Miracles

[Boxing Pythagoras]

Really? I can show you a set of ten objects, can you show me a set of infinite objects.

I sure can.

However, for the sake of argument, can you show me a set of a googol plex of objects? Can you show me a set of 256^1024 objects? Do you think these numbers are less "actual" than 2 or 10 or 6048?

No, even if you had all eternity you can never, ever, have less than infinity in front of you.

Do you have any real justification for this claim? Because, thus far, you have only baldly asserted it, or presented finite cases which are obviously not extensible to infinite ones.

[Carrikature]

Let me ask you a question. Suppose you are given two boxes with limitless capacity and one of those boxes contain an infinite amount of marbles. You are then asked to move all of the marbles from the box containing them to the empty box. When will you have moved the last marble from the box that contained the marbles in the first place to the empty box?

ETA: And if you're going to claim that me speaking about moving the last marble shows that I misunderstand infinities I'm going to smack you over the head for missing my point.

I'm on a self-enforced reduced posting phase, but I wanted to insert a comment here. You're essentially asking when an endless task would be completed. How does that make sense? Assuming the amount of time required to move each marble is static, it's pretty simple to determine how long it takes to move a finite amount of them. By the same token, moving an infinite amount of marbles requires an infinite amount of time. It's not an impossible task in the sense that you can't move an infinite amount of marbles in an infinite amount of time. Rather, it's an impossible task because you're asking for a finite time to move an infinite amount of material.

That's the essence of seer's mistake: he's asking for a finite time to complete an infinite task. It doesn't make sense on the face of it, but it doesn't actually show that an infinite task is impossible. It only shows that his constraints are nonsensical.

[JimL]

Just amuse me Jim, if we have an infinite number of universe and an infinite number of possibilities, then it would be possible, in principle to walk on water - correct?

No it wouldn't seer. I explained my position to you on that above. If other universes produced human beings and water such as does this universe, then the physics would be the same and there would be no walking on water. If the physics manifest themselves differently in other universes then there wouldn't be human beings or water so you have the same answer, there would be no human beings walking on water

No he doesn't and I also read one of his papers on this. He does literally mean out of nothing. So here we have a foremost scientist in this field suggesting creation ex nihilo. Now this doesn't sit well with you and that is fine, but I suspect that Mr. Vilenkin thought more about this than both of us.

Well, so you say, and perhaps he mistated his position, or you misinterpreted him, but my own understanding of the subject is that the quantum vacuum is not nothing.

Jim, I said nothing about infinite time. I'm speaking of moving through and infinite number of events to get to this present universe. Infinite regression.

Let me repeat:

Yes infinite regression is irrational if you think you can pass through an infinite number of past events to get to this present universe. Just look at the problem going backwards - if you go backwards and visit every universe or event that gave rise to our present universe could you ever visit them all? Even given an eternity of time? No, of course not, for no matter how many visits you made you would still have an infinite number ahead.

Infinite time is implied in your question. In order to pass through an infinite number of universes, one would need to pass through time. You can concieve of infinite space, an unending expanse, in the same sense as you think of God as being infinite, but you can't concieve of unending time. You can concieve of infinite space, but you can't concieve of an infinite space changing its form an infinite amount of times. So basically what you are arguing is that infinite time is impossible. So if you can define for me what time is, convince me that there is such a thing as timelessness, then maybe you can convince me that an infinite cosmos containing infinitely many universes is impossible. I understand its a cunundrum, but you will run into the same problem concerning an infinite Creator, particularly one who took seven days "time" to complete the job.

[seer]

I sure can.

OK, then show me an infinite set of actual objects.

Do you have any real justification for this claim? Because, thus far, you have only baldly asserted it, or presented finite cases which are obviously not extensible to infinite ones.

Of course I have proven my point, again:

1. If I move backward and reached ten past events - how many do I still have ahead?

2. If I move backward and reached a thousand past events - how many do I still have ahead?

3. If I move backward and reached a billion past events - how many do I still have ahead?


Time is irrelevant, as we can see. It doesn't matter - whether I have reached ten events or a billion events the same number of events are always before me - an infinite number of events. That never changes, nor can it.

