[QUOTE=sheyzok;17353317][img]http://www.wowfailblog.com/wp-content/uploads/2009/06/pancake-bunny.jpg[/img][/QUOTE]
Neither have I, my alter personality takes over from time to time and I have no idea what he's talking about.
[QUOTE=EcksDee;17353235]If you walk over a line, you're not going to be 0.000000000000001 nanometers away from the line, you're going to cross the line. As is with the graph, if it is not parallell with the axes, it WILL cross them at one point or another.
And also infinity is just a model, it can not be replicated and it does not exist in real life.
[b]even if it is 1 x 10^24 meters,[/b]
I thought we were talking about nanometers here, not a billion million million kilometers.
Maybe you meant 1x10^-24M.
This doesn't make sense, if you're sprinting, you're not going to SLOW DOWN for the sole purpose of being 1 picometer away from the line, you're going to speed past it.
Sure you can think that you can keep on measuring the distance between your shoe and the finish line until they're like a picometer apart, and then keep going until the distance is infinitely small, that's just the thing, I don't remember there being anything that's infinitely small.Since real life doesn't work like that, you'll just go over the line.[/QUOTE]
You're missing the point of the paradox. In order to get anywhere, you have to travel across and infinite number of smaller distances, so how can you get anywhere at all?
So if you put a dot somewhere and I walked up to it and put my foot on it, would I still be a distance away from it? That doesn't make sense as I can't possibly get any closer to the dot.
This is like that "To get there you have to get half the way there, than half that, then half that and so on, so you'll never get there" No fuck off, I will.
Let me guess, you just learned what an asymptote is in school?...
[QUOTE=john_pelphre;17346396]I don't know if this have been theorized or not, but I though of something.
[img]http://imgkk.com/i/BhCpiC.png[/img]
This is a graph. This graph is special for one reason. It will continue for ever, but will never cross the Y-axis or X-axis. Ever. It goes on forever, but never contacts the axi's. It will go to the the smallest interval, but will never touch "0", Why?
Mathematically speaking, the reason this graph will never touch the axis is because is the graph of the equation (1/x). The reason it can never touch 0, is we have no clue what happens a number, such as 1, is divided 0 times. You also can have a square root of a negative number, because the answer becomes imaginary, but I digress.
The reason for this? Well, you can use graphs to show relation to things in real life, and I began to wonder. What happens if this graph is related to real life?
Now, lets use an example. Say you are walking to a destination one kilometer away. It takes 20 minutes to get there, average walking speed 3 Kilometer per hour, just as an example. . So, after 19 minutes, 30 seconds, your only about a meter away. So, you keep walking.
Your one decimeter away.
Continue.
Your a centimeter away.
Than, a millimeter. Pentameter. Hexameter. Septameter. Picometer. Nanometer.
You can continue forever, to the nth-meter. There is an infinite measure of how accurate, and you can continue forever. There is a infinte distance you can be.
From .01, to .000000000000000000000000000000000000000000000000000000001
Then how can you reach a destination, in anytime?
Well, people round everything to set amounts. Such as you wouldn't say 1000 meters, you most likely would say 1 kilo. Not 100 centi-seconds, but one second. Its weird, but if you think about it. You are always some distance from your destination, even if it is 1 x 10^24 meters, or a yoctometer, away.[/QUOTE]
This teory was created by some famous matematical philosopher, but i dont renember his name. If it was really you that thought of this, then i concratulate you.
[QUOTE=john_pelphre;17346396]I don't know if this have been theorized or not, but I though of something.
[img]http://imgkk.com/i/BhCpiC.png[/img]
This is a graph. This graph is special for one reason. It will continue for ever, but will never cross the Y-axis or X-axis. Ever. It goes on forever, but never contacts the axi's. It will go to the the smallest interval, but will never touch "0", Why?
