|
|
|
|
|
|
|
|
|
 Posted: Sun Jan 21, 2007 9:46 am
MistressPaco glitch11 MistressPaco glitch11 MistressPaco glitch11 quarks are the smallest thing we know aboot,but there most likely colossal compared to what really is the smallest thing in the universe. We still can't grasp forever so long as there is a smallest and a largest concept in the world, and to say that there is something always bigger or somethign always smaller -forever-...well to me would some how prove the existance of god XD but that's a bit off the topic. I don't believe in god, in such, any particular religious figure (Agnostic I suppose is the word). But my thoughts are how far does the universe extend, it can' tpossibly go on forever or could it? Trying to fathom the idea of largest, smallest, and furthest has just boggled the hell out of my mind. From M-Paco <_< Captain ADD. Well an infinite and a limited unverse both make no logical sense. Yeah. Nither can really be proven, ever. (well the limited one can) but...if it was limited, there has to be something after it. Doesn't there? nothing can simply just....stop, and there be 'nothing' after it x.x. Unless it were to continue onto it's self, like those old video games where you ran off the screen at the bottom and appeared back at the top. Are you suggesting the universe is round? Not so much round, as in having a 'shape' (because there'd need to be something that would be around that closed shape) but that it continues onto it's self. as in if you just kept going straight, you'd eventually end up back where you came, no matter which way you went. I heard the idea some where, and it seemed like as good an idea as any. Given it can't go on forever nor can it really just stop. So you suggesting the universe is spherical into itself?
|
 |
|
|
|
|
|
|
|
|
|
|
|
|
|
Posted: Sun Jan 21, 2007 7:56 pm
-[[Yreka!]]-
Think that you're walking towards a wall. You go half way, then another half way, and so on and so forth. You will always be going 1/2 of the distance you need to go. You technically would then never reach the wall. But we do. Why?
That's Zeno's paradox.
Do we reach the wall? I think that can be debated a bit. First, when you "touch" an object, you aren't really touching in in a sense. Your molecules remain somehow discreet from the molecules of that which you're "touching" so while there is a transfer of information there, there's still a layer between you and what you're touching. If there weren't you'd sort of become that object in as much as you'd be inseperable from it. Of course such a debate is silly to our everyday sensual awareness, but... eh, it just came to mind. whee
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Posted: Mon Jan 22, 2007 8:47 am
Starlock -[[Yreka!]]-
Think that you're walking towards a wall. You go half way, then another half way, and so on and so forth. You will always be going 1/2 of the distance you need to go. You technically would then never reach the wall. But we do. Why?
That's Zeno's paradox.
Do we reach the wall? I think that can be debated a bit. First, when you "touch" an object, you aren't really touching in in a sense. Your molecules remain somehow discreet from the molecules of that which you're "touching" so while there is a transfer of information there, there's still a layer between you and what you're touching. If there weren't you'd sort of become that object in as much as you'd be inseperable from it. Of course such a debate is silly to our everyday sensual awareness, but... eh, it just came to mind. whee
Technically, you're right. Nothing touches anything, so technically you could say that everything floats. xD But even so, what would be the force that stops us from "touching" the object? That and what the hell is logic/does it apply is what i'm trying to figure out.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Posted: Mon Jan 22, 2007 8:56 am
-[[Yreka!]]- Starlock -[[Yreka!]]-
Think that you're walking towards a wall. You go half way, then another half way, and so on and so forth. You will always be going 1/2 of the distance you need to go. You technically would then never reach the wall. But we do. Why?
That's Zeno's paradox.
Do we reach the wall? I think that can be debated a bit. First, when you "touch" an object, you aren't really touching in in a sense. Your molecules remain somehow discreet from the molecules of that which you're "touching" so while there is a transfer of information there, there's still a layer between you and what you're touching. If there weren't you'd sort of become that object in as much as you'd be inseperable from it. Of course such a debate is silly to our everyday sensual awareness, but... eh, it just came to mind. whee
Technically, you're right. Nothing touches anything, so technically you could say that everything floats. xD But even so, what would be the force that stops us from "touching" the object? That and what the hell is logic/does it apply is what i'm trying to figure out.
