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index.html
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<!doctype html>
<html lang="en">
<head>
<title>gravLox</title>
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<link rel="icon" type="image/x-icon" href="favicon.ico">
<style id="docStyles">
* {
box-sizing: border-box;
word-wrap: break-word;
--hue: 48;
--sat: 100%;
--lit: 88%;
--color: hsl(var(--hue), var(--sat), var(--lit));
--backcolor: hsl(120, 100%, 13%);
--litback: hsla(120, 50%, 25%);
}
body {
padding: 0px;
margin: 0px;
background-color: #000;
hyphens: auto;
text-align: center;
}
#holder {
display: inline-grid;
grid-template-columns: 1fr;
grid-template-rows: 1fr 1fr;
padding: 10px;
font-size: 24px;
text-align: justify;
max-width: 700px;
width: 100%;
height: 100vh;
margin: auto;
xxxborder: 1px solid #000;
background-color: var(--backcolor);
color: var(--color);
z-index: 2;
}
#discussion {
margin: 0px;
overflow-x: hidden;
overflow-y: auto;
min-height: 40px;
}
.addendum {
font-size: 0.9em;
opacity: .3;
}
div {
position: relative;
margin: 0;
padding: 0;
}
hr {
border-top: 1px solid var(--color);
border-bottom: none;
border-left: none;
border-right: none;
margin: 50px 0px 50px 0px;
}
img {
xxxwidth: 100%;
xxxmax-width: 400px;
}
a,
a:visited {
color: var(--color);
text-decoration: none;
transition: 300ms linear color;
}
a:hover {
color: #e86;
transition: 300ms linear color;
}
input {
--thumbH: 40px;
--color: 48, 100%;
--lightness: 88%;
--midness: var(--lightness);
/*calc(0.37 * var(--lightness));*/
}
input[type=range] {
-webkit-appearance: none;
-moz-appearance: none;
display: inline-block;
padding: 0;
margin: 0;
height: var(--thumbH);
width: 100%;
border-radius: calc(var(--thumbH) / 2);
background-color: hsla(0, 100%, 100%, 0.3);
pointer-events: none;
}
input[type=range]::-webkit-slider-thumb {
-webkit-appearance: none;
background-color: hsl(var(--color), var(--lightness));
opacity: 1.7;
height: var(--thumbH);
margin-bottom: 0px;
width: var(--thumbH);
border: calc(0.1 * var(--thumbH)) solid;
border-color: var(--backcolor);
border-radius: calc(var(--thumbH) / 2);
pointer-events: auto;
}
input[type=range]:focus {
outline: none;
}
/*possibly a portrait mobi-fone*/
@media screen and (max-width:500px) {
input {
--thumbH: 30px;
}
dd {
font-size: 16px;
margin-left: 20px;
}
}
/*possibly a mobile landscaper*/
@media screen and (orientation: landscape) and (max-width: 760px) {
#holder {
height: 500px;
width: 100%;
max-width: none;
}
}
</style>
<style id="svgStyles">
svg {
width: 100%;
padding: 0;
margin: 0;
}
#svgHolder {
border: 10px solid hsla(0, 100%, 100%, 0.3);
position: relative;
padding: 0;
margin: 0;
width: 100%;
padding-top: calc(40% - 7px);
overflow: hidden;
user-select: none;
--line-width: 2;
--line-color: 'purple';
--axis-width: 1;
--axis-color: #e90;
--ani-color: #c30;
--dot-color: var(--color);
--mass-color: #e90;
--mass-stroke: #c70;
--mass-stroke-width: 5;
--mass-line-width: 0.4;
--mass-line-color: purple;
--load-ball-color: #e90;
--load-ball-stroke: #c70;
}
#gravLox {
position: absolute;
right: 0px;
bottom: 0px;
padding: 2px;
opacity: 0.3;
font-style: italic;
font-size: 20px;
color: var(--axis-color);
user-select: none;
}
#menu {
position: absolute;
top: 0px;
right: 0px;
background-color: rgba(0, 0, 0, 0.3);
overflow: hidden;
visibility: hidden;
transition: height linear 250ms;
}
input[type=checkbox] {
width: 30px;
height: 30px;
vertical-align: middle;
accent-color: var(--axis-color);
}
label {
font-style: italic;
}
#svgGrid {
padding: 0;
margin: 0;
position: absolute;
top: 0;
overflow: visible;
xxxtransform: perspective(400px) rotateX(75deg);
z-index: -1;
user-select: none;
}
#svgMass {
padding: 0;
margin: 0;
top: 0;
position: absolute;
