(and 2 mins later he'll be a further 100m etc )
I learnt that from the movie/book "Contact". Can't remember the name of the paradox....1. Reminds me of the frog who lines up at the start of a 100m track.
In his first jump he jumps 50m,
then half the remainder, (25m),
then half the remainder, (12.5m) etc
Will he ever reach the end?
I mean, he will always have half the remaining distance to go ?
2. Suppose his forward speed is constant (say 50m / min) , so that each jump is made in half the time of the previous one.
In his first jump he jumps 50m, = 1 min
then half the remainder, (25m), = 0.5 min
then half the remainder, (12.5m) = 0.25 min. etc
Will he ever reach the end?
3. But hang on!! lol
If his speed is constant (at 50m/min) - of course he will reach the end !
and it will take 2 minutes
(and 2 mins later he'll be a further 100m etc )
Here it is-
The dichotomy paradox
http://en.wikipedia.org/wiki/Zeno's_paradoxes#The_Paradoxes_of_Motion
Movement is an illusion.
I like that one.... very good.The reasoning seems to be that because you must go through an infinite number of steps before reaching somewhere, it should take you an infinite amount of time.
.....because you must go through an infinite number of steps before reaching somewhere, it should take you an infinite amount of time....
Questions. / multiple choice
Does he fall into a time warp at the finish line ?
Does he fall into a black hole at the finish line
or
Does he go to heaven at the finish line ?
Yop could say a super frog in a sock...or maybe the jumpin green flash?PS Does the frog turn into a little pool of hot melted green butter at the finish line?
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 feet. 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 feet, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, for example 10 feet. It will then take Achilles some further time to run that distance, in 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.
Status of the paradoxes today
Mathematicians thought they had done away with Zeno's paradoxes with the invention of the calculus and methods of handling infinite sequences by Isaac Newton and Gottfried Wilhelm Leibniz in the 17th century .....
However, some philosophers [14] insist that the deeper metaphysical questions, as raised by Zeno's paradoxes, are not addressed by the calculus. That is, while calculus tells us where and when Achilles will overtake the Tortoise, philosophers do not see how calculus takes anything away from Zeno's reasoning that concludes that this event cannot take place in the first place. Most importantly, many philosophers do not see where, according to the calculus, Zeno's reasoning goes wrong .
The frog doesn't get faster, his speed is constant (which you stated) 50m/1min = 25m/0.5min = 12.5m/0.25 min....
And if he only ever jumps half of the remaining distance, he will never quite get to the 100m line.
sounds good to meThe series 1/2 + 1/3 + 1/4 + 1/5 + ... adds up to infinity,
but the series 1/2 + 1/4 + 1/8 + 1/16 + ... adds up to 1, bye bye Zeno.
I think there's a nice little youtube cartoon type video posted on this somewhere in this thread, or the old science/astronomy type thread...Now just to complicate things, I want to throw the Heisenberg uncertainty principle out there....explanation
patI think there's a nice little youtube cartoon type video posted on this somewhere in this thread, or the old science/astronomy type thread...
2020 do you remember?
LOL but I`m pretty sure it`s Faster than light!
Here is something else you might enjoy 2020 et all.
A little look into the strange world of Quantum Physics ...but don`t let it know you are watching
It’s a rare event anyway, but this is the last time ever. Two shuttles are now sitting on NASA's two launchpads at Kennedy Space Center. Space shuttle Endeavour completed a 4.2-mile journey to Launch Pad 39B Friday morning, Sept. 19, at 6:59 a.m. EDT, and this is the first time a shuttle has stood by as a rescue vehicle.
Dive right in to this image that contains a sea of distant galaxies! The Very Large Telescope has obtained the deepest ground-based image in the ultraviolet band, and here, you can see this patch of the sky is almost completely covered by galaxies, each one, like our own Milky Way galaxy, and home of hundreds of billions of stars . . . .
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