<?xml version="1.0" encoding="UTF-8"?><rss version="2.0" xmlns:content="http://purl.org/rss/1.0/modules/content/"><channel><title>Shu Hu</title><description>Personal website and blog</description><link>https://angushushu.com/</link><item><title>致2021年以来参与过CubeX管理的朋友</title><link>https://angushushu.com/blog/%E8%87%B42021%E5%B9%B4%E4%BB%A5%E6%9D%A5%E5%8F%82%E4%B8%8E%E8%BF%87cubex%E7%AE%A1%E7%90%86%E7%9A%84%E6%9C%8B%E5%8F%8B/</link><guid isPermaLink="true">https://angushushu.com/blog/%E8%87%B42021%E5%B9%B4%E4%BB%A5%E6%9D%A5%E5%8F%82%E4%B8%8E%E8%BF%87cubex%E7%AE%A1%E7%90%86%E7%9A%84%E6%9C%8B%E5%8F%8B/</guid><description>自2021至今，我作为创办者之一，虽然多次主动退休并且也长期处于退休状态，但是仍然不断地以管理者的身份与服主或者管理进行沟通。在此之间产生过大量的摩擦，也导致我和不少管理出现了难以弥补的裂缝。在这样数不尽的分分合合中，反思是不可避免的。这里我希望能够说明我个人的看法，如果能够扭转和一些人的关系也是最好的。但是最重要的，</description><pubDate>Mon, 18 May 2026 00:00:00 GMT</pubDate><content:encoded>&lt;p&gt;自2021至今，我作为创办者之一，虽然多次主动退休并且也长期处于退休状态，但是仍然不断地以管理者的身份与服主或者管理进行沟通。在此之间产生过大量的摩擦，也导致我和不少管理出现了难以弥补的裂缝。在这样数不尽的分分合合中，反思是不可避免的。这里我希望能够说明我个人的看法，如果能够扭转和一些人的关系也是最好的。但是最重要的，我希望大家能够理解我在做什么，服务器在做什么，这对于我们服务器的未来发展会有好处。&lt;/p&gt;
&lt;p&gt;首先，对于服务器中的管理者来说，会有两种视角。一种就是把服务器视作以一部分具有较高权力的人（管理，包括服主）为中心，围绕着玩家的一个社交圈子。而具有最高权力的人（服主或者主事）就是这个社交圈子里具有最高地位的存在。在这个视角下，不可避免地会出现对权力的崇拜，因为权力意味着在社交圈子中的地位。谁不想更受欢迎呢？可是权力是有限的，也就意味者需要去争取，这不是说管理之间会互相争夺权力或者社交影响力，实际上这个事情在CubeX的历史中鲜有发生。大部分时间，CubeX的管理组是稳定的，大家默认谁是核心，谁是次核心。而另一种视角，是关于如何让服务器存活和长久运营。在这个视角下，每个管理或玩家都只是服务器这个系统的组成部分。而目标是让服务器健康的运转并且不断迭代。在这个视角下，权力也好社交地位也好，只是系统组成部分所附带的属性，需要做的是确保这些组成部分以正确的方式组合起来从而不影响服务器的运转。&lt;/p&gt;
&lt;p&gt;很多时候冲突并不是直接发生在个人的利益上，更多的是这两种视角的差异引发了误会并导致了冲突。在第二种视角下，如果一个权力结构或者管理的组合方式导致服务器运转不正常，那么权力结构和管理组成就应当被调整。在调整的过程中不可避免的会导致权力结构发生改变，在第一种视角下，服务器的权力结构和社交圈子会出现大洗牌。如果目标是保持社交状态的稳定，这自然而然就构成了一种威胁。同理，如果反过来，第一个视角的目标是保持服务器权力结构的稳定以及社交圈子的和谐，即便长久的保持稳定或者去追求某一个稳定的状态会对服务器的长久运行（例如游戏体验）构成影响。而对于第二种视角这恰恰是对服务器的威胁。&lt;/p&gt;
&lt;p&gt;CubeX中几乎所有的管理层冲突都可以用这两种视角的冲突来理解。而在视角内产生的直接冲突（单纯为了权力的斗争，或者单纯为了不同路线的斗争）几乎没有出现过。如果说有，可能并不是在管理层，有些老玩家可能会记得一周目方块学院和猫奴工会以及玩家代表时期的几次玩家间的大规模冲突，这些本质上是路线上的冲突。而管理之间的冲突则更微妙和复杂一些，本质上因为管理之间本都是相互信任的朋友。但是由于这两种视角的不同，不断地累积了很多误会，最终导致了严重的冲突甚至关系上的破裂。&lt;/p&gt;
&lt;p&gt;希望这一观点能让大家理解为什么在筹备合并和改革的当选，我们要花费大量时间和精力去起草一份严格的去中心化的，有些死板和不近人情的《章程》。我们引入了基于贡献的股份制，引入了有期限的维护者合同。这些机制本质是为了彻底消除第一个视角带来的管理间的内耗，让管理者权力从身份象征完全回归到维持系统运转的工具。&lt;/p&gt;
&lt;p&gt;我写这段话是希望在改革的阵痛期，无论是认同或者不认同的管理和玩家，都能理解其背后的考量。如果这套基于视角二的系统能让CubeX长久健康的运转下去，我想2021年至今我们所有玩家和管理在服务器中所受的苦难和混乱，都是值得的。&lt;/p&gt;</content:encoded></item><item><title>Why Gradients Point Up?</title><link>https://angushushu.com/blog/why-gradients-point-up/</link><guid isPermaLink="true">https://angushushu.com/blog/why-gradients-point-up/</guid><description>As what I recall when I learned about the gradient I was taught that the gradient represents the vector with the direction of fastest climbing I didn&apos;t really u</description><pubDate>Wed, 04 Feb 2026 00:00:00 GMT</pubDate><content:encoded>&lt;p&gt;As what I recall when I learned about the gradient, I was taught that the gradient represents the vector with the direction of fastest climbing. I didn&apos;t really understand it. It is known that &lt;span class=&quot;katex&quot;&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∂&lt;/mi&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∂&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;annotation encoding=&quot;application/x-tex&quot;&gt;\frac{\partial f}{\partial x}&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt; represents the rate of change for &lt;span class=&quot;katex&quot;&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding=&quot;application/x-tex&quot;&gt;f&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt; at &lt;span class=&quot;katex&quot;&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding=&quot;application/x-tex&quot;&gt;x&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;, then shouldn&apos;t the gradient just tell you the rate of change for each direction?&lt;/p&gt;
&lt;p&gt;I&apos;m using &lt;span class=&quot;katex&quot;&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∇&lt;/mi&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;i&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;j&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding=&quot;application/x-tex&quot;&gt;\nabla f = a\mathbf{i} + b\mathbf{j}&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt; for instance, but it should also apply to higher dimensions.&lt;/p&gt;
&lt;p&gt;Proof: &lt;span class=&quot;katex&quot;&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∇&lt;/mi&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding=&quot;application/x-tex&quot;&gt;\nabla f&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt; is in the direction where &lt;span class=&quot;katex&quot;&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding=&quot;application/x-tex&quot;&gt;f&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt; increases the fastest.&lt;/p&gt;
&lt;p&gt;Let the direction of the gradient be &lt;span class=&quot;katex&quot;&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;u&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∇&lt;/mi&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∥&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∇&lt;/mi&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∥&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;annotation encoding=&quot;application/x-tex&quot;&gt;\mathbf{u} = \frac{\nabla f}{\|\nabla f\|}&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;.&lt;br&gt;
