From Points A to B: Newsletter Challenge (05/09/06)

It is quite obvious that your daughter is disturbed by something other than traveling from A to B. Sounds like she is depressed, they make drugs for that, but a good pep talk may lift her spirits, but if it happens more frequently she should seek counselling. You could also mention that if you only travel half way to somewhere, that you will never get there. The world is full of people not willing to go the full distance, so she should be extraordinary and put in the extra effort to take that final nano-step just before time goes to infinity.

basic math....sum to infinity A divided by B minus the ratio

A smart girl. It's true to go from A to B, you must travel half the distance, then half the distance again, then half the distance again, so on and so forth. Each half distance takes a finite amount of time to get there, that is true as well.

Your daughters misconception is that the sum of an infinite number of finite values is equal to infinity. This is not always the case. For instance, say you add .1 + .01 + .001 + .0001 + ... I think it's clear that the sumation would not equal infinity, just a finite value. So she can rest assured that it's possible to travel from A to B.

Now would be a good time to teach her calculus.

This was one of the reasons for the invention of the calculus. Suffice it to say that the sum of an infinite series of infinitesimals yields a finite result. The continuous halving of the distance results in a series of infinitesimal distances. Beloved daughter may not be ready yet for calculus, but she has a mind sharp enough to take her there.

This is an interesting blend of the sublime and the ridiculous -- not unlike Benny Hills' humor. My calculus teacher had a joke about never being able to reach the object of your affection (but you could get close enough, re: Benny Hill humor). If getting somewhere means achieving exact registry of your center of mass with the center of mass of some other object in the space time continuum, at some point the volume of your body interferes. At some point further down the line, Heizenberg's Uncertainty Principal kicks in. So maybe we can't get anywhere, but in a converging, finite, and often short period of time -- we can get closer than our senses can register.

The sum of the series is only 1 because at some point we assume that the distance is so small that we make it zero. However the kid is right, if you keep only moving half the distance to a point you will never get there. I suggest you should stop making assumptions and just admit the kid was right

I agree with anonymous coward. All you guys are doing is rounding to the closest integer.

You're the one making assumptions. You're not answering the question she asked, pay attention. She asks:

" If I keep this up, traveling half the remaining distance each time, I end up with an infinite number of segments. But since each segment has to take finite time, this means it takes infinite time to get to point B. It seems to me I've just proved you can't go anywhere!"

She's saying an infinite number of finite segments of time added together is equal to infinity. This is an incorrect assumption:

Let's say the first half trip takes 1 second, and the next takes 1/2 a second, and the next takes 1/4 of a second and the next takes 1/8 of a second. How long will the trip take if an infinite number of steps are taken?

The anwer is 2 seconds and the reason is that 1 + 1/2 + 1/4 + 1/8 + ... = 2

Please understand that this is an exact answer, not an estimate. It is what's known as an infinite series that converges. So you see, the daughters (and Zeno's) mistake is the assumption that the sum of an infinite number of steps must take an infinite amount of time, regardless of the size of the steps.

True, you never quite get there, but you get close!

However, if you really want to get somewhere I would recommend the 911 Turbo, which has an uncanny ability to fold space and time between any two points.

That and it kills bugs fast!

I thought I read once that the smallest possible distance is the 'plank' Once this distance is reached there is nothing left but the walk.

Interesting to note, since nothing can travel faster than speed of light; the plank also defines the smallest possible unit of time.
t=d/s

So perhaps dividing this final distance causes the distance to be too small to exist in time, thus she arrives at point B.

Very well known ancient paradox of Xenon, just it was the arrow at the time, not she traveling.

I thought this was Zeno.

Replying to Mevel123 (1004) on Tuesday May 09, @11:35PM (#4826)

The smallest length is the "planck", named after Max Planck (see article in Great Engineers and Scientists, to give him a plug!)

Length is 10^-35m, so it doesn't take long to walk it.

Thank you for the correction.
My credit to Max Planck.

Well, duh, this is an easy one! Tell the young, unimaginative, and obviously non-blond, daughter to pick a point C to go to from point A, in line with point B, which is twice as far from A as B is. When you get halfway to C, you're at B. Simple . . .

