{"id":23381,"date":"2022-03-25T17:47:06","date_gmt":"2022-03-25T09:47:06","guid":{"rendered":"http:\/\/www.qiusir.com\/?p=23381"},"modified":"2022-03-25T17:47:06","modified_gmt":"2022-03-25T09:47:06","slug":"%e5%be%ae%e7%a7%af%e5%88%86%e7%9a%84%e5%8a%9b%e9%87%8f","status":"publish","type":"post","link":"https:\/\/www.qiusir.com\/?p=23381","title":{"rendered":"\u5fae\u79ef\u5206\u7684\u529b\u91cf*"},"content":{"rendered":"<p><center><img decoding=\"async\" alt=\"read\" src=\"http:\/\/www.qiusir.com\/wp-content\/gallery\/net\/infinitepowers.jpg\" width=\"480\" class=\"framed\" \/><\/center><br \/>\nInfinite Powers<br \/>\nHow Calculus reveal the Secrets of the Universe<br \/>\nSteven Strogatz \u65af\u6258\u52a0\u8328\u8457 \u4efb\u70e8\u8bd1<br \/>\n@qiusir:\u6211\u8ba4\u8bc6\u7684\u4eba\uff0c\u4e0d\u7ba1\u6709\u5b66\u95ee\u6ca1\u5b66\u95ee\u7684\u90fd\u77e5\u9053\u8bfb\u4e66\u662f\u4e00\u4ef6\u503c\u5f97\u9f13\u52b1\u7684\u4e8b\uff0c\u4f46\u8eab\u8fb9\u771f\u6b63\u80fd\u8bfb\u4e66\u7684\u4eba\u5374\u5f88\u5c11\uff0c\u800c\u90a3\u79cd\u5bf9\u4e66\u7684\u8d5e\u8a89\u4e5f\u591a\u6765\u81ea\u62bd\u8c61\u6216\u662f\u76f2\u76ee\u3002\u6211\u81ea\u5df1\u4e5f\u662f\u8fd9\u4e9b\u5e74\u624d\u771f\u6b63\u53bb\u8bfb\u4e66\uff0c\u6df1\u611f\u8d8a\u65e9\u5728\u8eab\u8fb9\u9047\u5230\u771f\u6b63\u7684\u8bfb\u4e66\u4eba\u5f88\u91cd\u8981\uff0c\u611f\u6fc0\u80fd\u5f15\u5bfc\u81ea\u5df1\u771f\u6b63\u53bb\u8bfb\u4e66\u7684\u4eba\uff0c\u90a3\u624d\u662f\u8001\u5e08\u771f\u6b63\u5e94\u8be5\u505a\u7684\u4e8b&#8230;\u4e66\uff0c\u624d\u62e5\u6709infinite powers<br \/>\n\u5f15\u8a00<br 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\/>\n<strong>\u4f5c\u4e3a\u4e00\u540d\u5e94\u7528\u6570\u5b66\u5bb6\uff0c\u771f\u6b63\u5438\u5f15\u6211\u7684\u662f\u6211\u4eec\u5468\u56f4\u7684\u73b0\u5b9e\u4e16\u754c\u548c\u6211\u4eec\u5934\u8111\u4e2d\u7684\u7406\u60f3\u4e16\u754c\u4e4b\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\u3002\u5916\u754c\u7684\u73b0\u8c61\u5f15\u5bfc\u7740\u6211\u4eec\u63d0\u51fa\u6570\u5b66\u95ee\u9898\uff1b\u53cd\u8fc7\u6765\uff0c\u6211\u4eec\u7684\u6570\u5b66\u60f3\u8c61\u6709\u65f6\u4e5f\u4f1a\u9884\u8a00\u73b0\u5b9e\u4e16\u754c\u7684\u4e8b\u60c5\u3002<\/strong><br 