A Paradox

[RodReynolds 87]

A wealthy man approaches you, and offers you one of the following two choices. Option 1. He will give you a dollar in 0.5 seconds. He will give you a second dollar at 0.75 seconds. He will continue to give you dollar bills at the next halfway point between the time he gave the last dollar bill and 1 second. So, after 1 second, you of course will find yourself with an infinite stack of dollar bills. Can't get much better? Or can it?Option 2. Same as option 1, except that now he gives you 7 dollar bills at each interval. Now, he has written a number on each dollar bill, #1-7 on the first 7, 8-14 on the second set, etc. The one condition is that when he hands you the money, you have to burn the lowest numbered bill. So, you burn bill #1 at 0.5 seconds, burn bill #2 at 0.75 seconds, etc. Which option do you take? Option #1 you'll end up with an infinite stack, and Option #2, it would seem that you'll get 6x as many bills.But hold the phone. I suggest that in Option #2, you will have no bills. Why you ask? Well, any bill you could think of, bill #289045676 for example , well you burned it at the 289045676th interval. You burned all the bills that have numbers on them, and every bill was numbered. To make it clear, I understand that prior to the second being over, you'll always have 6x as many bills. If it's obvious to you that this will be the case after one second, well it seems obvious to me too. But "obvious" is not a counter arguement to the claim that all the bills are burned. How can some bills not be burned? That is the question.That is all. Just interesting I thought.

[Mercury69 3]

OK. How's that LSD working for ya?

[diamondhead 0]

Interesting, but I don't see why this shows that infinity does not exist?

[Petoria 0]

You're thinking about infinity as though it existed in real-life situations, but the fact is that infinity is only a mathematical tool, used usually to describe things with some sort of limit.For instance, suppose we have a funnel that is infinitely long and the radius is defined in terms of a geometric sequence such that it is half as long as it was one unit further. An interesting result is that you can fill the funnel with a finite amount of fluid, but it would take an infinite amount of liquid to paint the entirety of the surface area. Wrap your head around that one, why dont ya.

[RodReynolds 87]

You're thinking about infinity as though it existed in real-life situations, but the fact is that infinity is only a mathematical tool, used usually to describe things with some sort of limit.

Yes, I guess that was my point, only you said it better.

[Mercury69 3]

Actually, couldn't it be said the infinity is a tool with which we impose an arbitrary limit on something other than infinity, which is a measurment of that which has no beginning or end? An open ended benchmark, if you like. Just sayin'.

[dna4ever 2]

[screech 0]

So why doesn't infinity exist? How does time exist? What is the lowest time interval that one can approach to the 1 second mark without hitting it? It has to be something, or we would never reach 1 second. Or is it just that our perception of space time is too ****ed up?

[Petoria 0]

So why doesn't infinity exist? How does time exist? What is the lowest time interval that one can approach to the 1 second mark without hitting it? It has to be something, or we would never reach 1 second. Or is it just that our perception of space time is too ****ed up?

This actually is an area of study strangely enough. The hypothesis is that time should move in some type of discrete unit, and that shortest time should be measurable. Tough to think about, but you can apply some modern theoretical physics formulae to the problem. Nothing has come out of it yet, but there is some progress.This is probably one of the most interesting things i've ever read about because of it's real-world application.

[Mercury69 3]

Infinity, in reality, exists only WITHIN the confines of structure:If you reduce time (ie: 1 second) by half and so on, you will never reach zero. Within that framework, inifinity exists, but only because an arbitrary designation of beginning and end have been imposed on it. Also:Infinity, in its conceptual form, is the only true representation of something that has no beginning or end. As a matter of fact, time itself is the truest form of infinity. The fact that we have imposed an arbitrary structure on time means nothing. It is simply a gauge of where we were, where we are and where we will be, in the context of the passing moments.Therefore, there is more than one form of infinity.

