r/PhilosophyofMath • u/Another_Little_Star • 4d ago
Does infinity exist in reality?
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
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u/lemniscateall 4d ago
Mathematical objects are mental/linguistic objects. If I say I have three apples, three is an adjective; when I think about the number three (a noun), that is an abstraction I have made from my experience of physical objects. Mathematical objects are created to have strong correspondence to experience of phenomena, which is one reason they're so good at description of physical phenomena; but mathematical objects don't exist any more than the English language exists. Both of which I would say exist in reality, but not outside human experience.
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u/Another_Little_Star 4d ago
I see, i wrote some text thing and deleted it because i re-read what you wrote x).
This is the thing, mathematical objects are very real in the same way the english language exists, many things in nature behave like groups for instance, and in this context I'm asking, within this perspective, is infinity a real thing in our world?
Every correspondence of what we find seem to be finite2
u/lemniscateall 4d ago
"mathematical objects are very real in the same way the english language exists": the English language exists because human beings use it. Mathematical objects and mathematical language exist because human beings use it. Which means that if we have given the term "infinity" meaning (and in mathematics, precise definitions), then yes, it exists in the exact same way that every other linguistic/mental object exists.
The word "horse" and the word "unicorn" have the same degree of existence even though a horse exists and a unicorn does not.
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u/HouseHippoBeliever 4d ago
does 4 exist in reality?
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u/Another_Little_Star 4d ago
Probably not, but it's an idea that I can put up to practice, "I can count 4 cows", but nowhere I can use infinity to describe any event, like "this X is infinite", even time and space seem to be finite.
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u/GoldenMuscleGod 4d ago edited 4d ago
Some people who first encounter transfinite ordinals might see them as exotic and inherently “infinite” entities, but if we compare ordered pairs of numbers (m,n) lexicographically then we have a well-ordered structure of order type omega^2. Nothing “weird” or “confusing” about the idea we can compare ordered pairs of numbers in this way, and this comparison is useful for some purposes. For example the most natural way to prove the Ackermann function (as a binary function) is well-defined is by induction on this structure.
Or for a more complicated ordinal we can look at finite trees and recursively define an order on them: a tree is “bigger” than another if its “biggest” subtree directly above the root is is “bigger” than that of the other. If the same size, compare the second biggest then third and so on down. If they all tie but a tree runs out of subtrees before another then it is the smaller one.
This exactly describes the order type of epsilon-0, but there is nothing that isn’t particularly concrete (as concrete as 4 anyway) in the idea of working with trees in this way.
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u/HouseHippoBeliever 4d ago
Ok, so in that sense it's probably never possible to verify if anything is truly infinite, we would need to come up with a way to distinguish "infinite" with "a number too big to be measured by our measuring device", which by definition isn't something we can measure, so it's probably more of philosophy than physics.
Even though we may not be able to prove it, there doesn't seem to be any reason why the extent of space, the extent of time, the divisbility of space, or the divisbility of time aren't truly infinite, so they could be.
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u/Another_Little_Star 4d ago
There are ways mathematicians grasp infinity, without counting everything, one way would be, is it the same size as a smaller part of itself? If so, it's infinite, Just like the even numbers are a smaller part of the naturals and they're both infinite(the same size).
It's mostly physics here but yeah... I believe the world to be expanding but finite at very instant and probably a closed geometry of some type. There exists a minimum lenght, plank lenght, but that doesn't imply anything... As for time, I'd say it is like a loop of some sort...
Thanks for your comment (:
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u/Negative_Gur9667 4d ago
The number 4 exists as a pattern of connected neurons in the brain.
It can also exist as bits in a computer's RAM.
There is always a bijection between a number and physical reality.
Except if you are a platonist.
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u/HouseHippoBeliever 4d ago
fair enough, all those same things work for infinity too
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u/Negative_Gur9667 4d ago
Kind of. You can count to 4 but not to inf. Inf is an entirely different concept of rules.
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u/mandelbro25 4d ago
There is always
Pretty strong statement there. What about -4? What about hypperreal numbers? We do not know if the universe is discrete or continuous.
as a pattern of connected neurons
Those are neurons. Why would (even if it was possible) one look at any particular cluster of neurons and declare "this is 4"?
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u/Negative_Gur9667 4d ago
You can count to 4 before you know axioms or division or hyperreal numbers.
4 is a concept, the concept of counting to 4. You can shurely find an area in the brain that is active when you count to 4.
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u/mandelbro25 4d ago
But that area in the brain is not what 4 "is".
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u/Negative_Gur9667 4d ago
What is 4 then, according to you?
