Simple hypothetical question - designed to test an idea... If you had an infinitely long rope and were lowering it into an infinitely deep hole - how far could you actually lower it?
I'd give it five minutes - maybe 500 metres - but after that, I'd be bored. Theoretically though - do you mean how long before the rope snapped under its own weight ? Or some other event?
Assuming 10mm nylon rope with a breaking strength of 14.4kN and a mass per metre length of 0.053kg/m. 27,696 metres.
It was explained to me once that no one can every truly travel anywhere. It's completely logical. In order to travel a kilometre in distance, you must first travel 500 metres. However, in order to travel 500 metres, you must first travel 250 metres. However, in order to travel 250 ... you see how it goes. You need to successfully complete an infinite number of steps in order to make a journey, and since you cannot do so within a finite timeline, no one can ever go anywhere. This is the best evidence I have seen in support of the idea that the universe is virtual, with entirely made-up rules
The best one I've ever heard regarding the difference between an engineer and a scientist comes from a time when all, well nearly all, engineers and scientists were male, and when the term sexism had been invented: An engineer and the scientist stand about 10 feet apart with a beautiful young lady between them. They may approach the young lady halving the distance with every move. The scientist says "but I've never get there". The engineer says "in 4 moves I'll be close enough for all practical purposes".
how does one start lowering this rope? i mean it must have an end to start with and if it has one end it must have another?
This is a variant of the "Achilles and the Tortoise" so-called paradox. Try this. The element of time has been omitted from the postulate. You can travel 500 metres in (say) 10 seconds, or 250 metres in 5 seconds, or 1 metre in a fraction of a second; those steps are not equal in time taken. You can describe any journey as an "infinite number of steps", but only if each of those steps is infinitesimally small in both time and distance. The postulate, having assumed an infinite number of (thus infinitesimally small) steps, jumps without notice into assuming that the steps are now large again. That is what gives rise to the seeming impossibility.
