How can you define an infinite past without the idea of an infinite succession of previous moments? (infinite past = infinite past moments). There was a REAL PAST, in other words a real amount of past events
Please, take a look at this picture: http://image.tutorvista.com/content/feed/tvcs/rays203.PNG. Imagine that y is the present moment, and x is an infinite amount of past behind us. The line IS the real events which have happened, and the walker stands for what moment you are in in the past. So, can you imagine it possible, that the walker walks from the arrow to ‘y’ which is OUR now? That an impossible succession of ‘nows,’ to get to THIS now.
An infinite length of ‘nows’ must have happened before THIS ‘now’ in order to get to this ‘now.’ That means that the walker CAN walk through an infinite length of line before he gets to a point.
I admit it is possible, but I don’t see how what I am saying it is wrong by the same token.
And the distance to any moment in that real past, the time that has elapsed since then, is finite. It’s just like the infinite number line: there’s infinitely many numbers to the left, but the distance to any of those numbers is finite.
The idea that he ‘walks from the arrow’ is where you get it wrong. The arrow suggests that the line somewhere has a beginning, but it doesn’t—it’s infinite. From any point where the walker could actually start walking, it’s a finite, though arbitrarily large, distance to y.
The statements ‘the walker walks from the arrow’ and ‘there is an infinite amount of past behind us’ are in contradiction. Either there is an infinite amount of past behind us—then, the walker can’t start from the arrow, since that would be ‘longer than infinitely long ago’. Or, the walker starts somewhere—then, there would be a point such that there is no other point before it, and hence, a beginning, thus not an infinite amount of past behind us.
[QUOTE=Half Man Half Wit]
… The arrow suggests that the line somewhere has a beginning, but it doesn’t—it’s infinite.
[/QUOTE]
I think we may not be talking about the same thing here, but the arrow suggests it infinitely goes in that direction, not that it has a beginning.
I agree. There must be a beginning event for the walker to reach the point Y. If he arbitrarily started at one point, it leaves out the rest of the line behind him. In other words, those moments behind him didn’t ACTUALLY happen leading up to where he started, thus (perhaps with different logic) you are saying exactly what I am: events/time had a beginning.
This is exactly what I am saying. I am saying that there is not an infinite amount of moments behind us, because the walker had to start from somewhere.
When I say “imagine that the picture represents the past” I am not saying that it actually represents the past. I am using the picture to illustrate how it ultimately cannot represent the past… I was thinking that your argument was that the picture CAN represent the past… are we both debating for the argument here?
No. Just that everything that happened, did so a finite time ago—which is true even in the case of an infinite past. Think about the spatial analogy: in an infinite universe, there are nevertheless no two things infinitely far away from each other.
You’re saying that there can’t be an infinite past, because this implies that an infinite amount of time must have passed for us to get to now. But this is wrong, just as saying that in an infinite universe, there are (necessarily) two things infinitely far apart from each other (or do you believe that to be true?).
Think about any starting point for the walker, say at -n. Is that the earliest, in an infinite universe? No, he always could have started at -n-1. But nevertheless, with -n being finite, so is -n-1. So in an infinite universe, there’s no infinite distance to cover for the walker; thus, your argument fails. It depends on the existence of a beginning, and thus, can’t prove that there is one.
Without a beginning, at any point, there can be a walker who’s walked there from any arbitrarily far away point; there’s no problem at all with that picture. It’s just your intuition that’s used to considering finite matters that misleads you, as is often the case with infinite quantities.
It’s a bit like Hilbert’s hotel, which has infinitely many rooms, all of which are occupied. When a new guest arrives, all the inhabitants just move one room further up. In fact, even if infinitely many new guests check in simultaneously, you can make enough room, by having the one in room 1 move to room 2, the one in room 2 to room 4, the one in room 4 to room 8, thus opening up infinitely many rooms. In fact, you can even make enough room if infinitely many buses with infinitely many guests each arrive!
So consider now the infinite line completely studded with walkers. At some time, they all start walking. Position y is our ‘now’. At all times after the starting time, some walker will be arriving at y—if the walker from -n arrives at time t, the walker from -n-1 arrives at t+1, and so on. From every point on the line, if you wait long enough, a walker will arrive at y. So there is no point on the line such that the walker would never arrive at y. Turned the other way around, y can be reached from any point on the line.
