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<p><em>本文没有使用生成式 AI 技术。</em></p>
<p>去年,每星期一节的私教课,让我学会了许多健身的技巧。今年,为了学会自由泳,我报名了成人游泳课。</p>
<p>我并非没有接触过游泳。二十年前的暑假,我学习过蛙泳。那时候学得不好,二十五米的池子,游一圈回来必须要在泳池边歇一会儿。由于一些奇怪的原因,后来再也没有尝试过游泳,这么多年过去了,想必已忘得一干二净。</p>
<p>美国的成人游泳课程与国内不同。零基础的学员从自由泳起手,不像中国从蛙泳开始教。另外,这里没有新手保护,身体不会绑浮块,开局就是真实难度。</p>
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<a href="/2025/04/11/civ7-deity-guide/" class="post-title-link" itemprop="url">文明7神祗难度攻略</a>
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<p>前不久,我在文明7神祗难度下取得了胜利。战胜神祗 AI 的基本思路是:尽可能多铺设城市定居点,让多座城市具备较大的人口规模和较高的生产力,并且运用专家获得比 AI 更快的科技和文化发展速度。</p>
<p>在这篇文章中,我们讲解使用本杰明·富兰克林和玛雅文明开局,在神祗难度下赢得科技胜利的方法。</p>
<p>本杰明·富兰克林建造生产力建筑加快50%,且生产力建筑提供科研值,配合玛雅文明的特色城区,在古典时代就能实现科技腾飞。虽然使用其他任意领袖和文明也可以达成胜利,但是难度会增加。</p>
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<h2 id="旅行的意义"><a href="#旅行的意义" class="headerlink" title="旅行的意义"></a>旅行的意义</h2><p>2024 年的关键词是『旅行』。一月在日本过新年,八月辗转丹麦和瑞典,十月探访加拿大温哥华,十一月在法国,此时此刻在墨西哥望着大西洋。</p>
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<p>以下是旅行途中的一些趣闻和感想。</p>
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<p>关于十三机兵防卫圈,大多数玩家是被游戏精巧的剧情吸引来的。除了剧情之外,这款游戏也提供了高难度的战斗关卡。这篇攻略,为那些想要在战斗中取得好成绩的玩家提供一些建议。</p>
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<p>如果你对艺术鉴赏感兴趣,请不要错过贡布里希的《艺术的故事》。作者精心挑选了从史前时代到二十世纪的数百件艺术作品,将艺术史发展的脉络娓娓道来。每件作品除了解说之外,还配有图片,这样读者不费吹灰之力,便可将文字描述与作品本身对应起来。</p>
<p>在这里,我写下几点阅读后的感受。下面将要讨论的主题,只占原书篇幅的冰山一角。请有兴趣的读者阅读原书,以获得更全面的体验。</p>
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<p>今年值得回忆的事情并不少:回国举办婚礼、解锁高空跳伞的成就、深度体验意大利的风土人情。不过,我打算跳过年终总结,聊一个更为重要的话题。</p>
<p>对我来说,今年是世界观和方法论走向成熟的一年。我逐渐感觉到,面对纷繁万千的事物,自己形成了特定的思维模式,并且在价值判断上持有越来越鲜明的立场。世界观、方法论和价值判断没有对错之分,但是有高下之别。有一些世界观更准确地描述了世界发展变化的规律。有一些方法论和价值判断让我们做出更好的人生选择。希望我的分析和解释能为你带来一点点启发。</p>
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<h2 id="最小结婚成本"><a href="#最小结婚成本" class="headerlink" title="最小结婚成本"></a>最小结婚成本</h2><p>在中国大陆办理结婚登记,以前需要花 9 块钱人民币,现在是免费服务。在美国,结婚需要花多少钱呢?这要从美国的结婚流程说起。</p>
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<p>你的数学老师可能向你提及过『哥德巴赫猜想』。这个猜想认为,任何一个大于 2 的偶数,都可以表示成两个质数之和。这个猜想自 1742 年提出,尽管未能找到任何反例,但没有人能证明它。是否存在这样一种可能,即虽然哥德巴赫猜想是一个真命题,但是我们永远都无法证明它呢?哥德尔向世人展示,这种可能性是存在的。</p>
<p>哥德尔证明了,在一个定义了自然数(非负整数)、加法和乘法的数学体系中,假设这个体系没有矛盾,也就是不存在既真又假的数学命题,那么一定存在无法被证明的真命题。这一结论被称作『哥德尔不完备定理』。所谓的不完备,是指无法从几条有限的公理出发,推导出<strong>所有</strong>真命题。也就是说,我们可能无法从自然数公理出发,证明哥德巴赫猜想。哥德尔不完备定理的证明过程十分巧妙,本文将向读者展示,哥德尔是怎么做到的。</p>
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