Say &lt;span class=&quot;katex&quot;&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∇&lt;/mi&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding=&quot;application/x-tex&quot;&gt;\nabla f&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt; is not the direction where &lt;span class=&quot;katex&quot;&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding=&quot;application/x-tex&quot;&gt;f&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt; increases the fastest. Then &lt;span class=&quot;katex&quot;&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∃&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding=&quot;application/x-tex&quot;&gt;\exists&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt; unit vector &lt;span class=&quot;katex&quot;&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding=&quot;application/x-tex&quot;&gt;\mathbf{v}&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt; s.t. the directional derivative along &lt;span class=&quot;katex&quot;&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding=&quot;application/x-tex&quot;&gt;\mathbf{v}&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt; is greater than the gradient&apos;s magnitude&lt;/p&gt;
&lt;span class=&quot;katex&quot;&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;v&lt;/mi&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∇&lt;/mi&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∥&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∇&lt;/mi&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∥&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding=&quot;application/x-tex&quot;&gt;\mathbf{v} \cdot \nabla f &gt; \|\nabla f\|&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;
&lt;p&gt;So&lt;span class=&quot;katex&quot;&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∥&lt;/mi&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;v&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∥&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∥&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∇&lt;/mi&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∥&lt;/mi&gt;&lt;mi&gt;cos&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∥&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∇&lt;/mi&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∥&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding=&quot;application/x-tex&quot;&gt;\|\mathbf{v}\| \|\nabla f\| \cos(\theta) &gt; \|\nabla f\| &lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;Since &lt;span class=&quot;katex&quot;&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding=&quot;application/x-tex&quot;&gt;\mathbf{v}&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt; is a unit vector, &lt;span class=&quot;katex&quot;&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∥&lt;/mi&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;v&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∥&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;annotation encoding=&quot;application/x-tex&quot;&gt;\|\mathbf{v}\|=1&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span class=&quot;katex&quot;&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;cos&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;annotation encoding=&quot;application/x-tex&quot;&gt;\cos(\theta) \leq 1&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;.&lt;span class=&quot;katex&quot;&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mo&gt;⇒&lt;/mo&gt;&lt;mo&gt;⇐&lt;/mo&gt;&lt;/mrow&gt;&lt;annotation encoding=&quot;application/x-tex&quot;&gt;\Rightarrow \Leftarrow&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;Thus, &lt;span class=&quot;katex&quot;&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∇&lt;/mi&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding=&quot;application/x-tex&quot;&gt;\nabla f&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt; is in the direction where &lt;span class=&quot;katex&quot;&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding=&quot;application/x-tex&quot;&gt;f&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt; increases the fastest.&lt;/p&gt;</content:encoded><category>math</category><category>skill</category></item><item><title>Update Hexo Blog</title><link>https://angushushu.com/blog/update-hexo-blog/</link><guid isPermaLink="true">https://angushushu.com/blog/update-hexo-blog/</guid><description>This is a cheat sheet for updating your hexo blogs which assumes you have already set up the theme Add a blog In my case I generally use post for layout also si</description><pubDate>Thu, 27 Nov 2025 14:13:12 GMT</pubDate><content:encoded>&lt;p&gt;This is a cheat sheet for updating your hexo blogs, which assumes you have already set up the theme.&lt;/p&gt;
&lt;h2&gt;Add a blog&lt;/h2&gt;
&lt;pre&gt;&lt;code class=&quot;language-bash&quot;&gt;$ hexo new [layout] &amp;#x3C;title&gt;
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;In my case I generally use &lt;code&gt;post&lt;/code&gt; for layout, also since I&apos;m using local environment I run commands with &lt;code&gt;npx&lt;/code&gt;.&lt;/p&gt;
&lt;h2&gt;Build &amp;#x26; Deploy&lt;/h2&gt;
&lt;pre&gt;&lt;code class=&quot;language-bash&quot;&gt;$ hexo clean &amp;#x26;&amp;#x26; hexo g
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;This will clean the old generated files and regenerate the static files.&lt;/p&gt;
&lt;pre&gt;&lt;code class=&quot;language-bash&quot;&gt;$ hexo s
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;This allows you to preview locally.&lt;/p&gt;
&lt;pre&gt;&lt;code class=&quot;language-bash&quot;&gt;$ hexo d # or directly hexo clean &amp;#x26;&amp;#x26; hexo g &amp;#x26;&amp;#x26; hexo d
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;This will deploy the static files to the platform (should be configured in the _config.yml).&lt;/p&gt;
&lt;hr&gt;
&lt;p&gt;For more detail check &lt;a href=&quot;https://hexo.io/docs/&quot;&gt;official docs&lt;/a&gt;&lt;/p&gt;</content:encoded><category>skill</category></item><item><title>Why is the Dot Product related to Cosine?</title><link>https://angushushu.com/blog/why-is-the-dot-product-related-to-cosine/</link><guid isPermaLink="true">https://angushushu.com/blog/why-is-the-dot-product-related-to-cosine/</guid><description>Since graduating from my undergrad much of my knowledge has faded Recently I&apos;m reviewing some core concepts Here I show an example of dot products for 2 vectors</description><pubDate>Sat, 26 Oct 2024 00:00:00 GMT</pubDate><content:encoded>&lt;p&gt;Since graduating from my undergrad, much of my knowledge has faded. Recently, I&apos;m reviewing some core concepts. Here I show an example of dot products for 2 vectors with length 2 to help understand the idea of dot product (not a proof).&lt;/p&gt;
