For the record, my point in these posts may be coming off as rude but know that my intention is to communicate my idea not put you down.
[Quote=Gateway]
You are saying there is no infinite distance on an infinite line.
[/quote]
It’s not the same thing. Not as I see it anyway (and this is coming from my logic not my imagination ability).
What I mean is when you are starting with an infinite line, you are starting with an infinite distance. That is where the infinite distance is. That is the definition of an infinite line: A line which HAS an infinite distance. To say an infinite line is finite is a contradiction in terms.
On a line/segment/ray, any 2 intervals will be a finite distance. True. Yet in on an infinite line, your starting point (not a line point) is an infinite distance. And an infinite distance cannot be reached through consecutive steps (e.g. you can’t begin counting at this moment and reach infinity).
I don’t disagree with those points. Unfortunately I only understand the first two. In and of itself, from what I understand of the bullet points they are correct, but they break down when you use them in the infinite past scenario, for the reasons I wrote.
Well, but that’s simply not true; the counterexample is the infinite number line, a line which has no infinite distance, but nevertheless is infinite.
Furthermore, your argument for this statement, so far, has simply been asserting it. What concretely makes you believe that there has to be an infinite distance on an infinite line, other than that it ‘seems right’ to you?
But nobody’s saying that. What I’m saying is that on an infinite line, there need not be any infinite distance—which is simply true, as there’s a concrete object (the number line) for which it’s correct. But your argument needs the infinite distance, which does not follow from an infinite past.
But that’s once again adding some point ‘at infinity’ from which to start. If the infinite number line is a model for the infinite past, then all moments in the past are points on the line. There is absolutely zero need for adding a point to it, other than to get your argument to work.
In other words, the object
-∞,…,-4,-3,-2,-1,0
the infinite (negative) number line with a point at -∞, is not the same as the object
…,-4,-3,-2,-1,0
the infinite negative number line. On the former, there is an infinite distance from the -∞ point to any finite number; but there is no reason the past should be structured that way, if all that is stipulated is that it ought to be infinite. The second object fulfills that requirement just as well, and contains no such infinite distance; so simply having an infinite past does not imply an infinite distance.
If you want to add a point at infinity, then yes, you have an infinite distance, but you’ve also just arbitrarily added that point without any need. So your argument works against the former object, but those arguing in favour of an infinite past can simply point to the latter, which is just as good a model of an infinite past without any of these troubles arising.
Perhaps, think about having a time machine: on the first, extended, number line, you could not reach all moments in the past; but on the second, any given moment, any given number, can be reached. This, in fact, shows the infinite past case to be perfectly symmetrical to the infinite future, which you seem to have no problem with.
That doesn’t make sense to me. So the points are correct, but somehow not anymore when applied to the past? But they’re completely independent of what you’re modeling, whether it’s the past, the future, spatial distances, or anything else. They’re logical properties of a certain kind of infinite object, independently of what you use that object for. They can’t suddenly ‘break down’ just because your intuition says so.
is a much worse model of an infinite past, if the intent is to get around the need for a beginning, a from-nothing origin of the universe (problematic in itself), since there, the universe clearly has a beginning—it was created at -∞! So if you want an infinite, beginning-less universe, it seems like the ordinary infinite number line would even on these grounds be a much better choice, apart from the fact that it doesn’t lead to the absurdity of ‘traversing an infinite amount of time’. So you’d really have to present good justification for considering the model based on the extended line even on these grounds; what seems most naturally to be meant by an ‘infinite universe without a beginning’ also naturally doesn’t lead to infinite timespans. But this just parenthetically.
**A line, then, essentially is length. Line = Length. To say you have an infinite line is to say you have infinite length RIGHT OFF THE BAT. Do you really not see this point? To say that 2 points on a line are finite and that’s all there is to it is to not see the full picture.
** INFINITE Definition & Meaning | Dictionary.com
So, another word for infinite is essentially unlimited. Infinite=Unlimited.
