Jekyll2023-01-18T08:24:45+00:00https://ernwong.github.io/feed.xmlThe Duck PondA blog about making machines, programs, music, maths, physics... and ducks?
Terminal copy and paste2017-10-05T00:00:00+00:002017-10-05T00:00:00+00:00https://ernwong.github.io/hobby/2017/10/05/copy-and-paste<p>I want to digress from talking about mechanical differentials and talk more in the realm of shells, software, and productivity. September 17. That day was a special day. That day was the beginning of a new era. That day was the day I began copying and pasting correctly from my terminal.</p>
<h2 id="tldr">tl;dr</h2>
<p>Don’t have time to read the entire thing? In a nutshell:</p>
<ul>
<li>vimrc: <a href="https://github.com/ErnWong/vimfiles-wsl/commit/8314ec0c487c592982fe869fc0d1e35ecdcd2c25">Added ability to use Windows clipboard inside WSL</a>.</li>
<li>tmux: <a href="https://github.com/ErnWong/dotfiles-nix/commit/0b51e8fa4b6838d02534e60eed7e3f0893dcee04">Added tmux bindings for tmux and Windows clipboard</a>.</li>
<li>tmux: <a href="https://github.com/ErnWong/dotfiles-nix/commit/08a3d8ce3b694004290e9fdf60ba4913a570368d">Added tmux bindings for yanking</a>.</li>
</ul>
<h2 id="the-problem-before-september-17">The Problem Before September 17</h2>
<p>Life was really hard before September 17. Let me show you why. In the midst of my typical productive web browsing…</p>
<figure title="Please excuse the sound. I'm testing the software under typical user YouTube-ing conditions.">
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<figcaption><p>Figure 1. Don’t worry boss. I’m 100% focused on my work.</p>
</figcaption>
</figure>
<p>I found a very useful webpage whose information I wanted to copy down into one of my project files.</p>
<figure>
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<figcaption><p>Figure 2. Just your normal copying and pasting, right?</p>
</figcaption>
</figure>
<p>As common and as ordinary as this process may sound, there were actually no direct, satisfactory methods of doing this available to me.</p>
<ul>
<li>No, I can’t Control-C and Control-V my way through life, because I am using Vim as my editor.</li>
<li>No, I can’t yank and paste from the + or * registers, because my Vim is running inside my Ubuntu subsystem (aka the Bash-on-Ubuntu-on-Windows thing) and that has its own system clipboard, which is different to the Windows Clipboard.</li>
<li>I can’t use the tmux paste buffer as well, for the same reasons as above.</li>
<li>I technically <em>can</em> use the copy and paste functionality of the default Windows Console I’m using, but I can’t use the default Control-C/V hotkeys because they will clash with Vim key bindings.</li>
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<p>I was left with two options. One way would be to exit out of full-screen mode in order to access the context menu, on which is the copy and paste options that I can select with my mouse. In the process of exiting full-screen mode, my vim and tmux pane sizes are usually ruined.</p>
<figure>
<img src="/files/2017-10-05-copy-and-paste/vim-context-menu.png" width="600" title="...but I don't want to touch the mouse..." />
<figcaption><p>Figure 3. One way of inserting the copied text is through the context menu.</p>
</figcaption>
</figure>
<p>The other way would be to create a temporary file on the Windows file system, paste the data in there, and open it up from Vim.</p>
<figure title="As you can see, this is super efficient">
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<path sodipodi:nodetypes="cccccccc" inkscape:connector-curvature="0" id="path4736" d="m 100.54166,381.66667 h 7.93751 V 376.375 l 7.93749,7.9375 -7.93749,7.9375 v -5.29167 h -7.93751 z" style="fill:none;stroke:#000000;stroke-width:0.5291667;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1" />
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<text xml:space="preserve" style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:3.52777767px;line-height:1.25;font-family:Arial;-inkscape-font-specification:'Arial Bold';letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.26458332" x="31.750006" y="52.260422" id="text6345"><tspan sodipodi:role="line" id="tspan6343" x="31.750006" y="52.260422" style="text-align:center;text-anchor:middle;stroke-width:0.26458332">COPY TEXT</tspan></text>
<text xml:space="preserve" style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:3.52777767px;line-height:1.25;font-family:Arial;-inkscape-font-specification:'Arial Bold';letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.26458332" x="103.14788" y="5.897172" id="text6345-4"><tspan sodipodi:role="line" id="tspan6343-6" x="103.14788" y="5.897172" style="text-align:center;text-anchor:middle;stroke-width:0.26458332">PASTE TO TEMPORARY FILE VIA NOTEPAD</tspan></text>
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</svg>
<figcaption><p>Figure 4. The other way of inserting the copied text.</p>
</figcaption>
</figure>
<p>Oh! Yuk! As you can see, both of these options are anything but elegant. There must be a better way. By September 7, a little idea manifested in my head and I began configuring my workspace.</p>
<h2 id="the-yanky-idea">The yanky idea</h2>
<p>Here’s a little bit of background. Vim provides a very neat mechanism to copy and paste text internally using the <code class="language-plaintext highlighter-rouge">y</code> and <code class="language-plaintext highlighter-rouge">p</code> commands (where <code class="language-plaintext highlighter-rouge">y</code> stands for <em>yank</em>, and <code class="language-plaintext highlighter-rouge">p</code> stands for either <em>paste</em> or <em>put</em>). We can tell Vim which register to copy. Say, to copy to and paste to the ‘a’ register, we can prepend the <code class="language-plaintext highlighter-rouge">y</code> and <code class="language-plaintext highlighter-rouge">p</code> commands with <code class="language-plaintext highlighter-rouge">"a</code> to form <code class="language-plaintext highlighter-rouge">"ay</code> and <code class="language-plaintext highlighter-rouge">"ap</code>. A list of available registers is available <a href="http://vimdoc.sourceforge.net/htmldoc/change.html#registers">here</a>.</p>
<p>The Vim commands like yank <code class="language-plaintext highlighter-rouge">y</code> and paste <code class="language-plaintext highlighter-rouge">p</code> are Verb commands, and can be combined with many “Noun” commands that specify the block of text to perform the Verb in. In Vim terminology, these are Operators and Movements. An example of Movements are: inside-brackets <code class="language-plaintext highlighter-rouge">i)</code>, word <code class="language-plaintext highlighter-rouge">w</code>, up <code class="language-plaintext highlighter-rouge">k</code>, etc. which you can learn more about <a href="http://vimdoc.sourceforge.net/htmldoc/motion.htm">here</a>. For example, to copy the current sentence into the ‘e’ register, we could press <code class="language-plaintext highlighter-rouge">"eyis</code>, which stands for select register <code class="language-plaintext highlighter-rouge">"</code>, and <code class="language-plaintext highlighter-rouge">y</code>ank <code class="language-plaintext highlighter-rouge">i</code>nside <code class="language-plaintext highlighter-rouge">s</code>entence. This makes Vim a really nice editor to use.</p>
<figure>
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<figcaption><p>Figure 5. Vim normal mode commands.</p>
</figcaption>
</figure>
<p>Have I lost you yet? Yes? Great! You may now move on to the next section.</p>
<p>Perhaps everything makes sense for you? Clearly, you haven’t read things carefully. Go back to the start of this subsection.</p>
<p>Now, wouldn’t it be nice if we could somehow “create” or mimic a new register such that we can copy and paste from the Windows clipboard? The next question would be which letter to use for this “new” register. Ideally, such letter would not be pointing to a pre-existing register, and it should be easy to type when used with the <code class="language-plaintext highlighter-rouge">"</code> key. How about the <code class="language-plaintext highlighter-rouge">"</code> key itself? Well, why not. It is not a pre-existing register, and it is super convenient to type <code class="language-plaintext highlighter-rouge">""</code>.</p>
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<figcaption><p>Figure 6.</p>
</figcaption>
</figure>
<h2 id="implementing-the-yank">Implementing the yank</h2>
<p>The next step is to figure out how to script this in. I can’t seem to find a built-in mechanism to make <code class="language-plaintext highlighter-rouge">"</code> behave like a register so that <code class="language-plaintext highlighter-rouge">""</code> behaves like <code class="language-plaintext highlighter-rouge">"a</code> but with a custom <code class="language-plaintext highlighter-rouge">"</code> register instead of the <code class="language-plaintext highlighter-rouge">a</code> register. It seems like the only way is to map the commands individually for yank and pasting. We want something along the lines of this:</p>
<div class="language-vimscript highlighter-rouge"><div class="highlight"><pre class="highlight"><code>nnoremap <span class="s2">""</span><span class="k">y</span> <span class="p"><</span>something here<span class="p">></span> <span class="p">!</span><span class="k">copy</span> <span class="p"><</span>something <span class="k">else</span> here<span class="p">></span>
</code></pre></div></div>
<p>It is possible to run Windows binaries within WSL, so we could leverage <a href="https://ss64.com/nt/clip.html">this small program called clip.exe</a> to somehow pour the clipboard contents into the stdout.</p>
<div class="language-vimscript highlighter-rouge"><div class="highlight"><pre class="highlight"><code>nnoremap <span class="s2">""</span><span class="k">y</span> <span class="p"><</span>something here<span class="p">></span> <span class="p">!</span>clip<span class="p">.</span>exe <span class="p"><</span>something <span class="k">else</span> here<span class="p">></span>
</code></pre></div></div>
<p>Things are not all that straightforward though. Remember how the original yank and paste commands allow the person to type a Movement (ie. the Noun)? There are a gazillion, if not infinite, possible combinations of these Movement Nouns that yank and paste can handle, so if we were to map a key binding for each, it will be slightly challenging…</p>
<div class="language-vimscript highlighter-rouge"><div class="highlight"><pre class="highlight"><code>nnoremap <span class="s2">""</span>yk <span class="p"><</span>something here<span class="p">></span> "<span class="p">.....</span>etc<span class="p">.....</span>
nnoremap <span class="s2">""</span>y2k <span class="p"><</span>something here<span class="p">></span> "<span class="p">.....</span>etc<span class="p">.....</span>
nnoremap <span class="s2">""</span>y3k <span class="p"><</span>something here<span class="p">></span> "<span class="p">.....</span>etc<span class="p">.....</span>
nnoremap <span class="s2">""</span>y4k <span class="p"><</span>something here<span class="p">></span> "<span class="p">.....</span>etc<span class="p">.....</span>
nnoremap <span class="s2">""</span>y5k <span class="p"><</span>something here<span class="p">></span> "<span class="p">.....</span>etc<span class="p">.....</span>
nnoremap <span class="s2">""</span>y6k <span class="p"><</span>something here<span class="p">></span> "<span class="p">.....</span>etc<span class="p">.....</span>
<span class="c">" ... followed by an infinitely more lines ...</span>
<span class="c">" you get the idea</span>
</code></pre></div></div>
<p>Is there a way to handle these Movement commands without defying the laws of physics? I began thinking: maybe these Verb commands, like yank and paste, are just special mappings. Maybe there’s a certain type of mapping similar (but different) to the <code class="language-plaintext highlighter-rouge">nmap</code>s that deals with these Movement commands. Does it exist? I turn to my old friend, Mr Google.</p>
<p>Mr Google, is there such special mapping command? He responds. Apparently, there’s this thing called <a href="http://learnvimscriptthehardway.stevelosh.com/chapters/15.html">Operator-Pending Mappings</a>. It’s very close to what I’m looking for, except, it’s the exact opposite of what I wanted. Operator-Pending Mappings, using the command <code class="language-plaintext highlighter-rouge">onoremap</code> or <code class="language-plaintext highlighter-rouge">omap</code>, allows us to implement the Movement (aka the verb) and not the Operator (the noun). We want to make an Operator, not a Movement.</p>
<p>Mr Google, Mr Google. Is there anything else? He then showed me something interesting. It’s a <a href="https://stackoverflow.com/questions/8994276/defining-a-new-vim-operator-with-a-parameter">StackOverflow Q&A</a>, because good stuff is always on stack overflow right? However, I’m not always a fan of copying and pasting from the internet (even though I do), so I decided to find help on this interesting keyword I kept seeing on this page called <code class="language-plaintext highlighter-rouge">opfunc</code>. Vim help, here I go: <code class="language-plaintext highlighter-rouge">:h opfunc</code>.</p>
<div class="language-plaintext highlighter-rouge"><div class="highlight"><pre class="highlight"><code> *'operatorfunc'* *'opfunc'*
'operatorfunc' 'opfunc' string (default: empty)
global
{not in Vi}
This option specifies a function to be called by the |g@| operator.
