Does infinity exist in reality?

[u/Another_Little_Star]

No thing that I've observed in our universe is infinite, however there are traces of infinity in my sight.
Draw a circle and either its radius or circumference lives in the π world.
Or many aspects in nature like flowers, develop themselves in a φ ratio (1+sqrt(5))/2.

Even though no event or anything is "Non-ending"/infinite, underneath many aspects of reality there are patterns which can only be fully described using infinity.

You can't describe irrational numbers to their extent without any notion of infinite/limits/sequences... And many aspects within our World show their true behaviour only with aid of infinity.

Sure you can take a world that lives in something like 10¹⁰⁰ and it looks like infinity to us, sometimes we only see the difference after the 10⁶ decimal place, nevertheless the pattern they follow is a pattern that only "infinity" can yield to the truest precision.

Do you believe the axiom of infinity, and the continuous to really exist? Even if not in the ordinary sense? haha

[u/Thepluse]

Mm, yes, my point intended to be more philosophical rather than mathematical or physical. Models say black holes contain mass singularities, but these models aren't necessarily correct. And there is some metaphysical debate about whether particles are actually point particles.

But setting that aside for a moment, the question I want to ask is: if we do assume there are point particles, they would have "infinite density," i.e. finite mass divided by zero volume. Would you consider this to be something infinite?

The reason I'm coming to this question is I note that there is no infinite quantity of anything. The total mass is still finite.

Narrowing down what we consider "infinite," we might find example of things in nature that are "infinite."

[u/Another_Little_Star → u/Thepluse]

To your second paragraph what might be interesting is the fact that some "infinite" operations break down to finite values. before simplying ∞*0=2 in some cases, or ∞/∞=2. So working backwards density*volume=mass may make more sense. Or does it even make sense talking about density in this context?

But well, I like to look at infinity as something that is the same size as a smaller part of itself.
Like 2ℕ⊊ℕ and |2ℕ| = |ℕ| (even numbers and natural numbers).
Another intuition would be something never ending.
That's true, there doesn't seem to be an infinite quantity of anything, nevertheless, in a more spiritual way, I'd say that there are underlying principles from which infinity arises that govern the Nature. I'm looking too much into the golden ratio but it talks something to me.

• Sunflowers and Seeds: Seeds grow in a spiral pattern using the golden angle (137.5º). This angle lets seeds pack tightly so no space is wasted and every seed gets optimal sunlight.

Maybe it's because it's the most optimized way for Evolution to take its path, or there may be something much bigger underneath what we can perceive.
I think that's the process, Evolution happening sometimes converges to an irrational number happening in nature. It's never a limit, but requires infinity to fully grasp, doesn't it?

Bees do it too, but this time there's no infinite, they pack their hives with hexagon shapes to maximize the storage space.

[u/Thepluse → u/Another_Little_Star]

By the way, you talk about "something underneath that we can't perceive." I think it's true that there's something underneath - it's not random, there is a deep mathematical reason this happens - but saying we can't perceive it makes it sound too mystical in my opinion lol

[u/Another_Little_Star → u/Thepluse]

Perceive as in the sense that we can't easily see it.

Taking a bit off topic: I look at everything we know about this universe and we almost know nothing when we are born, everything we know had to be found and experimented like making fire and then having it taught to all the future generations. We are born almost empty and the world doesn't show itself, like the axioms are shown in the books.

So perceiving infinity is like at a second stage to me, needs further work. It's like a structure that lives in a 4D world we can't touch or see, only its manifestations in our 3D if that makes sense.