Infinity does not exist in the real world.

[thefisherman]

Maybe this has been posted a million times, and flame me if it has, but does anyone disagree that infinity -- as a concept -- does not exist in the real world. Maybe in math, but not in the real world. It seems as if a number of questions here ask where the logical error is in something, and many times this is where it is.

Anyway, if someone thinks they have an example of a "real world" infinity, I will gladly explain why it doesn't exist. However, be warned, that most often infinity doesn't exist becaue whatever a person is talking about requires infinite time, which everyone should know, certainly is not true in our universe.

[Galois]

What does it matter? Infinity as a concept in an integral part of mathematics, and mathematics has nothing to do with the real world (i.e., physical world).

[Bork]

I am not sure what you mean by 'infinity the concept', but nonetheless here are some examples off the top of my head that I am curious what you have to say about.

The amount of different possible sentences is infinite.

The number of spatial points in any extended volume is also infinite.

God (if he exists) could create an infinitely large object.

[FredBoots]

What's at the center of a black hole?

[Demiparadigm]

[ QUOTE ]
What's at the center of a black hole?

[/ QUOTE ]

Any mass with a gravitational pull such that the escape velocity is greater than the speed of light.

A more important question is what is the point?

[billygrippo]

existence is quite possibly infinite.

there are infinite solutions to some puzzles.

sup bro has infinite wisdom.

[bunny]

I dont see the problem with concepts occurring in the real world. Infinity is a concept and is contained within the non-physical part of the universe. After all, you cant point at a "lump" of unhappiness yet unhappiness clearly exists in the real world.

[Demiparadigm]

[ QUOTE ]

The amount of different possible sentences is infinite.

[/ QUOTE ]
This is not true as long as we assume that sentences can only be made from words. Since there are a finite number of words, it follows that there are a finite number of sentences, though that number would be very large.
[ QUOTE ]

The number of spatial points in any extended volume is also infinite.

[/ QUOTE ]
I don't think that this is a good "real world example" but along the same lines is there are an infinite number of places to stand in a room, or an infinite number of positions that you can make with your hand.
[ QUOTE ]

God (if he exists) could create an infinitely large object.

[/ QUOTE ]
Like the universe?

[billygrippo]

[ QUOTE ]
[ QUOTE ]

God (if he exists) could create an infinitely large object.

[/ QUOTE ]
Like the universe?

[/ QUOTE ]

isnt the univrse finite?

[atrifix]

[ QUOTE ]
This is not true as long as we assume that sentences can only be made from words. Since there are a finite number of words, it follows that there are a finite number of sentences, though that number would be very large.

[/ QUOTE ]No, this follows in essentially the same way that infinite numbers do: we can always add the word "very" or whatever to a sentence. Or, consider the language {0, 1} where words are composed of the Kleene closure {0, 1}*. I don't know what a "real world" example is supposed to mean, though.

[ QUOTE ]
I don't think that this is a good "real world example" but along the same lines is there are an infinite number of places to stand in a room, or an infinite number of positions that you can make with your hand.

[/ QUOTE ]Presumably, this could be false. If quantum physics is true, then we should expect that the matter that occupies space is discrete.

[soon2bepro]

infinity is just a concept. we know of nothing that is infinite; i agree with the thread creator (how do you call that? OP? no idea what that stands for /images/graemlins/smile.gif)

(edit: oh, maybe Original Poster)

[thefisherman]

This correct on the quantum part. But more importantly, the point is infinity is a theoretical concept. Only that.

Infinite number of places you can stand? That would require an infinite amount of time to actually stand in all those places. Be "real world" here. Stand in all the places you want, but you can only stand in a finite amount. Plus, as mentioned before, the number is still finite due to the fact that quantum mechanics requires uncertainty in position, so the idea of position as a concept is flawed.

Secondly, I would say a sentence is something someone uses to communicate language. An infinite number of infinite length sentence, while in math, is possible, but not a "real world" example. Time prohibits it.

>>>>>>>>>>>>>>>>>>>>>>>>>
The point is:
People seem to think of infinity as something that is real world. To those of you who differentiate real world and theoretical, congrats, that's the point. But I think it's astounding the number of people who believe infinity transcends that boundary. I'm just out to show that it does not. It is confined only to the mathematical/theoretical region.

