Zeno’s Paradox of the Tortoise and Achilles - The Sequel

Dell / Inspiron one 2320
August 1, 2014 at 12:53:40
Specs: Windows 7 Home Premium, 3.3 GHz / 4001 MB
Zeno’s Paradox of the Tortoise and Achilles can be stated as follows:

Suppose I wish to cross a room. First, of course, I must cover half the distance. Then, I must cover half the remaining distance. Then, I must cover half the remaining distance. Then I must cover half the remaining distance…and so on forever. The consequence is that I can never get to the other side of the room.

I'm trying to figure out why a dropped object hits the floor.

If I drop an object from 10 feet, at some point it will be 5 feet from the floor. At some point later on, it will be 2.5 feet from the floor, then 1.25 feet, then .625 feet, and so on.

If I can't reach the wall by walking across the room, how can the object hit the floor?

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#1
August 1, 2014 at 13:54:13
mmm - it's all relative - and gravity hath its own rules... Much like the "Why is a mouse when it squeals?" koan/conundrum (from the days of the Beat Generation in the late 50s...)

As regards walking across the room - who said you have to walk; you could fly... (with apologies to Alexander the Great and Gordian Knot approach...)


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#2
August 1, 2014 at 14:06:04
You obviously never studied the sums of infinite series.

The sum of the series

1/2 + 1/4 + 1/8 + ...

is 1. Sorry, there is no paradox to see here. Move along please.


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#3
August 1, 2014 at 16:23:52
Ah yes, the sum to infinity. However, one might describe infinity as the place that when you get there you still have a little further to go.

Always pop back and let us know the outcome - thanks

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#4
August 1, 2014 at 20:31:49
That reminds me of a story about John von Neumann. Here's one source:

http://stepanov.lk.net/mnemo/legend...

"Two bicyclists start twenty miles apart and head toward each other, each going at a steady rate of 10 m.p.h. At the same time a fly that travels at a steady 15 m.p.h. starts from the front wheel of the southbound bicycle and flies to the front wheel of the northbound one, then turns around and flies to the front wheel of the southbound one again, and continues in this manner till he is crushed between the two front wheels. Question: what total distance did the fly cover ? The slow way to find the answer is to calculate what distance the fly covers on the first, northbound, leg of the trip, then on the second, southbound, leg, then on the third, etc., etc., and, finally, to sum the infinite series so obtained. The quick way is to observe that the bicycles meet exactly one hour after their start, so that the fly had just an hour for his travels; the answer must therefore be 15 miles. When the question was put to von Neumann, he solved it in an instant, and thereby disappointed the questioner: "Oh, you must have heard the trick before!" "What trick?" asked von Neumann; "all I did was sum the infinite series."

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#5
August 3, 2014 at 14:12:54
Ijack, please send me a postcard from infinity when you get there.

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#6
August 3, 2014 at 14:44:31
... but the postcard would take an infinite time to reach you.

Always pop back and let us know the outcome - thanks


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#7
August 3, 2014 at 14:57:17
Not really - according to Hoos' Law - infinity has an infinite number of possibilities; and thus one of them is that the impossible will happen and the card will arrive, and on time - subject of course to the vagaries of the postal system which will deliver it...

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#8
August 3, 2014 at 16:58:14
Errr..."Who's Hoo" (if you'll pardon the expression)?
Anything to do with Who's on base?

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#9
August 4, 2014 at 00:33:15
I see you were paying attention 007 & a half...

You hit the nail on the head - fortunately not your own thumb nail too...

Hoo as in "who's law" - as in never heard of him...

Bentine, Milligan, the rest of the Goons, and then later Cleese and Python influences still pervade; not forgetting the 40s or 50s Abbott & Costello classic sketch which was a play on who/hoo etc...


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#10
August 4, 2014 at 01:14:24
Sounds like a Dr. Seuss character.

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#11
August 4, 2014 at 17:51:38
Derek @ #8... "Hoyles Law" perhaps!

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#12
August 5, 2014 at 14:47:39
Just the other day Dr. Seuss and I were discussing a Thing or 2.

