Infinity... Can God conceive it?

[mooeypoo]

Ever heard of "Exponentials" ?

 

That's all it means.. this is decreasing exponentially, which means it would never get to zero - but will keep getting smaller and smaller. The smaller fractions are showing you that principle.

 

Our brain is "trained" to find patterns even when none are intentionally there. Think of the clouds, for example. Look up to the clouds and see shapes and patterns, same goes with the stars, and ink blots. That's how our brain evolved. We will find patterns anywhere, but that doesn't mean a pattern was designed to be there.

[Baby Astronaut]

No, I meant literally add them up, to look for a pattern.

1/2 =

1/2 + 1/4 =

1/2 + 1/4 + 1/8 =

1/2 + 1/4 + 1/8 + 1/16 =

1/2 + 1/4 + 1/8 + 1/16 + 1/32 =

...

See if you can find a pattern.

The denominator of the last added fraction matches the denominator of the answer.

 

1/2 = 1/2

 

1/2 + 1/4 = 3/4

 

1/2 + 1/4 + 1/8 = 7/8

 

1/2 + 1/4 + 1/8 + 1/16 = 15/16

 

1/2 + 1/4 + 1/8 + 1/16 + 1/32 = 31/32

 

1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 = 63/64

 

1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 = 127/128

 

 

What's the relevance to time?

[Mr Skeptic]

I see the pattern, what are you trying to show though? What does this mean?

 

If you were to go on forever, even though you add an infinite number of them, you would never get higher than 1. Even though you add up an infinite number of terms, because they get smaller at a fast enough rate, you end up with a finite number. So in your example with a Zeno type paradox, what you have is an infinite number of time intervals, but a finite amount of time.

[Baby Astronaut]

Oops, cross-posted before. Took me a while to add up the fractions and compare

 

I have a paradox for you....

 

It is similar to Zeno's room paradox.

 

Consider that one second of time has occurred. Before one half of a second can occur, one quarter must elapse . Before a forth can elapse; one eighth must occur; and so on.

 

Is it fair to say that an infinite amount of "time" has happened within one second?

You've expanded my mind. Wow. How dare you?

 

That is fascinating. So it's possible that from the Big Bang to the Next Big Thing, we might actually exist in one infinite second, and within our portion of that second, we've created even more units of time to sub-divide further, and each of those new units might be infinite as well.

 

w

o

o

o

o

o

o

o

o

o

o

o

o

 

 

Ever heard of "Exponentials" ?

 

That's all it means.. this is decreasing exponentially, which means it would never get to zero - but will keep getting smaller and smaller.

 

If you were to go on forever, even though you add an infinite number of them, you would never get higher than 1.

That is exactly what Syntho-sis's Zeno paradox (mental-exercise) concluded. Or at least it seemed to.

 

(we'd never reach "1")

 

Even though you add up an infinite number of terms, because they get smaller at a fast enough rate, you end up with a finite number.

But they won't *dissipate* into a finite number, regardless of how crazily fast you add up the sub-divided terms. Even at planck lengths, it might sub-divide -- we only lose the ability to measure the division, but time itself might still be able to keep dividing.

[padren]

It is similar to Zeno's dichotomy paradox

 

Consider that one second of time has occurred. Before one half of a second can occur, one quarter must elapse . Before a forth can elapse; one eighth must occur; and so on.

 

Until the actual second is realized.

 

This is puzzling...Has a second even really "happened"? By this reasoning it would not even be able to be 1/2...because you could continuously divide.

 

Or could you use the argument that the measurement of one second encompasses all the irrational measurements that make it up?

 

Now I know that mathematicians no longer consider Zeno's paradoxes valid, but I think they bring an interesting perspective to the infinite as both a mathematical property and a metaphysical concept.

 

Is it fair to say that an infinite amount of "time" has happened within one second?

 

First, the fun thing about paradoxes is they apparently show how the universe contradicts itself, because they play on our model of the universe - it's only our understanding, not the universe itself, that is flawed.

 

With regards to the question of "one second" and whether it's an infinite amount of time - answer would be "no, but you could have an infinite number of slices each half the size of the previous slice, in one finite second."

 

If space and mass could be infinitely dividable, take one grain of sand that weighs x. That grain is the sum of two halves of a grain of sand. Each of those halves, are the sum of two halves of that... Since you can keep dividing forever without running out of mass to cut in half, you could have an infinite number of "parts" of sand in that one grain of sand. Does that mean it's infinitely massive? Of course not, because while you can have an infinite number of slices, each slice accounts for half of the last, and the sum does equal one grain of sand.

 

More importantly, these divisions don't exist in the grain of sand itself - but in our minds, in how we choose to think about that grain of sand. We may look at it in a way that boggles our minds, but that's just our mind failing to process the model in a manner that reconciles with our observations about the universe.

[Baby Astronaut]

I came back to post that I concluded a similar thing. You're entirely correct, padren.

 

The universe doesn't really have these units called seconds, nor would it have it conveniently quantified for our benefit and/or instruments we use for measuring time's passage. So my error was in following the thought based on our self-assigned, numerical divisions of time -- instead of on reality (i.e. the actual universe).

[Syntho-sis]

I came back to post that I concluded a similar thing. You're entirely correct, padren.

 

The universe doesn't really have these units called seconds, nor would it have it conveniently quantified for our benefit and/or instruments we use for measuring time's passage. So my error was in following the thought based on our self-assigned, numerical divisions of time -- instead of on reality (i.e. the actual universe).

 

That is the point I was trying to get across...The way we measure is simply just a system of organized amounts and symbols based off of their numerical values.

 

Time is a real effect in our universe. Just because humans invented a way of measuring it, does not mean that it is simply an abstract idea.

 

That is like saying that volume does not exist, if you have no way of measuring it. Or length, there are many examples.

 

The packets that you spoke of earlier sort of reminded me of the quanta- packets of energy.

 

There's a thought, in what ways do quantum mechanics apply to the infinite or vice-versa. Both are mysterious concepts, that we have yet to fully understand.

 

Or something along those lines haha