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bdeg 06-05-2009 02:07 AM

this is assuming the bags are on the bus, which was not necessarily a given..

are the bags on the bus?

bdeg 06-05-2009 02:21 AM

if not, 14.

Slainte 06-05-2009 04:00 AM

Buses have wheels not legs/10990

Comanche 06-05-2009 06:24 AM

Quote:

Originally Posted by bdeg (Post 5818911)
if 0
2(busdriver)+7x7x7x7x4+7x7x7x4+7x2
2+9604+1372+14
10992
if busdriver is a female with a backpack then

10990

The riddle didn't say a bus driver was ON the bus. The bus driver was in taking a leak and wasn't on the bus.

headsnap 06-05-2009 07:07 AM

Quote:

Originally Posted by orange (Post 5818807)
If you think it's a very simple question - yes there's something wrong with you. Try googling it. Baby Lee mentioned one site that has 300 PAGES of comments.

there is a depressing amount of DUMB in this world...


Quote:

Mud is a better example.
If your 747 is in your said mud, will it move?

tiptap 06-05-2009 08:01 AM

Ok I will put my 2 cents in.

The bullet question represents more of a math discussion than science. All linear transformations can be described by the two independent normal basis transformations. And in this case both bullets have the same force field, g, applied in the vertical direction representing one basis and the fired bullet has an additional momentum vector along the horizontal axis representing the other independent basis. And to the degree that you align actions along different basis directions you will have independent consequences. But along the same basis they will be the same. This is straight out of vector or matrix or linear algebras. Not so much science except to note what forces or momentum is aligned with what basis.

As far as the plane question, somewhere along the discussion, the "plane don't fly" gang stated that momentum and forces where not part of the problem. That speed was the only concern. So that the speed of the jet and the treadmill canceled out leaving no airspeed for lift. And yet in order to get lift anytime, whether in this scenario or just everyday flight, you have interjected forces and momentum. You can't ignore this then with the jet engines and that system of transfer of forces and momentum and just look at speeds and then talk about flight and use forces and momentum to describe how flight would or would not take place. After all MOMENTUM is what is conserved, not speed in science, in the real world. Therefore while you can create a system in which your premise is correct, it is not part of the science and this world AT ANY SCALE. So the jet takes off in this universe.

So next are the the questions concerning Special Relativity and General Relativity involving speed of light and Black Holes respectively. I would like to point people to my discussion with patteu about Copernican vs Ptolemian representations of the solar system. I made part of my arguments concerning Einstein's theories on the GPS representing a test of Special Theory and Atomic Clocks at different gravitational fields proving the validity of General Relativity.

So for the question of what will be the speed of light emitted from some object traveling close the speed of light, the answer "that the speed will be the speed of light" is not complete. You must go on to say that the speed measured from the near light speed object as well as an earth bound observer both will see the same speed for the light. This being the case, the independent observers will not see the same distances and times that the other observers note for each other. Leading to the lack of being able to agree upon a unit of measure in distance or alignment of clocks. However both observers will agree that ds^2=d-ct^2 + dx^2 +dy^2 +dz^2 which is an analogue for pythagorean distance that includes time as a negative component of distance.

As far as the Black Hole, Baby Lee's description of both views of two observers, one outside and the falling inside observer, are actually the view and only the view of the outside observer. They would see the stretching of the falling object at the event horizon and such. The actual falling observer would not even notice he passed through the event horizon. He would feel no forces (ignoring tidal forces say by having so large of black hole that the event horizon is essentially flat). He is in free fall and as such is not subject to gravitational forces. Acceleration and gravity being the same. The stars would still twinkle above and the black hole would still be black though it would be getting bigger blocking out some stars in its direction.

That is all for now.

Coach 06-05-2009 08:14 AM

E=mc˛

EyePod 06-05-2009 09:41 AM

Quote:

Originally Posted by mikeyis4dcats. (Post 5816356)
how many gallons are in a 5 gallon bucket?

There are 5 gallons of AIR.

Buck 06-05-2009 09:53 AM

Holy crap this thread went on forever last night. I believe it is time for a new question.

MagicHef 06-05-2009 10:37 AM

Quote:

Originally Posted by MediaCenterJunkie (Post 5819258)
Holy crap this thread went on forever last night. I believe it is time for a new question.

