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Paradox

mongeese
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1/4/2010 4:21:35 PM
Posted: 6 years ago
To explain this paradox, time will mean the medium through which change occurs.

Through the Parade Analogy, it can be shown to be logically impossible for time to be infinite:
Say that you and numerous fellow men were marching due north on a completely flat plane at a steady rate of 1mph. You have no clue how long you've been marching, or where you came from. For all you know, you've been marching forever. One day, you and your fellows come across a jet, and you decide to take this jet due south at an amazing speed of 1000mph. The question is, will you come to the starting point of the parade?
The answer must be yes, because the answer cannot be no. If you, with your 1000mph jet plane, never reach any kind of starting location at all, even travelling just short of forever, then how could you and your friends have possibly marched in the opposite direction at a slower speed?

However, if, at any one point, there is no change occuring, how can change suddenly start to occur without another change to trigger that change? There would have to be an infinite series of change.

And with that, I have a paradox on my hands. Change must be infinite, yet change cannot be infinite.

Any explanations?
mongeese
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1/4/2010 6:01:52 PM
Posted: 6 years ago
I'm not assuming time to be circular. However, the paradox can apply for a timeline just as well as a distance. It must always take a finite number of years to go from Time A to Time B.
Xer
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1/4/2010 7:30:30 PM
Posted: 6 years ago
At 1/4/2010 6:01:52 PM, mongeese wrote:
I'm not assuming time to be circular. However, the paradox can apply for a timeline just as well as a distance. It must always take a finite number of years to go from Time A to Time B.

Except time doesn't go from point to point. Time doesn't have points. Time is abstract.
Kleptin
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1/4/2010 10:24:48 PM
Posted: 6 years ago
The problem with analogies is that the simpler the analogy, the easier it is to get caught up in its simplicity and make ignorant conclusions on complicated topics.

Let's put a Parade center at the start. After the parade marches for 100 miles, the center still exists. After the parade marches for 500 miles, the center still exists. After the parade enters the jet plane, the center still exists, so the center will eventually be found.

After one moment in time, the moment prior ceases to exist. Plain and simple. It is as if though in an empty and vast flat plane, marchers are spawned under the assumption that they have already marched for some unknown time. In this case, yes, the jet plane will never find the original point.
: At 5/2/2010 2:43:54 PM, innomen wrote:
It isn't about finding a theory, philosophy or doctrine and thinking it's the answer, but a practical application of one's experiences that is the answer.

: At 10/28/2010 2:40:07 PM, jharry wrote: I have already been given the greatest Gift that anyone could ever hope for [Life], I would consider myself selfish if I expected anything more.
Ragnar_Rahl
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1/4/2010 10:35:37 PM
Posted: 6 years ago
You seem to think infinity is a specific quantity.
It came to be at its height. It was commanded to command. It was a capital before its first stone was laid. It was a monument to the spirit of man.
mongeese
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1/5/2010 4:45:33 AM
Posted: 6 years ago
@Kleptin: The point is to show that any two points on a time ray must be a finite distance from each other. Time travel isn't necessary to bring this point accross.

@RR: How so?
Kahvan
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1/5/2010 6:43:28 AM
Posted: 6 years ago
I just started a debate that one could travel a finite distance for an infinite amount of time. If you look at the debate it will be easier to understand what I mean.
mattrodstrom
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1/5/2010 6:54:10 AM
Posted: 6 years ago
At 1/4/2010 6:01:52 PM, mongeese wrote:
It must always take a finite number of years to go from Time A to Time B.

I think that the theory of relativity disagrees.

You can go forward in time on Earth by going away fast and coming back.

For example,
Earth time at departure: 2009
Earth time at return: 3009
Time of Travel: 25 years
"He who does not know how to put his will into things at least puts a meaning into them: that is, he believes there is a will in them already."