Mathematically speaking, the reason this graph will never touch the axis is because is the graph of the equation (1/x). The reason it can never touch 0, is we have no clue what happens a number, such as 1, is divided 0 times. You also can have a square root of a negative number, because the answer becomes imaginary, but I digress.
The reason for this? Well, you can use graphs to show relation to things in real life, and I began to wonder. What happens if this graph is related to real life?
Now, lets use an example. Say you are walking to a destination one kilometer away. It takes 20 minutes to get there, average walking speed 3 Kilometer per hour, just as an example. . So, after 19 minutes, 30 seconds, your only about a meter away. So, you keep walking.
Your one decimeter away.
Continue.
Your a centimeter away.
Than, a millimeter. Pentameter. Hexameter. Septameter. Picometer. Nanometer.
You can continue forever, to the nth-meter. There is an infinite measure of how accurate, and you can continue forever. There is a infinte distance you can be.
From .01, to .000000000000000000000000000000000000000000000000000000001
Then how can you reach a destination, in anytime?
Well, people round everything to set amounts. Such as you wouldn't say 1000 meters, you most likely would say 1 kilo. Not 100 centi-seconds, but one second. Its weird, but if you think about it. You are always some distance from your destination, even if it is 1 x 10^24 meters, or a yoctometer, away.[/QUOTE]
And there happens to be a Coke Machine vending Dr. Pepper at my destination. And I reach that machine, buy my goddamn Dr. Pepper, take a hearty swig of that delicious brown liquid, and the entire universe implodes because I fucked over the Laws of Mathematics.
But goddamn, that was a good Dr. Pepper.
I advise you to look up 'Achilles And The Turtoise' by Zeno.
It's whole point is to prove that even the most perfect logic can be proven wrong with a turtoise soup.
[QUOTE=PacificV2;17351913]I didn't say "math is useless", I only said mathematicians continuously try to find a ridiculous application for much of their theories.[/QUOTE]
Oh sure? Show me an example. I never heard of any mathematician trying this. (Except he is getting asked by someone - then he might "find" some quick answers to please the interviewer)
Basically, they study "the logic". They find connections between concepts nobody else might have thought of and may become useful in future or not.
[QUOTE=PacificV2;17351913] Leave that to the physicists, they're much better at it. [/QUOTE]
We (I'm one of them) Physicists are actually studying nature with the help of math (as tool), yes. But on quite a low level too. The actual people who then build cool things upon our ideas are engineers. So we aren't really better than mathematicians. Hell, we even have hypothesis which by now are purely mathematical (String-Hypothesis for example).
[QUOTE=aVoN;17353616]Oh sure? Show me an example. I never heard of any mathematician trying this.
Basically, they study "the logic". They find connections between concepts nobody else might have thought of and may become useful in future or not.
We (I'm one of them) Physicists are actually studying nature with the help of math (as tool), yes. But on quite a low level too. The actual people who then build cool things upon our ideas are engineers. So we aren't really better than mathematicians. Hell, we even have hypothesis which by now are purely mathematical (String-Hypothesis for example).[/QUOTE]
I don't understand why the name "String theory" has caught on so well when it's clear that the "theory" has never been directly tested nor can it be in the near future.
Well, as pointed out, space isn't infinitely divisible. Therefore you don't have to move over an infinite number of tiny distances, but a finite number of tiny distances instead. You can either move a Planck length or more, or you don't move at all. Right?
I love paradoxes, they make my head hurt.
[QUOTE=Camundongo;17353637]Well, as pointed out, space isn't infinitely divisible. Therefore you don't have to move over an infinite number of tiny distances, but a finite number of tiny distances instead. You can either move a Planck length or more, or you don't move at all. Right?[/QUOTE]
It shouldn't really matter though. You don't even need that to resolve the paradox. You can divide space into infinitesimal intervals, but every time you do, the time it takes to cross these intervals becomes infinitesimal as well, and the sum of these will always equal the time it takes for you to cross the total distance.