So then, if a line is length, and infinite is unlimited, then to have an infinite line is to have an unlimited length. That is where your infinite length is: It is “defined” in, right off the bat. Do you really not see that? To say that, “2 points on a line are finite and that’s it,” is to not see the full picture.
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By the way, as far as infinity existing (at least in a way) in a circle:
If you try to color in a circle, it takes a limited amount of time. If you try to color in a ray or a line (not a segment), it will take forever. If it would take forever, *then how did we go through forever to get to this present moment? Ya can’t. *
================= These arrows imply a never-ending distance. Never-ending distance = Infinite. That is where the infinite distance is. That is the DEFINITION of an infinite line: Infinite distance.
=================
As far as the bullet points. I don’t agree with the idea that an infinite line does not have infinite distance (as outlined above). I agree with the any two point idea though. I agree with points 2 and 3. I’m not sure what you mean by ‘differently sized intervals’ in #4, so I can’t comment on it.
So, it didn’t begin, but it wasn’t forever… what was it then?
It doesn’t have an infinite time-span, but it doesn’t have a finite time-span?
Of course the line is infinite in length; I’ve said so several times very clearly (it’s the same as saying ‘there are infinitely many numbers on the number line’). But still, there are no infinite differences between two numbers, no infinite intervals between two points, no infinite lengths of time between any two moments in time. No matter how many definitions you quote, this is a simple mathematical fact. Your adding a moment at -infinity adds a moment beyond all moments in time just to introduce such an infinite length of time.
Time elapses between two points in time; if there is no infinite distance between any two points, there is no infinite length of time, no matter how little you like it.
If you just straight away color the circle, you destroy the structure that makes it a representation of the infinite line. Just coloring the circle at uniform speed would be like coloring the line in the following way: First, color the interval between 0 and 1 in 1 second, then the interval between 1 and 2 in 1/2 second, the interval between 2 and 3 in 1/4 second, etc. That way, you’ll have colored the infinite line in 2 seconds.
If you want to color the circle in a way such that it is analogous to coloring the interval between 0 and 1 in 1 second, the interval between 1 and 2 in 1 second, the interval between 2 and 3 in 1 second, etc., you’ll have to color a progressively smaller amount per unit of time: color the half circle in 1 second, the next quarter in 1 second, the next 1/8 in 1 second, and so on, and it will take you exactly as long to color the circle as it would to color the line. Essentially, the points on the circle corresponding to equidistant points on the line move ever closer together, such as in this representation of the Poincaré disk by M. C. Escher.
Also note that in this way you will never (not in finite time) color the whole circle; but you will color any fraction of it eventually. No matter where you start coloring, you will reach every point in finite time.
And of course, ya don’t need to.
Well, then you’re saying you don’t agree with the idea that there is no infinite distance on the line, but agree with the idea that there is no infinite distance on the line.
Well, it always existed, but never endured an infinite timespan, because there simply are no such timespans. This may not appeal to the intuition, which is why we use math to enhance our intuition: it shows us the ways it is logically possible for things to be. In this case, it shows us that the idea of an infinite interval and an infinite amount are not co-extensive: there are objects such that you have an infinite amount of something, but no infinite interval, such as the infinite number line.
It’s like coloring the circle (in the way I outlined): there’s no beginning anywhere, and you’ll never color it wholly, but you will eventually reach any given point. If that doesn’t fit your metaphysics, I’m sorry; but it’s how things are.
I hate to appeal to authority here, but Quentin Smith knows what he’s talking about better than either you or I do, and his arguments are to the best of my knowledge uncontested. The problem you see with an infinite past simply does not exist (in fact, Smith discusses other, more sophisticated objections, and likewise convincingly demolishes them).
So you agree with the line being an infinite length. Good.
Any two numbers on the would be a finite distance, but: when you are talking about the totality of ALL of the numbers of the past, you move into an infinite distance. (If not, you don’t actually have an infinite line standing for the past but a finite one).
