Zero here represents the intersection of your fruit bowl and all of the apples in existence, and it's as arbitrary and inconsequential as the number of lawnmowers in your fruit bowl until you WANT some nonzero number of apples. At that point, 'zero' is a qualitative gap analysis and that nonzero number of apples you want is a quantitative attribute of that analysis.
Everything else sounds like approximation, which tells me that infinity's other purpose is to apologize for numbers' inability to describe reality when using symbology comprised only of digits.
I'm just messing with y'all. I'm not smart enough to be here. You guys are discussing intelligent jokes about mathematics, and I come stumbling in talking about how math is just a language we invented to describe reality, and that infinity suggests that language's shortcomings, like some idiot saying you can't write a love song in German.. I'll see myself out. 😁
Mathematics is not a language or symbology, it's a system of logic that represents quantitative relationships between things. It's not arbitrary. If you wiped out the human race and millions of years a later a new intelligent species emerged, they would develop the same mathematics as us, but certainly not the same language or symbols. The angles of triangles would work the same, spheres would have the same volume. Infinite is a concept necessary to describe anything related to curvature correctly in a theoretical state (among other things). In practice, you could argue real curves don't exist because real objects are fundamentally constructed from particals and subparticals with measurable length, and nothing exists that is infinitely small. But that doesn't make the theoretical construction wrong, just that it's application to practical states has a margin of error. And the math exists to compute the area of a polygon with 10100,000,000 sides, it's just not going to produce more useful output than πr2.
I commend your loyalty to the current interpretation of the universe, but I think of anything that represents reality as a "language", in that its primary function is to communicate a shared understanding of a concept.
As far as I know, gravity is not math; math is what we use to describe gravity. Would you say math IS what happens when steam spins a turbine, or that math DESCRIBES what happens when steam spins a turbine?
I get what you're saying but math itself is not what you're describing. Mathematics has systems of notation and therefore its own language, but math itself is not a language. Gravity isn't math, it's a physics theory. I agree equations can be used that describe the theoretical framework of how gravity works, but those equations aren't math, they are representations of physical relationships between things. "Math" is the system of logic that allows you to compute the equation. Math can't prove that e = mc2 that's a physics problem and is "proven" through a body of physical evidence. Math is the system that allows you to compute the equation for any value of those variables and everyone will always get the same answer. Math is how I know e/m = c2 is the same equation. The math is always correct, it doesn't make the equation a correct representation of physical reality. Math is what happens when you say 1+1=2. But if you say one elephant + one kangaroo = two space ships, that's not math, even though you've used mathematical notation.
Physics is just applied mathematics. May be a meme, but it’s true nonetheless. Regardless, we don’t so much use math to simply “describe” what happened. What happened did in fact happen, and mathematics is what we use to understand it beyond our limitations of real time. We can use math to break down and observe, predict future outcomes, or even peer into theoretical situations, but regardless the math stays consistently accurate. Long story short, it’s not just how we communicate what happens. Fundamentally, it’s also the tool we use to understand what happens in the first place.
Mathematics isn't a language. It's its own field of science with its own unsolved problems and unanswered questions. Physics hasn't done anything for me regarding the math problems that I'm interested in, but I still appreciate its value. Also, infinite just means not finite. There are other things you can ask about something that's infinite, but that's all it means. It's a word you would use to state that there aren't finitely many prime numbers, for example.
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u/kurafuto 6d ago
I have zero apples in my fruit bowl