Maths doesn’t intrinsically describe anything. It’s a set of logic that, it seems, lets us predict some behaviour of what we see around us pretty well if we plug in the right numbers in the right places, but it doesn’t tell us what numbers to put where.
Also, atoms are not information. They are atoms. I can use bottle caps to store and transmit information, but that doesn’t make them intrinsically special.
Not realy.
Math is a tool that can describe things that exists but also things that dont exists. The rules that describe what is possible is not math but physics. This is the meta anwser.
The other anwser to your question/thought that everything around is just information is a question that is often debated in physics and is called deterministic universe theory. Which basicly means that if you know the state of everything at somepoint and all the “rules to the universe” that you could determine all states afterwards. It is currently unclear if this is the case because at it is we think it is impossible to get know all states of everything because of the uncertainty principle and other quatum effects.
Kinda. It’s more just that… it’s a set of rules. Different kinds of maths use different rules, called axioms, to create different internally consistent systems.
One axiom from geometry is that two straight lines parallel to each other at any point will never meet. This is used in what we call Euclidian geometry (among other axioms) and we use these to develop equations and ways of drawing conclusions. The area of a square, for example, depends heavily on each of the two pairs of sides being parallel and equidistant at all points. But we don’t have to use that axiom if it doesnt suit us. Einstein showed us that the real world doesn’t follow this axiom. Straight, parallel lines may meet in curved spacetime.
These are both valid and useful systems that we can use, even if they’re not consistent with each other and give different answers. Mathematics, number theory, arithmetic, etc, are all just sets of axioms that we can use to figure stuff out, and we can make literally ANY sort of system or axiom you can think of.
Math is a special kind of logic based on counting, and making it more complicated. So I can count how many apples I have, and then I can take a shortcut and add two of those groups rather than re-counting them together. And then I can add those apples I have today and add the ones I will get tomorrow and the day after… which I can shortcut by multiplying. Etc.
I can do the same with distance, for example – one step. 100 steps. My lawn is 50 steps by 50 steps, which is 2500 squares that are 1 step by 1 step.
And energy. I have a battery. That’s one battery of energy. To boil a pot of water, I need 100 batteries of energy.
But there are things that math doesn’t really explain. How do you use math to explain this sentence? Sure, you can convert it to ones and zeroes, but the words don’t really make more sense that way. Math probably can’t explain why green is my favourite colour, and many similar things.
Because math isn’t the thing. Math is the language we invented to make things more intuitive.
I’d say you’re on the right track, but not quite there.
Yes, math is a set of rules to describe what we observe. But it’s important to recognize that it only describes what we observe, not the truth. It’s a useful tool to understand the universe around us.
And strictly speaking, everything around us is not information, just described by large amounts of information. And we don’t really discover the rules, we invent them. We invent rules that allow us to describe what we see and predict what we will see.
Not really an ELI5, but sure, math is sometimes called ‘the language of the universe’. Everything in it can be described with math the same way it can be described with words.
Similarly to how it’s impossible for all words to exist or for a word to perfectly describe something, math too will always be incomplete and imperfect.
Some things will make more sense in a different language, such as binary, but for the most part it will always grow and get better at describing the universe around us
Math is a set of rules that are *trying* to describe everything that exists. It’s a journey that we have to go down multiple times, and each time we get more congruent to reality. The better our math gets, the farther out we have to look to find an anomaly.
* “Crystal Spheres” and “Gods” describe the motions of the planets in the sky very badly.
* Later on, we got the Copernican system, which at least describes them as moving in the right direction.
* Later on we got Newton, who was able to describe the motions of the planets in terms of mass and force and long distance relationships. Newtonian planetary motion is extremely accurate: more accurate than anyone was able to measure, except for Mercury. Mercury does it’s own thing.
* later on Einstein worked out the math that can describe the spacetime curvature from the sun’s gravity. Now Mercury’s orbit makes sense again, but there’s still weird stuff up in the sky.
* Right now we’re confused about something called “Hubble Tension” which is a dramatic way of saying the math doesn’t add up on the expansion of the universe. We’re still waiting for the math that fixes this one.
We don’t know if math can describe everything that exists. You’re asking what the end of the journey looks like, and we can’t know that. We don’t know if there *is* an end to this journey. All we can do is take the next step.
Side note: I’m really glad we still use the names of the gods for the other worlds in our system. It’s a great reminder of how far we’ve come.
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