You preempted me. Ever notice it's always Point A to B. Seems no one ever want to go to C anymore. Landlubbers! ;)

Those that are truly blonde are intelligent; it's the idiot blondes that bleach themselves that give us a bad rep. Watch it Bill!

Dang! I've been accused of being insensitive a couple of other times this week! Hmmm . . . Maybe I am . . . NAH! Heck -- I used to be a redhead. Now, it's blondish and a good bit of it's missing!

But if you are only ever travelling half the distance surely you don't ever get from point A to point B...so isn't it a valid point irrespective of time for each segment as you can't quantify the total distance

This is reply to Anonymous Coward on Thursday may 11.... See, another way of saying ur comment is "the total distance can be divided in to infinite no. of segments". This is certainly true.. But there itself lies the fault.. Lets see the problem like this.. U have to travel 200m.. U travel 100, then 50, 25, 12.5, 6.75..so on.. Lets say u take 12 secs, then 6, 3, 1.5, .75..so on.. The sum of the series being 24 secs.. If u talk in terms of distances, and intensionally travel only half the distance, from ur destination; Yes, u will never reach.. That will mean, u travel for 12 sec and STOP, travel for 6 sec and stop, for 3 sec and stop...so on.. and u will never reach..( m not limiting myself with smallest quantas) But if u travel for 25 sec, as the total time taken to cover the distance cant exceed 24 secs if travelled with constant speed without stopping, u certainly would reach beyond the point B.. So, its about how u are travelling.. Intensionally travelling half the distance only, will certainly not take u to the point B {until u reach some smallest quanta, if exists)..

I respond: "Ye Gads! You're Right, You've confirmed the oft heard statement that YOU CAN'T GET THERE FROM HERE!"

The zero's and decimal point will dissapear over the horizon and you will not know the value of the figure you have as it will be unnamed. You will however, have a figure to divide in half again and again and yet know not what it is. If you desire a name, it should be the reverse of Infinity or Ytinifni Del

As the distances keep halving, the time it takes to get there also gets cut in half. It all cancels and you get there as though there were no complex calculus involved.

hhmm ..i think a definition of a step needs to be introduced here. the smallest progress a person can do in a journey is a step forward, which actually the only thing a person can do to progress in their life journey. so, for A to B every time you finish half of the distance you make it closer to a step. And sooner or later BUT for sure, you will reach the time where your destination is just a step away, SO why do the 'half step' which actually just PROVE that : it's not that you can't reach your destination/dream, you just don't want to ^_^ a step a time bring you everywhere. ^_^

How many times can the young girl divide her bag of marbles in half until she no longer has a marble? How many times can she divide the last marble in half until she no longer has glass? How many times can she divide that last molecule until there is just an single proton or nutron left? If you continue this further the answer is becomes obvious. There comes a point when there is no longer a distance left to cut in half. You can be in one place or another but you cannot be in between. The same applies to time. It is not infinitely divisible either. There comes a point when events happen in succession, sequence, in frames. So the universe is like a bag of marbles in a grid jumping about from place to place in a frame by frame movie picture. We humans lack the resolution to see the jumps and merely imagine smoothness. We imagine smoothness so well that we invented a number system with infinite fractions, even though they could never exist in reality. So, her mistake is assuming time is smooth and infinitely divisible, that distance is smooth, and that mathamatics is correct letting you use certain kinds of infinitely variable fractions for a real world calculation. But she caught herself in time... ---Chris Cieslewicz

it is true mathematically that if you keep halving the distance you will never get there.that being said here is a little story. a beautiful young lady was seated at the far end of a room, in turn a mathemetition , a physicist and an engineer were asked to start halving the distance. the mathemetion said there is no point in starting because you can never get there. the physicist gave the same answer. the engineer said "well for all practical purpouses" and took off and was soon there.

We all know how freakin' stupid and easily brainwashed Liberals are, so challenge them to drive 60 MPH into a brick wall 1/4 mile away. Use this same logic to explain they WILL NEVER hit the wall. If you succeed, congrats, one less dumbarse in the world that can screw up our country any worse than it is!