@mhg/blog

<?xml version="1.0" encoding="utf-8"?> <feed xmlns="http://www.w3.org/2005/Atom"> <title>Magicland</title> <icon>https://blog.mhuig.top/favicon.ico</icon> <subtitle>宠辱不惊，看庭前花开花落；去留无意，望天上云卷云舒。</subtitle> <link href="https://blog.mhuig.top/atom.xml" rel="self"/> <link href="https://blog.mhuig.top/"/> <updated>2026-05-05T04:18:00.000Z</updated> <id>https://blog.mhuig.top/</id> <author> <name>MHuiG</name> </author> <generator uri="https://hexo.io/">Hexo</generator> <entry> <title>空白的答案</title> <link href="https://blog.mhuig.top/p/cb3fc42/"/> <id>https://blog.mhuig.top/p/cb3fc42/</id> <published>2026-05-05T03:51:00.000Z</published> <updated>2026-05-05T04:18:00.000Z</updated> <content type="html"><![CDATA[<img style="display: none;" no-lazy src="https://api.mhuig.top/pixel-blog-atom-12138.gif">当唐僧师徒历经九九八十一难抵达灵山，阿傩、伽叶却因未得 “人事” 而传无字真经。孙悟空怒而质问，佛祖却笑着说：“白本者，乃无字真经，倒也是好的。” 这像极了《功夫熊猫》里的神龙秘籍：阿宝打开卷轴，只映出自己的脸，茫然失措时，阿宝的父亲传授祖传面汤 “那鲜汤的秘密配方就是不加料，根本就没什么秘方，要做出特别的东西你必须相信他很特别。” 原来，所谓的秘密配方，不过是让你相信自己手中的汤就是最好的汤。“昨天是段历史，明天是个谜团，而今天是天赐的礼物，像珍惜礼物那样珍惜今天。” 我们总在追逐未来的答案，却忘了当下的每一刻都是答案本身。唐僧在取经路上经历的每一次磨难，都是无字真经的注脚，燃灯古佛曾暗笑 “东土众生愚迷，不识无字之经”；阿宝在厨房领悟的 “相信自己”，才是神龙秘籍的真谛。那些看似空白的智慧，其实藏在我们对当下的专注里，就像鲜汤的秘密，不在于添加多少调料，而在于你是否相信自己手中的食材本就独一无二。“昨日已成过去，未来充满可能，唯有珍惜现在。” 当我们不再执着于寻找某个 “标准答案”，而是相信自己正在创造答案时，空白就变成了无限的可能。阿傩的无字经不是敷衍，而是让师徒明白：真经不在纸上，而在取经的每一步；神龙秘籍的空白不是欺骗，而是让阿宝明白：力量不在卷轴里，而在他对自己的信任中。就像那碗鲜汤，真正的秘方，是你愿意为它倾注的热爱与信心。或许，生活给我们的每一个 “空白”，都是在邀请我们写下自己的答案。毕竟，最珍贵的秘籍，从来不是别人给的，而是你相信自己能创造的。]]></content> <summary type="html">昨天是段历史，明天是个谜团，而今天是天赐的礼物，像珍惜礼物那样珍惜今天。</summary> <category term="随笔" scheme="https://blog.mhuig.top/categories/%E9%9A%8F%E7%AC%94/"/> <category term="探索" scheme="https://blog.mhuig.top/tags/%E6%8E%A2%E7%B4%A2/"/> </entry> <entry> <title></title> <link href="https://blog.mhuig.top/p/person-archive/"/> <id>https://blog.mhuig.top/p/person-archive/</id> <published>2026-05-04T06:59:00.000Z</published> <updated>2026-05-04T10:18:00.000Z</updated> <content type="html"><![CDATA[<img style="display: none;" no-lazy src="https://api.mhuig.top/pixel-blog-atom-12138.gif"><svg style="width: 50px; margin: 0 auto; display: block;" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 320 512"><path d="M0 64C0 46.3 14.3 32 32 32l128 0c88.4 0 160 71.6 160 160S248.4 352 160 352l-96 0 0 96c0 17.7-14.3 32-32 32S0 465.7 0 448L0 64zM64 288l96 0c53 0 96-43 96-96s-43-96-96-96l-96 0 0 192z"></path></svg>History of mathematics <a class="button" href="/notes/person/" title="开始阅读">开始阅读</a> <h1 hidden="">History of mathematics</h1>]]></content> <summary type="html">历史人物梳理历史人物的生平轨迹与重大事迹，深入剖析了其时代背景下的关键抉择与行动，并系统评估了其在文化或科学领域所产生的持久历史影响与贡献。</summary> <category term="数学" scheme="https://blog.mhuig.top/categories/%E6%95%B0%E5%AD%A6/"/> <category term="History" scheme="https://blog.mhuig.top/categories/%E6%95%B0%E5%AD%A6/History/"/> <category term="Math" scheme="https://blog.mhuig.top/tags/Math/"/> <category term="Notes" scheme="https://blog.mhuig.top/tags/Notes/"/> </entry> <entry> <title>爱与时空的星际救赎：《星际穿越》中的生存抉择与人性光辉</title> <link href="https://blog.mhuig.top/p/56c48370/"/> <id>https://blog.mhuig.top/p/56c48370/</id> <published>2025-11-22T00:08:00.000Z</published> <updated>2025-11-23T22:18:00.000Z</updated> <content type="html"><![CDATA[<img style="display: none;" no-lazy src="https://api.mhuig.top/pixel-blog-atom-12138.gif"><h3 id="地球危机与生存觉醒"><a href="#地球危机与生存觉醒" class="headerlink" title="地球危机与生存觉醒"></a>地球危机与生存觉醒</h3><img src="https://unpkg.com/mhgoos@0.0.1763936965667/img_moment_1763936851306_edit_518957029171458.jpg" class="lazyload" data-srcset="https://unpkg.com/mhgoos@0.0.1763936965667/img_moment_1763936851306_edit_518957029171458.jpg" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="我们曾经仰望星空">We used to look up at the sky and wonder at our place in the stars, now we just look down and worry about our place in the dirt.我们曾经仰望星空并且期许总有一天可以登陆其他星球，但现在我们只能低头担心我们居住地的废土。<img src="https://unpkg.com/mhgoos@0.0.1763773377454/v2-fbae8e21a69fbad845fc06e2c9df1a09_r.webp" class="lazyload" data-srcset="https://unpkg.com/mhgoos@0.0.1763773377454/v2-fbae8e21a69fbad845fc06e2c9df1a09_r.webp" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="玉米地">Cooper: Mankind was born on Earth. It was never meant to die here.