Thus, any argument that the present moment can’t ever be reached in a universe with an infinite past is mistaken: from any point in the past, the present moment can, in fact, be reached.
It’s only adding a point ‘beyond’ all the points on the line that the problem of ‘infinitely many moments must have elapsed’ arises. But then, since you use that problem to argue for a beginning, you’ve assumed a beginning in order to prove one.
This is a contradiction. ‘Everything’ includes an infinity to pass through.
By infinite universe, do you mean the spacial analogy? I don’t think this is the same as saying there is an infinite amount of time. For one, if you use the paradox for space, it looks like we don’t even have an infinite universe. I can’t say therefore that our universe is spacially or temporally infinite. Even if there were infinite space (which would be an infinity of NOTHING so it likely wouldn’t count), it is not the same as saying that the walker started from an infinitely far away
What I say is if he started at -n, there IS no -n-1. Nothing before -n actually happened, so it doesn’t count when measuring WHAT ACTUALLY TOOK PLACE in the past.
Well, I’m open to hear how my intuition is wrong on the matter. The problem is that IN REAL LIFE (at least in the 4D), it looks to me that the term: infinite quantity, is a self contradiction. Possibly it works on paper, but the problem is that I don’t see how you could point out to me any infinite quantity anywhere around us.
That is the problem: infinity isn’t an actual number to where an infinite amount could arrive at once. If it is, can you describe how many zeros infinity has in it without using the word “infinite?”
Once again, the same issue. If there were walkers at every space on an infinite line, that means you have “infinite” walkers. That would be why your example doesn’t work, if I understand it correctly.
From any point the present can be reached, true. But the beginning is a point. The line cuts off at the beginning and you don’t have a ray, you have a line segment. Anything behind the beginning point didn’t really happen so it doesn’t exist, so it’s not on the line. To say that there is an infinite length behind any point is to say that: we progressed through an infinite amount to get to this moment, which is a false statement in the 4D. For an infinity is only conceptual, to say that we have an infinite amount means that we have “numbered” that which is beyond numbering.
It is a point beyond all points because infinity is beyond all numbers. Beyond all numbers that we have the capability of reaching anyway, from what I can see.
How can it be possible to have an infinite amount of a finite substance? That is one of my key points.
To me, to say “we have an infinite amount of (lets say) people.” The problem with this is there is now a fixed amount of people, to which you can denote a numerical value (1, 25, 900, 10,000,000, etc.). If infinity is supposed to be beyond all numbers, then how can you have a fixed amount? This fixed amount can have another person added to it, and another… you end up with infinity+X. If infinity is beyond any amount, then how can you end up with a fixed number which you can add to?
The idea is that if he BEGAN at -n, that is where events started. The line (time-line) is only representing real events. Thus if he started at point -n, there is no points before that because that is the beginning of actual events (within that time-space construct)
But if you look at the line of integers, there is no such point, and nevertheless, the line is infinite. The past may be infinite in exactly the same way, and not contain a point beyond all points. And in such a case, there’s no infinity of past moments to pass through to get to now.
Really, by now your argument seems to boil down to ‘but I can’t imagine an infinite amount of stuff, hence, it can’t exist’. But that obviously cuts no ice. If spacetime is continuous, for example, then there’s an infinite amount of moments between any given two moments, and an infinite amount of intervals in any finite spatial interval. According to quantum field theory, there’s an infinite amount of degrees of freedom associated with every point in spacetime. If space is infinite, there may well be an infinite number of stars (there’s no reason for it all to be ‘nothing’ after some point). So there’s no problem with infinitely many walkers on an infinite line. And so on.
we break down time to “days,hours, minutes, seconds” - even if there is an “infinite” amount of time between 1 second to the next - we can still count that as ‘1 second’ - and therefore have accounted for the “infinite” between it.
But no one really talks about infinitey the way Gateway is describing it - all points between a and b is finite - even if you could ‘slice up’ that finite an infinite number of ways.