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#13
August 5, 2014 at 15:51:20
No "Hoyle's Law simply states that without hoyle things don' t run or progress smoothly; and thus one is less likely to reach or secure ones objective... Things gets a little ruff 'and hot 'n bothered due to excessive friction...

As for Dr. Seuss he has seussed out more than thing or three in the past...


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#14
August 8, 2014 at 07:46:23
re: "Hoyle's Law simply states that without hoyle things don' t run or progress smoothly..."

Could you point me to a reference where I can read more on that theory. All of my searches for Hoyle's Law lead to Fred Holye, the astromer, or Edmond Hoyle, the "father of Whist".

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#15
August 8, 2014 at 10:03:33
mmm... It's a very obscure and little known law, and often taken for granted these days; its origins being lost - probably buried somewhere in the annals of Bentine (of It's a Square World fame) and the later Seacombe/Milligian/Seller entrourage...

The reference will probably advise the dedicated novice scholar/historian to delete the aspirant "h" when searching for, or pronouncing "(h)oyle - at which time it all becomes as clear as pure refined crude ((h)oyle....)

As some here of a certain age/generation may recall...The Square World was a classic BBC tv series in the early-mid 60s... It was hosted by Michael Bentine; and written by him and a few like minded chums "of equal brilliance..." It had six episodes only per season; and ran I think for three seasons only. 'Twas a joy and pleasure to work on...

Fred Hoyle as I recall was also the author of an excellent sci-fi novel "The Black Cloud" way back in the mid-sixties in the last century...

Thank you for the reference re' Edmond Hoyle and Whist... A new one for me...

To quote (and I hope accurately) the late Harry Seacombe - "It's these little snippets of information that make it all seem worthwhile..." - or was it "useless information"...?


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#16
August 8, 2014 at 20:25:14
Oh I get it---'oyle instead of Hoyle becasue of the odd way British have of being unable to pronounce the leading 'h'. Like when Watson was talking to Sherlock and referred to him as 'olmes. Or Herman's Hermits, ♪ I'm 'enry the eighth I am, 'enry the eighth I am I am

I think I still have the Fred Hoyle book in my sci fi library in a box in the garage.

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#17
August 9, 2014 at 01:06:41
Pay attention 007... The chaps/chapesses in parts of east London drop the "H", and a few elsewhere may do similarly; but the rest of us wot is proper edikated, went t'skool, an lernd t'spel... don't drop it. And "Holmes" never dropped the "H" - he was far too well edikated and brung up like wot we is here. The only time he ever didn't/doesn't speak "correctly" (as in what many call RP - received prononciation - or what was once BBC radio//tv style of speech) is when he went/goes undercover in pursuit of the criminal?

Eliza Doolittle - My Fair Lady - is a prime example of the different styles of speech still around; educated, upper and middle class, against east London (generally called Cockney, although that is really only applied to one smallish part of east London). You'll also hear references to Essex speech too - but let's not go there just now.

Incidentally "most" Brits can and do pronounce the "H"... But few pronounce the "H" in herbs... 'cos it's silent - as is the "H" in dog or the "D" in cat...


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#18
August 9, 2014 at 01:37:05
It was Watson who dropped the 'h' at least in the Basil Rathbone movies. I don't know who played Watson in those but he really stretched it out. It was more like 'o-o-olmes.

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#19
August 9, 2014 at 04:17:42
as in ohm's law and 'ome on the range... Perhaps Watson was a wannabe electronics geek ,and also a closet cowboy...

Incidentally, other actors in later performances of the Watson character generally had Watson pronounce the "H" in Holmes; and also he was generally portrayed as less a bumbling soul than in the Basil Rathbone/Nigel Bruce combination (thanks to Wikepedia for the Nigel Bruce confirmation).

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#20
August 15, 2014 at 11:06:51
re: "as in ohm's law and 'ome on the range... Perhaps Watson was a wannabe electronics geek, and also a closet cowboy..."

...or a cook.

My favorite cast iron skillet has found a home on the range.

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