Infinity -- The Other Way

[Lestat]

Infinity is a hard concept to grasp. I've always found infinitely large a little easier to concieve than infinitely small.

Try not to make fun of me here, but one thing that's boggled my mind since I was a kid is what I've always called, "crossing infinity" (hey, I was a kid). It's not at all complicated, I just don't get it.

Place yourself some distance from a doorway. Say 10 feet. Of course there is no real measurement between you and this doorway. If you were start walking towards the doorway, yet somehow got proportionally smaller and smaller with every step, theoretically you would never reach your destination. You would walk forever without ever reaching the threshold of the doorway.

Of course, there'd probably come a point where you would drop into nothingness (an atom perhaps?), and drift aimlessly forever (I don't know this, but would expect something to that effect). In other words, there would come a point where you couldn't survive, but I digress....

My point is that the starting distance between you and the door is infinite. Am I wrong in this assumption and if so will someone please point out where? If I'm right and it IS theoretically infinite then what boggles my mind is that we are constantly crossing infinity. This is obvious because we can walk right through the doorway and past the infinite measurement that separates us and the doorway.

I know this is dumb, but I can't help wonder if this has something to do with dimensions and why we can't understand the universe.

[Bork]

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

Try that link or google: zeno dichotomy

I certainly dont think the door is an infinite distance away from you, just because you shrink as you walk towards it. The distance is measurable just like any other distance though perhaps YOU would have difficulty measuring it.

I believe we are constantly crossing infinite space can be divided infinitely, and that a good way to think about this is through calculus.

[behemoth2006]

It would never become infinite because the only reason you couldn't reach it would be your lack of mobility... or lack of existance.

But I do know what you mean, it was a weird thought as a kid, and thanks to the above poster for the link.

[Lestat]

Thanks for the link. I'll check it out tomorrow when I have some time.



<font color="blue"> The distance is measurable just like any other distance though perhaps YOU would have difficulty measuring it. </font>

How can any distance be truly measurable? Are there not infinite half-way points between any two objects?

[Lestat]

<font color="blue"> It would never become infinite because the only reason you couldn't reach it would be your lack of mobility... or lack of existance. </font>

Can't any positive integer be divisible by 2?

[Edit:] And still be left with a positive number?

[Bork]

I dont see how the fact that distances could be divided an infinite amount is a problem for measuring.

The temperature could be divided an infinite amount of times yet this doesnt somehow undermine thermometers as far as I know.

You measure it with your ruler that is some accepted standard length, or you could have your friend do it if your shrinking is causing you problems.

[Metric]

Two points:

1) Your example is similar to the convergence of an infinite series in mathematics. There are an infinite number of steps, but that need not imply that the total sum is infinite.

2) Actual physical space is unlikely to actually be infinitely divisible. Advances in quantum gravity (which is also a quantum theory of spacetime), in fact, show that volume and area are fundamentally quantized at the Planck scale, as one might expect from dimensional analysis. It would make no more sense to divide a fundamental quantum of volume that it would make sense to excite "half an electron." Philosophically, this is a nice result -- infinities are never welcome in physics.

[atrifix]

This seems more or less correct. Any continuous interval has an infinite amount of members by the definition of continuity. That does not entail that the sum is infinite because of convergence.

Although quantum physics is based on discrete constants, one of the interesting things is that quantum field theory makes infinite predictions. The renormalization process involves reconstructing finite values from infinite ones.

[malorum]

[ QUOTE ]
lack of existance.

[/ QUOTE ]

Yes. At some stage under the extrapolation proposed your "existence" would no longer be adequately defined according to most physical models.

[ QUOTE ]
Can't any positive integer be divisible by 2?

[Edit:] And still be left with a positive number?

[/ QUOTE ]

Yes you just make a new model that allows infinitely small people. Perhaps not as usefull as a predictive model but much better for understanding fairies.

[Lestat]

<font color="blue"> I dont see how the fact that distances could be divided an infinite amount is a problem for measuring.
</font>

Maybe it's because your mind is more logical than mine (I really have to force myself to think logically).

What I'm saying is that there is an infinity that exists between any two points. It's not infinitive to us, because we can butt a ruler between them or even cross them. However, if you kept shrinking it is theoretically possible that you could walk for eternity trying to get from point 'A' to point 'B' due to halving.