库珀：人类生在地球，但绝不应该在这里灭亡。<img src="https://unpkg.com/mhgoos@0.0.1763773454016/v2-152e036633262d8396e6f7bce14b899e_r.webp" class="lazyload" data-srcset="https://unpkg.com/mhgoos@0.0.1763773454016/v2-152e036633262d8396e6f7bce14b899e_r.webp" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="灰尘密码"><h3 id="告别地球与父女约定"><a href="#告别地球与父女约定" class="headerlink" title="告别地球与父女约定"></a>告别地球与父女约定</h3><img src="https://unpkg.com/mhgoos@0.0.1763806815832/img_moment_1763805976973_edit_447736074900450.jpg" class="lazyload" data-srcset="https://unpkg.com/mhgoos@0.0.1763806815832/img_moment_1763805976973_edit_447736074900450.jpg" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="墨菲汽车"><img src="https://unpkg.com/mhgoos@0.0.1763904344597/109951172312274244.jpg" class="lazyload" data-srcset="https://unpkg.com/mhgoos@0.0.1763904344597/109951172312274244.jpg" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="墨菲定律并非指的是那些变坏的事情必会发生">Murphy’s law doesn’t mean that something bad will happen. It means that whatever can happen, will happen.墨菲定律并非指的是那些变坏的事情必会发生，而是指那些能够发生的事情，就会发生。<img src="https://unpkg.com/mhgoos@0.0.1763907572121/IMG_20251123_221737.jpg" class="lazyload" data-srcset="https://unpkg.com/mhgoos@0.0.1763907572121/IMG_20251123_221737.jpg" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="墨菲玉米地"><img src="https://unpkg.com/mhgoos@0.0.1763770729655/Screenshot_20251122_065116.jpg" class="lazyload" data-srcset="https://unpkg.com/mhgoos@0.0.1763770729655/Screenshot_20251122_065116.jpg" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="你难道没有告诉你女儿你是去拯救世界的吗">Brand: Couldn’t you’ve told her you were going to save the world?布兰德：你难道没有告诉你女儿你是去拯救世界的吗？<img src="https://unpkg.com/mhgoos@0.0.1763770808653/Screenshot_20251122_065219.jpg" class="lazyload" data-srcset="https://unpkg.com/mhgoos@0.0.1763770808653/Screenshot_20251122_065219.jpg" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="No"><img src="https://unpkg.com/mhgoos@0.0.1763770894468/Screenshot_20251122_065237.jpg" class="lazyload" data-srcset="https://unpkg.com/mhgoos@0.0.1763770894468/Screenshot_20251122_065237.jpg" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="当你为人父母了以后"><img src="https://unpkg.com/mhgoos@0.0.1763770964363/Screenshot_20251122_065300.jpg" class="lazyload" data-srcset="https://unpkg.com/mhgoos@0.0.1763770964363/Screenshot_20251122_065300.jpg" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="你会非常清楚一件事"><img src="https://unpkg.com/mhgoos@0.0.1763771019202/Screenshot_20251122_065407.jpg" class="lazyload" data-srcset="https://unpkg.com/mhgoos@0.0.1763771019202/Screenshot_20251122_065407.jpg" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="那就是你得确保你的孩子有安全感">Cooper: No. When you become a parent, one thing becomes really clear. And that’s that you want to make sure your children feel safe.库珀：没有。当你为人父母了以后，你会非常清楚一件事，那就是你得确保你的孩子有安全感。Dr. Brand: Not sure of what I’m more afraid of, them never coming back, or coming back to find we’ve failed.布兰德博士：不知道我更害怕哪个，是他们不会再回来了，还是回来却发现我们失败了。Murph: Then let’s succeed.墨菲：那我们就成功啊。<h3 id="星际航行与伦理抉择"><a href="#星际航行与伦理抉择" class="headerlink" title="星际航行与伦理抉择"></a>星际航行与伦理抉择</h3><img src="https://unpkg.com/mhgoos@0.0.1763773552032/v2-b7b860ceb25cbb7974385003e3998c11_1440w.webp" class="lazyload" data-srcset="https://unpkg.com/mhgoos@0.0.1763773552032/v2-b7b860ceb25cbb7974385003e3998c11_1440w.webp" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="TARS">Cooper: What’s your trust setting TARS?库珀：塔斯，你的信任值是多少？ TARS: Lower than yours apparently.塔斯：显然比你们低。<img src="https://unpkg.com/mhgoos@0.0.1763937053575/img_moment_1763936847156_edit_518937970275892.jpg" class="lazyload" data-srcset="https://unpkg.com/mhgoos@0.0.1763937053575/img_moment_1763936847156_edit_518937970275892.jpg" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="TARSsea">Absolute honesty isn’t always the most diplomatic, nor the safest form of communication with emotional beings. 跟情绪化的存在体沟通，绝对的坦诚既是不明智的外交手段，也是不安全的做法。<img src="https://unpkg.com/mhgoos@0.0.1763806995944/img_moment_1763805950477_edit_447688182805155.jpg" class="lazyload" data-srcset="https://unpkg.com/mhgoos@0.0.1763806995944/img_moment_1763805950477_edit_447688182805155.jpg" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="永恒号">Brand: You might have to decide between seeing your children again and the future of the human race.