See |:map-operator| for more info and an example.
This option cannot be set from a |modeline| or in the |sandbox|, for
security reasons.
</code></pre></div></div>
<p><em>(from <a href="http://vimdoc.sourceforge.net/htmldoc/options.html#'opfunc'">http://vimdoc.sourceforge.net/htmldoc/options.html#’opfunc’</a>)</em></p>
<p>Interesting. Heeding to its advice, I press <code class="language-plaintext highlighter-rouge">Ctrl-]</code> above the <code class="language-plaintext highlighter-rouge">:map-operator</code> to navigate to the <a href="http://vimdoc.sourceforge.net/htmldoc/map.html#:map-operator">relevant page</a>.</p>
<div class="language-plaintext highlighter-rouge"><div class="highlight"><pre class="highlight"><code>1.11 MAPPING AN OPERATOR *:map-operator*
An operator is used before a {motion} command. To define your own operator
you must create mapping that first sets the 'operatorfunc' option and then
invoke the |g@| operator. After the user types the {motion} command the
specified function will be called.
*g@* *E774* *E775*
g@{motion} Call the function set by the 'operatorfunc' option.
The '[ mark is positioned at the start of the text
moved over by {motion}, the '] mark on the last
character of the text.
The function is called with one String argument:
"line" {motion} was |linewise|
"char" {motion} was |characterwise|
"block" {motion} was |blockwise-visual|
Although "block" would rarely appear, since it can
only result from Visual mode where "g@" is not useful.
{not available when compiled without the |+eval|
feature}
Here is an example that counts the number of spaces with <F4>: >
nmap <silent> <F4> :set opfunc=CountSpaces<CR>g@
vmap <silent> <F4> :<C-U>call CountSpaces(visualmode(), 1)<CR>
function! CountSpaces(type, ...)
let sel_save = &selection
let &selection = "inclusive"
let reg_save = @@
if a:0 " Invoked from Visual mode, use gv command.
silent exe "normal! gvy"
elseif a:type == 'line'
silent exe "normal! '[V']y"
else
silent exe "normal! `[v`]y"
endif
echomsg strlen(substitute(@@, '[^ ]', '', 'g'))
let &selection = sel_save
let @@ = reg_save
endfunction
Note that the 'selection' option is temporarily set to "inclusive" to be able
to yank exactly the right text by using Visual mode from the '[ to the ']
mark.
Also note that there is a separate mapping for Visual mode. It removes the
"'<,'>" range that ":" inserts in Visual mode and invokes the function with
visualmode() and an extra argument.
</code></pre></div></div>
<p>Jackpot. This is exactly what I wanted: the “API”s sorta speak to implementing my own motion-handling operator. Interestingly, in the example code that they give, the code copies the selected text’s contents into the unnamed register in order to use the text content for processing.</p>
<p>After <del>copy and pasting</del> getting inspiration from the example code, the paste key binding is implemented:</p>
<div class="language-vimscript highlighter-rouge"><div class="highlight"><pre class="highlight"><code>nnoremap <span class="p"><</span><span class="k">silent</span><span class="p">></span> <span class="s2">""</span><span class="k">y</span> <span class="p">:</span><span class="k">set</span> <span class="nb">opfunc</span><span class="p">=</span>WindowsYank<span class="p"><</span>CR<span class="p">></span><span class="k">g</span>@
vnoremap <span class="p"><</span><span class="k">silent</span><span class="p">></span> <span class="s2">""</span><span class="k">y</span> <span class="p">:<</span>C<span class="p">-</span>U<span class="p">></span><span class="k">call</span> WindowsYank<span class="p">(</span><span class="nb">visualmode</span><span class="p">(),</span> <span class="m">1</span><span class="p">)<</span>CR<span class="p">></span>
<span class="k">function</span><span class="p">!</span> WindowsYank<span class="p">(</span><span class="nb">type</span><span class="p">,</span> <span class="p">...)</span>
<span class="c">" (1) Save original values for the selection setting</span>
<span class="c">" and the unnamed register</span>
<span class="k">let</span> sel_save <span class="p">=</span> &<span class="nb">selection</span>
<span class="k">let</span> &<span class="nb">selection</span> <span class="p">=</span> <span class="s2">"inclusive"</span>
<span class="k">let</span> reg_save <span class="p">=</span> @@
<span class="c">" (2) Yank text to unnamed register</span>
<span class="k">if</span> <span class="nv">a:0</span> " Invoked from Visual <span class="k">mode</span><span class="p">,</span> use gv command<span class="p">.</span>
<span class="k">silent</span> exe <span class="s2">"normal! gvy"</span>
<span class="k">elseif</span> <span class="nv">a:type</span> <span class="p">==</span> <span class="s1">'line'</span>
<span class="k">silent</span> exe <span class="s2">"normal! '[V']y"</span>
<span class="k">else</span>
<span class="k">silent</span> exe <span class="s2">"normal! `[v`]y"</span>
<span class="k">endif</span>
<span class="c">" (3) Send contents of @@ to Windows clip.exe</span>
<span class="c">" Note: I've included a pushd-to-windows-directory to suppress warning</span>
<span class="c">" because windows warns about failing to translate working directory</span>
<span class="c">" when current working directory is inside wsl.</span>
echo <span class="nb">system</span><span class="p">(</span><span class="s1">'pushd /mnt/c/ > /dev/null && clip.exe && popd > /dev/null'</span><span class="p">,</span> <span class="nb">getreg</span><span class="p">(</span><span class="s1">''</span><span class="p">,</span> <span class="m">1</span><span class="p">,</span> <span class="m">1</span><span class="p">))</span>
<span class="c">" (4) Restore original settings and value of unnamed register</span>
<span class="k">let</span> &<span class="nb">selection</span> <span class="p">=</span> sel_save
<span class="k">let</span> @@ <span class="p">=</span> reg_save
<span class="k">endfunction</span>
</code></pre></div></div>
<h2 id="how-it-works">How it works</h2>
<p>Let’s look at the key binding for <code class="language-plaintext highlighter-rouge">normal</code> mode:</p>
<div class="language-vimscript highlighter-rouge"><div class="highlight"><pre class="highlight"><code>nnoremap <span class="p"><</span><span class="k">silent</span><span class="p">></span> <span class="s2">""</span><span class="k">y</span> <span class="p">:</span><span class="k">set</span> <span class="nb">opfunc</span><span class="p">=</span>WindowsYank<span class="p"><</span>CR<span class="p">></span><span class="k">g</span>@
</code></pre></div></div>
<p>When the keys <code class="language-plaintext highlighter-rouge">""y</code> are pressed, Vim will do the following:</p>
<ol>
<li>The <code class="language-plaintext highlighter-rouge">:</code> tells Vim to enter the command-line mode, so the line tells Vim to enter <code class="language-plaintext highlighter-rouge">:set opfunc=WindowsYank</code> and press Enter (the <code class="language-plaintext highlighter-rouge"><CR></code> key) to let Vim parse the command line.</li>
<li>The command <code class="language-plaintext highlighter-rouge">g@</code> is executed. This tells Vim to enter operator-pending mode, and will wait for the user to enter some Movements.</li>
<li>Once the movements are done, the <code class="language-plaintext highlighter-rouge">g@</code> command calls whatever function is set into the <code class="language-plaintext highlighter-rouge">opfunc</code> option. The <code class="language-plaintext highlighter-rouge">[`` mark and the</code>]`` mark are now set to the start and the end of the text selection. Since we’ve set <code class="language-plaintext highlighter-rouge">opfunc</code> to <code class="language-plaintext highlighter-rouge">WindowsYank</code>, Vim will now call the <code class="language-plaintext highlighter-rouge">WindowsYank</code> function. It will also pass an argument (<code class="language-plaintext highlighter-rouge">a:type</code> of <code class="language-plaintext highlighter-rouge">WindowsYank</code>) that describes what type of motion it was:
<div class="language-plaintext highlighter-rouge"><div class="highlight"><pre class="highlight"><code>"line" {motion} was |linewise|
"char" {motion} was |characterwise|
"block" {motion} was |blockwise-visual|
</code></pre></div> </div>
</li>
</ol>
<p>Inside the <code class="language-plaintext highlighter-rouge">WindowsYank</code> function, the following line grabs the content of the selected text:</p>
<div class="language-vimscript highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="k">elseif</span> <span class="nv">a:type</span> <span class="p">==</span> <span class="s1">'line'</span>
<span class="k">silent</span> exe <span class="s2">"normal! '[V']y"</span> " <span class="p"><---</span> this uses <span class="k">visual</span> <span class="nb">line</span> <span class="k">mode</span> V <span class="k">to</span> <span class="k">copy</span>
<span class="c">" everything between the '[ and '] marks</span>
<span class="c">" into the unnamed register</span>
<span class="k">else</span>
<span class="k">silent</span> exe <span class="s2">"normal! `[v`]y"</span> " <span class="p"><---</span> this uses <span class="k">visual</span> <span class="k">mode</span> <span class="k">v</span> <span class="k">to</span> <span class="k">copy</span>
<span class="c">" everything between the `[ and `] marks</span>
<span class="c">" into the unnamed register</span>
<span class="k">endif</span>
<span class="c">" Side note: ` jumps to the location, while</span>
<span class="c">" ' jumps to the first character</span>
<span class="c">" in the line of the location</span>
</code></pre></div></div>
