Here are some questions about time that are not scientific but are philosophical. Does time flow? Does it pass? What does it pass? Does it move? If so, how fast? If speed (s) = d/t, what is d/t when s is the speed of time? What temporal distance does time travel in a unit time? Surely the unity distance. But then the speed of time is 1 sec. per sec. How can time be measured, as the past does not exist and the future does not exist and the present is merely a point - nothing to measure there! - dividing the past and future? Does time exist? What (if anything) is it made of? Is time travel possible? In a completely unchanging universe, would time pass anyway? If every true statement corresponds to a fact, how can statements about the future be true now, in the present, as there are no facts about the future now, in the present? If there were, they wouldn't be future. Does it mean anything to say that time has a direction? What does it mean? If omelets came first and then eggs afterwards, time would surely still be going forwards, whatever that means; it's just that omelets would come first and eggs afterwards. And (as Andrew points out) how - in what way - do we experience time? This last question, though, might be thought to have a wholly psychological sense. Perhaps there is no such thing as the experience of time itself, but only of things changing. Would there be any difference in our experience of the world if we did not experience time as such? In fact the conceptual problems of time are interesting partly because so little in the way of answers can be extracted from science. In "Time and Physical Geometry" (1967) Hilary Putnam took the view that science gives the answer to problems about time. Science tells us that the death of Mr. A. is earlier in your reference frame than the death of Mr. A in my reference frame. That leaves a huge philosophical problem about the place of Mr. A's death in reality. One can see how simultaneity is relative to a reference frame, but it is much harder, if not impossible, for philosophical reasons, to see how the reality of something like Mr. A's death could be taken relative to a reference frame. But this is implied by its position in the temporal order.
You clearly hang out with interesting people. These issues are much discussed amongst proponents/critics of various forms of 'telological' or 'design' arguments. You can find in Aquinas the idea that if time stretches back to infinity then eventually every logically possible outcome occurs, which he uses to argue that not every existing being exists contingently, at least one exists necessarily. You see the response (eg in Hume against Paley's biological design argument) that for all we know the alleged design in nature occurred via a very long series of random permutations, some of which are bound to be ordered, and obviously any one which includes us would be an ordered one so there's certainty that if we are doing the investigation we shall discover the order -- Nietzsche famously argued for the 'eternal recurrence' suggesting that an infinite time not only does everything happen but that it happens over and over again an infinite amount of time ... but you're raising the question in terms of probabilities and certainties -- which is strong langauge -- if Aquinas/Nietzsche are right, this very conversation is itself an eventual certainty to occur -- but does that make it any less amazing, meaningful, reason to base beilef in (say) a designing God on? Hm.
You are right. The key to understanding the paradox is that although Achilles must complete an infinite number of tasks in order to catch up to the Tortoise, he can do so in a finite amount of time, since each successive task takes much less time than its predecessor (as you noted). Of course, today we understand how to add an infinite sequence of terms that converge to a finite quantity. But this wasn't well understood until millenia after Zeno -- and the logical foundations for doing so required Cauchy and Weierstrass in the nineteenth century. So we shouldn't be too hard on old Zeno.
By the way, you might find it amusing to consider some more recent Zeno-like puzzles, such as the "New Zeno" discussed by Stephen Yablo in the journal ANALYSIS, vol 60 (April 2000).
Philosophers have expressed wide ranging views on the infinite, and even distinguished different kinds of infinites. In terms of the 'infinite' standing for a sequence of events without end, then (just as there is no greatest possible number) it is difficult for someone to claim to have experienced that (experienced all numbers, none of which is lacking in a greater number), though not perhaps difficult for one to claim to understand it (that is, understanding that there is no greatest possible number) or for someone to have an experience of time or space, along with the feeling that this will never end.
There has been some interesting testimony by some philosophers to have experienced soemthing related that may be of interest. Some philosophers have claimed to experience that which is boundless or, in some sense, eternal. Probably the two most famous philosophers to have spoken and analyzed such experiences are Boethius and Augustine. Boethius spoke of God's eternity (and having some experiential acquaintance with God as eternal) in terms of God possessing the 'whole, simultansous, and complete fruition of a life without bounds' (interminabilis vitae tot simul et perfecta possessio'). This would be different from claiming to experience what you might think of as 'forever' or 'endless'; it is more like experiencing an event so overwhelming and perhaps good that you seem to lose track of future and the past. This has been analyzed by some philosophers as experiencing something that is atemporal or beyond metric time or not bound by it. The philosopher A.E. Taylor in an interesting book in the early part of the last century wrote of the experience of eternity in ways that are (to use your term) intense, but more satisfying than jarring or incredible (not worthy of belief). In one example, he describes 'spending an evening of prolonged enjoyment in the company of wholly congenial friends. The past may be represented for us, if we stay to think of it at all, by whatever happened before the party began, the future -but when we are truly enjoying ourselves we do not anticipate it- by what will happen when the gathering is over. The enjoyment of the social evening has, of course, before and after within itself; the party may last two or three hours. But while it lasts and while our enjoyment of it is steady and at the full, the first half-hour in not envisaged as past, nor the third as future, while the second is going on....' Taylor goes on to defend the coherence and importance of experiences that seem to be in response to a value that we wish to last forever or not be bound by time, a state in which one or more people might be completely present to each other that they would never wish it to end. See Taylor's book The Faith of a Moralist --the title is a bit misleading given what we mean by 'moralist' or 'moralistic' today versus when he wrote the book in 1930. It is a good text for thinking about the experience of values and time. (See especially chapters three to six.)
