#1
I'm not sure if this falls into the philosophy or the math thread since it's quite a bit of both.

My understanding of infinity has various degrees of infinity, i.e. there are an infinite amount of numbers between 1 and 2 but then there are also an infinite number of integers. So, there are naturally more irrational numbers than rational, even though there are an infinite number of both. These are called Aleph Numbers.

So, my basic idea of infinity is the integral of everything from negative infinity to positive infinity. Since infinity is infinitely far away, as Carl Sagan said, infinity is just as far away from a googleplex as it is from the number one.


That brings me to my main point..

If you think of this: time=∫ moments dm, [beginning, end] or time= ∫ moments dm , [-eternity, eternity], then assuming that time continues forever (not my view, I think it's like an oscillating thing, with possible infinite expansion then contraction of the universe), what would make today any different from 500 years ago or 3000 years from now?

So, doesn't this disprove the idea of eternity? That there can't be an infinite # of days, since there would be no distinction between the moments or days.

Would this same concept not apply to the idea of infinity? If there are an infinite amount of numbers, then how can we tell the difference between 1 and 20? How can one even get from the number one to the number two if you have to pass an infinite number of irrational numbers?
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#4
Quote by Psalm 150:4
How can one even get from the number one to the number two if you have to pass an infinite number of irrational numbers?


There may be infinite irrational numbers but there's only 1 integer between them
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#7
Yeah, I know it's not a number. But people talk of infinity eternity like they're real, when there's really no mathematical proof that they exist. Unless someone can find a proof of infinity.
I'm not a Bible-thumper anymore. Realized I had a brain in '09.

I like guitars, running, and math.
#8
Quote by Psalm 150:4
Then how can we tell the difference between 1 and 20?

Pick up 1 of something. Then pick up 20 of something. They're clearly different.
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#9
Quote by Random88
Pick up 1 of something. Then pick up 20 of something. They're clearly different.


That's not my point. I don't see how if the concept of infinity is true, then in my mind there's no distinction between any numbers.
I'm not a Bible-thumper anymore. Realized I had a brain in '09.

I like guitars, running, and math.
#10
Quote by Psalm 150:4
Unless someone can find a proof of infinity.

A proof of infinty??? What the tits are you talking about? It's the concept of something without limits, how can that be proved or disproved?
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#11
Quote by Psalm 150:4
Yeah, I know it's not a number. But people talk of infinity eternity like they're real, when there's really no mathematical proof that they exist. Unless someone can find a proof of infinity.

A proof of infinity What's the biggest number you can think of?

Add that many zeros to the end of it. You've got a bigger number.

[IN PHIL WE TRUST]


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#12
Quote by Random88
A proof of infinty??? What the tits are you talking about? It's the concept of something without limits, how can that be proved or disproved?


I mean a mathematical proof. There aren't an infinite number of particles in the universe, so how can there be a number that exists that is higher than everything that ever existed?
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#13
You're doing infinity wrong. It's not a number.

[IN PHIL WE TRUST]


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#14
Quote by Psalm 150:4
I mean a mathematical proof. There aren't an infinite number of particles in the universe, so how can there be a number that exists that is higher than everything that ever existed?

Just because it doesn't exist doesn't mean it can't exist in theory.

And again, infinity is not a number.
#15
Quote by Psalm 150:4
If you think of this: time=∫ moments dm, [beginning, end] or time= ∫ moments dm , [-eternity, eternity

You can't really do that. Take for example calculating the mass of a singularity with a triple integral, you can't.
edit: and what you would be doing is an improper integral, and I really don't know if that converges.
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Last edited by damian_91 at Aug 2, 2010,
#16
Quote by Psalm 150:4
I mean a mathematical proof. There aren't an infinite number of particles in the universe, so how can there be a number that exists that is higher than everything that ever existed?