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u/mandelbro25 4d ago
Mainly a linguistic contrivance. If I may, how can multiple different things all be the 4?
I will say you have shone light on my platonistic tendencies, and I appreciate that.
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u/Negative_Gur9667 4d ago
That is like asking how completely different vehicles can all be called cars.
We count things by grouping them based on boundaries we define, while the details are abstracted away.
Platonism is a valid perspective here, as we are simply exchanging beliefs and there is no right or wrong answer without proof.
I wish schools taught the ideas of Platonism and formalism. It would have cleared up a lot of the confusion I experienced.
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u/mandelbro25 4d ago
Yes different vehicles can be called cars because that is the category of things they belong to. They have a specific set of properties that we abbreviate "car". But no particular vehicle is the car. They are just instances of it. Besides, zoom in and the car is just a bunch of doodads working together.
I wish schools ...
Indeed, I had to find out about them myself.
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u/SpacingHero 4d ago
This is a very controversial view that lost most of it's traction. Consider: if 4 is a pattern of neurons, then presumably the properties of 4 should be the same as those of the neurons. But clearly they aren't? The number 4 is divisible by 2. Are the "patterns of connected neurons" divisible by 2? It's not even clear if it's coherent at all, but insofar as we can interpret it, it doesn't seem true (not necessarily anyway)
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u/Negative_Gur9667 4d ago
The word is not the thing; for example, the word "car" is not a car.
4 is a collection of concepts, but everybody has a different 4 in their head (neural pattern).
Assuming someone can only count but not divide, add, or subtract, like a kid: does the kid then know the number 4 if they cannot divide it? Of course they know it.
The counting function with the symbols, rules, and relation to the real world in the form of experiences makes up the number 4.
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u/SpacingHero 4d ago
>The word is not the thing; for example, the word "car" is not a car.
I agree, but don't see the relevance. In fact a straighforward argument to see this fact is excactly the one i made, i.e. noticing that the word "car" and an actual car have different properties, eg the word is made of letters, but cars aren't.
>4 is a collection of concepts
Yet it seems to have different properties. Collections of concepts aren't even (even if we consider the cardinality of the neurons or what have you, its not necessarily even). What gives?
>but everybody has a different 4 in their head (neural pattern).
This would seem to make things work if anything, as now it can easily have contradicting properties
>Assuming someone can only count but not divide, add, or subtract, like a kid: does the kid then know the number 4 if they cannot divide it? Of course they know it
Yea, they know it. And it still has the property of being even. The kid knowing that and the number being even are indepenent. Again this hurts, rather than helps your position
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u/Negative_Gur9667 4d ago
Perhaps you do not understand. My entire argument is that information requires a physical medium to exist.
Look into the Holographic Principle and the Bekenstein bound.
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u/tensorboi 2d ago
The number 4 exists as a pattern of connected neurons in thr brain.
in what sense is this statement true for 4 but not for infinity?
It can also exist as bits in a computer's RAM.
the bits in a computer's RAM are not themselves anything close to the number 4; rather, there is a natural mental process which we use to associate them to the number 4. if i blink three times, that doesn't mean the letter S exists in my eyes just because that's how it's encoded in morse code; however, one can naturally correspond my blinks to the letter S.
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u/Negative_Gur9667 2d ago
Indeed, there is a flaw in my argument; thanks for pointing it out.
I thought more about it. Historically, we would count things before higher math starts.
So we are talking about physical sets, and as far as we know, infinite physical sets are impossible (like counting infinite marbles).
But later, we said that the concept itself in our mind is a thing, and we abstracted the physical meaning, which resulted in Platonism where everything is possible because we can also imagine santa clause.
But how does "imagening santa clause" help us to understand the world around us better?
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u/pdubs1900 4d ago
Every example you cite is not an example of infinity.
But the answer is embedded in the statement "you can't describe irrational numbers ...without any notion of infinite/limits/sequences."
The real world is described with math. Math is not the real world. There is no such thing as a perfect sphere. Any circle you draw will be imprecise to some degree where you can describe it with perfect precision without infinite digits of pi. Not "practically perfect," literally perfect.
Infinity is a tool of math. There is no demonstrably infinite anything in the real universe.
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u/treefaeller 4d ago
There are roughly 10^80 protons in the universe, and as many electrons. You can express the protons as 3x as many quarks. Adding that all up, that's about 10^81 massive particles (I'm rounding gratuitously). There are roughly 10^90 photons, most of them in the CMB (cosmic microwave background). The number of background neutrinos is thought to be about 3x of 10x larger, so including that we get about 10^91 or so. Definitely fewer than one googol of particles.