The question of God's omniscience is a deep one that has received considerable attention from philosophers. Your formulation of the issue, I think, raises three distinct questions: whether (divine) omniscience is compatible with temporal existence; whether (divine) omniscience can be achieved by a sentient being; and the nature of (divine) omniscience itself. I'll treat each of these issues in reverse order. First, the omniscience at issue in treatments of divine omniscience isn't merely (!) knowledge of what will happen to that being itself at any given moment, but what will happen everywhere in the universe at any given moment, throughout time: so the knowledge at issue is very broad in scope indeed. Second, and given that omniscience is knowledge of what is happening everywhere in the universe, throughout time, it seems impossible that a being that receives all knowledge from the senses--which is what I take you to mean by "sentient"--could know everything that is happening everywhere in the universe at any given moment. (Even the philosopher Leibniz, who believed that all perceptions included information about the past, present, and future, did not think that finite minds were in a position to understand this information.) Thus it would seem that omniscience requires a different cognitive relation to the world than that of finite beings--indeed, it may even require that one has an infinite mind (depending on how much information one thinks is contained in the universe, regardless of whether one thinks that the universe or world was created.) Finally, and perhaps most importantly, and especially given my characterization of the second issue, I think that it must be the case that an omniscient being stands outside of time: it seems to me that any being located at a particular point in time would necessarily be limited with respect to the information that it had access to, and, consequently, could not be omniscient.
I agree with everything that Allen writes in his last comment. Some time travel scenarios are ruled out a priori : these are the inconsistent ones, and there may be others, for all I know. Are the consistent ones ruled out by anything? I can't see that they are, as the only reason I am clear about for thinking time travel is possible is the grandfather paradox. But it may only rule out the inconsistent cases. So I am in agreement with Allen here too, and in the dark as to whether anything in physics allows or rules out non-contradictory time travel. Time is a dimension, and dimensions are things that allow you to scale. A direction in the structure of the dimension itself seems a slightly incoherent idea to me, as opposed to the direction of the thing moving in the dimension, e.g. a place moving through colour space, such as the sky going from blue to red, or a bullet moving from there to here.
Well, for one piece of evidence, no confirmed time travelers attended the Time Traveler's Convention held at MIT in 2005 (http://web.mit.edu/adorai/timetraveler/). The organizers do note that some might have attended in disguise, to avoid questions about the future.
More seriously, some philosophers have argued that time travel involves logical contradictions, and if that's right, then we can be sure that time travel doesn't happen. And certainly many time travel stories do seem to involve contradiction or incoherence. When Marty McFly travels back in time and then returns to the present day, the present day has been changed. So it looks as if 1985 the second time around differs from 1985 the first time around. But 1985 only occurs once, so it can only occur one way. You might think of this as "the second time around fallacy."
Another famous contradiction discussed relative to time travel is the Grandfather Paradox. If time travel were possible, then you could go back in time and kill your grandfather before your mother was conceived, which would in turn ensure that you'd never exist. But then how could you have killed your grandfather?
A good discussion of time travel and an attempt to resolve some of these issues is in David Lewis' paper "The Paradoxes of Time Travel."
You may be a high school drop out, but you have a genius for asking great questions! Let me try to break up the questions a bit. There is a difference between motion and change insofar as motion appears to involve physical objects and events. If there is motion, there is change, but some philosophers have either denied the existence of physical objects or events (some idealists) or they are theists who believe that there was a time when God (an immaterial / non-physical reality) existed and there were no physical objects. These philosphers would allow that change could exist, but without motion. In any case, once you have change, you have time, for change presumably involves there being one time when X occurs and then another time when X is not in the same state. If motion ceased, would time cease? Not necessarily, if there could be a nonphysical reality (God or souls or...) that change. But what if all change ceased? Would time then cease? Well, if by 'all change' we include 'temporal change' then I suppose the answer would have to be 'yes', but let's refine the question. Imagine all physical and non-physical (if there are any) realities ceased to involve or undergo any changing states; imagine everthing (as it were) freezes and there is no change in thinking, feeling, breathing etc. Can we imagine this happening for, say, 10 minutes and then everything starting back up again? Well, no one would know there had been a 10 gap, and indeed the very idea of there being a gap of 10 minutes as opposed to 9 suggests we can make sense of clock time when there are no changes among any clocks anywhere. Even so, I think the thought experiment makes some sense, and insofar as it does, then there is some reason to think that time is more basic than non-temporal changes.
An analogy with space may be useful. One reason for thinking that space is more than the spatial objects that make up the spatial world is as follows: Can you imagine everything spatial doubling in size in an instant? I think one can, though this would be utterly undetected in our experience. People would still be the same heighth, the moon would still be the same distance from earth according to all our systems of measurement. Nonetheless, there could be a fact of the matter that every spatial thing doubled.
Space and time, I suggest may be more fundamental than motion or change. You may need space and time for there to be motion, as well as change.
Granted, 10 years in comparison to infinity is as short as 10 seconds is in comparison to infinity. But it does not follow that 10 years and 10 seconds are equally long (or short). In comparison to any finite span of time, 10 years is longer than 10 seconds. The same applies to lengths and heights.
I see no reason to say that there is no common reference for duration. The amount of time it takes for the earth to go once around the sun (or to spin once on its axis) is commonly used as a unit of duration.