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<!DOCTYPE html>
<html class="no-js" lang="">
<head>
<meta charset="utf-8" />
<meta http-equiv="x-ua-compatible" content="ie=edge" />
<title>Math is a Simulation of Reality</title>
<meta
name="description"
content=" Math is reality, but simulated with symbols on paper. It's a low level language for the physical world, it's representation and manipulation."
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<header class="flex items-center justify-between">
<p><a href="/">back to home</a></p>
<p>2022-Apr-20</p>
</header>
<article>
<h1>Math is a Simulation of Reality</h1>
<p>
I have hated maths for the longest time, from school all through
college. I loved it until \(x\) and \(y\) showed up. I never really
understood how abstract mathematics would help me in real life, hence
never gave any effort to the subject.
</p>
<p>
I rediscovered math while watching
<a
href="https://www.youtube.com/watch?v=kjBOesZCoqc&list=PL0-GT3co4r2y2YErbmuJw2L5tW4Ew2O5B"
>3blue1brown on Youtube</a
>
and the detailed visual explanations helped me understand mathematics in
a far deeper level that I ever could in school. Going down that path has
helped me realise and love what mathematics really is, a simulation of
reality.
</p>
<section>
<h2>Math is the Physical World on Paper</h2>
<p>
Although I never loved math, I was intensely curious about it. Math
had consistent properties and patterns that always intrigued me, how
equations can accurately predict physical outcomes and how certain
quantities relate beautifully to each other.
</p>
<p>
Consider the famous equation \( E=mc^2 \). When we were deriving this
formula in school, We would start out with the formula for one
dimensional motion, and after derivations and integration we would
arrive at the formula for making Nuclear Bombs. Even though this was
fascinating, I never really gave it any thought in school.
</p>
<p>
Everytime I came across equations and numbers
<a href="https://twitter.com/fermatslibrary">Fermats Library</a> that
are remotely interesting, the thought of how one mathematical symbol
flows effortsly to another comes to mind.
</p>
<p>
During my zoning out in the middle of the day ritual, I was thinking
about numbers and wanted to know exactly why \(2+2 = 4\), and what is
the deeper meaning of mathematics. I came to the conclusion that
\(2+2=4\) is so because \(4=2+2\).
</p>
<p>
Consider an apple. Now consider another apple. How many apples do we
have now? We have \(2\) apples. So what is \(2\) then? \(2\)
symbolically represents the amount of apples we have when we take one
apple and another apple. Let's say we have another \(2\) apples, so
the total number of apples we have is \(4\). So in that respect if we
take one apple, then another, then another, and finally another, \(4\)
denotes the thing that we have now.
</p>
<p>
Math is then an abstraction on top of the physical world. It's a way
for us to work with symbols that can be easily manipulated on paper as
our primary medium. Math is then a language for representing the
physical world. It's nothing more. But that is the sole reason why it
reflects the physical world so beautifully. It's a language as close
to the metal as possible. It is the shallowest usable abstraction that
we have.
</p>
<p>
When we are working with maths, we are working in a reduced set of the
world with clearly defined rules. We are manipulating a clearly
defined model of the physical world.
</p>
<p>Consider the formula.</p>
\[ \begin{aligned} F &= ma \\ a &= \frac{v - u}{t} \\ F &=
m(\frac{v-u}{t}) \end{aligned} \]
<p>
What this formula is saying is that Force \(F\) is what we get when we
throw a mass \(m\) with an accelration \(a\). Whatever that is
required to throw a mass with \(m\) with accelration \(a\) is denoted
by \(F\). Accelaration \(a\) is whatever the change in final velocity
\(v\) and initial velocity \(u\) over a period of time \(t\). So force
\(F\) becomes the effort requried to stop a moving body in a given
time \(t\). That is the conceptual model of force. Hence \(F\) denotes
that quantity, which is also denoted as <code>Force</code> in the
English language. We can then mathematically calculate that quantity
on paper, instead of physically moving that object and measuing it.
</p>
<p>
This is the reason why we have formulas that makes sense and meshes so
well with the real world. The real world does not obey the rules of
mathematics, mathematics is the real world in abstraction.
</p>
</section>
<section>
<h2>Math is beautiful</h2>
<p>
Math hence is beautiful. Math is what asembly is to the CPU. Not
binary but close enough to be tremendously useful. Math makes sense,
it's the only true language. It reduces complex physical interactions
into easily manipulatable symbols without the chaos of the physical
world.
</p>
<p>
We need to teach students that math is nothing more than an
abstraction, but an abstraction that mirrors the real world in it's
entirety. Having mastering over it, not only helps you understand it,
but gives you a sandbox to test your theory that you can use it to
bend reality. Math is now very, very interesting, go I wish I knew
this earilier.
</p>
</section>
</article>
</body>
</html>