{"id":21251,"date":"2020-10-14T14:30:00","date_gmt":"2020-10-14T06:30:00","guid":{"rendered":"https:\/\/swarma.org\/?p=21251"},"modified":"2020-10-14T14:30:00","modified_gmt":"2020-10-14T06:30:00","slug":"%e2%80%8b%e8%9d%b4%e8%9d%b6%e6%95%88%e5%ba%94%e5%92%8c%e6%b7%b7%e6%b2%8c%e6%95%85%e4%ba%8b-%e9%99%88%e5%85%b3%e8%8d%a3","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=21251","title":{"rendered":"\u200b\u8774\u8776\u6548\u5e94\u548c\u6df7\u6c8c\u6545\u4e8b | \u9648\u5173\u8363"},"content":{"rendered":"
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\u2014\u2014\u7231\u5fb7\u534e\u00b7\u8bfa\u987f\u00b7<\/span><\/span><\/strong><\/span>\u6d1b<\/span><\/span><\/span>\u4f26\u8328<\/span><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n


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\u4ed6\u4e0d\u662f\u6587\u5b66\u5bb6\uff0c\u5374\u5728\u4e0d\u7ecf\u610f\u95f4\u7559\u4e0b\u4e86\u4e00\u4e2a\u810d\u7099\u4eba\u53e3\u7684\u65b0\u6210\u8bed\uff1a\u8774\u8776\u6548\u5e94\u3002<\/span><\/p>\n


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\u4ed6\u662f\u9ebb\u7701\u7406\u5de5\u5b66\u9662<\/span>\uff08MIT\uff09<\/span>\u6c14\u8c61\u7cfb\u5df2\u6545\u6559\u6388\u7231\u5fb7\u534e\u00b7\u8bfa\u987f\u00b7\u6d1b\u4f26\u8328<\/span>\uff08Edward Norton Lorenz\uff0c1917\u5e745\u670823\u65e5\uff0d2008\u5e744\u670816\u65e5\uff09<\/span>\u3002<\/span><\/p>\n


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Edward Norton Lorenz<\/span><\/p>\n


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1961\u5e74\u7684\u4e00\u5929\uff0c\u4ed6\u548c\u540c\u5728\u201cMIT\u4e00\u822c\u73af\u6d41\u7814\u7a76\u9879\u76ee\u201d\u5de5\u4f5c\u800c\u540e\u6765\u6210\u4e3a\u201c\u73b0\u4ee3\u6c14\u5019\u7406\u8bba\u4e4b\u7236\u201d\u7684\u5df4\u91cc\u00b7\u8428\u5c14\u8328\u66fc<\/span>\uff08Barry Saltzman\uff09<\/span>\u6559\u6388\u4e00\u8d77\u63a2\u8ba8\u4e86\u4ed6\u7684\u6a21\u578b\u7b80\u5316\u95ee\u9898\u3002\u90a3\u65f6\u8428\u5c14\u8328\u66fc\u6b63\u5728\u7814\u7a76\u975e\u7ebf\u6027Benard\u5bf9\u6d41\uff0c\u901a\u8fc7\u8c31\u5c55\u5f00\u5f97\u5230\u4e867\u4e2a\u53d8\u91cf\u7684\u964d\u9636\u975e\u7ebf\u6027\u65b9\u7a0b\u7ec4\u3002\u8428\u5c14\u8328\u66fc\u544a\u8bc9\u6d1b\u4f26\u8328\uff0c\u8bf4\u4ed6\u5f97\u5230\u4e86\u4e00\u4e9b\u5468\u671f\u89e3\uff0c\u4f46\u4e5f\u6709\u4e0d\u7a33\u5b9a\u7684\u89e3\u3002\u6d1b\u4f26\u8328\u4ed4\u7ec6\u89c2\u5bdf\u4e86\u90a3\u4e9b\u7ed3\u679c\uff0c\u53d1\u73b07\u4e2a\u53d8\u91cf\u4e2d\u76844\u4e2a\u5468\u671f\u89e3\u5f88\u5feb\u8870\u51cf\u4ece\u800c\u53d8\u5f97\u4e0d\u91cd\u8981\u4e86\uff0c\u800c\u5176\u4ed63\u4e2a\u5219\u4f1a\u4fdd\u6301\u957f\u65f6\u95f4\u7684\u975e\u5468\u671f\u6027\u53d8\u5316\u3002\u6d1b\u4f26\u8328\u975e\u5e38\u611f\u6fc0\u8428\u5c14\u8328\u66fc\u7684\u5b9e\u9a8c\u7ed3\u679c\u7ed9\u4ed6\u63d0\u4f9b\u7684\u542f\u793a\uff0c\u611f\u89c9\u5230\u7c7b\u4f3c\u8fd9\u6837\u76843\u4e2a\u53d8\u91cf\u65b9\u7a0b\u7ec4\u5e94\u8be5\u8db3\u4ee5\u7528\u6765\u63cf\u8ff0\u4ed6\u6240\u671f\u671b\u7684\u6c14\u6d41\u8fd0\u52a8\u7684\u975e\u5468\u671f\u6027\u3002\u679c\u7136\uff0c\u4ed6\u5c06\u81ea\u5df1\u7684\u6a21\u578b\u4f5c\u4e86\u76f8\u5e94\u7684\u7b80\u5316\u540e\uff0c\u4ec5\u4fdd\u7559\u4e863\u4e2a\u53d8\u91cf\uff0c\u53d1\u73b0\u80fd\u591f\u89c2\u5bdf\u5230\u975e\u5468\u671f\u6027\u52a8\u529b\u5b66\u73b0\u8c61\u3002<\/span><\/p>\n


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\u5f53\u5e74\u6d1b\u4f26\u8328\u6c42\u89e3\u8fd93\u4e2a\u53d8\u91cf\u7684\u65b9\u7a0b\u7ec4\u7528\u7684\u662f\u4e00\u53f0Royal McBee LGP-30\u8ba1\u7b97\u673a\uff0c\u653e\u7f6e\u5728MIT\u7b2c24\u53f7\u697c\u7b2c\u4e94\u5c42\u3002\u8fd9\u53f0\u673a\u5668\u6bd4\u4e66\u684c\u8fd8\u5927\uff0c\u91cd\u7ea6260\u516c\u65a4\uff0c\u53ef\u662f\u901f\u5ea6\u6781\u5176\u7f13\u6162\uff0c\u8fde\u4eca\u5929\u7684\u7b14\u8bb0\u672c\u7535\u8111\u90fd\u6bd4\u5b83\u5feb\u4e0a\u4e00\u767e\u4e07\u500d\u3002\u5f53\u5e74\uff0c\u8ba1\u7b97\u673a\u7a0b\u5e8f\u662f\u7531\u4e24\u4f4d\u5e74\u8f7b\u5973\u52a9\u624b\u827e\u4f26\u00b7\u8d39\u7279<\/span>\uff08Ellen Fetter\uff09<\/span>\u548c\u739b\u683c\u4e3d\u7279\u00b7\u54c8\u5bc6\u987f<\/span>\uff08Margaret Hamilton\uff09<\/span>\u8d1f\u8d23\u7f16\u5199\u7684\u3002\u827e\u4f26\u548c\u739b\u683c\u4e3d\u7279\u5206\u522b\u4eceMount Holyoke College\u548cEarlham College \u6570\u5b66\u4e13\u4e1a\u672c\u79d1\u6bd5\u4e1a\uff0c\u4e24\u4eba\u6765\u5230\u6d1b\u4f26\u8328\u5b9e\u9a8c\u5ba4\u5de5\u4f5c\u540e\u624d\u5f00\u59cb\u5b66\u4e60\u7f16\u5199\u8ba1\u7b97\u673a\u7a0b\u5e8f\u3002\u4e0d\u8fc7\u5979\u4fe9\u90fd\u5f88\u79f0\u804c\u3002\u7279\u522b\u503c\u5f97\u4e00\u63d0\u7684\u662f\u90a3\u4f4d\u54c8\u5bc6\u987f\u5973\u58eb\uff0c\u806a\u660e\u7684\u5979\u5f88\u5feb\u5c31\u6210\u4e3a\u4e00\u4f4d\u7f16\u7a0b\u80fd\u624b\u3002\u5979\u79bb\u5f00MIT\u6bd4\u8f83\u65e9\uff0c\u540e\u6765\u52a0\u76df\u56fd\u5bb6\u5b87\u822a\u5c40<\/span>\uff08NASA\uff09<\/span>\uff0c\u5148\u540e\u4e3a\u767b\u6708\u98de\u8239\u7f16\u5199\u63a7\u5236\u7a0b\u5e8f\u548c\u4e3a\u7a7a\u4e2d\u8bd5\u9a8c\u5ba4<\/span>\uff08Skylab\uff09<\/span>\u7f16\u5199\u64cd\u4f5c\u8f6f\u4ef6\uff0c2003\u5e74\u83b7NASA\u6388\u4e88\u822a\u5929\u6770\u51fa\u8d21\u732e\u5956<\/span>\uff08Exceptional Space Act Award\uff09<\/span>\uff0c2016\u5e74\u8363\u81ba\u7f8e\u56fd\u603b\u7edf\u81ea\u7531\u52cb\u7ae0<\/span>\uff08Presidential Medal of Freedom\uff09<\/span>\uff0c2017\u5e74\u8fd8\u88ab\u4e50\u9ad8<\/span>\uff08LEGO\uff09<\/span>\u6e38\u620f\u4ea7\u54c1\u9009\u5b9a\u4e3a\u6210\u529f\u5973\u58eb\u5076\u50cf\u4eba\u7269\u3002<\/span><\/p>\n


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Royal McBee LGP-30\u8ba1\u7b97\u673a<\/span><\/p>\n


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\u7ecf\u8fc7\u53cd\u590d\u6838\u67e5\uff0c\u5728\u6392\u9664\u4e86\u8ba1\u7b97\u673a\u6545\u969c\u7684\u53ef\u80fd\u6027\u4e4b\u540e\uff0c\u4ed6\u6ce8\u610f\u5230\u4e86\u4e24\u6b21\u4eff\u771f\u8bd5\u9a8c\u8fc7\u7a0b\u4e4b\u95f4\u7684\u4e00\u4e2a\u5fae\u5c0f\u5dee\u5f02\u3002\u5f53\u65f6\u7684\u8ba1\u7b97\u673a\u8fd0\u7b97\u7cbe\u786e\u5ea6\u662f\u4fdd\u7559\u5c0f\u6570\u70b9\u540e6\u4f4d\u6570\u5b57\u7684\uff0c\u56e0\u6b64\u4ed6\u5728\u7b2c\u4e00\u6b21\u8ba1\u7b97\u4e2d\u8f93\u5165\u4e86\u521d\u59cb\u503c0.506127\u3002\u4f46\u5728\u7b2c\u4e8c\u6b21\u8ba1\u7b97\u4e2d\uff0c\u4ed6\u56fe\u7701\u4e8b\u8f93\u5165\u4e860.506\uff0c\u89c9\u5f97\u8fd9\u4e0d\u5230\u5343\u5206\u4e4b\u4e00\u7684\u201c\u56db\u820d\u4e94\u5165\u201d\u4e0d\u4f1a\u5e26\u6765\u4ec0\u4e48\u5f71\u54cd\u3002\u73b0\u5728\u4ed6\u53d1\u73b0\u81ea\u5df1\u9519\u4e86\uff0c\u8fd9\u5f71\u54cd\u5176\u5b9e\u5927\u5f97\u5f88\u3002<\/span><\/p>\n