<p>…and pipes it into the shell command. Inspiration from the godly-gods of <a href="https://stackoverflow.com/a/2575656">StackOverflow</a>.</p>
<div class="language-vimscript highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="c">" (3) Send contents of @@ to Windows clip.exe</span>
<span class="c">" Note: I've included a pushd-to-windows-directory to suppress warning</span>
<span class="c">" because windows warns about failing to translate working directory</span>
<span class="c">" when current working directory is inside wsl.</span>
echo <span class="nb">system</span><span class="p">(</span><span class="s1">'pushd /mnt/c/ > /dev/null && clip.exe && popd > /dev/null'</span><span class="p">,</span> <span class="nb">getreg</span><span class="p">(</span><span class="s1">''</span><span class="p">,</span> <span class="m">1</span><span class="p">,</span> <span class="m">1</span><span class="p">))</span>
</code></pre></div></div>
<p>What about <code class="language-plaintext highlighter-rouge">visual</code> mode? It’s quite similar. We begin with the key binding:</p>
<div class="language-vimscript highlighter-rouge"><div class="highlight"><pre class="highlight"><code>vnoremap <span class="p"><</span><span class="k">silent</span><span class="p">></span> <span class="s2">""</span><span class="k">y</span> <span class="p">:<</span>C<span class="p">-</span>U<span class="p">></span><span class="k">call</span> WindowsYank<span class="p">(</span><span class="nb">visualmode</span><span class="p">(),</span> <span class="m">1</span><span class="p">)<</span>CR<span class="p">></span>
</code></pre></div></div>
<p>Let’s decode this. When the user types the keys <code class="language-plaintext highlighter-rouge">""y</code>, Vim does the following:</p>
<ol>
<li>The <code class="language-plaintext highlighter-rouge">:</code> tells Vim to enter command-line mode. Note that Vim is in <code class="language-plaintext highlighter-rouge">visual</code> mode, so Vim automatically adds <code class="language-plaintext highlighter-rouge">'<,'></code> to the command-line.</li>
<li>The <code class="language-plaintext highlighter-rouge"><C-U></code> emulates the user pressing Control-U. This tells Vim to remove that <code class="language-plaintext highlighter-rouge">'<v'></code> from the command-line.</li>
<li>The remaining stuff tells Vim to call the <code class="language-plaintext highlighter-rouge">WindowsYank</code> function. It sets the first argument <code class="language-plaintext highlighter-rouge">a:type</code> to <code class="language-plaintext highlighter-rouge">visualmode()</code> (which isn’t actually used in the function so we can ignore what this means). It then sets the optional argument <code class="language-plaintext highlighter-rouge">a:0</code> to <code class="language-plaintext highlighter-rouge">1</code>.</li>
<li>The <code class="language-plaintext highlighter-rouge"><CR></code> tells Vim to press Enter, so the command-line gets processed.</li>
</ol>
<p>Inside the <code class="language-plaintext highlighter-rouge">WindowsYank</code> function, things behave in a very similar way. The only behaviour that differs is in the way the function grabs the selected text:</p>
<div class="language-vimscript highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="k">if</span> <span class="nv">a:0</span> " Invoked from Visual <span class="k">mode</span><span class="p">,</span> use gv command<span class="p">.</span>
<span class="k">silent</span> exe <span class="s2">"normal! gvy"</span>
</code></pre></div></div>
<p>Here, the <code class="language-plaintext highlighter-rouge">gv</code> command tells Vim to re-select everything that had been previously selected in <code class="language-plaintext highlighter-rouge">visual</code> mode. This selected text is yanked into the unnamed register and gets piped into <code class="language-plaintext highlighter-rouge">clip.exe</code> just like it would in <code class="language-plaintext highlighter-rouge">normal</code> mode.</p>
<p>Because this function uses the unnamed register temporarily, we want to restore its previous value back once we’ve finished with it.</p>
<pre><code class="language-vimscrpt">let @@ = reg_save
</code></pre>
<p>That, my friend, is how this little script works.</p>
<h2 id="what-about-pasting">What about pasting?</h2>
<p>With the yanking part implemented, we need to implement the pasting part. Here’s what we need to do:</p>
<ol>
<li>Figure out how to grab the Windows clipboard contents and store it into a register or a variable.</li>
<li>Figure out how to paste it into the Vim buffer/window.</li>
</ol>
<p>For the yanking part, we had a helpful Windows program called <code class="language-plaintext highlighter-rouge">clip.exe</code> that we can pipe into its stdin to copy stuff. Is there an analogous version for pasting, like a <code class="language-plaintext highlighter-rouge">paste.exe</code> that dumps the clipboard contents into stdout? After some searching <a href="https://stackoverflow.com/a/2575656">here</a> and <a href="https://brianreiter.org/2010/09/03/copy-and-paste-with-clipboard-from-powershell/">there</a>, there doesn’t seem to be some quick and dirty, built-in solution that I can use satisfyingly.</p>
<p>Luckily, I discovered on <a href="https://github.com/neovim/neovim/issues/6227">neovim Github issue</a> that some lovely folk had made a simple <code class="language-plaintext highlighter-rouge">paste.exe</code> program on <a href="https://github.com/neosmart/paste">Github</a>. Even the name is exactly <code class="language-plaintext highlighter-rouge">paste.exe</code>, so how can I say no to that?</p>
<p>We can load the contents of the clipboard into the unnamed register like so:</p>
<div class="language-vimscript highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="k">let</span> @@ <span class="p">=</span> <span class="nb">system</span><span class="p">(</span><span class="s1">'pushd /mnt/c/ > /dev/null && paste.exe && popd > /dev/null'</span><span class="p">)</span>
</code></pre></div></div>
<p>Here comes the problem. If you look at the vim help documentation, there are eight different flavours of the paste command for <code class="language-plaintext highlighter-rouge">normal</code> mode: <code class="language-plaintext highlighter-rouge">p</code>, <code class="language-plaintext highlighter-rouge">P</code>, <code class="language-plaintext highlighter-rouge">gp</code>, <code class="language-plaintext highlighter-rouge">gP</code>, <code class="language-plaintext highlighter-rouge">]p</code>, <code class="language-plaintext highlighter-rouge">[p</code>, <code class="language-plaintext highlighter-rouge">]P</code>, and <code class="language-plaintext highlighter-rouge">[P</code>. On top of that, there are also two <code class="language-plaintext highlighter-rouge">visual</code> mode paste commands. Is there a way to elegantly deal with all these behaviours?</p>
<p>Then came a brilliant idea. We’re already storing the stdout of <code class="language-plaintext highlighter-rouge">paste.exe</code> into the unnamed register <code class="language-plaintext highlighter-rouge">@@</code>, so why not just run whatever command the user types in to paste it in? We can always restore the original <code class="language-plaintext highlighter-rouge">@@</code> values anyway.</p>
<p>On the first attempt, I used the <code class="language-plaintext highlighter-rouge">feedkeys</code> function to run the appropriate paste commands:</p>
<div class="language-vimscript highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="k">function</span><span class="p">!</span> WindowsPaste<span class="p">(</span>command<span class="p">,</span> <span class="p">...)</span>
<span class="c">" (1) Save original value of the unnamed register to restore later on</span>
<span class="k">let</span> reg_save <span class="p">=</span> @@
<span class="c">" (2) Load clipboard into register</span>
<span class="k">let</span> @@ <span class="p">=</span> <span class="nb">system</span><span class="p">(</span><span class="s1">'pushd /mnt/c/ > /dev/null && paste.exe && popd > /dev/null'</span><span class="p">)</span>
<span class="c">" (3) Run the given paste command</span>
<span class="k">call</span> <span class="nb">feedkeys</span><span class="p">(</span>command<span class="p">)</span>
<span class="c">" (4) Restore</span>
<span class="k">let</span> @@ <span class="p">=</span> reg_save
<span class="k">endfunction</span>
</code></pre></div></div>
<p>However, there was a problem. Whenever <code class="language-plaintext highlighter-rouge">WindowsPaste</code> is called, it actually pastes whatever’s in the unnamed register <em>before</em> it was modified. In other words, if the user copied the text <code class="language-plaintext highlighter-rouge">abc</code> into the Vim unnamed register in the conventional manner, and on copied the text <code class="language-plaintext highlighter-rouge">123</code> on Windows’ clipboard, running <code class="language-plaintext highlighter-rouge">WindowsPaste</code> pastes <code class="language-plaintext highlighter-rouge">abc</code> instead of <code class="language-plaintext highlighter-rouge">123</code>. What is going on?</p>
<p>It turns out that I have misused the <code class="language-plaintext highlighter-rouge">feedkeys</code> function. Looking at the <a href="http://vimdoc.sourceforge.net/htmldoc/eval.html#feedkeys()">documentation</a>:</p>
<blockquote>
<p>Characters in {string} are queued for processing as if they
come from a mapping or were typed by the user.
By default the string is <strong>added to the end</strong> of the typeahead
buffer, thus if a mapping is still being executed the
characters come after them.
