The distance between two points can be halved infinitely. How then, do I get from here to there? If I walk halfway there, the remaining distance can then be halved. This, theoretically, goes on forever. Since I obviously get to where I’m going(usually), what does this prove? Or disprove?
Forget the halves, just walk all the way there.
Wasn’t this answered by Cecil’s great great great great great great great great great great great great great great great uncle Zeno?
Beats me. When I see a bike rider in my rear-view mirror, and he may be going 10 or 15 mph and I’m going 30 or more, there’s no way he’s going to catch up with me, let alone pass me, Zeno’s paradox notwithstanding.
You’re here, you’re there, aren’t you everywhere?
It could only have been gilligan to have lead myself and my dope smoking friends to enlightenment. We thought we had something there. Turns out it had been had before. Looked up zenos paradox. Thought we were so wise…
…ahem…“From there to here, from here to there, funny things are everywhere…”
Doctor Seuss, * One Fish, Two Fish, Red Fish, Blue Fish *
“…send lawyers, guns, and money…”
Warren ZevonFor one thing I think this proves the concept of nesting. It proves that by simply extending decimal places infinitely you can express infinitely small numbers.
For one thing I think this proves the concept of nesting. It proves that by simply extending decimal places infinitely you can express infinitely small numbers.
There is no safety for honest men but by believing all possible evil of evil men.
–Edmund Burke
couldn’t it also prove that 1 = 2?
Zeno’s Paradox has long since been resolved. Zeno and his contemporaries were unaware of calculus. But since its invention it has been shown that an infinite series of diminishing amounts can add up to a finite number.
What’s the problem? You’re not walking half the remaining distance every time you take a step. You’re walking a set fraction of the total distance every time you take a step. What does one thing have to do with the other?
Chaim Mattis Keller
ckeller@schicktech.com
“Sherlock Holmes once said that once you have eliminated the
impossible, whatever remains, however improbable, must be
the answer. I, however, do not like to eliminate the impossible.
The impossible often has a kind of integrity to it that the merely improbable lacks.”
– Douglas Adams’s Dirk Gently, Holistic Detective
Even without appealing to calculus, look at this.
Say you are trying to walk one metre. You start by walking 50cm, then 25cm, then 12,5cm, etc. You’d think that it would take you an infinite amount of time to cover each of those halves.
However, say you are walking at a speed of 1m/sec. That means that the first step takes 0,5sec, then 0,25sec, then 0,125sec, etc. The vanishing fractions of seconds cancel out the vanishing fractions of metres. Easy as pi.