布兰德：你必须在再次见到你的孩子和人类的未来之间做出决定。<img src="https://unpkg.com/mhgoos@0.0.1763807051274/img_moment_1763805958764_edit_447701365238692.jpg" class="lazyload" data-srcset="https://unpkg.com/mhgoos@0.0.1763807051274/img_moment_1763805958764_edit_447701365238692.jpg" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="黑洞">We need to go well beyond the boundaries of our own existence. We can’t think as individuals…我们需要前往距离我们生存的世界极其遥远的地方，我们不可以作为一个个体来思考这个问题……<img src="https://unpkg.com/mhgoos@0.0.1763807093928/img_moment_1763805965071_edit_447722071749309.jpg" class="lazyload" data-srcset="https://unpkg.com/mhgoos@0.0.1763807093928/img_moment_1763805965071_edit_447722071749309.jpg" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="悬窗">We’ll find a way; we always have.我们会找到办法的，我们总有办法。<h3 id="时空错位与亲情回响"><a href="#时空错位与亲情回响" class="headerlink" title="时空错位与亲情回响"></a>时空错位与亲情回响</h3><img src="https://unpkg.com/mhgoos@0.0.1763771221744/Screenshot_20251122_065727.jpg" class="lazyload" data-srcset="https://unpkg.com/mhgoos@0.0.1763771221744/Screenshot_20251122_065727.jpg" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="今天是我的生日"><img src="https://unpkg.com/mhgoos@0.0.1763771271124/Screenshot_20251122_065747.jpg" class="lazyload" data-srcset="https://unpkg.com/mhgoos@0.0.1763771271124/Screenshot_20251122_065747.jpg" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="因为你当年走的时候说，等你回来的时候我们俩大概就一样大了"><img src="https://unpkg.com/mhgoos@0.0.1763771349668/Screenshot_20251122_065805.jpg" class="lazyload" data-srcset="https://unpkg.com/mhgoos@0.0.1763771349668/Screenshot_20251122_065805.jpg" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="因为你当年走的时候说，等你回来的时候我们俩大概就一样大了b"><img src="https://unpkg.com/mhgoos@0.0.1763771396438/Screenshot_20251122_065824.jpg" class="lazyload" data-srcset="https://unpkg.com/mhgoos@0.0.1763771396438/Screenshot_20251122_065824.jpg" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="现在我已经到了你离开时的年纪"><img src="https://unpkg.com/mhgoos@0.0.1763771444101/Screenshot_20251122_065850.jpg" class="lazyload" data-srcset="https://unpkg.com/mhgoos@0.0.1763771444101/Screenshot_20251122_065850.jpg" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="如果你能早点回来就太好了">Murph: Today is my birthday. And it’s a special one because you once told me that when you came back, we might be the same age. Well, now I’m the same age that you were when you left… and it’d be really great if you came back soon.墨菲：今天是我的生日。这个生日很特殊，因为你当年走的时候说，等你回来的时候我们俩大概就一样大了。现在我已经到了你离开时的年纪…… 如果你能早点回来就太好了。<img src="https://unpkg.com/mhgoos@0.0.1763770465733/Screenshot_20251121_203100.jpg" class="lazyload" data-srcset="https://unpkg.com/mhgoos@0.0.1763770465733/Screenshot_20251121_203100.jpg" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="你就是未来守护孩子的幽灵">Once you’re a parent, you’re the ghost of your children’s future.从孩子出生开始父母就成为了他们的幽灵。<h3 id="五维真相与文明救赎"><a href="#五维真相与文明救赎" class="headerlink" title="五维真相与文明救赎"></a>五维真相与文明救赎</h3><img src="https://unpkg.com/mhgoos@0.0.1763771591960/Screenshot_20251122_070034.jpg" class="lazyload" data-srcset="https://unpkg.com/mhgoos@0.0.1763771591960/Screenshot_20251122_070034.jpg" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="爱是唯一"><img src="https://unpkg.com/mhgoos@0.0.1763771612949/Screenshot_20251122_070121.jpg" class="lazyload" data-srcset="https://unpkg.com/mhgoos@0.0.1763771612949/Screenshot_20251122_070121.jpg" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="可以超越时间和空间的事物">Love is the one thing we’re capable of perceiving that transcends time and space.爱是唯一可以超越时间和空间的事物。<img src="https://unpkg.com/mhgoos@0.0.1763770250253/Screenshot_20251121_202441.jpg" class="lazyload" data-srcset="https://unpkg.com/mhgoos@0.0.1763770250253/Screenshot_20251121_202441.jpg" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="不要温顺地走进那良夜"><img src="https://unpkg.com/mhgoos@0.0.1763770318319/Screenshot_20251121_202535.jpg" class="lazyload" data-srcset="https://unpkg.com/mhgoos@0.0.1763770318319/Screenshot_20251121_202535.jpg" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="人之暮年，更当厚积薄发"><img src="https://unpkg.com/mhgoos@0.0.1763770383888/Screenshot_20251121_202615.jpg" class="lazyload" data-srcset="https://unpkg.com/mhgoos@0.0.1763770383888/Screenshot_20251121_202615.jpg" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="怒火，用怒火燃尽最后的光华">Do not go gentle into that good night,不要温和地走进那良夜，Old age should burn and rave at close of day;人之暮年，更当厚积薄发；Rage, rage against the dying of the light.