&lt;p&gt;Given &lt;span class=&quot;katex&quot;&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;v&lt;/mi&gt;&lt;mn mathvariant=&quot;bold&quot;&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mrow&gt;&lt;mo fence=&quot;true&quot;&gt;[&lt;/mo&gt;&lt;mtable rowspacing=&quot;0.16em&quot; columnalign=&quot;center&quot; columnspacing=&quot;1em&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mstyle scriptlevel=&quot;0&quot; displaystyle=&quot;false&quot;&gt;&lt;msub&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;/mstyle&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mstyle scriptlevel=&quot;0&quot; displaystyle=&quot;false&quot;&gt;&lt;msub&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;/mstyle&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mo fence=&quot;true&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;mo separator=&quot;true&quot;&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;v&lt;/mi&gt;&lt;mn mathvariant=&quot;bold&quot;&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mrow&gt;&lt;mo fence=&quot;true&quot;&gt;[&lt;/mo&gt;&lt;mtable rowspacing=&quot;0.16em&quot; columnalign=&quot;center&quot; columnspacing=&quot;1em&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mstyle scriptlevel=&quot;0&quot; displaystyle=&quot;false&quot;&gt;&lt;msub&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;/mstyle&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mstyle scriptlevel=&quot;0&quot; displaystyle=&quot;false&quot;&gt;&lt;msub&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;/mstyle&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mo fence=&quot;true&quot;&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;annotation encoding=&quot;application/x-tex&quot;&gt;\mathbf{v_1} = \begin{bmatrix} i_1 \\ j_1 \end{bmatrix}, \mathbf{v_2} = \begin{bmatrix} i_2 \\ j_2 \end{bmatrix}&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;Shown below:&lt;/p&gt;
&lt;p&gt;|               V1                |               V2                |&lt;br&gt;
| :-----------------------------: | :-----------------------------: |&lt;br&gt;
| &lt;img src=&quot;https://angushushu.com/images/cross_prod_v1.jpg&quot; alt=&quot;&quot;&gt; | &lt;img src=&quot;https://angushushu.com/images/cross_prod_v2.jpg&quot; alt=&quot;&quot;&gt; |&lt;/p&gt;
&lt;p&gt;So that dot product is&lt;/p&gt;
&lt;span class=&quot;katex&quot;&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;v&lt;/mi&gt;&lt;mn mathvariant=&quot;bold&quot;&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;msub&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;v&lt;/mi&gt;&lt;mn mathvariant=&quot;bold&quot;&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;annotation encoding=&quot;application/x-tex&quot;&gt;\mathbf{v_1} \cdot \mathbf{v_2} = i_1\cdot i_2 + j_1\cdot j_2&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;
&lt;span class=&quot;katex&quot;&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∣&lt;/mi&gt;&lt;msub&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;v&lt;/mi&gt;&lt;mn mathvariant=&quot;bold&quot;&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∣&lt;/mi&gt;&lt;mi&gt;sin&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∣&lt;/mi&gt;&lt;msub&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;v&lt;/mi&gt;&lt;mn mathvariant=&quot;bold&quot;&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∣&lt;/mi&gt;&lt;mi&gt;sin&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∣&lt;/mi&gt;&lt;msub&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;v&lt;/mi&gt;&lt;mn mathvariant=&quot;bold&quot;&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∣&lt;/mi&gt;&lt;mi&gt;cos&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∣&lt;/mi&gt;&lt;msub&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;v&lt;/mi&gt;&lt;mn mathvariant=&quot;bold&quot;&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∣&lt;/mi&gt;&lt;mi&gt;cos&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;annotation encoding=&quot;application/x-tex&quot;&gt;= |\mathbf{v_1}|\sin\theta_1\cdot|\mathbf{v_2}|\sin \theta_2 + |\mathbf{v_1}|\cos\theta_1\cdot|\mathbf{v_2}|\cos \theta_2&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;
&lt;span class=&quot;katex&quot;&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∣&lt;/mi&gt;&lt;msub&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;v&lt;/mi&gt;&lt;mn mathvariant=&quot;bold&quot;&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∣&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∣&lt;/mi&gt;&lt;msub&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;v&lt;/mi&gt;&lt;mn mathvariant=&quot;bold&quot;&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∣&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;sin&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mi&gt;sin&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;cos&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mi&gt;cos&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;annotation encoding=&quot;application/x-tex&quot;&gt;= |\mathbf{v_1}||\mathbf{v_2}|(\sin\theta_1\cdot\sin\theta_2+\cos\theta_1\cdot\cos\theta_2)&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;