Metaphysics:
"The science.. which deals with the fundamental errors of mankind - but as if they were the fundamental truths."
joedoe
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1/5/2010 4:40:55 PM
Posted: 6 years ago
Time does not exist as a separate entity, but is only a part of spacetime. Although it isn't "abstract" plain and simple it does not go from point a to point b but from event a to evnt b.
mongeese
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1/5/2010 7:26:20 PM
Posted: 6 years ago
At 1/5/2010 6:54:10 AM, mattrodstrom wrote:
At 1/4/2010 6:01:52 PM, mongeese wrote:
It must always take a finite number of years to go from Time A to Time B.


I think that the theory of relativity disagrees.

You can go forward in time on Earth by going away fast and coming back.

For example,
Earth time at departure: 2009
Earth time at return: 3009
Time of Travel: 25 years

25 is a finite number of years.
Kleptin
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1/5/2010 10:58:46 PM
Posted: 6 years ago
At 1/5/2010 4:45:33 AM, mongeese wrote:
@Kleptin: The point is to show that any two points on a time ray must be a finite distance from each other. Time travel isn't necessary to bring this point accross.

I am aware of what your point is. Points are illustrated by analogies and validated by evidence and logic. Time travel isn't necessary to bring the point across, but it is necessary for your argument to be valid in accordance with your analogy. You seem to think that your analogy contains common sense and logic that is applicable to the actual topic of discussion. I am pointing out key and crucial differences between the analogy and the actual topic of discussion to show that it is inadequate.

What I did was make your analogy closer to the actual topic. Theoretically, if your analogy is a good one, as the analogy gets closer to the true issue, the truth value should not change. However, upon altering your story to better reflect the actual issue at hand, your entire analogy falls apart.

What people need to understand is that when you use an analogy as an argument, there are conditions that need to be met. The analogy must portray a concept that can be 100% linked with the actual topic. The minor details can deviate, but the concept must remain the same. The problem with your analogy is that the deviations make all the difference. The connection between your analogy and the concept you wish to portray loses all truth and meaning.
: At 5/2/2010 2:43:54 PM, innomen wrote:
It isn't about finding a theory, philosophy or doctrine and thinking it's the answer, but a practical application of one's experiences that is the answer.

: At 10/28/2010 2:40:07 PM, jharry wrote: I have already been given the greatest Gift that anyone could ever hope for [Life], I would consider myself selfish if I expected anything more.
Danielle
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1/5/2010 11:02:43 PM
Posted: 6 years ago
At 1/5/2010 7:26:03 PM, mongeese wrote:
Event A, Point A, same difference. They're synonymous in the analogy.

But it will take me a different amount of time to go from Point A to Point B than it takes for you to travel between those same 2 points, even if we're traveling at the same speed (matt is right - the theory of relativity applies).
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Floid
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1/6/2010 1:34:23 PM
Posted: 6 years ago
Well, its probably already been hashed out, but I will give my basic interpretation:

I will use classical physics and ignoring relativity since your problem is one of mathematics and not really physical concepts.

Say that you and numerous fellow men were marching due north on a completely flat plane at a steady rate of 1mph. You have no clue how long you've been marching, or where you came from. For all you know, you've been marching forever.

Well I like worst cases so lets use that. You have been marching forever (an infinite amount of time if you will).

Distance traveled = velocity * time = 1mph * infinity = infinite distance

So you have traversed a infinite distance (already we can sense a disconnect between the example and reality). The key here is that you have travelled an infinite distance relative to where you are measuring from (i.e. where you are standing right now).

This is where your problem comes from: To mathematically describe what I have just said we have:

x(t) = equation that gives your current position = v * t

Where v is your velocity and t is the time. To define a few key points:

x(0) = 0 <-- at time 0 you are at location 0... the point from which we are starting

x(-infinity) = v * -infinity = -infinite <-- at an infinite time in the past, you were an infinite distance from where you are now

The above is just a basic linear equation

One day, you and your fellows come across a jet, and you decide to take this jet due south at an amazing speed of 1000mph. The question is, will you come to the starting point of the parade? The answer must be yes, because the answer cannot be no.

The answer is no: why? The equation x(t) = v*t has the solution -infinity for t = -infinity for any positive value of v. So you will never reach a starting point, irregardless of your velocity.