Well, no, and this is important. Space is not nothing. Space is most definitely something even if there is no mass or energy within that region of something. Space is a sort of material, even though intuitively we think of it as the absence of “things” because we associate “things” with matter and energy, and we think of the absence of things as nothing. It’s wrong, however, and when you get down to really advanced stuff, there is always either negative or positive energy due to vacuum fluctuations in any substantial volume of space. The net of course, appears to be positive.
Our brains are really bad at intuiting infinite things. To be fair, we come from an environment where infinity is not a value critical to our survival, so it’s no surprise that we’re not particularly well equipped to simply figure it out without some sort of external framework (like the rules we’ve built up for mathematics).
1/0 zeros?
The begining of a line is not a point. It is a direction. You most definitely have a ray going from now in the direction of begining.
“Begining” and “before begining” does not exist within space-time. It is, by definition, outside of it.
Also, why does the arrow of time matter when you’re talking about the formation of time? “Progress” is merely an illusion of the arrow of time, depending on the model of space-time you’re dealing with. There are plenty of perfectly valid models which posit that all inifnity of time already exists, and we experience time “progressing” merely as a byproduct of our minds/forms.
Look up “countable infinity.” It’s an interesting topic, but long story short, just because a set is infinitely large does not mean that it can’t be counted.
Well, infinity is beyond all real numbers on the same number line, but not all numbers. Remember the different infinities? And you can reach infinity with finite steps, just not a finite number of finite steps.
Is your definition of “linear time” one where the begining must be a point, which means it was never a line to begin with? Because there is your paradox. If you treat the begining and end as a point, then by definition you don’t have a line and what you’re dealing with is a segment. In other words, if by linear time you mean “a linear sequence of events between some point in the past and now?” then, as others have explained, it would have to be finite. But you’ve defined this “begining” into existance again.
From what we can observe, time seems to radiate outwards from a central point a finite number of years ago, rather like how integers radiate outwards from 0. It’s still a linear sequence, just like the integers, but there is no reason to assume that the “first” member of the infinite sequence is a point, just like there’s no reason to assume that the “first” integer - aka negative infinity - is a point.
What exists in the space-time that has radiated in the negative direction from this point of radiation we know nothing about. Physics appears to break down. I don’t believe that the propagation of time is limited by c (and I’d appreciate if someone can tell me if the propagation of space is limited by c), and in fact its propagation rate might be infinitely fast.
If that’s true, what you have is infinite time that functions as a linear sequence of events with no apparent paradox.
In antiquity, time was regarded as cyclical rather than a linear flow of events. It was Judaism that developed a linear perspective on time.
Time does not make a unique framework within which phenomena occur at the same pace or temporal relations can be established throughout the existence.
Regardless of the intellectual gimmicks that one may come up with to argue for the necessity of a point of origin of everything that exists, people will still wonder what may have happened before.
At the moment, I feel more uncomfortable about the arbitrary nature of a starting point than infinite regress.
Gateway, I don’t think you know much more about mathematics than you do about philosophy. You really need to do more reading on how infinity is treated in modern mathematics. Here are some fairly introductory books on infinity:
To Infinity and Beyond by Eli Maor Infinity and the Mind by Rudy Rucker One, Two, Three . . . Infinity by George Gamow The Art of the Infinite by Robert Kaplan and Ellen Kaplan
Perhaps other posters to this thread can suggest other books too. There are some online things you can read also. Your knowledge of what can be said about infinity is too limited, Gateway, and you really need to learn more before you start threads like this.
I think we have an impasse. An infinite line denoting moments is an infinite amount of past moments.
Really, by now your argument seems to boil down to ‘but I can’t imagine an infinite amount of stuff, hence, it can’t exist’. But that obviously cuts no ice.
I would have to agree, but my argument isn’t resting on not having enough imagination. To me, it is a contradiction in terms to have a fixed number which is infinite. I think you agree as well that it is a contradiction, but the our difference is I apply that to the past and you do not.
-The past = a fixed amount of moments because they actually happened. There is no adjusting them at this point. Fixed amount of past = fixed amount of time = fixed amount of moments.
-To say there is an infinite past IS an infinite amount of moments, for the past is made up of moments. (This is not being able to slice up any given distance over and over and saying you can go on to infinity, but the set distance you began with already is infinity).