怒火，用怒火燃尽最后的光华。Though wise men at their end know dark is right,智者虽明白，黑夜终将到来，Because their words had forked no lightning they他们的言语已无法化作闪电，Do not go gentle into that good night不要平静地走进那夜晚，Rage, rage against the dying of the light.怒火，用怒火燃尽最后的光华。<img src="https://unpkg.com/mhgoos@0.0.1763771704565/Screenshot_20251122_070235.jpg" class="lazyload" data-srcset="https://unpkg.com/mhgoos@0.0.1763771704565/Screenshot_20251122_070235.jpg" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="五维时空">Time is relative, okay? It... it can stretch and it can squeeze, but... it can't run backwards. Just can't. The only thing that can move across dimensions, like time, is gravity.时间是唯一能穿越所有维度的存在，它可以在不同维度空间里变慢或者变快，却无法倒流。<img src="https://unpkg.com/mhgoos@0.0.1763771793513/Screenshot_20251122_070341.jpg" class="lazyload" data-srcset="https://unpkg.com/mhgoos@0.0.1763771793513/Screenshot_20251122_070341.jpg" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="你就是我的幽灵"><img src="https://unpkg.com/mhgoos@0.0.1763904903192/Screenshot_20251123_210659.jpg" class="lazyload" data-srcset="https://unpkg.com/mhgoos@0.0.1763904903192/Screenshot_20251123_210659.jpg" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="STAY留下">It was me, Murph. I was your ghost.是我，墨菲，我就是你的幽灵。<img src="https://unpkg.com/mhgoos@0.0.1763771966919/Screenshot_20251122_071141.jpg" class="lazyload" data-srcset="https://unpkg.com/mhgoos@0.0.1763771966919/Screenshot_20251122_071141.jpg" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="但我知道你会回来"><img src="https://unpkg.com/mhgoos@0.0.1763806273096/Screenshot_20251122_180826.jpg" class="lazyload" data-srcset="https://unpkg.com/mhgoos@0.0.1763806273096/Screenshot_20251122_180826.jpg" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="我回来了墨菲"><img src="https://unpkg.com/mhgoos@0.0.1763772060684/Screenshot_20251122_071242.jpg" class="lazyload" data-srcset="https://unpkg.com/mhgoos@0.0.1763772060684/Screenshot_20251122_071242.jpg" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="穿越时空的是爱"><img src="https://unpkg.com/mhgoos@0.0.1763905930437/img_moment_1763905848915_edit_508649075123411.jpg" class="lazyload" data-srcset="https://unpkg.com/mhgoos@0.0.1763905930437/img_moment_1763905848915_edit_508649075123411.jpg" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="书架"><img src="https://unpkg.com/mhgoos@0.0.1763904270533/109951170322058844.jpg" class="lazyload" data-srcset="https://unpkg.com/mhgoos@0.0.1763904270533/109951170322058844.jpg" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="墨菲"><img src="https://unpkg.com/mhgoos@0.0.1763806361120/img_moment_1763805766172_edit_447525747956103.jpg" class="lazyload" data-srcset="https://unpkg.com/mhgoos@0.0.1763806361120/img_moment_1763805766172_edit_447525747956103.jpg" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="爱是永恒不变的力量"><div style="position: relative; width: 100%; height: 0; padding-bottom: 75%;"> <iframe src="https://bilibili.com/blackboard/html5mobileplayer.html?aid=899936521&bvid=BV18N4y1c7Mp&cid=816842812&p=1&hideCoverInfo=1&danmaku=0" scrolling="no" border="0" frameborder="no" framespacing="0" allowfullscreen="true" style="position: absolute; width: 100%; height: 100%; left: 0; top: 0;"></iframe></div>]]></content> <summary type="html">《星际穿越》中，地球危机下库珀率队星际航行寻找新家园，面临个人情感与人类未来的抉择。通过五维空间交流，他与女儿墨菲的思念诠释爱超越时空，最终人类团结寻得生存希望。