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\u5386\u53f2\u4e0a\u8bb8\u591a\u91cd\u5927\u673a\u9047\u90fd\u51fa\u73b0\u5728\u8fd9\u79cd\u6beb\u4e0d\u663e\u773c\u7684\u4e8b\u60c5\u548c\u6beb\u4e0d\u60ca\u4eba\u7684\u65f6\u523b\uff1a0.506\u4e0d\u591f\u7cbe\u786e\u4e48\uff1f\u6539\u4e3a0.506127\u518d\u7b97\u4e00\u904d\u5c31\u597d\u4e86\u561b\uff0c\u8fd8\u6765\u5f97\u53ca\u53bb\u591a\u559d\u676f\u5496\u5561\u5462\u3002\u7136\u800c\uff0c\u51fa\u8272\u7684\u79d1\u5b66\u5bb6\u548c\u666e\u901a\u7684\u5b9e\u9a8c\u5458\u4e4b\u95f4\u7684\u5dee\u522b\u53ef\u80fd\u5c31\u5728\u8fd9\u4e2a\u5730\u65b9\uff1a\u6d1b\u4f26\u8328\u89c9\u5f97\u8fd9\u4e0d\u5230\u5343\u5206\u4e4b\u4e00\u7684\u8bef\u5dee\u6240\u5e26\u6765\u7684\u5de8\u5927\u5f71\u54cd\u4ece\u5e38\u7406\u6765\u8bf4\u4e0d\u53ef\u601d\u8bae\uff0c\u6b64\u4e8b\u5fc5\u987b\u6709\u4e2a\u6570\u5b66\u89e3\u91ca\u3002\u968f\u540e\u7684\u51e0\u5929\u91cc\uff0c\u4ed6\u548c\u4e24\u4f4d\u7a0b\u5e8f\u5458\u4e00\u8d77\u518d\u6b21\u91cd\u590d\u4e86\u4e24\u79cd\u4e0d\u540c\u521d\u503c\u7684\u4eff\u771f\uff0c\u8bc1\u5b9e\u4e86\u4ed6\u609f\u51fa\u7684\u9053\u7406\uff1a\u7531\u4e8e\u8be5\u6570\u5b66\u6a21\u578b\u5bf9\u521d\u59cb\u6761\u4ef6\u5177\u6709\u9ad8\u5ea6\u654f\u611f\u6027\uff0c\u4e00\u4e2a\u5fae\u5c0f\u7684\u521d\u59cb\u8bef\u5dee\u968f\u7740\u53cd\u590d\u8fed\u4ee3\u8ba1\u7b97\u6700\u7ec8\u917f\u6210\u5de8\u5927\u7684\u7ed3\u679c\u5dee\u5f02\uff0c\u5bfc\u81f4\u4e86\u6a21\u578b\u672a\u6765\u884c\u4e3a\u7684\u201c\u4e0d\u53ef\u9884\u6d4b\u6027\u201d!<\/span><\/p>\n


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\u5bf9\u521d\u59cb\u6761\u4ef6\u7684\u9ad8\u5ea6\u654f\u611f\u6027<\/span><\/p>\n


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\u6d1b\u4f26\u8328\u628a\u4ed6\u7684\u53d1\u73b0\u5199\u6210\u4e86\u8bba\u6587\u201c\u786e\u5b9a\u6027\u7684\u975e\u5468\u671f\u6d41\u201d\uff0c\u4e8e1963\u5e74\u53d1\u8868\u5728\u300a\u5927\u6c14\u79d1\u5b66\u300b\u6742\u5fd7<\/span>\uff08\u201cDeterministic nonperiodic flow\u201d\uff0cJournal of the Atmospheric Sciences<\/em>, 20: 130-141, 1963\uff09<\/span>\u3002<\/span><\/p>\n


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\u6d1b\u4f26\u8328\u5f53\u65f6\u89c9\u5f97\u4ed6\u53d1\u73b0\u7684\u53ef\u80fd\u53ea\u662f\u6d41\u4f53\u529b\u5b66\u4e2d\u6e4d\u6d41\u7684\u4e00\u4e2a\u65b0\u7279\u5f81\uff0c\u6295\u7a3f\u65f6\u628a\u8bba\u6587\u6807\u9898\u62df\u5b9a\u4e3a\u201c\u786e\u5b9a\u6027\u7684\u6e4d\u6d41\u201d\u3002\u4f46\u6742\u5fd7\u7f16\u8f91\u5bf9\u6b64\u9887\u6709\u6000\u7591\u3002\u4e8e\u662f\u4ed6\u628a\u201c\u6e4d\u6d41\u201d\u6539\u6210\u4e86\u201c\u975e\u5468\u671f\u6d41\u201d\u3002\u6d1b\u4f26\u8328\u5728\u8bba\u6587\u4e2d\u6307\u51fa\uff1a\u201c\u4e24\u4e2a\u72b6\u6001\u4e4b\u95f4\u4e0d\u88ab\u5bdf\u89c9\u7684\u5fae\u5c0f\u5dee\u522b\u53ef\u80fd\u6700\u540e\u6f14\u5316\u4e3a\u5de8\u5927\u7684\u4e0d\u540c\u2026\u2026\u56e0\u6b64\uff0c\u5982\u679c\u5728\u89c2\u5bdf\u5f53\u524d\u72b6\u6001\u65f6\u4e0d\u7ba1\u6709\u4ec0\u4e48\u6837\u7684\u8bef\u5dee\u2014\u2014\u5728\u4efb\u4f55\u771f\u5b9e\u7cfb\u7edf\u4e2d\u8fd9\u4e9b\u8bef\u5dee\u662f\u4e0d\u53ef\u907f\u514d\u7684\u2014\u2014\u90a3\u4e48\u5bf9\u4e8e\u4e00\u4e2a\u4e0d\u592a\u4e45\u8fdc\u7684\u672a\u6765\u77ac\u95f4\u72b6\u6001\u505a\u51fa\u4efb\u4f55\u53ef\u63a5\u53d7\u7684\u9884\u6d4b\u90fd\u5c06\u662f\u4e0d\u53ef\u80fd\u7684\u2026\u2026\u975e\u5e38\u957f\u671f\u7684\u51c6\u786e\u5929\u6c14\u9884\u62a5\u770b\u6765\u5e76\u4e0d\u5b58\u5728\u3002\u201d\u5f53\u5e74\u6d1b\u4f26\u8328\u4f30\u7b97\uff0c\u51c6\u786e\u7684\u5929\u6c14\u9884\u62a5\u6700\u591a\u5728\u4e24\u5468\u65f6\u95f4\u4e4b\u5185\u53ef\u4ee5\u505a\u5230\u3002\u4e8b\u5b9e\u4e0a\uff0c\u4eca\u5929\u5728\u9ad8\u901f\u8ba1\u7b97\u673a\u548c\u5927\u6570\u636e\u652f\u6301\u4e0b\uff0c\u8fd9\u4e2a\u65f6\u95f4\u6bb5\u4e5f\u8fbe\u4e0d\u5230\u4e09\u5468\u3002<\/span><\/p>\n


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\u5728\u8bba\u6587\u672b\u5c3e\uff0c\u6d1b\u4f26\u8328\u8bda\u631a\u5730\u611f\u8c22\u4e86\u5df4\u91cc\u00b7\u8428\u5c14\u8328\u66fc\u548c\u827e\u4f26\u00b7\u8d39\u7279\u3002\u63a5\u4e0b\u6765\uff0c\u4ed6\u5728\u53e6\u4e00\u7bc7\u8bba\u6587\u4e2d\u4e5f\u540c\u6837\u5730\u81f4\u8c22\u4e86\u739b\u683c\u4e3d\u7279\u00b7\u54c8\u5bc6\u987f\u3002<\/span><\/p>\n


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\u57281963\u5e74\u8fd9\u7bc7\u91cc\u7a0b\u7891\u5f0f\u7684\u8bba\u6587\u4e2d\uff0c\u6d1b\u4f26\u8328\u7ed9\u51fa\u4e86\u523b\u753b\u4e0a\u8ff03\u4e2a\u4e3b\u8981\u53d8\u91cf\u7684\u975e\u7ebf\u6027\u65b9\u7a0b\u7ec4\uff0c\u5373\u4eca\u5929\u8457\u540d\u7684\u6d1b\u4f26\u8328\u7cfb\u7edf\u6216\u6d1b\u4f26\u8328\u65b9\u7a0b\uff1a<\/span><\/p>\n


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<\/section>\n


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\u5f53\u53c2\u6570 a = 10\uff0cb = 8\/3\uff0cc = 28\u65f6\uff0c\u6d1b\u4f26\u8328\u65b9\u7a0b\u7684\u89e3\u5728\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u7684\u8f68\u9053\u5448\u73b0\u4e00\u4e2a\u6f02\u4eae\u7684\u53cc\u6da1\u5377\u5f62\u72b6\u7684\u201c\u5438\u5f15\u5b50\u201d<\/span>\uff08attractor\uff09<\/span>\u3002<\/span><\/p>\n


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\u6d1b\u4f26\u8328\u5438\u5f15\u5b50<\/span><\/p>\n


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\u8fd9\u4e2a\u540e\u6765\u88ab\u79f0\u4e3a\u201c\u6d1b\u4f26\u8328\u5438\u5f15\u5b50\u201d\u7684\u51e0\u4f55\u5bf9\u8c61\u662f\u7a7a\u95f4\u4e2d\u4e00\u4e9b\u5e26\u7a33\u5b9a\u6027\u7684\u70b9\u7684\u96c6\u5408\uff0c\u5177\u6709\u67d0\u79cd\u52a8\u529b\u5b66\u7684\u5438\u5f15\u6027\uff0c\u6545\u79f0\u4e3a\u5438\u5f15\u5b50\u3002\u4f46\u8fd9\u4e2a\u70b9\u96c6\u5e76\u4e0d\u76f4\u89c2\u53ef\u89c1\u3002\u8ba1\u7b97\u673a\u753b\u51fa\u6765\u7684\u53ef\u89c6\u56fe\u53ea\u662f\u7ed5\u7740\u5438\u5f15\u5b50\u8fd0\u52a8\u7684\u65b9\u7a0b\u7684\u89e3\u8f68\u9053\uff0c\u5b83\u5904\u4e8e\u4e00\u79cd\u4e0d\u5bfb\u5e38\u7684\u6c38\u4e0d\u53d1\u6563\u3001\u6c38\u4e0d\u4f11\u6b62\u3001\u5e76\u4e14\u662f\u975e\u4e25\u683c\u5468\u671f\u7684\u201c\u6df7\u6c8c\u201d<\/span>\uff08chaos\uff09<\/span>\u8fd0\u52a8\u72b6\u6001\u3002\u5176\u4e2d\uff0c\u6df7\u6c8c\u8f68\u9053\u7684\u4e0d\u53d1\u6563\u7279\u5f81\u662f\u7531\u5b83\u7684\u5168\u5c40\u6709\u754c\u6027\u51b3\u5b9a\u7684\uff0c\u800c\u65e0\u4f11\u6b62\u7684\u8fd0\u52a8\u884c\u4e3a\u5219\u628a\u5b83\u533a\u522b\u4e8e\u901a\u5e38\u7684\u9aa8\u724c\u6548\u5e94\u3002\u6b64\u5916\uff0c\u89e3\u8f68\u9053\u7684\u975e\u4e25\u683c\u5468\u671f\u6027\u5c55\u73b0\u51fa\u5b83\u5bc6\u96c6\u7684\u8fd1\u4f3c\u5468\u671f\u6027\u8fd0\u52a8\uff0c\u4f46\u53c8\u4e0d\u4f1a\u4e25\u683c\u5730\u91cd\u590d\u8fc7\u53bb<\/span>\uff08\u7528\u6d1b\u4f26\u8328\u7684\u539f\u8bdd\u6765\u8bf4\uff0c\u5c31\u662f\u201csolutions which never repeat their past history exactly\u201d\uff09<\/span>\u3002<\/span><\/p>\n


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\u6b64\u5916\uff0c\u8fd9\u4e2a\u5fae\u5206\u65b9\u7a0b\u7ec4\u7684\u89e3\u7531\u521d\u59cb\u6761\u4ef6\u552f\u4e00\u51b3\u5b9a\uff0c\u5b83\u662f\u5b8c\u5168\u786e\u5b9a\u6027\u7684\u3002\u4ece\u65b9\u7a0b\u5f0f\u53ef\u4ee5\u770b\u51fa\uff0c\u5b83\u6ca1\u6709\u8bf8\u5982\u566a\u58f0\u6216\u5916\u6765\u5e72\u6270\u7684\u968f\u673a\u56e0\u7d20\u3002\u4f46\u7cfb\u7edf\u5bf9\u521d\u59cb\u72b6\u6001\u503c\u5177\u6709\u6781\u9ad8\u7684\u654f\u611f\u6027\uff0c\u8ba9\u5b83\u7684\u89e3\u8f68\u9053\u5728\u957f\u65f6\u95f4\u4e4b\u540e\u7684\u72b6\u6001\u53d8\u5f97\u4e0d\u53ef\u9884\u6d4b\u3002\u4eba\u4eec\u628a\u8fd9\u79cd\u7279\u6027\u79f0\u4e3a\u201c\u786e\u5b9a\u6027\u7684\u968f\u673a\u201d\u6216\u201c\u786e\u5b9a\u6027\u7684\u6df7\u6c8c\u201d\u3002\u7531\u4e8e\u6df7\u6c8c\u7cfb\u7edf\u7684\u89e3\u662f\u786e\u5b9a\u6027\u7684\uff0c\u5b83\u53ef\u4ee5\u7528\u5b8c\u5168\u76f8\u540c\u7684\u521d\u59cb\u6761\u4ef6\u6765\u91cd\u6f14\uff0c\u4f46\u5b83\u53c8\u5177\u6709\u4e0e\u4e0d\u53ef\u590d\u5236\u7684\u767d\u566a\u58f0\u76f8\u540c\u7684\u5404\u79cd\u968f\u673a\u7279\u6027\uff0c\u56e0\u6b64\u5728\u5de5\u7a0b\u5e94\u7528\u4e2d\u80fd\u6d3e\u4e0a\u4e00\u4e9b\u7279\u522b\u7528\u573a\u3002<\/span><\/p>\n