-If you have an infinite amount of time
When I say moment, what I mean is a fixed amount of time, such as a second, minute, or year. One second of time can only fit one second.
Have you ever SEEN infinity?
Let me ask you, if there is an infinite amount of walkers on the line, are they all observable at one time? No. Why not, considering that a walker should be a phenomenon that is observable?
Do you see how this fits with what I have been saying?
No, an infinite amount is exactly the opposite of a fixed amount. Where do you get that now the amount would be fixed?
Any amount of people is fixed. Refer to my last post for the point of observation.
How?
In my example, I am referring to this walker at the beginning. A beginning has nothing behind it, which is why it is defined as a beginning
Did you read up on countable infinities? Also, you’re dismissing transfinite numbers.
Is the area of a circle infinite? The area is the sum of infinitely many points (or lines, or whatever shape you feel like using).
Unless you subscribe to the big bang theory, which does not preclude time from expanding in the negative direction as well and nor would this expansion violate the linearity of the sequence of events.
Most people, at least that I’m aware of, define a moment as the limit of an interval of time [o,x) as x approaches to zero. In laymans terms, an “instant.” A “snapshot.” I have never heard any other definition used. I may well be wrong, but I believe the other poster was using this definition, and you should both clarify your definitions before assuming the other means what you mean. Does anyone here also see a moment as an interval longer than 0?
Which definition are you using for observable? Assuming walker n can observe n-1 and n+1, then yes, they are all observable at one time, because each walker can simultaneously observe every neighboring walker.
Do you mean to ask if there are an infinite number of walkers can one walker see them all at once? Well, probably not, because 1) he probably can’t see through the guy in front and behind him, 2) the intensity of light falls off with the square of the distance, meaning the n-HUGE_NUMBER and n+HUGE_NUMBER walker’s light would appear indistinguishable from noise, and 3) since walker -HUGE_NUMBER and walker +HUGE_NUMBER are presumably very far apart, they may be outside of each other’s light cones.
Yes, I’m using distance analogies instead of time based ones, but really, when you deal with space-time the two things are the same.
But, you should really read the article on hilbert’s hotel. It’s fascinating stuff! Just wiki it.
Cyclical, so in essence: time is a circle? To you find this to be true, and if so do you have evidence supporting this?
Not sure what is being said here.
[QUOTE=Zero-syde]
Space is not nothing.
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I understand space is considered to be a ‘something’ in modern science. it seems to be subjected to my paradox if this is the case. If it were not the case and it WERE a nothing, you also have the paradoxical statement of there being “an infinite amount of nothings.”
That is the problem: infinity isn’t an actual number to where an infinite amount could arrive at once. If it is, can you describe how many zeros infinity has in it without using the word “infinite?”
Okay, yes, but that is another way of saying “infinite zeros.” Perhaps another way to phrase the question: you go from hundreds, to thousands, to millions, to trillions. What comes RIGHT BEFORE infinity? Nothing, right?
[QUOTE=Zero-syde]
The begining of a line is not a point. It is a direction. You most definitely have a ray going from now in the direction of begining.
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What I meant by beginning was the beginning of time, not the beginning of a line. What I meant that if you think you have a ray, but you have two end points (“But the beginning is a point”) then you end with a segment.
I can’t say I understand. Do you mean everything already exists, and we only seem to progress? What is the evidence for that? We would have to show that this moment is linked to the future (or past) directly, and the “future” would already be here. What is your source or evidence for this, and why do we see a flow of events then?
I checked it out the other day. I didn’t research it extensively but so far I don’t see it contradicting what I am saying.
I remember hearing about it, but I didn’t remember what the explanation to different infinities was.
That is the point. The past is a number of finite steps. (If not moments, you can go with seconds, months, years, etc.)
No, linear time is just a succession of moments. Leaving the past, always going into the future. The question is if the time-line is a ray, line segment, or line. What I have concluded, not what I have initially defined my terms as, is that it would have to be a line segment.
As I noted above, I didn’t define my terms as “having a beginning” but concluding it by looking at what an infinite past would imply.
If there is a first, why would it not be a point? It’s not an assumption. The now is a point, five years ago exactly is a point, and if it exists, the beginning would be a point.
