Originally posted by vistesdThat is why I said something to the effect of
You’re right that I have been treating t as the dependent variable. That is why I substituted y=f(x): to get away from thinking about physical time, and just focus on the function itself first, and what values for y (or t) it would yield. Treating it that (seemingly straightforward) way, the function f(x) never yields y=2. So, treating it that way, the ...[text shortened]... on.
You’re saying, if I understand you, that I was looking at it the wrong way ‘round . . .
"Do you think time is slowing down as you approach 2 seconds?"
Your way of looking at it is correct if you think time is dependant upon n.
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Originally posted by wolfgang59You overlook the fact that if the past were infinite, the present moment would never have arrived. Therefore, it is irrelevant at what point in the past you make the arbitrary starting point.
That is a good argument but flawed.
If the past were infinite it would mean that you could go back [I]any[/I] amount
of years (ie the past is boundless) to [I]any[/I] point - but from that point (and
you can choose any from an infinite number) the time elapsed to the present
would be finite.
Originally posted by twhiteheadI am assuming a past-infinite universe has no starting point. If the past were infinite, the present would never arrive. We are talking about the elapsing of time, after all, as well as the arrow of time. The point is, the notion of a past-infinite universe leads to absurdity.
You are making the error of assuming a starting point. An infinite universe does not have a starting point.
There is also a flaw in your logic, in that you are dealing with two infinities and refusing to cancel them off one another.
Originally posted by sonhouseThat's all well and good, but in these sorts of theories, there is always the mulitverse itself (i.e., that which contains all of the island universes) which must be accounted for: is it past-infinite? If not, where did it come from?
You are making an analogy similar to the 'arrow can never strike you since it would have to cover half the distance and then half of that, etc.'
If the universe is organized how some theories propose, an endless universe of bubble universes where ours is just one, there would be also an infinite number of time zones, our universe being just one of many a ...[text shortened]... one the same BB on a time scale of a higher dimension where such tallies can be distinguished.
Originally posted by epiphinehasBut there is no starting point, not even an arbitrary one. And you are incorrect that the distance between an arbitrary point in time and now would be infinite. It would always be finite.
You overlook the fact that if the past were infinite, the present moment would never have arrived. Therefore, it is irrelevant at what point in the past you make the arbitrary starting point.
Originally posted by twhiteheadI never said there was a starting point. The point I was referring to was the arbitrary point starting at a finite time in the past. But, my "point" is it seems irrelevant to posit another point in the past, when neither that point nor the present point, would ever have arrived in a past-infinite universe.
But there [b]is no starting point, not even an arbitrary one. And you are incorrect that the distance between an arbitrary point in time and now would be infinite. It would always be finite.[/b]
Originally posted by epiphinehasWell how about giving an actual argument for why you think this is, rather than stating it as a fact.
..., when neither that point nor the present point, would ever have arrived in a past-infinite universe.
Make sure to explain how your argument doesn't rule out the existence of an arbitrary integer given that the set of integers is known to be infinite.
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Originally posted by epiphinehasSimilarly, If in order to travel a distance of 1m you traverse first 1/2 m then 1/4m after that, then 1/8m after that, and so on... you'll never reach your destination (since it requires an infinite number of steps to get there; and so, if you have performed N steps thus far you will still have infinitely more left!). Moreover by rescaling our units it can be shown that for any distance, to be travelled, the final destination shall never be reached!
You overlook the fact that if the past were infinite, the present moment would never have arrived. Therefore, it is irrelevant at what point in the past you make the arbitrary starting point.
Ergo the universe is completely stationary! 🙂
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Quoting a classical probability lecturer of mine from 3 years back: "don't mess with infinity - that stuff is toxic!"
Originally posted by AgergI think to be a more accurate analogy, suppose I claim that I arrived at the current point in time by first going through yesterday, and half the day before that, and a quarter of a day before that, in an infinite sequence. If epiphinehas is to be believed, then I could not possibly be here, even if time is finite.