[StinkWater]

there are an infinite number of dreams i could have tonight.

[Riddick]

Matter exists infinitely, since it cannot be destroyed.

Once you are dead, an infinite amount of time will pass before you come back to life.

[Smock8]

You seem to be arguing that infinity cannot be acted out in any way. However this does not mean that infinity deosnt exist, the example of an infinite number of possible sentances is a good one, yes there is an infinite number of sentances, no you cannot come up with a list of them because of the nature of infinity and the fact that we are assuming that we live in a finite time universe.

[Cyrus]

[ QUOTE ]
Here are some examples off the top of my head:
<font color="white"> . </font>
[1] The amount of different possible sentences is infinite.

[2] The number of spatial points in any extended volume is also infinite.

[3] God could create an infinitely large object.

[/ QUOTE ]

The OP specified that our subject is the real world.

Your example Nr 1 is incorrect. (It is a very large number but not infinity!) Your example Nr 2 belongs to the realm of Geometry, and specifically Euclidean Geometry. Again, not (http://mathworld.wolfram.com/Non-EuclideanGeometry.html) of the real world. While, of course, example Nr 3 is about fairy tales.

(I am using the term "real" in the conventional sense. I have difficulty defining reality, sorry.)

[Sephus]

[ QUOTE ]
This is not true as long as we assume that sentences can only be made from words. Since there are a finite number of words, it follows that there are a finite number of sentences, though that number would be very large.

[/ QUOTE ]

this reasoning is invalid for the reasons in the first response to it. the limit to the number of possible sentences comes from the limit to how much information can possibly be stored in our universe.

[Sephus]

[ QUOTE ]
yes there is an infinite number of sentances, no you cannot come up with a list of them because of the nature of infinity and the fact that we are assuming that we live in a finite time universe.

[/ QUOTE ]

no there's an infinite number of possible sentences only in theory. in the real world a sentence can only be so long as it's possible to store (or express) the information contained in the sentence using matter in the universe. at a certain point your sentence couldn't get any longer without requiring that no trace of the beginning of the sentence continued to exist.

[Sephus]

isn't there an infinite number of different points in space and time? just because we can't measure precisely enough doesn't mean they aren't infinite "in the real world" right? and just because we use theory like geometry to investigate things like space doesn't mean that the real world isn't being described, right?

[Roy Munson]

What is the "Real World"? I know that the TV show is infinitely unwatchable.

[bearly]

you use 'concept' and 'example' as if they were the same thing. they are not. you should know this..........b

[Bork]

[ QUOTE ]
Here are some examples off the top of my head:
.
[1] The amount of different possible sentences is infinite.

[2] The number of spatial points in any extended volume is also infinite.

[3] God could create an infinitely large object.


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The OP specified that our subject is the real world.

Your example Nr 1 is incorrect. (It is a very large number but not infinity!) Your

[/ QUOTE ]

No the number of possible sentences is infact infinity. You could make a sentence of any length and of almost any order.
If you are still not convinced remember:
You can always put any possible number in your sentences in any possible order.

He said the concept infinity doesn't exist in the real world. The concept does exist and its invoked in each of my examples. Now if he means there are no physical infinities he might be right, but I don't see any empirical reason to think this.

[thefisherman]

How do you know either of these are true? You're just guessing.

[SoloAJ]

[ QUOTE ]
[ QUOTE ]
Here are some examples off the top of my head:
.
[1] The amount of different possible sentences is infinite.

[2] The number of spatial points in any extended volume is also infinite.

[3] God could create an infinitely large object.


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The OP specified that our subject is the real world.

Your example Nr 1 is incorrect. (It is a very large number but not infinity!) Your

[/ QUOTE ]

No the number of possible sentences is infact infinity. You could make a sentence of any length and of almost any order.
If you are still not convinced remember:
You can always put any possible number in your sentences in any possible order.



[/ QUOTE ]

Aren't you goign back into the realm of mathematics by doing so? I agree that there are a finite number of words and an infinite number of numbers...but...

