Oh boy...I really do not know if I should be writing this because I hope I don't come off looking like a real weirdo!! Sometimes I think wayyyy too much. The word "Infinity" is a word that has always really bugged me. The reason it bugs me is because when you really think about this word, it just can't be. There cannot be such a think as infinity. Why you ask..? lol Well...We live in a universe. What is beyond that universe? It's supposed to be infinity. If you got into a spaceship and just kept going, infinity means that it never ends. You would be in this spaceship and you would just keep going and going and going...and going...it would never stop!? No...this cannot be. If you close your eyes and really try to visual this, you can't even do it. There just has to be an end. There is a beginning and an end to everything. Now this is going to sound really weird but, if there is infinity, which means it goes on forever, and there is no end...then we could be here. Like I said, this is going to sound weird, but it makes sense to me. I have talked about this subject over the years here and there with people and no one ever seems to understand what I mean. No one gets it. So I always think there must be something wrong with the way I am thinking...lol Until recently! Yayyy! I was watching the BIO channel not too long ago, and one segment of it was about the very word that drives me crazy. "Infinity." They said that there cannot be such a think as infinity because mathematically it just does not add up. It is impossible. OMG, I couldn't believe I heard this. I just knew it. So now, what I want to know is, what the heck is out there! I am going to stop here and if this post sound really strange, please don't laugh at me..lol I am kind strange sometimes and like I said, I think too much.
Infinity "In general, infinity is the quality or state of endlessness or having no limits in terms of time, space, or other quantity. In mathematics, infinity is the conceptual expression of such a "numberless" number. It is often symbolized by the lemniscate (also known as the lemniscate of Bernoulli ), which looks something like the numeral 8 written sideways ( ). This symbol for infinity was first used in the 1600s by the mathematician John Wallis.
Infinity can be defined as the limit of 1/ x as x approaches zero. Sometimes people say that 1/0 is equal to infinity, but technically, division by zero is not defined. Another notion is that infinity is a quantity x such that x + 1 = x . The idea is that the quantity is so large (either positive or negative) that increasing its value by 1 does not change it". Infinity defined
If you close your eyes and really try to visual this, you can't even do it.
It's true we can't visualise "infinity". Our brains didn't evolve the ability to comprehend it.
Whenever someone tries to describe the nature of the universe, however much they go on about four-dimensional mobious strips or whatever, a little voice in our brain still says, "Yes, but what's outside the universe? Where is the universe?"
That doesn't mean the universe can't be infinite, however, or that "infinity" itself can't exist. It just means that it's not easy for us to visualise the idea. We seem, instead, to have a particular world-view hard-wired into us - one that is, naturally, based on human scales and everyday occurrences. It's difficult enough for us to imagine the true size of our own little planet, let alone that of the universe.
Originally posted by Lynnie: BTW, how do you Edit here. I do know that I made some spelling errors. I wrote think instead of thing twice. Hate when that happens.
Down in the lower right hand corner of your post is the symbol of a pencil eraser. If you click on that you can edit your post. But you can't wait too long or it disappears along with the ability to make changes.
When I think about this word and what it means I know that there is just something else out there. If there is a god, maybe at the end of the supposed Infinity, maybe that is where God is. Or maybe there really is something to the String Theory/Parallel Universes. Seems like Infinity would definitely be easier to understand when you think about these theories. It even makes sense. Ok, so now tell me. How weird do you really think I am now!? lol I think wayyyyyy wayyyy too much!
Back in the late 1950s we were being taught at school that the universe had the outline, the shape,of a standard saddle (Happily, at that age, 11, we were not required to learn the mathematics connected to this statement )
Wikipedia has an article on hyperbolic geometry, including its history: Hyperbolic Geometry
János Bolyai and Nikolai Lobachevsky are both credited with its 'discovery' ca. 1830.
Saddles (and Pringles potato chips) are said to have negative curvature. On such a 3-D surface there are unusual properties:
The angles of a triangle have a sum less than 180 degrees.
Given a line and point not on the line, there are infinitely many 'parallel' lines that do not intersect the given line.
A Euclidean plane tangent to a point will cut the surface into some parts on one side the plane and other parts on the other side.
