I keep on thinking that everything around us is basically just information. Be it DNA, atoms, or spacetime itself. And math is the set of rules that explain the interaction, flow and existence of this information. We did not uncover all the rules yet. Does this make sense?
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i like that approach that the math is kind of language that helps to describe environment since every objects around could be quantified to certain degree.
also i doubt that we’re uncovering the rules, more likely we making them up basing on repetitiveness and reproducibility. in other words – there is no plan behind the universe, nor the stability
That’s the million-dollar question. Is mathematics the set of fundamental rules of the universe or is it the human mind’s best approximation of those rules? Philosophers have been debating that question for thousands of years and no one knows the answer.
Physics are the rules the universe follows. We do not know all of the rules, but we keep expanding our knowledge base.
Math is the language that allows you to understand the rules. If you cannot understand the math, you will not understand, say, quantum mechanics. You, me, whomever, can get a lay person’s understanding, but real knowledge and understanding requires speaking the language: math.
Just my opinion.
Some things defy perception. If I tried to explain the colour red to a person born blind, there are no words that I could ever use to convey a proper meaning (I could say vibrant, but what does a vibrant colour look like to someone who has seen no colour?)
But I could tell them that the colour is different based on wavelength. I could tell them that blue and red have 450nm and 750nm wavelengths. They won’t know what it means, but they will understand some of the difference, and how it behaves, even if they can’t *see* it.
We’re very much the sum of our experiences.
What’s beyond the event horizon of a black hole, why is there a functional limit on the speed of causality, etc. Math can describe those things without relying on perception and experience.
No. Math can be thought of as a set of rules that describe quantifiable ideas. These ideas can be usefully mapped to real things, but that mapping is just a model. Good mathematical models can have extraordinary predictive utility but they are still just models.
Many things can’t be modeled well with quantifiable ideas. For example, can you quantify the feeling of beauty and pleasure derived from smelling roses?
The best way to think about math is as elaborate bookkeeping.
If I want to understand the cycles of the moon, then I might mark on a stick the number of nights that pass between full moons. I can compare multiple such sticks to find patterns of monthly cycles. And so I’ve created numbers, tallies specifically, due to a need to do bookkeeping.
But there tallies are not useful for everything. If I want to track the position of the planets, then the tallies are too crude and the computations are too complex. We can do addition and subtraction real simply with elaborate tally systems, but not multiplication, division or trigonometry, especially when we need a high degree of precision. So we might create a place-value system. A place-value system should be thought of as a way to bookkeep our numbers in ways that are amenable to arithmetic manipulation AND precision. So the base-10 system is an elaborate bookkeeping technology.
But that might not be enough. You want to track planets and predict their motion based on first principles. So instead of just large tables of measurements, you come up with the idea of a “Function” which can keep track of paths over time. Moreover, you can do things with the function itself to make better predictions, like derivative or integrals. And so functions themselves become a way to bookkeep the actual path of the planets themselves – a huge step up from tallying the number of moons in a month. But, just like the tallies, it is merely a way to bookkeep information in a way that we can use productively.
The universe does whatever it does. We are just finding elaborate Dewey Decimal Systems to try and keep track of a little bit of it. That’s what math does.
No, actually.
This was proven by Kurt Gödel, who (in a move simplified for an ELI5) created a proof by contradiction that any set of consistent rules would have things that are true and can’t be proven, meaning that it can’t be claimed to be a complete system. One of the things that falls into that hole of incompleteness is a way to fundamentally prove that the system is consistent
Similarly, Alan Turing with the halting problem (also not really easy to do in ELI5 terms, I tried) proved that some problems are absolutely and categorically impossible to solve algorithmically, which for the purpose of this subject is all of math
Our brains are essentially pattern-recognition and future-predicting machines. We are also social creatures, and thus have developed language.
Math is definitely a very human extension of all these things. It is likely math is one step removed from the true nature of things.
Some models just seem to just miss the mark, and it becomes obvious when you imagine just how much computational power we would need to accurately simulate everything, if at all possible.
So yes, they are a set of rules humanity has iterated on to describe things as best we can in the way our brains can translate. It is possible some things may beyond the scope of (current) mathematical language though.
no. there is actually math that proves that math can’t even prove everything in math! and thats a thing so it must not be able to prove everything. Here is a veritasium video about it
No specifically math has an issue called Godel’s incompleteness theorem. Which basically states that any formal math system can’t do exactly what you described. There’s truths within any system that are not provable within it, but are still true.
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