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\u5bf9\u975e\u4e13\u4e1a\u4eba\u58eb\u6765\u8bf4\uff0c\u5927\u62b5\u4e0a\u53ef\u4ee5\u8fd9\u6837\u76f4\u89c2\u5730\u53bb\u7406\u89e3\u6df7\u6c8c\u7cfb\u7edf\u53ca\u5176\u6df7\u6c8c\u7279\u6027\u3002<\/span><\/p>\n


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\u5e55\u540e\u82f1\u96c4\u827e\u4f26\u00b7\u8d39\u7279\u548c\u739b\u683c\u4e3d\u7279\u00b7\u54c8\u5bc6\u987f<\/span><\/section>\n
[Artwork by Olena Shmahalo\u300aQuanta\u300b2019-5-20]<\/span><\/section>\n


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\u8fd9\u91cc\u56de\u987e\u4e00\u4e0b\u5386\u53f2\u662f\u86ee\u6709\u8da3\u7684\u3002\u6d1b\u4f26\u8328\u7684\u4e0a\u8ff0\u8bba\u6587\u5e76\u6ca1\u6709\u4f7f\u7528chaos\u4e00\u8bcd\u3002\u5728\u79d1\u5b66\u6587\u732e\u4e2d\uff0cchaos\u4e00\u8bcd\u6700\u65e9\u7531MIT\u7684\u6570\u5b66\u5bb6\u8bfa\u4f2f\u7279\u00b7\u7ef4\u7eb3<\/span>\uff08Norbert Weiner\uff09<\/span>1938\u5e74\u9898\u4e3a\u201cThe homogeneous chaos\u201d\u7684\u8bba\u6587\u4e2d\u5f00\u59cb\u4f7f\u7528\uff0c\u4f46\u90a3\u662f\u5b8c\u5168\u4e0d\u4e00\u6837\u7684\u6570\u5b66\u6982\u5ff5\u3002\u7b2c\u4e00\u6b21\u6b63\u5f0f\u7528chaos\u6765\u63cf\u8ff0\u7cfb\u7edf\u5bf9\u521d\u59cb\u6761\u4ef6\u6781\u7aef\u654f\u611f\u7279\u6027\u7684\uff0c\u662f\u5df2\u6545\u6570\u5b66\u5bb6\u674e\u5929\u5ca9<\/span>\uff081945-2020\uff09<\/span>\u548c\u4ed6\u7684\u5bfc\u5e08\u8a79\u59c6\u65af\u00b7\u7ea6\u514b<\/span>\uff08James A. Yorke\uff0c1941-\uff09<\/span>\u57281975 \u5e74\u53d1\u8868\u7684\u9898\u4e3a\u201cPeriod three implies chaos\u201d\u8bba\u6587\u4e2d\u7684\u8457\u540dLi-Yorke\u5b9a\u7406\u3002\u4e0d\u8fc7\u90a3\u662f\u79bb\u6563\u7cfb\u7edf\u7684\u6df7\u6c8c\uff0c\u662f\u53e6\u4e00\u4e2a\u8bba\u9898\u4e86\u3002<\/span><\/p>\n


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\u6d1b\u4f26\u83281963\u5e74\u8fd9\u7bc7\u79d1\u5b66\u53d1\u73b0\u62a5\u544a\u53d1\u8868\u540e\uff0c\u521d\u65f6\u53ea\u6709\u51e0\u4e2a\u6c14\u8c61\u5b66\u5bb6\u5173\u6ce8\u3002\u7f8e\u56fd\u79d1\u666e\u7545\u9500\u4e66\u4f5c\u5bb6\u8a79\u59c6\u65af\u00b7\u683c\u96f7\u514b<\/span>\uff08James Gleick\uff09<\/span>1987\u51fa\u7248\u7684\u540d\u8457\u300a\u6df7\u6c8c\u5b66\u4f20\u5947\u300b<\/span>\uff08Chaos: Making a New Science<\/em>\uff09<\/span>\u4e2d\u8bf4\uff1a\u201c\u6d1b\u4f26\u8328\u7684\u8fd9\u7bc7\u8bba\u6587\uff0c\u57281960\u5e74\u4ee3\u6742\u5fd7\u4e0a\u6bcf\u5e74\u4f1a\u88ab\u5f15\u7528\u4e00\u6b21\u3002\u53ef\u662f\u4e8c\u5341\u5e74\u540e\uff0c\u5b83\u6bcf\u5e74\u88ab\u5f15\u7528\u7684\u6b21\u6570\u8d85\u8fc7\u4e00\u767e\u3002\u201d\u4eca\u5929\uff0c\u8fd9\u7bc7\u6587\u7ae0\u5df2\u88ab\u5f15\u7528\u4e24\u4e07\u4e09\u5343\u591a\u6b21\u3002<\/span><\/p>\n


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\u987a\u4fbf\u8bf4\u8bf4\uff0c\u6d1b\u4f26\u8328\u7cfb\u7edf\u5c5e\u4e8e\u6240\u8c13\u7684\u8017\u6563\u7cfb\u7edf\uff0c\u5176\u8017\u6563\u91cf\u7531\u6d41\u4f53\u7c98\u5ea6\u51b3\u5b9a\uff0c\u7f3a\u5931\u7684\u80fd\u91cf\u5219\u4f9d\u9760\u70ed\u80fd\u8865\u7ed9\u3002\u540e\u6765\u4eba\u4eec\u77e5\u9053\uff0c\u8bb8\u591a\u522b\u7684\u8017\u6563\u7cfb\u7edf\u90fd\u53ef\u4ee5\u4ea7\u751f\u6df7\u6c8c\u5438\u5f15\u5b50\u3002\u6b64\u5916\uff0c\u4e5f\u6709\u8bb8\u591a\u80fd\u91cf\u4fdd\u5b88\u7cfb\u7edf\u5373\u54c8\u5bc6\u987f<\/span>\uff08Hamilton\uff09<\/span>\u7cfb\u7edf\u4e5f\u53ef\u4ee5\u4ea7\u751f\u4e0d\u540c\u7c7b\u578b\u7684\u6df7\u6c8c\uff0c\u4f46\u90a3\u53c8\u662f\u53e6\u4e00\u4e2a\u8bba\u9898\u4e86\u3002<\/span><\/p>\n


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\u5f00\u59cb\u65f6\uff0c\u6d1b\u4f26\u8328\u628a\u4ed6\u7684\u53d1\u73b0\u6bd4\u55bb\u4e3a\u201c\u6d77\u9e25\u98de\u7fd4\u5f15\u8d77\u4e86\u66b4\u98ce\u96e8\u201d\u3002\u540e\u6765\uff0c\u4ed6\u63a5\u53d7\u4e86\u4e00\u4f4d\u6c14\u8c61\u5b66\u5bb6\u670b\u53cbPhilip Merilees\u7684\u5efa\u8bae\uff0c\u57281972\u5e74\u628a\u4ed6\u7684\u4e00\u7bc7\u8bba\u6587\u53d6\u9898\u4e3a\uff1a\u201c\u5728\u5df4\u897f\u7684\u4e00\u53ea\u8774\u8776\u62cd\u6253\u4e00\u4e0b\u7fc5\u8180\u4f1a\u5728\u5f97\u514b\u8428\u65af\u5dde\u5f15\u53d1\u4e00\u573a\u9f99\u5377\u98ce\u5417\uff1f\u201d\u4e8e\u662f\uff0c\u540e\u6765\u7684\u79d1\u5b66\u6587\u732e\u3001\u6587\u5b66\u4f5c\u54c1\u548c\u4eba\u4eec\u65e5\u5e38\u751f\u6d3b\u91cc\u4fbf\u6709\u4e86\u4e00\u4e2a\u65b0\u6210\u8bed\uff1a\u201c\u8774\u8776\u6548\u5e94\u201d<\/span>\uff08\u201cbutterfly effect\u201d\uff09<\/span>\u3002<\/span><\/p>\n


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\u6d1b\u4f26\u8328\u5438\u5f15\u5b50\u9177\u4f3c\u4e00\u53ea\u8774\u8776\u3002\u626b\u7801\u9605\u8bfb\u201c\u8774\u8776\u6548\u5e94\u201d\u96c6\u667a\u767e\u79d1\u8bcd\u6761<\/span><\/p>\n


<\/span><\/span>\u6d1b\u4f26\u8328\u5728\u4ed61993\u5e74\u51fa\u7248\u7684\u79d1\u666e\u8457\u4f5c\u300a\u6df7\u6c8c\u7684\u672c\u8d28\u300b\u4e2d\u8fd8\u6709\u53e6\u4e00\u79cd\u6bd4\u55bb\uff1a\u201c\u4e00\u4e2a\u4eba\u5728\u4e2d\u56fd\u6253\u4e2a\u55b7\u568f\u4e5f\u53ef\u80fd\u4f1a\u8ba9\u7ebd\u7ea6\u7684\u4eba\u4eec\u53bb\u94f2\u96ea\u3002\u201d<\/span>
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UCL Press\uff0cUSA\uff0c1993\uff08\u4e2d\u8bd1\u672c\uff0c1997\uff09<\/span><\/p>\n


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\u663e\u7136\uff0c\u201c\u6df7\u6c8c\u201d\u7684\u672c\u8d28\u5c31\u662f\u5bf9\u521d\u59cb\u6761\u4ef6\u7684\u9ad8\u5ea6\u654f\u611f\u6027\u3002\u53ef\u662f\uff0c\u5f88\u591a\u4e8b\u7269\u5bf9\u521d\u59cb\u6761\u4ef6\u5177\u6709\u9ad8\u5ea6\u654f\u611f\u6027\u7684\u8fd9\u79cd\u89c2\u5bdf\u6216\u8ba4\u77e5\uff0c\u5176\u5b9e\u53e4\u6765\u6709\u4e4b\u3002<\/span><\/p>\n