Numbers aren't attached to things, they're just 'theoretical' so to speak. I could probably think of a number that is higher than the number of particles in the universe, doesn't mean that ammount of things has to exist.
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#17
Quote by Psalm 150:4
I mean a mathematical proof. There aren't an infinite number of particles in the universe, so how can there be a number that exists that is higher than everything that ever existed?

Yes, but since there isn't a 'smallest' distance that can exist, there are an infinite number of divisions that could be made between two numbers/points/'moments'/whatever

And like has been said, infinity is not a number
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#19
This is crap.

Kind of like the Greek philosopher who claimed that there is no such thing as movement, because in order to get from point A to point B, you must get halfway, and before you get there, you must get halfway to that point, and before you get to THAT point you must get halfway, and that can go on forever making it impossible for you to get anywhere.

A person in the audience at this lecture stood up and walked out...
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#20
Quote by Random88
Yes, but since there isn't a 'smallest' distance that can exist, there are an infinite number of divisions that could be made between two numbers/points/'moments'/whatever

And like has been said, infinity is not a number



That's where my understanding falls short...if you can subdivide something an infinite number of times, then how can we distinguish between whole numbers? Like, how can you prove that the number 2 exists if you can't prove that 1.9- exists?
I'm not a Bible-thumper anymore. Realized I had a brain in '09.

I like guitars, running, and math.
#21
Quote by Gman400
This is crap.

Kind of like the Greek philosopher who claimed that there is no such thing as movement, because in order to get from point A to point B, you must get halfway, and before you get there, you must get halfway to that point, and before you get to THAT point you must get halfway, and that can go on forever making it impossible for you to get anywhere.

A person in the audience at this lecture stood up and walked out...


That's exactly what I don't understand. I see his reasoning and I can't apply it to anything in my life. If life were just theory, I would say that it would be impossible for one to get from 1 to 2 by adding half of the number before.
I'm not a Bible-thumper anymore. Realized I had a brain in '09.

I like guitars, running, and math.
#22
Quote by Gman400
This is crap.

Kind of like the Greek philosopher who claimed that there is no such thing as movement, because in order to get from point A to point B, you must get halfway, and before you get there, you must get halfway to that point, and before you get to THAT point you must get halfway, and that can go on forever making it impossible for you to get anywhere.

A person in the audience at this lecture stood up and walked out...


If only Zeno were here now.
#23
I forget who said it, but I once read that eternity was defined in a certain culture by the time it would take for a pigeon to beat a ball of gold the size of the sun to dust with a single wing hit every 10000 years.
#24
Quote by Psalm 150:4
That's where my understanding falls short...if you can subdivide something an infinite number of times, then how can we distinguish between whole numbers? Like, how can you prove that the number 2 exists if you can't prove that 1.9- exists?

If you can't grasp the concept of the number 2, I find it hard to believe you can accurately calculate your own momentum.

Count how many hands you have. 2. Proof.
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#25
Quote by Psalm 150:4

That brings me to my main point..

If you think of this: time=∫ moments dm, [beginning, end] or time= ∫ moments dm , [-eternity, eternity], then assuming that time continues forever (not my view, I think it's like an oscillating thing, with possible infinite expansion then contraction of the universe), what would make today any different from 500 years ago or 3000 years from now?


'dm' ? Are you integrating with respect to mass?

Quote by Psalm 150:4

So, doesn't this disprove the idea of eternity? That there can't be an infinite # of days, since there would be no distinction between the moments or days.


There are not an infinite number of days?

Quote by Psalm 150:4

Would this same concept not apply to the idea of infinity? If there are an infinite amount of numbers, then how can we tell the difference between 1 and 20? How can one even get from the number one to the number two if you have to pass an infinite number of irrational numbers?


By that same logic, it is impossible for you to reach anywhere.
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#26
TS, has it ever occured to you that maths is just a mere tool invented by us humans? the reason why 1+1=2 is because we all agree on the fact that it does. just like we all agree on the fact that infinity is (as the name suggest) infinite, and thus is not a number. You're treating maths like it's some kind of fundamental law that has been here long before anything else, which is nonsense.
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#27
Quote by rock.freak667
'dm' ? Are you integrating with respect to mass?