[Petoria 0]

Infinity, in reality, exists only WITHIN the confines of structure:If you reduce time (ie: 1 second) by half and so on, you will never reach zero. Within that framework, inifinity exists, but only because an arbitrary designation of beginning and end have been imposed on it. Yeah, I wouldnt consider that a real-world situation though, it's arbitrary. You can design problems but they won't really mean anythingAlso:Infinity, in its conceptual form, is the only true representation of something that has no beginning or end. As a matter of fact, time itself is the truest form of infinity. The fact that we have imposed an arbitrary structure on time means nothing. It is simply a gauge of where we were, where we are and where we will be, in the context of the passing moments.I'm not sure what you mean by that, but the universe is not infinitely oldTherefore, there is more than one form of infinity.

[Mercury69 3]

I'm not disputing the fact that the universe has an age. What is disputable is that time has no boundaries. Consider:When did Time begin? When the first iota was born? Or when a sentient being first began to perceive the notion of one moment moving into the next, as measured by the passing of the sun, or the ebb and flow of the tide?The more one considers the concept of infinity, the more one is inclined to box it into a framework that makes it understandable, thereby nullifying it's infinitesimalness (sic).Anyway, I'm just playin'. This is fun.

[madtrix72 0]

A wealthy man approaches you, and offers you one of the following two choices. Option 1. He will give you a dollar in 0.5 seconds. He will give you a second dollar at 0.75 seconds. He will continue to give you dollar bills at the next halfway point between the time he gave the last dollar bill and 1 second. So, after 1 second, you of course will find yourself with an infinite stack of dollar bills. Can't get much better? Or can it?Option 2. Same as option 1, except that now he gives you 7 dollar bills at each interval. Now, he has written a number on each dollar bill, #1-7 on the first 7, 8-14 on the second set, etc. The one condition is that when he hands you the money, you have to burn the lowest numbered bill. So, you burn bill #1 at 0.5 seconds, burn bill #2 at 0.75 seconds, etc. Which option do you take? Option #1 you'll end up with an infinite stack, and Option #2, it would seem that you'll get 6x as many bills.But hold the phone. I suggest that in Option #2, you will have no bills. Why you ask? Well, any bill you could think of, bill #289045676 for example , well you burned it at the 289045676th interval. You burned all the bills that have numbers on them, and every bill was numbered. That is all. Just interesting I thought, and the main reason why infinity does not exist.

That is asinine...At said interval in option #1 you will have $289,045,676, while in option #2 you would have $1,734,274,056; 289,045,676 X the $6 you get to keep every interval. Use your head for something other than a hat rack.

[Petoria 0]

I'm not disputing the fact that the universe has an age. What is disputable is that time has no boundaries. Consider:When did Time begin? When the first iota was born? Or when a sentient being first began to perceive the notion of one moment moving into the next, as measured by the passing of the sun, or the ebb and flow of the tide?The more one considers the concept of infinity, the more one is inclined to box it into a framework that makes it understandable, thereby nullifying it's infinitesimalness (sic).Anyway, I'm just playin'. This is fun.

Yeah, I'm pretty sure you're just speaking gibberish at this point.

[RodReynolds 87]

That is asinine...At said interval in option #1 you will have $289,045,676, while in option #2 you would have $1,734,274,056; 289,045,676 X the $6 you get to keep every interval. Use your head for something other than a hat rack.

I'm not sure if you're smiley emoticon was meant to apply to the whole post, so I'm not sure if you're just screwing with me or not.In case you really don't understand the paradox, then I ask you to tell me which bills in option #2 you have left once the second is done. Please give me the numbers, even of one bill, that you have not burned.

[Petoria 0]

I'm not sure if you're smiley emoticon was meant to apply to the whole post, so I'm not sure if you're just screwing with me or not.In case you really don't understand the paradox, then I ask you to tell me which bills in option #2 you have left once the second is done. Please give me the numbers, even of one bill, that you have not burned.

Mathematically, infinity doesnt have to be a set number, some infinities are bigger than other infinities. For instance, the cardinality of the set of all even integers is infinity, but so is the set of all integers. Clearly the set of all integers is twice as large though.

[Mercury69 3]

Yeah, I'm pretty sure you're just speaking gibberish at this point.