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\u8fdc\u81f3\u5b54\u5b50<\/span>\uff08\u524d551-\u524d479\uff09<\/span>\u7684\u300a\u793c\u8bb0\u00b7\u7ecf\u89e3\u300b\uff0c\u5176\u4e2d\u300a\u6613\u300b\u91cc\u5c31\u8bf4\u8fc7\uff1a\u201c\u541b\u5b50\u614e\u59cb\uff0c\u5dee\u82e5\u6beb\u5398\uff0c\u7f2a\u4ee5\u5343\u91cc\u3002\u201d\u53e4\u5e0c\u814a\u54f2\u5b66\u5bb6\u4e9a\u91cc\u58eb\u591a\u5fb7<\/span>\uff08\u524d384-\u524d322\uff09<\/span>\u4e5f\u8bf4\u8fc7\uff1a\u201c\u5bf9\u771f\u5b9e\u6027\u6781\u5c0f\u7684\u521d\u59cb\u504f\u79bb\uff0c\u5f80\u540e\u4f1a\u88ab\u6210\u5343\u500d\u5730\u653e\u5927\u3002\u201d\u8fd1\u4ee3\u7269\u7406\u5b66\u5bb6\u8a79\u59c6\u65af\u00b7\u9ea6\u514b\u65af\u97e6<\/span>\uff08James Clerk Maxwell\uff09<\/span>\u57281873\u5e74\u4ea6\u8bf4\u8fc7\uff1a\u201c\u7cfb\u7edf\u521d\u59cb\u72b6\u6001\u7684\u4e00\u4e2a\u65e0\u7a77\u5c0f\u53d8\u5316\u53ef\u80fd\u4f1a\u5f15\u8d77\u8be5\u72b6\u6001\u5728\u6709\u9650\u65f6\u95f4\u5185\u51fa\u73b0\u6709\u9650\u7684\u504f\u5dee\uff0c\u8fd9\u6837\u7684\u7cfb\u7edf\u79f0\u4e3a\u662f\u4e0d\u7a33\u5b9a\u7684\u2026\u2026\u5e76\u4e14\u4f1a\u4f7f\u5f97\u5bf9\u5c06\u6765\u4e8b\u4ef6\u7684\u9884\u6d4b\u6210\u4e3a\u4e0d\u53ef\u80fd\u3002\u201d\u6570\u5b66\u5bb6\u96c5\u514b\u00b7\u963f\u8fbe\u9a6c<\/span> (Jacques Hadamard) <\/span>\u5728 1898 \u5e74\u4e5f\u63d0\u5230\uff0c\u201c\u521d\u59cb\u6761\u4ef6\u4e2d\u7684\u8bef\u5dee\u6216\u8005\u4e0d\u7cbe\u786e\u6027\u53ef\u80fd\u4f1a\u4f7f\u7cfb\u7edf\u957f\u65f6\u95f4\u7684\u52a8\u529b\u884c\u4e3a\u53d8\u5f97\u4e0d\u53ef\u9884\u6d4b\u3002\u201d<\/span><\/p>\n


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\u5230\u4e8c\u5341\u4e16\u7eaa\u521d\uff0c\u901a\u624d\u6570\u5b66\u5bb6\u4ea8\u5229\u30fb\u5e9e\u52a0\u83b1<\/span> (Jules Henri Poincar\u00e9\uff0c1854-1912\uff09<\/span>\u57281908\u5e74\u4ed6\u7684\u4e66\u300a\u79d1\u5b66\u4e0e\u65b9\u6cd5\u300b\u4e2d\u5199\u9053\uff1a\u201c\u521d\u59cb\u6761\u4ef6\u7684\u5fae\u5c0f\u8bef\u5dee\u5728\u6700\u540e\u7ed3\u679c\u4e2d\u4ea7\u751f\u6781\u5927\u5dee\u522b\u7684\u60c5\u51b5\u53ef\u80fd\u53d1\u751f\u2026\u2026\u4e8e\u662f\u9884\u6d4b\u53d8\u4e3a\u4e0d\u53ef\u80fd\uff0c\u4ece\u800c\u6211\u4eec\u5c31\u770b\u5230\u4e86\u8bb8\u591a\u5076\u7136\u73b0\u8c61\u3002\u201d\u4f46\u662f\uff0c\u6240\u6709\u5148\u8d24\u4eec\u7684\u601d\u60f3\u3001\u89c2\u5ff5\u548c\u77e5\u8bc6\u90fd\u505c\u7559\u5728\u6216\u8005\u8bf4\u5c40\u9650\u4e8e\u54f2\u5b66\u548c\u6570\u5b66\u7684\u601d\u8fa8\u4e0a\uff0c\u6ca1\u6709\u5c55\u793a\u4e00\u4e2a\u5177\u4f53\u7684\u79d1\u5b66\u5b9e\u4f8b\u3002\u6d1b\u4f26\u8328\u7684\u4f1f\u5927\u8d21\u732e\uff0c\u662f\u4ed6\u7b2c\u4e00\u6b21\u4e3a\u8fd9\u79cd\u6781\u7aef\u654f\u611f\u6027\u548c\u540e\u6765\u7684\u6df7\u6c8c\u7406\u8bba\u63d0\u4f9b\u4e86\u4e00\u4e2a\u7b80\u5355\u53c8\u7cbe\u51c6\u7684\u7269\u7406\u7cfb\u7edf\u7684\u6570\u5b66\u6a21\u578b\u3002\u4e0d\u8fc7\uff0c\u4e25\u683c\u7684\u6df7\u6c8c\u6570\u5b66\u7406\u8bba\u5e76\u4e0d\u5f52\u529f\u4e8e\u6d1b\u4f26\u8328\u3002<\/span><\/p>\n


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\u73b0\u4ee3\u6df7\u6c8c\u6570\u5b66\u7406\u8bba\u7684\u9f3b\u7956\uff0c\u662f\u521a\u624d\u63d0\u5230\u7684\u90a3\u4f4d\u901a\u624d\u6570\u5b66\u5bb6\u5e9e\u52a0\u83b1\u30021887\u5e74\uff0c\u745e\u5178\u56fd\u738b\u5965\u65af\u5361\u4e8c\u4e16<\/span>\uff08Oskar, II\uff09<\/span>\u60ac\u8d4f\uff0c\u5f81\u6c42\u592a\u9633\u7cfb\u7a33\u5b9a\u6027\u95ee\u9898\u7684\u89e3\u7b54\uff0c\u671f\u671b\u89e3\u51b3\u5929\u4f53\u529b\u5b66\u4e2d\u7684\u4e09\u4f53\u751a\u81f3N\u4f53\u95ee\u9898\u3002\u56fd\u738b\u7ec4\u7ec7\u4e86\u4e09\u4f4d\u5f53\u65f6\u6700\u6709\u6743\u5a01\u7684\u6570\u5b66\u5bb6\u62c5\u4efb\u8bc4\u59d4\uff1a\u7c73\u5854-\u5217\u592b\u52d2<\/span>\uff08Magnus Mittag-Leffler\uff09<\/span>\u3001\u9b4f\u5c14\u65af\u7279\u62c9\u65af<\/span>\uff08Karl Weierstrass\uff09<\/span>\u548c\u5384\u7c73\u7279<\/span>\uff08Charles Hermite\uff09<\/span>\u3002\u5728\u90a3\u6b21\u9ad8\u7aef\u79d1\u5b66\u8bba\u6587\u7ade\u8d5b\u4e2d\uff0c\u5e9e\u52a0\u83b1\u4ee5\u4ed6\u5bf9\u4e09\u4f53\u95ee\u9898\u7684\u7814\u7a76\u6210\u679c\u83b7\u5f97\u4e86\u5927\u5956\u3002<\/span><\/p>\n


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\u5f97\u5956\u8bba\u6587\u6309\u89c4\u5b9a\u8981\u5728\u745e\u5178\u7687\u5bb6\u79d1\u5b66\u9662\u6570\u5b66\u5b66\u62a5<\/span>\uff08Acta Mathematica<\/em>\uff09<\/span>\u4e0a\u53d1\u8868\u3002\u5176\u65f6\u5b66\u62a5\u6709\u4e00\u4f4d\u8d1f\u8d23\u8bba\u6587\u6821\u5bf9\u768425\u5c81\u5e74\u8f7b\u4ebaLars E. Phragmen\uff0c\u90a3\u65f6\u4ed6\u662f\u4e2a\u6570\u5b66\u7231\u597d\u8005\uff0c\u9605\u8bfb\u5e9e\u52a0\u83b1\u8bba\u6587\u65f6\u53d1\u73b0\u6709\u4e2a\u5730\u65b9\u8001\u7ed5\u4e0d\u8fc7\u53bb\uff0c\u4e8e\u662f\u4fbf\u53bb\u8be2\u95ee\u4f5c\u8005\u3002\u5e9e\u52a0\u83b1\u5728\u8bd5\u56fe\u4f5c\u51fa\u89e3\u91ca\u7684\u8fc7\u7a0b\u4e2d\u53d1\u73b0\u539f\u6587\u6709\u9519\uff0c\u8fde\u4ed6\u81ea\u5df1\u4e5f\u7ed5\u4e0d\u8fc7\u53bb\u3002<\/span><\/p>\n


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\u5728\u8fd9\u79cd\u65f6\u5019\uff0c\u8bda\u5b9e\u7684\u6570\u5b66\u5bb6\u53ef\u80fd\u4f1a\u9009\u62e9\u653e\u5f03\uff0c\u4e0d\u8bda\u5b9e\u7684\u6570\u5b66\u5bb6\u53ef\u80fd\u4f1a\u542b\u7cca\u5176\u8f9e\u6577\u884d\u4e86\u4e8b\u3002\u800c\u8fd9\u4f4d\u9876\u5c16\u7684\u6570\u5b66\u5bb6\u5e9e\u52a0\u83b1\u5462\uff0c\u5728\u91cd\u8981\u9519\u8bef\u9762\u524d\uff0c\u6df1\u601d\u719f\u8651\u4e4b\u540e\u5f7b\u5e95\u5730\u6539\u53d8\u4e86\u539f\u6765\u6cbf\u7528\u7684\u4f20\u7edf\u5b9a\u91cf\u5206\u6790\u65b9\u6cd5\uff0c\u4ee5\u5168\u65b0\u7684\u5b9a\u6027\u5206\u6790\u65b9\u6cd5\u91cd\u65b0\u63a2\u8ba8\u4e86\u8fd9\u4e2a\u6570\u5b66\u4e0a\u6781\u5176\u8270\u6df1\u7684\u95ee\u9898\u3002\u6b64\u4e3e\u8ba9\u5e9e\u52a0\u83b1\u5f00\u542f\u4e86\u4e8c\u5341\u4e16\u7eaa\u52a8\u529b\u7cfb\u7edf\u5b9a\u6027\u7406\u8bba\u3001\u7279\u522b\u662f\u6df7\u6c8c\u6570\u5b66\u7406\u8bba\u7684\u5148\u6cb3\uff0c\u5c3d\u7ba1\u8be5\u5f97\u5956\u8bba\u6587\u62d6\u5ef6\u52301890\u5e74\u624d\u95ee\u4e16<\/span>\uff0813\u5377,1-270\u9875\uff09<\/span>\u3002<\/span><\/p>\n

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Henri Poincar\u00e9                 Stephen Smale<\/span>
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\u56e0\u4e3a\u8bf4\u5230\u6df7\u6c8c\u7684\u6570\u5b66\u7406\u8bba\u4e86\uff0c\u8fd8\u5f97\u5148\u628a\u5b83\u8bf4\u5f97\u66f4\u6e05\u695a\u4e00\u4e9b\uff0c\u624d\u80fd\u56de\u53bb\u628a\u6d1b\u4f26\u8328\u7684\u6545\u4e8b\u8bb2\u5b8c\u3002<\/span><\/p>\n


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\u5e9e\u52a0\u83b1\u5bf9\u4e09\u4f53\u95ee\u9898\u52a8\u529b\u5b66\u4f5c\u4e86\u7cbe\u8f9f\u7684\u5b9a\u6027\u5206\u6790\u4e4b\u540e\uff0c\u65f6\u95f4\u4e00\u4e0b\u5b50\u8fc7\u4e86\u534a\u4e2a\u591a\u4e16\u7eaa\u3002\u5176\u95f4\uff0c\u9664\u4e86\u5927\u6570\u5b66\u5bb6\u4e54\u6cbb\u00b7\u4f2f\u514b\u970d\u592b<\/span>\uff08George D. Birkhoff\uff0c1884-1944\uff09<\/span>\u548c\u5b89\u5fb7\u70c8\u00b7\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b<\/span>\uff08Andrey N. Kolmogorov\uff0c1903-1987\uff09<\/span>\u7684\u8d21\u732e\u4e4b\u5916\uff0c\u8fd8\u6709\u975e\u5e38\u91cd\u8981\u4f46\u5e76\u4e0d\u5e7f\u4e3a\u4eba\u77e5\u7684\u739b\u4e3d\u00b7\u5361\u7279\u8d56\u7279<\/span>\uff08D. Mary Cartwright\uff0c1900-1998\uff09<\/span>\u548c\u7ea6\u7ff0\u00b7\u674e\u7279\u5c14\u4f0d\u5fb7<\/span>\uff08John E. Littlewood\uff0c1885-1977\uff09<\/span>\uff0c1945\u5e74\u95f4\u4e24\u4eba\u5408\u4f5c\u53d1\u5c55\u4e86\u65e0\u7ebf\u7535\u5de5\u7a0b\u95ee\u9898\u8bf1\u5bfc\u51fa\u6765\u7684van der Pol\u632f\u5b50\u7684\u201c\u5947\u5f02\u5438\u5f15\u5b50\u201d<\/span>\uff08strange attractor\uff09<\/span>\u7684\u6570\u5b66\u7406\u8bba\u3002<\/span><\/p>\n