…
The function <strong>does not wait</strong> for processing of keys contained in
{string}.</p>
</blockquote>
<p>(Emphasis by me)</p>
<p>This meant that the unnamed register <code class="language-plaintext highlighter-rouge">@@</code> is restored back to <code class="language-plaintext highlighter-rouge">reg_save</code> before the paste commands were executed. This explains the symptoms we’re experiencing.</p>
<p>Let’s scrap the use of <code class="language-plaintext highlighter-rouge">feedkeys</code>. Turns out we can use the <code class="language-plaintext highlighter-rouge">execute</code> command instead:</p>
<div class="language-vimscript highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="c">" (3) Run the given paste command</span>
exe <span class="s2">"normal! "</span> <span class="p">.</span> <span class="nv">a:command</span>
</code></pre></div></div>
<p>This seems to work really nicely. As for <code class="language-plaintext highlighter-rouge">visual</code> mode, I can’t seem to find a <code class="language-plaintext highlighter-rouge">:visual</code> command that behaves like the <code class="language-plaintext highlighter-rouge">:normal</code> command. The <code class="language-plaintext highlighter-rouge">:visual</code> command appears to do something else. That’s okay though, we can use the <code class="language-plaintext highlighter-rouge">:normal</code> command and re-enter visual mode and select everything that was previously selected using <code class="language-plaintext highlighter-rouge">gv</code>.</p>
<div class="language-vimscript highlighter-rouge"><div class="highlight"><pre class="highlight"><code>exe <span class="s2">"normal! gv"</span> <span class="p">.</span> <span class="nv">a:command</span>
</code></pre></div></div>
<p>That is it. That is all. All that’s left are the key bindings:</p>
<div class="language-vimscript highlighter-rouge"><div class="highlight"><pre class="highlight"><code>nnoremap <span class="p"><</span><span class="k">silent</span><span class="p">></span> <span class="s2">""</span><span class="k">p</span> <span class="p">:</span><span class="k">call</span> WindowsPaste<span class="p">(</span><span class="s1">'p'</span><span class="p">)<</span>CR<span class="p">></span>
nnoremap <span class="p"><</span><span class="k">silent</span><span class="p">></span> <span class="s2">""</span>P <span class="p">:</span><span class="k">call</span> WindowsPaste<span class="p">(</span><span class="s1">'P'</span><span class="p">)<</span>CR<span class="p">></span>
nnoremap <span class="p"><</span><span class="k">silent</span><span class="p">></span> <span class="s2">""</span><span class="nb">gp</span> <span class="p">:</span><span class="k">call</span> WindowsPaste<span class="p">(</span><span class="s1">'gp'</span><span class="p">)<</span>CR<span class="p">></span>
nnoremap <span class="p"><</span><span class="k">silent</span><span class="p">></span> <span class="s2">""</span>gP <span class="p">:</span><span class="k">call</span> WindowsPaste<span class="p">(</span><span class="s1">'gP'</span><span class="p">)<</span>CR<span class="p">></span>
nnoremap <span class="p"><</span><span class="k">silent</span><span class="p">></span> <span class="s2">""</span><span class="p">]</span><span class="k">p</span> <span class="p">:</span><span class="k">call</span> WindowsPaste<span class="p">(</span><span class="s1">']p'</span><span class="p">)<</span>CR<span class="p">></span>
nnoremap <span class="p"><</span><span class="k">silent</span><span class="p">></span> <span class="s2">""</span><span class="p">[</span><span class="k">p</span> <span class="p">:</span><span class="k">call</span> WindowsPaste<span class="p">(</span><span class="s1">'[p'</span><span class="p">)<</span>CR<span class="p">></span>
nnoremap <span class="p"><</span><span class="k">silent</span><span class="p">></span> <span class="s2">""</span><span class="p">]</span>P <span class="p">:</span><span class="k">call</span> WindowsPaste<span class="p">(</span><span class="s1">']P'</span><span class="p">)<</span>CR<span class="p">></span>
nnoremap <span class="p"><</span><span class="k">silent</span><span class="p">></span> <span class="s2">""</span><span class="p">[</span>P <span class="p">:</span><span class="k">call</span> WindowsPaste<span class="p">(</span><span class="s1">'[P'</span><span class="p">)<</span>CR<span class="p">></span>
vnoremap <span class="p"><</span><span class="k">silent</span><span class="p">></span> <span class="s2">""</span><span class="k">p</span> <span class="p">:</span><span class="k">call</span> WindowsPaste<span class="p">(</span><span class="s1">'p'</span><span class="p">,</span> <span class="m">1</span><span class="p">)<</span>CR<span class="p">></span>
vnoremap <span class="p"><</span><span class="k">silent</span><span class="p">></span> <span class="s2">""</span>P <span class="p">:</span><span class="k">call</span> WindowsPaste<span class="p">(</span><span class="s1">'P'</span><span class="p">,</span> <span class="m">1</span><span class="p">)<</span>CR<span class="p">></span>
</code></pre></div></div>
<p>The overall pasting script in its final form:</p>
<div class="language-vimscript highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="k">function</span><span class="p">!</span> WindowsPaste<span class="p">(</span>command<span class="p">,</span> <span class="p">...)</span>
<span class="c">" (1) Save original value of the unnamed register to restore later on</span>
<span class="k">let</span> reg_save <span class="p">=</span> @@
<span class="c">" (2) Load clipboard into register</span>
<span class="k">let</span> @@ <span class="p">=</span> <span class="nb">system</span><span class="p">(</span><span class="s1">'pushd /mnt/c/ > /dev/null && paste.exe && popd > /dev/null'</span><span class="p">)</span>
<span class="c">" (3) Run whatever command was being run</span>
<span class="k">if</span> <span class="nv">a:0</span>
exe <span class="s2">"normal! gv"</span> <span class="p">.</span> <span class="nv">a:command</span>
<span class="c">" Don't revert unnamed register if inside visual mode</span>
<span class="k">else</span>
exe <span class="s2">"normal! "</span> <span class="p">.</span> <span class="nv">a:command</span>
<span class="c">" Revert unnamed register</span>
<span class="k">let</span> @@ <span class="p">=</span> reg_save
<span class="k">endif</span>
<span class="k">endfunction</span>
</code></pre></div></div>
<h2 id="daddy-look-i-can-copy-and-paste">Daddy, look! I can copy and paste!</h2>
<figure>
<img src="/files/2017-10-05-copy-and-paste/vim-demo.gif" width="500px" title="Yeah, ignore the weird newline thing. I might fix that later." />
<figcaption><p>Demo 1.</p>
</figcaption>
</figure>
<h2 id="finishing-up-with-tmux">Finishing up with Tmux</h2>
<p>After taming Vim to our liking, surely tmux isn’t that hard to change right?</p>
<p>Tmux has this concept of <a href="http://man7.org/linux/man-pages/man1/tmux.1.html#BUFFERS">paste buffers</a> and something called the <a href="http://man7.org/linux/man-pages/man1/tmux.1.html#WINDOWS_AND_PANES">copy mode</a>.</p>
<p>In order to copy something, one would usually enter this <em>copy mode</em> by pressing the tmux prefix key (usually <code class="language-plaintext highlighter-rouge">Ctrl-b</code>) followed by <code class="language-plaintext highlighter-rouge">[</code>. Tmux then freezes the pane, and you can navigate up and down the history of the pane. The user would then select the text, and copy it using the keybindings specified <a href="http://man7.org/linux/man-pages/man1/tmux.1.html#WINDOWS_AND_PANES">here</a>. Finally, the user can exit copy mode and paste it by pressing the prefix key (usually <code class="language-plaintext highlighter-rouge">Ctrl-b</code>) followed by <code class="language-plaintext highlighter-rouge">]</code>.</p>
<p>The first thing I will configure would be the default key bindings in copy-mode to vi-like. Note that these configurations are being put in a file <code class="language-plaintext highlighter-rouge">~.tmux.conf</code>.</p>
<pre><code class="language-tmux">set-window-option -g mode-keys vi
</code></pre>
<p>The default key bindings are a little bit less intuitive, so I add the following as well. Inspiration from these <a href="http://jasonwryan.com/blog/2011/06/07/copy-and-paste-in-tmux/">nice</a> <a href="https://awhan.wordpress.com/2010/06/20/copy-paste-in-tmux/">bloggers</a>.</p>
<pre><code class="language-tmux">bind P paste-buffer
bind -T copy-mode-vi v send-keys -X begin-selection
bind -T copy-mode-vi y send-keys -X copy-selection
bind -T copy-mode-vi r send-keys -X rectangle-toggle
bind -T copy-mode-vi Q send-keys -X stop-selection
</code></pre>
<p>Next up, we’ll try to bind a key that pastes from the windows clipboard. We can use the <code class="language-plaintext highlighter-rouge">tmux load-buffer</code> to load the outputs of our <code class="language-plaintext highlighter-rouge">paste.exe</code> into a tmux paste buffer. Looking at the man page, this <code class="language-plaintext highlighter-rouge">load-buffer</code> command accepts a file path and loads the contents of it into the specified buffer:</p>
<div class="language-plaintext highlighter-rouge"><div class="highlight"><pre class="highlight"><code> load-buffer [-b buffer-name] path
(alias: loadb)
Load the contents of the specified paste buffer from path.
</code></pre></div></div>
<p><em>(from <a href="http://man7.org/linux/man-pages/man1/tmux.1.html#BUFFERS">http://man7.org/linux/man-pages/man1/tmux.1.html#BUFFERS</a>)</em></p>
<p>Hmm, our <code class="language-plaintext highlighter-rouge">paste.exe</code> doesn’t readily produce a file, so we’ll have to pipe it into a new file ourselves. To be safe, we’ll create a temporary directory with <a href="https://www.mktemp.org/manual.html"><code class="language-plaintext highlighter-rouge">mktemp</code></a>, and create our file there:</p>
<div class="language-plaintext highlighter-rouge"><div class="highlight"><pre class="highlight"><code>cd $(mktemp -d) \
&& paste.exe > ./data \
&& tmux load-buffer ./data -b windows-paste-buffer \
&& rm -r $(pwd)
</code></pre></div></div>
<p>Note that the line <code class="language-plaintext highlighter-rouge">rm -r $(pwd)</code> is potentially dangerous if <code class="language-plaintext highlighter-rouge">mktemp</code> fails, as it may delete the current directory. This is, however, safe guarded by the ampersands, as <code class="language-plaintext highlighter-rouge">mktemp</code> should return 1 upon failure.</p>
<p>After the buffer is loaded, we can call the <code class="language-plaintext highlighter-rouge">tmux paste-buffer</code> command to finish the pasting process. We can turn this mini script snippet into a tmux key binding like so:</p>
<pre><code class="language-tmux">bind C-p run "\
cd $(mktemp -d) \
&& paste.exe > ./data \
&& tmux load-buffer -b windows-paste-buffer ./data \
&& rm -r $(pwd) \
&& tmux paste-buffer -b windows-paste-buffer"
</code></pre>
<p>Can we avoid creating this temporary file? Yes. Because, in linux, you’ll find that almost everything is a file. There is a (virtual?) file at <code class="language-plaintext highlighter-rouge">/dev/stdin</code> that we can use to pipe directly into the buffer:</p>
<pre><code class="language-tmux">bind C-p run "\
paste.exe \
| tmux load-buffer -b windows-paste-buffer /dev/stdin \
&& tmux paste-buffer -b windows-paste-buffer"
</code></pre>
<p>In short form that works in <code class="language-plaintext highlighter-rouge">tmux</code>, we can use <code class="language-plaintext highlighter-rouge">-</code> in place of <code class="language-plaintext highlighter-rouge">/dev/stdin</code> (for no particular reason).</p>
<pre><code class="language-tmux">bind C-p run "\
paste.exe \
| tmux load-buffer -b windows-paste-buffer - \
&& tmux paste-buffer -b windows-paste-buffer"
</code></pre>
<p>Finally, we can implement the yanking part for tmux, simply by binding the <code class="language-plaintext highlighter-rouge">Y</code> key in copy-mode to the copy-mode command <code class="language-plaintext highlighter-rouge">copy-pipe</code> and use that to pipe to the <code class="language-plaintext highlighter-rouge">clip.exe</code> program.</p>
<pre><code class="language-tmux">bind -T copy-mode-vi Y send-keys -X copy-pipe "clip.exe"
</code></pre>
<h2 id="demo">Demo!</h2>
<figure>
<img src="/files/2017-10-05-copy-and-paste/tmux-demo.gif" width="500px" title="Yeah, ignore the missing newlines. I might fix that later." />
<figcaption><p>Demo 2.</p>
</figcaption>
</figure>
<h2 id="wrap-up">Wrap up</h2>
<p>Is all of this nerdiness necessary? Does quality of life actually improve?</p>
<p>Without doubt, the answer is yes. As I write this post, I feel empowered by how easy it was to saturate the page with hyperlinks.</p>
<p>Happy Guy Fawkes day. Have fun with fireworks. Don’t burn your houses down, and remember to not put too much CO2 into the air.</p>