No, not really. My thoughts on the concept of infinity have no basis in mathematical or philosophical theorems. They are simply riffs on a theme. I'm not contending they are right or wrong, just saying that anything that involves a concept that cannot be proven warrants discussion and has room for interpretation. Now, stop being a joykill and open your mind!

[Petoria 0]

No, not really. My thoughts on the concept of infinity have no basis in mathematical or philosophical theorems. They are simply riffs on a theme. I'm not contending they are right or wrong, just saying that anything that involves a concept that cannot be proven warrants discussion and has room for interpretation. Now, stop being a joykill and open your mind!

Read this again, and then tell me who the one on LSD is. It's certainly not the OP.

[Mercury69 3]

Read this again, and then tell me who the one on LSD is. It's certainly not the OP.

Maybe I am, Petoria, maybe I am...

[keith crime 8]

Steven Wright: I had a job interview and the guy said do you have any questions so I asked "If you were driving at the speed of light and you turned on your headlights would anything happen?"He said " I don't know" So I said then i don't want to work for you

[madtrix72 0]

I'm not sure if you're smiley emoticon was meant to apply to the whole post, so I'm not sure if you're just screwing with me or not.In case you really don't understand the paradox, then I ask you to tell me which bills in option #2 you have left once the second is done. Please give me the numbers, even of one bill, that you have not burned.

Whatever the last interval is +1 through the last interval X 7. I.e. Last interval is interval 1,000,000,000,000. You wil have #'s 1,000,000,000,001 through 7,000,000,000,000. You are getting $6 more than you burn every interval. 6+6+6 to the end. Do you really not understand that? At interval 2 you have #'s 3-14 @ #3 4-21, @ #4 5-28. You are gaining $6 every interval. I'm sure someone smarter than me could show an equation that illustrates this. I don't want to spend the time, besides it would make my head hurt. You will always have the interval times $6 remaining.

[RodReynolds 87]

Whatever the last interval is +1 through the last interval X 7. I.e. Last interval is interval 1,000,000,000,000. You wil have #'s 1,000,000,000,001 through 7,000,000,000,000. You are getting $6 more than you burn every interval. 6+6+6 to the end. Do you really not understand that? At interval 2 you have #'s 3-14 @ #3 4-21, @ #4 5-28. You are gaining $6 every interval. I'm sure someone smarter than me could show an equation that illustrates this. I don't want to spend the time, besides it would make my head hurt. You will always have the interval times $6 remaining.

LOL..are you still screwing with me?? This is the paradox! Your explanation of course is one side of the paradox. Prior to the second being over, you will always have 6x as much money in option #2 as in option #1. After the second is over, however, there seems to be no way around the fact that every dollar bill is burned in option #2, so you are left with nothing. How does this happen? Welcome to the paradox.Rereading your post, you seem to think that there is a last interval. There is no last interval, there are an infinite number of intervals.

[madtrix72 0]

LOL..are you still screwing with me?? This is the paradox! Your explanation of course is one side of the paradox. Prior to the second being over, you will always have 6x as much money in option #2 as in option #1. After the second is over, however, there seems to be no way around the fact that every dollar bill is burned in option #2, so you are left with nothing. How does this happen? Welcome to the paradox.Rereading your post, you seem to think that there is a last interval. There is no last interval, there are an infinite number of intervals.

Then you will never run out of money. If it never ends you will always have 6 X the interval. OK. It took me awhile but I got there. You are saying a second is finite, but the intervals are not. Therein lies the paradox. Sorry. But I still don't see how every dollar bill is burned because no matter what interval you are at you will always have 6X the interval.

[Petoria 0]

LOL..are you still screwing with me?? This is the paradox! Your explanation of course is one side of the paradox. Prior to the second being over, you will always have 6x as much money in option #2 as in option #1. After the second is over, however, there seems to be no way around the fact that every dollar bill is burned in option #2, so you are left with nothing. How does this happen? Welcome to the paradox.Rereading your post, you seem to think that there is a last interval. There is no last interval, there are an infinite number of intervals.

It's not a paradox, stop calling it one. It's just the result of math. MATH.

[Mercury69 3]

But...paradox and math are spelled differently...?