This either means (to my limited capacity mind) that infinity might not exist at all, or that it does exist, but that it can be "breached". I know this is probably silly, but why can't this be a reason why we don't understand the universe? Who's to say that we're not living in a realm that is infinite to us, but not infinite to some other realm? Much in the same way that the distance between two points is finite to us, but would not be if you kept halving the distances.

[jthegreat]

[ QUOTE ]
Much in the same way that the distance between two points is finite to us, but would not be if you kept halving the distances.

[/ QUOTE ]

Even if you keep halving the distances, the distance is finite. As someone said above, the sum of an infinite series can be a finite number.

[luckyme]

[ QUOTE ]
What I'm saying is that there is an infinity that exists between any two points.

[/ QUOTE ]

Yes, but it's not an infinity of distance, it's an infinity of the method of measuring it. You're comparing a measurement to the measuring.

luckyme

[Lestat]

[ QUOTE ]
[ QUOTE ]
What I'm saying is that there is an infinity that exists between any two points.

[/ QUOTE ]

Yes, but it's not an infinity of distance, it's an infinity of the method of measuring it. You're comparing a measurement to the measuring.

luckyme

[/ QUOTE ]

Of course I see what you're saying, but can you find a better way to help me grasp it?

Theoretically there is no limit to how small something can get (or is there?). If so, and you kept shrinking, then the distance from point 'A' to point 'B' would be infinite. That is to say, you'd never get there.

[Lestat]

[ QUOTE ]
As someone said above, the sum of an infinite series can be a finite number.

[/ QUOTE ]

It sounds like this is the correct explanation. Unfortunately, I don't understand it. /images/graemlins/confused.gif

[luckyme]

[ QUOTE ]
If so, and you kept shrinking, then the distance from point 'A' to point 'B' would be infinite. That is to say, you'd never get there.

[/ QUOTE ]

Ok, one more try :-)

Given your view of it, it still is not the distance that is infinite it is the 'steps' taken to cross it that would be.

Say it's 6 ft to the door. You can take it in 2 3ft steps, and it's still 6 ft to the door. You can take it in 3 two ft steps and it's still 6 ft to the door. You can take the steps your way, and it'll take an infinite number of steps, but it's still 6 ft to the door.

It's not even apples and oranges, it's apples and the way we eat them. enjoy

luckyme

[weaklyatomic]

[ QUOTE ]
Infinity is a hard concept to grasp.

[/ QUOTE ]

Then does anybody care to totally blow his mind with an explanation of the different sizes of infinite cardinality, i.e. the fact that there are more real numbers between 0 and 1 then there are positive integers?

[Lestat]

Got it. Thanks. You should be a teacher.

One last thing:

I still say it's not 6 ft to the door. It might be 5.999 (and so on), or 6.000 (and so on), but it will never be exactly 6 ft. To me that means 6 ft can't truly exist, so no maybe no number truly exists. Now I'm confusing myself all over again, so I'll just drop it. It sucks to have such a warped mind. Thanks again.

[Piers]

[ QUOTE ]
Place yourself some distance from a doorway. Say 10 feet. Of course there is no real measurement between you and this doorway. If you were start walking towards the doorway, yet somehow got proportionally smaller and smaller with every step, theoretically you would never reach your destination. You would walk forever without ever reaching the threshold of the doorway.

[/ QUOTE ]

Curious model.

[ QUOTE ]
My point is that the starting distance between you and the door is infinite. Am I wrong in this assumption and if so will someone please point out where? If I'm right and it IS theoretically infinite then what boggles my mind is that we are constantly crossing infinity. This is obvious because we can walk right through the doorway and past the infinite measurement that separates us and the doorway.

[/ QUOTE ]

You make a good case for your model not being particularly useful for opening doors.


[ QUOTE ]
I know this is dumb, but I can't help wonder if this has something to do with dimensions and why we can't understand the universe.

[/ QUOTE ]

Not really. You make a dud model, and observe that it does not fit well with observed reality. You’re looking for mystery where it does not exist.

[ QUOTE ]
Infinity is a hard concept to grasp. I've always found infinitely large a little easier to concieve than infinitely small.

[/ QUOTE ]

Try taking a Maths course.

[atrifix]

Presumably there is some fact of the matter about how far it is to the door. Just because we may not be able to measure it (epistemological premise) doesn't mean that it does not exist (metaphysical conclusion). You are assuming that it is 6 feet to the door, but even if we were talking about real doors, you could just say it's 'about' 6 feet to the door.

