Miracles

[Adrift]

I have no idea what you mean. Real lines have beginnings and ends. Imaginary lines may not.

seer, you're referring to something in conventional speech as though its the same as something found in mathematics. You're probably imagining something like a line to see a movie theater, or a line of cable, but these are not true lines in the same way that a line is in geometry. If they were represented in math, they would be considered line segments, not lines. And as BP points out, if they're not being represented within geometry, technically, what you see in real life is not even a line segment because the real world has more than one dimension, unlike the world of...lines. Have you ever read the book Flatland?

[JimL]

By "traverse," I absolutely mean to say that it is possible to span a particular infinite sequence. I would dispute that this is a meaningless statement.

But to traverse something and to span something are two different things. And a particular infinite sequence and an unbounded infinite are also different things. An infinite whether bounded or unbounded can logically be spanned, but the latter cannot be traversed because traversed means starting from point A at a particular point in time, and ending at point B, but for an unbounded infinite no matter where within it one begins or what direction he travelled, he would never come to an ending point, either in distance or in time, because there isn't one.

And this is exactly what Seer has been objecting to. He stated that he objects to the idea that time could be past-infinite (the "infinite regression" problem) because he does not believe it is possible to traverse an actual infinite quantity.

Seer, at least originally, was talking about distance, not time, although as I pointed out to him, time is implied in the question of traversing an infinite distance. But the same logic follows for infinite time as for infinite distance, being that neither has a beginning or an ending point, neither could be traversed. You could make the argument that they could be spanned, such as would be the case if you distiguished between infinite distance and infinite time, being that they would both be infinite, the one would span the other, but for either to be incrementally traversed is logical obsurdity afaics.

[Juvenal]

Therefore, it would take 20M minutes to traverse M miles, in this example.

If M is infinite, 20M = M

[Boxing Pythagoras]

...traversed means starting from point A at a particular point in time, and ending at point B...

I disagree that "traversal" implies endpoints. Traversing a certain distance simply means moving through all of the points which comprise that distance over some period of time.

Seer, at least originally, was talking about distance, not time

No, the conversation really did take this turn when Seer was discussing the problem of infinite regression as it relates to time and events. It was back in this post that we began on this topic.

If M is infinite, 20M = M

If M is an infinite Hyperreal number, then .

[Paprika]

I disagree that "traversal" implies endpoints. Traversing a certain distance simply means moving through all of the points which comprise that distance over some period of time.

Isn't the argument regarding an infinite past, the entire duration terminating in the present?

[Boxing Pythagoras]

Isn't the argument regarding an infinite past, the entire duration terminating in the present?

Right-- that specific case would have a single endpoint. However, I don't believe endpoints are necessary for a traversal. So, for the question of past-infinite time, traversal would imply having moved through all points in time which have led up to the present.

[JimL]

I disagree that "traversal" implies endpoints. Traversing a certain distance simply means moving through all of the points which comprise that distance over some period of time.

The key word above though BP is "moving". To traverse a distance is to incrementally "move" from point a to point b, to span a distance, like a bridge spanning a river, is to cover the whole distance without moving. The former, i.e traversing an infinite requires "time, the latter, spanning an infinite, does not. Seer, I think is confusing the idea of infinite space, with infinite distances in time and questioning how could our universe come to be at this place in space at this point in time if there is an infinite time and an infinite distance which would need to have been traversed in order to arrive at the place and time of our universes beginning?

No, the conversation really did take this turn when Seer was discussing the problem of infinite regression as it relates to time and events.

It was back in this post that we began on this topic.
Well, I brought up the notion of time myself in response to seer, and he replied that he never said anything about time. But regardless, the question he poses implies time.

[JimL]

Right-- that specific case would have a single endpoint. However, I don't believe endpoints are necessary for a traversal. So, for the question of past-infinite time, traversal would imply having moved through all points in time which have led up to the present.

Infinite past is an oxymoron since it would require both a beginning and and ending point, making it finite. That may be a mathamatical infinite, i'm no mathamatician, but it is not the unbounded infinity that answers to seers question.

