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Have you lost your marbles?...

Heineken
Posts: 1,230
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10/31/2012 1:03:50 PM
Posted: 4 years ago
If I place two marbles 10" apart on a table and.....

...after one minute has passed, I will move the marbles closer together by half of the distance between them.
How many times must I move the marbles before they touch?
Will they ever touch?
Vidi, vici, veni.
(I saw, I conquered, I came.)
AlwaysMoreThanYou
Posts: 2,900
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10/31/2012 1:09:47 PM
Posted: 4 years ago
At 10/31/2012 1:03:50 PM, Heineken wrote:
If I place two marbles 10" apart on a table and.....

...after one minute has passed, I will move the marbles closer together by half of the distance between them.
How many times must I move the marbles before they touch?
Will they ever touch?

Oh, Zeno.
'When the Spirit of truth comes, he will guide you into all the truth; for he will not speak on his own authority, but whatever he hears he will speak, and he will declare to you the things that are to come.' - John 16:13
TheBloodyScot
Posts: 59
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10/31/2012 2:26:06 PM
Posted: 4 years ago
You could only do so about 114 times.
Due to the fact that the smallest measurement is a Plank Length, apx. 636.30"10^(−36) inches.
http://en.wikipedia.org...
Here is the math:
http://www.wolframalpha.com...+*+%282^x%29+%3D+10
Something is not worth doing if it is not worth doing right.

"Is God willing to prevent evil, but not able? Then he is not omnipotent. Is he able, but not willing? Then he is malevolent. Is he both able and willing? Then whence cometh evil? Is he neither able nor willing? Then why call him God?"
-Epicurus

"I am the wisest man alive, for I know one thing, and that is that I know nothing."
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TheBloodyScot
Posts: 59
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10/31/2012 2:27:31 PM
Posted: 4 years ago
At 10/31/2012 2:26:06 PM, TheBloodyScot wrote:
You could only do so about 114 times.
Due to the fact that the smallest measurement is a Plank Length, apx. 636.30"10^(−36) inches.
http://en.wikipedia.org...
Here is the math:
http://www.wolframalpha.com...+*+%282^x%29+%3D+10

The bottom link doesn't work, but here is the math equation that I used:
636.30"10^(−36) * (2^x) = 10
and I solved for x
Something is not worth doing if it is not worth doing right.

"Is God willing to prevent evil, but not able? Then he is not omnipotent. Is he able, but not willing? Then he is malevolent. Is he both able and willing? Then whence cometh evil? Is he neither able nor willing? Then why call him God?"
-Epicurus

"I am the wisest man alive, for I know one thing, and that is that I know nothing."
-Socrates
Heineken
Posts: 1,230
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10/31/2012 2:37:53 PM
Posted: 4 years ago
At 10/31/2012 2:27:31 PM, TheBloodyScot wrote:
At 10/31/2012 2:26:06 PM, TheBloodyScot wrote:
You could only do so about 114 times.
Due to the fact that the smallest measurement is a Plank Length, apx. 636.30"10^(−36) inches.
http://en.wikipedia.org...
Here is the math:
http://www.wolframalpha.com...+*+%282^x%29+%3D+10

The bottom link doesn't work, but here is the math equation that I used:
636.30"10^(−36) * (2^x) = 10
and I solved for x

Way to overthink the question. They will never touch. No matter if the distance between them is a nanometer. If I keep cutting the distance in half, you never get to zero.....ever.
Vidi, vici, veni.
(I saw, I conquered, I came.)
Heineken
Posts: 1,230
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10/31/2012 2:41:51 PM
Posted: 4 years ago
At 10/31/2012 2:37:53 PM, Heineken wrote:
At 10/31/2012 2:27:31 PM, TheBloodyScot wrote:
At 10/31/2012 2:26:06 PM, TheBloodyScot wrote:
You could only do so about 114 times.
Due to the fact that the smallest measurement is a Plank Length, apx. 636.30"10^(−36) inches.
http://en.wikipedia.org...
Here is the math:
http://www.wolframalpha.com...+*+%282^x%29+%3D+10

The bottom link doesn't work, but here is the math equation that I used:
636.30"10^(−36) * (2^x) = 10
and I solved for x


Way to overthink the question. They will never touch. No matter if the distance between them is a nanometer. If I keep cutting the distance in half, you never get to zero.....ever.

10,5,2.5,1.25,.625,.312,.156,.078,.039,.019,.009,.0048,.0024,.0012,.00061,.000305....etc, etc..you can do this 20 more times and reach 2.273736754432321e-12.
Never zero.....
Vidi, vici, veni.
(I saw, I conquered, I came.)
TheBloodyScot
Posts: 59
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10/31/2012 2:44:26 PM
Posted: 4 years ago
Strictly speaking, it is impossible to go all the way and touch it if you wanted to because the electromagnetic forces at the atomic level would repel.
Something is not worth doing if it is not worth doing right.