Okay:

Quote:

A group of people with assorted eye colors live on an island. They are all perfect logicians -- if a conclusion can be logically deduced, they will do it instantly. No one knows the color of their eyes. Every night at midnight, a ferry stops at the island. Any islanders who have figured out the color of their own eyes then leave the island, and the rest stay. Everyone can see everyone else at all times and keeps a count of the number of people they see with each eye color (excluding themselves), but they cannot otherwise communicate. Everyone on the island knows all the rules in this paragraph.

On this island there are 100 blue-eyed people, 100 brown-eyed people, and the Guru (she happens to have green eyes). So any given blue-eyed person can see 100 people with brown eyes and 99 people with blue eyes (and one with green), but that does not tell him his own eye color; as far as he knows the totals could be 101 brown and 99 blue. Or 100 brown, 99 blue, and he could have red eyes.

The Guru is allowed to speak once (let's say at noon), on one day in all their endless years on the island. Standing before the islanders, she says the following:

"I can see someone who has blue eyes."

Who leaves the island, and on what night?


There are no mirrors or reflecting surfaces, nothing dumb. It is not a trick question, and the answer is logical. It doesn't depend on tricky wording or anyone lying or guessing, and it doesn't involve people doing something silly like creating a sign language or doing genetics. The Guru is not making eye contact with anyone in particular; she's simply saying "I count at least one blue-eyed person on this island who isn't me."

And lastly, the answer is not "no one leaves."

I've done my best to make the wording as precise and unambiguious as possible (after working through the explanation with many people), but if you're confused about anything, please let me know. A word of warning: The answer is not simple. This is an exercise in serious logic, not a lateral thinking riddle. There is not a quick-and-easy answer, and really understanding it takes some effort.

Buck 06-05-2009 10:42 AM

Do you already know the answer?

MagicHef 06-05-2009 10:43 AM

Quote:

Originally Posted by MediaCenterJunkie (Post 5819376)
Do you already know the answer?

Yes, because I cheated. I definitely did not figure this out on my own.

Buck 06-05-2009 10:45 AM

My only guess is that someone with lets say blue eyes, sees someone counting the amount of people with blue eyes (they can tell that person is counting the people with blue eyes because they themselves can see those people have blue eyes), and they see themselves getting grouped in with that count.

Otherwise, I have no clue.

MagicHef 06-05-2009 10:53 AM

Quote:

Originally Posted by MediaCenterJunkie (Post 5819392)
My only guess is that someone with lets say blue eyes, sees someone counting the amount of people with blue eyes (they can tell that person is counting the people with blue eyes because they themselves can see those people have blue eyes), and they see themselves getting grouped in with that count.

Otherwise, I have no clue.

Nope.

Buck 06-05-2009 10:57 AM

Ok, I just read the answer. There was no way I was getting that. We have some smart minds on here, but I really doubt anyone gets it.

Baby Lee 06-05-2009 11:02 AM

Quote:

Originally Posted by MediaCenterJunkie (Post 5819392)
My only guess is that someone with lets say blue eyes, sees someone counting the amount of people with blue eyes (they can tell that person is counting the people with blue eyes because they themselves can see those people have blue eyes), and they see themselves getting grouped in with that count.

Otherwise, I have no clue.

You're not completely on the wrong track though.

Perhaps the most important aspect is the specific [and complete] wording of the question.

Buck 06-05-2009 11:09 AM

Okay, I'm guessing this is an easier one.

I haven't read the answer to it, so I am playing along too.

A man who lives on the tenth floor takes the elevator down to the first floor every morning and goes to work. In the evening, when he comes back; on a rainy day, or if there are other people in the elevator, he goes to his floor directly. Otherwise, he goes to the seventh floor and walks up three flights of stairs to his apartment.
Can you explain why?
(This is one of the more popular and most celebrated of all lateral thinking logic puzzles. It is a true classic. Although there are many possible solutions that fit the conditions, only the canonical answer is truly satisfying.)

Buck 06-05-2009 11:12 AM

I think I already figured it out.

Spoiler!

MagicHef 06-05-2009 11:13 AM

Quote:

Originally Posted by MediaCenterJunkie (Post 5819470)
Okay, I'm guessing this is an easier one.

I haven't read the answer to it, so I am playing along too.

A man who lives on the tenth floor takes the elevator down to the first floor every morning and goes to work. In the evening, when he comes back; on a rainy day, or if there are other people in the elevator, he goes to his floor directly. Otherwise, he goes to the seventh floor and walks up three flights of stairs to his apartment.
Can you explain why?
(This is one of the more popular and most celebrated of all lateral thinking logic puzzles. It is a true classic. Although there are many possible solutions that fit the conditions, only the canonical answer is truly satisfying.)

