If you walked forward half way towards a person, and half way of that half way and half way of the half way?

and so on and so forth, would that mean you would technically never get there?





but surely if you were moving forward all the time you would ultimately need to get there in the end.





does it make sense?
If you walked forward half way towards a person, and half way of that half way and half way of the half way?
Eventually you would be moving microscopic amounts, so you probably would never actually arrive.
If you walked forward half way towards a person, and half way of that half way and half way of the half way?
it makes crazy sense, I think that in the end you%26#039;d only make one step and that%26#039;s a step back, lol
Reply:You%26#039;d never get there.
Reply:I guess you%26#039;d never make it there because you%26#039;d always be moving in smaller and smaller amounts.
Reply:no. but you will be very close. There will always be halfway to go.
Reply:yeah you would have to get there eventually but it would take a very very long time or you would end up not moving at all. if you are halving the distance there still remains distance to walk and then distance to halve. you can%26#039;t halve nothing so yes you would get there or get stuck b/c nothing would remain.
Reply:No, you never get there because you are only ever walking half way.


So there will always be half the distance between you and the person.
Reply:Let%26#039;s say you start one yard away from the person.


After the first step you%26#039;re 1/2 yard away.


After the second step you%26#039;re 1/4 yard away.


After the third step you%26#039;re 1/8 yard away.


....


After the 10th step you%26#039;re 1/1024 yard away (0.035 inches)


...


After the 20th step you%26#039;re 1/1048576 yard away. (0.000034 inches)


...


After the 40th step you%26#039;re 1/1099511627776 yard away. (really tiny number).





Your distance away gets tinier and tinier, but never quite hits zero.
Reply:go figure....and what if ...what you was %26#039;walking%26#039; towards...was also %26#039;walking%26#039; toward you in the same manner......





Keep stepping up...and keep stepping forward...be pure of thought and action...there will be a time they Unite.





Peace and Love to All


R.R.B.
Reply:well if it was a human walking then you would get there because the measurment between the 2 persons will eventuly get so small that you would touch. this would be the same if you were as big as a sky scraper or as small as a flee. you would eventuly touch.





I hope this helps.





P.S i like your imagination
Reply:yes you%26#039;re moving in the same direction but slowing down with each section so you will never truly get to touch (unless you hold out your hands).





if the distance eis 10 m and you do the 1/2 in a minute you do:


5 metres/ minute to 50%


2.5 metres/minute to 75%


1.25 metres/minute to 87.5%


0.625 metres/minute to 93.75%


0.3125 metre/minute to 96.825%


0.15625 metre/minute to 98.38725%


.... till boredom sets in.





its called the law of diminishing returns basically the ime/effort involved meand syou never achieve 100% but effectively stop at just over 99% (its also used to demonstrate that stopping at 75% is the greatest usable return for the effort involved)
Reply:There is a mathematical term for this - it is an asymptote. It is the value a function approaches but would only reach when the input was infinity. It sounds like nonsense, because in the real world it is. If you continued for long enough you would be so close to your %26#039;ultimate destination%26#039; that no measuring device on earth could detect a separation, nor measure any remaining forward velocity.





Indeed the real world gets even more in the way, because matter is made of atoms, which are constantly on the move and even jumping away. When two bodies get close enough they will even exchange atoms. It%26#039;s a bit hard to say they haven%26#039;t touched at that point. So, that%26#039;s why it sounds like nonsense. It%26#039;s only true for idealised points (i.e. zero size) in a continuous (not quantised, but infinitely divisible) space.
Reply:Makes perfect sense. I once thought about this too.





My theory is that as your half-ways gets tinier, the time for you to travel that half way gets faster until a point where time is at an infinity and the distance of the half ways is at zero, essentially crunching space and time together to a point so that you could travel to your destination.





Hope this makes sense to you.
Reply:Theoretically you%26#039;d never get there. Realistically you%26#039;d be as close to there as you%26#039;d ever want to be (you%26#039;d eventually be down to microscopic distances that you couldn%26#039;t even measure half of).
Reply:this is an old greek thought experiment, that if you shoot an arrow it must first travel half the distance to the target, then half of that, and so on thus the arrow should never get there because it is always travelling half the distance first.





i think the flaw in this logic, is that the arrow is traveling in fact to a point past the target, and thus must travel half the distance and so on but at some point the target will be in the way.





for your walking experiment it is different, since you are suggesting that a person would be walking first halfway to a point and then so on, so the person will never make it to the point, assuming they could shrink and continuously travel half the distance for an infinity.





no you can continuously move forward and never reach your destination, because you can move forward by smaller and smaller increments, infinitely small, though forward by an infinitely small amount it would still be forward.
Reply:you would never get there..and yes it makes sense...any number divided by 2 will never equal zero...I assume zero is considered getting there.
Reply:Every time anything moves a particular distance, it will move through distances as you have described. In an idealised world, a point object, if it paused between such distances then it would never cover the original distance halved. If no gaps in time are made between successive steps then it will just be a continuous movement like any other. For each distance there will correspond a time small enough such that their ratio gives the average speed for that interval. The sum of the infinite series,


1/2 + 1/4 + 1/8 +1/16 + 1/32 + 1/64 + ...


is finite, so there is a finite distance and time associated with the motion. This is somewhat analogous to a finite area or volume being enclosed by an infinite perimeter or surface area.
Reply:You wouldn%26#039;t actually get there before you died, because you%26#039;d have to be able to move in microscopic, atom-sized movements.


So, it%26#039;s impossible to actually do that, but what you%26#039;re basically asking is how many times can you divide a number by half, and that goes on forever. But you wouldn%26#039;t reach them.