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\/>\n\u829d\u8bfa\u8bd5\u56fe\u8bc1\u660e\u6539\u53d8\u65f6\u4e0d\u53ef\u80fd\u53d1\u751f\u7684\u3002\u5728\u829d\u8bfa\u770b\u6765\uff0c\u5c3d\u7ba1\u611f\u5b98\u544a\u8bc9\u6211\u4eec\u8fd9\u4e0d\u662f\u4e8b\u5b9e\uff0c\u4f46\u5b83\u5b9e\u9645\u4e0a\u6b3a\u9a97\u4e86\u6211\u4eec\uff1b\u6539\u53d8\u662f\u4e00\u79cd\u9519\u89c9&#8230;\u5728\u4f60\u8d70\u4e00\u6b65\u4e4b\u524d\uff0c\u4f60\u9700\u8981\u5148\u8d701\/2\u6b65\uff1b\u5728\u4f60\u8d70\u53bb1\/2\u6b65\u4e4b\u524d\uff0c\u4f60\u9700\u8981\u8d701\/4\u6b65\uff0c\u6362\u4e00\u6b21\u7c7b\u63a8&#8230;\u4f60\u975e\u4f46\u8d70\u4e0d\u5230\u5899\u6839\u5904\uff0c\u751a\u81f3\u6ca1\u529e\u6cd5\u51fa\u53d1\u3002<br \/>\n\u5982\u679c\u4f60\u8ba4\u4e3a\u81ea\u5df1\u5728\u505a\u65e9\u9910\u524d\u6709\u5f88\u591a\u4e8b\u60c5\u8981\u505a\uff0c\u5c31\u53ef\u4ee5\u60f3\u8c61\u4f60\u5fc5\u987b\u5b8c\u6210\u65e0\u7a77\u591a\u9879\u4efb\u52a1\u4e4b\u540e\u624d\u80fd\u5230\u8fbe\u53a8\u623f\u3002<br \/>\n\u867d\u7136\u829d\u8bfa\u5bf9\u963f\u5580\u7409\u65af\u8981\u5b8c\u6210\u65e0\u7a77\u591a\u9879\u4efb\u52a1\u7684\u5224\u65ad\u662f\u5bf9\u7684&#8230;<br \/>\n<strong>\u98de\u77e2\u4e0d\u52a8<\/strong>\uff1a\u5982\u679c\u7a7a\u95f4\u548c\u65f6\u95f4\u662f\u79bb\u6563\u7684\uff0c\u98de\u77e2\u5c31\u672a\u66fe\u79fb\u52a8\uff0c\u56e0\u4e3a\u5728\u6bcf\u4e00\u4e2a\u77ac\u95f4\uff0c\u98de\u77e2\u90fd\u5728\u67d0\u4e2a\u786e\u5b9a\u7684\u4f4d\u7f6e&#8230;\u5728\u4efb\u4f55\u7ed9\u5b9a\u7684\u77ac\u95f4\uff0c\u98de\u77e2\u90fd\u6b7b\u9759\u6b62\u4e0d\u52a8\u7684\u3002<br \/>\n\u666e\u6717\u514b\u957f\u5ea6$$\\sqrt{\\frac{\\hbar G}{c^3}}$$<br \/>\n2<br \/>\n\u9a7e\u9a6d\u65e0\u7a77\u7684\u52c7\u58eb<br \/>\n\u963f\u57fa\u7c73\u5fb7\u5341\u5206\u75f4\u8ff7\u51e0\u4f55\u5b66\uff0c\u4ee5\u81f3\u4e8e\u201c\u5fd8\u4e86\u5403\u996d\uff0c\u84ec\u5934\u57a2\u9762\u201d&#8230;\u5fc5\u987b\u6709\u4eba\u201c\u5f3a\u884c\u62fd\u7740\u4ed6\u53bb\u6d17\u6fa1\u201d\u3002<br \/>\n$$S=1+2\\times\\frac{1}{8}+2\\times\\frac{1}{16}+$$<br \/>\n$$4S=4(1+2\\times\\frac{1}{8}+2\\times\\frac{1}{16}+)=4+S$$<br \/>\n\u798f\u5c14\u6469\u65af\uff1a\u201c\u5728\u4f60\u6392\u9664\u4e86\u4e0d\u80fd\u7684\u60c5\u51b5\u4e4b\u540e\uff0c\u5269\u4e0b\u7684\u65e0\u8bba\u591a\u4e48\u4e0d\u53ef\u601d\u8bae\uff0c\u90fd\u4e00\u5b9a\u662f\u771f\u76f8\u3002\u201d<br \/>\n\u6570\u5b66\u5bb6\u4e0d\u4f1a\u4e00\u4e0b\u5b50\u60f3\u5230\u8bc1\u660e\u65b9\u6cd5\uff0c\u800c\u662f\u5148\u4ea7\u751f\u76f4\u89c9\uff0c\u518d\u8003\u8651\u4e25\u8c28\u6027\u7684\u95ee\u9898\u3002\u9ad8\u4e2d\u7684\u51e0\u4f55\u8bfe\u7a0b\u5e38\u5e38\u5ffd\u7565\u76f4\u89c9\u548c\u60f3\u8c61\u529b\u7684\u91cd\u8981\u4f5c\u7528\uff0c\u4f46\u4ed6\u4eec\u5bf9\u6240\u6709\u521b\u9020\u6027\u6570\u5b66\u7814\u7a76\u6765\u8bf4\u90fd\u662f\u4e0d\u53ef\u6216\u7f3a\u7684\u3002<br \/>\n\u963f\u57fa\u7c73\u5fb7\u6700\u540e\u63d0\u51fa\u4e86\u4ed6\u7684\u5e0c\u671b\uff1a\u201c\u5728\u73b0\u5728\u548c\u672a\u6765\u7684\u51e0\u4e2a\u4e16\u4ee3\u4e2d\uff0c\u67d0\u4e9b\u4eba\u4f1a\u5229\u7528\u8fd9\u79cd\u65b9\u6cd5\uff0c\u627e\u5230\u6211\u4eec\u5c1a\u672a\u638c\u63e1\u7684\u5176\u4ed6\u5b9a\u7406\u3002\u201d\u8fd9\u53e5\u8bdd\u51e0\u4e4e\u8ba9\u6211\u70ed\u6cea\u76c8\u7736\u3002<br \/>\n\uff08\u62bd\u7a7a\u8981\u628a\u963f\u57fa\u7c73\u5fb7\u7684\u65b9\u6cd5\u6784\u56fe\u8865\u4e0a\u3002\uff09<br \/>\n\u963f\u57fa\u7c73\u5fb7\u4f4e\u8c03\u5730\u79f0\u81ea\u5df1\u7684\u65b9\u6cd5\u77e5\u8bc6\u8868\u660e\u7ed3\u8bba\u6b63\u786e\u7684\u201c\u67d0\u79cd\u8ff9\u8c61\u201d\u3002<br \/>\n22\u4e2a\u4e16\u7eaa\u4e4b\u524d\uff0c\u963f\u57fa\u7c73\u5fb7\u7ed9\u4ed6\u7684\u670b\u53cb\u3001\u4e9a\u5386\u5c71\u5927\u56fe\u4e66\u9986\u9986\u957f\u57c3\u62c9\u6258\u8272\u5c3c\u5199\u4fe1&#8230;\uff08\u6d4b\u91cf\u5730\u7403\u534a\u5f84\uff09<br \/>\n3<br \/>\n\u8fd0\u52a8\u5b9a\u5f8b\u7684\u63a2\u7d22\u4e4b\u65c5<br \/>\n\u963f\u57fa\u7c73\u5fb7\u53bb\u4e16\u540e\uff0c\u5173\u4e8e\u81ea\u7136\u7684\u6570\u5b66\u7814\u7a76\u4e5f\u51e0\u4e4e\u968f\u4e4b\u6d88\u901d\uff0c\u76f4\u52301800\u5e74\u540e\u4e00\u4e2a\u65b0\u7684\u201c\u963f\u57fa\u7c73\u5fb7\u201d\u767b\u4e0a\u5386\u53f2\u821e\u53f0\u3002\u5728\u6587\u827a\u590d\u5174\u65f6\u671f\uff0c\u4e00\u4f4d\u540d\u53eb\u4f3d\u5229\u7565\u00b7\u4f3d\u5229\u96f7\u7684\u5e74\u8f7b\u6570\u5b66\u5bb6\u91cd\u62fe\u963f\u57fa\u7c73\u5fb7\u7684\u672a\u7adf\u4e4b\u4e1a\u3002<br \/>\n\u4e0e\u6b64\u540c\u65f6\uff0c\u5e74\u8f7b\u7684\u5fb7\u56fd\u6570\u5b66\u5bb6\u5f00\u666e\u52d2\u7814\u7a76\u4e86\u884c\u661f\u662f\u5982\u4f55\u5728\u5929\u7a7a\u4e2d\u8fd0\u884c\u7684\u3002\u4ed6\u4eec\u4fe9\u90fd\u88ab\u5404\u81ea\u6570\u636e\u4e2d\u7684\u6a21\u5f0f\u6df1\u6df1\u5438\u5f15\uff0c\u5e76\u610f\u8bc6\u5230\u5b58\u5728\u67d0\u79cd\u6df1\u5c42\u6b21\u7684\u4e1c\u897f\u3002<br \/>\n\u4f3d\u5229\u7565\u548c\u5f00\u666e\u52d2\u5192\u9669\u51b2\u51fa\u4e86\u963f\u57fa\u7c73\u5fb7\u7684\u9759\u6001\u4e16\u754c\uff0c\u53bb\u63a2\u7d22\u7269\u4f53\u662f\u5982\u4f55\u8fd0\u52a8\u7684\u3002<br \/>\n\u884c\u661fplanet\u7684\u539f\u610f\u662f\u6d41\u6d6a\u8005&#8230;<br \/>\n\uff08\u9006\u884c\uff09<br \/>\n\u5c3d\u7ba1\u671b\u8fdc\u955c\u5e76\u4e0d\u662f\u4f3d\u5229\u7565\u53d1\u660e\u7684\uff0c\u4f46\u4ed6\u5bf9\u671b\u8fdc\u955c\u505a\u51fa\u4e86\u6539\u8fdb\uff0c\u5e76\u4e14\u662f\u7b2c\u4e00\u4e2a\u5229\u7528\u5b83\u53d6\u5f97\u91cd\u5927\u79d1\u5b66\u53d1\u73b0\u7684\u4eba\u3002\uff081609\u5e74&#8212;2009\u5e74\u4e16\u754c\u5929\u6587\u5e74\uff09<br \/>\n\u300a\u5173\u4e8e\u4e24\u95e8\u65b0\u79d1\u5b66\u7684\u5bf9\u8bdd\u300b\u662f\u4f3d\u5229\u7565\u6bd5\u751f\u7684\u5dc5\u5cf0\u4e4b\u4f5c\uff0c\u4e5f\u662f\u73b0\u4ee3\u7269\u7406\u5b66\u7684\u7b2c\u4e00\u90e8\u6770\u4f5c\u3002\u7528\u7684\u662f\u610f\u5927\u5229\u8bed\u800c\u4e0d\u662f\u62c9\u4e01\u8bed\uff0c\u76ee\u7684\u662f\u8ba9\u6240\u6709\u4eba\u90fd\u80fd\u770b\u61c2\u5b83\u3002\u4ed6\u5b89\u6392\u4eba\u628a\u4e66\u7a3f\u5077\u5077\u5e26\u53bb\u8377\u5170\uff0c\u5e76\u4e8e1638\u5e74\u5728\u90a3\u91cc\u51fa\u7248\u3002<\/p>\n<blockquote><p>\u4e9a\u91cc\u58eb\u591a\u5fb7\u88ab\u590d\u6742\u7684\u56e0\u7d20\u5f15\u5165\u6b67\u9014\uff0c\u4ee5\u81f4\u5f97\u51fa\u4e86\u9519\u8bef\u7684\u843d\u4f53\u5b9a\u5f8b\u3002<br \/>\n<strong>\u4e9a\u91cc\u58eb\u591a\u5fb7\u8fc7\u4e8e\u5173\u6ce8\u566a\u58f0\uff08\u7a7a\u6c14\u963b\u529b\uff09\uff0c\u800c\u4e0d\u591f\u91cd\u89c6\u4fe1\u53f7\uff08\u60ef\u6027\u548c\u5f15\u529b\uff09\u3002<\/strong>\uff08\u5e38\u4eba\u90fd\u662f\u88ab\u5c0f\u4e8b\u803d\u8bef\u7684\uff0c\u5927\u4e8b\u53cd\u800c\u4e0d\u8ba1\u8f83\u3002\uff09<br \/>\n\u4ee3\u8868\u4f3d\u5229\u7565\u7684\u4eba\u7269\u529b\u529d\u5934\u8111\u7b80\u5355\u7684\u4e9a\u91cc\u58eb\u591a\u5fb7\u5b66\u6d3e\u7684\u63d0\u95ee\u8005\uff0c\u4e0d\u8981\u201c\u504f\u79bb\u8ba8\u8bba\u7684\u4e3b\u9898\uff0c\u800c\u6293\u7740\u6211\u7684\u67d0\u4e9b\u548c\u771f\u76f8\u53ea\u6709\u6beb\u53d1\u4e4b\u5dee\u7684\u9648\u8ff0\u4e0d\u59a8\uff0c\u6b8a\u4e0d\u77e5\u5728\u8fd9\u6839\u5934\u53d1\u4e4b\u4e0b\uff0c\u9690\u85cf\u7740\u53e6\u4e00\u4e2a\u4eba\u7684\u50cf\u8239\u8236\u7f06\u7ef3\u4e00\u6837\u663e\u773c\u7684\u9519\u8bef\u3002\u201d<\/p><\/blockquote>\n<p>\u8fd9\u6b63\u662f\u95ee\u9898\u7684\u5173\u952e\u6240\u5728\u3002\u5728\u79d1\u5b66\u4e2d\uff0c\u6beb\u53d1\u4e4b\u5dee\u662f\u53ef\u4ee5\u63a5\u6536\u7684\uff0c\u4f46\u50cf\u8239\u8236\u7f06\u7ef3\u90a3\u6837\u663e\u773c\u7684\u8bef\u5dee\u5c31\u4e0d\u884c\u4e86\u3002<br 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\/>\n\u5c31\u50cf\u5bfc\u6570\u6bd4\u659c\u7387\u66f4\u91cd\u8981\uff0c\u79ef\u5206\u4e5f\u6bd4\u9762\u79ef\u91cd\u8981\u3002<br \/>\n\u5fae\u79ef\u5206\u662f\u6570\u5b66\u9886\u57df\u7684\u201c\u5bd2\u6b66\u7eaa\u5927\u7206\u53d1\u201d(\u4ea6\u79f0\u5bd2\u6b66\u7eaa\u751f\u547d\u5927\u7206\u53d1\uff0cCambrian Explosion)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Infinite Powers How Calculus reveal the Secrets of the  &#8230; <a title=\"\u5fae\u79ef\u5206\u7684\u529b\u91cf*\" class=\"read-more\" href=\"https:\/\/www.qiusir.com\/?p=23381\" aria-label=\"\u9605\u8bfb 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