Infinite distance between two fingers.

[imported_Armen]

Hey could someone disprove my theory. Well I'm sure there were people before me who taught about it but I'd like to name it mine, since I discovered it without out side knowledge.

Two lines are approaching to each other.
You get to a point that the two lines are very close and about to hit each other.
You zoom in to that region, and the distance appears to be bigger.
again you get them to be as close as they can and zoom in that region where they are about to meet.
Thats a loop right there.

now imagine the lines are fingers.

--------------------------------------------------------SOLVED or BUSTED.
basically by zooming in your slowing the speed of lines that are approaching.
you can infinitly slow down time until you stop almost stop it.
Lim(time) when time --->0
-------------------------------------------------------------------------------

EDIT:
HOW about this one, I already posted this at the end of the thread.
SO here is another one i though of 5 years ago.
According to Einstein there should be future references that exist respect to us (present time dwellers) right?
If that is true and also the concept of NOTING IS IMPOSSIBLE, even inventing a time machine, then why
our future people haven't yet visited us?

Stupid I know, but I'd like to hear YOUR VOICES. that's right. I want YOUR opinion. YOU.

 

[FleshLight]

No it isn't infinite. However, there are an infinite number of unit conversions you can do.

 

[dugweb]

Originally posted by: Armen
Hey could someone disprove my theory. Well I'm sure there were people before me who taught about it but I'd like to name it mine, since I discovered it without out side knowledge.

Two lines are approaching to each other.
You get to a point that the two lines are very close and about to hit each other.
You zoom in to that region, and the distance appears to be bigger.
again you get them to be as close as they can and zoom in that region where they are about to meet.
Thats a loop right there.

now imagine the lines are fingers.

:shocked:

edit: what about when you zoom in onto the two lines so close that you are looking at two atoms approaching each other. do those ever touch?

 

[chuckywang]

This is just a version of Zeno's Paradox.

http://en.wikipedia.org/wiki/Zeno's_paradoxes

 

[imported_Armen]

ok ok. When i saw it, i was using illustrator and as you know vectors don;t loose quality. so i was doing it for a long time until the magnifier didn;t allow me to zoom in more, but if it did, I would have done it for ever.
For fingers, maybe they never touch but the molecule forces repel each other. I can go with that, but what about if you draw two lines on a paper. you can still treat the lines as a vector.

 

[George P Burdell]

Isn't that the difference between x -> y and x = y?

 

[Cerpin Taxt]

The difficulty talking about things like this is in the different senses of "infinite" which can be brought to bear on the circumstances you described. On the one hand, the interval between your two objects (lines, fingers, whatever) is bounded by those objects as endpoints. You can say that the interval is finite. However, if that interval is properly modeled as a continuum (which it is, IMO), then you can halve the interval ad infinitum. That is to say, you can infinitely subdivide the "finite" interval.

 

[imported_Armen]

Originally posted by: George P Burdell
Isn't that the difference between x -> y and x = y?

you mean lim of x approches y?

Originally posted by: Garth
The difficulty talking about things like this is in the different senses of "infinite" which can be brought to bear on the circumstances you described. On the one hand, the interval between your two objects (lines, fingers, whatever) is bounded by those objects as endpoints. You can say that the interval is finite. However, if that interval is properly modeled as a continuum (which it is, IMO), then you can halve the interval ad infinitum. That is to say, you can infinitely subdivide the "finite" interval.

I understand the concept of infinite subdivision in a finite interval. but that doesn't prove why bounded points theoretically never reach. my point is different though. I think i understood my out theory.
I think it has to do with time. my two lies are approaching with speed v=10 m/s and are close enough then we zoom in.
now we make them get closer to each other with speed v=10 m/s respect to this scale (the zoomed in). so by zooming infinity we are basically slowing down time for the two lines to meet.

 

[Skyclad1uhm1]

You can zoom in infinitely, but the points will meet if you do not slow or stop the movement of time.

Look at it this way: if y=5 and x=0, but x is raised by 1 every second, you can say it will reach y at 5 seconds. But if you look at 1/millionth of a second instead if will seem it will take almost infinite time to get to it, simply because you look at a fraction of the time.

You will never be able to type a character if you zoom in on time enough and keep looking at those tiny fragments of time. But still here you are, typing away. Simply because time does not work like that, it does continue

 

[AeroEngy]

Originally posted by: Armen
I understand the concept of infinite subdivision in a finite interval. but that doesn't prove why bounded points theoretically never reach. my point is different though. I think i understood my out theory.
I think it has to do with time. my two lies are approaching with speed v=10 m/s and are close enough then we zoom in.
now we make them get closer to each other with speed v=10 m/s respect to this scale (the zoomed in). so by zooming infinity we are basically slowing down time for the two lines to meet.