"Is God willing to prevent evil, but not able? Then he is not omnipotent. Is he able, but not willing? Then he is malevolent. Is he both able and willing? Then whence cometh evil? Is he neither able nor willing? Then why call him God?"
-Epicurus

"I am the wisest man alive, for I know one thing, and that is that I know nothing."
-Socrates
Heineken
Posts: 1,230
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10/31/2012 2:56:19 PM
Posted: 4 years ago
At 10/31/2012 2:44:26 PM, TheBloodyScot wrote:
Strictly speaking, it is impossible to go all the way and touch it if you wanted to because the electromagnetic forces at the atomic level would repel.
Vidi, vici, veni.
(I saw, I conquered, I came.)
TheBloodyScot
Posts: 59
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10/31/2012 3:11:15 PM
Posted: 4 years ago
Now try that.
Something is not worth doing if it is not worth doing right.

"Is God willing to prevent evil, but not able? Then he is not omnipotent. Is he able, but not willing? Then he is malevolent. Is he both able and willing? Then whence cometh evil? Is he neither able nor willing? Then why call him God?"
-Epicurus

"I am the wisest man alive, for I know one thing, and that is that I know nothing."
-Socrates
FREEDO
Posts: 21,057
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10/31/2012 3:17:16 PM
Posted: 4 years ago
I say no but for a completely different reason than you're thinking.

Nothing ever touches unless they bind.
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fnord
drafterman
Posts: 18,870
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10/31/2012 3:42:56 PM
Posted: 4 years ago
At 10/31/2012 1:03:50 PM, Heineken wrote:
If I place two marbles 10" apart on a table and.....

...after one minute has passed, I will move the marbles closer together by half of the distance between them.
How many times must I move the marbles before they touch?
Will they ever touch?

Define: "touch"
lewis20
Posts: 5,093
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10/31/2012 3:53:05 PM
Posted: 4 years ago
Ya the atoms of the marbles will never touch each other.
Though brings back good memories of my 7th grade math teacher explaining Zeno and his paradox to us.
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bossyburrito
Posts: 14,075
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10/31/2012 4:26:49 PM
Posted: 4 years ago
http://www.physicsforums.com...
#UnbanTheMadman

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Ore_Ele
Posts: 25,980
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11/1/2012 1:06:27 AM
Posted: 4 years ago
At 10/31/2012 2:26:06 PM, TheBloodyScot wrote:
You could only do so about 114 times.
Due to the fact that the smallest measurement is a Plank Length, apx. 636.30"10^(−36) inches.
http://en.wikipedia.org...
Here is the math:
http://www.wolframalpha.com...+*+%282^x%29+%3D+10

Technically the a Plank Length is a theoretical minimum, we don't know if it is a real minimum.
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Ore_Ele
Posts: 25,980
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11/1/2012 1:10:38 AM
Posted: 4 years ago
At 10/31/2012 1:03:50 PM, Heineken wrote:
If I place two marbles 10" apart on a table and.....

...after one minute has passed, I will move the marbles closer together by half of the distance between them.
How many times must I move the marbles before they touch?
Will they ever touch?

If we leave the equation as utterly simplistic as possible (such as by ignoring electromagnetic forces and gravitational forces, and really all forces in general), then they were never touch.

While the limit of the distance between them reaches zero, the number of steps reaches infinite. If each step is a constant 1 minute apart, an infinite number of 1 minute steps is an infinite span of time.

This is actually different from Zeno, because his paradox (namely with reaching a wall, or catching up to a tortoise) does not have a constant time between each interval, it is also changing so that it has it's own approaching limit.
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R0b1Billion
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11/1/2012 11:03:09 PM
Posted: 4 years ago
Seems like it is to me... the swift-footed achilles can never close on the plodding tortoise because every instance only closes the gap by... oh wait you're right. Zeno's paradox depended on the tortoise moving a certain amount every time achilles moved as well.
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Ore_Ele
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11/1/2012 11:20:20 PM
Posted: 4 years ago
At 11/1/2012 11:03:09 PM, R0b1Billion wrote:
Seems like it is to me... the swift-footed achilles can never close on the plodding tortoise because every instance only closes the gap by... oh wait you're right. Zeno's paradox depended on the tortoise moving a certain amount every time achilles moved as well.

Zeno came up with multiple paradoxes, not just the tortoise. There was always one approaching a wall as well. The difference was that as he approached, while the distance was always cut in half, so was the time before the next instance, so the limit of the infinite was a finite number.
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