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\u5341\u4e8c\u5e74\u540e\uff0c1957\u5e74\u65af\u8482\u82ac\u00b7\u65af\u6885\u5c14<\/span>\uff08Stephen Smale\uff0c1930-\uff09<\/span>\u4ece\u5bc6\u6b47\u6839\u5927\u5b66\u6570\u5b66\u535a\u58eb\u6bd5\u4e1a\uff0c\u5728\u666e\u6797\u65af\u987f\u9ad8\u7b49\u7814\u7a76\u9662<\/span>\uff08IAS\uff09<\/span>\u8bbf\u95ee\u4e86\u4e00\u6bb5\u65f6\u95f4\u4e4b\u540e\uff0c\u5728\u56fd\u5bb6\u81ea\u7136\u79d1\u5b66\u57fa\u91d1\u8d44\u52a9\u4e0b\u4e8e1959\u5e74\u5e95\u6765\u5230\u4e86\u5df4\u897f\u91cc\u7ea6\u70ed\u5185\u5362\u8457\u540d\u7684\u7eaf\u7cb9\u548c\u5e94\u7528\u6570\u5b66\u7814\u7a76\u9662<\/span>\uff08IMPA\uff09<\/span>\u505a\u535a\u58eb\u540e\u7814\u7a76\u3002\u8fd9\u6bb5\u65f6\u95f4\u4ed6\u7ecf\u5e38\u5230\u6c99\u6ee9\u53bb\u6652\u592a\u9633\uff0c\u89c9\u5f97\u6c99\u6ee9\u7684\u55a7\u95f9\u4e1d\u6beb\u4e0d\u4f1a\u5f71\u54cd\u4ed6\u6df1\u5165\u601d\u8003\u5404\u79cd\u6570\u5b66\u95ee\u9898\u3002<\/span><\/p>\n


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\u5e74\u8f7b\u7684\u65af\u6885\u5c14\u5728\u4e00\u7bc7\u81ea\u5df1\u611f\u5230\u81ea\u8c6a\u7684\u6587\u7ae0\u4e2d\u63d0\u53ca\u4e86\u4ed6\u7684\u4e00\u4e2a\u201c\u731c\u60f3\u201d\uff1a\u201c\u6df7\u6c8c\u4e0d\u5b58\u5728\uff01\u201d<\/span>\uff08”chaos doesn’t exist!”\uff09<\/span>\u4f46\u662f\uff0c\u4ed6\u5f88\u5feb\u5c31\u63a5\u5230 MIT \u7684\u6570\u5b66\u5bb6\u8bfa\u66fc\u00b7\u83b1\u6587\u68ee<\/span>\uff08Norman Levinson\uff0c1912-1975\uff09<\/span>\u7684\u6765\u4fe1\uff0c\u7ed9\u4ed6\u4e3e\u4e86\u4e00\u4e2a\u53cd\u4f8b\uff0c\u540c\u65f6\u5411\u4ed6\u4ecb\u7ecd\u4e86\u5361\u7279\u8d56\u7279-\u674e\u7279\u5c14\u4f0d\u5fb7\u7684\u7814\u7a76\u6210\u679c\u3002\u540e\u6765\uff0c\u65af\u6885\u5c14\u57281998\u5e74\u4e3a\u300a\u6570\u5b66\u4fe1\u4f7f\u300b<\/span>\uff08Mathematical Intelligencer<\/em>\uff09<\/span>\u5199\u7684\u4e00\u7bc7\u9898\u4e3a\u201c\u5728\u91cc\u7ea6\u70ed\u5185\u5362\u6d77\u6ee9\u4e0a\u53d1\u73b0\u9a6c\u8e44\u201d\u7684\u6587\u7ae0\u4e2d\u56de\u5fc6\u9053\uff1a\u201c<\/span> [\u5f53\u65f6] <\/span>\u6211\u591c\u4ee5\u7ee7\u65e5\u5730\u5de5\u4f5c\uff0c\u8bd5\u56fe\u89e3\u51b3\u8fd9\u4e2a\u6311\u6218\u2026\u2026\u6211\u6700\u540e\u8bf4\u670d\u4e86\u81ea\u5df1\uff0c\u83b1\u6587\u68ee\u662f\u5bf9\u7684\u800c\u6211\u7684\u731c\u60f3\u662f\u9519\u4e86\u3002\u6df7\u6c8c\u5df2\u7ecf\u9690\u542b\u5728\u5361\u7279\u8d56\u7279-\u674e\u7279\u5c14\u4f0d\u5fb7\u7684\u5206\u6790\u4e4b\u4e2d\uff01\u73b0\u5728\u8ff7\u56e2\u5df2\u7ecf\u89e3\u5f00\uff0c\u662f\u6211\u4f5c\u51fa\u4e86\u9519\u8bef\u7684\u731c\u6d4b\u3002\u4f46\u662f\u5728\u8fd9\u4e2a\u5b66\u4e60\u7684\u8fc7\u7a0b\u4e2d\uff0c\u6211\u53d1\u73b0\u4e86\u9a6c\u8e44\uff01\u201d \u2014\u2014\u597d\u4e00\u4e2a\u5e9e\u52a0\u83b1\u5f0f\u7684\u6570\u5b66\u5bb6\uff01<\/span><\/p>\n


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\u65af\u6885\u5c14\u7684\u201c\u9a6c\u8e44\u201d\u7406\u8bba\u53ef\u4ee5\u7528\u4e0b\u9762\u7684\u793a\u610f\u56fe\u4f5c\u4e00\u4e2a\u7b80\u5355\u89e3\u91ca\u3002\u60f3\u8c61\u4e00\u4e2a\u6620\u5c04f<\/em>\u628a\u5de6\u4e0a\u89d2\u7684\u692d\u5706\u72b6\u9762\u79ef\u6295\u5f71\u5230\u5de6\u4e0b\u89d2\u7684\u9a6c\u8e44\u5f62\u9762\u79ef\u53bb\u3002\u5b83\u53ef\u4ee5\u901a\u8fc7\u53f3\u9762\u7684\u538b\u7f29\u3001\u62c9\u4f38\u548c\u6298\u53e0\u4e09\u6b65\u64cd\u4f5c\u800c\u5408\u6210\u3002\u7136\u540e\uff0c\u628a\u9a6c\u8e44\u653e\u5230\u5de6\u4e0a\u89d2\u53bb\u53d6\u4ee3\u692d\u5706\u7684\u4f4d\u7f6e\uff0c\u518d\u6b21\u7528\u6620\u5c04f<\/em>\u6295\u5f71\u5230\u5de6\u4e0b\u89d2\u53bb\uff0c\u8fd9\u4e5f\u53ef\u4ee5\u901a\u8fc7\u540c\u6837\u7684\u538b\u7f29\u3001\u62c9\u4f38\u548c\u6298\u53e0\u4e09\u6b65\u64cd\u4f5c\u800c\u5b8c\u6210\u3002\u81f3\u6b64\uff0c\u505a\u5b8c\u4e86\u4e8c\u6b21\u8fed\u4ee3\uff0cf2<\/sup><\/span><\/em>\u3002\u7136\u540e\uff0c\u518d\u91cd\u590d\u540c\u6837\u7684\u6b65\u9aa4\uff0c\u76f4\u5230\u5b8c\u6210 n \u6b21\u8fed\u4ee3\uff0cfn<\/sup><\/span><\/em>\u3002\u7406\u8bba\u4e0a\uff0cn\u2192\u221e\uff0c\u4fbf\u53ef\u4ee5\u5f97\u5230\u5bc6\u5bc6\u9ebb\u9ebb\u65e0\u7a77\u591a\u4e2a\u70b9\uff0c\u662f\u524d\u9762\u6240\u6709\u5927\u5927\u5c0f\u5c0f\u9a6c\u8e44\u7684\u4ea4\u70b9\u96c6\u5408\uff0c\u79f0\u4e3a\u5eb7\u6258<\/span>\uff08Cantor\uff09<\/span>\u96c6\u3002\u5bb9\u6613\u770b\u51fa\uff0c\u5f00\u59cb\u65f6\u5728\u692d\u5706\u4e0a\u76f8\u8ddd\u5f88\u8fdc\u7684\u4e24\u4e2a\u70b9\uff0c\u901a\u8fc7\u591a\u6b21\u6620\u5c04<\/span>\uff08\u53cd\u590d\u538b\u7f29\u3001\u62c9\u4f38\u548c\u6298\u53e0\uff09<\/span>\u4e4b\u540e\uff0c\u4f1a\u88ab\u8f6c\u79fb\u5230\u975e\u5e38\u63a5\u8fd1\u7684\u76f8\u90bb\u4f4d\u7f6e\u4e0a\u3002\u73b0\u5728\uff0c\u5982\u679c\u4ece\u4efb\u610f\u4e24\u4e2a\u65e0\u8bba\u600e\u6837\u63a5\u8fd1\u7684\u4e0d\u540c\u70b9\u51fa\u53d1\uff0c\u8fdb\u884c\u9006\u6620\u5c04f<\/span>-n<\/sup><\/span><\/em>\uff0c\u4fbf\u4f1a\u53d1\u73b0\u5f53n\u8d8a\u6765\u8d8a\u5927\u65f6\uff0c\u4e24\u6761\u8fed\u4ee3\u8f68\u9053\u5c31\u4f1a\u5206\u79bb\u5f97\u8d8a\u6765\u8d8a\u8fdc\uff0c\u5373\u5f00\u59cb\u65f6\u6781\u5c0f\u7684\u5dee\u522b\u4f1a\u5bfc\u81f4\u540e\u6765\u6781\u5927\u7684\u5dee\u522b\u3002\u76f4\u89c2\u5730\u8bf4\uff0cfn<\/sup><\/span><\/em>\u628a\u5f00\u59cb\u79bb\u5f97\u5f88\u8fdc\u7684\u4e24\u4e2a\u70b9\u6620\u5c04\u5230\u5eb7\u6258\u96c6\u91cc\u975e\u5e38\u63a5\u8fd1\u7684\u76f8\u90bb\u4f4d\u7f6e\u4e0a\uff0c\u800cf-n<\/sup><\/span><\/em>\u5219\u5b8c\u6210\u76f8\u53cd\u7684\u5de5\u4f5c\u3002\u8fd9\u4e2af<\/em>\u79f0\u4e3a\u65af\u6885\u5c14\u9a6c\u8e44\u6620\u5c04\u3002\u65af\u6885\u5c14\u7684\u9a6c\u8e44\u7406\u8bba\u7528\u6e05\u6670\u5177\u4f53\u7684\u6570\u5b66\u65b9\u5f0f\u6765\u8868\u8fbe\u5e76\u4e25\u683c\u8bc1\u660e\u4e86\u6df7\u6c8c\u7684\u6700\u57fa\u672c\u5c5e\u6027\uff1a\u5bf9\u521d\u59cb\u6761\u4ef6\u7684\u6781\u7aef\u654f\u611f\u6027\u3002<\/span><\/p>\n


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\u65af\u6885\u5c14\u9a6c\u8e44\u6620\u5c04\u793a\u610f\u56fe<\/span><\/p>\n