</summary> <category term="随笔" scheme="https://blog.mhuig.top/categories/%E9%9A%8F%E7%AC%94/"/> <category term="探索" scheme="https://blog.mhuig.top/tags/%E6%8E%A2%E7%B4%A2/"/> </entry> <entry> <title></title> <link href="https://blog.mhuig.top/p/zeta-archive/"/> <id>https://blog.mhuig.top/p/zeta-archive/</id> <published>2025-09-14T06:59:00.000Z</published> <updated>2025-11-20T10:18:00.000Z</updated> <content type="html"><![CDATA[<img style="display: none;" no-lazy src="https://api.mhuig.top/pixel-blog-atom-12138.gif"><svg style="width: 50px; margin: 0 auto; display: block;" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 384 512"><path d="M0 64C0 46.3 14.3 32 32 32l320 0c12.4 0 23.7 7.2 29 18.4s3.6 24.5-4.4 34.1L100.3 416 352 416c17.7 0 32 14.3 32 32s-14.3 32-32 32L32 480c-12.4 0-23.7-7.2-29-18.4s-3.6-24.5 4.4-34.1L283.7 96 32 96C14.3 96 0 81.7 0 64z"></path></svg>Zeta Archive <a class="button" href="/notes/Zeta/" title="开始阅读">开始阅读</a> <h1 hidden="">Zeta Archive</h1>]]></content> <summary type="html">黎曼Zeta函数是解析数论核心工具，通过级数展开式定义于复平面，经解析延拓覆盖全平面，非平凡零点位于实部0到1的临界带内。函数具对称性，其整函数变换形式满足自变量s与1-s对应值相等，与素数分布紧密关联。Riemann猜想提出所有非平凡零点实部均为1/2。</summary> <category term="数学" scheme="https://blog.mhuig.top/categories/%E6%95%B0%E5%AD%A6/"/> <category term="Zeta" scheme="https://blog.mhuig.top/categories/%E6%95%B0%E5%AD%A6/Zeta/"/> <category term="Math" scheme="https://blog.mhuig.top/tags/Math/"/> <category term="Notes" scheme="https://blog.mhuig.top/tags/Notes/"/> </entry> <entry> <title></title> <link href="https://blog.mhuig.top/p/notes-datacom/"/> <id>https://blog.mhuig.top/p/notes-datacom/</id> <published>2023-12-03T05:59:00.000Z</published> <updated>2025-11-20T10:18:00.000Z</updated> <content type="html"><![CDATA[<img style="display: none;" no-lazy src="https://api.mhuig.top/pixel-blog-atom-12138.gif"><svg style="width: 50px; margin: 0 auto; display: block;" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 640 512"><defs><style>.fa-secondary{opacity:.4}</style></defs><path d="M64 240a64 64 0 1 0 64 64 64.06 64.06 0 0 0-64-64zm88 80h48v-32h-48zm294.4-106.8l19.2 25.6 48-36-19.2-25.6zM576 64a64 64 0 1 0 64 64 64.06 64.06 0 0 0-64-64z" class="fa-secondary"></path><path d="M576 384a63.84 63.84 0 0 0-38.3 13l-96-57.6a109.91 109.91 0 0 0 6.3-35.5 111.94 111.94 0 0 0-112-112 108.64 108.64 0 0 0-24.4 2.9l-40.8-87.4A63.84 63.84 0 1 0 224 128c1.1 0 2.1-.3 3.2-.3l41 87.8C241.5 235.9 224 267.8 224 304a111.71 111.71 0 0 0 193.2 76.7l95.8 57.5a63.87 63.87 0 1 0 63-54.2zm-240-32a48 48 0 1 1 48-48 48 48 0 0 1-48 48z" class="fa-primary"></path></svg>数据通信网络 <a class="button" href="/notes/datacom/" title="开始阅读">开始阅读</a> <h1 hidden="">数据通信网络</h1>]]></content> <summary type="html">数据通信网络依赖分层架构实现设备互联，核心为OSI七层模型与TCP/IP四层模型。物理层定义比特流传输规范，数据链路层通过MAC地址与帧同步确保节点通信，网络层依赖IP协议完成路由寻址，传输层提供TCP可靠传输与UDP实时传输选项。应用层集成HTTP、DNS等协议直接服务用户，通过封装与解封装机制实现跨层协作，是互联网通信的基础框架</summary> <category term="Web" scheme="https://blog.mhuig.top/categories/Web/"/> <category term="计算机网络" scheme="https://blog.mhuig.top/categories/Web/%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%BD%91%E7%BB%9C/"/> <category term="Notes" scheme="https://blog.mhuig.top/tags/Notes/"/> </entry> <entry> <title>辛普森悖论|你还相信数据吗</title> <link href="https://blog.mhuig.top/p/2f345bb/"/> <id>https://blog.mhuig.top/p/2f345bb/</id> <published>2022-09-22T08:14:00.000Z</published> <updated>2025-11-20T10:18:00.000Z</updated> <content type="html"><![CDATA[<img style="display: none;" no-lazy src="https://api.mhuig.top/pixel-blog-atom-12138.gif"><blockquote>数据是一个有力的武器，它既能被用来澄清现实，也能被用来混淆是非</blockquote>你知不知道，数据也会说谎？<div class="story post-story"><h2 id="一个栗子"><a href="#一个栗子" class="headerlink" title="一个栗子"></a>一个栗子</h2>假设您患有肾结石并去看医生。医生告诉你有两种治疗方法，治疗 A（开放手术 open surgery）和治疗 B（体外冲击波碎石术 ESWL）。你问哪种治疗效果更好，医生说：“一项研究发现治疗 A 的成功概率高于治疗 B。”你说：“我会接受治疗 A，谢谢！”这时医生打断你，“但同样的研究还研究了哪种治疗效果更好，这取决于患者是大肾结石还是小肾结石。”你说：“好吧，我有大肾结石还是小肾结石？”你说话的时候，医生又打断了你，说：“其实没关系。你看，他们发现治疗 B 比治疗 A 成功的概率更高，不管你的肾结石是大还是小。”你可能想知道你是否没看错。听起来不可能。但这是真的：在<a href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1339981/">一项实际研究</a>中，发现治疗 B 比治疗 A 对大肾结石和小肾结石起作用的概率更高，尽管事实上治疗 A 的总体概率高于治疗 B。这是研究数据：<table><thead><tr><th align="center"></th><th align="center">治疗 A 有帮助</th><th align="center">治疗 B 有帮助</th></tr></thead><tbody><tr><td align="center">大肾结石</td><td align="center">69% (55 / 80)</td><td align="center">73% (192 / 263)</td></tr><tr><td align="center">小肾结石</td><td align="center">87% (234 / 270)</td><td align="center">93% (81 / 87)</td></tr><tr><td align="center">所有患者</td><td align="center">83% (289 / 350)</td><td align="center">78% (273 / 350)</td></tr></tbody></table>表中的第一项显示，80 名大肾结石患者接受了 A 治疗，治疗帮助了其中 55 人，成功率为 69%。