The problem you have is that you don't really understand the situation your analogy creates. Your starting point is where you start in your analogy (marching in one direction at 1mph). You then claim that you have already spanned an infinite distance. You then try to solve for where the starting point some infinite distance back is at. But this point doesn't exist, because no matter how far back you place that point, I can give you a point further away through which you must have travelled.
DevinKing
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1/6/2010 1:45:11 PM
Posted: 6 years ago
At 1/4/2010 4:21:35 PM, mongeese wrote:
To explain this paradox, time will mean the medium through which change occurs.

Through the Parade Analogy, it can be shown to be logically impossible for time to be infinite:
Say that you and numerous fellow men were marching due north on a completely flat plane at a steady rate of 1mph. You have no clue how long you've been marching, or where you came from. For all you know, you've been marching forever. One day, you and your fellows come across a jet, and you decide to take this jet due south at an amazing speed of 1000mph. The question is, will you come to the starting point of the parade?
The answer must be yes, because the answer cannot be no. If you, with your 1000mph jet plane, never reach any kind of starting location at all, even travelling just short of forever, then how could you and your friends have possibly marched in the opposite direction at a slower speed?

However, if, at any one point, there is no change occuring, how can change suddenly start to occur without another change to trigger that change? There would have to be an infinite series of change.

And with that, I have a paradox on my hands. Change must be infinite, yet change cannot be infinite.

Any explanations?

--Of course you will not come to the starting point of the parade. THERE WAS NO STARTING POINT OF THE PARADE FOR YOU TO GO TO. In order for the parade to be infinite, there must never have been a starting point. This is not a paradox.
After demonstrating his existence with complete certainty with the proposition "I think, therefore I am", Descartes walks into a bar, sitting next to a gorgeous priest. The priest asks Descartes, "Would you like a drink?" Descartes responds, "I think not," and then proceeds to vanish in a puff of illogic.
mongeese
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1/6/2010 7:07:35 PM
Posted: 6 years ago
At 1/5/2010 11:02:43 PM, theLwerd wrote:
At 1/5/2010 7:26:03 PM, mongeese wrote:
Event A, Point A, same difference. They're synonymous in the analogy.

But it will take me a different amount of time to go from Point A to Point B than it takes for you to travel between those same 2 points, even if we're traveling at the same speed (matt is right - the theory of relativity applies).

The distance, however, is still finite, which is all that the analogy requires.
mongeese
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1/6/2010 7:09:56 PM
Posted: 6 years ago
At 1/6/2010 1:34:23 PM, Floid wrote:
Well, its probably already been hashed out, but I will give my basic interpretation:

I will use classical physics and ignoring relativity since your problem is one of mathematics and not really physical concepts.

Say that you and numerous fellow men were marching due north on a completely flat plane at a steady rate of 1mph. You have no clue how long you've been marching, or where you came from. For all you know, you've been marching forever.

Well I like worst cases so lets use that. You have been marching forever (an infinite amount of time if you will).

Okay, the "for all you know" part was not meant to be taken literally, as it is impossible to have been marching forever. The fact that you could not have been marching forever is established by the fact that you actually got to where you are from a starting point, and there is no reason for this distance to be traversible in one direction, but not the other.
mongeese
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1/6/2010 7:13:08 PM
Posted: 6 years ago
At 1/6/2010 1:45:11 PM, DevinKing wrote:
At 1/4/2010 4:21:35 PM, mongeese wrote:
To explain this paradox, time will mean the medium through which change occurs.

Through the Parade Analogy, it can be shown to be logically impossible for time to be infinite:
Say that you and numerous fellow men were marching due north on a completely flat plane at a steady rate of 1mph. You have no clue how long you've been marching, or where you came from. For all you know, you've been marching forever. One day, you and your fellows come across a jet, and you decide to take this jet due south at an amazing speed of 1000mph. The question is, will you come to the starting point of the parade?
The answer must be yes, because the answer cannot be no. If you, with your 1000mph jet plane, never reach any kind of starting location at all, even travelling just short of forever, then how could you and your friends have possibly marched in the opposite direction at a slower speed?