<p><strong><em>Side Note: The Gender of Google.</em></strong> <em>Eh, I don’t actually know. I thought it’ll be more interesting to personify it, so I flipped a coin, and arbitrarily considered Google as a he for the day.</em></p>Ernest WongI want to digress from talking about mechanical differentials and talk more in the realm of shells, software, and productivity. September 17. That day was a special day. That day was the beginning of a new era. That day was the day I began copying and pasting correctly from my terminal.How Diffs Work – Mechanical Adding Machines2017-08-06T00:00:00+00:002017-08-06T00:00:00+00:00https://ernwong.github.io/hobby/2017/08/06/how-diffs-work<p>Hi boys and girls. It is my pleasure to talk about diffs today. What are diffs? They are wonderful creatures in the <code class="language-plaintext highlighter-rouge">mecheng</code> kingdom. Known by their full, technical name: <em>differential gears</em>, or more correctly, <em>differentials</em>. If you’ve ever witnessed one, they may seem to behave rather magically. Here’s why.</p>
<h2 id="conventional-gears">Conventional Gears</h2>
<p>Before looking at diffs, let’s first look at spur gears. Spur gears have some properties which are interesting despite being rather obvious.</p>
<p>Gears <em>couple</em> the mechanical rotation of multiple axles. That’s a fancy way of saying that if two axles are geared together, like that shown in the figure below, then the axle’s rotation are directly linked with each other. A rotation of one axle will definitely imply the rotation of the other axle.</p>
<figure>
<img src="/files/2017-08-06-how-diffs-work/spurgears2.gif" alt="Animation showing two spur gears spinning together at two different speeds. This is to illustrate what 'coupling' means, as well as to show how both axles influence each other when they are coupled, meaning that it is a symmetric relation." />
<figcaption><p><strong>Figure 1.</strong> Coupling two gears is a <a href="https://en.wikipedia.org/wiki/Symmetric_relation">symmetric relation</a></p>
</figcaption>
</figure>
<p>If the left axle is coupled with the right axle, then we can also say that the right axle is coupled with the left axle. When two axles are coupled, both axles influence each other. If you like names, this kind of relationship can be said as <a href="https://en.wikipedia.org/wiki/Symmetric_relation">symmetric</a>.</p>
<p>Now, look at the following set of three gears. It makes sense that if (1) we couple the left axle with the middle axle, and (2) we also couple the middle axle with the rightmost axle, then (3) the leftmost axle is now coupled with the rightmost axle. Everything is coupled together. It is a <a href="https://en.wikipedia.org/wiki/Transitive_relation">transitive relation</a>.</p>
<figure>
<img src="/files/2017-08-06-how-diffs-work/spurgears3.gif" alt="Animation showing three spur gears coupled together and spinning together at different speeds. This is to show how spur gears behave like a transitive relation." title="It's like the zeroth law of thermodynamics, or like the mathematical equality relation." />
<figcaption><p><strong>Figure 2</strong>. Coupling three spur gears is a <a href="https://en.wikipedia.org/wiki/Transitive_relation">transitive relation</a>.</p>
</figcaption>
</figure>
<p><em>What the hell, why did this bloke on the internet make these simple spur gears much more complicated?</em> It’s not all bad*. First, you get to show off to your friends with your newly expanded vocabulary, with fancy terms like <em>transitive</em> and <em>symmetry</em>. Secondly, and this applies to many things in academia, when we give something a name, it is much easier to understand what is going and the clouds of confusion will gradually part away. Names give ideas an anchor.</p>
<p><em>*I acknowledge that sometimes making things complicated is not a good idea…</em></p>
<h2 id="a-look-at-diffs">A Look At Diffs</h2>
<p>This is a diff. It’s a bunch of bevel gears attached to a frame (called the housing). Technically, it’s better to call it a <em>differential</em>, not a differential gear (because it’s <em>made up</em> of gears). The housing is made with teeth on them so that we can “capture” the housing’s rotation by attaching another spur gear to the differential housing.</p>
<figure>
<img src="/files/2017-08-06-how-diffs-work/diff.gif" alt="Three bevel gears coupled together and held onto by the differential housing, which itself has teeth that can couple to another spur gear." title="Notice the teeth on the differential housing." />
<figcaption><p><strong>Figure 3.</strong> A set of differential gears provided in Vex Robotics.</p>
</figcaption>
</figure>
<p>There are <em>three</em> input/output parts that you can rotate in a diff, which we will call A, B, and C for the left, right, and centre piece respectively. All of these parts seem to have some effect on the other in some way similar to three spur gears…</p>
<figure>
<img src="/files/2017-08-06-how-diffs-work/diffio.gif" />
<figcaption><p><strong>Figure 4.</strong> The three parts you can rotate in a diff.</p>
</figcaption>
</figure>
<p>But they’re not all directly coupled; You could stop C from moving and yet still rotate A. A reasonable question one might ask at this point is: <em>Are they coupled in some way, but not really?</em></p>
<p>If you investigate the GIF animation with a bit more detail, if you rotate A and B, it looks like C is the <em>average rotation of A and B!</em> (Exclamation marks are obviously necessary here just to emphasise its importance. Besides, this observation is interesting, right? <em>Right?</em> No? Man you have no life.) For example, if we rotate both A and B by 360 degrees in the same direction, C also rotates 360 degrees the same direction.</p>
<figure>
<img src="/files/2017-08-06-how-diffs-work/diffio-abc.gif" />
<figcaption><p><strong>Figure 5.</strong> Rotating A and B at the same rate moves C at the same rate as well.</p>
</figcaption>
</figure>
<p>If we move A and B together but in a way such that B is completely opposite to A, then we find that C doesn’t move at all.</p>
<figure>
<img src="/files/2017-08-06-how-diffs-work/diffio-onlyab.gif" />
<figcaption><p><strong>Figure 6.</strong> Rotating A and B at the opposite direction keeps C still.</p>
</figcaption>
</figure>
<p>Finally, if A rotates 360 degrees, but B doesn’t move, then C moves 180 degrees.</p>
<figure>
<img src="/files/2017-08-06-how-diffs-work/diffio-onlya.gif" />
<figcaption><p><strong>Figure 7.</strong> When keeping B still, C always rotates half the speed as A.</p>
</figcaption>
</figure>
<p>Hmm. Interesting. It looks like the equation $C = \frac{A+B}{2}$ is true. But why?</p>
<h2 id="thinking-outside-the-box">Thinking Outside the Box*</h2>
<p>Imagine a box with two gears attached to the side of it like so. (*I am sincerely sorry for the shameful pun, but I have no choice.)</p>
<figure>
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<figcaption><p><strong>Figure 8.</strong> A box with two gears attached and coupled together.</p>
</figcaption>
</figure>
<p>You look at it and say “Welp, looks like there are two axles coupled together”. Indeed, turn one axle, and the gear causes the other axle to turn assuming that the box doesn’t move.</p>
<blockquote>
<p>…assuming that the box doesn’t move…</p>
</blockquote>
<p>Now I’m not sure about you, but that last phrase is begging me to ask another question: What happens if you turn the box, and treated the box itself as a thing that you can rotate (i.e. an input or output just like another axle)?</p>
<p>That is pretty much what a diff is: a bunch of gears inside some sort of frame, but which the <em>frame itself</em> can also be rotated. Another mechanism that uses this idea is the <a href="https://en.wikipedia.org/wiki/Epicyclic_gearing">planetary gearing</a> (aka epicyclic gearing).</p>
<p>There is nothing stopping us from rotating the frame. We live in a universe where there is translational symmetry and rotational symmetry built into the laws of physics. However, it’s not the “symmetry” we talked about in high school maths class, in the usual sense, where something is mirrored about, well, a mirror. The symmetry we’re talking about goes like this (it takes more than a sentence to describe). You take a purely mechanical device, such as linkage systems and gearing systems. It doesn’t matter where it is on Earth, or up in space even, and what orientation it is in, it will still behave exactly the same. It also doesn’t matter whether we are standing on the ground looking at the machine (which, by the way, is also on the ground), or whether we are on a moving train while the machine is on the ground. The machine will still behave the same kinematically because the behaviour of the machine only depends on the relative positions of the internal parts matter to the machine. We will rely on this concept in the next section to prove that what it does is what it really does.</p>
<h2 id="proof-that-diffs-does-what-it-does">Proof that Diffs does what it does</h2>
<p>We will analyse three types of mechanisms which I believe are worth knowing. Looking at the figure below, the first mechanism is a linkage with three external parts A, B, and C that can slide backwards and forwards sideways. A linkage is a bunch of rods of fixed length that are attached together such that each joint is rotatable. Note that if you swap A and B around, the mechanism is exactly the same. We will now move on to the next mechanism sitting on the top right. It consists of two racks put on opposite sides of a pinion gear, and these three parts A, B and C can slide up and down. Finally, living at the bottom of the figure is our beloved diff which happens to be the subject of this post. Note that in all three mechanisms, A and B can be swapped around without changing the function of the mechanisms.</p>
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<figcaption><p><strong>Figure 9.</strong> Here are the three types of adding machines we will analyse. If it’s hard to see what’s going on, there are some nice videos of real-life me in the real world playing with real, physical versions of these machines.</p>
</figcaption>
</figure>
<p>Why are we analysing all three mechanisms? Because these are all adding machines. It turns out that the very same proof/derivation works for all three of them, and that we end up with the following equation that the amount of movement of C can indeed be described by</p>
\[C = \frac{A+B}{2}\;.\]
<p>The proof first begins with an observation.</p>
<h3 id="step-1-note-how-they-all-act-like-inverters">Step 1. Note how they all act like “inverters”</h3>
<p>Keep C still and obedient. For example, you could tape C down to the ground. What happens to B when you move A?</p>
<figure>
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<figcaption><p><strong>Figure 10.</strong></p>
</figcaption>
</figure>
<p>In all three machines, B’s movement mirrors the movement of A.</p>
<h3 id="step-2-quantify-this-motion">Step 2. Quantify this motion</h3>
<p>Keep C still, and let A move by $x$ units forward. Intuitively, B moves $x$ units backward, aka $(-x)$ units forward.</p>
<figure>
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<figcaption><p><strong>Figure 11.</strong></p>
</figcaption>
</figure>
<h3 id="step-3-move-again">Step 3. Move again</h3>
<p>Keep C still, and now from the starting position, move A by $x$ units forward, followed by $y$ units backwards. Altogether, it means A has moved $(x-y)$ units forward. Because the mechanisms make B move opposite to A, altogether, B has moved $(y-x)$ units forward.</p>
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<text xml:space="preserve" style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;text-align:end;letter-spacing:0px;word-spacing:0px;text-anchor:end;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" x="1844" y="462.36221" id="text29488-7-5-8-5-2" sodipodi:linespacing="125%"><tspan sodipodi:role="line" id="tspan29490-5-09-5-9-9" x="1844" y="462.36221" style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:15px;font-family:Arial;-inkscape-font-specification:'Arial Bold';text-align:end;text-anchor:end">A = x − y</tspan></text>
<text xml:space="preserve" style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;text-align:start;letter-spacing:0px;word-spacing:0px;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" x="1954" y="292.36221" id="text29488-7-8-2-7-1" sodipodi:linespacing="125%"><tspan sodipodi:role="line" id="tspan29490-5-4-9-2-6" x="1954" y="292.36221" style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:15px;font-family:Arial;-inkscape-font-specification:'Arial Bold';text-align:start;text-anchor:start">B = y − x</tspan></text>
<text xml:space="preserve" style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;text-align:center;letter-spacing:0px;word-spacing:0px;text-anchor:middle;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" x="1900" y="412.36221" id="text29488-7-1-2-2-9" sodipodi:linespacing="125%"><tspan sodipodi:role="line" id="tspan29490-5-6-5-5-5" x="1900" y="412.36221" style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:15px;font-family:Arial;-inkscape-font-specification:'Arial Bold'">C</tspan></text>
