Recognitions:
Gold Member

 We get the same paradox if we ask how we can be sitting on zero non-physical unicorns, if there are infinitely many non-physical unicorns.

Try this thought experiment, think back to big bang, but instead of an outside view of a small space, think of an inside view of a large space about the same as we see today as if Planck's scale were truly relative.

 It began with motion. No motion = no time. When a “Single Something” separated creating motion that was the beginning of time. Let that “ Single Something” = S S = No motion = No Speed = No Mc^2. = No Energy. S is outside the bun. It is not imaginary. The original motion, like all other motion cannot be duplicated, so S is not Divine, yet S can be moved. Wierd, huh?

Can we please have a discussion about eternalism? Pretty please? Example. Here is a excerpt from the Penrose's Andromeda Paradox that seemingly supports four-dimensionalism (otherwise known as eternalism).

 "people pass each other on the street; and according to one of the two people, an Andromedean space fleet has already set off on its journey, while to the other, the decision as to whether or not the journey will actually take place has not yet been made. How can there still be some uncertainty as to the outcome of that decision? If to either person the decision has already been made, then surely there cannot be any uncertainty. The launching of the space fleet is an inevitability. In fact neither of the people can yet know of the launching of the space fleet. They can know only later, when telescopic observations from earth reveal that the fleet is indeed on its way. Then they can hark back to that chance encounter, and come to the conclusion that at that time, according to one of them, the decision lay in the uncertain future, while to the other, it lay in the certain past. Was there then any uncertainty about that future? Or was the future of both people already 'fixed'?"

Recognitions:
Gold Member
 Quote by NightShift I think I know what you mean with Zeno's paradoxes. You can divide a interval of time to an infinite amount, it is similar to the analogy that there will be an infinite amount of steps you have to take to walk across a room if the amount of distance your walking is half of what is left. So, to demostrate this notion from what I read in a calculus book(which is also where I read Zeno's paradox). Let x be the amount of time one perceives a constant amount of time. So, we take the Limit as x --> infinity of (x/(constant interval of time)) = infinity We can examine that anything less of infinity would give us a figure that tells us the multiples of time the being feels regarding the (constant interval of time). And to finally answer your question...I'm not sure...time still passes for us regardless. It could be infinite for the being that has his perception of time that continuously increases so that he will fall deeper and deeper into an eternity of time...
In zeno's Achilles vs the turtle paradox, the solution is to realize that the steps make up a series. When the limit of the series is taken, it will converge into a finite distance; therefore, if Achilles is running at a constant speed, he will catch the turtle in a finite time.

Recognitions:
 Quote by SixNein In zeno's Achilles vs the turtle paradox, the solution is to realize that the steps make up a series. When the limit of the series is taken, it will converge into a finite distance; therefore, if Achilles is running at a constant speed, he will catch the turtle in a finite time.
The core of the problem is whether and how it makes sense to do an infinite amount of tasks. The series of lengths does converge, but why would one say that the limit is the "total length"? (It seems obvious of course, but why?)

The main point here is that there has been a decision; we have decided that the "total length" of an infinite number or converging lengths is excactly the limit. We have given meaning to the notion of the total length of an infinite number of lengths.

This could of course have been different. We might as well say that the "total length" of an infinite number of lengths is 0. This would have been a different decision, but doesn't contradict anything prior to it. We just didn't know beforehand what to make of the total length. My point is that Zeno's paradox is not solved by referring to convergence, as this is - in a naive way - an arbitrary solution.

The notion of total length is however decided upon and incorporated into our logical machinery (to the point of which we take no notice...), but it is important to be aware of that there has been decisions all along.

In my opinion, the paradox is just that we arrive upon a physical situation for which we have no answer. There are ways to an answer that would seem more "appropriate" than others, but there is no logical reason for deciding upon one or another.

I must stress that this paradox is purely a logical one. It has nothing to do with the physics to it, nor the physical counterpart we would associate the situation with (though it is relevant when it comes to the point of deciding one way or another).

Recognitions:
Gold Member
 Quote by disregardthat The core of the problem is whether and how it makes sense to do an infinite amount of tasks. The series of lengths does converge, but why would one say that the limit is the "total length"? (It seems obvious of course, but why?)
Since the limit of the sum represents the total area under the curve, the total length is the limit.

Although a task can be broken up into an infinite number of steps, it may also be possible to accomplished in a finite number of steps.

 The main point here is that there has been a decision; we have decided that the "total length" of an infinite number or converging lengths is excactly the limit. We have given meaning to the notion of the total length of an infinite number of lengths.

We have determined that a infinite sequence of measurements, when summed, can be equal to a finite number.

 This could of course have been different. We might as well say that the "total length" of an infinite number of lengths is 0. This would have been a different decision, but doesn't contradict anything prior to it. We just didn't know beforehand what to make of the total length. My point is that Zeno's paradox is not solved by referring to convergence, as this is - in a naive way - an arbitrary solution.
The assumption I have made is Achilles' decent upon the turtle is such that it causes the series to converge.