[Boxing Pythagoras]

OK, then show me an infinite set of actual objects.

I noticed you balked on the second half of my response, here. So, before I actually go through this trouble, perhaps you could answer my counter-questions in order to determine whether this is actually even necessary.

Of course I have proven my point, again:

You don't seem to understand what "proven" means, in mathematics.

Time is irrelevant, as we can see. It doesn't matter - whether I have reached ten events or a billion events the same number of events are always before me - an infinite number of events. That never changes, nor can it.

No, you do not always have "the same number of events" before you. Subtracting a finite number from an infinite number still yields an infinite number, but not necessarily the same infinite number-- just like subtracting a finite number from a finite number does not necessarily yield the same finite number.

Furthermore, you continue to use finite cases as if they tell us anything at all about infinite cases. If there is some number, x, of past events, and I can move through those events at a rate of k, then the time, t, which it will take to completely visit those events is . This is the same regardless of whether x is a finite number or an infinite number.

[seer]

I noticed you balked on the second half of my response, here. So, before I actually go through this trouble, perhaps you could answer my counter-questions in order to determine whether this is actually even necessary.

First, Boxing I have no idea concerning your counter question. But you did say that you could show me an infinite set of real objects.

No, you do not always have "the same number of events" before you. Subtracting a finite number from an infinite number still yields an infinite number, but not necessarily the same infinite number-- just like subtracting a finite number from a finite number does not necessarily yield the same finite number.

What do you mean not the same infinite number? What do you get if you subtract from infinity except infinity? Does not the fact remain that no matter how many past events we reach we still have an infinite number ahead?

[Boxing Pythagoras]

First, Boxing I have no idea concerning your counter question. But you did say that you could show me an infinite set of real objects.

You have no idea whether a googol plex or 256^1024 are actual numbers?

What do you mean not the same infinite number? What do you get if you subtract from infinity except infinity? Does not the fact remain that no matter how many past events we reach we still have an infinite number ahead?

Infinity is not a number. You can't subtract 5 from Infinity any more than you can subtract 5 from Square. However, you can subtract 5 from a number which is infinite, just as you can subtract 5 from a number which is square.

[seer]

You have no idea whether a googol plex or 256^1024 are actual numbers?

I have no idea what a googol plex is, and I have no idea if 256^1024 corresponds to anything real.

Infinity is not a number. You can't subtract 5 from Infinity any more than you can subtract 5 from Square. However, you can subtract 5 from a number which is infinite, just as you can subtract 5 from a number which is square.

Ok, but it remains a fact, that no matter how many past events I reach I still have an infinite number ahead. Or look at it this way - I start a journey and have an infinite number of miles ahead - it wouldn't matter how long I walked for, or how many miles I covered, I would never have less than an infinite number of miles ahead. Correct?

[Boxing Pythagoras]

I have no idea what a googol plex is, and I have no idea if 256^1024 corresponds to anything real.

A googol plex is 10^(10^100). And what do you mean by "corresponds to anything real?" Do you think numbers need to be represented by actual objects in order for them to have any meaning?

Ok, but it remains a fact, that no matter how many past events I reach I still have an infinite number ahead. Or look at it this way - I start a journey and have an infinite number of miles ahead - it wouldn't matter how long I walked for, or how many miles I covered, I would never have less than an infinite number of miles ahead. Correct?

No, that is incorrect. If you start a journey and have an infinite number of miles ahead, then you covered that same infinite number of miles, you would not have any more miles ahead of you.

[seer]

A googol plex is 10^(10^100). And what do you mean by "corresponds to anything real?" Do you think numbers need to be represented by actual objects in order for them to have any meaning?

Hey, stop side tracking. I asked if you could show me a set of infinite objects. You said yes.

No, that is incorrect. If you start a journey and have an infinite number of miles ahead, then you covered that same infinite number of miles, you would not have any more miles ahead of you.