An infinite process can take a finite amount of time if each step of the process takes an infinitesimal amount of time. That's what Zeno didn't understand.
[QUOTE=Bomimo;17351953]you have bad writing sir, and i didn't quite under stand, but dividing 1 by 0 is the same as not dividing at all, not that big of a mystery.[/QUOTE]
Not really.
[QUOTE=Bomimo;17351953]a square root of anything negative is impossible since the result would be positive and there's no way to convert positive to negative following the theories of[/QUOTE]
Take the squareroot expanded to the complex plane:
[img]http://math.daggeringcats.com/?\sqrt{-1} = \pm i[/img] with the definition of [img]http://math.daggeringcats.com/?i^2 = -1[/img]
this is known as zeno's paradox, after the greek man who discovered it. his version is a bit different, though.
from wikipedia:
Achilles and the tortoise
“ In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead. ”
—Aristotle, Physics VI:9, 239b15
In the paradox of Achilles and the Tortoise, Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 metres. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run 100 metres, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, say, 10 metres. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise. Of course, simple experience tells us that Achilles will be able to overtake the tortoise, which is why this is a paradox.[4][5]
heres the solution:
[url]http://philsci-archive.pitt.edu/archive/00001197/02/Zeno_s_Paradoxes_-_A_Timely_Solution.pdf[/url]
Edit
well that's pretty late of me
[QUOTE=JohnnyMo1;17353655]It shouldn't really matter though. You don't even need that to resolve the paradox. You can divide space into infinitesimal intervals, but every time you do, the time it takes to cross these intervals becomes infinitesimal as well, and the sum of these will always equal the time it takes for you to cross the total distance.
An infinite process can take a finite amount of time if each step of the process takes an infinitesimal amount of time. That's what Zeno didn't understand.[/QUOTE]
Makes sense that infinity is cancelled out by an infinitesimal.
too many 12 year olds on fp who think [b]they're[/b] philosophical :sigh:
Screw dy/dx lnx, e^iPi = -1 is where it is at.
[editline]04:10PM[/editline]
[QUOTE=:smug:;17353879]too many 12 year olds on fp who think [b]they're[/b] philosophical and intelligent:sigh:[/QUOTE]
Fixed
[QUOTE=john_pelphre;17346396]I don't know if this have been theorized or not, but I though of something.
[img]http://imgkk.com/i/BhCpiC.png[/img]
This is a graph. This graph is special for one reason. It will continue for ever, but will never cross the Y-axis or X-axis. Ever. It goes on forever, but never contacts the axi's. It will go to the the smallest interval, but will never touch "0", Why?
Mathematically speaking, the reason this graph will never touch the axis is because is the graph of the equation (1/x). The reason it can never touch 0, is we have no clue what happens a number, such as 1, is divided 0 times. You also can have a square root of a negative number, because the answer becomes imaginary, but I digress.
The reason for this? Well, you can use graphs to show relation to things in real life, and I began to wonder. What happens if this graph is related to real life?
Now, lets use an example. Say you are walking to a destination one kilometer away. It takes 20 minutes to get there, average walking speed 3 Kilometer per hour, just as an example. . So, after 19 minutes, 30 seconds, your only about a meter away. So, you keep walking.
Your one decimeter away.
Continue.
Your a centimeter away.
Than, a millimeter. Pentameter. Hexameter. Septameter. Picometer. Nanometer.
You can continue forever, to the nth-meter. There is an infinite measure of how accurate, and you can continue forever. There is a infinte distance you can be.
From .01, to .000000000000000000000000000000000000000000000000000000001
Then how can you reach a destination, in anytime?
Well, people round everything to set amounts. Such as you wouldn't say 1000 meters, you most likely would say 1 kilo. Not 100 centi-seconds, but one second. Its weird, but if you think about it. You are always some distance from your destination, even if it is 1 x 10^24 meters, or a yoctometer, away.[/QUOTE]
Didn't you pass English?
