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For you math nerds
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K9 Carlos
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Joined: 13 Mar 2005
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PostPosted: Mon Mar 12, 2012 8:25 am 
Post subject: For you math nerds
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http://listverse.com/2012/03/12/10-enormous-numbers/
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Erwin Rommel
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Joined: 02 Aug 2005
PostPosted: Mon Mar 12, 2012 6:56 pm 
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I agree up until #3.

Infinity is not a number. However, we can say lots of different things about different sizes of infinity.
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Stealth
▲RAWR TRIANGLE RAWR▲


Joined: 13 Mar 2005
PostPosted: Mon Mar 12, 2012 7:07 pm 
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I'm one that is very skeptical at the concept of infinity as I feel there can not be infinity in our universe, multiverse and beyond.
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Wang Chung
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Joined: 13 Mar 2005
Location: Virginia Tech
PostPosted: Mon Mar 12, 2012 7:43 pm 
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I don't really understand how you can be skeptical of it. Infinity is an important mathematical concept to understand. It certainly exists.
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Stealth
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Joined: 13 Mar 2005
PostPosted: Mon Mar 12, 2012 9:03 pm 
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In equation form, yes.

In reality, no.

The ten dimensions of the universe. The tenth dimension is in which all possible infinities are recorded as a single dot. How can there be more than infinity?

I find, based on the data, that the infinity is finite. However, there could be more dimensions undiscovered.

I should say that it's important to note that I am not ruling out the possibility of infinity actually existing, merely find a lot of it highly questionable and shouldn't believe the theory of infinity to be a pure fact.
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Erwin Rommel
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Joined: 02 Aug 2005
PostPosted: Mon Mar 12, 2012 9:41 pm 
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You're referring to this?

http://www.youtube.com/watch?v=aCQx9U6awFw

I found it to be full of ill-defined but pleasant-sounding nonsense.
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Stealth
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Joined: 13 Mar 2005
PostPosted: Mon Mar 12, 2012 9:57 pm 
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Well that's where I first saw it, but later attended lectures in college that were more involved. Interesting stuff, but I'm a very abstract kind of guy and realize most math gurus will disagree with me.

I am in the minority. Much like me leaning more towards Plasma Cosmology.

I like to leave my doors open to the impossibility. Could be something grand.

But back to infinity, I'd love to see how you guys define infinity.
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Erwin Rommel
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Joined: 02 Aug 2005
PostPosted: Tue Mar 13, 2012 2:42 am 
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The real issue here is that, in mathematics, the term "infinity" is actually not commonly used. We often say that a limit "equals infinity". What that really means, however, is that the limit diverges in a very particular way. This can be defined very precisely.

A word that mathematicians use all of the time, however, is "infinite". For instance, infinite-dimensional spaces and sets with infinitely many elements are very common objects. In this case, "infinite" simply means "not finite". And finite is very easy to define. I guess you could say that infinity "exists" insofar as there are mathematical objects that are not finite.

****

If you want a way to actually construct some object to call "infinity", you can look at the theory of Ordinal Numbers (very technical article, though). It's basically a way of taking the natural numbers and adding new numbers that behave a little bit like how you might want infinity to. But mathematicians are very careful to never actually use the word "infinity" while doing this.

Another way to tackle "defining infinity" is through the theory of cardinal numbers. This basically centers around measuring the "number of elements" in a set and asking when two sets have the same number of elements. This lets you actually talk about different "sizes of infinity" by finding infinite sets that nonetheless have different "sizes"

I'm being vague about these because I have to. Both of these are very technical mathematical constructions that are usually covered in a third-year undergrad course.

