change(/wiki/introduction): omit square-cube law

- S.C.-Law is now a footnote.
- Changed heading to a formula.
- Make math voxels only one byte.
- Fix all the math.
- Fix grammar.

content/wiki/introduction/index.md

@@ -172,44 +172,35 @@ Let me repeat: <b style="color:red">Don't do this.</b>
 
 
 
-But you know what isn't complicated, but **extremely important** to know?
 
-## The Square-Cube Law
+## Volume = Distance ³
 
-{% figure(class="float", caption="Relationship between Length, Area & Volume.", author="[Cmglee](https://commons.wikimedia.org/wiki/User:Cmglee)", license="[CC-BY-SA-4.0](https://commons.wikimedia.org/wiki/File:Relationship_between_length_and_area_and_volume.svg)") %}https://upload.wikimedia.org/wikipedia/commons/a/ae/Relationship_between_length_and_area_and_volume.svg{% end %}
-
-When dealing with voxels/bloxels and their various algorithms,
-you'll quite often be up against the **Square&#8209;Cube&nbsp;Law**:
-
-{% quote(author="[Wikipedia](https://en.wikipedia.org/wiki/Square%E2%80%93cube_law)") %}
-When an object undergoes a proportional *increase in size*, its new **surface area** is proportional to the *square* of the multiplier and its new **volume** is proportional to the *cube* of the multiplier.
-{% end %}
-
-<div style="clear:both"></div>
+A fundamental reality of many voxel algorithms
+is that the data they deal with **cubically**[^squarecube].
+What does that mean, in practice?
 
 Let's do a tiny bit of math (<small>feel free to grab a calculator</small>):
 
 1. Think of how far into the distance you want to 'see', in meters/voxels.
 2. Using that distance, calculate `(D*2)³` to get the visible volume.
-3. Assume a voxel takes 64 bits, i.e. 8 bytes of space...
-4. ...so multiply the volume by 8 bytes.
-5. Divide by `1024` to get it as kilobytes.
-6. Divide by `1024`, again, for megabytes.
+3. Assume a voxel takes just a single byte of space...
+4. Divide by `1024` to get it as kilobytes.
+5. Divide by `1024`, again, for megabytes.
    - Divide again to get gigabytes, if needed.
-7. Look at the amount of memory used.
-8. Change the distance and repeat a few times.
+6. Look at the amount of memory used.
+7. Change the distance and repeat a few times.
 
 {{ volume_memory_calc(id="calculator") }}
 
 {% info_notice(summary="Fun Fact: Planet-sized Volumes") %}
-If you solve for the size of the earth (a radius of 6371km), you will get a fun number of roughly **16550 exabyte**... which is more than half of the *entire* contents of the world-wide-web (in ~2024) at about **27000 exabyte**!
+If you solve the volume for the size of the earth (a radius of 6371km), you will get a fun number of roughly **2068 exabyte**... which is roughly seven percent of the world-wide-webs *entire* contents (in ~2024), at about **27000 exabyte**!
 
 Luckily, most of any planets volume is unreachable, hidden under the surface,
 so it can be treated as if it didn't exist, vastly reducing the needed volume.
 {% end %}
 
 While computers these days are pretty darn powerful, **they still have limits**,
-and working with voxels can push things there *very* quickly...
+and working with voxels can push them there *very* quickly...
 
 - Your RAM may be large (many gigabytes, usually ~4-8 GB),<br/>
   but the bits'n'bytes still need to go to/fro the CPU and back.
@@ -251,3 +242,7 @@ Perhaps [share](/wiki/community) your creation?
 ## Next
 
 Choosing a programming language!
+
+---
+
+[^squarecube]: <https://en.wikipedia.org/wiki/Square%E2%80%93cube_law>

templates/shortcodes/volume_memory_calc.html

@@ -2,7 +2,7 @@
 <div id='{{id}}' class='notice info' style='display:none'>
     <div style="text-align:center">Interactive <b>Distance ⇒ Memory</b> Calculator</div>
     <div style="display:flex;justify-content:center;align-items:center;padding:0.5rem">
-        <div>(<input type=number required min=16 max=65536 step=16 value=16 style='width:5em;text-align:end;border-radius:5px;border:1px solid grey;font-family:monofont' title='View Distance'>&hairsp;m * 2)³ * 8</div>
+        <div>(<input type=number required min=16 max=65536 step=16 value=16 style='width:5em;text-align:end;border-radius:5px;border:1px solid grey;font-family:monofont' title='View Distance'>&hairsp; * 2)³</div>
         <div>&nbsp;=&nbsp;</div>
         <code style='font-weight:bold;text-align:end;min-width:7em;background:#0000007a' title='Memory Usage'>0 kB</code>
     </div>
@@ -26,7 +26,7 @@
         }
         function put(b, u) {calc_output.innerHTML = b.toFixed(2) + '&hairsp;' + u}
         var V = Math.pow(D*2, 3), K = 1024;
-        var bytes = V * 8, kilobytes = bytes / K, megabytes = kilobytes / K, gigabytes = megabytes / K, terabytes = gigabytes / K;
+        var bytes = V, kilobytes = bytes / K, megabytes = kilobytes / K, gigabytes = megabytes / K, terabytes = gigabytes / K;
         if(terabytes >= K) {return put(terabytes / K, 'PiB')}
         if(gigabytes >= K) {return put(terabytes, 'TiB')}
         if(megabytes >= K) {return put(gigabytes, 'GiB')}