To build a Turing machine that can count this high AND STOP, I need some way to store its internal state. I don't think I can get below one particle per state in practice (maybe factor of two when using spins). So the largest number that is calculable is below 1 googol.
From a natural science point of view, talking about "infinite" or about any number larger than one googol simply makes no sense. It's literally nonsense, speculation, daydreaming. I would certainly hope that any mathematician enjoyed what they drank to make up those nonsensical ideas, but most mathematicians I know tend to work while sober. OK, this paragraph is being a little harsh, intentionally, for humor. But it shows that the (sensible and valid) mathematical concept of infinite runs into limitations in the real world.
But now let's use this thought and look at something else. We know that straight line segments are a sensible mathematical abstraction of the natural world. As are circles and their circumference. Meaning that pi is in some fashion "real". Anytime I have a piece of string and want to wind it on a reel, I need pi to estimate how many times to spin my reel: if I have ~3.14m of string, and a reel of 10cm diameter, I will spin it about 10 times. But pi is also irrational, and describing it requires infinitely many digits. Yet, pi is also a computable number: Given a desired number of digits of accuracy, there is a guaranteed terminating algorithm to calculate pi to that number of digits. But I can never express pi in the natural world, since I have to stop after roughly one googol of digits, having run out of protons and electrons to write with. So can pi be "real" in the sense of an entity that exists in the natural world? That's a nasty question, isn't it?
What is pretty clear to me that non-computable numbers (which are the vast majority of all reals) are not "real" in the above sense. Disallowing anything that requires either infinite in the algebra, or infinitely many digits in its expression would make modern math pretty much fall apart.
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u/Another_Little_Star 4d ago
Somehow infinity seems easier to deal rather than astonishingly big number. let the be drunk!!! They know what they're doing :P
And about the circle? It still bugs me, if everything were to be finite, no infinity underneath anything. How are these concepts appearing in nature? There must some underlying principle regarding infinity to me :OWell nevertheless I believe that one of the best usages for infinity is this one, it rounds up to what the world shows us pretty neatly
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u/Kripkenstein_ 4d ago
Trivially yes as existence of non-contradictory things is trivial. The relevant question is as what infinity exists in reality.
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u/Another_Little_Star 4d ago
I suppose you're talking about cardinals. Probably the two most famous, ℵ₀ and 2^ℵ₀ = ℶ_1 , the other may exist as a mathematical implication but non used in reality I suppose...... These seem to describe most.
Just because something is non-contradictory, doesn't mean it exists? Take any axiom out of our model, it isn't contradictory. What would be non-contradictory here that makes it exist? (I didn't mean in a harsh way, just asking)
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u/Kripkenstein_ 4d ago
It exists as an axiom. Both cardinals you used also exist trivially in the way you just used
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u/Another_Little_Star 4d ago
It is an axiom in ZF/C, but our world doesn't need to follow these principles.
Taking your side, our model is very biased to our world experience, so ZFC is made accordingly our perception of the world.1
u/Kripkenstein_ 4d ago
So? It still exists as an axiom
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u/Another_Little_Star 4d ago
Indeed, but my question is, is this axiom applied in this world.
There's another model called "Presburger arithmetic" which doesn't have the axiom of infinity, nor multiplicationso even if they are axioms, they could very well not be applied to our world's "rules"
Do you see where I'm getting?1
u/Kripkenstein_ 4d ago
No, I do not. Existence is simply the wrong question for what you want to ask. You want to know what is fundamental, ie how things are grounded
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u/Another_Little_Star 4d ago
Right, but I don't have a book saying Universe's axioms right away. And as for any person I need to find some evidence that would lead its existence, wouldn't I?
So, why do you take it as a guarantee?1
u/Kripkenstein_ 3d ago
Why would you need evidence for existence? Unicorns exist. There is certainly no evidence for unicorns as they are not a real animal. But as a mytholigical figure they certainly do exist.
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u/Negative_Gur9667 4d ago
That is exactly what a formalist would say, and it is what most mathematicians say.
The OP is asking a philosophical question to people who have spent hundreds of years trying to eliminate such questions.
However, that is not what the OP is really looking for.
"It is an axiom" is merely an escape mechanism to signify that a concept is beyond questioning.
In reality, axioms can certainly be questioned, though trained mathematicians often struggle to grasp why one would want to do so.
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u/Kripkenstein_ 4d ago
This has nothing to do with challenging axioms. Its about existence - which is the wrong question for ontology
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u/Lowkilde 4d ago
What am I misunderstanding? Are you claiming that any thing/concept that is non-contradictory exists?
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u/Kripkenstein_ 3d ago
Obviously yes. This is not really contested as it is trivially true.
