Thread by @paraschopra

It shouldn’t be surprising that our fundamental reality is describable using mathematics.

A mini 🧵

1/ Maths is like English, but with far fewer degrees of freedom.

e.g. “We want to move forward with this” can mean so many things, while Area of circle = pi * r ^ 2 in zero curvature manifolds means only one thing.

Math is a language you use when you want to be precise.

2/ In theory, I can imagine that a large part of our everyday language can also be systemised into math.

Analytic philosophy traditions did exactly that.

So math is a language where you make it explicitly what exactly do you mean.

3/ Of course, you can capture randomness into your equations via random variables (statistics being the prime example).

So even if you want to describe something that’s not deterministic, math can be used.

4/ Since anything can be captured into math (you can even convert a painting into a matrix of numbers), it’s not surprising that we can talk about fundamental reality in a mathematical way.

5/ But what’s surprising is that the math of fundamental reality is so simple.

Simple in the sense of being describable using few deep principles, rather than thousands of random data/equations.

6/ For example, it could have been the case that we have thousands of fundamental particles (like we have thousands of fruits).

But we only have 17 of these.

7/ This relative simplicity of fundamental reality is the mystery, and not that it’s describable by math.

After all, you can imagine capturing everyday language into a mathematical model (like GPT-3 or knowledge graphs).

A complex enough math object can capture anything.

8/ that’s why going from

equations —> insight

is more likely to tell you about reality than the reverse mostly because human thought (being in English) is imprecise and hence likely to contain inconsistencies and hidden details while reality seems to be consistent and simple.

9/ Schrödinger equation captures what’s happening precisely.

It’s our everyday language of “wave” or “particle” that’s ambiguous and loaded with implicit details / connotations.

10/ As a side note, this is also why it’s so easy to have crank-pot theories.

Many (seemingly intelligent) people take our everyday words and start proposing things like: “universe is a simulation” or “consciousness is a field we tap into”.

11/ This path of

insight —> simple equations

almost never happens (except in rare cases like for Einstein), and all that’s left is ambiguous and untestable vague proposals that fall apart in a minute of honest questioning.

12/ To summarise, the mystery isn’t why reality is describable by math but why is that math so simple that it can be printed on a T-shirt.

That’s it!

Hope you enjoyed it.