xxxtransform: perspective(400px) rotateX(-15deg);
xxxoverflow hidden;
user-select: none;
}
.gridline {
stroke-width: var(--line-width);
stroke: var(--line-color);
stroke-linecap: round;
fill: none;
pointer-events: stroke;
vector-effect: non-scaling-stroke;
xxxtransition: opacity 1s linear;
}
.xlineDots {
marker-start: url(#dot);
marker-mid: url(#dot);
marker-end: url(#dot);
}
.xline {}
.yline {}
.axisline {
fill: none;
stroke: var(--axis-color);
stroke-width: var(--axis-width);
vector-effect: non-scaling-stroke;
}
.aniline {
stroke-dasharray: 10 4;
stroke-dashoffset: 0;
animation: move-grid-line 0.5s linear infinite;
}
#loadball {
fill: var(--load-ball-color);
stroke: var(--load-ball-stroke);
stroke-width: 10;
vector-effect: non-scaling-stroke;
}
.massdot {
fill: var(--mass-color);
stroke: none;
}
#massouts {
transition: opacity 1s linear;
}
.massout {
fill: none;
stroke: var(--mass-stroke);
stroke-width: var(--mass-stroke-width);
vector-effect: non-scaling-stroke;
}
.massline {
fill: none;
stroke: var(--mass-line-color);
stroke-width: var(--mass-line-width);
vector-effect: non-scaling-stroke;
xxxstroke-dasharray: 5 1;
xxxstroke-dashoffset: 0;
xxxanimation: move-mass-line 2s linear infinite;
transition: opacity 1s linear;
}
@keyframes move-mass-line {
0% {
stroke-dashoffset: 0;
}
100% {
stroke-dashoffset: -6;
}
}
@keyframes move-grid-line {
0% {
stroke-dashoffset: 0;
}
100% {
stroke-dashoffset: -14;
}
}
/*possibly a portrait mobi-fone*/
@media screen and (max-width:500px) {
#svgHolder {
border-width: 2px;
}
}
</style>
<style id="mathStyles">
/* (c) Aardvark Aaronson */
frac {
display: inline-grid;
grid-template-columns: 1fr;
grid-template-rows: 1fr 1fr;
font-style: italic;
font-size: 0.6em;
vertical-align: middle;
text-align: center;
}
num {
border-bottom: 1px solid;
}
num::before {
content: "\00a0\00a0";
}
num::after {
content: "\00a0\00a0";
}
sup {
font-size: 0.6em;
}
sub {
font-size: 0.6em;
}
com {
font-size: 0.5em;
}
com::before {
content: "\00a0\00a0\00a0[";
}
com::after {
content: "]";
}
whr {
border-left: 1px solid;
padding: 0.5em;
margin-left: 1.25em;
font-size: 0.7em;
vertical-align: middle;
}
dd {
margin-top: 15px;
}
</style>
</head>
<body>
<div id="holder">
<div id="svgHolder">
<div id="gravLox">grav·LoX</div>
<div id="menu">
<div style="padding:10px;">
<input id="checkbox0" type="checkbox">
<label id="label0" for="checkbox0">hide grid</label>
<br>
<input id="checkbox1" type="checkbox">
<label id="label1" for="checkbox1">unmask mass</label>
</div></div>
<svg id="svgGrid"
xmlns:xlink="http://www.w3.org/2000/svg"
width="100%"
viewbox="-50 -20 100 40"
preserveAspectRatio="none"
>
<defs>
<marker id="dot" refX="10" refY="10"
vector-effect="non-scaling-size"
markerUnits="userSpaceOnUse"
markerWidth="20"
markerHeight="20"
orient="auto"
>
<circle cx="10" cy="10" r="0.4"
vector-effect="non-scaling-size"
fill="var(--dot-color)"
stroke="none"
></circle>
</marker>
<g id="massdots"></g>
<mask id="hole">
<rect
x="-50" y="-20"
width="100%" height="100%" fill="white" />
<use href="#massdots" />
</mask>
</defs>
<circle id="loadball" cx="0" cy="0" r="1" transform="scale(0,0)"/>
<g id=gridgroup mask="url(#hole)">
<g id="xgridlines"></g>
<g id="ygridlines"></g>
<g id="axgridlines"></g>
</g>
<g id="massgroup">
<g id="xmasslines"></g>
<g id="ymasslines"></g>
<g id="axmasslines"></g>
</g>
<g id="massouts"></g>
</svg>
</div>
<div id="slideDiv" style="
padding: 10px 0px 5px 0px;
margin: 0;
">
<input
id="slide0"
type="range"
min="0"
max="100"
step="1"
value="0"
/>
</div>
<div id="discussion">
<div id="equation">
<p>
In this scene,
<i>E</i> = m<i>c</i><sup>2</sup>
and you probably recognize that the letter <i>c</i>
in that equation
refers to a <i>speed</i>; specifically,
the speed of light.