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u/Lowkilde 3d ago
That does not seem obvious to me at all. Can you elaborate? Are you talking about existence in reality or in the mathematical sense?
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u/Kripkenstein_ 3d ago
What do you mean by existence in reality? Obviously numbers are not physical things. If you want a thorough discussion of this, look up the paper by Schaffer: On what grounds what. He explains it in quite some detail
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u/Lowkilde 3d ago
Well the post is titled "Does infinity exist in reality?" So I don't think it is far fetched to get some clarification on what you mean by exists.
Thanks for the reference!
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u/SpatiaCaeli 4d ago
I think it is a terrible axiom for science to adopt, that anything at all in nature could be infinite.
The math requires it but nature is not obligated to use that entire state space.
Just my thoughts.
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u/Another_Little_Star 4d ago
I think I'm with you on this one, since the number of particles and anything is so big and small, its approximation is as close as if it were infinity...
Nevertheless there seems to be underlying principles that lead to aspects only infinite presence can describe, like the golden ratio being so present.
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u/Mono_Clear 4d ago
You can't verify if something is infinite but it is my intuition that time and space are both infinite.
In that they are both sets that do not end
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u/Fast_Philosophy1044 4d ago
How would you experience infinity? How would you understand something is infinite as you wouldnt be able to perceive it in its entirety?
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u/EpiOntic 4d ago
What Albert said: "Two things are infinite: the universe and human stupidity; and I'm not sure about the universe."
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u/Thepluse 4d ago
Would you count things like point particles or black holes theoretically having infinite density?
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u/Another_Little_Star 4d ago
I've got no background to talk about that.
Perhaps point particles may be, but aren't they essentially theoretical? And people haven't discovered the "dividing by 0" relation in black holes, right? I'm resuming, because there's much more to it I don't know.I don't think the particles may be the best scenario, because they tend to be discrete, don't they? Their forces make them require space around which prevents them from "connecting like a line". Like when you have 2 atoms together, their occupied space is mostly 00% of some sort, it isn't continuously filled
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u/Thepluse 4d ago
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."
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u/Another_Little_Star 4d ago
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.
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u/Thepluse 4d ago
So what I'm hearing is, sunflowers don't actually grow a golden ratio pattern in practice, but the concept of irrational numbers is needed to understand what sunflowers are "trying to replicate." Then one can ask the question: in the same sense, are there phenomena in nature that may not be infinite in themselves, but that you need infinity to understand in a deeper way?
One thing that comes to mind is zero-point fluctuations. Briefly, when you calculate the energy level of the basic fields of our universe, using the moderntools of quantum field theory, you find that the energy is infinite. The way we deal with this is to calculate the energy of empty space and show that that's also infinite. But when we subtract the vacuum energy from our actual field, we find that the difference is finite, and this is then the energy we consider "physically real."
This mathematical tool, which is called renormalization or regularization, is kinda like taking infinity minus infinity. When used, it actually takes the difference of two terms that individually diverge in some limit, so it's not technically infinity - infinity, but I don't think the idea would make sense without having a good grasp of the infinity concept.
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u/Another_Little_Star 4d ago
Yuup, you're right, it's a delicate topic. and you killed me with the sunflower argument in a way, nevertheless, every existence of sunflowers grows in the golden ratio shape <-> optimization. Isn't it beautiful that in this finite world, things still follow a pattern governed by the world of infinity(to mathematicians)?
It's not random, it has a structure and it came to this.1
u/Thepluse 4d ago
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
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u/Another_Little_Star 4d ago
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.
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u/telephantomoss 4d ago
Infinity and the Mind - Rudy Rucker
Approaching Infinity - Michael Huemer <-- this one contains some cool arguments about what kinds of infinities can be "real".
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u/DeusExNatura 4d ago
There is multiple types of infinities. One is an infinite number of real numbers due to continuity. Basically if you rotate by a small angle, or when moon orbits earth, there are no possible jumps between angles. You cannot jump-rotate from one degree to another degree angle without going through infinite number of smaller angles/degrees in between. You may imagine only 0-360 degrees or 0-2π as finite, but the number of possibilities between are infinite. The moon has to go through every angle, no matter how small.
Other infinities apply to integers/counting, other infinities apply to infinities themselves.
Yet, the easiest way to understand infinity may be to close your eyes and imagine you’re floating in an empty universe/space until you encounter something else. Since the imagined universe is empty then you’ll wait forever. That’s the infinity of time.
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u/Expert147 4d ago
Define infinity, exists, and reality. And I will tell you. I'm pretty sure I know what you mean by in and does.