Short. Umbrella.

Baby Lee 06-05-2009 11:14 AM

Quote:

Originally Posted by MediaCenterJunkie (Post 5819470)
Okay, I'm guessing this is an easier one.

I haven't read the answer to it, so I am playing along too.

A man who lives on the tenth floor takes the elevator down to the first floor every morning and goes to work. In the evening, when he comes back; on a rainy day, or if there are other people in the elevator, he goes to his floor directly. Otherwise, he goes to the seventh floor and walks up three flights of stairs to his apartment.
Can you explain why?
(This is one of the more popular and most celebrated of all lateral thinking logic puzzles. It is a true classic. Although there are many possible solutions that fit the conditions, only the canonical answer is truly satisfying.)

He hopes to see the woman at the next funeral.

Buck 06-05-2009 11:15 AM

You are in a room with no metal objects except for two iron rods. Only one of them is a magnet.
How can you identify which one is a magnet?

Buck 06-05-2009 11:16 AM

Quote:

Originally Posted by Baby Lee (Post 5819490)
He hopes to see the woman at the next funeral.

What?

Jenson71 06-05-2009 11:17 AM

Quote:

Originally Posted by MediaCenterJunkie (Post 5819470)
Okay, I'm guessing this is an easier one.

I haven't read the answer to it, so I am playing along too.

A man who lives on the tenth floor takes the elevator down to the first floor every morning and goes to work. In the evening, when he comes back; on a rainy day, or if there are other people in the elevator, he goes to his floor directly. Otherwise, he goes to the seventh floor and walks up three flights of stairs to his apartment.
Can you explain why?
(This is one of the more popular and most celebrated of all lateral thinking logic puzzles. It is a true classic. Although there are many possible solutions that fit the conditions, only the canonical answer is truly satisfying.)

Because he is sleeping with a girl on the 7th floor who happens to have broken windows that lets in a lot of rain. He doesn't want anyone to know this so he won't get off on the 7th when people are in the elevator with him. And he doesn't want to get wet.

He doesn't attempt to get back on the elevator after doing the deed, because the stairs are very close to her room, and he would otherwise have to go down a long hallway.

Baby Lee 06-05-2009 11:17 AM

Quote:

Originally Posted by MediaCenterJunkie (Post 5819494)
You are in a room with no metal objects except for two iron rods. Only one of them is a magnet.
How can you identify which one is a magnet?

That's not so much a logic question as a magnetic properties question.

EyePod 06-05-2009 11:17 AM

Quote:

Originally Posted by MediaCenterJunkie (Post 5819470)
Okay, I'm guessing this is an easier one.

I haven't read the answer to it, so I am playing along too.

A man who lives on the tenth floor takes the elevator down to the first floor every morning and goes to work. In the evening, when he comes back; on a rainy day, or if there are other people in the elevator, he goes to his floor directly. Otherwise, he goes to the seventh floor and walks up three flights of stairs to his apartment.
Can you explain why?
(This is one of the more popular and most celebrated of all lateral thinking logic puzzles. It is a true classic. Although there are many possible solutions that fit the conditions, only the canonical answer is truly satisfying.)

I'd say that there's a chick he likes to watch who sunbathes on the 7th floor, but he doesn't want other people to know. And she's only out when it's not raining.

Buck 06-05-2009 11:18 AM

Quote:

Originally Posted by Baby Lee (Post 5819498)
That's not so much a logic question as a magnetic properties question.

I found it on a logic website, i cant figure it out, and this thread started as a physics thread in the first place.

Baby Lee 06-05-2009 11:21 AM

Quote:

Originally Posted by MediaCenterJunkie (Post 5819503)
I found it on a logic website, i cant figure it out, and this thread started as a physics thread in the first place.

Magnets have poles. Touch the end of one to the center of the other. If it sticks, the center touched is the plain iron and the end touched is the magnet. If the end touched tries to deflect to one end or the other of the center touched, the center touched is the magnet and the end touched is the plain iron.

MagicHef 06-05-2009 11:37 AM

Hey. Figure mine out.

Buck 06-05-2009 11:43 AM

Quote:

Originally Posted by MagicHef (Post 5819539)
Hey. Figure mine out.

I already cheated and read the answer.

Baby Lee 06-05-2009 11:53 AM

Quote:

Originally Posted by MagicHef (Post 5819539)
Hey. Figure mine out.

