## I cannot understand how things move. Consider the leading point of a pool ball:

I cannot understand how things move. Consider the leading point of a pool ball: for the ball to move, that leading point has to dematerialise from Point A and materialise at Point B. When I attempt to explain this to others, they invariably respond with something along the lines of 'But it just moves a small distance'. This is what causes me a problem because, regardless of the distance moved, small or large, the leading edge of the pool ball must be in one place at one moment, and the next moment, it is in a different place. What else can this be other than dematerialisation / materialisation. Which, as I understand, is not possible. So how do things move?

I shall begin with a 'philosophical' kind of answer, the kind of answer that philosophers ever since Aristotle's time might have given. (Indeed, it is closely related to the answers that Aristotle himself gave to Zeno's paradoxes of motion. Perhaps you're already familiar with those paradoxes: but, if not, then I'd invite you to look them up, for you might enjoy pondering them). I think the flaw in your question lies in that phrase "the next moment". In the case of space, you seem to be treating it as continuous in the sense that, between any two points, no matter how close they might be, there will still be further spatial points between them -- so that to jump straight from one to the other would have to involve some sort of teleportation, bypassing all those intervening points. And yet (as a philosopher might tell you) time itself is equally continuous, and in exactly the same way. At any given moment of time, there is simply no such thing as the next moment. The continuous nature of time means that, between any two moments, let's call them t0 and t1, there must be an intervening moment, call it t0.5. And, between t0 and t0.5, a further moment, t0.25. And then also t0.125, t0.0625, t0.03125, etc., all standing between you and the moment you initially took to be the 'next' one. In a certain sense (and I don't intend this as an account of how motion works physically; just how it could work, logically), the mistake is to try to build up a big motion out of lots of little ones. The big motion ought to be the starting point. (It is said that Diogenes' response, when he heard Zeno spouting off about his 'proof' that motion was impossible, was simply to walk across the room!). Once you have the entire motion, between A and B, only then should you start to break it down and contemplate its component parts: getting half way between them by t0.5, getting a quarter of the way by t0.25, etc. The fact that there is no mathematical end to this process of breaking the motion down -- as opposed to trying to build it up from its 'least' parts -- means that there is no moment at which the object has to cross any real distance at all.

That, as I say, is the kind of answer that a 'philosopher' might give: but, particularly when it comes down to the kinds of topics that are nowadays studied by physicists, we philosophers ought to accept that we can't do everything on our own. (I've mentioned Aristotle already in this reply. Of course, in his day, there was no distinction to be drawn between a philosopher and a physicist -- but that's no longer the case). Now, I am not a physicist, and so here I cannot even pretend to approach the full story. But, for a start, quantum mechanists seem quite comfortable with the notion that an object might indeed just dematerialise from one place and materialise in another. Indeed, according to quantum mechanics, it's not at all clear that an object is ever in any fully determinate place at all. And then the string theorists will go on to tell you that, when you get down to the level of something called the "Planck length" (of the order of 10-35 metres, about a trillion trillion times smaller than something already as tiny as an atom -- a shorter distance than I suspect your friends could ever even have approached imagining!), alongside something called the "Planck time" (of the order of 10-44 seconds -- if anything, even more mind-bogglingly tiny!), then everything to do with space and time starts to go a bit haywire. For a start, there are ten dimensions down there! Now, it's not yet clear where all this cutting-edge physical research is going: but, who knows, maybe space and time will turn out not to be quite as continuous as Aristotle suggested after all. Although space and time certainly do still remain fascinating topics for philosophers, and philosophers surely do still have something to offer in this area, Einstein and his ilk taught us that we're not really competent to lay down the law about them on the basis of pure a priori speculation alone.

But, rather like Diogenes, I'm tempted just to get up and walk across the room. No one seriously believes that motion doesn't exist: the philosophers will explain how it's possible that there should be such a thing at all, and the physicists will endeavour to find the laws of nature that explain how it actually works in the real world.

## Is time simply movement? The physicist Brown said that all atoms are always

Is time simply movement? The physicist Brown said that all atoms are always moving. And all what happens simply happens because atoms move, doesn't it? So, if you could stop all atoms from moving, would there still be time?

Nice question.

Is it not the case, however, that everything you say is compatible with the proposition 'Time is a dimension or framework within which things happen'? If all the atoms stopped moving then time would carry on, so to speak, but nothing would happen.

Similarly, we could suggest that 'time is that which allows the measurement of movement'. If all the atoms stopped moving, there would have to be time for the statement 'they have stopped moving' to make sense.

## If there is an all-knowing God who knows the future, then he knows I'm going to

If there is an all-knowing God who knows the future, then he knows I'm going to sneeze in 10 seconds. But if I do something to control my sneeze, then I have just changed the future. Does this mean there is not an all-knowing God who knows the future, because we have control over our future. This would suggest multiple futures and abolish the theory of God. Or is there some way for there to be multiple futures and an all-knowing God?

## Is time a philosophical concept or a scientific concept?

Is time a philosophical concept or a scientific concept?

How about neither? Or both? (Or both neither and both?)

Put another way... Time is just one of our many concepts. By far most people who use the concept of time aren't philosophers and aren't scientists either. And so the concept of time as such isn't a peculiarly philosophical concept, nor a peculiarly scientific one.

That said, time has a special place in science as a fundamental parameter. We can do a lot of science without the concept of sex, for example, even though there's a place in science for the study of sex. (And of course, if there were no sex, science would grind to a halt in a few decades!) But outside of mathematics, we can't do much science without the concept of time. Moreover, physicists have things to say about time that are deep and surprising and were mostly beyond the imagination of the philosophers and the folk until relatively recently.