Essentially you are slowing down the relative speed of the approaching lines as you zoom in. So Basically they are initially approaching at 10 (units/s) then if you zoom in 10x and say they are 10 (units/s) with respect to the new scale. Then that means they you slowed them down to only 1 (unit/s) in the original reference frame. If you keep repeating this they they their relative velocity will approach zero in the original reference frame.

So No they are not infinitely apart you are just reducing their speed as they get closer together. So as time approaches infinity their distance approaches zero only because you keep slowing them down.

 

[NikolaeVarius]

Well, there's Planck Distance which is the smallest distance something can move. Once you hit that, its over

 

[RadiclDreamer]

Originally posted by: Armen
ok ok. When i saw it, i was using illustrator and as you know vectors don;t loose quality. so i was doing it for a long time until the magnifier didn;t allow me to zoom in more, but if it did, I would have done it for ever.
For fingers, maybe they never touch but the molecule forces repel each other. I can go with that, but what about if you draw two lines on a paper. you can still treat the lines as a vector.

LOSE

 

[rivan]

Are the fingers in your example bulk? Or are they about the size of a car battery?

 

[nakedfrog]

Originally posted by: chuckywang
This is just a version of Zeno's Paradox.

http://en.wikipedia.org/wiki/Zeno's_paradoxes

Yeah, Achilles and the Tortoise immediately came to mind upon reading the OP.

 

[Triumph]

Originally posted by: Armen
Hey could someone disprove my theory. Well I'm sure there were people before me who taught about it but I'd like to name it mine, since I discovered it without out side knowledge.

Two lines are approaching to each other.
You get to a point that the two lines are very close and about to hit each other.
You zoom in to that region, and the distance appears to be bigger.
again you get them to be as close as they can and zoom in that region where they are about to meet.
Thats a loop right there.

now imagine the lines are fingers.

I don't understand where the paradox is. Do you not understand how zooming works? It makes things look bigger. Eventually you would zoom to the point where the lines are out of frame. Or, if you were microscopic, you would get closer and closer to the intersection until you were between the two points. At that point, put your miniature ruler between the ends and measure. Where is the paradox?

And why would the distance be infinite? Two parallel lines never touch, that doesn't make the distance between them infinite.

 

[BrownTown]

Yes, its just a mind game there, they are most definitely a finite distance apart. Achilles will outrun the tortoise, the 20 other similar "paradoxes" will all actually work out. Its just using fancy definitions and such to try to confuse people into getting an obvious question wrong. So if you are an idiot (like Achilles) than you can get tricked into losing a race to a turtle, if not then your fine.

 

[bvalpati]

If you sample music at a rate of 44,000 samples per second (standard compact disc resolution) how much music are you not capturing?

 

[MrPickins]

L2calculus.

 

[Chryso]

The distance doesn't increase just because you zoom in.

 

[Cerpin Taxt]

Originally posted by: Armen

Originally posted by: Garth
The difficulty talking about things like this is in the different senses of "infinite" which can be brought to bear on the circumstances you described. On the one hand, the interval between your two objects (lines, fingers, whatever) is bounded by those objects as endpoints. You can say that the interval is finite. However, if that interval is properly modeled as a continuum (which it is, IMO), then you can halve the interval ad infinitum. That is to say, you can infinitely subdivide the "finite" interval.

I understand the concept of infinite subdivision in a finite interval. but that doesn't prove why bounded points theoretically never reach. my point is different though. I think i understood my out theory.

The bolded part is false. They will reach, given an infinite amount of time.

 

[Aluvus]

"Dude, my hands are huge. They can touch anything but themselves... Oh, wait."

 

[Dacalo]

I remember this theory in a philosophy class.

The distance doesn't change though, only your perception. You can zoom in and zoom out as much as you want, but the distance remains the same. Go have fun with Google map.

 

[silverpig]

0.999... = 1

 

[Triumph]

Originally posted by: Chryso
The distance doesn't increase just because you zoom in.

Haha, I struggled for a while to explain exactly this. It was like my brain saw the true paradox in trying to figure out how exactly this was a paradox. Thanks.

"Hay guys, if I bring my face closer to the monitor, the edges get farther away from each other! Eventually, if I do this for a while, I'll have a 24" monitor instead of 20"!"

 

[imported_Armen]

I got it. Thank you.
Now how about this one. and thank you RadiclDreamer for cathcing mye mestakes.

SO here is another one i though of 5 years ago.
According to Einstein there is a future, past present future, they all co exist.
If that is true and also the concept of NOTING IS IMPOSSIBLE, which i strongly believe it does, even inventing a time machine, then why our future people haven't yet visited us?
or they have?

Stupid I know, but I'd like to hear YOUR VOICES. that's right. I want YOUR opinion. YOU.