</p>
<p>
Now, you also know that the little number
two: <sup>2</sup> means <i>squared</i>,
which is the same as saying "times itself"
</p>
<p>
We can re-write that equation as:
<dd>
<i>E</i> = m · <i>c</i> · <i>c</i>
</dd>
</p>
<p>
Normally when you think of speed, you think of it in terms
of some <i>fraction</i> - that is,
"some distance per time" as in:
"miles per hour" or "meters per second" or "furlongs per
fortnight" - whatever you want, <i>speed</i> is typically
expressed as some quantity of distance being covered in
some amount of time.
</p>
<p>
That distance could be in any direction, in three dimensions;
it doesn't <i>have</i> to be in only one dimension.
Normally you drive straight ahead, but you could go
left-and-right, forward-and-backwards, or even up-and-down
if you're flying - so
speed can be thought of as an amount of <i>space</i>
being covered in a given <i>time</i>.
</p>
<p>
We could say that:
<dd>
<i>speed</i> = <frac> <num>space</num> time </frac>
</dd>
</p>
<p>
Exactly how much space being covered, and passing time,
the speed of light contains is not imporant -
whatever the
exact numbers are, we don't care for now; we just need
to understand that the letter <i>c</i> refers to
some amount of <frac><num>space</num>time</frac>
</p>
<p>
Substituting that fraction for <i>c</i>
in the equation, we should get:
<dd>
<i>E</i> = m · <i>c</i> · <i>c</i>
<whr>
<i>c</i> = <frac><num>space</num>time</frac>
⇒
</whr>
<br><br>
<i>E</i> = m
· <frac><num>space</num>time</frac>
· <frac><num>space</num>time</frac>
</dd>
</p>
<p>
With a little algebra, we can move one of those fractions
to the other side:
<dd>
<i>E</i> = m
· <frac><num>space</num>time</frac>
· <frac><num>space</num>time</frac>
</dd>
<dd>
<i>E</i>
·
<frac><num>time</num>space</frac>
=
m
· <frac><num>space</num>time</frac>
· <frac><num>space</num>time</frac>
· <frac><num>time</num>space</frac>
<com>
multiply both sides by
<frac><num>time</num>space</frac>
</com>
</dd>
<dd>
<i>E</i>
·
<frac><num>time</num>space</frac>
=
m
· <frac><num>space</num>time</frac>
·
<frac><num>
<s>space</s>
</num><s>time</s>
</frac>
·
<frac><num>
<s>time</s>
</num><s>space</s>
</frac>
<com> cancel out </com>
</dd>
<dd>
<i>E</i>
·
<frac><num>time</num>space</frac>
=
m
· <frac><num>space</num>time</frac>
</dd>
</p>
<p>
This is the relationship between energy <i>E</i>
and mass <i>m</i>
used for the computations
in this scene.
Energy and mass are proportional to eachother
in this way:
</p>
<p>
<dd>
<frac>
<num>E · time</num>
space
</frac>
∝
<frac>
<num>m · space</num>
time
</frac>
</dd>
</p>
</div>
<hr>
<div id="existing">
<p>
When you have a fraction, it means that one thing
is <i>divided up</i>
over some other thing - if you have, say $80, and
you 'divided it up' among ten people, what that
means is, you're 'spreading out' the eighty dollars
over the ten people.
</p>
<p>
If a farm has 30,000 stalks of corn 'per acre' that means
the stalks are spread out over the acres.
</p>
<p>
What we mean by
<frac><num>m · space</num> time</frac>
is that some amount of mass and space is evenly distributed
over <i>time.</i>
</p>
<p>
Saying that something is 'evenly distributed over time'
just means that the thing <i>exists.</i>
</p>
<p>
If an object did not persist for any amount of time,
then it wouldn't exist by the standards of what
the term 'exist' typically means. That an object
has length and width and depth is only applicable
if it also has <i>persistence.</i>
</p>
<p>
Your company leases a storage unit - the unit is
rented based on its dimensions, length, width, height,
but also by its duration, that is, the time of
the lease. If you have a six-month lease on a storage
unit, sure your company has access to
8×10×12 feets
of space, but after that six months expires, it's
no longer applicable to anything your company does.