[TimM]

Here's one that will really bake your noodle.

Is it possible for something to have always existed? That is, it was created and has existed since T minus infinity. But for that to have happened, an infinite amount of time must have passed to get to the present. How is this possible?

[godBoy]

perhaps the bounds of time a just another creation. Maybe time was created from an eternal place. So time as we know it may not have existed for ever, but something has outside of it.

If time was created at some point it is possible for something that was around before time to have existed for T minus infinity.

Perhaps.

[MidGe]

god"boy",

ease off on using another creation whenever you don't understand something. /images/graemlins/smile.gif

A time unit is only the smallest possible amount of change in the universe (all that there is, however you want to define it). If there is no change there is no time in any conceivable or measurable way. The smallest possible change (whatever that is, ie the slowing town of the spin of one electron, for instance), allows you to compare one moment with the other and note that time has elapsed. Time is a derived measure, not an absolute one! No changes whatsoever means no time, in any meaningful way!

[godBoy]

Do you just look for my name and prep for attack, i'm yet to hear your thoughts on the threads question, after all you understand much more than I do about most things, right?

[ QUOTE ]
If there is no change there is no time in any conceivable or measurable way.

[/ QUOTE ]

This is kinda silly. To be no change at all means there is nothing living, moving. Absolute nothing. Because this is surely not the case, defining time on something this theoretical is useless. Time exists now, you don't understand why, it is surely possible it was created.

Doesn't the Big Bang suggest a beginning? or are you a fan of the expanding collapsing universes, or maybe the parralell universe theory, these are all far more rational ideas.

[MidGe]

You are getting there godboy, and, of course, I wait with anticipation your appearance on the forums. /images/graemlins/smile.gif

[ QUOTE ]

To be no change at all means there is nothing living, moving. Absolute nothing

[/ QUOTE ]

Indeed... and no time!

As far as the big bang is concerned, the theory doesn't offer any speculation about before!

[lufbradolly]

[ QUOTE ]

2) Actual physical space is unlikely to actually be infinitely divisible. Advances in quantum gravity (which is also a quantum theory of spacetime), in fact, show that volume and area are fundamentally quantized at the Planck scale, as one might expect from dimensional analysis. It would make no more sense to divide a fundamental quantum of volume that it would make sense to excite "half an electron." Philosophically, this is a nice result -- infinities are never welcome in physics.

[/ QUOTE ]

How can the physical space not be infinitely divisable?

The real number set isn't finite.

[Zygote]

In short, special relativity solves the problems.

Don't bother with the wikipedia link, though, and, rather, go to this webpage for the best explanation of the paradoxs that i've ever seen: http://mathpages.com/rr/s3-07/3-07.htm

[Lestat]

Cool link. Thanks!

[Metric]

[ QUOTE ]

How can the physical space not be infinitely divisable?

The real number set isn't finite.

[/ QUOTE ]
What is meant is that the operators corresponding to volume, area, etc. have a discrete spectrum -- 0, 1, 2, 3, etc. in appropriate units.

[_TKO_]

[ QUOTE ]
How can any distance be truly measurable? Are there not infinite half-way points between any two objects?

[/ QUOTE ]

Consider the fact that all measurements have some degree of error. While there are an infinite number of half-way points between two points, there are not an infinite number of <u>measurable</u> half-way points between two points.

[_TKO_]

[ QUOTE ]
Can't any positive integer be divisible by 2?

[/ QUOTE ]

Yes, but integers only exists in pure mathematics. Natural numbers exist when counting (ie 1 apple, 2 cards, 3 of a kind). All physical measurements are real numbers.

[Meromorphic]

[ QUOTE ]
How can the physical space not be infinitely divisable?

The real number set isn't finite.

[/ QUOTE ]

This is almost like insisting that you must be able to get lumber of any length at Home Depot because your tape measure is continuous. /images/graemlins/wink.gif

[bearly]

there is a distinction to be made between 'infinite' and 'infinitly divisable'. that is your conceptual confusion. although i am not schooled in math i can understand the concepts involved in 'infinitesimal' calculus. they may not use that exact formulation today, but that doesn't invalidate the point--ie. the use that the concept of infinite divisibilaty was put to.............b