People are in love with the magic of infinity. It’s ideal for research as it generates all sorts of mad ideas. Anything that can happen will happen; an infinite number of times! Endless possibilities! But whilst infinity is fun I can’t help but think it is a source of confusion in many instances and is holding back scientific progress.
Many, many paradoxes and speculative theories disappear at a stroke if we are simply willing to acknowledge the actually infinite cannot exist.
There are strong arguments against the actually infinite. For example, no matter how many times you add one you never reach infinity so actual infinity is impossible to achieve.
On paradoxes, for example, Zeno’s paradoxes, there is a very simple solution if you take the view that the actually infinite is impossible:
- Assume time is continuous
- Examine any system over a fixed time period
- Then the system goes through an actually infinite number of states in a finite period
- Actually infinite is impossible so reductio ad absurdum time is discrete
- Time is discrete so Archilles only has to cover a finite number of steps to reach the tortoise
In the physical sciences we used to be quite strict with infinity:
- used only as approximation of very large/small
- indicate of logic error when occurs elsewhere
- even in maths infinity = divide by zero = logic error
But I guess belief in the actually infinite keeps cosmologists in a job for an actually infinite period of time... — Devans99
Then I have to say no. A lot of things can be modelled by using infinity in some way or another, but I don't see it in reality as applied to real world entities. Modeling is one thing, reality another. The number 3 or pi don't physically exist, even they are extremely useful in modeling reality.I mean actual infinity in the context of the physical sciences. I.e. when it is applied to real world entities. — Devans99
What disturbs me is when people just mix math with reality in general and forget the model part.. It’s the use of actual infinity to stand real world quantities that disturbs me. Statements like space or time maybe actually infinite... nonsense. — Devans99
Statements like space or time maybe actually infinite... nonsense. — Devans99
in many instances and is holding back scientific progress. — Devans99
Many, many paradoxes and speculative theories disappear at a stroke if we are simply willing to acknowledge the actually infinite cannot exist.
There are strong arguments against the actually infinite. For example, no matter how many times you add one you never reach infinity so actual infinity is impossible to achieve.
On paradoxes, for example, Zeno’s paradoxes, there is a very simple solution if you take the view that the actually infinite is impossible: — Devans99
In the physical sciences we used to be quite strict with infinity:
- used only as approximation of very large/small
- indicate of logic error when occurs elsewhere
- even in maths infinity = divide by zero = logic error — Devans99
But I guess belief in the actually infinite keeps cosmologists in a job for an actually infinite period of time... — Devans99
- Empty space has vacuum or dark energy associated with it. Total energy content of universe has to be finite. Space is finite.
- If time reaches back infinitely then it’s impossible to reach today. Time is finite. — Devans99
People are is love with the magic of infinity. It’s ideal for research as it generates all sorts of mad ideas. Anything that can happen will happen; an infinite number of times! Endless possibilities! But whilst infinity is fun I can’t help but think it is a source of confusion in many instances and is holding back scientific progress. — Devans99
Not only do we lack evidence for the infinite but we don’t need the infinite to do physics. Our best computer simulations, accurately describing everything from the formation of galaxies to tomorrow’s weather to the masses of elementary particles, use only finite computer resources by treating everything as finite. So if we can do without infinity to figure out what happens next, surely nature can, too—in a way that’s more deep and elegant than the hacks we use for our computer simulations.
Our challenge as physicists is to discover this elegant way and the infinity-free equations describing it—the true laws of physics. To start this search in earnest, we need to question infinity. I’m betting that we also need to let go of it. — Infinity Is a Beautiful Concept – And It’s Ruining Physics - Max Tegmark
We take what mathematicians and logicians say seriously when we adopt the formal systems they create. That means that to use such systems we are committing ourselves to a particular kind of metaphysics. If you accept standard mathematics you cannot possibly claim that actual infinities are impossible in virtue of a contradiction. You might say that not every aspect of our particular universe can be infinitized, but there's no argument that the concept itself precludes instantiation in the world. — MindForged
But if one removed all phyiscal mass and energy, both the visible and dark, wouldn't empty space simply be infinite vacuum? — InfiniteZero
I’m not suggesting dropping infinity from maths. It’s fine with the limit concept and set concept. I’m suggesting dropping actual infinity in physics and metaphysics when used as the value for real world quantities. — Devans99
Relativity is an approximation of reality not reality - We don’t know for sure if space is continuous. Anyway continuous space is a Potential Infinity whereas I’m talking about Actual Infinity. — Devans99
There is an argument that the natural numbers are only potentially infinite - we have used finitely many of them so far and that will remain the case. — Devans99
’m hardly the only person to have a problem with actual infinity. The great German mathematician Hilbert posed his Infinite Hotel paradox. Just one of many paradoxes that stem from actual infinity — Devans99
I know it’s possible to construct consistent mathematical systems around infinity; that is not what I’m objecting to. I’m objecting to the use of actual infinity in physical sciences. — Devans99
There is a big difference adopting the maths because it is a useful model and accepting it as the actual metaphysics. And it should be telling that the central problems of modern physics/cosmology revolve around finding ways to avoid the mathematical infinities, or singularities, that are contained in the current best models. — apokrisis
Time is nothing more than measure of co-ocurences of events with human–created time measure, which is clock... Unverse works as unconscious machine, that removes necessity to count or regard time as important. — Victoria Nova
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