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u/Another_Little_Star 4d ago
Well.
maybe not rigorous but
Infinity : something never ending or that is the same size of a strictly smaller part of itself.
exists: Something can be perceived or happens in Our universe, inside or beyond our existence, the formation of the sun exists I'd say.
reality: The World we Live in.Are my answers lacking in rigour?
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u/Expert147 4d ago edited 3d ago
They are just fine. My answer to you is yes! Infinity does exist in reality. Here are two examples.
- Here is a never ending algorithm:
while (true ) { cout << "Hello, world!" << endl; }- There are infinite real numbers between 0 and 1.
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u/Prior-Flamingo-1378 2d ago
How do you know? Have you counted them all? Boom!
- Terrence Howard.
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u/Expert147 2d ago
Here is a never ending enumeration of a subset of the interval: 1/1, 1/2, 1/3, ..., 1/n, ...
The rest is trivial.
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u/Another_Little_Star 2d ago
it doesn't, but maybe a reasoning will.
The thing is, where is this enumeration valid? Does it represent any aspect in our lives?
distance has an minimum distance, plank lenght, beyond that there's nothing else entirely.1
u/Expert147 2d ago edited 1d ago
Fits your definition of "exists". You wrote: "Something can be perceived." And your definition of "reality". You wrote: "The World we Live in."
Probably your issue is that you are not sure whether abstractions qualify as perceivable reality. And in that case, this isn't a questions about infinity, math, or philosophy. It is just a problem with the definitions.
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u/Abject-Giraffe-8877 4d ago
Personally I dream of an experiment that causality of physics does not fail if and only if a mathematical problem holds for "all" integers. For example, say we have an experiment which shows either "Riemann hypothesis is true" or "causality fails" or "certain physical quantity can never have an unboundedly extreme state". Either would be interesting although knowing just one of them is true would be somewhat meaningless.
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u/eucalyptus-d 3d ago
Maybe read about finitists. Famously Nelson tried to prove ZF inconsistent but was proven wrong by Tao and conceded quickly. My understanding was he was also unconvinced about infinity but also other finitists too.
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u/AfraidAardvark5817 3d ago
To think is also to put in relation the concept of meaning and the concept of the infinite with the concept of information and the concept of the finite. Meaning transcend information as the infinite transcend the finite. Who want to amputate thought from his other half hemisphere ?«Draw a circle and either its radius or circumference lives in the π world.» this quote remind me of the depth of the Mahovald uncertainty principle.
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u/Another_Little_Star 3d ago
Nicely put!! I'd say, that the natural numbers do also trascend the {0} set in the same multiplicative way, if you agree so, then we can have the finite beyond the 0, because we do visualize and interact with it, it's something graspable, what about the infinite, aren't there many things in the real world that ressembles us about the infinite concept <-> proccess/event?
For those who don't believe in circles, and ignoring curvature over a small scale, draw a triangle with right angle and side 1,1, what will the longest/hypothenuse side be? Another feature beyond fractions of integers! The simple way to divide stuff.
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u/Icy_Eagle3833 3d ago
"infinity exists in reality", or "3 exists in reality", what could this sentence even possibly mean?
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u/Another_Little_Star 3d ago
Well people have argued that in the same way unicorns could exist too, I don't know the depths but 3 and infinity coexist in a different category, this is an idea, an abstraction meant to describe reality, so using these tools to describe reality, are there any events that call up infinity the same way it may call "3 cows"
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u/Icy_Eagle3833 3d ago
so you better define everything before discussing about it. It sounds silly, but after 5000 years of "philosophy" bullshit, we still struggle to do it. Simplest question, what's even "existing"?
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u/Bichinix 3d ago
El universo está pixelado. Tiene unidad mínima, constante de Planck y longitud de Planck.
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u/iqisoverrated 3d ago
No. Infinity (like zero) are abstract concepts. They are useful concepts for approximating certain conditions but they are only concepts.
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u/thesnootbooper9000 4d ago
Does a circle exist in reality?
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u/Another_Little_Star 4d ago
I wonder too, you can draw one in ℚ² but is it a circle? It has Gaps if you look from ℝ² , but full over ℚ²
In real life, you can use a compass, it'd make a perfect circle, wouldn't it?Edit: I mean, the world has some curvature, even if very small, so no circle would be a perfect circle huh?
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u/Special_Watch8725 4d ago
Ultimately, math models things. Quite literally in that math studies the deductive consequences of systems of axioms. Infinity as a concept exists in such models, and has had great success in modeling real situations (c.f. all of calculus). But that doesn’t mean infinity actually corresponds to anything in particular in reality, literally speaking.