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Maybe it is the wine - but. . . (infinity question)

episodic

episodic

Lifer
Ok so my wife and I were talking.

A second has infinite divisions. . . 1/2 sec, 1/8 sec, 1/16 sec, and so on forever.

Yet we experience infinite divisions in only a second. How can the infinite be finite?

So we experience infinity during each second we live - so how many infinities are there. And what if our universe is just an infinite second in some other world.

Yea. . .

Happy new years.
 
Originally posted by: episodic
Yet we experience infinite divisions in only a second. How can the infinite be finite?
Click to expand...
Read a bit about limits. An infinite series can converge to a finite result.
 
Originally posted by: Chaotic42
Some people think that time is granular and that there is a smallest unit of time, called the planck second. Link
Click to expand...


whatever, think he went to get the pics? 🙂
 
Originally posted by: Heisenberg
Originally posted by: episodic
Yet we experience infinite divisions in only a second. How can the infinite be finite?
Click to expand...
Read a bit about limits. An infinite series can converge to a finite result.
Click to expand...

True, but convergence doesn't mean the exact result, just a closer and closer approximation.

To the OP, the only way we perceive time (even seconds) is through gradual changes and the changes made in the firing of the neurons in our brains.

There is no way to conclusively proof that "time" doesn't in our closed system (observable universe) uniformly fluctuate. A second right now could actually be a millenia in another second... Of course this idea is very abstract. The point is that you cannot express time without expressing change (from the clicking of the gears in a clock, the movement of the stars and planets, the rotation and decay of an atom... all show change and we observe these changes in incremental steps that can be measured. There is no way to measure the "second" itself without measuring the "change". (this concept is even discussed in Aristotle's works) Hope that helps. Or maybe it just mucks up the pointless discussion anyways.
 
Good question, and one that's been thought on for a long time (see Zeno's Paradox on Wikipedia). What you said about time holds for distance as well. How can your hand ever reach out and touch an object if first it must reach the midpoint (m) between itself and the object, and then the midpoint (mm) between that point (m) and the object, and then the midpoint (mmm) between that point (mm) and the object, ad infinitum... An apparent infinity of points between your hand and the object, yet you easily touch the object. Interesting stuff!
 
Originally posted by: thehstrybean
Originally posted by: bctbct
Originally posted by: Chaotic42
Some people think that time is granular and that there is a smallest unit of time, called the planck second. Link
Click to expand...


whatever, think he went to get the pics? 🙂
Click to expand...

I hope so...
Click to expand...


we must be cool because the nerds are still talkng about the main topic :laugh:
 
Originally posted by: DaShen
Originally posted by: Heisenberg
Originally posted by: episodic
Yet we experience infinite divisions in only a second. How can the infinite be finite?
Click to expand...
Read a bit about limits. An infinite series can converge to a finite result.
Click to expand...

True, but convergence doesn't mean the exact result, just a closer and closer approximation.

To the OP, the only way we perceive time (even seconds) is through gradual changes and the changes made in the firing of the neurons in our brains.

There is no way to conclusively proof that "time" doesn't in our closed system (observable universe) uniformly fluctuate. A second right now could actually be a millenia in another second... Of course this idea is very abstract. The point is that you cannot express time without expressing change (from the clicking of the gears in a clock, the movement of the stars and planets, the rotation and decay of an atom... all show change and we observe these changes in incremental steps that can be measured. There is no way to measure the "second" itself without measuring the "change". (this concept is even discussed in Aristotle's works) Hope that helps. Or maybe it just mucks up the pointless discussion anyways.
Click to expand...
Usually, convergence means that a series/sequence approaches a finite limit. There are ways to determine this limit in some cases without working out every term, in which case the limit is exact. And what you're describing about the nonuniformity of time is essentially Einstein's theory of special relativity - i.e. every inertial frame has its own time, and there is no absolute reference for time.

/steps off super-nerd soapbox
 
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