Someone shed some light on infinity and dimensions... i am wandering.....?

somebody_nobody

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Posts: 1

Someone shed some light on infinity and dimensions... i am wandering.....?

« on: July 15, 2011, 02:00:54 PM »

I was watching a video about parallel universes. I know that according to some theories (i dont know which ones) that there are an infinite number of parallel universes. so in this infinite number of parallel universes... some of them would have life... and some of them would not support it (because the law of physics would be different). so that means that only a small fraction of the universes will have life..... but if there are an infinite number of universes... then the fraction of universes that have life will be inifinite.... so a fraction of infinity is infinity. that kind of makes sense but doesnt make sense

how is half of infinity, infinity i mean that is wierd. cause like half of zero is zero. so maybe infinity is zero.... or maybe infinity is the zero of a WHOLE NOTHER SET OF NUMBERS. like maybe infinity is nothingingness in some place... and its like the zero of that place. probably not actually

i guess infinity just has its own laws... but its very similiar to zero... its like to opposite of zero. its like... maybe the way there are dimensions for shapes.... maybe there are dimensions for numbers...

in three dimensions we have negative infinity, zero, and infinity... maybe in a higher dimension there would be more infinities outside infinity. cause if we could understand infinity... what if it doesnt end in the traditional sense.... but it ends in a whole new way.

i am not high. please someone who knows what they are talking about please shed some light.


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Irv_S

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Re: Someone shed some light on infinity and dimensions... i am wandering.....?

« Reply #1 on: July 15, 2011, 11:29:34 PM »

Yes, "infinity has its own laws."
Stop thinking of it as a number, zero is, but infinity isn't.
Think of the whole number set.
It is of infinite length because the set of integers is infinite.
(You can allways add one right?)
Now if to that scale, you add tenths, the scale IS still infinite, (endless) right?
At the same time there's no way to ignore that there are more tenths than whole numbers right?


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BerkeleyEECS

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Re: Someone shed some light on infinity and dimensions... i am wandering.....?

« Reply #2 on: July 16, 2011, 10:14:54 PM »

Are you sure you're not high?

Well, I am assuming that the documentary you were watching was discussing the many worlds interpretation of quantum mechanics. This is just an interpretation, and the subject of considerable contention. Basically in quantum mechanics you can have a system in a superposition of states. When the system is subject to an interaction, the superposition collapses and the system "chooses" one of the states and sticks with it. This is know as wave-function collapse. Some physicists think that if the system was originally in a superposition of, say 3 states, then when when in our known universe the system collapses to state 1, two more parallel universes are created where the system had instead collapsed into sate 2 and state 3, respectively. Since wave-functions collapse all the time then as time progresses there are more and more parallel universes, one for each possible outcome of the wave-function collapse. Of course this is cannot be proven and is all just speculation.

Now, concerning infinity, there are indeed different kinds of infinity. For example, there is the infinitely large, and also the infinitely small, although in physics some believe the infinitely small does not quite exist (i.e., some think that space is not actually continuous and thus not infinitely divisible into smaller and smaller parts). In mathematics, where they are much more rigorous, there are also different kinds of infinity. Some infinities can be proven to be larger than other infinities. A nice popular exposition is given in the BBC Horizon documentary titled "Dangerous Knowledge," which among other topics discusses the life and work of Cantor. Cantor was a mathematician who worked on this problem of there being different kinds of infinities, and from this developed a very useful branch of mathematics known as set theory. He was obsessed with the concept of infinity and it eventually drove him mad. He actually died in a mad house. The "Dangerous Knowledge" documentary is available on Google Video if you are interested. Another nice popular exposition of the concept of infinity in mathematics and the sciences can be found in a book by Rudy Rucker, titled "Infinity and the Mind: The Science and Philosophy of the Infinite." Although parts of it can get kind of boring it is a decent read overall, especially if you have never been exposed to the material it covers.


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Dave77

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Re: Someone shed some light on infinity and dimensions... i am wandering.....?

« Reply #3 on: July 17, 2011, 02:59:15 PM »

This apparent paradox that you've "discovered" is not a paradox at all, but rather a side-effect of the definition of infinity and infinite sets. Any fraction (or multiple) of an infinite set is still infinite. Part of your problem is that you're thining of infinity as a number, but (unlike 0, or 1, or 2, etc), infinity is not a number, it is a concept. Therefore, saying something is "half of infinity" is technically meaningless. An infinite set can have half the number of elements as another infinite set, but they are both still infinite.

For example, consider the set of positive integers (aka natural numbers): 1, 2, 3, ... The set is infinite because you can always add one more the largest number you can think of. Now, consider the set of even, positive integers (2, 4, 6, ...). You've taken out half the numbers from the set of positive integers, but this set is still infinite as well, because you can always add two the largest even number you can think of. Consider also, _all_ (including negative) integers. It is twice the size of the set of positive integers, yet both are still infinite. The set of all integers is said to be countably infinite becase you can count the numbers one by one, though you would never get to the end. So, now, consider the set of all real numbers (including decimals and fractions). There are an infinite number of numbers between 0 and 1 because you can divide that interval into an infinite number of segments (1/2, 1/10, 1/100, 1/1,000,000, etc.). Similarly, there are an infinite number of numbers between 1 and 2, and between 2 and 3, etc. So, by extrapolation, the set of all real numbers is infinitely larger than the set of all integers (which, as we've already said, is infinite itself). The set of real numbers is called uncountably infinite because you couldn't even count one by one the numbers between 0 and 1, let alone all the other numbers.

Your statement about "maybe in a higher dimension there would be more infinities outside infinity" doesn't make any sense. The concept of infinity is independent of the dimension in which it exists, but as I've already said, there are different degrees of infinity (countably infinite versus uncountably infinite).

It's confusing only because the human mind isn't equipped to truly understand the concept of infinity--every thing we encounter in our everyday lives is finite, so the human mind and concept of numbers has developed to understand the finite, not the infinite.


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obelix

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Re: Someone shed some light on infinity and dimensions... i am wandering.....?

« Reply #4 on: July 17, 2011, 03:11:40 PM »

as some have pointed out, set of integers is a nice example ... it's infinite ... but half of them are even numbers, right?
and I agree with some of the others that you cannot think of infinity as a number, it's a mathematical concept and difficult to think in terms of everyday life.


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