****

Whether or not any of this means "infinity exists" is unclear. The above-mentioned mathematical objects exist. I can prove stuff about them and manipulate them. When I say something mathematical, I can be 100% certain what I mean. It's just very frustrating discussing infinity and similar topics with non-mathematicians who seem to be much less precise about what they mean.
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Wang Chung
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Joined: 13 Mar 2005
Location: Virginia Tech
PostPosted: Tue Mar 13, 2012 7:42 am 
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That's really interesting, I'm actually writing a paper now on the "Ordinal Controversy" :O
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Stealth
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Joined: 13 Mar 2005
PostPosted: Tue Mar 13, 2012 11:59 am 
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I see we are in agreeance as you have proven my point.
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Messy Recipe
El Gran Capitán
<b>El Gran Capitán</b>


Joined: 13 Mar 2005
Location: Inter Veritates
PostPosted: Tue Mar 13, 2012 12:14 pm 
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Can't cite "ten dimensions of the universe" to support anything as that is in no way supported by any actual evidence:

http://en.wikipedia.org/wiki/Dimension#Additional_dimensions

That's somewhat misleading, in that it implies there's no evidence to support anything above three, when there is quite obviously a fourth dimension, but the fact remains that string theory has not been verified.


To support some form of actual infinity existing: Divide the mathemathical object "one" by the other mathematical object "two". Append the result to a list, and recurse on the result. The list of all possible results is infinitely long and the time to finish obtaining the results is infinite...
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Stealth
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Joined: 13 Mar 2005
PostPosted: Tue Mar 13, 2012 12:31 pm 
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It's a theory. And like all theories, while although may be widely accepted, they can still be false.

As to my reference, it doesn't matter as it was just an example. It can't be proven and it can't be disproven. This is the problem that lies with so many scholars. When you treat all known evidence as complete fact, you limit yourself.

Yes, I realize you must base your findings on knowledge already known. Why reinvent the wheel? But some widely known scientists often have thought there was a large piece missing of their puzzle.

Perhaps the "Law of Gravity" is 1/4th the puzzle. Consistant data states that the object will fall toward the Earth. But why? Because atoms like to group? Because that's the way it is?

My point being, completely dismissing an idea due to lack of evidence is illogical.

This Reminds me of the scientists who adamently believed the world was flat.
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Erwin Rommel
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Joined: 02 Aug 2005
PostPosted: Tue Mar 13, 2012 3:03 pm 
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Sure, if you're talking about the physical universe not being "infinite", you can make a statement to this effect.

My major objection to the whole ten-dimensional business is that it is very undisciplined in how it goes from one dimension to the next. In fact, I'd be very curious to hear what his definition of "dimension" is. He uses the term all the time, so he should be able to define it, right?

But regardless, let's say we can call all the possible timelines of all possible universes a single point in the 10th dimension. So what? The point still represents something infinite. We can call anything a point if we like. That shouldn't change what it actually is.
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El Gran Capitán
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Joined: 13 Mar 2005
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PostPosted: Tue Mar 13, 2012 4:31 pm 
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Stealth wrote:
My point being, completely dismissing an idea due to lack of evidence is illogical.

This Reminds me of the scientists who adamently believed the world was flat.


Most scientists didn't.... in fact very few people did at all.... even the ancient Greeks knew it was round. Because of evidence, like the round shadow it casts on the moon.

Anyway, I wasn't dismissing string theory or anything else for lack of evidence; I was saying something with no evidence to support it, cannot itself be used as evidence against something else.

At any rate, it may be illogical to completely dismiss something for lack of evidence, but discounting such things is very logical. If someone tells you there is a vicious tiger in the room, but you check every corner and cannot see/hear/smell/etc it, nothing shows up on infrared, you let loose a boar in the room and nothing attacks it... it wouldn't be logical to take precautions to protect yourself from said tiger. It could somehow be there, but the lack of evidence implies an extremely low probability of that being true.

Now, the above doesn't quite apply to string theory, because from what little I understand of it, it's somewhat sound mathematically / is good progress to the goal of a theory of everything. But the fact is that there isn't anything currently behind it to back it up -- so arguments that depend on it being true aren't valid arguments unless you're working with the assumption that it's true.
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Berry Punch
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Joined: 04 Sep 2011
PostPosted: Tue Mar 13, 2012 4:40 pm 
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Crows nest makes me feel stupid everytime I look at it's threads. Sad
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