The saddle-shaped (i.e., negatively curved) universe is actually a 4-dimensional model that's reduced to the 3 dimensions of a saddle shape so that we can visualize it by analogy, just as the notion of a hypersphere (positively-curved or Gaussian 4-D geometry) is reduced to that of a sphere for the same purpose.
From what I read, the overall large-scale geometry of the universe is still an open question.
Posts: 2221 | Location: U.S. | Registered: 06-03-02
Returning to the original question, the concept of infinity is central to much of mathematics and is surely not regarded as 'impossible' -- though it might require a human brain to imagine it. I'd have to agree that it's 'mind-boggling'.
You can find infinity in humble places. A finite line segment, for instance, contains an infinite number of points.
Georg Cantor, a late-19th C mathematician, developed the theory of transfinite numbers to create a whole hierarchy of infinities, each bigger (in a strictly defined sense) than its predecessors -- an infinity of infinities!
Off topic as usual, but did you know Wallace committed suicide in September? Everything and More was originally published in 2003, Professor..you have been waiting long enough.
Why is infinity impossible? Say you went to the end of the 'universe', I guess we could define that as absolutely the last sun, planet, speck of dust, cosmic particle -- and yet you kept going.
What would stop you?
Posts: 6961 | Location: British Columbia, Canada | Registered: 06-11-02
Dvd, I have a question. You wrote about the circle. Is the circle supposed to represent our universe? I really do not think that infinity represents the circumference of the circle. My question is...what is outside of the circle? If the circle does represent our universe and outside of the circle are other universe's, how far out do those other universes go? According to the word infinity, it would go on forever and never ends. Kind of hard to imagine isn't it? I hope I am explaining this right, but do you understand what I am saying?
There's no "end" to the two-dimensional line that is the circle's circumference, and there is no "outside" to our three-dimensional universe (assuming it does have just three dimensions, for a moment):
'Finally, there's the "edge" defined by the fact that you cannot leave the universe. All paths slowly curve around objects of mass, and curve around the whole thing like someone driving on a highway spanning the equator: no "outside" can possibly be encountered. All this suggests that the cosmos is like a big expanding balloon. So everyone naturally pictures this balloon as if they were observing it from an external perspective, which makes it reasonable to ask, "What's outside the universe?" But that viewpoint doesn't exist. No one can BE outside the universe to see it as a balloon, because there is no outside to something that is everything. Still not satisfactory, but too bad. Our mind's logic got created to deal with diets and mortgages, not this kind of stuff. You get what you pay for."Time, Eternity, and Infinity
So apparently, to answer Bab's question, if you just kept going, nothing would stop you but you'd eventually end up back where you started, even though your path would seem to be absolutely straight.
originally posted by dg: ...Wallace committed suicide in September. Everything and More was originally published in 2003, Professor..you have been waiting long enough.
Well, I just added that book to my list a few months ago after reading what I thought was a recent review of it. I saw Wallace's obit in September but didn't recognize the name. Infinite Jest looks interesting.
quote:
Originally posted by nnn: ...if you just kept going, nothing would stop you but you'd eventually end up back where you started, even though your path would seem to be absolutely straight.
Astronomers have actually looked for repeating images (as in a hall of mirrors) of distant galaxy clusters. A common cosmological phrase to describe the universe is "finite but unbounded." The expanding balloon analogy (often with ants as astronomers!) also explains why, no matter where you are in the universe, all the galaxies seem to be flying away from you.
Posts: 2221 | Location: U.S. | Registered: 06-03-02
But...if you say that there is nothing OUTSIDE of the circle, then there is an end...right? Where is this circle? Inside of something? If it is inside of something, what is outside of it. lol...this is driving me nuts!
Lynnie, as far as we know the universe is a 4-dimensional entity (space-time) that contains "everything" that exists. Asking what's "outside" is a more or less meaningless question. String theories of higher dimensionality (10, 11, 26, etc.) or multiverses -- of which our observable universe is but one of uncountably many -- are pure speculation.
The problem with the sphere analogy is that we humans can plainly see that a 3-D sphere has an inside and an outside, even if the 2-D flatlanders living on it cannot. But we can 't necessarily make that leap to four dimensions and conclude that the universe also has an inside and an outside.
Posts: 2221 | Location: U.S. | Registered: 06-03-02
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