&lt;p&gt;Then by cosine identity, which is &lt;span class=&quot;katex&quot;&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;cos&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;cos&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mi&gt;cos&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;sin&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mi&gt;sin&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;annotation encoding=&quot;application/x-tex&quot;&gt;\cos(\theta_1-\theta_2) = \cos\theta_1\cdot\cos\theta_2+\sin\theta_1\cdot\sin\theta_2&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;, we get&lt;/p&gt;
&lt;span class=&quot;katex&quot;&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;v&lt;/mi&gt;&lt;mn mathvariant=&quot;bold&quot;&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;msub&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;v&lt;/mi&gt;&lt;mn mathvariant=&quot;bold&quot;&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∣&lt;/mi&gt;&lt;msub&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;v&lt;/mi&gt;&lt;mn mathvariant=&quot;bold&quot;&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∣&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∣&lt;/mi&gt;&lt;msub&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;v&lt;/mi&gt;&lt;mn mathvariant=&quot;bold&quot;&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∣&lt;/mi&gt;&lt;mi&gt;cos&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;annotation encoding=&quot;application/x-tex&quot;&gt;\mathbf{v_1} \cdot \mathbf{v_2} = |\mathbf{v_1}||\mathbf{v_2}|\cos(\theta_1-\theta_2)&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;
&lt;span class=&quot;katex&quot;&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∣&lt;/mi&gt;&lt;msub&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;v&lt;/mi&gt;&lt;mn mathvariant=&quot;bold&quot;&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∣&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∣&lt;/mi&gt;&lt;msub&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;v&lt;/mi&gt;&lt;mn mathvariant=&quot;bold&quot;&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∣&lt;/mi&gt;&lt;mi&gt;cos&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;Δ&lt;/mi&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;annotation encoding=&quot;application/x-tex&quot;&gt;= |\mathbf{v_1}||\mathbf{v_2}|\cos(\Delta\theta)&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;
&lt;span class=&quot;katex&quot;&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∣&lt;/mi&gt;&lt;msub&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;v&lt;/mi&gt;&lt;mn mathvariant=&quot;bold&quot;&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∣&lt;/mi&gt;&lt;mi&gt;cos&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;Δ&lt;/mi&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∣&lt;/mi&gt;&lt;msub&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;v&lt;/mi&gt;&lt;mn mathvariant=&quot;bold&quot;&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∣&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding=&quot;application/x-tex&quot;&gt;= |\mathbf{v_1}|\cos(\Delta\theta)\cdot|\mathbf{v_2}|&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;
&lt;p&gt;When put two vectors together, we see the intuitive meaning of it, which is multiplication of the length of projection of &lt;span class=&quot;katex&quot;&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;v&lt;/mi&gt;&lt;mn mathvariant=&quot;bold&quot;&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;annotation encoding=&quot;application/x-tex&quot;&gt;\mathbf{v_1}&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt; on &lt;span class=&quot;katex&quot;&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;v&lt;/mi&gt;&lt;mn mathvariant=&quot;bold&quot;&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;annotation encoding=&quot;application/x-tex&quot;&gt;\mathbf{v_2}&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt; with the length of &lt;span class=&quot;katex&quot;&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;v&lt;/mi&gt;&lt;mn mathvariant=&quot;bold&quot;&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;annotation encoding=&quot;application/x-tex&quot;&gt;\mathbf{v_2}&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;.&lt;br&gt;
&lt;img src=&quot;https://angushushu.com/images/cross_prod_3.jpg&quot; alt=&quot;&quot;&gt;&lt;br&gt;
Which is a scale related to the angle between two vectors (more specifically, in what degree they are in the same line) and the length between them. So when people only care about the level of parallel, they do cosine similarity:&lt;/p&gt;
&lt;span class=&quot;katex&quot;&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mtext&gt;cosine similarity&lt;/mtext&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;v&lt;/mi&gt;&lt;mn mathvariant=&quot;bold&quot;&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;msub&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;v&lt;/mi&gt;&lt;mn mathvariant=&quot;bold&quot;&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∣&lt;/mi&gt;&lt;msub&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;v&lt;/mi&gt;&lt;mn mathvariant=&quot;bold&quot;&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∣&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∣&lt;/mi&gt;&lt;msub&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;v&lt;/mi&gt;&lt;mn mathvariant=&quot;bold&quot;&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;∣&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;cos&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;Δ&lt;/mi&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;annotation encoding=&quot;application/x-tex&quot;&gt;\text{cosine similarity} = \frac{\mathbf{v_1}\cdot\mathbf{v_2}}{|\mathbf{v_1}||\mathbf{v_2}|} = \cos(\Delta\theta)&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;
&lt;p&gt;Hope this example helps you build more &lt;strong&gt;intuition&lt;/strong&gt; about the operation, it does for me a little bit. If not, let&apos;s go through an real life example:&lt;br&gt;
&lt;img src=&quot;https://angushushu.com/images/anti_gravity_lean.jpg&quot; alt=&quot;&quot;&gt;&lt;br&gt;
