\u673a\u5e26\u6765\u4e86\u4e0d\u53ef\u5224\u5b9a\u6027\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u8ba1\u7b97\u505c\u673a\u5bf9\u5e94\u4e8e\u5c06\u9e2d\u5b50\u5e26\u5230\u67d0\u4e2a\u7279\u5b9a\u533a\u57df\u7684\u7535\u6d41\uff0c\u800c\u6c38\u65e0\u6b62\u5883\u7684\u8ba1\u7b97\u5219\u5bf9\u5e94\u4e8e\u9e2d\u5b50\u6c38\u8fdc\u907f\u5f00\u90a3\u4e2a\u70b9\u7684\u7535\u6d41\u3002\u56e0\u6b64\uff0c\u8be5\u56e2\u961f\u57282021\u5e74\u53d1\u8868\u7684\u4e00\u7bc7\u8bba\u6587[20]\u4e2d\u8bc1\u660e\uff1a\u5224\u5b9a\u9e2d\u5b50\u6700\u7ec8\u547d\u8fd0\u65e0\u6cd5\u5b9e\u73b0\u3002<\/span><\/section>\n

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\u5c3d\u7ba1\u8fd9\u4e9b\u7cfb\u7edf\u5177\u6709\u7269\u7406\u4e0a\u4e0d\u5408\u7406\u7684\u7279\u6027\uff0c\u4f7f\u5f97\u5b9e\u9a8c\u8005\u65e0\u6cd5\u6784\u5efa\u5b83\u4eec\uff0c\u4f46\u5373\u4f7f\u4f5c\u4e3a\u84dd\u56fe\uff0c\u5b83\u4eec\u4e5f\u8868\u660e\u8ba1\u7b97\u673a\u53ca\u5176\u4e0d\u53ef\u5224\u5b9a\u95ee\u9898\u5df2\u6df1\u6df1\u5d4c\u5165\u7269\u7406\u5b66\u7684\u67b6\u6784\u4e2d\u3002<\/span><\/section>\n

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\u201c<\/span>\u6ca1\u6709\u4eba\u77e5\u9053\u73b0\u5b9e\u4e2d\u662f\u5426\u5305\u542b\u8fd9\u4e9b\u65e0\u9650\u6027\uff0c\u4f46\u5b9e\u9a8c\u80af\u5b9a\u6ca1\u6709\u3002\u201d<\/span><\/section>\n<\/blockquote>\n

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\u201c\u6211\u4eec\u751f\u6d3b\u5728\u4e00\u4e2a\u53ef\u4ee5\u6784\u5efa\u8ba1\u7b97\u673a\u7684\u5b87\u5b99\u4e2d\uff0c\u201dMoore\u572812\u6708\u4e00\u4e2a\u9633\u5149\u660e\u5a9a\u7684\u4e0b\u5348\uff0c\u901a\u8fc7Zoom\u4ece\u4ed6\u4f4d\u4e8e\u5723\u5854\u83f2<\/span>\uff08Santa Fe\uff09<\/span>\u7684\u540e\u9662\u82b1\u56ed\u4e2d\u544a\u8bc9\u6211\uff0c\u201c\u8ba1\u7b97\u65e0\u5904\u4e0d\u5728\u3002\u201d<\/span><\/section>\n

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\u7136\u800c\uff0c\u5373\u4f7f\u6709\u4eba\u8bd5\u56fe\u6784\u5efa\u8fd9\u4e9b\u84dd\u56fe\u4e2d\u63cf\u7ed8\u7684\u673a\u5668\uff0c\u7814\u7a76\u4eba\u5458\u4e5f\u6307\u51fa\uff0c\u4e0d\u53ef\u5224\u5b9a\u6027\u662f\u7269\u7406\u7406\u8bba\u7684\u7279\u6027\uff0c\u65e0\u6cd5\u5728\u771f\u5b9e\u5b9e\u9a8c\u4e2d\u771f\u6b63\u5b58\u5728\u3002\u53ea\u6709\u6d89\u53ca\u65e0\u9650\u6027\u7684\u7406\u60f3\u5316\u7cfb\u7edf\u2014\u2014\u65e0\u9650\u957f\u7684\u7eb8\u5e26\u3001\u65e0\u9650\u6269\u5c55\u7684\u7c92\u5b50\u7f51\u683c\u3001\u65e0\u9650\u53ef\u5206\u7684\u7a7a\u95f4\u6765\u653e\u7f6e\u5f39\u7403\u548c\u6a61\u76ae\u9e2d\u2014\u2014\u624d\u53ef\u80fd\u771f\u6b63\u4e0d\u53ef\u5224\u5b9a\u3002\u6ca1\u6709\u4eba\u77e5\u9053\u73b0\u5b9e\u4e2d\u662f\u5426\u5305\u542b\u8fd9\u4e9b\u65e0\u9650\u6027\uff0c\u4f46\u5b9e\u9a8c\u80af\u5b9a\u6ca1\u6709\u3002<\/strong>\u5b9e\u9a8c\u5ba4\u5de5\u4f5c\u53f0\u4e0a\u7684\u6bcf\u4e2a\u7269\u4f53\u90fd\u6709\u6709\u9650\u6570\u91cf\u7684\u5206\u5b50\uff0c\u6bcf\u4e2a\u6d4b\u91cf\u7684\u4f4d\u7f6e\u90fd\u6709\u6709\u9650\u5c0f\u6570\u4f4d\u3002<\/span><\/section>\n