However, if, at any one point, there is no change occuring, how can change suddenly start to occur without another change to trigger that change? There would have to be an infinite series of change.

And with that, I have a paradox on my hands. Change must be infinite, yet change cannot be infinite.

Any explanations?

--Of course you will not come to the starting point of the parade. THERE WAS NO STARTING POINT OF THE PARADE FOR YOU TO GO TO. In order for the parade to be infinite, there must never have been a starting point. This is not a paradox.

Alright, then, eliminate the starting point. Let's say that every ten miles, you drop a red chip on the ground. When you go back, you should be able to eventually find every red chip that you dropped, because you are going even faster than you were before in the opposite direction. However, if there's never a point at which there are no more red chips, then there's no starting point. The problem here is that you HAVE to be able to relocate every red chip. Hence, there must be a starting point.
LeafRod
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1/6/2010 7:15:15 PM
Posted: 6 years ago
I don't even understand this. You travel one way and then come back. If you're walking forever or "to infinity" when you travel the first way, though, then you'll never come back by definition.
mongeese
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1/6/2010 8:03:44 PM
Posted: 6 years ago
At 1/6/2010 7:15:15 PM, LeafRod wrote:
I don't even understand this. You travel one way and then come back. If you're walking forever or "to infinity" when you travel the first way, though, then you'll never come back by definition.

The entire point is to show that you can't have been walking forever or "to infinity," because you would never come back.
omelet
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1/6/2010 8:17:27 PM
Posted: 6 years ago
At 1/4/2010 4:21:35 PM, mongeese wrote:
To explain this paradox, time will mean the medium through which change occurs.

Through the Parade Analogy, it can be shown to be logically impossible for time to be infinite:
I don't think you know how hard it is to prove things with analogies.

Say that you and numerous fellow men were marching due north on a completely flat plane at a steady rate of 1mph. You have no clue how long you've been marching, or where you came from. For all you know, you've been marching forever.
Okay, we'll even be extremely generous and say that I have been marching for an infinite amount of time, which necessarily implies that the flat plane I have been marching on is of infinite length.

One day, you and your fellows come across a jet, and you decide to take this jet due south at an amazing speed of 1000mph. The question is, will you come to the starting point of the parade?
If I've been marching for an infinite amount of time, there isn't a starting point, so that's not even a valid question.

The answer must be yes, because the answer cannot be no.
The answer is necessarily no if I have been marching an infinite amount of time.

If you, with your 1000mph jet plane, never reach any kind of starting location at all, even travelling just short of forever
There is no such thing as "just short of forever." One million years is just as far from infinite as five seconds is.
Further, there is no starting location, since there would by definition not have been a time when you started marching if you'd been marching for an infinite amount of time.

However, if, at any one point, there is no change occuring, how can change suddenly start to occur without another change to trigger that change? There would have to be an infinite series of change.

And with that, I have a paradox on my hands. Change must be infinite, yet change cannot be infinite.

Any explanations?
Even though your paradox is a false one for the reasons I listed above, there is another solution to your paradox that does not require time to be infinite in length. It could simply be a limit, which is quite possible based on evidence so far.

Allow me to explain slightly better. Let us say the age of the universe in its totality is 15 billion years, but let us say that there was no first moment. This is just like the function ln(x), stopping at x=15. It has no value at zero, but it has a value at any value above zero. For any point you pick, there are an infinite number of points before it. However, it does not extend infinitely in the negative direction (on the X axis). There are no events that do not have preceding events, but there is no first event and it has finite length.
mongeese
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1/6/2010 8:24:37 PM
Posted: 6 years ago
At 1/6/2010 8:17:27 PM, omelet wrote:
At 1/4/2010 4:21:35 PM, mongeese wrote:
To explain this paradox, time will mean the medium through which change occurs.

Through the Parade Analogy, it can be shown to be logically impossible for time to be infinite:
I don't think you know how hard it is to prove things with analogies.

