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PeteH

Math problem: Zeno's paradox

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No need to resort to quantization of spacetime.



why not? its always fun to resort to quanti-something of space, it makes you sound smart...
B|

O



ooh. ohh. can I quantificate some things? 3. there I quantificated. (I spose I just like that word)
Goddam dirty hippies piss me off! ~GFD
"What do I get for closing your rig?" ~ me
"Anything you want." ~ female skydiver
Mohoso Rodriguez #865

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If you have a letter size paper, can you divided oon half? can you divided that half on half, can you keep going forever?



When you fold something, the area is divided in half, but the thickness is doubled.

IIRC, a piece of paper is .004" thick. 2 to the 10th is 1024. By folding a piece of paper 10 times, it quickly becomes real thick and real small.

2 to the 20th is a little over a million.

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IIRC, a piece of paper is .004" thick. 2 to the 10th is 1024. By folding a piece of paper 10 times, it quickly becomes real thick and real small.


point being?
anyway a paper is not a good example because at somepoint, at the molecular level, if you divide it, it wont be a paper anymore...
"Carpe diem, quam minimum credula postero."

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1 - the race - already explained by smaller time increments

2 - the arrow doesn't move, the entire universe moves past the still arrow - I realize this is flip. so was the question

3 - the bird flew at 150 MPH for an hour. the rest is left as an exercise for the student

This is on another post, but it died out quickly so only one person worked it.

I have three bags of marbles:

1 - has 6 black marbles
1 - has 6 white marbles
1 - has 3 black and 3 white marbles

all are labeled incorrectly with the lables (no particular order here) "Black" "White" "Mixed"

1 - What is the mininum number of marbles you pick to be able to move the labels to the correct bag?

2 - From which bag or combination of bags did you pick how many marbles from? in what order?

(these are not clear bags, these are not talking bags, these are not zombie bags or marbles, the marbles don't change colors, the bags may or may not be racing on a train towards a collision at infinitely small intervals, etc. etc.)

another:

Four guys are lined up in a row facing north. On their backs are colored spots in this order Blue, Pink, Blue, Pink (back to front). They can only look forward and see the people in front of them. Unforetuneately the person in the front of the line is wearing a sweatshirt so the dot color is hidden. No ones knows the dot he himself is wearing.

I announce to them that there are two Blue dots, and two pink dots. And I'll give the person to correctly guess their color $5000 dollars. But if they guess incorrectly, I'll shoot them in the head.

Who wins the money? (ok, they can't discuss it amongst themselves, only one person gets to guess out loud then it's over, no one wants to die)

...
Driving is a one dimensional activity - a monkey can do it - being proud of your driving abilities is like being proud of being able to put on pants

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easy - three marbles is the minimum although, thats if you are lucky.

You pick one, its white. Same back pick a seccond, its black. You know thats the mixed.

Pick a third from a seccond bag - its black. You know thats the black bag and the other is the white.

If you want to pick enough marbles to guarantee you can find out you need 8

you need four from the first to see its black, and four from the seccond to know its white - last is mixed by elimination.

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IIRC, a piece of paper is .004" thick. 2 to the 10th is 1024. By folding a piece of paper 10 times, it quickly becomes real thick and real small.


point being?
anyway a paper is not a good example because at somepoint, at the molecular level, if you divide it, it wont be a paper anymore...



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If you have a letter size paper, can you divided oon half? can you divided that half on half, can you keep going forever?



Someone asked this question, I was giving a practical near-answer. More interesting. Try folding a really big piece of paper 10 times.

If you want the true math answer, it is a matter of using limits. The height is multiplied by 2n and the area is divided by 2n. N is the number of folds, where n approaches infinity.

So it gets infinitely tall, but the area approaches zero.

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So it gets infinitely tall, but the area approaches zero



or in other words, going back to being a paper only standing up now ;)



A stack of paper is where the area is spread horizontally. This one will be vertical, but have an area of zero. Therefore, you can keep all the paper on hand that you need, but you won't need a place to store it.

That seems handy, doesn't it? ;)

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So it gets infinitely tall, but the area approaches zero



or in other words, going back to being a paper only standing up now ;)



Actually, wouldnt as the folds continued toward infinity, it become more like a line? Of course its volume would still be measurable, in fact constant (in theory). so, as it approached an infinite number of folds it would become infinitely thin and long, yet still hold a constant volume? hummm... did I get that right? :o
Goddam dirty hippies piss me off! ~GFD
"What do I get for closing your rig?" ~ me
"Anything you want." ~ female skydiver
Mohoso Rodriguez #865

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Interesting, what can we, as skydivers learn from this?

Age: 37,39
Sex: Male, male
Time in Sport: Infinate
Cause of death: Starvation. (Never reached pull altitude).

Description:
Two experienced jumpers known by others as Achilles and Turtlespeed decide to perform a two-way. After an uneventful set up in the door, Turtlespeed gives a weak count, causing Achilles to leave late. This late count, combined with the jumpers nicknames, inadvertantly engaged xeno's paradox, causing both jumpers to fall only half the distance to pull alt at any given time. Therefore, neither jumper deployed and spent eternity in freefall.

Conclusion:
Jumpers should be careful not to trigger paradoxical mathmetics in freefall.
“There are more things in Heaven and Earth, Horatio, than are dreamt of in your philosophies.”

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It cant become infinately thin and long. At some point you would get down to a hugely tall stack of individual atoms. That point would be measurable an predictable, assuming you knew how many atoms you had in a sheet of paper.

Good luck trying to fold the atoms in half, and please ensure you do it away from an populated areas ;)

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It's called Calculus, I believe we're talking about limits here. It's the first thing you learn in class.



Well, since you bring up the subject of calculus, have you come across the 3-d surface whose area is infinite but whose contained volume of revolution is finite? That means if you completely fill it with paint, you still don't have enough paint to paint its surface. Wierd.
...

The only sure way to survive a canopy collision is not to have one.

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It cant become infinately thin and long. At some point you would get down to a hugely tall stack of individual atoms. That point would be measurable an predictable, assuming you knew how many atoms you had in a sheet of paper.

Good luck trying to fold the atoms in half, and please ensure you do it away from an populated areas ;)



mmm... me likes splosions. but yea... I forgot we were dealing w/ a finite quantity of mass.

this made me LMFAO!
***
Goddam dirty hippies piss me off! ~GFD
"What do I get for closing your rig?" ~ me
"Anything you want." ~ female skydiver
Mohoso Rodriguez #865

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didnt say all the atoms were "paper" atoms - just that you would have a stack of "atoms".

The atoms of carbon, hydrogen, oxygen etc etc would be all mixed up - end to end you would have the constituant parts of paper. you wouldnt be able to see it front end on. looking at it from the side you would probably still not see it cos it would let all the light through (it being only one atom thick an all) but if you could see it im guessing you would see what looked like paper.

This is of course asssuming you could prevent all those individual atoms from just floating off.

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easy - three marbles is the minimum although, thats if you are lucky.
.



No, that's not it. Less. And the answer has no luck involved. You will know!

samhussey got the shirt thing right.

...
Driving is a one dimensional activity - a monkey can do it - being proud of your driving abilities is like being proud of being able to put on pants

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