<text xml:space="preserve" style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;text-align:center;letter-spacing:0px;word-spacing:0px;text-anchor:middle;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" x="1520" y="552.36224" id="text29488-7-2-8-2-3" sodipodi:linespacing="125%"><tspan sodipodi:role="line" id="tspan29490-5-3-1-9-9" x="1520" y="552.36224" style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:15px;font-family:Arial;-inkscape-font-specification:'Arial Bold'">A</tspan></text>
<text xml:space="preserve" style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;text-align:center;letter-spacing:0px;word-spacing:0px;text-anchor:middle;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" x="1900" y="552.36224" id="text29488-7-4-4-9-6" sodipodi:linespacing="125%"><tspan sodipodi:role="line" id="tspan29490-5-64-0-3-2" x="1900" y="552.36224" style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:15px;font-family:Arial;-inkscape-font-specification:'Arial Bold'">B</tspan></text>
<text xml:space="preserve" style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;text-align:center;letter-spacing:0px;word-spacing:0px;text-anchor:middle;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" x="1660" y="512.36224" id="text29488-7-0-9-8-3" sodipodi:linespacing="125%"><tspan sodipodi:role="line" id="tspan29490-5-44-9-0-4" x="1660" y="512.36224" style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:15px;font-family:Arial;-inkscape-font-specification:'Arial Bold'">C</tspan></text>
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<path style="fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1;marker-start:url(#marker47430)" d="m 1650,298.36223 40,0" id="path29622-1-9-9-1" inkscape:connector-curvature="0" sodipodi:nodetypes="cc" />
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<path style="fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:2;stroke-linecap:round;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:4, 4;stroke-dashoffset:0;stroke-opacity:1;marker-end:url(#TriangleOutM-0-0-1-9-2)" d="m 1960,352.36224 0,-50.00002" id="path29622-4-7-0-1-3" inkscape:connector-curvature="0" sodipodi:nodetypes="cc" />
<path style="opacity:1;fill:none;fill-opacity:1;stroke:#000000;stroke-width:2;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:4;stroke-dasharray:4, 4;stroke-dashoffset:0;stroke-opacity:1;marker-end:url(#marker31878-1-9-7)" id="path31870-0-0-8" sodipodi:type="arc" sodipodi:cx="1540.6862" sodipodi:cy="570.68915" sodipodi:rx="10.150758" sodipodi:ry="23.725506" sodipodi:start="0.85038342" sodipodi:end="5.6542082" sodipodi:open="true" d="m 1547.3826,588.51966 a 10.150758,23.725506 0 0 1 -11.3887,3.20794 10.150758,23.725506 0 0 1 -5.3964,-23.65958 10.150758,23.725506 0 0 1 7.4876,-20.31222 10.150758,23.725506 0 0 1 10.8093,8.97521" />
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<text xml:space="preserve" style="font-style:normal;font-weight:normal;font-size:15px;line-height:125%;font-family:sans-serif;text-align:start;letter-spacing:0px;word-spacing:0px;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" x="1620" y="232.36223" id="text50004" sodipodi:linespacing="125%"><tspan sodipodi:role="line" x="1620" y="232.36223" style="font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:12.5px;font-family:Arial;-inkscape-font-specification:Arial;text-align:start;text-anchor:start" id="tspan50008">These two arrows represent a movement</tspan><tspan sodipodi:role="line" x="1620" y="247.98723" style="font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:12.5px;font-family:Arial;-inkscape-font-specification:Arial;text-align:start;text-anchor:start" id="tspan50012">of (x − y), which are then simplified into a</tspan><tspan sodipodi:role="line" x="1620" y="263.61224" style="font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:12.5px;font-family:Arial;-inkscape-font-specification:Arial;text-align:start;text-anchor:start" id="tspan50014">single dashed arrow in the other diagrams.</tspan></text>
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<figcaption><p><strong>Figure 12.</strong></p>
</figcaption>
</figure>
<h3 id="step-4-move-the-entire-setup">Step 4. Move the entire setup</h3>
<p>This is the fun part. Look at the machines. It doesn’t matter whether you play with them on the ground or on a moving train because B is inverted only <em>relative</em> to C. Therefore, you can move the entire setup by, say, $k$ units forward like so.</p>
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<text xml:space="preserve" style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;text-align:center;letter-spacing:0px;word-spacing:0px;text-anchor:middle;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" x="510" y="742.36218" id="text29488-7-8-2-2" sodipodi:linespacing="125%"><tspan sodipodi:role="line" id="tspan29490-5-4-9-3" x="510" y="742.36218" style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:15px;font-family:Arial;-inkscape-font-specification:'Arial Bold'">B</tspan></text>
<text xml:space="preserve" style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;text-align:center;letter-spacing:0px;word-spacing:0px;text-anchor:middle;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" x="450" y="652.36218" id="text29488-7-1-2-7" sodipodi:linespacing="125%"><tspan sodipodi:role="line" id="tspan29490-5-6-5-7" x="450" y="652.36218" style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:15px;font-family:Arial;-inkscape-font-specification:'Arial Bold'">C</tspan></text>
<text xml:space="preserve" style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;text-align:center;letter-spacing:0px;word-spacing:0px;text-anchor:middle;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" x="70" y="932.36218" id="text29488-7-2-8-7" sodipodi:linespacing="125%"><tspan sodipodi:role="line" id="tspan29490-5-3-1-2" x="70" y="932.36218" style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:15px;font-family:Arial;-inkscape-font-specification:'Arial Bold'">A</tspan></text>
<text xml:space="preserve" style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;text-align:center;letter-spacing:0px;word-spacing:0px;text-anchor:middle;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" x="450" y="932.36218" id="text29488-7-4-4-90" sodipodi:linespacing="125%"><tspan sodipodi:role="line" id="tspan29490-5-64-0-5" x="450" y="932.36218" style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:15px;font-family:Arial;-inkscape-font-specification:'Arial Bold'">B</tspan></text>
<text xml:space="preserve" style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;text-align:center;letter-spacing:0px;word-spacing:0px;text-anchor:middle;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" x="210" y="892.36218" id="text29488-7-0-9-7" sodipodi:linespacing="125%"><tspan sodipodi:role="line" id="tspan29490-5-44-9-4" x="210" y="892.36218" style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:15px;font-family:Arial;-inkscape-font-specification:'Arial Bold'">C</tspan></text>
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<text xml:space="preserve" style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;text-align:start;letter-spacing:0px;word-spacing:0px;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" x="90" y="842.36218" id="text29488-7-6-5-1-3-5-17" sodipodi:linespacing="125%"><tspan sodipodi:role="line" id="tspan29490-5-0-8-9-6-7-1" x="90" y="842.36218" style="font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:15px;font-family:Arial;-inkscape-font-specification:'Arial Bold';text-align:start;text-anchor:start">x − y</tspan></text>
<text xml:space="preserve" style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;text-align:start;letter-spacing:0px;word-spacing:0px;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" x="350" y="752.36218" id="text29488-7-6-5-1-3-5-8" sodipodi:linespacing="125%"><tspan sodipodi:role="line" id="tspan29490-5-0-8-9-6-7-7" x="350" y="752.36218" style="font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:15px;font-family:Arial;-inkscape-font-specification:'Arial Bold';text-align:start;text-anchor:start">x − y</tspan></text>
<text xml:space="preserve" style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;text-align:start;letter-spacing:0px;word-spacing:0px;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" x="41.27882" y="982.36224" id="text29488-7-6-5-1-3-5-7" sodipodi:linespacing="125%"><tspan sodipodi:role="line" id="tspan29490-5-0-8-9-6-7-5" x="41.27882" y="982.36224" style="font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:15px;font-family:Arial;-inkscape-font-specification:'Arial Bold';text-align:start;text-anchor:start">x − y</tspan></text>
<text xml:space="preserve" style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;text-align:start;letter-spacing:0px;word-spacing:0px;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" x="170" y="682.36218" id="text29488-7-6-5-1-8-0-1" sodipodi:linespacing="125%"><tspan sodipodi:role="line" id="tspan29490-5-0-8-9-0-7-6" x="170" y="682.36218" style="font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:15px;font-family:Arial;-inkscape-font-specification:'Arial Bold';text-align:start;text-anchor:start">y − x</tspan></text>
<text xml:space="preserve" style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;text-align:start;letter-spacing:0px;word-spacing:0px;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" x="493.82986" y="622.36224" id="text29488-7-6-5-1-8-0-3" sodipodi:linespacing="125%"><tspan sodipodi:role="line" id="tspan29490-5-0-8-9-0-7-3" x="493.82986" y="622.36224" style="font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:15px;font-family:Arial;-inkscape-font-specification:'Arial Bold';text-align:start;text-anchor:start">y − x</tspan></text>
<text xml:space="preserve" style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;text-align:start;letter-spacing:0px;word-spacing:0px;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" x="350" y="982.36218" id="text29488-7-6-5-1-8-0-4" sodipodi:linespacing="125%"><tspan sodipodi:role="line" id="tspan29490-5-0-8-9-0-7-4" x="350" y="982.36218" style="font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:15px;font-family:Arial;-inkscape-font-specification:'Arial Bold';text-align:start;text-anchor:start">y − x</tspan></text>
<text xml:space="preserve" style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;text-align:center;letter-spacing:0px;word-spacing:0px;text-anchor:middle;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" x="102.72119" y="746.36218" id="text29488-7-6-5-1-8-0-1-6" sodipodi:linespacing="125%"><tspan sodipodi:role="line" id="tspan29490-5-0-8-9-0-7-6-0" x="102.72119" y="746.36218" style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:15px;font-family:Arial;-inkscape-font-specification:'Arial Bold';text-align:center;text-anchor:middle">k</tspan></text>
<text xml:space="preserve" style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;text-align:center;letter-spacing:0px;word-spacing:0px;text-anchor:middle;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" x="166.72119" y="842.36218" id="text29488-7-6-5-1-8-0-1-6-4" sodipodi:linespacing="125%"><tspan sodipodi:role="line" id="tspan29490-5-0-8-9-0-7-6-0-3" x="166.72119" y="842.36218" style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:15px;font-family:Arial;-inkscape-font-specification:'Arial Bold';text-align:center;text-anchor:middle">k</tspan></text>
<text xml:space="preserve" style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;text-align:center;letter-spacing:0px;word-spacing:0px;text-anchor:middle;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" x="246.72119" y="662.36218" id="text29488-7-6-5-1-8-0-1-6-7" sodipodi:linespacing="125%"><tspan sodipodi:role="line" id="tspan29490-5-0-8-9-0-7-6-0-8" x="246.72119" y="662.36218" style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:15px;font-family:Arial;-inkscape-font-specification:'Arial Bold';text-align:center;text-anchor:middle">k</tspan></text>
<text xml:space="preserve" style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;text-align:start;letter-spacing:0px;word-spacing:0px;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" x="383.44238" y="822.36218" id="text29488-7-6-5-1-8-0-1-6-9" sodipodi:linespacing="125%"><tspan sodipodi:role="line" id="tspan29490-5-0-8-9-0-7-6-0-9" x="383.44238" y="822.36218" style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:15px;font-family:Arial;-inkscape-font-specification:'Arial Bold';text-align:end;text-anchor:end">k</tspan></text>
<text xml:space="preserve" style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;text-align:start;letter-spacing:0px;word-spacing:0px;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" x="516" y="712.36218" id="text29488-7-6-5-1-8-0-1-6-1" sodipodi:linespacing="125%"><tspan sodipodi:role="line" id="tspan29490-5-0-8-9-0-7-6-0-4" x="516" y="712.36218" style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:15px;font-family:Arial;-inkscape-font-specification:'Arial Bold';text-align:start;text-anchor:start">k</tspan></text>
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</g>
</svg>
<figcaption><p><strong>Figure 13.</strong></p>
</figcaption>
</figure>
<p>If we calculate the total movement each piece have made, we get the following:</p>
\[\begin{align}
A &= (x-y) + k\\
B &= (y-x) + k\\
C &= k.