There are not an infinite number of days?


By that same logic, it is impossible for you to reach anywhere.

sorry, i meant m=moments


I don't know? I don't think so..I think the universe will fizzle out.


Yeah, that's what I don't get..
I enjoy math a lot (engineering major), but sometimes I have a hard time grasping the so-called "simple" concepts that two year olds never question. It's when I start thinking about stuff that I get all messed up...
I'm not a Bible-thumper anymore. Realized I had a brain in '09.

I like guitars, running, and math.
#28
Quote by the bartender
TS, has it ever occured to you that maths is just a mere tool invented by us humans? the reason why 1+1=2 is because we all agree on the fact that it does. just like we all agree on the fact that infinity is (as the name suggest) infinite, and thus is not a number. You're treating maths like it's some kind of fundamental law that has been here long before anything else, which is nonsense.



What's wrong with thinking of math like a fundamental law? That's what it is to me, the purest of all things that one can learn. You can question all things about everything, but it's impossible to imagine a triangle in Euclidean geometry that doesn't have 3 sides and angles that add to 180*. (Descartes' though, I believe)
I'm not a Bible-thumper anymore. Realized I had a brain in '09.

I like guitars, running, and math.
#29
Quote by Psalm 150:4
That's where my understanding falls short...if you can subdivide something an infinite number of times, then how can we distinguish between whole numbers? Like, how can you prove that the number 2 exists if you can't prove that 1.9- exists?

Why can't I prove either of those exists again?

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#30
Quote by Psalm 150:4

Yeah, that's what I don't get..
I enjoy math a lot (engineering major), but sometimes I have a hard time grasping the so-called "simple" concepts that two year olds never question. It's when I start thinking about stuff that I get all messed up...


How I think of it, is that if you want to move from A to B, you need to sum all of the infinitesimal distances from A to B which gives the distance you have to move. If you want to move from A to B/2, then you need to sum the distances again.
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#31
Quote by rock.freak667
How I think of it, is that if you want to move from A to B, you need to sum all of the infinitesimal distances from A to B which gives the distance you have to move. If you want to move from A to B/2, then you need to sum the distances again.


yeah, that's the calculus that I get. I just can't visualize it. I mean, of course I can visualize the simple line segment and adding all the little parts, but I still have a hard time visualizing the infinitesimal distances and how they relate to the total.
I'm not a Bible-thumper anymore. Realized I had a brain in '09.

I like guitars, running, and math.
#32
One should never attempt to visualize infinty as an aspect of reality, it just can't be done. The concept of infinity is only useful in mathematics, any application of it to reality is meaningless.
#33
Quote by In absentia
One should never attempt to visualize infinty as an aspect of reality, it just can't be done. The concept of infinity is only useful in mathematics, any application of it to reality is meaningless.


so... you mean that my infinite sexyness doesn't mean a thing ?
You who build these altars now

To sacrifice these children
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#34
Quote by the bartender
so... you mean that my infinite sexyness doesn't mean a thing ?


I'm terribly sorry, but yes

However that does not mean your amount of sexyness isn't very high
#35
Quote by In absentia
I'm terribly sorry, but yes

However that does not mean your amount of sexyness isn't very high


I like where you're going
You who build these altars now

To sacrifice these children
You must not do it anymore
#36
Quote by Psalm 150:4
yeah, that's the calculus that I get. I just can't visualize it. I mean, of course I can visualize the simple line segment and adding all the little parts, but I still have a hard time visualizing the infinitesimal distances and how they relate to the total.


Which is why you really can't visualize infinity in terms of a finite distance. It is a concept.
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#37
I don't really understand much of this thread, but i think the human mind is conditioned to put everything in terms of everything having a beginning and an end, so things like infinity, the size of the universe, and just the general concept of something not having an end or and being completely absolute are nigh on impossible to comprehend, at least, for now.
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