Do we agree with that?
Time elapses between two points… you just made my case. We have the now (first point) and by your own definition, a beginning point.
Unless you mean one integer to the next on a line, in which case I see my above argument still holding.
Circles are ‘uncolorable’? Perhaps on some level, you may have a point. But I am not talking about some kind of progressive coloring as you are suggesting. Just a real human, with a real marker, with a real circle (lets say 3 inches in diameter) on a paper, coloring at his own pace. It won’t take a long time.
How long would that take for an infinite line, if I had to color one in real life? (And please explain if your answer is not ‘forever’)
You’ll have to define “always existed.”
From the looks of it you are saying it always existed (it existed forever) but never endured an infinite timespan. Like you are saying it was infinite and not infinite at the same time.
Can you point to a number-line with every possible number on it written out in nature?
I do not see how an infinite interval and infinite amount are not co-extensive. By the way, the infinite number line is purely conceptual (can you point to a number-line with every possible number ACTUALLY existing?)
Are you referencing a book, or specific argument within a book? Can you cite what you are talking about?
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How I both agree and “disagree” with the two point idea is outlined above in my first answer.
From where to where is the infinite distance? You keep saying things like ‘from the beginning’, etc., but the point of an infinite line is that it has no beginning. You can’t start at the beginning because there simply isn’t one.
Nope. There is no beginning point on the infinite line; that’s the whole reason one might want to have an infinite universe, because one doesn’t have to worry about its beginning.
Yes, but as I said, then you’re effectively doing the same thing as coloring the infinite line in a progressively accelerating way, which also only takes a finite time.
Maybe an illustration helps. Every point on the infinite line can be mapped onto a circle like this (apologies for the crudeness, I’m working from a tablet): From a point on the top of the circle, draw a line to a point on the number line. The point where that line crosses the circle is the projection of the number onto the circle. Every point on the line can, in this way, be projected onto the circle.
Now, think of the circle unfolded, like this. The lower line now contains all the points of the infinite number line within a finite length. Effectively, the infinitely many integers get projected to an interval of rational numbers (of which there are infinitely many in a finite interval). Say, just for illustration, the point in the middle is 0, and the left bracket ‘(’ corresponds to -1, while the right bracket ‘)’ corresponds to +1. Then, the integers are e.g. mapped in the following way:
-1 –> -1/2
-2 –> -3/4
-3 –> -7/8
-4 –> -15/16
.
.
.
-n –> -(2[sup]n[/sup]-1)/2[sup]n[/sup]
.
.
.
And analogously for positive values. So, every integer is mapped to a rational number in the open interval (-1,1).
Now, the important property of this interval is that it has no smallest number: 1 and -1 are not part of the interval, they are simply the smallest number larger than any contained in the interval, and the largest number smaller than any in the interval respectively. They’re the analogues of ∞ and -∞. But this means that for whatever you want to do, you have no ‘beginning point’ to start doing it: there is no smallest number in the sub-interval (-1,0], so for every number you take, say -1/n, there is a number -1/m with m > n such that it is smaller. This is what it means for there to be no beginning.
You want to start at -1, but this is simply not a moment in time. ‘-1’, just as ‘-∞’, can never have been ‘now’: it’s not contained in the past. And from any moment in the past, it’s only a finite amount of time to now.
From any point to any other point, it takes a finite time. You want to color the infinite line starting at the beginning; but that simply makes no sense: there is no beginning, just as there is no smallest number in an open interval of rational numbers.
In other words, I can tell you how long it takes to color the line if you tell me where (on the line!) to start.
I can’t even point to one with all the numbers up to 10[sup]100[/sup]. Does that mean there are no bigger numbers?
I’ve given the reference and posted the relevant quote above.