这不如治疗 B 好，它帮助了 263 名大肾结石患者中的 192 人，成功率为 73%。以类似的方式，第二行显示治疗 B 比治疗 A 对患有小肾结石的人更有效。但是当你把每一列的数字加起来时，你会发现治疗 A 确实比治疗 B 整体效果更好。值得花时间检查所有数字加起来检验一下，并说服自己我没有欺骗你.刚刚展示的这种现象被称为辛普森悖论。如果你和包括我在内的大多数人一样，那么辛普森悖论在你第一次见到它时就会令人震惊。因为它违反了我们对世界推理的本能方式。而且，正如我们看到的那样，辛普森悖论不仅是一种怪异的现象，而且它经常在具有重要决策后果的地方出现。</div><div class="story post-story"><h2 id="表达式"><a href="#表达式" class="headerlink" title="表达式"></a>表达式</h2>我们抽离出符号表达：<table><thead><tr><th align="center"></th><th align="center">统计对象 1</th><th align="center">统计对象 2</th></tr></thead><tbody><tr><td align="center">分项指标 1</td><td align="center"><mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align: -1.091ex;" xmlns="http://www.w3.org/2000/svg" width="2.499ex" height="2.878ex" role="img" focusable="false" viewBox="0 -789.7 1104.4 1271.9"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\frac{q_1}{p_1}"><g data-mml-node="mfrac" data-latex="\frac{q_1}{p_1}"><g data-mml-node="msub" transform="translate(240.2,477.2) scale(0.707)" data-latex="q_1 "><g data-mml-node="mi" data-latex="q"><path data-c="1D45E" d="M372 377C352 420 321 442 280 442C215 442 158 409 109 342C63 280 40 216 40 149C40 62 90-13 173-13C209-13 245 4 282 38L241-126C238-141 229-150 215-153C210-154 197-155 174-155C168-156 164-156 162-156C153-157 148-165 148-179L148-183C151-190 157-194 165-194C184-194 244-191 263-191C282-191 345-194 364-194C378-194 385-186 385-170C385-160 375-155 356-155C338-155 313-156 313-144C313-140 314-133 317-123L452 427C452 436 447 441 438 441C420 441 382 391 372 377M340 373C349 352 354 338 354 329C354 328 353 322 351 313L327 216C308 144 299 107 298 105C279 70 224 16 176 16C137 16 117 46 117 105C117 151 148 263 162 300C181 347 225 412 280 412C307 412 327 399 340 373Z"></path></g><g data-mml-node="mn" transform="translate(479,-150) scale(0.707)" data-latex="1"><path data-c="31" d="M269 666C228 624 168 603 89 603L89 564C141 564 184 572 217 588L217 82C217 64 213 52 204 47C195 42 170 39 130 39L95 39L95 0C120 2 174 3 257 3C340 3 394 2 419 0L419 39L384 39C343 39 318 42 310 47C302 52 297 64 297 82L297 636C297 660 295 666 269 666Z"></path></g></g><g data-mml-node="msub" transform="translate(220,-345) scale(0.707)" data-latex="p_1 "><g data-mml-node="mi" data-latex="p"><path data-c="1D45D" d="M355 442C311 442 269 419 228 373C217 419 186 442 137 442C96 442 66 409 45 344C35 311 30 292 30 286C30 277 35 272 46 272C51 272 54 273 57 275C62 284 65 291 66 298C84 374 107 412 134 412C152 412 161 398 161 371C161 356 159 339 154 321L44-118C35-151 34-155-5-155C-23-155-32-163-32-178C-32-189-26-194-15-194C0-194 52-191 67-191C86-191 146-194 165-194C180-194 187-186 187-170C187-160 178-155 159-155C141-155 114-156 114-144C114-131 155 26 159 43C179 6 209-13 249-13C314-13 371 20 421 87C467 148 490 213 490 280C490 367 438 442 355 442M352 412C391 412 411 382 411 323C411 296 405 260 394 215C371 128 342 71 307 42C286 25 267 16 248 16C219 16 199 29 188 56C179 77 174 92 174 100L225 309C230 331 248 354 276 377C304 400 329 412 352 412Z"></path></g><g data-mml-node="mn" transform="translate(536,-150) scale(0.707)" data-latex="1"><path data-c="31" d="M269 666C228 624 168 603 89 603L89 564C141 564 184 572 217 588L217 82C217 64 213 52 204 47C195 42 170 39 130 39L95 39L95 0C120 2 174 3 257 3C340 3 394 2 419 0L419 39L384 39C343 39 318 42 310 47C302 52 297 64 297 82L297 636C297 660 295 666 269 666Z"></path></g></g><rect width="864.4" height="60" x="120" y="220"></rect></g></g></g></svg></mjx-container></td><td align="center"><mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align: -1.091ex;" xmlns="http://www.w3.org/2000/svg" width="2.499ex" height="2.878ex" role="img" focusable="false" viewBox="0 -789.7 1104.4 1271.9"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\frac{q_2}{p_2}"><g data-mml-node="mfrac" data-latex="\frac{q_2}{p_2}"><g data-mml-node="msub" transform="translate(240.2,477.2) scale(0.707)" data-latex="q_2 "><g data-mml-node="mi" data-latex="q"><path data-c="1D45E" d="M372 377C352 420 321 442 280 442C215 442 158 409 109 342C63 280 40 216 40 149C40 62 90-13 173-13C209-13 245 4 282 38L241-126C238-141 229-150 215-153C210-154 197-155 174-155C168-156 164-156 162-156C153-157 