Re: Does mathematics describe reality?
There is certainly a substrate and it has Rules. Initially it was called an Aether. M&M didn't understand the rules and couldn't prove its existence. So the idea of an Aether lost face. Later, Einstein found that without a Substrate, he was blocked from further progress in his Field Equations. Distance had to have Scale for anything to hold together or make sense at Atomic Scales. So he introduced a substrate concept, but the word Aether had gotten a bad rap, so he called it Space-Time. This substrate has Scale, described in Planck Units.
This underlying Scale is what makes Atomic Particles compatible. We don't have an issue with combining one tiny Oxygen Atom with two gigantic Hydrogen Atoms to produce Water. We don't get a 19% Spin, it's always evenly divisible. Energy levels don't climb like a straight Line, but more like a staircase with discrete steps.
Matter responds to Speed in the same way it reacts to Gravity. The cyclic nature of Matter slows down, clocks slow down, aging slows down. Gravity and Speed have the same effect on Matter. How can Matter KNOW how Much to slow down.. unless it's sensitive to its personal velocity. How does Matter KNOW how fast it is moving?
This Substrate is the Computer itself. The best Model I can offer is a Neural Network made of Cells, with each Cell doing its own private task of processing information that passes through it. We are that Information. Or more specifically, Matter/Energy is the information being processed by that Network, not unlike how your Brain processes Thoughts.
If it helps, think of the whole Universe being one Giant Quantum Computer and the program is embedded into every single Cell of that Quantum Network as a simple set of rules for the processing behavior of any given Cell. This set of Rules is passed on to every New Cell the Universe Creates. The Creation of New Cells is literally the Expansion (growth) of the Universe. Our concept of "Now" is because we exist on the surface Growth of New Cells.
The Arrow of Time is because New Cells are always being Created at the Speed of Light on the previous surface of this Substrate. The Information that is you (Matter) always propagates into the New Cells from the previous Cells and we call that "Time".
So.. if You and I and everything we can Touch, Smell, Taste or Experience is just Information, like thoughts through a Brain.. Then this substrate is the only Real thing that can be said to Exist. Everything else is purely Informational, not unlike your Thoughts.
So if your Brain is a clump of Cells and the Universe is a clump of Quantum Cells, then what are these Quantum Cells made of?
That's the Million Dollar question.
In my book, these Quantum Cells are a discrete packet of Rules, with inputs and outputs that connect to Neighbor Cells. Thus the Whole Universe is a Quantum processing Machine and it is composed solely of Logic Rules.
Thus, in my Book, the whole Universe is purely composed of Logic (a branch of math).
For every variation in the Basic Rule Set, a completely different Universe results. Most are pure trash, but ours is among a few unique ones where the rules can form enough complexity to establish Chemistry, Life and self-aware beings.
You will never understand this.. as long as you keep trying to force what I've said into your own personal Model of Reality.
I started from scratch and figured it all out because that's what I'm good at. Others, like Max Tegmark, have drawn the same conclusions independent of each other. We have an advantage in that Max is a skilled Mathematician and Physics Major and I am just a Programmer. I've built VR Realities and I understand them and how they work. Some of you have played inside these Mathematical Realities in the form of Computer Games. Killed Dragons, evil minions, and saved the Princess or whatever. Granted those games cheat a lot via shortcuts, because we don't have the resolution that our Universe has.
Bottom line: Your existence is Virtual, mathematically speaking. In fact, the whole freaking Quantum Universe is Virtual.
But if the Quantum Universe is a massive Quantum Computer then is it self-aware? That question is far more interesting in my book. But rather off Topic here by the OP.
Again, I prefer you read the Thread I linked to above. I've answered almost every conceivable question there as simply as possible.
But, for those too lazy to do so, I will answer questions here, until Ron accuses me of snagging another thread on my favorite topic. Honestly, if someone posted a thread saying God Doesn't Exist because there is no Proof.. I doubt even Ron could stay his hand.
I mostly enter such Threads because there are always new readers browsing through these great halls, and they don't have the Time to Browse every Thread on a given Topic. So exposure to these ideas can be very New to many. To capture new readers one must Hook them. Get their Interest. Via advertising, they are paying the bills to support this great site, that I call Home.
Regards and best wishes,