UY Scuti, Thanks for the book recommendations.
For the record, I’m not saying my argument is undefeatable, but so far I haven’t had someone show me how I am wrong (at least to where I can understand how what I am saying is clearly not the case)
. I checked up ‘countable infinity’ before on wikipedia though before you mentioned it. I didn’t see it running counter to my theory (although I really only skimmed it a little). I am looking at your countable infinity post just right now however. I got to the other posts before yours.
By this I believe you are getting at pi, right? Hmm, very good point. It’s not infinite. I see the point here… I need to consider this a bit.
Time expanding in the negative direction, this is the first I have heard of this concept. Interesting.
Most people, at least that I’m aware of, define a moment as the limit of an interval of time [o,x) as x approaches to zero. In laymans terms, an “instant.” A “snapshot.” I have never heard any other definition used. I may well be wrong, but I believe the other poster was using this definition, and you should both clarify your definitions before assuming the other means what you mean. Does anyone here also see a moment as an interval longer than 0?
Yeah, like, “I’m going to be coming upstairs in just a moment.” I suppose thinking about it now its not the way the term is supposed to be used, defining a year for a moment in most contexts. My mistake.
No, it’s not just that their vast distance gets in the way of observing them all at once. It is the fact that given ANY ability with being able to perceive greater and greater things, you would never be able to see all of them at once. Can anyone perceive all of the numbers of pi at once? Can anyone hold in their hand an infinite amount of objects? Can an infinite amount of years have passed by (not moments) to get to this year?
There is a reason why an infinite amount can never be observable, and it doesn’t have to do with the capabilities of your eyes.
I looked at the hotel example. I didn’t go into too much depth with it, but it already implied infinity (there is an infinite amount of people). I should look at it more in depth though.
This is where your problem lies.
You keep saying that an infinite amount is somehow a fixed amount.
But then you correctly state:
Seems like you got it.
But then…
What do you mean with “at one time”? Like all together?
This is also a recurring point of yours; You seem to add some sort of importance to things being observable or having been observed. Why is that important?
Pondering the recent question about the area of a circle, I am not AS sure of my answer now, but I can still answer from where I was coming from as well as what I am not truly unconvinced of…
Any certain amount of people is fixed. Infinity in the case of people actually existing is a certain amount. I explain this in my last 2 paragraphs.
[QUOTE=Latro]
Ho there! you first said:
[QUOTE=Gateway]
To me, to say “we have an infinite amount of (lets say) people.” The problem with this is there is now a fixed amount of people,
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[/QUOTE]
I brought up the infinite amount of people to try to disprove that the idea can truly exist. The next sentence says that “there is a problem with this.”
[QUOTE=Gateway]
Let me ask you, if there is an infinite amount of walkers on the line, are they all observable at one time?
[QUOTE=Latro]
What do you mean with “at one time”? Like all together?
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Forget the ‘on the line’ part, just take the idea of having an infinite amount of people. How can there exist all of them at once? Like, it implies that infinity is subscribed a numerical value. Ten = 10. Forty Eight = 48. Infinity = ??? That is what I mean. To say that infinity exists in a real, solid, I can touch it way, is to have a fixed amount which can have a numerical value attached to it. Though, you can’t attach a numerical value to infinity because it is not the same thing as any other number, if infinity can be referred to as a number.
[QUOTE=Latro]
This is also a recurring point of yours; You seem to add some sort of importance to things being observable or having been observed. Why is that important?
[/QUOTE]
It’s important because of this: if you think about pi, you can say it is an infinite number. But by the same token, to observe all of the numbers at one time in a hypothetical situation is to say that we have “fully written out pi.” This cannot be. It is different to say “pi is infinite” vs saying “I have written out all of the numbers of pi.” When you say you have infinity people, you are saying: “I have written out all of the numbers of pi.”
Observing the infinite is impossible for us, and people existing should be observable. It is contradictory. Not because we can’t look at all of them, but because of the reason why it is impossible to look at all of them (“I have written out all of the numbers of pi”)
This is exactly what I am saying. I am saying that there is not an infinite amount of moments behind us, because the walker had to start from somewhere.
