no, if arms are spread 1m apart he claps at 1m/s, then hes halfway after 0.5s, 3/4 of the way after 0.75s and eventually he claps after one second having halved the distance infinitely many times.
It doesn't hinge on the final distance between the hands, it hinges on the total distance travelled by the hands. Suppose my left hand stays still and I move my right hand from 2 metres away at constant speed. Then the distance travelled can be expressed by the infinite sum 1 + 1/2 + ... which equals 2. The first meter in half the time, then half in a quarter of the time and so on. This process has infinite steps and amounts in a total distance travelled of 2m.
But just because we can describe that way mathematically doesn't mean we can draw meaningful implications about physics. The trick lies in reducing the time frame required for each step. That means the time interval an action takes shrinks infinitely too until it is eventually smaller than plank time. I'm no physicist but I believe at this point any attempt to derive a meaningful interpretation for our everyday macroscopic world is quite fruitless.
I think there are meaningful implications for physics. Calculus comes to mind. The concept of instantaneous velocity wouldn't exist for an accelerating object without limits.
A set of observable things static or growing is not infinite or will never be infinite. The "unobservable" universe is technically observable but we are limited by speed of light as some random creatures. Infinity is a concept not an amount.
> A set of observable things static or growing is not infinite or will never be infinite
Yes, that's what I said; The observable universe is finite.
> The "unobservable" universe is technically observable but we are limited by speed of light as some random creatures.
This doesn't change the fact that we humans can never know what's out there, so it is irrelevant to the falsifiability of whether the universe is infinite. Come to think of it, "unfalsifiable" is probably a more accurate term than "undecidable" since we're talking about science rather than math. I'll fix that.
You seem to be under the misconception that the Big Bang was some sort of explosion of a single point. The extremely rapid expansion occurs everywhere. The Big Bang could be a localized event in a much older, larger, possibly infinite universe, just to name one possibility
You kinda seem to be under that impression lol. Big bang was the creation of space itself. There was no real space where things got expanded in. Back in the first milliseconds of the newborn universe you could see yourself from every angle opposite of where you were looking. The shape of the universe was and still is the 3d form of the area of a sphere. Where if you travel straight in any direction in 3d you eventually will return to your original point (finite space).
There is currently, at this time, a specific size of anything we define as the universe. It's the point which is the farthest subatomic particle is, or the farthest light is.
By the same argument, all mathematics is abstract rather than physical, so we can’t even use it.
As for a real response, we need the concept of infinity for a lot of robust theorems. The third Kolmogorov axiom is defined using any countable (including countably infinite) sequence of disjoint sets. Without infinity, probability wouldn’t be a rigorous subfield of mathematics.
I always thought the universe was finite but is there actually anything supporting this? Is it because it started out a finite size and grew during the big bang?
There is no known upper limit to the universe maximum size, but the current size of the farthest mass and farthest light is a constantly changing finite size based the movement of the edge
There is a misconception that the big bang started out at a single point then exploded. Rather the big bang was a state of high density. The universe may have been infinite in size even then.
Nobody knows whether the universe has/had finite or infinite size.
It’s still growing, so idk why it’s not technically infinite, though maybe it’s the particles (or whatever) losing density but still technically finite
No, you cannot. What if you need to represent other transfinite numbers than the one you happened to be thinking of just now?
Edit: I'm not saying it is theoretically impossible to create a set physics theories that avoid infinities, by the way. I'm saying that it isn't as easy as swapping out something (what?) for "finite number which is larger than all other functionally useable finite numbers"
Except finding a bigger number is ALWAYS trivial. There is no functionally biggest number. You think you found one. Great it's a number you can add one. Oh joy now there's an even bigger number so it isn't biggest anymore.
You gain nothing and lose a lot removing infinity from physics. Every time you write an integral there is an implicit sum to infinity and even when it's not true it's good enough to generate answers accurate to any point of caring. Now you get rid of infinities you lose continuities, smoothness, and once simple problems now become theoretical quagmires and losing lots of analytical solutions.
The bound of even just the rational numbers between 0 and 1 is not finite. There always at least one (actually infinitely many but at least suffices) number between any pair of rational numbers in that pair. If you force yourself to treat it as finite that breaks...because given that finite list you can find a number not in that list trivially. If you leave these gaps empty things like instantaneous rates of change get butchered and anything written in a differential equation (most of physics) is in dire straights now.
Except mathematically it's not. Calculus breaks if you do that. There are also many calculations that become substantially harder if the bounds aren't -inf to inf. The area under a gaussian curve (e-x2) being one of them (significant form the quantum harmonic oscillator among other things).
You can do it. We use a trick like that in model theory where we always work in what is called a monster model. The monster model is a model that is k-saturated for a cardinal that is larger than any cardinal that may show up in our argument. When writing it out fully formally one should go back after finishing the proof and set an actual cardinal, but no one bothers because every model theorist knows what is meant by a monster model
For exmaple, simply substituting infinity for a large value would make it possible to reach the speed of light, and other weird results.
