Do curves actually exist in nature or are they a concept we use to describe the macroworld since everything physical is made out of particles (points). How can a curve naturally exist?
If you had met my wife you would not ask that.?
Mathematics is exact and abstract. That's why it's so useful in describing physics, economics and other complicated systems. A curve is a well defined path in some mathematical space. It is not found in nature. There can be approximates in the physical world that are modeled adequately by the concept of a curve. For example, I can model the position of an object vs time as a curve. This is usually a good model in everyday life although both space and time are discrete.
Do lines exist?
"There is no such thing as a linear relationship in real life."
If you date people that don't miss leg days at the gym then yes curves are real and a lot of fun.
Curves exist. They can be defined my mathematical formulas. [reviewcivilpe.com]
You're right, they don't exist in nature. In order for a curve to exist in the physical sense it would have to be made out of something. We don't measure curves, so they don't exist as far as we know. Maybe string theory will turn out to be true then one could argue that strings are curves.
But still the concept of a curve is extremely useful to us and it helps us make better predictions about the world, so not existing is not the worst a thing can be
To the eye and in the larger expanse of the universe yes. At the micro level, maybe not, just like a block wall is mostly empty space, but punch it and see how your hand feels.
It seems to me that curves are either an abstraction, or they exist, and if they exist, that would mean other mathematical abstractions should exist too.
Have you ever looked at the path of a river?
Have you ever seen a snake in real life?
Have you ever watched ocean waves cresting?
Have you ever seen seashells?
Have you seen a chart representation of Pluto's orbit around our sun?
Etc.
You're welcome.
They are all made up of smaller components which make them look like a curve. Orbits around the sun aren't physical, they're an abstraction.
@agnostictheist they don't "look like a curve" they ARE curves. You can chop up anything into pixels....in which case, NOTHING exists in nature except pixels.
don't get geometry confused with nature.
But when we're talking about nature, we're essentially talking about matter, made up of particles. Where do curves come in?
@agnostictheist just after the tap-dancing comedian.
@agnostictheist define curve?
@hankster a line which cannot be defined by any number of points, unlike a straight line which can be defined by at least two points.
@agnostictheist ah... perhaps that little infinity symbol is where the curves come from.
@agnostictheist I'm no physicist nor mathematical whiz....but even as infintesimal as a particle is some process must be occurring there, so some dimension must be required? a point is simply a location with no dimension, it is a location. it does not move. I do not understand the relationship you're trying to build between matter and geometry.
@agnostictheist if time we're somehow divided/sliced, especially on that infintesimal scale. does that create a faceted arc? is a curve the matter or its trajectory? hmmmm...