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.