In dealing with the past, we start with the point of the ‘now.’ The now is represented by the point, and what is before that is a ray. We start therefore with a ray, then…
[QUOTE=Half Man Half Wit]
Time elapses between two points in time; if there is no infinite distance between any two points, there is no infinite length of time, no matter how little you like it.
[/QUOTE]
I was actually unclear about his post. He was either saying that time happens between two points, or that time happens consecutively (one second comes after one second comes after one second). In my first sentence I address this first possibility in saying that if time only happens between 2 points then we have a line segment, and if he is saying that time only happens consecutively then “my above argument is still holding.” In other words what I wrote before still holds true, even if time happens consecutively.
I’m sorry, actually my first 2 sentences deals with the first possibility, the third sentence deals with the second possibility
No, even if we consider the whole line, time only ‘happens’ (though that is a strange wording) between two points. The past is the set of all points that once were ‘now’. For time to elapse, we must ‘move’ from one ‘now’ to another. But in the past, there is no point—no former ‘now’—such that the distance to the present is infinite. The past contains no point -∞, just like the infinite number line contains no infinite number. ‘-∞’ never was ‘now’; it doesn’t make sense to talk about time elapsed since then. It’s not a point in time, but a point beyond all points in time. But then, again: nothing has ever endured an infinite length of time.
A) You start with an infinite line, or an infinite ray.
B) An infinite line or ray IS infinite length
C) Infinite length IS infinite distance
So if you start with an infinite line or an infinite ray, THAT is where your infinite distance is.
The your idea ( 2 points = 2 finite distances = only finite distances exist) is a red herring, as it is not the full story.
Did you not see my previous point:
Do you actually understand what I am saying above?
=======================
As far as the circle stuff goes: No matter the math you use, if your end argument is that it’s impossible for a human to color in a circle in a set amount of time, you are wrong. Also, you cannot color in a never-ending distance (never-ending means you will never get to the end, so you will never color it ALL in)
=======================
[QUOTE=Half Man Half Wit]
I can’t even point to one with all the numbers up to 10100. Does that mean there are no bigger numbers?
[/QUOTE]
But time elapses only between two points in time, between two 'now’s. The totality of the line is infinite, but that simply doesn’t imply an infinite elapsed time; and per your own argument, only the latter would be problematic. The infinite length of the line simply doesn’t mean that an infinite amount of moments have passed, but the latter is what you would have to establish for you argument.
It is regarding the question of how much time has elapsed in the universe. Time elapses from ‘now’ to ‘now’. If you claim that an infinite amount of time has elapsed, you have to point to a ‘now’ from which this time has elapsed.
Well, it’s not, and I don’t see how you get this from what I wrote. My argument is that it’s impossible if you color it one interval at a time, when the interval length progressively decreases, and the time interval you take to color it remains constant. Only under this rule does the circle continue to be a representation of the infinite line; when you disregard it, you destroy the structure that makes the circle such a representation.
Well, you can: color the interval between 0 and 1 in 1 second, the interval between 1 and 2 in 1/2 second, the interval between 2 and 3 in 1/4 second, and so on, and you’ll have colored the whole infinite line in 2 seconds. The problem is that this again disregards what makes the infinite line a model for an infinite amount of time, just as coloring the circle at uniform speed does: each second lasts a second, so you need to take one second to color in an elementary interval.
By your argument that insists there is no infinity because there is no representation of infinity (which is wrong—see the circle), there are no such numbers, since they are just as impossible to represent in a universe which contains only ~10[sup]80[/sup] nucleons. Of course, there are such numbers; this simply shows that your argument establishes nothing.
Post 43 contains the reference to the paper, post 98 quotes his argument (same as my argument: infinite line doesn’t imply infinite length of time having elapsed).
Perhaps to one last time be as clear as I can be: for the argument ‘if the past is infinite, an infinite amount of time must have passed to get to now; an infinite amount of time can’t pass; we thus could never get to now; thus, the past can’t be infinite’ to work, you first need to establish its key premise, namely that an infinite past implies an infinite amount of time must have been passed through. This you haven’t done, nor have attempted to do: you merely point to the infinite line saying ‘Look, but it’s infinite! So, there’s an infinite amount of time!’.
