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#37 - gweetle (01/16/2013) [-]
Actually, he does reach it.

en.wikipedia.org/wiki/Geometric_series
#95 to #37 - gweetle (01/16/2013) [-]
Yes, obviously if you think about it logically it doesn't make sense, but if anyone here has ever taken any level of calculus, you'd know that it is mathematically true. Please don't dispute me just because you haven't learned it yet.
User avatar #82 to #37 - gmarrox (01/16/2013) [-]
If we're being technical and anal about it, he never actually touches the wall anyway because electrons atoms never touch so the atoms of the frog will never touch the atoms of the wall.
User avatar #46 to #37 - sasorikingofrocks (01/16/2013) [-]
starting at 1
1 divided by 2 = 1/2
1/2 divided by 2 = 1/4
1/4 divided by 2 (now going to be a comma for the pleasure of the reader) = 1/8
1/8, = 1/16
1/16, = 1/32
1/32, = 1/64, however the distance the frog is from the wall, will never reach 0 :)
User avatar #55 to #46 - lordbyronxiv (01/16/2013) [-]
once you get down to the Plank length, you reach the wall. anything smaller than the Plank length loses it's physical sense of reality.
User avatar #78 to #55 - churrundo (01/16/2013) [-]
planck*
User avatar #91 to #78 - lordbyronxiv (01/16/2013) [-]
ahh thanks for that, how disrespectful of me to spell his name wrong!
User avatar #58 to #55 - sasorikingofrocks (01/16/2013) [-]
There may be no measurement we know of that can measure something smaller than the planck length, however, it does not mean we do not have the means to discover it :) so according to current sciences, yes the frog can reach the wall. But that's the good thing about science, is that it's constantly changing.
User avatar #61 to #58 - lordbyronxiv (01/16/2013) [-]
that's the beautiful thing about it. science used to say the frog shouldn't reach the wall, but of course he does! the idea is that once 2 things get down to the plank length within each other, it's by all means impossible to distinguish between the atoms of the two objects. there essences literally intercede and become one. the frog;s atoms and the walls intermingle, and they "touch."

its marvelous really.
User avatar #65 to #61 - sasorikingofrocks (01/16/2013) [-]
Now back to serious mode, that's why I said CURRENT SCIENCES. We do not truly know anything in this world, because there will always be someone there to prove you wrong. We say the planck length is the smallest measurement, but that's only the smallest measurement that we can see, if we were able to 'zoom in' on that object even more, we would see an even smaller measurement take place.
Think of it as two stars. If we can only observe them at a certain distance, it may seem as though they are right next to each other, or touching, and that's all that our current distance system can give us. In forty years or so, Johnny Pearpit can come along and invent a device that allows you to view things 300x closer than what we saw before, and now we realize that they are not in fact touching, but they are so close they look as if they're touching :).
User avatar #63 to #61 - sasorikingofrocks (01/16/2013) [-]
I have to applaud you, because you are the only person who can make the slow approach of a frog to a wall, by only jump half the distance, sound so sexual, just by adding those quotes around touch.
User avatar #67 to #63 - lordbyronxiv (01/16/2013) [-]
Hahahh, thanks for the applause. But you're right quantum theory stands to be disproved. That's physical sciences for ya.

But the mathematical solution to the paradox allows for the frog to take an infinite amount of steps in a finite amount of time. which is really cool, and proven. both by rigorous mathematical proof, and of course, by demonstration.
User avatar #62 to #61 - lordbyronxiv (01/16/2013) [-]
*their
#45 to #37 - psykobear ONLINE (01/16/2013) [-]
That... is wrong
That... is wrong
User avatar #56 to #45 - lordbyronxiv (01/16/2013) [-]
nope. it's right, and has been proven.
User avatar #93 to #56 - psykobear ONLINE (01/16/2013) [-]
The frog would never hop to the wall by hopping halfway.
But, eventually, it would be impossible for him to hop halfway: He would overshoot it.
If you can give me a link to this proof, I will gladly read it.
Gweetie's link was a wiki page about geometric series in general, not the frog problem
User avatar #96 to #93 - lordbyronxiv (01/16/2013) [-]
en.wikipedia.org/wiki/Zeno%27s_paradoxes#Achilles_and_the_tortoise

there are a couple of solutions on this page, though i could show you the short proof that it takes a finite amount of time to take the infinite amount of steps which does indeed involve the geometric series.
User avatar #97 to #96 - psykobear ONLINE (01/16/2013) [-]
Again, I couldn't find, on the page, this particular problem.
I tried ctrl + f and searched for frog, found nothing.
Also searched for half and found a few things, but nothing relating to this problem in particular.
User avatar #98 to #97 - lordbyronxiv (01/16/2013) [-]
They're all analogous paradoxes, the dichotomy paradox being the same as that of the frog, except being Homer and a stationary bus instead of a frog and wall.
User avatar #99 to #98 - psykobear ONLINE (01/16/2013) [-]
True, Homer does reach the locomotive in the second scenario...
But Homer isn't attempting to go half the distance with each step.
Eventually, one step will step over the remaining distance, regardless of how small or large.
He wouldn't be traveling half the distance anymore.
This is like saying that Pi has a definite end because circles are closed.
User avatar #100 to #99 - lordbyronxiv (01/17/2013) [-]
He reaches it in both cases.
and well pi definitely is a finite number, no question about it.
but take it like this:
say the frog is traveling at a speed v, and starts out at a distance d from the wall.
then the time (d/2)*v + (d/4)*v + (d/8)*v + ... = (vd)*(the infinite sum of the reciprocals of powers of 2)
vd is finite.
the infinite sum of the reciprocal of powers of 2 is finite.
if ab=c and both a and b are finite, then c must also be finite.
which means that t is finite.
the frog can and does reach the wall.
and both physics and mathematics back that up.
#101 to #100 - psykobear ONLINE (01/17/2013) [-]
Ok... I just spent a while trying to come up with a response, but deleted it realizing that it made no sense.
The only thing I can come up with to say is that, as a word problem, it makes no sense that the frog would touch the wall.
Maybe if the amount of time was infinite, i don't know.
I quit.
My brain hurts...
You win.
User avatar #102 to #101 - psykobear ONLINE (01/17/2013) [-]
Sidenote: The conversation above ours puts a nice spin on it
#42 to #37 - hipsophobadon (01/16/2013) [-]
You sir are wrong.
You sir are wrong.
User avatar #57 to #42 - lordbyronxiv (01/16/2013) [-]
no he's not. you'll see once you see some big boy math.
User avatar #64 to #57 - hipsophobadon (01/16/2013) [-]
The frog just doesn't have enough time in his life to accomplish such a feat.
User avatar #66 to #64 - lordbyronxiv (01/16/2013) [-]
that's the incredible thing about it. using the geometric series you can show that the frog can take an "infinite" amount of steps in a finite amount of time.
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