[Boxing Pythagoras]

The key word above though BP is "moving". To traverse a distance is to incrementally "move" from point a to point b

Again, I see nothing about moving which requires endpoints. It is entirely possible for something to move incrementally through a sequence without a starting point or an ending point.

Infinite past is an oxymoron since it would require both a beginning and and ending point, making it finite. That may be a mathamatical infinite, i'm no mathamatician, but it is not the unbounded infinity that answers to seers question.

How do you figure? When I talk about past-infinite time, I'm specifically making reference to an unbounded infinity, and discussing a model of time which does not have a beginning.

[JimL]

Again, I see nothing about moving which requires endpoints. It is entirely possible for something to move incrementally through a sequence without a starting point or an ending point.

It is true that it is entirely possible for something to move incrementally through a sequence without an ending point, I don't think anyone is disputing that fact, but you must understand that to begin to move within an unbounded infinite requires a starting point, Correct? And in order to completely traverse an unbounded infinite from a starting point, there would need be and ending point, Correct? Which, if that be the case, and that something came to an end, it could not be an unbounded infinite that was traversed. How do can something arrive at the end of an unbounded infinite, if, as you seem to be in agreement with, an unbounded infinite has no end?

How do you figure? When I talk about past-infinite time, I'm specifically making reference to an unbounded infinity, and discussing a model of time which does not have a beginning.

Okay, but you've yet to make it clear how this is done, how does a finite or temporal thing pass through either an unbounded infinite distance or unbounded infinite time. How do you get to the end of that which has no end?

[Boxing Pythagoras]

...to begin to move within an unbounded infinite requires a starting point, Correct?

To begin to move requires a starting point. However, a thing which did not begin to move, but which has rather always been in motion, requires no starting point.

And in order to completely traverse an unbounded infinite from a starting point, there would need be and ending point, Correct?

No, this is not correct. This is what I have been explicitly denying. There does not need to be an ending point in order to completely traverse something.

Okay, but you've yet to make it clear how this is done, how does a finite or temporal thing pass through either an unbounded infinite distance or unbounded infinite time. How do you get to the end of that which has no end?

You don't "get to the end of that which has no end." I have explicitly denied that traversal requires "getting to the end" of something. All that is required of a complete traversal is to have occupied all points along a particular sequence.

[JimL]

To begin to move requires a starting point. However, a thing which did not begin to move, but which has rather always been in motion, requires no starting point.

I agree, if it has always existed, and has always been moving, but Seers question is not about an infinitely existing, infinitely moving thing, he is distinguishing between the universe, our finite and temporal universe, and its emergence within an infinite distance of infinite spacetime. Your argument now is the same argument that I've been making, i.e. that our universe, being a part, and so one with the infinite whole Cosmos, needn't have travresed anything to emerge 14 billion years ago within the Cosmos, because, though it is finite and temporal with respect to itself, it is infinite and eternal with respect to its cause. As a part of the greater and infinite Cosmos, it has always existed nor did it have need to traverse an infinite distance to emerge where it did within the Cosmos.

No, this is not correct. This is what I have been explicitly denying. There does not need to be an ending point in order to completely traverse something.

There does need be an ending point, if there is a starting point, but the unbounded infinite we are discussing has no starting point.

You don't "get to the end of that which has no end." I have explicitly denied that traversal requires "getting to the end" of something. All that is required of a complete traversal is to have occupied all points along a particular sequence.

And how does something occupy all points of an unending infinite, unless it to is also an unending infinite?

[Boxing Pythagoras]

Your argument now is the same argument that I've been making, i.e. that our universe, being a part, and so one with the infinite whole Cosmos, needn't have travresed anything to emerge 14 billion years ago within the Cosmos, because, though it is finite and temporal with respect to itself, it is infinite and eternal with respect to its cause. As a part of the greater and infinite Cosmos, it has always existed nor did it have need to traverse an infinite distance to emerge where it did within the Cosmos.