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\u201c\u4f60\u8bd5\u56fe\u63ed\u793a\u5b87\u5b99\u6216\u6570\u5b66\u7684\u8fd0\u884c\u89c4\u5f8b\uff0c\u201dCubitt\u8bf4\uff0c\u201c\u8bc1\u660e\u95ee\u9898\u672c\u8eab\u65e0\u89e3\u7684\u4e8b\u5b9e\uff0c\u5c31\u662f\u7b54\u6848\u3002\u201d<\/span><\/section>\n

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\u53c2\u8003\u6587\u732e<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n

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1.https:\/\/www.dr-qubit.org\/qubit.html<\/span><\/section>\n
2.https:\/\/web.mat.upc.edu\/eva.miranda\/nova\/<\/span><\/section>\n
3.https:\/\/www.santafe.edu\/people\/profile\/david-wolpert<\/span><\/section>\n
4.https:\/\/sites.santafe.edu\/~moore\/<\/span><\/section>\n
5.https:\/\/www.cs.virginia.edu\/~robins\/Turing_Paper_1936.pdf<\/span><\/section>\n
6.https:\/\/www.quantamagazine.org\/how-godels-proof-works-20200714\/<\/span><\/section>\n
7.https:\/\/journals.aps.org\/prl\/abstract\/10.1103\/PhysRevLett.64.2354<\/span><\/section>\n
8.https:\/\/www.ucm.es\/mathqi\/david-perez-garcia<\/span><\/section>\n
9.https:\/\/journals.aps.org\/prl\/abstract\/10.1103\/PhysRevLett.54.735<\/span><\/section>\n
10.https:\/\/www.sciencedirect.com\/science\/article\/abs\/pii\/0167278984902550<\/span><\/section>\n
11.https:\/\/www.math.cit.tum.de\/en\/math\/people\/professors\/wolf-michael\/<\/span><\/section>\n
12.https:\/\/www.claymath.org\/millennium\/yang-mills-the-maths-gap\/<\/span><\/section>\n
13.https:\/\/arxiv.org\/abs\/1502.04573<\/span><\/section>\n
14.Cubitt, T., Perez-Garcia, D. & Wolf, M. Undecidability of the spectral gap. Nature<\/em> 528<\/strong>, 207\u2013211 (2015). https:\/\/doi.org\/10.1038\/nature16059https:\/\/www.nature.com\/articles\/nature16059<\/span><\/section>\n
15.https:\/\/journals.aps.org\/prx\/abstract\/10.1103\/PhysRevX.10.031038<\/span><\/section>\n
16.https:\/\/arxiv.org\/abs\/2410.02600<\/span><\/section>\n
17.https:\/\/www.nature.com\/articles\/s41467-021-25053-0<\/span><\/section>\n
18.https:\/\/www.quantamagazine.org\/a-fluid-new-path-in-grand-math-challenge-20140224\/<\/span><\/section>\n
19.https:\/\/www.claymath.org\/millennium\/navier-stokes-equation\/<\/span><\/section>\n
20.https:\/\/www.pnas.org\/doi\/10.1073\/pnas.2026818118<\/span><\/section>\n
21.http:\/\/tph.tuwien.ac.at\/~svozil\/<\/span><\/section>\n


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\uff08\u53c2\u8003\u6587\u732e\u53ef\u4e0a\u4e0b\u6ed1\u52a8<\/strong>\u67e5\u770b\uff09<\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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<\/section>\n

\u5176\u4ed6\u63a8\u8350\u9605\u8bfb\uff1a<\/span><\/strong><\/p>\n

With Fifth Busy Beaver, Researchers Approach Computation\u2019s Limits, https:\/\/www.quantamagazine.org\/amateur-mathematicians-find-fifth-busy-beaver-turing-machine-20240702\/<\/span><\/section>\n
How Many Numbers Exist? Infinity Proof Moves Math Closer to an Answer.https:\/\/www.quantamagazine.org\/how-many-numbers-exist-infinity-proof-moves-math-closer-to-an-answer-20210715\/<\/span><\/span><\/section>\n

