Question related to an actual problem about infinite sums, Zeno's Paradox.

[Anonymous No.8463816]

so I was browsing videos on youtube and checking if there is anything related to my new most favourite may-may™ and stumbled over an interesting problem.
So let's say you play a video which is 100 seconds in length and every 10 seconds you play the same video but with the same condition except it's at double the speed of the previous video. So it's recursive.
At the start you should, for example, quickly get a stack of "paused" nested videos which are all waiting for the video one layer below to finish playing.
So the question is: Does the whole video have a finite length?
Because of 1 + 1/2 + 1/4... converges on 2 I have the feeling that it should. However while it is easy to understand that Achilles must overtake the turtle in Zeno's Paradox, I have trouble seeing if any video ever "passes" the first 10 seconds to reach the 20 second mark or eventually totally finish and let the superordinate video continue.

[Anonymous No.8463830]

>>8463816
>So let's say you play a video which is 100 seconds in length
>Does the whole video have a finite length?
how is that a question?

[Anonymous No.8463844]

>>8463830
well that's an interesting point you raise

[Anonymous No.8463848]

>>8463830
>>8463844
oh actually that's not really a problem, I was just retarded for a second.
You have 100 seconds of video footage you use. The length of the assembled video at the end is unknown.

[Anonymous No.8463865]

>>8463848
I don't even understand the wording of your problem
do you mean that you have a set of videos, such that first one is 10 seconds long and each next is twice shorter, then we play them back to back to see what is the total length of footage?
in that case, obviously, length is 20 seconds

elaborate pls

[Anonymous No.8463873]

>>8463865
p is a video of length 100 with markers at 10 seconds each.
p is played.
if a marker is reached, p is played at double the speed.
the 100 and 10 are just arbitrary aswell as tthe factor of 2. It might be that those numbers have an influence on convergence so change them around as you like.

[Anonymous No.8463881]

>>8463873
there are less markers here but it should show the concept.

[Anonymous No.8463891]

>>8463873
ah, well in that case
0-10: 10 s worth of footage
10-20: 20 s worth of footage
20-30: 40 s worth of footage
<we have 70 s worth of footage here
30-40: 80 s, but we here have exceeded the limit, so uh.. divide 30 by 80 and multiply by ten equals 3.75 s

TOTAL: 33.75s for 100s worth of footage
did I get it this time?

[Anonymous No.8463898]

>>8463891 cont'd
if we used infinite markers and video sped up by (1+infinitesimal) value, I bet, total length would converge to [math]e[/math] times something

[Anonymous No.8463910]

>>8463891
I'm not sure because i don't know the answer either but I think you have a mistake.
Look at 10-20. You probably say 20 seconds of footage because from the first marker to the second one it's 10 seconds + 5 from the first video on double speed + 2.5 from the second nested video... and it converges to 20.
However if you do that you only count the very first segment of all nexted videos and add them up.
But if I understood you you're missing out on a lot of tine.

[Anonymous No.8463921]

>>8463910
are you baiting?
like, you keep responding, even with images, but they make no sense to me
>nested videos
I don't understand this concept you introduced, cyka blyatt

I say, 10-20 has 20s worth of footage because presumably, video speeds up 2 times after the first marker, and remains at this speed till second one

[Anonymous No.8463941]

>>8463921
oh fuck mate I'm so bad at explaining this shit.
I will actually write some pseudo code alright?

def function(i, d, n, speed)
{
while i < n:
if i % d = 0:
function(i, d, n, speed * 2)
i += speed
}
function(i, distance_between_marker, length, 1)
print "finished"

Maybe this helps?
the speed is how much you increase i which is basically the current time. This obviously wouldn't work in a programm because i would "skip over" the points where i % d == 0 sometimes and all that but in the real problem everything is continuous.

[Anonymous No.8463945]

>>8463941
def function(i, d, n, speed)
{
while i < n: {
if i % d = 0: {
function(i, d, n, speed * 2)
}
i += speed
}
}
function(i, distance_between_marker, length, 1)
print "finished"

>tfw 4chen deletes your intendation
>everything that could go wrong is going wrong

[Anonymous No.8463953]

>he thinks I know code
>my sides come back to earth
fuck, I'm not bad at languages, really, I'm not
but it seems you have fucked up again

you had better made a flowchart, for I am a total brainletto when it comes to coding

[Anonymous No.8463957]

>>8463953
also I gotta go sleep

see you in 8 hours or so

[Anonymous No.8463981]

Well anyways I believe I've got a formula for the solution but I lack the pure math skills to get it.
I'll just leave it here:

[Anonymous No.8464015]

>>8463816
The way you have phrased this, the length is bounded by 2 but not finite.

Xeno's paradox isn't really a paradox. You are dividing distance by 2 but also dividing time by 2. So you end up with a limit that is a 0/0 (distance remaining / time remaining). We understand limits now and the paradox disappears.

[Anonymous No.8464075]

>>8464015
I should have never mentioned Zeno's paradox.
Just think of it as a recursive function whose goal is to go from 0% to 100%. But when it reaches 10% it calls itself again except the speed of progress is doubled.

I transformed this >>8463981
interpretation and it turns out that the length is
l * (n/(c-n)) where l is the 100 seconds, n is the number of markers and c the factor by which the speed increases. The condition for convergence is that n > c, otherwise it goes to infinity.
But maybe this was wrong from the start.
The thing is I kind of fucked up wording myself properly and now no one understands it.

[Anonymous No.8465230]

>>8464075
okay I'm back and if I understand correctly it goes like this, where the overlapping footage is omitted
0000000000
__________00000
_______________00(and a half)
_________________0(and a quarter)
__________________(about half)
then a total length is 100+50+20+10+6.25=186.25
did I win?