Say that you and numerous fellow men were marching due north on a completely flat plane at a steady rate of 1mph. You have no clue how long you've been marching, or where you came from. For all you know, you've been marching forever.
Okay, we'll even be extremely generous and say that I have been marching for an infinite amount of time, which necessarily implies that the flat plane I have been marching on is of infinite length.

Okay, I really should not have said the "for all you know" part. You don't know how long you have been marching. The rest of the analogy explains why you can figure out that it can't have been forever.

Allow me to explain slightly better. Let us say the age of the universe in its totality is 15 billion years, but let us say that there was no first moment. This is just like the function ln(x), stopping at x=15. It has no value at zero, but it has a value at any value above zero. For any point you pick, there are an infinite number of points before it. However, it does not extend infinitely in the negative direction (on the X axis). There are no events that do not have preceding events, but there is no first event and it has finite length.

The first event would naturally be the minimum of the domain of the function. In this case, it would be just above 0.
mongeese
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1/6/2010 8:25:19 PM
Posted: 6 years ago
At 1/6/2010 8:14:10 PM, LeafRod wrote:
Where's the paradox?

There cannot be an infinite series of events, but by the second method of reasoning in my first post, there must be an infinite series of events.
Ragnar_Rahl
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1/6/2010 8:35:00 PM
Posted: 6 years ago
At 1/5/2010 4:45:33 AM, mongeese wrote:
@RR: How so?

Because it attempts quantitative reasoning-- if something comes one way, then if it goes the other way the "Same distance,", it reaches the starting point-- ignoring the fact that there is no same distance.

Humans aren't immortal btw. They didn't walk from infinity. They were born. The matter has simply always been a walking, so to speak, the "walking" is not a distinct period.
It came to be at its height. It was commanded to command. It was a capital before its first stone was laid. It was a monument to the spirit of man.
Kleptin
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1/6/2010 9:06:12 PM
Posted: 6 years ago
At 1/6/2010 7:13:08 PM, mongeese wrote:
Alright, then, eliminate the starting point. Let's say that every ten miles, you drop a red chip on the ground. When you go back, you should be able to eventually find every red chip that you dropped, because you are going even faster than you were before in the opposite direction. However, if there's never a point at which there are no more red chips, then there's no starting point. The problem here is that you HAVE to be able to relocate every red chip. Hence, there must be a starting point.

What do the red chips represent? You can't just decide to arbitrarily introduce something into an analogy just to counter someone's criticism.
: At 5/2/2010 2:43:54 PM, innomen wrote:
It isn't about finding a theory, philosophy or doctrine and thinking it's the answer, but a practical application of one's experiences that is the answer.

: At 10/28/2010 2:40:07 PM, jharry wrote: I have already been given the greatest Gift that anyone could ever hope for [Life], I would consider myself selfish if I expected anything more.
Floid
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1/7/2010 4:47:02 AM
Posted: 6 years ago
Alright, then, eliminate the starting point. Let's say that every ten miles, you drop a red chip on the ground. When you go back, you should be able to eventually find every red chip that you dropped, because you are going even faster than you were before in the opposite direction. However, if there's never a point at which there are no more red chips, then there's no starting point. The problem here is that you HAVE to be able to relocate every red chip. Hence, there must be a starting point.

Well, lets say you marched 1000 miles to the north. This trip took you 1000 hours (at 1mph) and you dropped 100 chips. You then turn around and head back south at 1000mph, you arrive at your starting point in 1 hour for a net total of 1001 hours for the trip. In the process you passed every chip you dropped.

This same basic formula can be used to solve the situation you propose for any real, positive distance. The only break down is when you use "infinite distance" because you can never traverse and infinite distance.

I don't see the problem at all...
Floid
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1/7/2010 4:52:31 AM
Posted: 6 years ago
In rereading your latest twist I think I see the problem. You still have the problem of introducing infinite distance in your analogy.

So you start at some random point and travel backwards counting the chips in an effort to determine your starting point. If it is the case that you never reach the end of those chips, then you never had a starting point and you are merely going towards a negative infinity. But you did have a starting point for your journey... the point at which you started working backwards, so there is no paradox. The problem is the terminology in your analogy.