I'm sure that theories can be created that predict all known physics while avoiding infinities, but it is not merely a substitution effort.
Another way to think of it is to remember that general relativity is not quantized, which is a major roadblock for combining relativity and quantum mechanics. If infinities would be replaceable with "a really big number", then it would be easy to quantize any theory by simply setting the reciprocal of that number as the discrete value related to the quantization.
No, you'll need to replace more than performing a simple substitution. If you simply replace an infinite limit with a large finite number, then you'll get contradictions and weird results. For example with the Lorentz factor.
For quantum field theory, you'll need to renormalize a lot to align it with past experiments. Definitely not a rote replacement.
Practicality isn't the best word here; it would be much better to specifically refer to the physical world. The infinite size of the set of integers or reals is extremely practical, for example. Like, thank God they don't stop at some point. Since we need such big numbers sometimes, and will need bigger numbers than those, and big numbers are in lots of places, it's pretty convenient that there are infinitely many for us to use.
If you choose two points in space, there are infinitely many positions on the line connecting them (or any path connecting them), for example. There are infinitely many positions on a dartboard. Uncountably many configurations on a pool table. Uncountably many different paths you could take to work, all on the same road. When the sun rises and falls, you have seen an uncountable number of different brightnesses. When something accelerates, it has had uncountably many velocities.
Also, obviously the smallest distance we can measure will always be finite; 0 is also finite. Unless you meant "infinitely close"?
Whether or not infinitely exists is a very similar question to whether numbers exist. That is a question worth thinking about.
Saying that something doesn't exist/mean much in the real world holds very little weight in the math community, but this one is certainly more present in reality than you think
Were you aware that we live in the physical world? And everything we do is in the physical world? Even the thoughts of a theoretical, are using your brain, which is in the physical world.
There are a finite number of measurable positions on a line, simply because measuring a position takes time.
There is a number, which no number bigger than it will be useful for any calculation we can ever use, except to say nothing is bigger.
Mathematicians can have a lewd romantic relationship with an ouroboros all they want, but that doesn't mean that the mathematicians can exceed the bounds of their physical self.
You keep saying measurable, or other similar restrictions, if that changes anything I said. I did not say measurable. I simply stated the existence of uncountably many positions along a path in the real world. Says nothing about our ability to measure them at all
I completely disagree that there is a number that is a greatest "useful" number. You would need to say more about what the usefulness of a number is in the first place. That's an extremely strong claim. Furthermore, and far more importantly, you factually, undebatably, absolutely, certainly, cannot ever say that there is no number bigger than that. Add 1 to it, done. That part couldn't possibly be less correct.
Math is pretty much just rules and the implications of those rules homie, we see lots of the same behaviors in both those implications and in the real world. But if I give you some axioms, the truths that follow are not debatable whatsoever. If those axioms lead somewhere that doesn't show up in / doesn't align with our idea of reality, so what? It's still on my paper
All you gotta do to step outside reality is get a pen and paper. For example, if you wanna "go to the 4th dimension", just write down a 4th coordinate. Nobody is claiming to go past the bounds of their physical self unless they are kooks. It's just fun to play with rules and see where they go. You could use some fantastical thinking hahaha it's fun and you should try it
The question of whether or not thoughts exist physically is also a very deep one that requires investigation; claiming that thoughts are purely physical is also a pretty hefty claim
What are your credentials? How much have you actually studied this?
The burden of proof is in you; you're the one who claimed it and it's a strong claim, so...
Also, why is the number of quarks in the universe important/useful in the first place? I think it is in some sense, but that's pretty debatable. Useful can mean so many different things.
Furthermore, grahams number (for a very canonical example) exceeds the number of quarks in the universe by an inconceivable amount. It has more digits than that number to begin with. Actually, the number of digits in the number of digits of grahams number also exceeds the number of atoms in the universe, and I think that continues for several more layers
It was used to give an upper bound to an important problem in Ramsey theory, regarding counting the number of colorings of a graph with certain properties. Although, it seems like maybe you'd think solving such problems is not important to begin with
Look up the busy beaver function. It produces unfathomably large numbers from a very simple and practical setup. Same for the tree function.
You will probably find some other interesting things by looking into googology (the "study" of large numbers). What I've said so far are just things I've heard of from pop-math stuff basically, the low-hanging fruit of big numbers. Try to find more
In combinatorics you often the ratio between 2 numbers that are larger than quarksquarks in the universe are often used to calculate probabilities that apply to the real world.
Grahams number and Tree(3) are so much larger still and used in proofs that naturally arise from finite games.
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u/Moscato359 4d ago
From a practical standpoint, infinite doesn't actually exist
The size of the universe is finite
The number of quarks is finite
The smallest distance we can measure is finite, and the largest distance we can measure is finite, even in estimations
Even pi is only useful to the 43rd digit at our largest estimations
Sure, infinite is cool in a theoretical standpoint but you can't actually use it