If you're talking to me, I think my clue to MCJ indicates that I've figured it out, though I'll be glad to express it if you wish.

If you're not, disregard

Sorry if a repost.

Pitt Gorilla 06-05-2009 01:06 PM

I know when the blue-eyed folks leave, but it doesn't seem that the others would ever leave.

orange 06-05-2009 05:43 PM

Quote:

Originally Posted by headsnap (Post 5818997)
there is a depressing amount of DUMB in this world...




If your 747 is in your said mud, will it move?


No.


http://www.jetphotos.net/news/media/...0866175100.jpg


United Parcel Service (Atlanta and Louisville) DC-8-73F N806UP (msn 46006) ran off the runway Thursday night while attempting takeoff from Greensboro-Piedmont Triad Airport (GSO), North Carolina. Just after 11:30pm, the package freighter was commencing a flight to the Louisville hub when the jet departed the right side of the runway, becoming stuck in the mud. The NTSB is investigating.

Photo: The UPS DC-8 is seen in the mud at GSO (Photo Copyright L. Gustavo Oliveira)

http://www.jetphotos.net/news/index....&c=1&tb=1&pb=1

http://www.uspermafrost.org/gallery/...ane1_small.jpg


DC-3 stuck in the mud on the Isachsen runway. Five Twin Otter flights were required to bring the equipment and people into Isachsen. The DC-3 was planned to reduce the number of Twin Otter flights required on the return trip, but this proved to be a mistake. During the days prior to this picture, the previously dry runway had developed wet patches due to water wicking up from the permafrost table. This condition went unnoticed until the DC-3 tried to turn on a soft spot. Once the plane was stuck, vibration from the engines caused the wheels to sink deeper until they contacted the permafrost table.


http://images.google.com/imgres?imgu...a%3DN%26um%3D1



Many, many more. I'm amazed you even asked - you're right, there is a depressing amount of DUMB in this world...

http://images.google.com/images?hl=e...tart=0&ndsp=18

headsnap 06-05-2009 05:57 PM

Quote:

Originally Posted by orange (Post 5820402)
No.


http://www.jetphotos.net/news/media/...0866175100.jpg


United Parcel Service (Atlanta and Louisville) DC-8-73F N806UP (msn 46006) ran off the runway Thursday night while attempting takeoff from Greensboro-Piedmont Triad Airport (GSO), North Carolina. Just after 11:30pm, the package freighter was commencing a flight to the Louisville hub when the jet departed the right side of the runway, becoming stuck in the mud. The NTSB is investigating.

so, are you really saying that if they fired up the JET engines, those planes won't move an inch?

Baby Lee 06-05-2009 06:43 PM

Quote:

Originally Posted by Pitt Gorilla (Post 5819761)
I know when the blue-eyed folks leave, but it doesn't seem that the others would ever leave.

This what you came up with

Spoiler!

orange 06-05-2009 06:49 PM

Quote:

Originally Posted by Baby Lee (Post 5820565)
This what you came up with

Spoiler!

I think you're a day late. Read your rep for why.

[edit] Then again, you may be counting the first ferry as day 2 (since it's at midnight), in which case we are in agreement.

Hog's Gone Fishin 06-05-2009 07:30 PM

Quote:

Originally Posted by Gonzo (Post 5816345)
WTF? Wouldn't the powder charge make a difference?

Let's say Im shooting a 10 mm ball bearing with about 55 grains of rifle powder.

I'm shooting this bearing from a height of 4 ft. I drop the bearing in my other hand at the same time from 4 ft. and the hit the ground at the same time...

Ok, now I adjust the powder charge to 75 grains. I shoot from the same height, but now I have adjusted the velocity of the projectile by about 800-1,000 feet per second. This would have to be a variable somehow.




Yes , you have to be correct. I was thinking the same thing more along the lines of,

IF I was jacking off a boar with one hand and jerking myself with the other and the boars velocity was 15 feet per second and mine was 10 feet per second would they really land at the same time ?

Pitt Gorilla 06-05-2009 09:19 PM

Quote:

Originally Posted by Baby Lee (Post 5820565)
This what you came up with

Spoiler!

Yes. But as far as I can tell, none of the remaining folks have any way of telling what color eyes they have.

MagicHef 06-05-2009 11:25 PM

What new information does the Guru give everyone?

beach tribe 06-06-2009 05:04 AM

I think I learned that when I was like 8 yrs old.

Heres one for ya.

When you see ducks flying in a V, you know why one side is always longer than the other??