This would be sufficient for a finite length, since there, you can just start at the beginning and traverse it from one end to another, and the distance traversed will be equal to the length of the line. But this ceases to work in the infinite case: there is no beginning from which you can start, just as there is no smallest number in the open rational interval (-1, 1).
In the finite case, there is a ‘now’ at the beginning of the line such that the time traversed from that ‘now’ to any later one is the distance between the two, which is maimally equivalent to the length of the line. This is not the case for an infinite past. There is no ‘now’ at -∞. This would be a point with no predecessor, which doesn’t exist in an infinite past. It never was ‘-∞ o’clock’. It was ‘-n o’clock’ for any given n, but from all of those n’s, it’s only a finite time till now—n hours.
Until and unless you can show that an infinite past implies an infinite length of time between two moments that once were the present, between two times the universe was ‘at’, in the same sense that it was ‘at’ -2 hours ago and ‘is’ now, you simply haven’t established your key premise. Pointing to just the infinity of time in total cuts no ice.
Also, you’ve never replied to the ‘time travel’ argument: if we just reverse the flow of time, there is nothing that stops us, at least in principle, from going back arbitrarily far, meaning that there is not necessarily a moment in the past such that we can’t go back farther. But this implies the possibility of an infinite past; it’s just the same as an infinite future. And from every point in that past, if our time machine broke, we could just wait until the present, and it would take finitely long. So, from every point in an infinite past, a finite amount of time elapses until now; thus, there is no problem with an infinite past. If your argument held, there would be a point in the past such that we could never once again get to ‘now’; but this is clearly not the case.
The key point in your argument is “any two given points=finite length”. This ACTUALLY begins with the premise of time being a line segment (if time can only exist between 2 points, then the totality of time can only exist between 2 points, which means you have a line segment and not a ray)
Your argument is deceptive because any distance in the past could be said to be from the now to that point and on and on. The reality though is the FULL PICTURE is this: you go from the now to the next point and on and on to infinity. And an infinite time period cannot be traversed.
If it can be done consider a drill sergeant in hell who tells you to “drop down and give him infinity.” He also says that he will give you a nice cold glass of water when you have done so. That infinity will never pass and the water will never come because no matter how many pushups you do you will always have one more to go. You will always have 1 more. Thus your task will NEVER be done.
The task of letting “infinity seconds” to pass by before we get to this present second is the same, it will NEVER be done. And an infinite length of time in the past is “infinity seconds.” Now that I think of it the drill sergeant from hell might as well have said, “fine, fine, I’ll give you a glass of water, after you let me beat you up for infinity seconds.” Would you ever expect to get that water, Half Man Half Wit?
That implies an infinite amount of time from the getgo, past and future, which shouldn’t be the starting point. You can’t go farther in the past if at some point in the future there is no more time, same with the past.
The idea that we can half a thing infinite times is for one a conceptual leap even if all “halfs” are “written into the thing” and with this example it doesn’t “take up infinity” but an infinite line does. Hmm, wow, I actually have to pause myself here. But no, if you try to jump sequentially from one half to the next to the next you will never reach all of the potentials. An infinite sequence of nows behind this ‘now’ can not have therefore been traversed. IF YOU ONLY ANSWER ONE THING ANSWER THIS: Do you TRULY NOT see what I am talking about with that?
I checked out the Quentin Smith (sp?) argument and the math is beyond my comprehension. Please define these:
What is -∞ ?
Aleph-zero event
order type w*
and explain this: There is no smallest number in the open rational interval (-1,1)
Perhaps infinities CAN exist (at least in some way) but they don’t correlate to a passable sequence of infinity which is what we are talking about on the line. None that I can see anyway, can you point to one?