</p>
<p>
Similarly, if there weren't any <i>dimension</i>
for an object to exist in, then it wouldn't exist.
If you only had two dimensions, then 'spheres'
would only exist as whatever circle happens to
be intersecting the plane of your existence.
There needs to be some space for mass to occupy.
Your company better rent a storage unit with
enough dimensions to hold whatever you need to store.
</p>
<p>
By saying
<frac><num>m · space</num>time</frac>
we mean that there is some stuff, <i>mass</i>,
and it occupies some dimension, <i>space</i>,
and all of that is evenly distributed over
<i>time</i> - it all persists.
</p>
</div>
<div id="devouring">
<p>
On the other side of the equation, we have
<frac><num>E · time</num>space</frac>
by which we mean that there is some amount
of energy and some time, and all of that is
evenly distributed throughout space. Both
energy and time are spread out into the space.
</p>
<p>
In this scene, the universe has had a grid
laid out over it, in order for you to visualize
it more easily - each section of the grid
contains some amount of energy as well as some time.
</p>
<p>
Scrolling over the scene causes specific locations
to begin <i>consuming</i> the universe around them.
[Scroll left-to-right over the scene, or drag the
slider - click in the slider bar to animate.]
</p>
<p>
These locations devour the surrounding grid
and convert that into an object; an object
that occupies the dimensions that were converted
from the space around them, and which
persists throughout the time which was also
pulled through from the grid.
</p>
<p>
That is to say, when you start scrolling,
things start moving from one side of the
equation to the other.
<dd>
<i>E</i> · <frac><num>time</num>space</frac>
⇉
⇶
m · <frac><num>space</num>time</frac>
</dd>
<br>
Initially, nothing exists on the <i>mass</i>
side of the equation.
When you start scrolling,
objects get formed; those objects need some dimensions
to occupy. The dimensions they occupy are the ones
sucked through from the space on the other side of the
equation. The objects and the dimensions need to persist
for some time; the time they exist during is the time
from the other side of the equation.
</p>
<p>
Again, the masses ingest the grid, and turn
it into more mass - this consumption causes
the grid to warp.
Eventually, the distortion forms a very strong
and noticable connection between the
centers of each object.
</p>
</div>
<div id="denial">
<p>
The grid does not warp to accomodate the mass;
neither does the presence of the mass cause
space to warp.
</p>
<p>
The masses <i>are</i> the wrapping of space
up into a ball.
Energy and time-space are sucked through to
the opposite side of the equation, and that
forms an object.
</p>
<p>
The 'attraction' the objects have towards
eachother's center <i>is</i> the distortion
that occurs as the objects swallow the
surrounding grid-space.
</p>
</div> <hr>
<div id="fabric">
<p>
<i>If</i> space-time is a 'fabric', imagine that
fabric laid out on a table. Then, <i>pinch</i>
the fabric somewhere in the middle and start
crumpling it up into a ball in your hand.
<br><br>
Eventually, the fabric will be distorted and
wrinkled up, and there will appear to be a ball
in the middle of it. There <i>isn't</i> a ball,
or an object, or a mass, or anything - it's just
the fabric being crunched up. The fabric isn't
distorting because of some object that's inside
it - the object IS the distortion of the fabric.
</p>
<p>
Now imagine that someonelse <i>also</i> starts
pinching the fabric in a different place.
[This is a big piece of fabric - imagine it's
a large bed sheet, and it's spread out on
a hard wooden floor.]
<br><br>
You both pinch the sheet at a different place
somewhere in the
middle and start crumpling it up into a ball.
After a little while, your hands are
going to start getting closer to eachother.
<br><br>
That is, since you're both pulling the sheet
into your hands, the part of the sheet that's
between your two hands is getting pulled into
both of your hands at once; unless you <i>tear</i>
the sheet [don't tear the sheet! you'll get
in trouble], your hands will start getting
closer to eachother until the two wads of
fabric you're both crunching up touch one another,
and become a single big ball.
If we're both eating the same string of spaghetti,
from opposite sides, either the spaghetti is going
to snap, or we're going to kiss.