Because it has more ducks in it.

beach tribe 06-06-2009 05:07 AM

Quote:

Originally Posted by Hog Farmer (Post 5820667)
Yes , you have to be correct. I was thinking the same thing more along the lines of,

IF I was jacking off a boar with one hand and jerking myself with the other and the boars velocity was 15 feet per second and mine was 10 feet per second would they really land at the same time ?

No hes not correct. It just means that the ball will have traveled further before it hits the ground. Unless you change the trajectory, the ball is going to fall to the earth at the same speed. More FPS does not change when the ball hits the ground in its fight against gravity.

Baby Lee 06-13-2009 05:22 PM

Interesting, I've heard a lot about relativity, but I guess I'd never heard Einstein's precise 'a ha!' moment.
According to Radiolab, he was thinking on looking back at the second hand on a clock as he accelerated to the speed of light. And he realized that, while for someone at rest the clock swept at an even pace, for the accelerating person the sweep would slow, coming to a complete stop at the speed of light. And that hand would never move again [for him] so long as he travelled at the speed of light.

Buck 08-25-2009 04:10 PM

I had to bump this.

Braincase 08-25-2009 04:15 PM

Quote:

Originally Posted by Hog Farmer (Post 5820667)
Yes , you have to be correct. I was thinking the same thing more along the lines of,

IF I was jacking off a boar with one hand and jerking myself with the other and the boars velocity was 15 feet per second and mine was 10 feet per second would they really land at the same time ?

This thread is worthless without... oh, god, did I really go there?

Buck 08-25-2009 05:13 PM

If anyone can explain this to me in plain english, I'll rep the shit out of you.

http://en.wikipedia.org/wiki/Banach%...Tarski_paradox

Buehler445 08-25-2009 05:32 PM

Quote:

Originally Posted by BuckinKaeding (Post 6000776)
If anyone can explain this to me in plain english, I'll rep the shit out of you.

http://en.wikipedia.org/wiki/Banach%...Tarski_paradox

Why the **** did you even look this up?

Buck 08-25-2009 05:36 PM

Quote:

Originally Posted by Buehler445 (Post 6000794)
Why the **** did you even look this up?

I've known about it for years, but I've never understood it. I thought somebody here might have some insight.

Jenson71 08-25-2009 05:37 PM

Quote:

Originally Posted by BuckinKaeding (Post 6000776)
If anyone can explain this to me in plain english, I'll rep the shit out of you.

http://en.wikipedia.org/wiki/Banach%...Tarski_paradox

That's just depressing, really.

Zebedee DuBois 08-25-2009 08:24 PM

I just want to say:
F=MA
We use that every day.

MagicHef 08-25-2009 11:59 PM

Quote:

Originally Posted by BuckinKaeding (Post 6000776)
If anyone can explain this to me in plain english, I'll rep the shit out of you.

http://en.wikipedia.org/wiki/Banach%...Tarski_paradox

Mathematics: Not necessarily applicable to the real world.

kcxiv 08-26-2009 12:13 AM

Here is what i can tell you about it. EA and their football games have no clue how to implement them properly in their football games. lol

orange 08-28-2009 07:25 PM

Quote:

Originally Posted by BuckinKaeding (Post 6000776)
If anyone can explain this to me in plain english, I'll rep the shit out of you.

http://en.wikipedia.org/wiki/Banach%...Tarski_paradox

I found the answer:

http://www.mopo.ca/uploaded_images/five-729113.jpg

Buck 12-17-2009 05:53 PM

I was just researching the Taos Hum.

http://en.wikipedia.org/wiki/The_Hum

Pretty crazy.

Buck 04-08-2011 03:44 PM

Bump

orange 04-08-2011 04:11 PM

In the 1920’s two mathematicians proved a very interesting but at the same time very puzzling theorem, known as the Banach-Tarski Paradox. In plain English, the theorem states that it is possible to divide a solid ball into a few pieces and reassemble those pieces together to make two balls, each of which has the same size as the original ball that was divided. A more striking consequence of their theorem is (you may want to sit down before you read this) a solid ball the size of a small pea can be cut into a number of pieces and reassembled into a new ball the size of the sun! Strange as it may sound, it is a valid mathematical argument, not a myth. (We have to note that it is not something one can do at home using a knife and a cutting board, because some of the pieces have no volume!) The analogy that we would like to establish under SMT is to map that solid ball of the theorem to a small amount of water which could quench the thirst of an army of about 30,000 in Tabuk in year 631. This was a miracle given to Prophet Muhammad, peace be upon him. A similar miracle of Prophet Jesus, peace be upon him, is described in the Bible, Matthew 14:21 (Volker Runde, in the Sky 2 (2000), 13–15).