The Hidden Heroines of Chaos, https:\/\/www.quantamagazine.org\/the-hidden-heroines-of-chaos-20190520\/<\/span><\/p>\n


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\u975e\u5e73\u8861\u7edf\u8ba1\u7269\u7406\u8bfb\u4e66\u4f1a\u542f\u52a8\uff01<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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2024\u5e74\u8bfa\u8d1d\u5c14\u7269\u7406\u5b66\u5956\u6388\u4e88\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\uff0c\u8fd9\u662f\u4e00\u573a\u7edf\u8ba1\u7269\u7406\u5f15\u53d1\u7684\u673a\u5668\u5b66\u4e60\u9769\u547d\u3002\u7edf\u8ba1\u7269\u7406\u5b66\u4e0d\u4ec5\u80fd\u89e3\u91ca\u70ed\u5b66\u73b0\u8c61\uff0c\u8fd8\u80fd\u5e2e\u52a9\u6211\u4eec\u7406\u89e3\u4ece\u5fae\u89c2\u7c92\u5b50\u5230\u5b8f\u89c2\u5b87\u5b99\u7684\u5404\u4e2a\u5c42\u7ea7\u5982\u4f55\u8054\u7cfb\u8d77\u6765\uff0c\u590d\u6742\u73b0\u8c61\u5982\u4f55\u6d8c\u73b0\u3002\u5b83\u901a\u8fc7\u7814\u7a76\u5927\u91cf\u7c92\u5b50\u7684\u96c6\u4f53\u884c\u4e3a\uff0c\u6210\u529f\u5730\u5c06\u5fae\u89c2\u4e16\u754c\u7684\u968f\u673a\u6027\u4e0e\u5b8f\u89c2\u4e16\u754c\u7684\u786e\u5b9a\u6027\u8054\u7cfb\u8d77\u6765\uff0c\u4e3a\u6211\u4eec\u7406\u89e3\u81ea\u7136\u754c\u63d0\u4f9b\u4e86\u5f3a\u5927\u7684\u5de5\u5177\uff0c\u4e5f\u4e3a\u673a\u5668\u5b66\u4e60\u548c\u4eba\u5de5\u667a\u80fd\u9886\u57df\u7684\u53d1\u5c55\u63d0\u4f9b\u4e86\u91cd\u8981\u63a8\u52a8\u529b\u3002<\/span><\/p>\n


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\u70b9\u51fb\u201c\u9605\u8bfb\u539f\u6587\u201d\uff0c\u62a5\u540d\u8bfb\u4e66\u4f1a<\/span><\/section>\n<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

\u5bfc\u8bed \u5728\u6570\u5b66\u548c\u8ba1\u7b97\u673a\u79d1\u5b66\u9886\u57df\uff0c\u7814\u7a76\u4eba\u5458\u65e9\u5df2\u660e\u767d\uff0c\u6709\u4e9b\u95ee\u9898\u4ece\u6839\u672c\u4e0a\u5c31\u65e0\u89e3\u3002\u5982\u4eca\uff0c\u7269\u7406\u5b66\u5bb6\u6b63\u5728\u63a2\u7d22\uff0c\u5373\u4f7f\u662f\u666e\u901a\u7684\u7269\u7406\u7cfb\u7edf\uff0c\u4e5f\u4f1a\u5bf9\u6211\u4eec\u80fd\u591f\u9884\u6d4b\u7684\u5185\u5bb9\u8bbe\u7f6e\u4e25\u683c\u7684\u9650\u5236\uff0c\u751a\u81f3\u5728\u7406\u8bba\u4e0a\u4e5f\u662f\u5982\u6b64\u3002 \u7814\u7a76\u9886\u57df\uff1a\u4e0d\u53ef\u5224\u5b9a\u6027\u3001\u6df7\u6c8c\u7cfb\u7edf\u3001\u62c9\u666e\u62c9\u65af\u5996\u3001\u91cf\u5b50\u529b\u5b66\u3001\u56fe\u7075\u505c\u673a\u95ee\u9898\u3001\u80fd\u9699\u95ee\u9898\u3001\u81ea\u6307\u7cfb\u7edf\u3001\u9884\u6d4b\u6781\u9650 Charlie Wo…<\/p>\n","protected":false},"author":1,"featured_media":57520,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"special":[],"_links":{"self":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/57533"}],"collection":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=57533"}],"version-history":[{"count":0,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/57533\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/media\/57520"}],"wp:attachment":[{"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=57533"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=57533"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=57533"},{"taxonomy":"special","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fspecial&post=57533"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}