I'm pretty sure it's just the intrinsic properties of the molecules. Unless a covalent bond forms between the toucher and thing touched, there's no literal connection between the two things.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Posted: Tue Jan 23, 2007 1:10 am
The smallest unit would be at the Planck scale. Anything smaller simply does not make any sense in using current physics [for the record, elementary particles — electrons, quarks and the like — are modelled as point particles and do not have a well-defined concept of "size" beyond their mass; "touch" is an artefact of the appearance of size from the electromagnetic repulsion].
Anyway, Zeno's Paradox sets up the scenario so that with each iteration you asymptotically approach the time where you reach the wall, so we just have to show that the geometric series converges on a finite value. It's logical, just set up in a flawed fashion.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Posted: Tue Jan 23, 2007 10:18 am
A Lost Iguana The smallest unit would be at the Planck scale. Anything smaller simply does not make any sense in using current physics [for the record, elementary particles — electrons, quarks and the like — are modelled as point particles and do not have a well-defined concept of "size" beyond their mass; "touch" is an artefact of the appearance of size from the electromagnetic repulsion]. Anyway, Zeno's Paradox sets up the scenario so that with each iteration you asymptotically approach the time where you reach the wall, so we just have to show that the geometric series converges on a finite value. It's logical, just set up in a flawed fashion.
Except then you'd have to define logic in a fluid enough way to cover that thought and everything else it would apply to.
It was part of my original question....
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Posted: Fri Feb 16, 2007 1:31 am
Rookherst[KOS] Zeno's paradox is solved with simple Mathematical Fact/ Truth .999 Repeating = 1 0.999 Repeating =/= 1 Decimals are approximations. 1/3 does not equal 0.333 Repeating, 2/3 does not equal 0.666 Repeating and 3/3 does not equal 0.999 Repeating. The fractions are accurate (3/3 = 1) but the decimals are not.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Posted: Fri Feb 16, 2007 1:34 am
oh yes 123 Rookherst[KOS] Zeno's paradox is solved with simple Mathematical Fact/ Truth .999 Repeating = 1 0.999 Repeating =/= 1 Decimals are approximations. 1/3 does not equal 0.333 Repeating, 2/3 does not equal 0.666 Repeating and 3/3 does not equal 0.999 Repeating. The fractions are accurate (3/3 = 1) but the decimals are not. Sorry... I don't have the Proof for you now, but it is a Mathematical Fact.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Posted: Fri Feb 16, 2007 1:37 am
-[[Yreka!]]-
So today after my Physics final (last one, yay), I started thinking of Zeno's Paradox. It's kinda logical in one sense, but illogical like all other paradoxes. What is logic? Without knowing what it is, there is no feasible way to figure out a paradox I think.
I'm assuming that this is the paradox... -[[Yreka!]]-
Think that you're walking towards a wall. You go half way, then another half way, and so on and so forth. You will always be going 1/2 of the distance you need to go. You technically would then never reach the wall. But we do. Why?
Technically, you're not always going half the distance. Am I missing something?
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Posted: Fri Feb 16, 2007 1:39 am
Rookherst[KOS] oh yes 123 Rookherst[KOS] Zeno's paradox is solved with simple Mathematical Fact/ Truth .999 Repeating = 1 0.999 Repeating =/= 1 Decimals are approximations. 1/3 does not equal 0.333 Repeating, 2/3 does not equal 0.666 Repeating and 3/3 does not equal 0.999 Repeating. The fractions are accurate (3/3 = 1) but the decimals are not. Sorry... I don't have the Proof for you now, but it is a Mathematical Fact. In that case, I'll want the proof later. You do realise that decimals are only approximations though, don't you?