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\u65af\u6885\u5c14\u662f\u975e\u5e38\u6709\u4e2a\u6027\u7684\u6570\u5b66\u5bb6\u30021968\u5e74\uff0c\u7ea6\u7ff0\u900a\u603b\u7edf\u7684\u79d1\u5b66\u987e\u95eeDonald Hornig \u5728\u300a\u79d1\u5b66\u300b<\/span>(Science<\/em>) <\/span>\u6742\u5fd7\u520a\u6587\u6279\u8bc4\u65af\u6885\u5c14\uff0c\u8bf4\u4ed6\u9886\u7740\u56fd\u5bb6\u81ea\u7136\u79d1\u5b66\u57fa\u91d1\u53bb\u5df4\u897f\u6c99\u6ee9\u6652\u592a\u9633\uff1a\u201c\u6570\u5b66\u5bb6\u4eec\u4e00\u672c\u6b63\u7ecf\u5730\u63d0\u51fa\u8981\u7eb3\u7a0e\u4eba\u8ba4\u540c\u6570\u5b66\u521b\u9020\u5e94\u8be5\u7531\u516c\u6b3e\u8d44\u52a9\u5230\u91cc\u7ea6\u70ed\u5185\u5362\u53bb\u8eba\u6c99\u6ee9\u2026\u2026\u201d\u591a\u5e74\u4ee5\u540e\uff0c\u65af\u6885\u5c14\u5728\u4e0a\u9762\u63d0\u53ca\u76841998\u5e74\u6587\u7ae0\u201c\u5728\u91cc\u7ea6\u70ed\u5185\u5362\u6d77\u6ee9\u4e0a\u53d1\u73b0\u9a6c\u8e44\u201d\u4e2d\u5bf9Donald Hornig\u4f5c\u51fa\u4e86\u516c\u5f00\u7684\u53cd\u9a73\uff0c\u8bf4\u81ea\u5df1\u5728\u91cc\u7ea6\u70ed\u5185\u5362\u6c99\u6ee9\u4e0a\u6240\u4f5c\u7684\u6570\u5b66\u521b\u9020\u201c\u6b63\u662f\u9a6c\u8e44\u7406\u8bba\u548c\u9ad8\u7ef4<\/span> [\u6240\u6709\u9ad8\u4e8e4\u7ef4] <\/span>\u5e9e\u52a0\u83b1\u731c\u60f3\u7684\u8bc1\u660e\u201d\uff0c\u5176\u4e2d\u540e\u9762\u4e00\u9879\u6210\u5c31\u8ba9\u65af\u6885\u5c14\u8363\u81ba1966\u5e74\u83f2\u5c14\u5179\u5956<\/span>\uff08Fields Medal\uff09<\/span>\u3002<\/span><\/p>\n


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\u7ee7\u7eed\u56de\u987e\u5386\u53f2\uff0c\u8fd8\u6709\u5f88\u591a\u6545\u4e8b\u3002\u524d\u9762\u8bf4\u5230\uff0c\u5728\u6570\u5b66\u6587\u732e\u4e2d\u7b2c\u4e00\u6b21\u6b63\u5f0f\u7528chaos\u6765\u63cf\u8ff0\u7cfb\u7edf\u5bf9\u521d\u59cb\u6761\u4ef6\u6781\u7aef\u654f\u611f\u7279\u6027\u7684\uff0c\u662f1975\u5e74\u7684\u674e\u5929\u5ca9-\u7ea6\u514b<\/span>\uff08Li-Yorke\uff09<\/span>\u5b9a\u7406\u3002\u800c\u6700\u65e9\u628a\u82f1\u6587chaos\u7ffb\u8bd1\u4e3a\u4e2d\u6587\u201c\u6df7\u6c8c\u201d\u7684\uff0c\u662f\u5317\u4eac\u5927\u5b66\u8363\u4f11\u6559\u6388\u6731\u7167\u5ba3\u5148\u751f<\/span>\uff081930-\uff09<\/span>\u3002\u8fd9\u4e00\u540d\u79f0\u5f15\u6765\u8bb8\u591a\u6709\u8da3\u7684\u4e2d\u56fd\u795e\u8bdd\u6545\u4e8b\u3002\u5df2\u6545\u90dd\u67cf\u6797\u9662\u58eb<\/span>\uff081934-2018\uff09<\/span>\u5728\u4ed6\u82f1\u6587\u7248\u300a\u6df7\u6c8c\u300b\u6249\u9875\u4ee5\u53ca\u300a\u6e4d\u9274\u2014\u6df7\u6c8c\u7406\u8bba\u4e0e\u6574\u4f53\u6027\u79d1\u5b66\u5bfc\u5f15\u300b\u4e00\u4e66\u524d\u8a00\u4e2d\uff0c\u90fd\u5f15\u7528\u8fc7\u300a\u5e84\u5b50\u00b7\u5e94\u5e1d\u738b\u300b\u4e2d\u7684\u4e00\u53e5\u8bdd\uff1a\u201c\u5357\u6d77\u4e4b\u5e1d\u4e3a\u500f\uff0c\u5317\u6d77\u4e4b\u5e1d\u4e3a\u5ffd\uff0c\u4e2d\u592e\u4e4b\u5e1d\u4e3a\u6d51\u6c8c\u201d\u3002\u5176\u4e2d\uff0c\u500f\u548c\u5ffd\u540e\u6765\u53d8\u4e3a\u6210\u8bed\u201c\u500f\u5ffd\u4e4b\u95f4\u201d\uff0c\u800c\u53e4\u65f6\u7684\u201c\u6d51\u6c8c\u201d\u5c31\u662f\u4eca\u5929\u7684\u201c\u6df7\u6c8c\u201d\u3002\u4e2d\u56fd\u9053\u6559\u59cb\u7956\u8001\u5b50<\/span>\uff08\u524d\u7ea6571-\u524d471\uff09<\/span>\u7559\u4e0b\u300a\u592a\u4e0a\u8001\u541b\u516b\u5341\u4e00\u5316\u56fe\u300b\uff0c\u5176\u4e2d\u7b2c\u4e8c\u5316\u66f0\uff1a\u201c\u2026\u2026\u7a7a\u6d1e\u4e4b\u4e2d\uff0c\u53c8\u751f\u592a\u65e0\uff0c\u592a\u65e0\u4e4b\u5185\u751f\u7384\u5143\u59cb\u4e09\u6c14\uff0c\u4e09\u6c14\u76f8\u5408\uff0c\u79f0\u4e3a\u6df7\u6c8c\u201d\u3002\u5c31\u662f\u8bf4\uff0c\u53e4\u4eba\u5fc3\u4e2d\u7684\u5b87\u5b99\u4ece\u65e0\u5230\u6709\uff0c\u7531\u67d0\u79cd\u6df7\u6c8c\u72b6\u6001\u5f00\u59cb\u3002<\/span><\/p>\n


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\u5373\u4f7f\u4ee5\u4eca\u5929\u7684\u79d1\u5b66\u89c2\u6765\u770b\u592a\u9633\u7cfb\u3001\u94f6\u6cb3\u7cfb\u3001\u4ee5\u81f3\u6574\u4e2a\u5b87\u5b99\uff0c\u90fd\u53ef\u4ee5\u628a\u5b83\u4eec\u770b\u4f5c\u662f\u6df7\u6c8c\u7cfb\u7edf\u3002\u9996\u5148\uff0c\u8fd9\u4e9b\u7cfb\u7edf\u957f\u671f\u5728\u5982\u5e38\u8fd0\u884c\uff0c\u65e2\u4e0d\u53d1\u6563\u4e5f\u4e0d\u4f11\u6b62\u3002\u5176\u6b21\uff0c\u5728\u5929\u6587\u65f6\u7a7a\u5c3a\u5ea6\u4e0b\uff0c\u5e76\u6ca1\u6709\u4e25\u683c\u5468\u671f\u8fd0\u52a8\u7684\u5929\u4f53\u3002\u8981\u8ba1\u7b97\u5468\u671f\u5c31\u5f97\u4f7f\u7528\u65f6\u95f4\u3002\u6211\u4eec\u4eca\u5929\u4f7f\u7528\u7684\u5386\u6cd5\uff0c\u4fd7\u79f0\u9633\u5386\uff0c\u662f\u5929\u4e3b\u6559\u7687\u683c\u91cc\u54e5\u522913\u4e16<\/span>\uff08Gregorius XIII\uff0c1502-1585\uff09<\/span>\u5728\u516c\u51431582\u5e74\u8bbe\u5b9a\u7684\u3002\u5728\u8fd9\u4e2a\u5e74\u5386\u91cc\uff0c\u4e8c\u6708\u4efd\u53ea\u670928\u5929\uff0c\u4ece\u800c\u6bcf\u5e74\u6709365.2425\u5929\uff0c\u4f46\u6bcf\u56db\u4e2a\u4e16\u7eaa\u518d\u52a0\u5165\u4e00\u4e2a\u95f0\u5e74\u5373\u589e\u591a1\u5929\u7684\u8bdd\u5386\u6cd5\u4f1a\u66f4\u51c6\u786e\uff0c\u4f46\u8fd9\u6837\u4e00\u6765\u5e73\u5747\u6bcf\u5e74\u5c31\u6709\u4e86365.24242424\u5929\uff0c\u56e0\u4e3a\u8fd9\u4e2a\u505a\u6cd5\u8ba9\u6bcf\u5e74\u591a\u51fa\u4e8626\u79d2\u3002\u4e0d\u8fc7\uff0c\u5982\u679c\u6bcf\u9694128\u5e74\u518d\u6263\u6389\u4e00\u4e2a\u95f0\u5e74\uff0c\u5219\u6bcf\u5e74\u6709365.242190419\u5929\uff0c400\u5e74\u5c06\u76f8\u5dee\u4e0d\u52303\u4e2a\u5c0f\u65f6\u3002\u76ee\u524d\u6ca1\u6709\u6bd4\u8fd9\u4e2a\u66f4\u7cbe\u786e\u7684\u5386\u6cd5\u4e86\u3002\u53ef\u662f\uff0c\u5b83\u8fd8\u4e0d\u662f\u6570\u5b66\u610f\u4e49\u4e0b\u7684\u4e25\u683c\u5468\u671f\u3002<\/span><\/p>\n


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\u56fd\u9645\u5ea6\u91cf\u8861\u603b\u5c40<\/span>\uff08International Bureau of Weights and Measures\uff09<\/span>\u4f7f\u7528\u56fd\u9645\u539f\u5b50\u65f6\u95f4<\/span>\uff08International Atomic Time\uff09<\/span>\uff0c\u89c4\u5b9a\u6bcf\u5e74\u76841\u67081\u65e5\u62167\u67081\u65e5\u5bf9\u65f6\u95f4\u4f5c\u51fa\u5fae\u8c03\uff0c\u6bcf\u6b21\u589e\u52a0\u6216\u8005\u51cf\u5c11\u539f\u5b50\u949f\u5b9a\u4e49\u76841\u79d2\u3002\u8fd9\u6837\u4e00\u6765\uff0c\u5c3d\u7ba1\u5e74\u6709\u56db\u5b63\uff0c\u51ac\u53bb\u6625\u6765\uff0c\u4eba\u7c7b\u5b9e\u9645\u4e0a\u6c38\u8fdc\u65e0\u6cd5\u8ba9\u201c\u4e00\u5e74\u65f6\u95f4\u201d\u4e25\u683c\u5468\u671f\u5316\u3002\u56e0\u6b64\uff0c\u6309\u524d\u9762\u5bf9\u201c\u6df7\u6c8c\u201d\u7684\u901a\u4fd7\u7406\u89e3\uff0c\u6240\u6709\u7684\u5929\u4f53\u5728\u5929\u6587\u65f6\u7a7a\u5c3a\u5ea6\u4e0b\u90fd\u662f\u6df7\u6c8c\u7cfb\u7edf\u2014\u2014\u770b\u6765\u5728\u5b87\u5b99\u5b8c\u5168\u574d\u584c\u4e4b\u524d\u5927\u6982\u5c31\u662f\u8fd9\u6837\u3002<\/span><\/p>\n


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\u73b0\u5728\u518d\u56de\u6765\uff0c\u7ee7\u7eed\u8bf4\u6d1b\u4f26\u8328\u7684\u6545\u4e8b\u3002<\/span><\/p>\n


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\u8bb8\u591a\u79d1\u5b66\u5bb6\u6709\u4e00\u79cd\u5171\u8bc6\uff0c\u4e8c\u5341\u4e16\u7eaa\u79d1\u5b66\u53f2\u4e0a\u4e09\u4ef6\u6700\u91cd\u5927\u7684\u4e8b\u4ef6\u662f\u76f8\u5bf9\u8bba\u3001\u91cf\u5b50\u8bba\u548c\u6df7\u6c8c\u8bba\u3002\u76f8\u5bf9\u8bba\u754c\u5b9a\u4e86\u725b\u987f\u529b\u5b66\u6709\u6548\u7684\u6700\u5927\u65f6\u7a7a\u754c\u9650\uff0c\u5c31\u662f\u5f53\u7269\u4f53\u8fd0\u52a8\u63a5\u8fd1\u5149\u901f\u4ee5\u53ca\u5728\u5341\u4ebf\u5149\u5e74\u7684\u5927\u5c3a\u5ea6\u5b87\u5b99\u7a7a\u95f4\u91cc\uff0c\u725b\u987f\u529b\u5b66\u4e0d\u518d\u9002\u7528\uff1b\u91cf\u5b50\u529b\u5b66\u5219\u754c\u5b9a\u4e86\u725b\u987f\u529b\u5b66\u6709\u6548\u7684\u6700\u5c0f\u65f6\u7a7a\u754c\u9650\uff0c\u5c31\u662f\u5728\u5fae\u89c2\u4e16\u754c\u91cc\u725b\u987f\u529b\u5b66\u4e0d\u518d\u9002\u7528\uff1b\u800c\u6df7\u6c8c\u8bba\u5219\u6253\u6d88\u4e86\u786e\u5b9a\u6027\u610f\u5473\u7740\u4e00\u5207\u5747\u53ef\u9884\u6d4b\u7684\u4fe1\u5ff5\u3002<\/span><\/p>\n