\end{align}\]
<p>In fact, we can replace $k$ with anything we want. On the previous setup we ended up with in step 3, let’s see what happens if we move the entire setup by $k = x+y$. In other words, we move the setup by $x$ first, then an additional $y$ units forward.</p>
<figure>
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<text xml:space="preserve" style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;text-align:start;letter-spacing:0px;word-spacing:0px;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" x="41.27882" y="982.36224" id="text29488-7-6-5-1-3-5-7" sodipodi:linespacing="125%"><tspan sodipodi:role="line" id="tspan29490-5-0-8-9-6-7-5" x="41.27882" y="982.36224" style="font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:15px;font-family:Arial;-inkscape-font-specification:'Arial Bold';text-align:start;text-anchor:start">x − y</tspan></text>
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<text xml:space="preserve" style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;text-align:start;letter-spacing:0px;word-spacing:0px;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" x="350" y="982.36218" id="text29488-7-6-5-1-8-0-4" sodipodi:linespacing="125%"><tspan sodipodi:role="line" id="tspan29490-5-0-8-9-0-7-4" x="350" y="982.36218" style="font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:15px;font-family:Arial;-inkscape-font-specification:'Arial Bold';text-align:start;text-anchor:start">y − x</tspan></text>
<text xml:space="preserve" style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;text-align:start;letter-spacing:0px;word-spacing:0px;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" x="86" y="746.36218" id="text29488-7-6-5-1-8-0-1-6" sodipodi:linespacing="125%"><tspan sodipodi:role="line" id="tspan29490-5-0-8-9-0-7-6-0" x="86" y="746.36218" style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:15px;font-family:Arial;-inkscape-font-specification:'Arial Bold';text-align:start;text-anchor:start">x + y</tspan></text>
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<text xml:space="preserve" style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;text-align:start;letter-spacing:0px;word-spacing:0px;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" x="230" y="662.36218" id="text29488-7-6-5-1-8-0-1-6-7" sodipodi:linespacing="125%"><tspan sodipodi:role="line" id="tspan29490-5-0-8-9-0-7-6-0-8" x="230" y="662.36218" style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:15px;font-family:Arial;-inkscape-font-specification:'Arial Bold';text-align:start;text-anchor:start">x + y</tspan></text>
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<text xml:space="preserve" style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;text-align:start;letter-spacing:0px;word-spacing:0px;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" x="440" y="982.36218" id="text29488-7-6-5-1-8-0-1-6-77" sodipodi:linespacing="125%"><tspan sodipodi:role="line" id="tspan29490-5-0-8-9-0-7-6-0-93" x="440" y="982.36218" style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:15px;font-family:Arial;-inkscape-font-specification:'Arial Bold';text-align:start;text-anchor:start">x + y</tspan></text>
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</g>
</svg>
<figcaption><p><strong>Figure 14.</strong> There’s a lot going on in the diagram - more than I hoped. Here’s what each thing means. The thin dotted arrows show the movement that was previously applied in step 3. The thick solid arrows show the movement we’re going to make in this step. Note how the thick arrows are all the same size and direction inside each mechanism. This is because we’re moving the <em>entire</em> setup.</p>
</figcaption>
</figure>
<p>We have reached the final part of this casual proof. Calculating the final positions of each piece gives us</p>
\[\begin{align}
A &= (x-y) + (x+y) = 2x\\
B &= (y-x) + (x+y) = 2y\\
C &= x + y.
\end{align}\]
<p>Rearranging completes the proof/derivation.</p>
\[C=x+y = \frac{A+B}{2}.\]
<h2 id="real-life-footage-of-diff-and-friends-at-their-natural-habitat">Real life footage of ‘diff and friends’ at their natural habitat</h2>
<p>Tip: turn up the volume for these videos.</p>
<figure>
<video controls="" src="/files/2017-08-06-how-diffs-work/linkage.mp4" width="600">
This video doesn't play nice with your web browser yet. In the mean time, feel free to download and watch it from <a href="/files/2017-08-06-how-diffs-work/linkage.mp4">here</a>.
</video>
<figcaption><p><strong>Video 1.</strong> Playing around with the linkage adder.</p>
</figcaption>
</figure>
<p>The one that started it all, introducing you to the linkage adder. When I built this in 2013, I was actually trying to create a <em>subtracting</em> machine instead. It never ceases to amaze me how different design intents lead to bizarrely accurate designs of other things that we don’t know about until many years later. Note that I included an additional linkage system that multiplies the output movement by two so that the output is actually the addition of the inputs, not just their average. When the young and naive version of me built this linkage, I thought that it was needed to “correct” the movement.</p>
<figure>
<video controls="" src="/files/2017-08-06-how-diffs-work/rack.mp4" width="600">
This video doesn't play nice with your web browser yet. In the mean time, feel free to download and watch it from <a href="/files/2017-08-06-how-diffs-work/rack.mp4">here</a>.
</video>
<figcaption><p><strong>Video 2.</strong> Playing around with a rack and pinion adder.</p>
</figcaption>
</figure>
<figure>
<video controls="" src="/files/2017-08-06-how-diffs-work/diff.mp4" width="600">
This video doesn't play nice with your web browser yet. In the mean time, feel free to download and watch it from <a href="/files/2017-08-06-how-diffs-work/diff.mp4">here</a>.
</video>
<figcaption><p><strong>Video 3.</strong> Here I assemble a Lego differential and play around with it.</p>
</figcaption>
</figure>
<h2 id="so-why-do-diffs-take-this-form">So Why do Diffs Take This Form?</h2>
<p>Why are we using bevel gears inside a housing, and not using linkage adders or rack and pinions?</p>
<p>Answer: diffs can go <em>round</em> and <em>round</em> and <em>round</em> and <em>round</em> <sub>and <sub><em>round</em> <sub>and…</sub></sub></sub></p>
<h2 id="where-do-we-go-from-here">Where do we go from here</h2>
<p>I hope someone will enjoy this post. In the next couple of posts, we will look at some fun applications of these differentials (fun by my standards anyway). We will also look at ways to further model the differential in terms of torque and energy transfers. In other words,</p>
<blockquote>
<p>Stay tuned for the next episode of The-Random-Bloke-On-The-Internet-Talking-About-Stuff.</p>
</blockquote>
<p>Yes.</p>Ernest WongHi boys and girls. It is my pleasure to talk about diffs today. What are diffs? They are wonderful creatures in the mecheng kingdom. Known by their full, technical name: differential gears, or more correctly, differentials. If you’ve ever witnessed one, they may seem to behave rather magically. Here’s why.Buffered Blog2017-07-16T00:00:00+00:002017-07-16T00:00:00+00:00https://ernwong.github.io/projects/2017/07/16/buffered-blog<h2 id="the-problem">The Problem</h2>
<p>I’m having a bit of difficulty keeping up with this blog…</p>
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<text xml:space="preserve" style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;text-align:start;letter-spacing:0px;word-spacing:0px;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" x="260" y="802.36224" id="text8436-0-52-7" sodipodi:linespacing="125%"><tspan sodipodi:role="line" x="260" y="802.36224" style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:12.5px;font-family:Arial;-inkscape-font-specification:'Arial Bold';text-align:start;text-anchor:start" id="tspan8584-8">UNI INCOMING!</tspan></text>
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<text xml:space="preserve" style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;text-align:start;letter-spacing:0px;word-spacing:0px;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" x="160" y="862.36224" id="text8436-0-52-7-0" sodipodi:linespacing="125%"><tspan sodipodi:role="line" x="160" y="862.36224" style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:12.5px;font-family:Arial;-inkscape-font-specification:'Arial Bold';text-align:start;text-anchor:start" id="tspan8584-8-6">STARTED SECOND POST</tspan></text>
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<text xml:space="preserve" style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;text-align:start;letter-spacing:0px;word-spacing:0px;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" x="280" y="912.36224" id="text8436-0-52-7-8" sodipodi:linespacing="125%"><tspan sodipodi:role="line" x="280" y="912.36224" style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:12.5px;font-family:Arial;-inkscape-font-specification:'Arial Bold';text-align:start;text-anchor:start" id="tspan8584-8-7">ASSIGNMENTS! </tspan></text>
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<text xml:space="preserve" style="font-style:normal;font-weight:normal;font-size:40px;line-height:120.00000477%;font-family:sans-serif;text-align:start;letter-spacing:0px;word-spacing:0px;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" x="410" y="842.36224" id="text8436-0-52-7-8-3" sodipodi:linespacing="120%"><tspan sodipodi:role="line" x="410" y="842.36224" style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:12.5px;line-height:120.00000477%;font-family:Arial;-inkscape-font-specification:'Arial Bold';text-align:start;text-anchor:start" id="tspan8584-8-7-9">I GUESS I'LL POST</tspan><tspan sodipodi:role="line" x="410" y="857.36224" style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:12.5px;line-height:120.00000477%;font-family:Arial;-inkscape-font-specification:'Arial Bold';text-align:start;text-anchor:start" id="tspan8755">DURING THE BREAK</tspan></text>
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<text xml:space="preserve" style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;text-align:center;letter-spacing:0px;word-spacing:0px;text-anchor:middle;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" x="-69.35144" y="1019.4486" id="text8436-0-8" sodipodi:linespacing="125%" transform="matrix(0.96680789,-0.25550442,0.25550442,0.96680789,0,0)"><tspan sodipodi:role="line" id="tspan8438-2-1" x="-67.618042" y="1019.4486" style="font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:12.5px;font-family:Arial;-inkscape-font-specification:Arial">ROBOTICS NATIONALS </tspan></text>