Zeno's paradox isn't a paradox since the claim that is stated by it is false.
[QUOTE=JohnnyMo1;17353347]You're missing the point of the paradox. In order to get anywhere, you have to travel across and infinite number of smaller distances, so how can you get anywhere at all?[/QUOTE]
That's because It's not an infinite amount of smaller distances, you can not have an infinite amount of finite things, It's impossible by definition. It's a finite amount of finite distances, which may be measured down to finitely small distances, Never infinitely. You can try, but you won't REALLY get there unless it's on paper.
If there were an infinite amount of smaller distances, you would not get anywhere AT ALL, no matter how small.
Let me rephrase that, what I mean is you can't divide a finite space into an infinite amount of smaller spaces.
Great, now I just feel stupid.
[QUOTE=EcksDee;17354435]That's because It's not an infinite amount of smaller distances, you can not have an infinite amount of finite things, It's impossible by definition. It's a finite amount of finite distances, which may be measured down to finitely small distances, Never infinitely. You can try, but you won't REALLY get there unless it's on paper.
If there were an infinite amount of smaller distances, you would not get anywhere AT ALL, no matter how small.
Let me rephrase that, what I mean is you can't divide a finite space into an infinite amount of smaller spaces.
Great, now I just feel stupid.[/QUOTE]
You can, however, fit an infinite number of infinitesimal distances in a finite space. And since a infinitesimal distance takes a infinitesimal time to cross, the paradox is no longer a paradox. Or at least that's how I understand it from what JohnnyMo said.
i shouldnt have clicked on this damn thread.
This has probably already been posted, but the whole 1 cm 1mm then 1 um is based on the assumption you accelerate equally as you close the distance, just like the slope of 1/x changes to become steeper and steeper as it approaches 0.
[QUOTE=wheresmyfish;17353688]
Achilles and the tortoise
“ In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead. ”
—Aristotle, Physics VI:9, 239b15
In the paradox of Achilles and the Tortoise, Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 metres. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run 100 metres, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, say, 10 metres. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise. Of course, simple experience tells us that Achilles will be able to overtake the tortoise, which is why this is a paradox.[4][5]
[/QUOTE]
Correct me if im wrong but surely he will simply pass the tortoise as he is moving 10 times fast, so on the next section of time he will simply be 80m ahead of the tortoise
[QUOTE=Camundongo;17355014]You can, however, fit an infinite number of infinitesimal distances in a finite space. And since a infinitesimal distance takes a infinitesimal time to cross, the paradox is no longer a paradox. Or at least that's how I understand it from what JohnnyMo said.[/QUOTE]
This is correct.
It's not an infinite number of finite steps, that would be an infinite distance. It's an infinite number of infinitesimal distances, which calculus deals with all the time.
[QUOTE=unseendamageUK;17359383]Correct me if im wrong but surely he will simply pass the tortoise as he is moving 10 times fast, so on the next section of time he will simply be 80m ahead of the tortoise[/QUOTE]
That's part of the paradox you dolt.
it's called zeno's paradox and it doesn't work.
[QUOTE=ulterior_motives;17363211]it's called zeno's paradox and it doesn't work.[/QUOTE]
Well, it certainly seemed a valid paradox before Newton came along.
[QUOTE=JohnnyMo1;17363316]Well, it certainly seemed a valid paradox before Newton came along.[/QUOTE]
heh, maybe i should have been more specific
what i meant was the theory that the distance will perpetually get smaller but never actually make contact doesn't physically happen.
if a soldier is running at half the speed an arrow is moving after him, he will still be hit by it. the arrow will not just get half way closer to him infintesimally, because the atoms of the arrow head and the atoms of the soldier will eventually become close enough to repel each other, the repulsion which is felt as an arrow hitting you in the back and pushing your flesh out the way to bury itself in you.
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