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Posted: Fri Feb 16, 2007 1:40 am
oh yes 123 In that case, I'll want the proof later. You do realise that decimals are only approximations though, don't you? Yes, I do. I'm no Mathematician though. I'll have to find where I read this.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Posted: Fri Feb 16, 2007 1:50 am
Rookherst[KOS] oh yes 123 In that case, I'll want the proof later. You do realise that decimals are only approximations though, don't you? Yes, I do. I'm no Mathematician though. I'll have to find where I read this. The "proof" I heard was the one I dealt with above. Though I lack a High School Graduate's knowledge of mathematics, so it's not as though I'd know any more than you...
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Posted: Mon Mar 05, 2007 12:16 pm
oh yes 123 Rookherst[KOS] Zeno's paradox is solved with simple Mathematical Fact/ Truth .999 Repeating = 1 0.999 Repeating =/= 1 Decimals are approximations. 1/3 does not equal 0.333 Repeating, 2/3 does not equal 0.666 Repeating and 3/3 does not equal 0.999 Repeating. The fractions are accurate (3/3 = 1) but the decimals are not. 0.333 and 0.999 are exact — 333/1000 and 999/1000, respectively — and 0.999… is: 9/10 + 9/100 + 9/1000 + 9/10000 + … = ∑_{n=1}^{∞} 9/(10^n) = 1 The "…" part is not to be underestimated. 0.999… is just another way of writing 1. Think about it another way: what would you right down if you tried to divide 1 by 3 using long division? You would forever be carrying the remainder and putting another digit on the end of the sequence. "0.333…" is how we refer to that action. http://en.wikipedia.org/wiki/0.999...This has been done to death far too many times. rolleyes
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Posted: Thu Mar 08, 2007 5:21 am
oh yes 123 -[[Yreka!]]-
So today after my Physics final (last one, yay), I started thinking of Zeno's Paradox. It's kinda logical in one sense, but illogical like all other paradoxes. What is logic? Without knowing what it is, there is no feasible way to figure out a paradox I think.
I'm assuming that this is the paradox... -[[Yreka!]]-
Think that you're walking towards a wall. You go half way, then another half way, and so on and so forth. You will always be going 1/2 of the distance you need to go. You technically would then never reach the wall. But we do. Why?
Technically, you're not always going half the distance. Am I missing something?
That bit isn't the paradox. The second part you quoted is.
You would be if going by the paradox. It seems logical (by current definition) and yet it doesn't seem to apply. But yes, you do go half the distance then half again until some barrier either stops us or our thoughts about it could just be superficial.
To the .999...=1 bit, there still is no logical explination for it even though the equations do offer relatively solid proof. We are still discovering things in math so it may be solved in a different way in the future. For now though it is a mathmatical truth. It doesn't solve the paradox though for the simple reason that reaching .999... is practically impossible.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Posted: Thu Mar 08, 2007 10:58 pm
A Lost Iguana 0.333 and 0.999 are exact — 333/1000 and 999/1000, respectively — and 0.999… is: 9/10 + 9/100 + 9/1000 + 9/10000 + … = ∑_{n=1}^{∞} 9/(10^n) = 1 The "…" part is not to be underestimated. 0.999… is just another way of writing 1. Think about it another way: what would you right down if you tried to divide 1 by 3 using long division? You would forever be carrying the remainder and putting another digit on the end of the sequence. "0.333…" is how we refer to that action. http://en.wikipedia.org/wiki/0.999... I didn't understand the equation; without it, I'm inclined to go with my Maths teacher who told me that decimals were approximations (and dealt with the 0.999 thing). A Lost Iguana This has been done to death far too many times. rolleyes I apologise, I'm working with limited knowledge.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
![-[[Yreka!]]-'s avatar](https://a1cdn.gaiaonline.com/dress-up/avatar/ava/2b/7b/2e4fb4412a7b2b_flip.png?t=1341960199_6.00_11)
![Rookherst[KOS]'s avatar](https://a1cdn.gaiaonline.com/dress-up/avatar/ava/1c/32/2b1f6af436321c_flip.png?t=1193918574_6.00_11)