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Page 234 in a nutshell: Sherlock and Watson, depressing posts about depressing posts, 7000th post, math facts, food facts, ants
@Dejan's rubber rope problem: only if the ant walks quickly and doesn't pause for a single second.

Hot dang.

An ant starts to crawl along a taut rubber rope 1 km long at a speed of 1 cm per second (relative to the rubber it is crawling on). At the same time, the rope starts to stretch uniformly by 1 km per second, so that after 1 second it is 2 km long, after 2 seconds it is 3 km long, etc. Will the ant ever reach the end of the rope?

No.

Yes.

What?

Yes, the ant will reach when time and rope length reaches infinity but only if the ant lives an infinite life span.

This doesn't work, however, if the rate of expansion is an accelerated one (Dt^2) or if the ant has a limited life span.

I really like the maths. Keep it up guys!

At first consideration it seems that the ant will never reach the end of the rope, but in fact it does. (In the form stated above, it would take 8.9×1043421 years.) Whatever the length of the rope and the relative speeds of the ant and the stretching, providing the ant's speed and the stretching remain steady the ant will always be able to reach the end given sufficient time. Once the ant has begun moving, the rubber rope is stretching both in front of and behind the ant, conserving the proportion of the rope already walked by the ant and enabling the ant to make continual progress.

Kevin made a really nice video on this topic (ant on rubber rope) a few weeks ago:
https://www.youtube.com/watch?v=OM9KepKsg6U

They key to the math problem is an ever increasing percentage of the rope gets covered so more and more of the increased length is behind the ant. Once he reaches the mid point, more stretch occurs behind him that in front. Additionally, each step, while a smaller over all percentage is more than half the previous times coverage so the ant can achieve half the length at which point success is inevitable. Let's say the ant rate was 1 unit per and the rope stretch was 2 per. After the first stretch the ant travels 1/4 the distance. Then 1/6th then 1/8th. He has crossed the halfway point.

If you have the rope accelerate, however, the ant won't achieve 50%. For instance, if the rope doubles it's length every unit, the ant covers half the relative distance of the previous move. 1/4, 1/8, 1/16. So the ant only reaches the mid point at infinity.

Further more, if the ant moves first and achieves mid point in the accelerated scenario then the aunt achieves completion at infinity.

I called it first, on Thursday at 1pm EST. kevdog8 1, JECE 0.

Got dang, this is a lot more fun than algebra class.

https://www.youtube.com/watch?v=OM9KepKsg6U&t=618s
In other words, no. The ant will never reach the end of the rope.

Also, ants are not points. Ants can't stretch like this at 1km/s without dying:
https://www.youtube.com/watch?v=OM9KepKsg6U&t=239s

Your math teacher lied to you.

According to my calculations, in general the ant will reach the end of the rope after (e^(u/v) - 1) / u units of time, where v is the speed of the ant, u is the speed at which the rope is stretched, and speed is measured in original length of the rope per units of time.

@JECE "Also, ants are not points. Ants can't stretch like this at 1km/s without dying"
The ant does not stretch at 1 km/s, the rope it is sitting on does. In fact, I have the suspicion that the speed at which the ant itself crawls - which is in this case 1 cm/s - always upper limits the speed at which the stretching of the rope can cause the ant to move.

Okay forget that last thing that I said, though it may apply to acceleration.

Mercy, JECE was being funny. His video proves the ant achieves his goal of string domination.

R/whoosh?

r/FoundTheMobileUser

Solve the riddle:
Alive without breath,
As cold as death;
Never thirsty, ever drinking,
All in mail never clinking.

It's the letter E

Easy peasy. It's a fish.

wait no it's the human experience

Excuse me what the fork?

https://en.wikipedia.org/wiki/Fork_of_Vevey

Have I died and gone to the Good Place?