Once yousay that if you put a number in it, it is infinite...I think you're cheating the "real world"

[gmch713]

you need to distinguish between degrees of infinity that you are talking about. as far as countable infinity there are many examples in the real world, such as the set of different books that can be written or the number of places you can stand. higher degrees though really are only applicable to math however these theorems and techniques are used in real world applications every day.

[Brom]

An infinitly long sentence would be one hell of a run-on sentence. If the sentence has to make sense or be grammatically correct, then there's no way there are infinity of them

[MaxWeiss]

Some of these responses are okay. Aside from all the stupid responses, yes, infinity does exist. In math, and in reality. Physics describes reality. Many of the equations for desribing reality use infinity. While we can get into a philosophical discussion about exactly what would qualify for something to be infinite in some respect, the fact that we MUST have the concept in order to describe reality accurately is proof alone that it does in fact exist. Somebody asked about a black hole and its singularity, which is an infinitesimal point.

[Cyrus]

[ QUOTE ]

No the number of possible sentences is infact infinity.

[/ QUOTE ] No, it is not. It is simply a very large number. There is a difference.

You can start by imagining the largest possible single sentence, which contains every single word of the English language once! Next, you can imagine the same sentence but with the words re-arranged. It's a new sentence. This would mean that there are x possible permutations of that ultra-sentence, where x is the number of possible permutations of y, where y is the number of all words in the English language. Start down from there, by taking out a word and re-arranging every time for y-1. And so on. Then you get on with mutliple use of the same word. And so forth.

Very, very large -- but not infinity. As long as the number of words in the English language is not infinite, then the number of possible sentences with English words is not either.

The concept of infinity is very specific in mathematics. We can certainly say that a number approaches infinity (or we can say, frivolously, that a number is practically infinite) but we cannot seriously claim that a number equals infinity when it is not.


That's about your first example. You still have not accounted for the other two examples' discrepancy. They do not exist in the "real world", either:

[ QUOTE ]
[2] The number of spatial points in any extended volume is also infinite.

[3] God could create an infinitely large object.

[/ QUOTE ]

#2 is Geometry and #3 is Religion.

[JoshuaD]

[ QUOTE ]
[ QUOTE ]

No the number of possible sentences is infact infinity.

[/ QUOTE ] No, it is not. It is simply a very large number. There is a difference.

You can start by imagining the largest possible single sentence, which contains every single word of the English language once! Next, you can imagine the same sentence but with the words re-arranged. It's a new sentence. This would mean that there are x possible permutations of that ultra-sentence, where x is the number of possible permutations of y, where y is the number of all words in the English language. Start down from there, by taking out a word and re-arranging every time for y-1. And so on. Then you get on with mutliple use of the same word. And so forth.

Very, very large -- but not infinity. As long as the number of words in the English language is not infinite, then the number of possible sentences with English words is not either.

[/ QUOTE ]

1) There are an infinite amount of numbers.
2) There is no rule in grammer saying you can't use the same word more than once in a sentence. (I just did it)
3) Function: Take any random word out of the dictionary. Place it first. Number it. Repeat, numbering it (last number)+1. Stop when you run out of numbers.

Here's a hint: You don't stop.


A countable infinity, but an infinity none the less.


edit: Although, if you wanted to get really precise about it, a sentence has to end with punctuation. If you insist on that, then you would be correct in saying that there is no infinitely long sentence.

A slight modification to the poster's point would substitute "String of Words" for "Sentence". There is an infinitely long string of words out there. (In fact, an infinite number of them).

[Piers]

Infintiy like all numbers does not exist in the real world, but its very useful for building models of the real world.

[madnak]

It's possible to create an arbitrarily long legal sentence by inserting clauses within clauses within clauses.

http://en.wikipedia.org/wiki/Longest_English_sentence

[Sephus]

[ QUOTE ]

You can start by imagining the largest possible single sentence, which contains every single word of the English language once! Next, you can imagine the same sentence but with the words re-arranged. It's a new sentence. This would mean that there are x possible permutations of that ultra-sentence, where x is the number of possible permutations of y, where y is the number of all words in the English language. Start down from there, by taking out a word and re-arranging every time for y-1. And so on. Then you get on with mutliple use of the same word. And so forth.

