Religion

Well now that's made we can relax and look at infinity.

No, really. Current concepts of infinity originate from either the material world or the idealism world.
Take the number line move in either direction until you reach the end add a number, you can never reach the end. this is a take off from Zenos paradox.
Define a function such that for any value in x there exits a y value. Because of the above statement the function is defined as continuous, and goes on until, wait for it, infinity.
This is a take of from Euclidian geometry.
Consider two functions, such that movement along their number lines converge. Wow imaginary numbers what a concept! Now divide one by the other with no number a zero. Wow a Möbius strip. iteration of rational functions!
We have moved from Arisotle to Euler. Let's get crazy now and look at Cantor sets.
but these are just continious algebras you protest, what about discontinuous algebras and regardless of how hard infinity is to prove, I haven't proven -1 times 1 is a negative number, or its converse -1 times -1 is a positive number. Ok, ok but that will take some Ring theory and Topology. I'll pretend you are ready for this . Back to Euler (Einstein was nothing) imagine (a dirty word) a something having no outside or inside a characteristic of 0, an algebraic extension of the möbius, a Klein bottle. Move now to a characteristic or manifold of two and you can morph a coffee cup into a doughnut. Let's move characteristic 11.

We have now gone from Euler to Hawking and string theory.

to understand infinity in the universe of ideas is to listen to a Bach Canon, an opera of Mozart, an Escher print, anything by Picasso, or watch ants build a bridge , so easy.

finishing the drink now, hope you google some of this stuff.
 

You're talking maths again.
Naughty boy, I'm steaming up!

Please talk about the way that some infinite sets are bigger than other infinite sets, because, as we all know, size matters.
 

Oboy set theory one of my favorites. Sets, infinite or otherwise, include groups that are part of that group,or not. This "hard" set definition was established by Bertrand Russell, who,by the way scripted an outstanding text science and religion if anyone is listening. Thus sets contain elements by groupings that may be a "union" or an "intersection "
(oh your bad). However this membership function is interruptus by slight characteristics belong to each group. This logic approach is "soft" in that it ask exactly when does it become a member of that set. Mark Koch (koosh, not the other one ) at Cal. tech and some others have termed this Fuzzy logic, and allows burned computer chips to learn by artificial intelligence how to think. This allows cars to drive themselves, etc, and machines to become sentient. Elon Musk and Hawkings can see, Bill Gates can now see it. So , bend over and kiss humanity, and arguements about religion and such goodbye.
 
There are an infinite number of whole numbers (integers) on the number line.

There are also an infinite number of other numbers (fractions) between each whole number.

Think about that. Both sets contain an infinite number of elements but the set of fractions is a more dense set than the set of integers.
We could say that this infinity is greater than the infinity of the set of whole numbers.

When we start talking about concepts like infinity, normal logic becomes rather difficult to follow.
 
Dame Warrigal said:
There are an infinite number of whole numbers (integers) on the number line.

There are also an infinite number of other numbers (fractions) between each whole number.

Think about that. Both sets contain an infinite number of elements but the set of fractions is a more dense set than the set of integers.
We could say that this infinity is greater than the infinity of the set of whole numbers.

When we start talking about concepts like infinity, normal logic becomes rather difficult to follow.
Click to expand...

That doesn't make sense - an infinity is an infinity, nothing to do with how dense it is. Maybe it's just that I'm a word person, not a math person.

... although this might explain some of the behaviors of my son, the Master's Math geek ... :rolleyes:
 
I've always liked the dropped ball theory about infinite numbers. In case you're not familiar it goes like this:

If you drop a ball from any height, before it can reach the floor it first must reach a point halfway from that height to the floor. From this halfway point, to reach the floor, the ball must again reach a point halfway between that point and the floor. As the ball continues falling, the halfway points keep getting smaller but from every point, no matter how small, there is an infinite number of halfway points the ball must reach before it can hit the floor. Therefore the ball will keep falling for an infinite amount of time and will never reach the floor.
 
rkunsaw said:
I've always liked the dropped ball theory about infinite numbers. In case you're not familiar it goes like this:

If you drop a ball from any height, before it can reach the floor it first must reach a point halfway from that height to the floor. From this halfway point, to reach the floor, the ball must again reach a point halfway between that point and the floor. As the ball continues falling, the halfway points keep getting smaller but from every point, no matter how small, there is an infinite number of halfway points the ball must reach before it can hit the floor. Therefore the ball will keep falling for an infinite amount of time and will never reach the floor.
Click to expand...

have you ever dropped a ball? Does it ever hit the floor?
 
But when the ball hits the floor; it is the effect of gravity ; it is not due to infinity theory; a different force, surely?!
 
Infinity is not a number like all other numbers.
For example - can we say that it is odd or even? Prime or composite? Real or complex? We cannot.

We can't place it on the number line. All we can do is use an arrow to indicate it's direction, not it's location.
The algebra of infinity doesn't make much sense either.

Infinity squared = what? infinity?
Infinity minus 1 does not equal infinity, or does it?
 
Both of these examples are different forms of Zeno's paradox. All come from an area of math called Number theory. To define a point in 3D space needs 6 points. Must stop thinking of infinity as a place. Won't work, so vectors are needed, new algebra, sort of a combination of an algebra and a geometry was made called Topology., Banach and Hilbert spaces. Relativity and an insight to infinity was actually solved by Minkowski and a thing called The Lorentz Transform.
transforms, Laplace, Fourier etc transform data in one group of math, to another group without loosing the information.
 
Vivjen said:
But when the ball hits the floor; it is the effect of gravity ; it is not due to infinity theory; a different force, surely?!
Click to expand...
Not so much as one would think. Infinity is an event, and in the words of Hawking, "There are no black holes". At this point gravity does not allow any information transfer to the outside observer (relativity). This has been termed an event horizon. This forms one of the foundations of string theory.
 
My head! My head! Owwwwwwwwwwwww why did I open this thread? I understand waterfalls, breezes, hummingbirds, puppies, why should In deal with this!
 
It's similar to show what critical mass is. Goes like this: Let's say you have an enclosed gymnasium floor (say) and fill the floor
with mouse traps, set with a ping pong ball on each trap. Then, you toss in a ping pong ball.
 
Falcon said:
It's similar to show what critical mass is. Goes like this: Let's say you have an enclosed gymnasium floor (say) and fill the floor
with mouse traps, set with a ping pong ball on each trap. Then, you toss in a ping pong ball.
Click to expand...

I saw the video. A Pepsi commercial.
 
The chain reaction or sustained critical mass is how stars create the matter we see in the Periodic table. What does all this have to do with string theory (quantum mechanic), The Grand Unification Theory and religion (faith)? Quantum reality.
 
AZ Jim said:
My head! My head! Owwwwwwwwwwwww why did I open this thread? I understand waterfalls, breezes, hummingbirds, puppies, why should I deal with this!
Click to expand...

Because if you take the square root of the number of waterfalls, factor in the square of breezes, take hummingbirds to the 9th exponential and multiply by Puppies! (= puppies factorial)(not puppy factory), then you have the Golden Mean, which, as any Mason can tell you, is of the highest importance ...
 
That commercial was interesting as well. Loved the synthesizer background music.

But I get the feeling that it's merely a tribute to the excess sugar energy Pepsi gives you, that you would spend the time and energy setting up something like this.

If that's how the universe began then God must have been a Pepsi addict.
 
If you sit inside a wooden pyramid shaped frame for exactly 20 minutes while reciting the words to your favorite rock song backwards, your gonna reach nirvana - but be careful, you might catch fire, so have a bucket of water handy before you go in. :D
 

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