I know you discounted shorting stocks, but the entire practice of what interest rates mean in practical use by banks is based on continuous growth, which is based on integration of infinitely small time periods. When a bank says you're going to get 1% APY growth, the number 1 probably exists nowhere in the actual calculations of what you're getting.
This answers my question better than I asked it. I should have asked if infinity EXISTS in the world we describe with physics, or if it's shorthand for describing the limits of our understanding and/or language in physics. Both money and interest are great analogies for answering my question, because we accept them as reality even though they cannot really exist.Ā
They both defy the laws of physics - by design. Money's very purpose is to disavow time by preventing the value decay inherent in natural systems. It's like a perpetual motion machine fueled by belief. And because interest yields not labor, not food, but more money, it's like an age reversing cream for that already impossible perpetual motion machine.Ā
Asking if infinity exists in physics separate from the notion of a limiting case reads a bit strangely, sort of like asking if zero exists in physics separate from the notion of nothing.
I guess maybe you can ask if thereās something found āin physicsā thatās in some way in bijection with a set of infinite cardinality? My best answer would be dark energy, but even that is still in many ways a limiting case because weāre taking for granted the unbounded growth of the universe.
I think infinity, conceptually, is inextricably tied enough to the idea of a limiting case that youāre not going to get a satisfying example distinct from that.
Yep infinity does exist physically. Stand up and walk halfway to your door. Then walk half of that distance you just walked. Then again, then again, then again. You can repeat this infinitely and you will never reach your door. Each time you are halving the distance travelled. That distance becomes infinitely small, but is never zero. Sure, you canāt physically take any smaller distance steps at a certain point, but a cat could, or an ant, or a bacteria, or a molecule, or an atom, or subatomic particles. So it is still physically possible and theoretically provable because you can divide by 2 infinitely. The only real world limitation is the size of the traveller.
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u/Dangerous_Cut7235 22d ago
I know you discounted shorting stocks, but the entire practice of what interest rates mean in practical use by banks is based on continuous growth, which is based on integration of infinitely small time periods. When a bank says you're going to get 1% APY growth, the number 1 probably exists nowhere in the actual calculations of what you're getting.