[/ QUOTE ]

i agree with you but your reasoning is flawed. in theory there is no limit to how many times you can use a particular word in a given sentence.

"this sentence is long."
"this sentence is very long.
"this sentence is very, very long."
ad infinitum.

the problem is there is a limit to how much information the universe can contain, so there is a limit to how "long" it's possible to make a sentence.

edit: also joshua makes a good point that there is no end to:

i have one apple.
i have two apples.
i have three apples...

i dont know why people are arguing about this.

[Sephus]

[ QUOTE ]
It's possible to create an arbitrarily long legal sentence by inserting clauses within clauses within clauses.

http://en.wikipedia.org/wiki/Longest_English_sentence

[/ QUOTE ]

right. so we all agree that in theory the number of possible sentences is clearly infinite. why aren't people commenting on my suggestion that the limit to the length of a possible sentence in the real world comes from the limitations in storing or expressing sentences of greater than a "certain" length even if the sentence is stored or expressed in the most efficient way possible?

[Slow Play Ray]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]

God (if he exists) could create an infinitely large object.

[/ QUOTE ]
Like the universe?

[/ QUOTE ]

isnt the univrse finite?

[/ QUOTE ]

what's outside of it then?

[Demiparadigm]

[ QUOTE ]
Somebody asked about a black hole and its singularity, which is an infinitesimal point.

[/ QUOTE ]

Can anyone explain why there *must* be a singularity at the center of a black hole as opposed to a significantly massive object that light cannot escape its gravitational field?


Back to the OP:

[ QUOTE ]


Infinite number of places you can stand? That would require an infinite amount of time to actually stand in all those places. Be "real world" here. Stand in all the places you want, but you can only stand in a finite amount. Plus, as mentioned before, the number is still finite due to the fact that quantum mechanics requires uncertainty in position, so the idea of position as a concept is flawed.

Secondly, I would say a sentence is something someone uses to communicate language. An infinite number of infinite length sentence, while in math, is possible, but not a "real world" example. Time prohibits it.


[/ QUOTE ]

I don't understand your obsession with "time" The point is not that you can systematically stand in an infinite number of places. The point is if I were in a room, I would have an infinite number of choices as to where to stand. There is no possible way to enumberate the number of points in any given volume. How many places do you think I could choose to stand in? 100? 1000? There are clearly an infinite number of possibilities.

Same with the sentence example. It is not that one could say an infinite number of sentences, just that if I were to choose to say a sentence, there are an infinite number of sentences I could choose from.

[madnak]

[ QUOTE ]
why aren't people commenting on my suggestion that the limit to the length of a possible sentence in the real world comes from the limitations in storing or expressing sentences of greater than a "certain" length even if the sentence is stored or expressed in the most efficient way possible?

[/ QUOTE ]

Because it's a circular argument. If the universe if infinite, then it is possible to represent a sentence of arbitrary length. This argument is only valid if the universe is presumed to be finite, so it can't be used as a way to prove that the universe is infinite.

By the way, this doesn't just apply to infinite space. For example, if a particle can have an infinite number of possible orientations, that particle can represent a sentence of infinite length.

Let's choose an arbitrary system of encoding. Space=00, A=01, B=02...Y=25, Z=26. Maybe a comma is 27 and a period is 28, etc. Not too smart, but it's easy. Now say the "infinite sentence" starts with "John jumps over the..." This sentence could be represented in our universe if a particle had the specific orientation represented as:

10.150814001021131619001522051800200805...

In fact, I believe some irrational number includes every possible sentence according to this system. So a particle oriented according to that number would itself be able to fully represent the entire library of sentences.

[MaxWeiss]

[ QUOTE ]
Can anyone explain why there *must* be a singularity at the center of a black hole as opposed to a significantly massive object that light cannot escape its gravitational field?

[/ QUOTE ]


Once you pass the event horizon, you know nothing--no information can come out, since not even light can escape (ignoring Hawking radiation for the moment). So to hypothesize the effects mathematically, since the gravitational pull is so strong, the event horizon becomes perfectly spherical (non-spinning), and so the math for describing it works out with a center of mass at a single point, the singularity. Of course, that doesn't mean much physically since we use a center of mass for things which we do know about, but you get the idea. However, you did prove that the black hole is a bad example of why infinity exists.