I didn’t respond to each of your points as I felt the above was (probably) sufficient. So even if I responded to each of your points, it would bring about the same answers as the above.
Thinking about it, perhaps not the ‘coloring’ example. And, TO the coloring example, the line would still never be fully colored. If you did more of the line and more of the line with each fraction of a second, it could still never be reached in this way because you are still trying to reach it sequencially. Furthermore, a normal person who didn’t have these abilities to speed up could never do it. If they tried to color in the circle in the way you said it (if memory and understanding serves with how you said to do it) they still could not because infinity can’t be reached in sequence.
That is pretty much the point: infinity can’t be reached in sequence, as would have to be the case with linear time. An infinite time before the now cannot have SEQUENCIALLY been passed to get to the now. So when using the framework of linear time, an infinite past is incompatable.
No. If it were a line segment, then there would be some maximum length (the length of the line segment). But the distance between two points is unbounded, something not possible for any line segment.
Yes, I’m not disputing that. But in an infinite past, you never have to traverse an infinite time, so it’s just beside the point.
What does ‘you can’t go farther in the past if at some point in the future there is no more time’ mean? I can’t parse this at all.
The point of the time travel example is the following: in a finite past, there is some point such that you can’t go farther in the past than that. If there is thus no such point, then we have an infinite past. And from any point you time travel to in the past, you can return to the future by simply waiting; thus, in an infinite past, the present can be reached from any point in the past. No infinite amount of time ever has to elapse, no infinity of moments has to be traversed.
If you meant that you can’t accomplish any task with infinite steps (an instance of what in philosophy is often called a ‘supertask’), then I’m inclined to agree. But of course, the point is that with an infinite past, you don’t have to, as the time travel example and the preceding arguments show.
Yet nevertheless, you seem confident that you have it right. This, if nothing else, should give you at least some pause.
A point in time infinitely long ago.
As I said in my previous post, it’s the ‘order’ of infinity equal to the amount of natural numbers.
An ‘elementary occurrence’, basically equal to what we’ve been calling a ‘moment’.
As I likewise explained, ordered in the same way the integers are, i.e.
…,-4,-3,-2,-1,0,
as opposed to e.g. order type ω* + ω*, like the example I gave:
…,-4,-2,…,-3,-1,0,
where there indeed exists an infinite distance between -4 and -3.
For any number in the interval, I can find one that is smaller: -15/16 is smaller than -7/8, -31/32 is smaller than -15/16, i.e. there is no number such that there is no number in the interval which is smaller—there is no smallest number.
We never have to traverse an infinite amount of time in a universe that has an infinite past. This is the key premise of your argument you have so far not even tried to substantiate (which of course you can’t, since it’s demonstrably wrong).
Infinite time yes, but not an infinite amount of time passing for anything. I’ve pointed out why this is not the case from the first post I made in this thread; if you haven’t picked up on that, I’m not really sure this is worth continuing.
Even in an infinite time, the time that passes from any moment in time to any other moment is fininte. There is no moment in time, no past ‘now’ such that it is separated from the present ‘now’ by an infinite amount of time. You can’t traverse the infinite line from the beginning, because there is no beginning, just as there is no smallest number in an open interval over the rational numbers. It is just not the case that there is some state of the universe in the far, far past such that it takes the universe ‘infinitely long’ to get here. Any moment in the past is separated from the present by a finite amount of time, just as any number on the infinite line is separated from zero by a finite amount (the absolute value of the number). It is just never the case that anything anywhere within the universe, or the universe itself, had to wait an infinite amount of time until the present.
Perhaps think a while on the time machine thought experiment. What you have to argue for is that it is in some sense logically necessary that there is a time n in the past such that the machine can’t go further back to an earlier time: this is the necessary condition for the past being finite. If you can go back further than any finite time in the past, then the past is infinite; if you moreover can then just ‘wait’ until it’s the present again, then you can reach the present from any point in the infinite past, without having to traverse an infinite timespan. This shows that an infinite past is perfectly well compatible with the existence of exclusively finite lengths of time elapsing—again, otherwise there would be an n such that you can’t go back further. Why should that necessarily be the case? Without an answer for this question, you have no argument.