148-165 148-179L148-183C151-190 157-194 165-194C184-194 244-191 263-191C282-191 345-194 364-194C378-194 385-186 385-170C385-160 375-155 356-155C338-155 313-156 313-144C313-140 314-133 317-123L452 427C452 436 447 441 438 441C420 441 382 391 372 377M340 373C349 352 354 338 354 329C354 328 353 322 351 313L327 216C308 144 299 107 298 105C279 70 224 16 176 16C137 16 117 46 117 105C117 151 148 263 162 300C181 347 225 412 280 412C307 412 327 399 340 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67-191C86-191 146-194 165-194C180-194 187-186 187-170C187-160 178-155 159-155C141-155 114-156 114-144C114-131 155 26 159 43C179 6 209-13 249-13C314-13 371 20 421 87C467 148 490 213 490 280C490 367 438 442 355 442M352 412C391 412 411 382 411 323C411 296 405 260 394 215C371 128 342 71 307 42C286 25 267 16 248 16C219 16 199 29 188 56C179 77 174 92 174 100L225 309C230 331 248 354 276 377C304 400 329 412 352 412Z"></path></g><g data-mml-node="mn" transform="translate(536,-150) scale(0.707)" data-latex="2"><path data-c="32" d="M237 666C186 666 143 648 106 612C69 576 50 534 50 483C50 449 75 424 106 424C136 424 161 450 161 480C161 513 137 536 105 536C102 536 100 536 98 535C117 584 161 627 224 627C306 627 352 556 352 470C352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0L450 180L417 180C409 129 402 100 396 91C391 86 361 84 306 84L139 84L236 179C304 243 390 312 419 365C439 400 449 435 449 470C449 588 357 666 237 666Z"></path></g></g><rect width="864.4" height="60" x="120" y="220"></rect></g></g></g></svg></mjx-container></td></tr><tr><td align="center">分项指标 2</td><td align="center"><mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align: -1.091ex;" xmlns="http://www.w3.org/2000/svg" width="2.499ex" height="2.878ex" role="img" focusable="false" viewBox="0 -789.7 1104.4 1271.9"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\frac{q_3}{p_3}"><g data-mml-node="mfrac" data-latex="\frac{q_3}{p_3}"><g data-mml-node="msub" transform="translate(240.2,477.2) scale(0.707)" data-latex="q_3 "><g data-mml-node="mi" data-latex="q"><path data-c="1D45E" d="M372 377C352 420 321 442 280 442C215 442 158 409 109 342C63 280 40 216 40 149C40 62 90-13 173-13C209-13 245 4 282 38L241-126C238-141 229-150 215-153C210-154 197-155 174-155C168-156 164-156 162-156C153-157 148-165 148-179L148-183C151-190 157-194 165-194C184-194 244-191 263-191C282-191 345-194 364-194C378-194 385-186 385-170C385-160 375-155 356-155C338-155 313-156 313-144C313-140 314-133 317-123L452 427C452 436 447 441 438 441C420 441 382 391 372 377M340 373C349 352 354 338 354 329C354 328 353 322 351 313L327 216C308 144 299 107 298 105C279 70 224 16 176 16C137 16 117 46 117 105C117 151 148 263 162 300C181 347 225 412 280 412C307 412 327 399 340 373Z"></path></g><g data-mml-node="mn" transform="translate(479,-150) scale(0.707)" data-latex="3"><path data-c="33" d="M303 353C369 378 431 441 431 526C431 569 410 604 369 631C333 654 292 666 246 666C201 666 162 654 127 631C88 605 68 571 68 528C68 495 90 472 122 472C154 472 176 495 176 527C176 560 157 578 119 580C145 615 186 633 242 633C302 633 332 598 332 527C332 485 324 450 309 421C282 373 245 364 183 364C171 362 165 357 165 348C165 333 172 333 192 333L235 333C310 333 348 280 348 173C348 88 317 14 241 14C176 14 128 36 99 80C134 79 160 105 160 139C160 173 135 198 101 198C62 198 42 178 42 137C42 88 64 49 108 18C147-9 193-22 244-22C301-22 350-3 393 34C436 71 457 117 457 173C457 267 383 332 303 353Z"></path></g></g><g data-mml-node="msub" transform="translate(220,-345) scale(0.707)" data-latex="p_3 "><g data-mml-node="mi" data-latex="p"><path data-c="1D45D" d="M355 442C311 442 269 419 228 373C217 419 186 442 137 442C96 442 66 409 45 344C35 311 30 292 30 286C30 277 35 272 46 272C51 272 54 273 57 275C62 284 65 291 66 298C84 374 107 412 134 412C152 412 161 398 161 371C161 356 159 339 154 321L44-118C35-151 34-155-5-155C-23-155-32-163-32-178C-32-189-26-194-15-194C0-194 52-191 67-191C86-191 146-194 165-194C180-194 187-186 187-170C187-160 178-155 159-155C141-155 114-156 114-144C114-131 155 26 159 43C179 6 209-13 249-13C314-13 371 20 421 87C467 148 490 213 490 280C490 367 438 442 355 442M352 412C391 412 411 382 411 323C411 296 405 260 394 215C371 128 