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\u5728\u7ecf\u5178\u7269\u7406\u5b66\u4e2d\uff0c\u8457\u540d\u6570\u5b66\u5bb6\u76ae\u57c3\u5c14-\u897f\u8499\u00b7\u62c9\u666e\u62c9\u65af<\/span>\uff08Pierre-Simon Laplace\uff0c1749-1827\uff09<\/span>\u4ee3\u8868\u4e86\u4ed6\u90a3\u4e2a\u65f6\u4ee3\u7edd\u5927\u90e8\u5206\u4eba\u7684\u79d1\u5b66\u89c2\uff0c\u8ba4\u4e3a\u5982\u679c\u4e00\u4e2a\u786e\u5b9a\u6027\u7684\u7cfb\u7edf\u6709\u786e\u5b9a\u7684\u521d\u59cb\u72b6\u6001\uff0c\u90a3\u4e48\u8fd9\u4e2a\u7cfb\u7edf\u5728\u672a\u6765\u6240\u6709\u65f6\u523b\u7684\u72b6\u6001\u90fd\u5df2\u7ecf\u88ab\u5b8c\u5168\u786e\u5b9a\u4e86\u5e76\u4e14\u53ef\u4ee5\u901a\u8fc7\u7cbe\u786e\u65e0\u8bef\u7684\u8ba1\u7b97\u800c\u83b7\u5f97\u3002\u4ed6\u8bf4\uff1a\u201c\u6211\u4eec\u53ef\u4ee5\u8ba4\u4e3a\u5b87\u5b99\u7684\u73b0\u5728\u662f\u7531\u5b83\u7684\u8fc7\u53bb\u6765\u51b3\u5b9a\u7684\uff1b\u73b0\u5728\u4e5f\u662f\u51b3\u5b9a\u672a\u6765\u7684\u539f\u56e0\u3002\u5982\u679c\u6709\u4e00\u4f4d\u667a\u8005\u5728\u67d0\u4e00\u65f6\u523b\u83b7\u77e5\u4e86\u81ea\u7136\u754c\u4e00\u5207\u7269\u4f53\u7684\u4f4d\u7f6e\u548c\u76f8\u4e92\u4f5c\u7528\u529b\uff0c\u5e76\u4e14\u4ed6\u5177\u6709\u8d85\u5e38\u7684\u6570\u636e\u5206\u6790\u80fd\u529b\uff0c\u90a3\u4e48\u4ed6\u5c31\u53ef\u4ee5\u628a\u5b87\u5b99\u8fd9\u4e2a\u6700\u5e9e\u5927\u7684\u7269\u4f53\u76f4\u81f3\u5230\u539f\u5b50\u8fd9\u4e2a\u6700\u7ec6\u5fae\u7684\u9897\u7c92\u5168\u90fd\u56ca\u62ec\u5230\u4e00\u4e2a\u516c\u5f0f\u4e2d\u53bb\u3002\u5bf9\u4e8e\u8fd9\u4f4d\u667a\u8005\u6765\u8bf4\uff0c\u6ca1\u6709\u4ec0\u4e48\u4e1c\u897f\u662f\u4e0d\u786e\u5b9a\u7684\u2014\u2014\u5b87\u5b99\u7684\u672a\u6765\u4f1a\u50cf\u5b83\u7684\u8fc7\u53bb\u4e00\u6837\u5b8c\u5168\u5448\u73b0\u5728\u4ed6\u7684\u773c\u524d\u3002\u201d\u6d1b\u4f26\u8328\u8ba9\u62c9\u666e\u62c9\u65af\u8fd9\u6bb5\u540d\u8a00\u53d8\u6210\u4e86\u201c\u9b54\u5492\u201d<\/span>\uff08Demon\uff09<\/span>\u3002<\/span><\/p>\n


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\u6d1b\u4f26\u8328\u7684\u975e\u51e1\u79d1\u5b66\u53d1\u73b0\u8ba9\u4ed6\u57281991\u5e74\u8363\u83b7\u88ab\u8a89\u4e3a\u201c\u65e5\u672c\u8bfa\u8d1d\u5c14\u5956\u201d\u7684\u4eac\u90fd\u5956<\/span>\uff08Kyoto Prize\uff09<\/span>\uff0c\u201c\u5956\u52b1\u4ed6\u53d1\u73b0\u4e86\u2018\u786e\u5b9a\u6027\u6df7\u6c8c\u2019\u8fd9\u4e00\u6770\u51fa\u79d1\u5b66\u8d21\u732e\uff0c\u5b83\u662f\u6df1\u523b\u5730\u5f71\u54cd\u4e86\u5e7f\u6cdb\u57fa\u7840\u79d1\u5b66\u9886\u57df\u7684\u4e00\u6761\u539f\u7406\uff0c\u63ed\u793a\u4e86\u725b\u987f\u4ee5\u6765\u4eba\u7c7b\u5bf9\u81ea\u7136\u8ba4\u77e5\u7684\u53c8\u4e00\u6b21\u7ffb\u5929\u8986\u5730\u7684\u53d8\u5316\u201d\u3002\u8be5\u5956\u52b1\u7ed9\u6d1b\u4f26\u8328\u9881\u53d1\u4e86\u4e00\u5e45\u5956\u72b6\u3001\u4e00\u4e2a20K\u91d1\u5956\u7ae0\uff0c\u4ee5\u53ca5\u5343\u4e07\u65e5\u5143<\/span>\uff08\u6298\u5408\u4eba\u6c11\u5e013\u767e\u591a\u4e07\u5143\uff09<\/span>\u7684\u5956\u91d1\u3002\u5386\u53f2\u4e0a\uff0c\u7b2c\u4e00\u6b21\u4eac\u90fd\u5956\u57281984\u5e74\u9881\u53d1\uff0c\u83b7\u5956\u8005\u662f\u6d1b\u4f26\u8328\u5728MIT\u7684\u6821\u53cb\u3001\u6570\u5b66\u5bb6\u514b\u52b3\u5fb7\u00b7\u9999\u519c<\/span>\uff08Claude E. Shannon\uff09<\/span>\uff0c\u5956\u52b1\u4ed6\u5728\u4fe1\u606f\u8bba\u65b9\u9762\u7684\u5960\u57fa\u6027\u8d21\u732e\u3002<\/span><\/p>\n


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Kyoto Prize\u9881\u5956\u5178\u793c<\/span><\/p>\n


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\u6d1b\u4f26\u8328\u4e00\u751f\u83b7\u5f97\u8fc7\u4e0d\u5c11\u8363\u8a89\u548c\u5956\u52b1\u3002\u4ed6\u4e8e1969\u5e74\u83b7\u7f8e\u56fd\u6c14\u8c61\u5b66\u4f1aCarl-Gustaf Rossby\u7814\u7a76\u5956\uff0c1973\u5e74\u83b7\u82f1\u56fd\u7687\u5bb6\u6c14\u8c61\u5b66\u4f1aSymons\u91d1\u8d28\u5956\u7ae0\uff0c1975\u5e74\u5f53\u9009\u4e3a\u7f8e\u56fd\u56fd\u5bb6\u79d1\u5b66\u9662\u9662\u58eb\uff0c1981\u5e74\u5f53\u9009\u4e3a\u632a\u5a01\u79d1\u5b66\u4e0e\u6587\u5b66\u9662\u5916\u7c4d\u9662\u58eb\uff0c1983\u83b7\u745e\u5178\u79d1\u5b66\u9662Crafoord \u5956\uff0c1984\u5e74\u83b7\u82f1\u56fd\u6c14\u8c61\u5b66\u9662\u6388\u4e88\u8363\u8a89\u9662\u58eb\uff0c1989\u5e74\u83b7\u7f8e\u56fd\u5bcc\u5170\u514b\u798f\u7814\u7a76\u9662\u9881\u53d1Elliott Cresson\u5956\u7ae0\u3002\u6b64\u540e\uff0c\u6d1b\u4f26\u8328\u4e8e2000\u5e74\u83b7\u4e16\u754c\u6c14\u8c61\u7ec4\u7ec7\u6388\u4e88\u56fd\u9645\u6c14\u8c61\u7ec4\u7ec7\u5956\uff0c2004\u5e74\u83b7\u4fc4\u7f57\u65af\u56fd\u5bb6\u79d1\u5b66\u9662\u6388\u4e88\u7f57\u8499\u6d1b\u7d22\u592b\u91d1\u8d28\u5956\u7ae0\uff0c\u5e76\u83b7\u8377\u5170\u827a\u672f\u4e0e\u79d1\u5b66\u9662\u4e8e1888\u5e74\u8bbe\u7acb\u3001\u5341\u5e74\u9881\u53d1\u4e00\u6b21\u7684Buys Ballot\u5956\u7ae0\u3002\u6d1b\u4f26\u8328\u751f\u524d\u6700\u540e\u4e00\u6b21\u6f14\u8bb2\u662f2008\u5e74\u521d\u5728\u610f\u5927\u5229\u7f57\u9a6c\u63a5\u53d7Tomassoni\u5956\u65f6\u7684\u9886\u5956\u6f14\u8bf4\uff0c\u9898\u76ee\u4f9d\u7136\u662f\u201c\u8774\u8776\u6548\u5e94\u201d<\/span>\uff08\u201cThe butterfly effect\u201d\uff09<\/span>\u3002<\/span><\/p>\n


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\u6d1b\u4f26\u8328\u662f\u4e2a\u53e4\u5178\u578b\u79d1\u5b66\u5bb6\u3002\u4ed6\u4e00\u751f\u53d1\u8868\u4e8661\u7bc7\u8bba\u6587\uff0c\u4efb\u804c\u540e\u81f3\u79bb\u4e16\u5e73\u5747\u6bcf\u5e74\u53d1\u88681\u7bc7\uff0c\u5176\u4e2d58\u7bc7\u662f\u4ed6\u81ea\u5df1\u4e00\u4e2a\u4eba\u5199\u7684\uff0c\u53e6\u59163\u7bc7\u5206\u522b\u548c\u4e00\u4f4d\u540c\u4e8b\u5408\u4f5c\uff0c\u4f46\u6ca1\u6709\u4ed6\u7684\u5bfc\u5e08\u3002\u8bb0\u5f55\u8868\u660e\uff0c\u4ed633\u5c81\u65f6\u53d1\u8868\u7b2c\u4e00\u7bc7\u8bba\u6587\uff0c\u572850\u5c81\u4ee5\u524d\u4ec5\u53d1\u8868\u4e8618\u7bc7\uff0c\u800c60\u5c81\u4ee5\u540e\u5374\u53d1\u8868\u4e8631\u7bc7\u3002\u4ed6\u7684\u53d1\u6587\u9ad8\u5cf0\u671f\u572845-75\u5c81\u4e4b\u95f4\u3002\u4ed6\u4eba\u751f\u6700\u540e\u4e00\u7bc7\u8bba\u6587\u4e5f\u662f\u81ea\u5df1\u5199\u7684\uff0c\u53bb\u4e16\u540e\u4e8e2008\u5e748\u6708\u7531Physica D<\/em>\u6742\u5fd7\u767b\u51fa\uff0c\u9898\u4e3a\u201cCompound windows of the H\u00e9non map\u201d <\/span>(vol.237,pp.1689-1704)<\/span>\u3002<\/span><\/p>\n


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\u6d1b\u4f26\u8328\u665a\u5e74\u8fd8\u7ecf\u5e38\u505a\u5b66\u672f\u6f14\u8bb2<\/span><\/p>\n