Similarly, If in order to travel a distance of 1m in one second you traverse first 1/2 m in half a second, 1/4m in the next quarter of a second, 1/8m in the next eighth of a second after that, and so on... you'll never reach your destination. Moreover by rescaling our units it can be shown that for any distance, to be travelled in any interval of time, the final destination shall never be reached!
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Originally posted by twhiteheadI agree - moreover, I now notice, by looking over older posts, that Zeno's paradox has already been mentioned before I turned up.
I think to be a more accurate analogy, suppose I claim that I arrived at the current point in time by first going through yesterday, and half the day before that, and a quarter of a day before that, in an infinite sequence. If epiphinehas is to be believed, then I could not possibly be here, even if time is finite.
Originally posted by vistesdZeno's Paradox looks like a koan that's been abducted by the Surrationalist International.
You’re right that I have been treating t as the dependent variable. That is why I substituted y=f(x): to get away from thinking about physical time, and just focus on the function itself first, and what values for y (or t) it would yield. Treating it that (seemingly straightforward) way, the function f(x) never yields y=2. So, treating it that way, the ...[text shortened]... on.
You’re saying, if I understand you, that I was looking at it the wrong way ‘round . . .
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Originally posted by AgergBut Zeno's paradox is not really analogous. The intervals traversed are potential and unequal, while an infinite past has intervals that are actual and equal. The claim that Achilles must pass through an infinite number of halfway points in order to cross the stadium is question-begging, since it assumes that that the whole interval is a composition of an infinite number of points. That is, it is conceptually prior to the physical act of measuring. Further, all of the potential intervals in Zeno's paradox sum to a finite distance, whereas an actual infinite past sums to infinity.
Similarly, If in order to travel a distance of 1m you traverse first 1/2 m then 1/4m after that, then 1/8m after that, and so on... you'll never reach your destination (since it requires an infinite number of steps to get there; and so, if you have performed N steps thus far you will still have infinitely more left!). Moreover by rescaling our units it can be cturer of mine from 3 years back: "don't mess with infinity - that stuff is toxic!"
Ergo, the Zeno's paradox critique is a no-go.
Originally posted by epiphinehasThe Zeno's paradox helps to illustrate that simply saying 'infinity', doesn't prove something is impossible.
Ergo, the Zeno's paradox critique is a no-go.
You are yet to give any actual argument as to why you believe infinite past time would be impossible. All you do is keep restating that it is impossible without any justification other than a vague reference to infinity.
I have already reposed Zenos paradox so that the intervals are 'actual' rather than 'potential'. So now you need to explain why the intervals being equal suddenly makes a difference.
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Originally posted by twhiteheadIf we're not assuming an actual infinite past, then what are we to assume? I'm not concocting infinities to explain anything; I'm assuming an infinite past and asking whether it is possible given what we know.
The Zeno's paradox helps to illustrate that simply saying 'infinity', doesn't prove something is impossible.
You are yet to give any actual argument as to why you believe infinite past time would be impossible. All you do is keep restating that it is impossible without any justification other than a vague reference to infinity.
I have already reposed Ze '. So now you need to explain why the intervals being equal suddenly makes a difference.
And, yes, I've provided an argument. I reiterate: In order for the present moment to have arrived in a beginning-less universe, temporal existence would have to pass through an infinite number of prior events (i.e., in order for the present moment to occur, the event immediately prior to it would have to occur, and the event before that, and the event before that, ad infinitum), making it impossible for any event to occur. But, obviously, events do occur, and do so successively. Therefore, it cannot be the case that the past is infinite and beginning-less since this would make the observation of present events an impossibility.
I have already reposed Zenos paradox so that the intervals are 'actual' rather than 'potential'...
But the half-way points in Zeno's paradox aren't actual. You can't just say, "well, what if they are actual..." and expect your critique to suddenly hold more water. It's like saying, what if unicorns existed. Well, yeah, if unicorns existed, I'd have to admit they are comparable to horses. But, given unicorns don't exist, it's an irrelevant point.