 The notion of total length is however decided upon and incorporated into our logical machinery, but it is important to be aware of that there has been decisions all along. In my opinion, the paradox is just that we arrive upon a physical situation for which we have no answer. There are ways to an answer that would seem more "appropriate" than others, but there is no logical reason for deciding upon one or another. I must stress that this paradox is purely a logical one. It has nothing to do with the physics to it, nor the physical counterpart we would associate the situation with.
Here is a rough introduction to the mathematical concept being used:
http://en.wikipedia.org/wiki/Riemann_sum

Recognitions:
 Quote by SixNein Since the limit of the sum represents the total area under the curve, the total length is the limit.
You are completely missing my point, and arguing on the exact basis I am refuting. We are back at a similar notion. That the total area under a curve is the riemann integral is also a decision.

I fail to see any relevance at all in your other responses.

Recognitions:
Gold Member
 Quote by disregardthat You are completely missing my point, and arguing on the exact basis I am refuting. We are back at a similar notion. That the total area under a curve is the riemann integral is also a decision. I fail to see any relevance at all in your other responses.
Then 1+1 is also a decision... what is your point exactly? Tis not like there isn't rigorous proofs on integration.

Recognitions:
 Quote by SixNein Then 1+1 is also a decision... what is your point exactly? Tis not like there isn't rigorous proofs on integration.
The notion of convergence as an answer to the "sum" of an infinite amount of numbers was not at the time used. The whole issue was that one didn't have an answer for it, and thus could not conclude from the data that achilles actually caught up with the turtle. My point exactly is that using converging series is not an answer for the intended point of the riddle, which was that one could not logically conclude that achilles caught up from what rules of calculation that was currently utilized. Now we do, but this is as I said - in a naive manner arbitrary.

(EDIT: The solution by using convergence is giving sense to the notion of completing an infinite number of tasks in this particular sense, a notion which was not present at the time the paradox was stated.)

This has nothing to do with rigour nor integration.

 Quote by Assist The problem is if there is an infinite amount of time in the past then how is there a present?
Because our perception of the present is independent of whether the universe is 15 billion years old or infinitely old.

 Isn't this one of those questions the greeks spent hundreds of years debating and never really making any grounds on??? Anyhow the way I figure it's the result of what happens when two paradox clash and only the stronger one wins. ----> Time has to have a starting point and yet time cannot have a starting point. Perhaps what you end up with is a mix of both that nobody can really make any sense of?
 Even if there has been an infinite mount of time, there is no reason why we cant add more time to it.

 Quote by Assist The problem is if there is an infinite amount of time in the past then how is there a present?
The solution is: your premise is faulty.

What on Earth makes you think there is an infinite amount of time in the past?

As far as modern science can tell, the amount of time in the past is 13.7 billion years.

[EDIT] Sorry. 13.7 billion years and ten seconds

[EDIT] Sorry. 13.7 billion years and twenty seconds

[EDIT] Sorry. 13.7 billion years and thirty seconds

 Quote by Willowz Can we please have a discussion about eternalism? Pretty please? Example. Here is a excerpt from the Penrose's Andromeda Paradox that seemingly supports four-dimensionalism (otherwise known as eternalism).
I read a bit of your first link- eternalism. They use the term block universe which is the term I'm familiar with. What Penrose is speaking of is the two people passing each other on the street and what is happening 'instantaneously' from each 'perspective'. The catch is that no one actually see's any present event. There is always a time-lag for the event information to reach the eye/ear or whatever and then the mind. The 'instantaneous' perspective is each observer's 'frame' and the scientific model is Special Relativity. In quantum mechanics John Wheeler extends the idea of a block universe with the delayed choice experiments he proposed. The experiments have been performed. Changing a photon's possible paths 'in flight' causes the results to conform to what would have happened if the set up was fixed 'before' the photons begin their flight. If the set up was 'left alone' different results for the photons occur.
The block universe AKA eternalism doesn't address beginnings or ends, it is more a model of the shape of the universe. In my interpretation it leans towards determinalism philosophically.
Unless a cyclic model of the universe 'eats its own tail' I can't see any way to have a 'beginning' or 'end'.
Such a model would necessarily be deterministic.

mathal

 Quote by Assist This has most likely been mentioned before and if so I apologise, I have seen a few similar discussions though didn't really see any answers that I was able to understand/accept. The problem is if there is an infinite amount of time in the past then how is there a present? (I know there can be issues with defining present as well but let's generalise it.) I got told this is similar to Zeno's paradox so just wondering if anyone can show me the similarities and logical arguments against it (in layman terms lol) Appreciate any answers.
The devil is in the framing. Let's say time is infinite. Let's divide it into the past and future which are also infinite. They can both be infinite because infinite + infinite = infinite

 yes infinity + infinity = infinity and an infinite amount of time can be equal to part of that time interval.