In your post: You are only referring to 2 given points which, I agree, are of a finite distance. You seem to be ignoring the totality of infinite intervals Any two of these intervals and you are finite, but deal with the total amount there and you go into an (impassable) infinite. Or is there not infinite intervals within an infinite amount of intervals?
~and from farther down~
Infinite integers which each only have finite distance. Makes sense and is almost the full story. But you are not taking into account that you sequentially have to pass infinite (impassable) integers of a finite (passable) distances. The finite distance would be the truth, if you didn’t have the infinite amount of finite distances to pass through.
Please explain what you mean by unbounded.
Can you please explain how there is a difference between infinite time and infinite past?
What I meant is, on a finite timeline, in other words a line segment, there will be a point on the timeline (past and future) where you cannot go any farther into the past and future. There is only a certain amount of time, and no more than that.
The point of the time travel example is the following: in a finite past, there is some point such that you can’t go farther in the past than that. If there is thus no such point, then we have an infinite past. And from any point you time travel to in the past, you can return to the future by simply waiting; thus, in an infinite past, the present can be reached from any point in the past. No infinite amount of time ever has to elapse, no infinity of moments has to be traversed.
I don’t feel that your point is proven in this example. This is another way to say that between 2 points there is only a finite distance, ignoring totality.
If you meant that you can’t accomplish any task with infinite steps (an instance of what in philosophy is often called a ‘supertask’), then I’m inclined to agree. But of course, the point is that with an infinite past, you don’t have to, as the time travel example and the preceding arguments show.
I don’t see how your preceding arguments prove this. Again, the totality issue stands in the way.
You may have to take my word for it, but it does give me pause. Much math I don’t know (at this point in my life/in this dimension). It is also generally pretentious to go to someone who has expertise in an area and say that “they are wrong” when you are not versed in the field. The reason why I have been asserting my theory/principle is because, at least to me, this all comes down to some basic principles which so far seem easy to work with. I could be wrong, but the simplicity of the principles (so far) make it seem self evident causing me to lean pretty strongly in the direction that my theory/law is true… I have an open mind and I am okay if I am shown to be wrong. If you can show me I am, then please do.
Thanks for the definitions. Okay, so aleph zero is counting from 1, 2, 3, in sequence “to infinity”? Does that mean it is the whole sequence at once? And when you say there is an aleph zero event, you mean … in one moment you go from zero to infinity? I have no clue what the ω* + ω* example means. In fact, I still don’t know what ω* means: you used negative numbers so does that mean that ω* is for negative numbers what aleph zero is to whole numbers?
This I don’t get either: so you are starting with (-1,1) which goes to -7/8 and -15/16 and one is smaller? Is this a set of numbers, or a comparisons of fractions like if you divide -7 by 8?
See, that’s probably the MAIN part of your argument I don’t get. Why don’t you have to travel an infinite amount of time where you have has an infinite past? To me, past = time. Thus infinite past = infinite time. No?
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Not sure what is meant by, “infinite time passing for anything”
I understand your point: it is picked up. I believe if there is a problem it is not picking up mine. Just remember: totality.
Still, if you start from zero and “look” all the way back to the full amount on an infinite line, you are still dealing with an infinite amount of (impassable) intervals. Totality.
Infinite integers which each only have finite distance. Makes sense and is almost the full story. But you are not taking into account that you sequentially have to pass infinite (impassable) integers of a finite (passable) distances. The finite distance would be the truth, if you didn’t have the infinite amount of finite distances to pass through.
Totality is my answer. The question of a PARTICULAR time you choose being finite is beside the point of there still being an infinite amount of past intervals when you look at the full amount, the totality.
