change webring

3 files changed, 19 insertions, 5 deletions

diff --git a/website/index.html b/website/index.html
index e483ac9..84a3a57 100644
--- a/website/index.html
+++ b/website/index.html
@@ -42,13 +42,13 @@ $$START CONTENT
 <p>Here, you will find topics related to: </p>
 <ul>
 	<li><a href="./about/">About</a> -- About me and this website.</li>
+	<li><a href="./mathematics/">Mathematics</a> -- An underlying framework for all things that are logical.</li>
+	<li><a href="./music/">Music</a> -- my piano playing and singing (and maybe other instruments too).</li>
 	<li><a href="./physics/">Physics</a> -- Rates of change!</li>
 	<li><a href="./economics/">Economics</a> -- Rates of exchange!</li>
 	<li><a href="./technology/">Technology</a> -- Rates of finger pain! (Just kidding, I'm not an emacs user).</li>
 	<li><a href="./projects/">Projects</a> -- programming and other projects.</li>
-	<li><a href="./mathematics/">Mathematics</a> -- An underlying framework for all things that are logical.</li>
 	<li><a href="./philosophy/">Philosophy</a> -- An underlying framework for all things that are.</li>
-	<li><a href="./music/">Music</a> -- my piano playing and singing (and maybe other instruments too).</li>
 </ul>
 
 <p>Many articles will be written in groff and compiled to pdf.</p>
@@ -59,7 +59,7 @@ $$START CONTENT
 <ul>
 	<li><a href="https://git.prestonpan.tech/prestonpan.git/atom">rss feed</a> -- atom feed for the website commit page to keep you updated on changes.</li>
 	<li><a href="https://fedi.andrei.website/u/LiCoO2/rss">rss feed (2)</a> -- rss feed for my honk account, a fediverse server.</li>
-	<li><a href="https://radio.prestonpan.tech">Radio</a> -- listen to music that I also listen to.</li>
+	<li><a href="https://radio.nullring.xyz">Radio</a> -- listen to music that Null Identity people have composed.</li>
 	<li><a href="gopher://prestonpan.tech">Gopherhole</a> -- logs for andrei.website and other cool stuff, must be viewed with a gopher client.</li>
 	<li><a href="https://git.prestonpan.tech">Git server</a> -- see the code that I write or my dotfiles and other stuff.</li>
 	<li><a href="https://nullring.xyz">The null webring</a> -- a webring that I made (apparently there is another one by this name but ignore that).</li>
@@ -71,7 +71,7 @@ $$START CONTENT
 
 <p>This website is a part of the following webrings:</p>
 <h3>The Null Webring</h3>
-<p><a href="https://kaistevenson.com">prev</a> <a href="https://nullring.xyz">Nullring</a> <a href="https://www.aberrantflux.xyz">next</a></p>
+<p><a href="https://kaistevenson.com">prev</a> <a href="https://nullring.xyz">Nullring</a> <a href="https://pen15.agency">next</a></p>
 
 <h2>Donating</h2>
 <p>
diff --git a/website/mathematics/linear_algebra/source/introduction.ms b/website/mathematics/linear_algebra/source/introduction.ms
index 106ffec..6b69a41 100644
--- a/website/mathematics/linear_algebra/source/introduction.ms
+++ b/website/mathematics/linear_algebra/source/introduction.ms
@@ -45,7 +45,8 @@ coord x 0, 11 y 0, 11
 Now, let's imagine that this point $(3, 2)$ represents a force in a certain direction.
 For example, we can draw a line from the origin to this point and the resulting force's
 magnitude will be represented by the length of the line in question (which can be obtained
-via the pythagorean theorem).
+via the pythagorean theorem), and the direction of the force will be outwards from the origin
+following the line.
 
 .G1
 draw solid
@@ -55,3 +56,16 @@ coord x 0, 11 y 0, 11
 "(3, 2)" above at 3,2
 "$sqrt {3 sup 2 + 2 sup 2}$" above at 1,2
 .G2
+
+.PP
+We can now imagine another line segment drawn from the origin $(-1, 3)$, which we can imagine
+to be another force acting in a different direction with a different magnitude:
+
+.G1
+draw solid
+coord x -10, 10 y -10, 10
+0 0
+3 2
+-1 3
+"(3, 2)" above at 3,2
+.G2
diff --git a/website/mathematics/linear_algebra/source/introduction.pdf b/website/mathematics/linear_algebra/source/introduction.pdf
index b74d28a..563569a 100644
--- a/website/mathematics/linear_algebra/source/introduction.pdf
+++ b/website/mathematics/linear_algebra/source/introduction.pdf