But that is the point, you never can cover an infinite number of miles. There is never, ever, a point in your journey when there still was not an infinite number of miles ahead.

[Boxing Pythagoras]

Hey, stop side tracking. I asked if you could show me a set of infinite objects. You said yes.

It's not sidetracking. The whole line of discussion is entirely irrelevant unless you believe that numbers need to be represented by actual objects in order for them to have any meaning. I promise that, even if we do agree that this line of discussion is irrelevant, I will still show you an infinite set of objects, if only for curiosity's sake. However, for the sake of the discussion, let's determine whether there's any actual purpose behind the exercise first.

But that is the point, you never can cover an infinite number of miles. There is never, ever, a point in your journey when there still was not an infinite number of miles ahead.

Your argument is circular. You can't cover an infinite number of miles because you can't cover an infinite number of miles. Allow me to illustrate the problem with your logic by paraphrasing it.

Let's say that the number of past events is a finite integer.

1. If I move backward and reached ten past events - how many do I still have ahead?

2. If I move backward and reached a thousand past events - how many do I still have ahead?

3. If I move backward and reached a billion past events - how many do I still have ahead?

No matter how many events I cover, there still remains a finite integer of events remaining. Therefore, it is impossible to traverse any finite integer of events.

If you can discover what is wrong with this logic, you'll have discovered the problem with your own logic.

[seer]

It's not sidetracking. The whole line of discussion is entirely irrelevant unless you believe that numbers need to be represented by actual objects in order for them to have any meaning.

I didn't say that, but for this discussion yes.

I promise that, even if we do agree that this line of discussion is irrelevant, I will still show you an infinite set of objects, if only for curiosity's sake. However, for the sake of the discussion, let's determine whether there's any actual purpose behind the exercise first.

Ok, I'm waiting

Your argument is circular. You can't cover an infinite number of miles because you can't cover an infinite number of miles. Allow me to illustrate the problem with your logic by paraphrasing it.

Let's say that the number of past events is a finite integer.

1. If I move backward and reached ten past events - how many do I still have ahead?

2. If I move backward and reached a thousand past events - how many do I still have ahead?

3. If I move backward and reached a billion past events - how many do I still have ahead?

No matter how many events I cover, there still remains a finite integer of events remaining. Therefore, it is impossible to traverse any finite integer of events.

If you can discover what is wrong with this logic, you'll have discovered the problem with your own logic.

No Boxing, my argument is self-evident. It is self evident that weather you covered ten miles or a billion miles and infinite number of miles lay ahead. The number of miles ahead never is less than infinite.

[Boxing Pythagoras]

I didn't say that, but for this discussion yes.

What are you saying "yes" to? I didn't ask a yes-or-no question in the lines you quoted. Are you saying that you agree the line of discussion is irrelevant, or are you saying that you believe that numbers need to be represented by actual objects in order for them to have any meaning?

No Boxing, my argument is self-evident. It is self evident that weather you covered ten miles or a billion miles and infinite number of miles lay ahead. The number of miles ahead never is less than infinite.

No, it is not self-evident. If it were self-evident, we would not be having this conversation.

[seer]

What are you saying "yes" to? I didn't ask a yes-or-no question in the lines you quoted. Are you saying that you agree the line of discussion is irrelevant, or are you saying that you believe that numbers need to be represented by actual objects in order for them to have any meaning?

No Boxing, I just want to see the set of infinite objects that you said you could produce.

No, it is not self-evident. If it were self-evident, we would not be having this conversation.

Then let's try it this way. You do agree that whether I covered ten miles or a billion miles that I would still have an infinite number of miles before me?

[Boxing Pythagoras]

No Boxing, I just want to see the set of infinite objects that you said you could produce.

So, you refuse to even clarify what you think a number is, yet you want me to demonstrate a particular number? That's rather disingenuous.

Then let's try it this way. You do agree that whether I covered ten miles or a billion miles that I would still have an infinite number of miles before me?

Yep. And, in my counter example, whether you've covered ten miles or a billion miles, you would still have a finite integer of miles before you. What's your point?