[bunny]

[ QUOTE ]
Can anyone explain why there *must* be a singularity at the center of a black hole as opposed to a significantly massive object that light cannot escape its gravitational field?

[/ QUOTE ]

I believe that the reason for this is due to the fact that there is no limit to gravitational strength. Usually, the weak and strong nuclear forces prevent matter from collapsing to an infinitesimal point as although they act over very short distances, they are usually stronger than gravity at those distances. Once the mass of the black hole reaches a critical point, however, gravity becomes stronger than even the strong nuclear force and nuclei themselves collapse into a point. Current theory suggests there would be nothing preventing the matter from being crushed together infinitely small creating a singularity.

I should add a caveat that it has been some years since I did mathematical physics but the correct argument is certainly close to this.

Edit: It's actually the weak nuclear force and the electromagnetic force I was speaking about as they are the ones responsible for limiting gravitational collapse in more usual circumstances....it's been a while /images/graemlins/frown.gif

[Piers]

[ QUOTE ]
Can anyone explain why there *must* be a singularity at the center of a black hole as opposed to a significantly massive object that light cannot escape its gravitational field?

[/ QUOTE ]

I think it just suggests that our current model breaks down, and we don't realy know what goes on.

[Double Down]

Can someone argue against the example given before of
"I have one apple."
"I have two apples."
and so on.

Why is this not an example of an infinite number of possible sentences?
Just because this sentence involves numbers should not make a difference. The word "two" represents an idea, just like every single word does.

And to the argument that there cannot be infinite sentences because we cannot carry out the task of saying or writing them all, that does not matter. Infinite things cannot be determined by whether or not finite beings such as ourselves can measure and observe them. After all, if they are infinite, then WE definitely won't be able to measure all possibilities.

[Cyrus]

[ QUOTE ]
Here's a hint: You don't stop.

[/ QUOTE ]
You do, in fact, have to stop somewhere. As long as this is the so-called "real world".

[ QUOTE ]
There is no rule in grammer saying you can't use the same word more than once in a sentence.

[/ QUOTE ] I believe that using a word an infinite number of times is not English. If I am making a statement, orally or in writing, and I begin repeating a word ad nauseam ("infinitely"), then the meaning of the sentence breaks down: This is no longer English but Jibberish.

Can we at least have an infinitely long string of words in Jibberish? We are still in the real world and Jibberish is real-world. Well, I'm not sure but I believe that there are certain (real world) limitations to all this. A person can create an infinity on paper by simply creating an algorithm that constructs such a sentence - but this is as "real world" as writing down the symbol of infinity on a piece of paper and declaring that we created infinity in the real world.

However, no human would be able to ever write that sentence or say it whole. He would be dead long before he finishes looking at it. The realm of numbers might be infinite in mathematics but the number of extant electrons in the cosmos is not.

A real world infinity would also violate the laws of thermodynamics. We would be able to create a constant motion machine, if we had real-world infinity.

...But here is some food for thought : Are not mathematics created in and (hence) part of our "real world"?

[madnak]

In theory a quantum computer could process the algorithm and create a representation of the sentence. It doesn't matter how many electrons are needed - only one is necessary to store the information.

[Cyrus]

[ QUOTE ]
In theory a quantum computer could process the algorithm and create a representation of the sentence.

[/ QUOTE ]

And I'm asking : Is a [i]representation the real thing?

The question was about the real world. And, at the risk of being accused of the most vulgar empiricism, I say we must place the infinite specimen formly within our real world - and not in the realm of symbols or the mind.

See my previous post about writing down (in a real-world paper with real-world pen) the symbol for infinity and proclaiming we created an example of infinity in the real world.

[madnak]

The point is the capacity for infinite information. If information isn't enough for you, then I suppose the universe would have to be spatially (or at least temporally) infinite in order to qualify. And since nobody can prove that either way, there's no room for discussion.

However, due to the capacity for infinite information, infinite orientation, etc, infinity has very concrete applications. Whether or not it "exists" according to your criteria.