342 71 307 42C286 25 267 16 248 16C219 16 199 29 188 56C179 77 174 92 174 100L225 309C230 331 248 354 276 377C304 400 329 412 352 412Z"></path></g><g data-mml-node="mn" transform="translate(536,-150) scale(0.707)" data-latex="3"><path data-c="33" d="M303 353C369 378 431 441 431 526C431 569 410 604 369 631C333 654 292 666 246 666C201 666 162 654 127 631C88 605 68 571 68 528C68 495 90 472 122 472C154 472 176 495 176 527C176 560 157 578 119 580C145 615 186 633 242 633C302 633 332 598 332 527C332 485 324 450 309 421C282 373 245 364 183 364C171 362 165 357 165 348C165 333 172 333 192 333L235 333C310 333 348 280 348 173C348 88 317 14 241 14C176 14 128 36 99 80C134 79 160 105 160 139C160 173 135 198 101 198C62 198 42 178 42 137C42 88 64 49 108 18C147-9 193-22 244-22C301-22 350-3 393 34C436 71 457 117 457 173C457 267 383 332 303 353Z"></path></g></g><rect width="864.4" height="60" x="120" y="220"></rect></g></g></g></svg></mjx-container></td><td align="center"><mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align: -1.091ex;" xmlns="http://www.w3.org/2000/svg" width="2.499ex" height="2.878ex" role="img" focusable="false" viewBox="0 -789.7 1104.4 1271.9"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\frac{q_4}{p_4}"><g data-mml-node="mfrac" data-latex="\frac{q_4}{p_4}"><g data-mml-node="msub" transform="translate(240.2,477.2) scale(0.707)" data-latex="q_4 "><g data-mml-node="mi" data-latex="q"><path data-c="1D45E" d="M372 377C352 420 321 442 280 442C215 442 158 409 109 342C63 280 40 216 40 149C40 62 90-13 173-13C209-13 245 4 282 38L241-126C238-141 229-150 215-153C210-154 197-155 174-155C168-156 164-156 162-156C153-157 148-165 148-179L148-183C151-190 157-194 165-194C184-194 244-191 263-191C282-191 345-194 364-194C378-194 385-186 385-170C385-160 375-155 356-155C338-155 313-156 313-144C313-140 314-133 317-123L452 427C452 436 447 441 438 441C420 441 382 391 372 377M340 373C349 352 354 338 354 329C354 328 353 322 351 313L327 216C308 144 299 107 298 105C279 70 224 16 176 16C137 16 117 46 117 105C117 151 148 263 162 300C181 347 225 412 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159-155C141-155 114-156 114-144C114-131 155 26 159 43C179 6 209-13 249-13C314-13 371 20 421 87C467 148 490 213 490 280C490 367 438 442 355 442M352 412C391 412 411 382 411 323C411 296 405 260 394 215C371 128 342 71 307 42C286 25 267 16 248 16C219 16 199 29 188 56C179 77 174 92 174 100L225 309C230 331 248 354 276 377C304 400 329 412 352 412Z"></path></g><g data-mml-node="mn" transform="translate(536,-150) scale(0.707)" data-latex="4"><path data-c="34" d="M353 677C344 677 336 672 330 663L28 199L28 163L289 163L289 81C289 63 285 51 278 46C271 41 252 39 219 39L194 39L194 0C223 2 269 3 331 3C393 3 439 2 468 0L468 39L443 39C410 39 391 41 384 46C377 51 373 63 373 81L373 163L471 163L471 202L373 202L373 660C373 670 366 677 353 677M295 553L295 202L67 202Z"></path></g></g><rect width="864.4" height="60" x="120" y="220"></rect></g></g></g></svg></mjx-container></td></tr><tr><td align="center">总计</td><td align="center"><mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg 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441C420 441 382 391 372 377M340 373C349 352 354 338 354 329C354 328 353 322 351 313L327 216C308 144 299 107 298 105C279 70 224 16 176 16C137 16 117 46 117 105C117 151 148 263 162 300C181 347 225 412 280 412C307 412 327 399 340 373Z"></path></g><g data-mml-node="mn" transform="translate(479,-150) scale(0.707)" data-latex="1"><path data-c="31" d="M269 666C228 624 168 603 89 603L89 564C141 564 184 572 217 588L217 82C217 64 213 52 204 47C195 42 170 39 130 39L95 39L95 0C120 2 174 3 257 3C340 3 394 2 419 0L419 39L384 39C343 39 318 42 310 47C302 52 297 64 297 82L297 636C297 660 295 666 269 666Z"></path></g></g><g data-mml-node="mo" data-latex="+" transform="translate(882.6,0)"><path data-c="2B" d="M698 274L413 274L413 559C413 575 405 583 389 583C373 583 365 575 365 559L365 274L80 274C64 274 56 266 56 250C56 234 64 226 80 226L365 226L365-59C365-75 373-83 389-83C405-83 413-75 413-59L413 226L698 226C714 226 722 234 722 250C722 263 711 274 698 274Z"></path></g><g data-mml-node="msub" 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