Imagine MJ performing his famous Anti-Gravity Lean over a line drawn on the ground. Let MJ be &lt;span class=&quot;katex&quot;&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;v&lt;/mi&gt;&lt;mn mathvariant=&quot;bold&quot;&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;annotation encoding=&quot;application/x-tex&quot;&gt;\mathbf{v_1}&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt; and the line be &lt;span class=&quot;katex&quot;&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;v&lt;/mi&gt;&lt;mn mathvariant=&quot;bold&quot;&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;annotation encoding=&quot;application/x-tex&quot;&gt;\mathbf{v_2}&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt; (we view from aside), there&apos;s sunshine above MJ head. We observe this performance from a location orthogonal to the plane formed by standing MJ and the line. &lt;span class=&quot;katex&quot;&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;cos&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;Δ&lt;/mi&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;msub&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;v&lt;/mi&gt;&lt;mn mathvariant=&quot;bold&quot;&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;annotation encoding=&quot;application/x-tex&quot;&gt;\cos\Delta\theta\cdot\mathbf{v_1}&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt; is the shadow of MJ on the line, the closer MJ is to being parallel with the line (the floor), the longer his shadow becomes, and therefore the larger the dot product of MJ and the line would be.&lt;br&gt;
To MJ, the dot product might be something correlated to his sense of the length of the line (when the line is beneath him). Since the more parallel they are, the longer the line is in his eyes.&lt;/p&gt;
&lt;p&gt;Note: this is not a formal proof, for formal proof you can see &lt;a href=&quot;https://tutorial.math.lamar.edu/classes/calcii/dotproduct.aspx&quot;&gt;here&lt;/a&gt;&lt;/p&gt;</content:encoded><category>math</category><category>skill</category></item><item><title>Build &amp; Publish a Python Package</title><link>https://angushushu.com/blog/build-publish-a-python-package/</link><guid isPermaLink="true">https://angushushu.com/blog/build-publish-a-python-package/</guid><description>Build Prepare setup py An example If you have previous build remember to clean them up by run optional to test package locally Publish Setup info on test pypi o</description><pubDate>Sun, 06 Oct 2024 20:28:00 GMT</pubDate><content:encoded>&lt;h2&gt;Build&lt;/h2&gt;
&lt;p&gt;Prepare setup.py&lt;br&gt;
An example:&lt;/p&gt;
&lt;pre&gt;&lt;code class=&quot;language-python&quot;&gt;from setuptools import find_packages, setup
  
with open(&quot;README.md&quot;, &quot;r&quot;) as f:  
    long_description = f.read()  
  
setup(  
    name=&apos;&amp;#x3C;package&gt;&apos;,  
    version=&apos;0.0.1&apos;,  # update this if you are updating new version
    description=&apos;&apos;,  
    packages=find_packages(include=[&apos;&amp;#x3C;package&gt;&apos;, &apos;&amp;#x3C;package&gt;.*&apos;]),  
    long_description=long_description,  
    long_description_content_type=&quot;text/markdown&quot;,  
    url=&apos;&apos;,  
    author=&apos;&apos;,  
    author_email=&apos;&apos;,  
    license=&apos;GPL-3.0&apos;,  
    classifiers=[  
        &quot;Programming Language :: Python :: 3&quot;,  
        &quot;License :: OSI Approved :: GNU General Public License v3 (GPLv3)&quot;,  
        &quot;Operating System :: OS Independent&quot;,  
    ],  
    install_requires=[  
        &apos;pandas&apos;,   
        &apos;numpy&apos; 
    ],  
    extras_require={  
        &apos;all&apos;: [],  
        &apos;dev&apos;: [&apos;pytest&gt;=7.0&apos;, &apos;twine&gt;=4.0.2&apos;]  
    },  
    python_requires=&apos;&gt;=3.6&apos;,  
)
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;If you have previous build, remember to clean them up by&lt;/p&gt;
&lt;pre&gt;&lt;code class=&quot;language-bash&quot;&gt;rm -rf dist build *.egg-info
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;run&lt;/p&gt;
&lt;pre&gt;&lt;code class=&quot;language-bash&quot;&gt;python -m build # recommended, requires &quot;build&quot; package
# or
python setup.py bdist_wheel sdist
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;(optional) to test package locally&lt;/p&gt;
&lt;pre&gt;&lt;code class=&quot;language-bash&quot;&gt;pip install .
&lt;/code&gt;&lt;/pre&gt;
&lt;h2&gt;Publish&lt;/h2&gt;
&lt;p&gt;Setup info on &lt;a href=&quot;https://test.pypi.org&quot;&gt;test.pypi&lt;/a&gt; or &lt;a href=&quot;https://pypi.org&quot;&gt;pypi&lt;/a&gt; if not yet. The API key for publishing can be found there.&lt;/p&gt;
&lt;p&gt;check:&lt;/p&gt;
&lt;pre&gt;&lt;code class=&quot;language-python&quot;&gt;twine check dist/* # requires &quot;twine&quot; package
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;publish to test.pypi:&lt;/p&gt;
&lt;pre&gt;&lt;code class=&quot;language-python&quot;&gt;twine upload -r testpypi dist/*
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;publish to pypi:&lt;/p&gt;
&lt;pre&gt;&lt;code class=&quot;language-python&quot;&gt;twine upload dist/*
&lt;/code&gt;&lt;/pre&gt;
&lt;hr&gt;
&lt;p&gt;For more detail check &lt;a href=&quot;https://www.youtube.com/watch?v=5KEObONUkik&amp;#x26;t=918s&quot;&gt;Youtube tutorial&lt;/a&gt;&lt;/p&gt;</content:encoded><category>skill</category></item><item><title>一些想法</title><link>https://angushushu.com/blog/%E4%B8%80%E4%BA%9B%E6%83%B3%E6%B3%95/</link><guid isPermaLink="true">https://angushushu.com/blog/%E4%B8%80%E4%BA%9B%E6%83%B3%E6%B3%95/</guid><description>四类人 一人之下里的全性掌门无根生把人分为四大类：无术无道，有术无道，有道无术，以及有术有道。我自然是希望做第四类人的，因此一直以来我认为我走在求道的路上，并且是在正确的路上。而术，则正是我现在所学的内容。 道 我的道十分简单，即是为了一种理想的社会的存在而努力着。这个道是在以下的假设之上而构建的：社会的核心是人，而大</description><pubDate>Mon, 05 Feb 2024 06:57:38 GMT</pubDate><content:encoded>&lt;h2&gt;四类人&lt;/h2&gt;