We don't seem to be making the same argument, at all. You seem to be instituting some arbitrary distinction between "our universe" and "the Cosmos" which I do not recognize. If space-time has a past-finite temporal boundary, then it is entirely nonsensical to discuss its "emergence" from something which is temporally past-infinite. Time is either past-finite or past-infinite. It cannot be both.

There does need be an ending point, if there is a starting point, but the unbounded infinite we are discussing has no starting point.

I disagree that there needs to be an ending point, whether there is a starting point or not.

And how does something occupy all points of an unending infinite, unless it to is also an unending infinite?

When did I ever claim otherwise? Again, I have been discussing a complete traversal, not necessarily a finite traversal. I reject the idea that completeness requires finitude.

[JimL]

We don't seem to be making the same argument, at all. You seem to be instituting some arbitrary distinction between "our universe" and "the Cosmos" which I do not recognize. If space-time has a past-finite temporal boundary, then it is entirely nonsensical to discuss its "emergence" from something which is temporally past-infinite. Time is either past-finite or past-infinite. It cannot be both.

Nope. We are just not understanding one another apparently. I do not make a distinction between "our universe" and "the Cosmos," other than its place and time within it. The problem with seers question, I think, is that he is confusing distances in space with the passage of time. Our universe, or, if you will, its place within the Cosmos, didn't need to traverse any distances in order to be where it is, so seers question is really about infinite time, not infinite distance. Perhaps I am misunderstanding your answer to this dilemma, but it seemed to me that by using the term traverse, you were asserting that something could begin to move at one particular point in time, and then in increments of time, pass through time in its infinite totality. If that is not your argument, then sorry for the misunderstanding, but if it is, then that seems to be logically absurd to me. For instance, a particular person/baby universe, begins to exist at a particular point along the infinite time line, and so begins at that point to move through infinite time, and since that timeline, like space itself is unbounded, goes on forever in all directions, that particular person/baby universe, could never move through the totality of an unbounded infinite time because an unbounded infinite time would not be something that moves, it would have no beginning or ending , things could come to be within infinite space, and come to be within infinite time, and they could move through infinite space and pass through infinite time, but not being infinite in and of themsleves they could never span or traverse or pass through the totality of an unbounded infinite spacetime.

I disagree that there needs to be an ending point, whether there is a starting point or not.

If a distance, or a passage of time, is to be traversed in its totality, and there is a starting point, then there must needs be and ending point, else how else could it be traversed in its totality?

When did I ever claim otherwise? Again, I have been discussing a complete traversal, not necessarily a finite traversal. I reject the idea that completeness requires finitude.

Well of course an infinite can logically be said to span an infinite, they're both infinite. But I think this is an answer to a question that seer was not asking. Lets face it, its a confusing subject, difficult to think about, but I am getting a better understanding of it, I think, just discussing it.

[Boxing Pythagoras]

Perhaps I am misunderstanding your answer to this dilemma, but it seemed to me that by using the term traverse, you were asserting that something could begin to move at one particular point in time, and then in increments of time, pass through time in its infinite totality. If that is not your argument, then sorry for the misunderstanding, but if it is, then that seems to be logically absurd to me.

You seem to be restricting the ability to traverse over a dimension only to finite subsets of that dimension. I do not see why this should be the case. Once again, I do not believe that "beginning to exist" (that is, coming into a state of existence following a state in which that entity did not exist) is a necessary requirement for traversal. All that is required to traverse a particular sequence is an ordered occupation of all points comprising that sequence. That requires neither an initial point nor a terminal point.

If a distance, or a passage of time, is to be traversed in its totality, and there is a starting point, then there must needs be and ending point, else how else could it be traversed in its totality?

It could be traversed in its totality by the ordered occupation of all points comprising that sequence. Again, that does not require a terminal point.

Well of course an infinite can logically be said to span an infinite, they're both infinite. But I think this is an answer to a question that seer was not asking. Lets face it, its a confusing subject, difficult to think about, but I am getting a better understanding of it, I think, just discussing it.

I agree-- a very confusing subject! But the nature of time and the mathematics of the infinite are two subjects which I find inordinately interesting.