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bluestocking babe

bluestocking babe
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Tokyo, Japan
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December 26
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Student Teacher
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Living my day to day adventure and hoping for the best.

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MARCH 18, 2012 8:50PM

Zeno's Paradox: The Dichotomy

Rate: 11 Flag

                         philosopher

" That which is in locomotion must arrive at the half-way stage before it arrives at the goal."  —Aristotle, Physics VI:9, 239b10

 

Say you set out to walk across a given distance. It could be from one end of your kitchen to another, or any length with two fixed points.  Your first step will cover half the distance. Your second step, half again. If you followed this pattern with each additional step...

Would you ever reach the other side? 

For the bonus-- What major scientific discovery did this head scratcher lead to?

 

 

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philosophy, maddening mind games, zeno

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...and no fair doing the wiki search.
bluestocking babe
March 18, 2012 08:52 PM
I'd quit three-quarters of the way through--math is hard!

I run into this kind of thinking all the time from people who don't want to do something and are being passive-aggressive. I tell them about Zeno's paradox, and how somehow the frog always gets to the end of the log because he doesn't have to compute it to do it.
Con Chapman
March 18, 2012 09:23 PM
I have sat here and thought about this and then asked Steve. I did not type it into anything as we tried to figure it out and just shook our heads.
No idea..:)
but I wouldnt think about it hahah
HUGGGGGGGGGGGGG
Linda Seccaspina
March 18, 2012 10:12 PM
I just wonder why he thought this up. I like his tortise and the hare paradox. It is comforting for those of us who move to a slower drum beat.
Mimetalker
March 18, 2012 10:47 PM
Calculus, but in the limit, as the number of steps grows infinite, one gets aribitrarily close to the wall, if, one doesn't of course actually touch the wall, unless Time is allowed to be reach an Infinite Value in a Finite Amount of Time. There remain ... difficulties with the treatment of the Very Large exactly the same as the Very Small.
Don Rich
March 18, 2012 10:54 PM
http://en.wikipedia.org/wiki/Epimenides_paradox
Don Rich
March 18, 2012 10:58 PM
I didn't know xeno's paradox led to a major scientific discovery. Perhaps in mathematics though perhaps you are talking about the convergence of infinite series, or else the idea of the infinitesimal, which was an essential concept for the foundation of differential and integral calculus. Is that what you mean?

Or perhaps it led to the discovery of the refrigerator, since that's at one end of my kitchen...;)
Jeff J.
March 18, 2012 11:23 PM
I talked to two doctors, and that "par a dox" did not know the answer....darn it!!!!
Reminds me of penalities in the NFL when close to the goal line...and they say "half the distance to the goal," pick the ball up..and set it down in the same place.
They are not allowed to say touchdown or touchback....
J D Smith
March 18, 2012 11:32 PM
The answer has to be no or they would not have tossed out a question phrased this way.
Looks like your comment worked here. Best wishes.
rated with love
RomanticPoetess
March 19, 2012 12:09 AM
No mention is made of speed. If each time you covered half the remaining distance it took half the time to do so, you'd eventually have such momentum, provided only that you didn't stop between steps, that you'd cover the remaining distance without taking a step. In fact your momentum ought to be great enough to provide quite an interesting impact!
.
skypixie0
March 19, 2012 12:22 AM
Love this...
.........(¯`v´¯) (¯`v´¯)
☼•*¨`*•.¸.(ˆ◡ˆ).¸.•*
............... *•.¸.•* ♥⋆★•❥ Thanx & Smiles (ツ) & ♥ L☼√Ξ ☼ ♥
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Algis Kemezys
March 19, 2012 03:43 AM
I've been wondering about this all night, BSB! My son is taking calculus with limits & all that, but everytime he talks about it, my mind seems to go completely blank. I think, if one had teeny, tiny feet, one would never get there...but maybe get pretty darn close? :)
clay ball
March 19, 2012 07:53 AM
In my younger, more resilient days I would dwell on this and on the one that poses the irresistible force against the immovable object. I don't anymore, as I need my sleep. I am curious as to what discovery came from Zeno's paradox.
Frosty Funk
March 19, 2012 09:14 AM
Zeno's Paradox leads directly to the notion of the limiting process in the calculus, and the same notion in analysis and measure theory, so long as one applies certain notions of the Real numbers having certain properties, and, curiously, something among them known as the Axiom of Choice, per Analytic-Measure Theoretic treatments, so actually, the problem he posed was rather a brilliantly deep one.
Don Rich
March 19, 2012 01:38 PM
....I .....think my head just exploded.....
Alysa Salzberg
April 06, 2012 05:18 PM
Boy I have no idea but am looking forward to finding out.
.........(¯`v´¯) (¯`v´¯)
☼•*¨`*•.¸.(ˆ◡ˆ).¸.•*
............... *•.¸.•* ♥⋆★•❥ Thanx & Smiles (ツ) & ♥ L☼√Ξ ☼ ♥
⋆───★•❥ ☼ .¸¸.•*`*•.♥ (ˆ◡ˆ) ♥⋯ ❤ ⋯ ★(ˆ◡ˆ) ♥⋯ ❤ ⋯ ★
Algis Kemezys
April 14, 2012 02:46 AM
Some mathematicians, such as Carl Boyer, hold that Zeno's paradoxes are simply mathematical problems, for which modern calculus provides a mathematical solution.-Marla Ahlgrimm
Stephen Gacho
June 25, 2012 08:15 AM

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