&lt;p&gt;一人之下里的全性掌门无根生把人分为四大类：无术无道，有术无道，有道无术，以及有术有道。我自然是希望做第四类人的，因此一直以来我认为我走在求道的路上，并且是在正确的路上。而术，则正是我现在所学的内容。&lt;/p&gt;
&lt;h2&gt;道&lt;/h2&gt;
&lt;p&gt;我的道十分简单，即是为了一种理想的社会的存在而努力着。这个道是在以下的假设之上而构建的：社会的核心是人，而大多数人的大多数行为都是被约束的。约束他们行为的，狭义上说是法律与道德，广义上说即是文化。简化的定义文化，就是一个群体共享的关于对于不同当前状态到达不同目标状态的路径以及目标的集合。在此假设之上，我的道是寻找如何高效的把文化传播到个体。我目前的专注方向是叙事。至于传播的内容，我现在不会也没有资格去管，不要好为人师嘛。&lt;/p&gt;
&lt;p&gt;&lt;img src=&quot;https://angushushu.com/images/sticker1.jpg&quot; alt=&quot;sticker1&quot;&gt;&lt;/p&gt;</content:encoded><category>thoughts</category></item><item><title>Existing Models</title><link>https://angushushu.com/blog/existing-models/</link><guid isPermaLink="true">https://angushushu.com/blog/existing-models/</guid><description>I&apos;ve found several existing models - Psi-thoery by Dietrich Dörner et al - OpenCog by Ben Goertzel et al The structure of both has some similarities with mine T</description><pubDate>Mon, 17 Apr 2023 16:27:51 GMT</pubDate><content:encoded>&lt;p&gt;I&apos;ve found several existing models.&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;Psi-thoery by Dietrich Dörner et al&lt;/li&gt;
&lt;li&gt;OpenCog by Ben Goertzel et al&lt;/li&gt;
&lt;/ul&gt;
&lt;p&gt;The structure of both has some similarities with mine. The quad of psi has similar features as the representations in my model, which include the sur/sub connection (corresponding to Connection 1) and a motor-state graph (corresponding to Connection 2). However, I just notice these two models so might take time to understand them.&lt;/p&gt;
&lt;p&gt;One note: both models, especially OpenCog focus on creating AGI, whereas my model is less focused on AI stuff but more about providing a cognitive (which indicates that it is not equivalent to neurological models) framework to better understand the human psychological processes. Another thing is that LLMs like ChatGpt is very popular recently and people consider it the best approach to AGI. I don&apos;t have much opinion on that since I&apos;m not an AI expert, but if our goal is understanding humans, I still prefer an explanatory model that relies less on statistics.&lt;/p&gt;</content:encoded><category>theory</category><category>model</category></item><item><title>Process - Bases</title><link>https://angushushu.com/blog/process-bases/</link><guid isPermaLink="true">https://angushushu.com/blog/process-bases/</guid><description>Given the structure processes are possible to be discussed The relationship between structure and process can be considered as the relation between hardware and</description><pubDate>Thu, 09 Feb 2023 19:59:01 GMT</pubDate><content:encoded>&lt;p&gt;Given the structure, processes are possible to be discussed. The relationship between structure and process can be considered as the relation between hardware and software. Anyhow, we have the structure ready and ready to start to talk about the processes.&lt;/p&gt;
&lt;h3&gt;NOTE&lt;/h3&gt;
&lt;blockquote&gt;
&lt;p&gt;Before we start, I want to emphasize that, all we are discussing here are theories not supported by evidence. Part of the theory may have been supported because they overlap with other existing theories that has been supported by empirical evidences.&lt;br&gt;
The structures and processes we discussed here are constructs that may not be directly reflected by neurological findings. However, since we are simulating human behavior and mind, which is based on neurological activity, let&apos;s assume there is a homeomorphism even if no homomorphism between them (this is an imprecise metaphor).&lt;/p&gt;
&lt;/blockquote&gt;
&lt;p&gt;One interesting observation is that the features of graphs have provided us with many potential operations, which can help us generate possible processes. The reason for processes to exist is to explain phenomena, thus I&apos;ll list the mechanisms by showing cases of phenomena.&lt;/p&gt;
&lt;h1&gt;Bases&lt;/h1&gt;
&lt;h2&gt;1. Needs/Motivation&lt;/h2&gt;
&lt;p&gt;The definition of needs and motivation is debatable and there are many theories about them. It&apos;s hard to define because it doesn&apos;t reflect any phenomenon directly but abstract features shared by phenomena. Therefore I&apos;ll define it with mechanisms established via our structure, and we will see whether the phenomena with &quot;needs&quot;/&quot;motivation&quot; involved match the consequences of the mechanisms.&lt;/p&gt;
&lt;p&gt;Here, let&apos;s define needs/motivation as a goal or a set of goals. Using the physiological need of Maslow&apos;s Hierarchy of needs as an example, it can contain multiple constructs such as the sufficiency of food or drink, the sufficiency of sexual behavior, avoidance of harm, and others. Whereas each construct can be represented as a set of states or representations (here representation and state are interchangeable since they will end up involved in connection 2 &lt;a href=&quot;https://angushushu.com/blog/structure-elements/&quot;&gt;structure-elements&lt;/a&gt;). Then, we can define either the set of states for each construct as a need or the union of the sets of states for multiple constructs as a need.&lt;/p&gt;
&lt;h3&gt;1.1 Behaviors Driven by Needs&lt;/h3&gt;
&lt;p&gt;Generally, Needs or Motivation are recognized as a driver of behaviors. In the framework, this is demonstrated by connection 2, where almost (I&apos;m using this because there are some more complicated mechanisms) every action is driven by needs. More specifically, people are using the graph of connection 2 as a guide for their behavior, either consciously or unconsciously. We will discuss the mechanisms in the future, but the main idea here is connections provide the gravity of needs, and the flow of action demonstrated this gravity.&lt;/p&gt;
&lt;h3&gt;1.2 Directional Relation Between Needs&lt;/h3&gt;