<br><br>
Again, there is no force pulling the two things
together - the 'pulling force' is the wadding
up of the sheet into a ball. It's the
drawing up of the sheet into your hand
that appears to draw the two things together.
<br><br>
<i>And</i> there aren't 'things' - there just
appear to be things because the sheet is
crunched up in different places.
</p>
<p>
[Note that this animation does not show the
part where the masses start getting closer
to eachother - though it could, ofcourse, do
that from the same calculation; it's simply
intended to emphasize, for now, the
grid-becoming-mass portion of what's happening.
<br><br>
You should also be able to see that the masses
are 'attracted' in <i>many</i> directions
at once - along every different line in the
grid, in fact - it's just that a preponderance
of grid-lines has been concentrated between
the 'centers of mass' of each object.]
</p>
</div> <hr>
<div id="boxing">
<p>
Make a box ...
<p style="width:100%;text-align:center;">
<img src="sketchBox.svg"
style="width:200px;">
</p>
How's that? Does that look like a box?
Close enough?
<br><br>
It's a box; it's got all the parts,
length, width, height - it even exists for some
period of time. It contains all of the dimensions
that a box usually has.
</p>
<p>
Now, <i>conceptually,</i> collapse the box,
in one direction; squoosh it down into a square ...
<p style="width:100%;text-align:center;">
<img src="collapsingBox.svg"
style="width:200px;">
</p>
Alright? It <i>still has</i> all of its dimensions.
We are just going to use this plane as a
representation of the dimensional space of
the box - we're going to imagine that
one of the box's dimensions has been flattened
down so far that the box now looks like a square.
All of the dimension, and space, and everything
that was originally inside the box is still there;
we're simply using a flat plane to represent
the whole box.
</p>
<p>
Now do that same thing with <i>another box</i>;
a different box that has been divided up using
a grid ...
<p style="width:100%;text-align:center;">
<img src="collapsingGrid.svg"
style="width:200px;">
</p>
The length, width, height, depth, time,
everything is still in there, we're just
collapsing one of the directions so that we
can use a square to represent the entire box.
</p>
<p>
At this point, we have two different
<i>planes of existence.</i> We have two
squares, or planes, that are representative
of fully-dimensional realms.
</p>
<p>
Take the two planes, and <i>intersect them</i>...
<p style="width:100%;text-align:center;">
<img src="intersectionPlanes.svg"
style="width:300px;">
</p>
That is, effectually, what is happening in
this scene.
<br><br>
There are two separate <i>realms of existence</i>.
One of them is the 'mass realm', the
<frac><num>m · space</num> time </frac>
side of the equation. The other is the
'energy realm' or the
<frac><num>E · time</num> space </frac>
side of the equation.
<br><br>
Initially, the mass-realm is completely empty;
there is nothing in it - no length or
width or height or mass. At first, the mass-realm
doesn't even <i>exist</i> because it doesn't
even have the time it would need in order to exist.
<br><br>
In the beginning of the scene, the <i>energy-realm</i>
exists. It has a grid laid out over it;
time and energy are spread throughout the space.
That particular realm is teaming with energy
and time, and all of that is contained in
dimensions. Here, we've visualized that as
a grided-plane.
<br><br>
As the grid gets ingested, things begin to
'transfer' into the mass-realm.
Things from the <i>Energy</i> side of the
equation begin projecting into the
mass-realm...
<p style="width:100%;text-align:center;">
<img src="intersectionMass.svg"
style="width:300px;">
</p>
Remember that the mass side of the equation
does not exist at first; as things
move from one side of the equation,
they <i>construct</i> the other.
The energy and grid-lines get projected
through <i>as mass</i>; the dimensions
transfer through to create the length
and width and height needed to hold the
mass; the time gets transposed into
the time needed for everything to persist.
<br><br>
This happens with every mass in the scene.
</p>
<p>
It would either be confusing or impractical
to attempt to show two different three-dimensional
realities intersecting eachother at right angles,
which is why they were reduced to planes for
this example.
</p>
</div> <hr>
<div id="threading">
It might be a little easier to see what a single line
itself is doing if the other grid-lines are removed.
<br><br>
<div id="toggleDiv" style="
width: 100%;
text-align: center;
font-style: italic;
user-select: none;
">~~~~~</div>
<br>
Again, the masses are not masses - they are conceptual
<i>locations</i>, indicated by coordinates, that consume
the grid in all directions, then spit it back out
into the mass-realm. It's more like the grid-lines are
threads that get pulled in through a pin hole, and make