I think the zero-volume pieces are the key.

Buck 04-08-2011 04:13 PM

Quote:

Originally Posted by orange (Post 7548091)
In the 1920’s two mathematicians proved a very interesting but at the same time very puzzling theorem, known as the Banach-Tarski Paradox. In plain English, the theorem states that it is possible to divide a solid ball into a few pieces and reassemble those pieces together to make two balls, each of which has the same size as the original ball that was divided. A more striking consequence of their theorem is (you may want to sit down before you read this) a solid ball the size of a small pea can be cut into a number of pieces and reassembled into a new ball the size of the sun! Strange as it may sound, it is a valid mathematical argument, not a myth. (We have to note that it is not something one can do at home using a knife and a cutting board, because some of the pieces have no volume!) The analogy that we would like to establish under SMT is to map that solid ball of the theorem to a small amount of water which could quench the thirst of an army of about 30,000 in Tabuk in year 631. This was a miracle given to Prophet Muhammad, peace be upon him. A similar miracle of Prophet Jesus, peace be upon him, is described in the Bible, Matthew 14:21 (Volker Runde, in the Sky 2 (2000), 13–15).

I think the zero-volume pieces are the key.

HOW IS THIS EVEN POSSIBLE

orange 04-08-2011 04:14 PM

A Layman’s Explanation of the Banach-Tarski Paradox
Posted on December 8, 2010 by Sean Li

The Banach–Tarski paradox is a theorem in set theoretic geometry which states that a solid ball in 3-dimensional space can be split into a finite number of non-overlapping pieces, which can then be put back together in a different way to yield two identical copies of the original ball.

—Wikipedia


Actually, regarding math topics, wiki often makes you more confused than you already were. But this one is not bad. (Not *too* bad.)

The Banach-Tarski Paradox as a topic was chosen by Patrick K, who attends SMU. The idea of the paradox is simply that you can double the volume of a 3-dimensional set of points without adding any new points. Why is it a paradox? Well, it defies intuition because in our everyday lives we normally never see one object magically turning into two.

It’s because it’s not possible in our physical world. The mathematical version of the paradox uses the concept of an immeasurable set. Every object in real life is measurable, because it is the set of a finite number of atoms taking up a finite amount of space. Mathematically, even when finite becomes infinite, you still usually have measurable sets. You really have to try very hard in order to create an immeasurable set.

The Banach-Tarski paradox splits the sphere into a finite number of immeasurable sets of points. The key word is finite. In fact, it can be shown that it can be split into just FIVE pieces, one of them being the point at the center. So with the other four pieces, we can separate them into two groups of two, and create an entire sphere out of each group, each the same size as the original sphere.

Though this is impossible to do in real life (because we are bounded by atoms), it is possible to make a real life analogy. This analogy will require basic knowledge of the gas laws, namely, that pressure and volume are inversely related. Here we go.

Consider an easily stretchable balloon with some volume of gas inside it. Now release the gas into some container and divide the gas in container to fill two balloons. Each new balloon will have one-half the volume of the original. But we’re going to introduce a trick. We’ll reduce the pressure of the room by half. This causes the balloons to each expand to double its size, so that each is as big as the original. We have reconstructed the paradox!

But wait, you say! Even though each new balloon has the same volume as the original, it has only one-half the density. So they’re not the same balloon as the original.

That objection is correct for the physical world. But in mathematics, we CAN get two identical spheres out of one. Here’s the catch. The mathematical sphere has infinite density. When you cut an infinite density in half, the new density is still… infinity. This explains the paradox.

Also, to have this paradox, you need this thing called the Axiom of Choice. You can check out the wiki article on it if you want; however, prepare to encounter some real math.

Sorry for the lateness of this post; I’ve had a busy day including a lot of writing. I got somewhat burnt out on writing by 5 pm, and by the time I started this post, I really did not feel like writing. To figure out some things about Banach-Tarski I did some actual research, both online and in my math textbook, which had a blurb about Lebesgue measure and a sentence about the Banach-Tarski paradox. Also, again there is NO hidden meaning or content in this post.

http://nargaque.wordpress.com/2010/1...arski-paradox/

orange 04-08-2011 04:17 PM

I'll take that rep, please. Mr. Li explains it very well.


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