&lt;p&gt;In multiple theories of needs or motivation, there is a hierarchical structure (e.g. &lt;a href=&quot;https://en.wikipedia.org/wiki/Maslow%27s_hierarchy_of_needs&quot;&gt;Maslow&apos;s hierarchy of needs&lt;/a&gt; and &lt;a href=&quot;https://en.wikipedia.org/wiki/Psi-theory&quot;&gt;Dörner&apos;s theory of motivation from the Psi Theory&lt;/a&gt;). I&apos;m not introducing the theories here. However, I&apos;d like to consider this relationship between different levels of needs as a directional relationship rather than a hierarchical relationship, since a directional relationship can lead to a more flexible structure.&lt;/p&gt;
&lt;p&gt;In Maslow&apos;s hierarchy of needs, the sufficiency of safety increases the possibility of completing one&apos;s physiological needs. Also, for social animals, the sufficiency of social needs indicates more protection and benefits from society and thus a higher level of safety.&lt;/p&gt;
&lt;p&gt;Similarly, considering the five basic human needs in Dörner&apos;s theory of motivation, the sufficiency of existential needs (thirst, hunger, and pain avoidance) provides the possibility of behaviors that may lead to the sufficiency of sexual needs (sexual behavior). Also, the sufficiency of certainty provides confidence in actions required in the process of completing the need for competence. In this case, the directional relationship can be considered a multilevel structure of states, where the sufficiency of higher-level needs provides a higher chance of completing the lower level.&lt;/p&gt;
&lt;p&gt;One issue from this directional relation is that people sometimes can focus on behaviors completing the higher-level needs but damage low-level needs. That may indicate, different needs can not be simply connected by connection 2 or there is some restriction of consequence prediction when people plan for behaviors. We will deeply discuss this in the future, but here we just need to realize the directional relation exists between needs.&lt;/p&gt;
&lt;h2&gt;2. Knowledge&lt;/h2&gt;
&lt;p&gt;When talking about knowledge, we are talking about memory. In the framework, any memory is represented by a combination of connections and basic elements. These can be categorized into the knowledge of actions, representations (connection 1), and solutions (path of states that, are connected by connection 2). The knowledge of action corresponds to not only procedural memory, which is how the involvement of consciousness distinguished them and how can we represent them in our models. The knowledge of representations and connection 1 corresponds to semantic knowledge (if we want, we can even bring it to the perceptual and sensual level). In the end, the knowledge of solutions and connection 2, knowledge of strategies and solutions can be mapped to the knowledge of strategies and solutions. We won&apos;t discuss how this knowledge function to fit into contemporary cognitive theories of memory and knowledge in this section but will spend more time on such discussion when we get to the blocks of implementations (since the framework only provides the ideas, and there will be multiple ways to implement the ideas, each implementation may provide a different explanation on phenomena).&lt;/p&gt;
&lt;h2&gt;3. Problem-Solving&lt;/h2&gt;
&lt;p&gt;Problem-solving is an outcome of knowledge and needs. I assume that is the meaning of the existence of individuals. Without the ability to solve problems, actions will lose their meaning and the social meaning of individuals will not be accomplished. To be able to solve problems, an individual needs to be able to recognize the problem/situation (matching of states), assign the goal (based on contemporary goal, which is induced by connection 2 from needs), and search for solutions (select the path that connects current state and the goal state).&lt;/p&gt;
&lt;h3&gt;3.1 Exploitation &amp;#x26; Exploration&lt;/h3&gt;
&lt;p&gt;The knowledge about the consequences of actions under different states is earned by trying and exploring. Exploitation and exploration demonstrate the idea of trial and error. This is the concept used in reinforcement learning, where exploitation indicates the agent applies actions it has successfully used for new situations and exploration indicates the gent trying new actions to the situation. The graph model will simulate this phenomenon by matching confronted situations to stored states, where the matching provides a continuous range between exploitation and exploration.&lt;/p&gt;
&lt;h2&gt;4. Consolidation &amp;#x26; Development&lt;/h2&gt;
&lt;p&gt;People&apos;s memory is consolidated in the background even if they don&apos;t retrieve or apply the knowledge actively. Similarly, there should be a process of the model simulating such process. Currently, the idea is using the functionality of a state (which is, a representation) for consolidation. I consider it a combination of the selection process and conditional function, which picks two paths first and then compares its middle parts and two ends. We shall talk more about these mechanisms in the future.&lt;/p&gt;</content:encoded><category>theory</category><category>model</category></item><item><title>Structure - Elements</title><link>https://angushushu.com/blog/structure-elements/</link><guid isPermaLink="true">https://angushushu.com/blog/structure-elements/</guid><description>naive example of the structure Above is a naive example that shows the main component of the potential model the connections between representations and the con</description><pubDate>Thu, 09 Feb 2023 19:59:01 GMT</pubDate><content:encoded>&lt;center&gt;
&lt;img src=&quot;https://angushushu.com/images/struct_example.png&quot; width=&quot;500&quot;&gt;
&lt;br&gt;naive example of the structure
&lt;/center&gt;
Above is a naive example that shows the main component of the potential model: the connections between representations, and the connections between states (by actions). There will be a lot of features needed to be adjusted, just providing an insight into the model.