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\u6d1b\u4f26\u8328\u4e3a\u81ea\u7136\u79d1\u5b66\u548c\u793e\u4f1a\u79d1\u5b66\u521b\u4e0b\u4e86\u4e00\u4e2a\u4e0d\u673d\u7684\u5947\u8ff9\uff0c\u7136\u800c\u4ed6\u7684\u751f\u5e73\u5374\u76f8\u5bf9\u7b80\u5355\u3002\u6d1b\u4f26\u8328\u4e8e1917\u5e745\u670823\u65e5\u51fa\u751f\u5728\u5eb7\u6d85\u72c4\u683c<\/span>\uff08Connecticut\uff09<\/span>\u5dde\u7684West Hartford\u3002\u4ed6\u7236\u4eb2Edward Henry Lorenz<\/span>\uff081882-1956\uff09<\/span>\u662fMIT\u673a\u68b0\u5de5\u7a0b\u6bd5\u4e1a\u751f\uff0c\u6bcd\u4eb2Grace Peloubet Norton<\/span>\uff081887-1943\uff09<\/span>\u4ece\u4ed6\u5e74\u5c11\u5f00\u59cb\u4e00\u76f4\u9f13\u52b1\u548c\u5f15\u5bfc\u4ed6\u548c\u9ad8\u624b\u4e0b\u68cb\u5e76\u505a\u535a\u5f08\u6e38\u620f\uff0c\u5341\u5206\u6ce8\u91cd\u4ed6\u7684\u667a\u529b\u53d1\u5c55\u3002\u4ed6\u7684\u5916\u7956\u7236Lewis M. Norton\u662fMIT\u6559\u6388\uff0c\u4e5f\u662f\u5f00\u8bbe\u5316\u5de5\u8bfe\u7a0b\u7b2c\u4e00\u4eba\u3002\u6d1b\u4f26\u83281938\u5e74\u4eceDartmouth College\u83b7\u5f97\u6570\u5b66\u5b66\u58eb\u5b66\u4f4d\uff0c1940\u5e74\u4ece\u54c8\u4f5b\u5927\u5b66\u83b7\u5f97\u6570\u5b66\u7855\u58eb\u5b66\u4f4d\uff0c1941\u5e74\u72ec\u81ea\u5728\u7f8e\u56fd\u79d1\u5b66\u9662\u9662\u520a<\/span>\uff08PNAS<\/em>\uff09<\/span>\u53d1\u8868\u4e86\u7b2c\u4e00\u7bc7\u8bba\u6587\u201cA generalization of the Dirac equations\u201d\u3002\u4ed6\u63a5\u4e0b\u6765\u5230\u4e86\u90e8\u961f\u670d\u5f79\uff0c\u4e8c\u6218\u671f\u95f4\u5728\u7a7a\u519b\u6c14\u8c61\u7ad9\u5f53\u5929\u6c14\u9884\u62a5\u5458\u3002\u671f\u95f4\uff0c1943\u5e74\u4ed6\u5728MIT\u5b8c\u6210\u4e86\u6c14\u8c61\u7855\u58eb\u5b66\u4f4d\uff0c\u6218\u540e1948\u5e74\u5728MIT\u53d6\u5f97\u4e86\u6c14\u8c61\u535a\u58eb\u5b66\u4f4d\u3002\u4ed6\u7684\u535a\u58eb\u5bfc\u5e08James Murdoch Austin<\/span>\uff081915-2000\uff09<\/span>\u662f\u65b0\u897f\u5170\u4eba\uff0c\u7f8e\u56fd\u79d1\u5b66\u4e0e\u827a\u672f\u79d1\u5b66\u9662\u9662\u58eb\uff0c\u66fe\u83b7\u5f97\u8fc7\u603b\u7edf\u9881\u53d1\u7684\u81ea\u7531\u52cb\u7ae0\u3002\u6d1b\u4f26\u8328\u7684\u535a\u58eb\u8bba\u6587\u9898\u4e3a\u201c\u5e94\u7528\u6c34\u529b\u5b66\u548c\u70ed\u529b\u5b66\u65b9\u7a0b\u7814\u7a76\u5927\u6c14\u6a21\u578b\u7684\u65b0\u65b9\u6cd5\u201d\u3002\u4ed6\u6bd5\u4e1a\u540e\u7559\u6821\u5728\u6c14\u8c61\u7cfb\u4efb\u6559\uff0c1962\u5e74\u664b\u5347\u4e3a\u6b63\u6559\u6388\uff0c1977-1981\u5e74\u95f4\u4efb\u7cfb\u4e3b\u4efb\uff0c1987\u5e74\u8363\u4f11\uff0c2008\u5e744\u670816\u65e5\u56e0\u60a3\u764c\u75c7\u5728\u5bb6\u4e2d\u79bb\u4e16\uff0c\u4eab\u5e7491\u5c81\u3002\u4ed6\u592b\u4ebaJane Loban\u4e8e2001\u5e74\u53bb\u4e16\u3002\u4ed6\u4eec\u6709\u4e09\u4e2a\u5b69\u5b50\uff1a\u5973\u513fNancy\u548cCheryl\u3001\u513f\u5b50Edward\u3002<\/span><\/p>\n


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\u6d1b\u4f26\u8328\u662f\u4e2a\u6e29\u6587\u5c14\u96c5\u7684\u8c26\u8c26\u541b\u5b50\u3002\u670b\u53cb\u4eec\u90fd\u8bf4\u4ed6\u201cModest and soft-spoken\u201d\u3002\u4ed6\u559c\u6b22\u91ce\u5916\u8dcb\u6d89\u548c\u9ad8\u5c71\u6ed1\u96ea\uff0c\u8fd8\u5e38\u5e38\u5728\u5b66\u672f\u4f1a\u8bae\u4e4b\u540e\u53bb\u9644\u8fd1\u7684\u5c71\u6797\u8fdc\u8db3\u3002\u4ed6\u53bb\u4e16\u65f6\uff0c\u5973\u513fCheryl\u5bf9\u4eb2\u53cb\u8bf4\uff1a\u201c\u4ed6\u4e24\u5468\u534a\u524d\u8fd8\u53bb\u722c\u5c71\uff0c\u4e00\u5468\u524d\u8fd8\u548c\u540c\u4e8b\u4e00\u8d77\u5b8c\u6210\u4e86\u4e00\u7bc7\u8bba\u6587\u3002\u201d<\/span><\/p>\n


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\u6d1b\u4f26\u8328 @ Mt Battie\uff08Lorenz Center\uff09<\/span><\/p>\n


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2011\u5e74\uff0cMIT\u6210\u7acb\u4e86\u6d1b\u4f26\u8328\u5b66\u672f\u7814\u7a76\u4e2d\u5fc3\uff0c\u79c9\u627f\u6d1b\u4f26\u8328\u7684\u65e8\u610f\uff0c\u201c\u8ffd\u6c42\u5bf9\u6c14\u8c61\u5b66\u57fa\u672c\u539f\u7406\u7684\u8ba4\u77e5\u201d\u3002\u7814\u7a76\u4e2d\u5fc3\u7684\u7b79\u5efa\u8005\u66fe\u5f15\u8ff0\u6d1b\u4f26\u8328\u57282005\u5e74\u5199\u4e0b\u7684\u4e00\u6bb5\u8bdd\uff1a\u201c\u4eba\u4eec\u7ecf\u5e38\u90fd\u4f1a\u770b\u5230\uff0c\u7eaf\u7cb9\u7406\u8bba\u7814\u7a76\u7684\u4e00\u70b9\u70b9\u6210\u679c\uff0c\u4e5f\u8bb8\u5728\u5f88\u957f\u65f6\u95f4\u4e4b\u540e\uff0c\u4f1a\u5bfc\u81f4\u8fde\u505a\u8be5\u7eaf\u7406\u8bba\u7814\u7a76\u7684\u79d1\u5b66\u5bb6\u90fd\u59cb\u6599\u4e0d\u53ca\u7684\u5b9e\u9645\u5e94\u7528\u3002<\/span>\u201d<\/span><\/span><\/p>\n


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\u6df7\u6c8c\u7406\u8bba\u5148\u9a71\u674e\u5929\u5ca9\u53bb\u4e16\uff0c\u6700\u65e9\u4e25\u683c\u5b9a\u4e49\u201c\u6df7\u6c8c\u201d\uff0c\u63d0\u51fa\u201c\u5468\u671f\u4e09\u5373\u6df7\u6c8c\u201d<\/strong><\/span><\/a><\/section>\n
\u4e0d\u7528\u7e41\u7410\u516c\u5f0f\uff0c\u5982\u4f55\u9884\u6d4b\u590d\u6742\u7684\u6df7\u6c8c\u7cfb\u7edf\uff1f<\/strong><\/span><\/a><\/section>\n
\u590d\u6742\u7cfb\u7edf\u5148\u9a71\u7f57\u4f2f\u7279\u00b7\u6885\u53bb\u4e16\uff0c\u4e00\u751f\u8de8\u8d8a\u6570\u7406\u3001\u751f\u6001\u548c\u590d\u6742\u6027<\/a><\/strong><\/strong><\/span><\/section>\n
\u9999\u519c\uff1a\u65e0\u7f18\u8bfa\u5956\u7684\u4fe1\u606f\u8bba\u4e4b\u7236\uff0c\u5374\u5728\u4e0d\u540c\u65f6\u7a7a\u4e0e22\u4f4d\u79d1\u5b66\u5bb6\u76f8\u9047<\/span><\/a><\/span><\/strong><\/strong><\/span>
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\u5546\u52a1\u5408\u4f5c\u53ca\u6295\u7a3f\u8f6c\u8f7d\uff5cswarma@swarma.org
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\u25c6 <\/span>\u25c6 <\/span>\u25c6<\/span><\/span><\/strong><\/strong><\/h1>\n<\/section>\n

\u641c\u7d22\u516c\u4f17\u53f7\uff1a\u96c6\u667a\u4ff1\u4e50\u90e8<\/span><\/strong><\/span><\/p>\n


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\u52a0\u5165\u201c\u6ca1\u6709\u56f4\u5899\u7684\u7814\u7a76\u6240\u201d<\/span><\/strong><\/span><\/p>\n

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\u8ba9\u82f9\u679c\u7838\u5f97\u66f4\u731b\u70c8\u4e9b\u5427\uff01<\/span><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


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\ud83d\udc47\u70b9\u51fb\u201c\u9605\u8bfb\u539f\u6587\u201d\uff0c\u8ffd\u8e2a\u590d\u6742\u79d1\u5b66\u6700\u65b0\u9876\u520a\u8bba\u6587<\/span><\/span><\/p>\n<\/section>\n

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\u5bfc\u8bed \u201c\u4eba\u4eec\u7ecf\u5e38\u90fd\u4f1a\u770b\u5230\uff0c\u7eaf\u7cb9\u7406\u8bba\u7814\u7a76\u7684\u4e00\u70b9\u70b9\u6210\u679c\uff0c\u4e5f\u8bb8\u5728\u5f88\u957f\u65f6\u95f4\u4e4b\u540e\uff0c\u4f1a\u5bfc\u81f4\u8fde\u505a\u8be5\u7eaf\u7406\u8bba\u7814\u7a76\u7684\u79d1\u5b66\u5bb6\u90fd\u59cb\u6599\u4e0d\u53ca\u7684\u5b9e\u9645\u5e94\u7528\u3002\u201d \u2014\u2014\u7231\u5fb7\u534e\u00b7\u8bfa\u987f\u00b7\u6d1b\u4f26\u8328 \u4ed6\u4e0d\u662f\u6587\u5b66\u5bb6\uff0c\u5374\u5728\u4e0d\u7ecf\u610f\u95f4\u7559\u4e0b\u4e86\u4e00\u4e2a\u810d\u7099\u4eba\u53e3\u7684\u65b0\u6210\u8bed\uff1a\u8774\u8776\u6548\u5e94\u3002 \u4ed6\u662f\u9ebb\u7701\u7406\u5de5\u5b66\u9662\uff08MIT\uff09\u6c14\u8c61\u7cfb\u5df2\u6545\u6559\u6388\u7231\u5fb7\u534e\u00b7\u8bfa\u987f\u00b7\u6d1b\u4f26\u8328\uff08Edward No…<\/p>\n","protected":false},"author":1,"featured_media":21231,"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\/21251"}],"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=21251"}],"version-history":[{"count":0,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/21251\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/media\/21231"}],"wp:attachment":[{"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=21251"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=21251"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=21251"},{"taxonomy":"special","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fspecial&post=21251"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}