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<text xml:space="preserve" style="font-style:normal;font-weight:normal;font-size:40px;line-height:120.00000477%;font-family:sans-serif;text-align:start;letter-spacing:0px;word-spacing:0px;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" x="440" y="902.36224" id="text8436-0-52-7-8-3-1" sodipodi:linespacing="120%"><tspan sodipodi:role="line" x="440" y="902.36224" style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:12.5px;line-height:120.00000477%;font-family:Arial;-inkscape-font-specification:'Arial Bold';text-align:start;text-anchor:start" id="tspan8755-6">EEK! NEVERMIND</tspan></text>
<path style="fill:#ffffff;fill-opacity:1;fill-rule:evenodd;stroke:#000000;stroke-width:2;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1" d="m 480.00001,942.36223 9.99998,-130 30.00001,0 10e-6,-30 -50.00001,2e-5 -10e-6,29.99998 10,0 z" id="path8586-5-5-8-7" inkscape:connector-curvature="0" sodipodi:nodetypes="cccccccc" />
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<path style="fill:#ffffff;fill-opacity:1;fill-rule:evenodd;stroke:#000000;stroke-width:2;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1" d="m 540.00001,942.36222 9.99998,-50.00002 70.00001,2e-5 10e-6,-29.99999 -90.00001,0 -10e-6,29.99997 10,0 z" id="path8586-5-5-8-7-8" inkscape:connector-curvature="0" sodipodi:nodetypes="cccccccc" />
<text xml:space="preserve" style="font-style:normal;font-weight:normal;font-size:40px;line-height:120.00000477%;font-family:sans-serif;text-align:start;letter-spacing:0px;word-spacing:0px;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" x="540" y="882.36224" id="text8436-0-52-7-8-3-4-5" sodipodi:linespacing="120%"><tspan sodipodi:role="line" x="540" y="882.36224" style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:12.5px;line-height:120.00000477%;font-family:Arial;-inkscape-font-specification:'Arial Bold';text-align:start;text-anchor:start" id="tspan8755-0-1">PROJECTS!</tspan></text>
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<text xml:space="preserve" style="font-style:normal;font-weight:normal;font-size:40px;line-height:120.00000477%;font-family:sans-serif;text-align:start;letter-spacing:0px;word-spacing:0px;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" x="610" y="842.36224" id="text8436-0-52-7-8-3-4-7" sodipodi:linespacing="120%"><tspan sodipodi:role="line" x="610" y="842.36224" style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:12.5px;line-height:120.00000477%;font-family:Arial;-inkscape-font-specification:'Arial Bold';text-align:start;text-anchor:start" id="tspan8755-0-5">EXAMS!!</tspan></text>
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<path style="fill:#ffffff;fill-opacity:1;fill-rule:evenodd;stroke:#000000;stroke-width:2;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1" d="m 570,942.36222 9.99999,-10 30.00001,0 10e-6,-30 -50.00001,2e-5 -10e-6,29.99998 10,0 z" id="path8586-5-5-8-7-6-3" inkscape:connector-curvature="0" sodipodi:nodetypes="cccccccc" />
<text xml:space="preserve" style="font-style:normal;font-weight:normal;font-size:40px;line-height:120.00000477%;font-family:sans-serif;text-align:start;letter-spacing:0px;word-spacing:0px;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" x="570" y="922.36224" id="text8436-0-52-7-8-3-4-8-4" sodipodi:linespacing="120%"><tspan sodipodi:role="line" x="570" y="922.36224" style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:12.5px;line-height:120.00000477%;font-family:Arial;-inkscape-font-specification:'Arial Bold';text-align:start;text-anchor:start" id="tspan8755-0-7-8">EEK!</tspan></text>
<text xml:space="preserve" style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;text-align:center;letter-spacing:0px;word-spacing:0px;text-anchor:middle;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" x="468.05966" y="956.94" id="text8436-0-8-3" sodipodi:linespacing="125%" transform="matrix(0.99695093,0.07803102,-0.07803102,0.99695093,0,0)"><tspan sodipodi:role="line" id="tspan8438-2-1-1" x="468.05966" y="956.94" style="font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:12.5px;font-family:Arial;-inkscape-font-specification:'Arial Bold'">CAD COMPETITION</tspan></text>
<text xml:space="preserve" style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;text-align:center;letter-spacing:0px;word-spacing:0px;text-anchor:middle;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" x="636.45837" y="890.72406" id="text8436-0-8-3-6" sodipodi:linespacing="125%" transform="matrix(0.98452611,0.17523792,-0.17523792,0.98452611,0,0)"><tspan sodipodi:role="line" id="tspan8438-2-1-1-9" x="636.45837" y="890.72406" style="font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:12.5px;font-family:Arial;-inkscape-font-specification:'Arial Bold'">CONCEPT PROJECT</tspan></text>
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<figcaption><p><strong>Figure.</strong> Artist’s impression of my semester.</p>
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<p>I don’t want another zoombie website.</p>
<h2 id="proposed-solution-1">Proposed Solution 1</h2>
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<text sodipodi:linespacing="125%" id="text18957" y="912.36224" x="630" style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;text-align:center;letter-spacing:0px;word-spacing:0px;text-anchor:middle;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" xml:space="preserve"><tspan id="tspan18961" style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:12.5px;font-family:Arial;-inkscape-font-specification:'Arial Bold';text-align:center;text-anchor:middle" y="912.36224" x="630" sodipodi:role="line">REPEAT AND</tspan><tspan style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:12.5px;font-family:Arial;-inkscape-font-specification:'Arial Bold';text-align:center;text-anchor:middle" y="927.98724" x="630" sodipodi:role="line" id="tspan18965">SUCCEED IN LIFE</tspan></text>
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<figcaption><p><strong>Figure.</strong> Boxes and lines drawn to connote a sense of quality to this article.</p>
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<h3 id="plus">Plus</h3>
<ul>
<li>
<p>No longer do I need to stress about writing stuff during the semester while I study for university.</p>
</li>
<li>
<p>I get continuous reward stimuli at times of need (especially in the midst of assignment deadlines and exams)</p>
</li>
<li>
<p>I can act like a time management ninja.</p>
<blockquote>
<p>“Whoa, you’re prepping for exams <em>and</em> blogging a new post every week?”</p>
</blockquote>
</li>
</ul>
<h3 id="minus">Minus</h3>
<ul>
<li>Posts are not fresh.</li>
</ul>
<h2 id="proposed-solution-2">Proposed Solution 2</h2>
<figure>
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<figcaption><p><strong>Figure.</strong> Additional collection of boxes and lines to further solidify the point.</p>
</figcaption>
</figure>
<h3 id="plus-1">Plus</h3>
<ul>
<li>
<p>Perfect opportunity to confuse and prank everyone.</p>
<blockquote>
<p>“You haven’t written for months.”</p>
<p>“What do you mean? :)”</p>
<p>“Wait what, these posts say they’re from last month, but they weren’t there before!”</p>
<p>“It must be your browser cache.”</p>
</blockquote>
</li>
</ul>
<h3 id="minus-1">Minus</h3>
<ul>
<li>Risk of losing all friends.</li>
</ul>
<p>Wait, <a href="http://i.imgur.com/0DpIA3o.gif">what friends</a>.</p>Ernest WongThe ProblemDuck Duck Goose2016-12-31T00:00:00+00:002016-12-31T00:00:00+00:00https://ernwong.github.io/thoughts/2016/12/31/duck-duck-goose<p>Ah, feel that nostalgia? We played this when we were young. In case you’ve forgotten, here’s a refresher.</p>
<h2 id="setup">Setup</h2>
<p>In this game, designate one person as <em>It</em>. Everyone else sits in a circle.</p>
<h2 id="phase-1---the-selection">Phase 1 - The Selection</h2>
<p><em>It</em> moves around the circle, tapping each person on the head.
At the same time, <em>It</em> calls “duck” out loud.</p>
<p>At some point, <em>It</em> may decide to say “goose” instead, upon tapping a particular person’s head. If so, let the person tapped be the <em>Goose</em>, and <em>Phase 2</em> begins.</p>
<h2 id="phase-2---the-chase">Phase 2 - The Chase</h2>
<p><em>It</em>’s objective is to run one full circle and sit at the <em>Goose</em>’s location before <em>Goose</em> tags <em>It</em>, and vice versa.</p>
<p>If <em>It</em> suceeds, <em>Goose</em> becomes the new <em>It</em>. Else, <em>It</em> tries again.
Whichever is the case, <em>Phase 2</em> ends and <em>Phase 1</em> restarts.</p>
<h2 id="the-duck-pond---the-fall">The Duck Pond - The Fall</h2>
<p>Here in New Zealand, we sometimes play a variant of this game. When the <em>Goose</em> catches <em>It</em>, the <em>Goose</em> will become the new <em>It</em> and the old <em>It</em> sits in the circle in the centre. We used to call the inner circle with a special name: <em>The Dirty Duck Pond</em>. Those of us who sat inside might remember the temporary feeling of failure, like that when the sports team you so dearly support loses a game. But, it wasn’t the end, because as soon as the next <em>It</em> gets caught, that person swaps places with you.</p>
<h2 id="rejoice---the-recovery">Rejoice - The Recovery</h2>
<p>You suffer earlier, but you recover earlier.</p>
<p>Without the dirty duck pond, the slowest kid will forever remain being <em>It</em>. <em>Goose</em> will always catch <em>It</em>, and the game will slowly degenerate into mere organised shaming, as <em>It</em> gets stuck being <em>It</em>. The kid will not realise at first, until it is too late.</p>
<p>As you can see, someone added a <em>Dirty Duck Pond</em> to the game. It’s a place that sounds bad and indeed inflicts a small dose of pain on the kid. Yet, this small and seemingly bad inclusion prevents a worse outcome.</p>
<h2 id="learn">Learn</h2>
<p>From this innocent game comes a wise insight. (It also encourages people like me to make statements as cliche as this….) Life is filled with things that look simple, things that seem obvious, apparent in nature. However, never be surprised by the reality when you start questioning the truth.</p>
<p><em>For example, this blog is better than it looks.</em></p>Ernest WongAh, feel that nostalgia? We played this when we were young. In case you’ve forgotten, here’s a refresher.