&lt;h1&gt;Elements&lt;/h1&gt;
&lt;p&gt;The two main elements required to generate this structure are representations (set of representations), and actions (sequence of actions). The finest elements of them (without elements constructing them) are the representation units and action units. These elements are connected by two types of connection, let&apos;s call them connection 1 and connection 2. Connection 1 is intended to simulate semantic memory, priming, activation of knowledge, etc. Connection 2 is intended to simulate procedural memory, knowledge of problem-solving, etc. Connection 2 is always directed, but the features of Connection 1 will need more discussion.&lt;/p&gt;
&lt;h2&gt;1 Representation&lt;/h2&gt;
&lt;p&gt;Representation is an abstract but simple concept. It&apos;s a set of certain information (elements), and the elements within a representation can be representation units, representations, ordered pairs of representations, or actions. You can consider it as a node in an artificial neural network that explicitly states its meaning (which makes the model more explanatory).&lt;/p&gt;
&lt;h3&gt;1.1 Representation Unit&lt;/h3&gt;
&lt;p&gt;A representation unit is the most basic unit of representation, which contains nothing. You can consider it as a sensory unit, which provides information by itself. In the implementation, representation is more like a starting point of the model, the implementer of the model could determine its level of specificity. For instance, in discourse psychology, a representation unit can be a letter, a word, or a thought unit.&lt;/p&gt;
&lt;h3&gt;1.2 State&lt;/h3&gt;
&lt;p&gt;A state is a representation in connection 2. Consider the experience of feeling hungry and finishing your meal, these are two states. It is a set of representations that might provide you with an experience. I&apos;m using &quot;might&quot; here because it&apos;s not guaranteed that any state would provide you with an experience, some of the states are generally retrieved unconsciously and thus cannot be experienced (if we define experience as something involving consciousness).&lt;/p&gt;
&lt;h3&gt;1.3 Goal&lt;/h3&gt;
&lt;p&gt;A goal is a desired state. That is, it involves connection 2. To make it more specific, we define it as a sink (without outgoing edges) representation in connection 2. That is, consider the case you feel hungry, and it is connected to a state of fullness. In a bigger graph of connection 2, where the state of full is pointing to a state of survival, the state of full cannot be considered as a goal. However, when we extract the subgraph, in which the state of full is pointing to nothing, it can then be considered as a goal.&lt;/p&gt;
&lt;h2&gt;2 Action&lt;/h2&gt;
&lt;p&gt;An action is an activity that leads individuals to change their state. Creature won&apos;t be able to generate movement with only observations of states. Thus, action is essential. I identify two types of action, physical and mental. However, how to define action precisely still faces some issues and we will introduce the issues later. Currently, let&apos;s define an action as a list of actions.&lt;/p&gt;
&lt;h3&gt;2.1 Action Unit&lt;/h3&gt;
&lt;p&gt;An action unit is the minimal unit of action, which contains nothing but represents a single individual change (physical or mental).&lt;/p&gt;
&lt;h3&gt;2.1 Physical Action&lt;/h3&gt;
&lt;p&gt;Physical action is straightforward, any movement of muscle can be considered physical activity. Thus physical actions have a strong relationship with the motor system. Generally, we can use the easy definition of action for physical activity. Consider the action of drinking water, it can include multiple actions such as picking up a bottle and pouring the water into your mouth. However, if we consider the action unit as the firing of our motor neurons, there might be some parallel action. Thus it might be better to use the graph to represent actions.&lt;/p&gt;
&lt;h3&gt;2.2 Mental Action&lt;/h3&gt;
&lt;p&gt;Mental action indicates mental functions, such as solving a math problem or thinking about philosophical problems. Similar to physical activity, it can be considered as a list of actions in the simple case. However, in most cases, there might be function calling or parallel actions going on. Also, there might be an information passing issue for the function calling of parallel actions, that is, how does an action distribute its input to multiple subactions? Mental action can be much more complicated than physical action, thus it is worth more discussion about how to implement mental action in the future.&lt;/p&gt;</content:encoded><category>theory</category><category>model</category></item><item><title>Theory - Init</title><link>https://angushushu.com/blog/theory-init/</link><guid isPermaLink="true">https://angushushu.com/blog/theory-init/</guid><description>What for Perhaps it would be a dream for most psychologists to construct a model to simulate all behaviors and cognitive processes of human beings It would not </description><pubDate>Thu, 20 Oct 2022 19:27:40 GMT</pubDate><content:encoded>&lt;h1&gt;What for&lt;/h1&gt;
&lt;p&gt;Perhaps it would be a dream for most psychologists to construct a model to simulate all behaviors and cognitive processes of human beings.&lt;br&gt;
It would not be impossible to fully achieve this goal, but we can gradually approach it by setting a more basic goal: create a creature that demonstrates some core features of human beings and other organisms. Who doesn&apos;t want to be a god?&lt;/p&gt;
&lt;h1&gt;What is a creature&lt;/h1&gt;
&lt;p&gt;Then we get a question: what is a creature?&lt;br&gt;
Let&apos;s say, a creature is something that performs actions, based on certain needs. The ultimate need of a creature is to maintain its blueprint.&lt;br&gt;
I don&apos;t want to discuss where this definition comes from now, but let&apos;s start with it.&lt;/p&gt;
&lt;h1&gt;Potential model&lt;/h1&gt;
&lt;p&gt;Now we have the two core factors of the creature we want to construct: need and action. When I was in middle school, I called them &quot;sensibility&quot; and &quot;rationality&quot; and my understanding of the relation between them was:&lt;/p&gt;
&lt;center&gt;
&lt;img src=&quot;https://angushushu.com/images/0.png&quot; width=&quot;300&quot;&gt;
&lt;br&gt;inside out
&lt;/center&gt;
In high school, I replaced &quot;sensibility&quot; with &quot;needs&quot; and &quot;rationality&quot; with &quot;methods&quot; (now &quot;actions&quot;). The terminology is not important, you get the idea. With this basic idea, we can start our journey of creating.
Before that, I want to say, every model consists of certain static structures and dynamic processes. We will use directed graphs as our static structure.
&lt;h1&gt;Now we can start&lt;/h1&gt;
&lt;ol&gt;
&lt;li&gt;&lt;a href=&quot;https://angushushu.com/blog/structure-elements/&quot;&gt;structure-elements&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href=&quot;https://angushushu.com/blog/process-bases/&quot;&gt;process-bases&lt;/a&gt;&lt;/li&gt;
&lt;/ol&gt;</content:encoded><category>model</category><category>theory</category></item><item><title>Music Time!</title><link>https://angushushu.com/blog/playlists/</link><guid isPermaLink="true">https://angushushu.com/blog/playlists/</guid><description>Shu&apos;s OST playlist Shu&apos;s Song playlist Some random music Leave your recommendation in the comment</description><pubDate>Fri, 31 Dec 2021 00:00:00 GMT</pubDate><content:encoded>&lt;p&gt;&lt;a href=&quot;https://www.youtube.com/playlist?list=PLBFR62-14ItltucyGPoAHxL_gQOu0Q-Wi&quot;&gt;Shu&apos;s OST playlist&lt;/a&gt;&lt;br&gt;
&lt;a href=&quot;https://www.youtube.com/playlist?list=PLBFR62-14ItlS-6Y99xPLCisbScvPX8xm&quot;&gt;Shu&apos;s Song playlist&lt;/a&gt;&lt;br&gt;
&lt;a href=&quot;https://space.bilibili.com/5054022/favlist?fid=1037697422&amp;#x26;ftype=create&amp;#x26;spm_id_from=333.1007.0.0&quot;&gt;Some random music&lt;/a&gt;&lt;/p&gt;
&lt;p&gt;Leave your recommendation in the comment&lt;/p&gt;</content:encoded></item></channel></rss>