Philosophers have long taken an interest in time as well, and have taken it as a special subject for philosophical analysis. They've considered the question of whether time "passes" or "flows." They've asked whether the idea of changing the past is coherent. They've considered the logic of temporal language, thought about the possibility of branching time and offered theories of the nature of time itself.

Truly sophisticated thinking about time benefits both from what we learn from physics and from the special kind of care that philosophers pay to the inner workings of our concepts. If you browse the answers to various questions about time on this site, you'll see that the answers draw both on what science has to say and on the need to make careful distinctions of the sort that philosophers are in the business of making. But in spite of the special place that it's had in philosophical and scientific thought, the concept of time belongs to everybody.

## Does a proposition about the future have to be true today? If so does this

Does a proposition about the future have to be true today? If so does this preclude contingency and is every proposition of the future necessary?

In connection with Professor Stairs' last two paragraphs, you might also read Question 997 and some of the further entries referred to there.

## How long is forever? I know this question is ambiguous, but I have often tried

How long is forever? I know this question is ambiguous, but I have often tried to understand the heavy anchor of time and infinity, but I think it's really just too big to understand with the tools I've been given. I would really like to know someone's thoughts on the subject, and if the question is too ambiguous, is it because we don't have the 'brain power' to understand?

You might ask: "How long is this performance going to last?" And you might get the answer: "Two hours." You might also ask, more ambitiously, how long is this universe going to last?" And you might get the answer (from physicists presumably): "Forever." Now, those two answers seem similar; certainly they are grammatically similar responses to the two questions. And this might encourage you to think that "Forever" picks out a specific temporal duration, just as "two hours" does -- except that the first duration is a lot longer than the second. And then you might start to get a real headache trying to understand the nature of this duration "forever".

But, that's not what "forever" means here. To say that the universe will last forever doesn't mean that there's some really big temporal interval, forever, during which it will be around; it means rather that there is no last temporal moment of the universe. So there is no really big temporal quantity of foreverness that you have to wrap your mind around. What you have to understand rather is the thought that no matter where you are in the universe, temporally speaking, there are later moments of time in its life as well.

## Space and time are measured in hours and metres, value is measured in utility.

Space and time are measured in hours and metres, value is measured in utility. In these three fundamental scales, I have read that zero and the unit are arbitrary. I can see that there is no beginning of time, and no bottom to the universe and no absolutely valueless state of affairs, but it seems perfectly sensible to talk of two states of affairs being of equal value, in which case the difference in value would be zero. Two durations could be of equal length, as could two bodies. So is there a non-arbitrary zero in space, time and value that corresponds to the difference in length, duration or utility between the equally long, enduring or valuable?

It may be that there are two questions hidden here. You're right: if we can compare things in terms of length or duration or utility, then we'll sometimes be able to say that they're the same on this scale -- that if we subtract one value from the other, we get zero. But there's another question: is there such a thing as a thing's having zero length, taking zero time or possessing zero utility?

Length and duration are not quite the same sorts of scales as utility. Length and duration are ratio scales. It makes sense to say that this stick of wood is twice as long as that one. Turns out that this goes with the fact that there is such a thing as having no length or lasting for no time. In these cases, we have a natural zero. However, it may not make sense to say that one thing has twice as much utility as another. Utility scales are interval scales. All that matters are the ratios of the differences.

Let's make this a bit more concrete. I might rate the utility of a cup of coffee at 1, the utility of a cup of tea at 3 and the utility of a glass of beer at 6. That makes it look as though the utility of a cup of tea is three times the utility of a cup of coffee, and that the utility of a glass of beer is twice that of a cup of tea. But for purposes of decision theory, what matters is that the difference between the utility of the tea and the coffee is two-thirds of the difference between beer and tea. As far as decision theory is concerned, we preserve all the relevant information if we re-write the utilities this way:

coffee: 5; tea: 9; beer: 15

Notice that the utility of tea no longer appears to be three times the utility of coffee. Likewise, the utility of beer no longer appears to be twice the utility of tea. But the difference between 9 and 5 -- i.e, 4 -- is 2/3 of the difference between 15 and 9 -- i.e., 6.

For that matter, we could even represent the same utilities as

coffee: 0; tea: 2; beer: 5

or even as

coffee: -20; tea: -14; beer: -5

When we start mixing our utilities and our probabilities together in the way that decision theory says we should if we want to figure out what to do, all that matters are the ratios of the intervals.

It could still be that there's a natural zero point for utilities -- a sort of neutral point, as it were. But decision theory can get along without assuming that.

So yes: if we can say that two things are equal on some scale, that automatically means that we can say that the difference between them on that scale is zero. But whether the scale has a natural zero point, as in "having zero length" or "having zero utility" is another question.

## It seems that most astronomers and theoretical physicists believe that time only

It seems that most astronomers and theoretical physicists believe that time only began at the formation of the universe with the "big bang". Assuming that this is correct, is it possible for time to end (to no longer exist)? If so, what conditions would be necessary for this to occur? JW (Australia)

The easiest way to think of this may be in terms of some regular relation between time and the size of the universe. Expressing this regular relation as some mathematical formula, it may turn out that, going back from the present in accordance with this formula, we get to a past point of time at which the size of the universe is zero. We would have reason to postulate such a starting point as the origin of the universe if all we know about the universe supports or is at least consistent with our backward extrapolation. Big bang theorists believe that this is (by and large) the case.

The same mathematical formula may be such that, going forward from the present, we get to a future point of time at which the size of the universe is zero once more. We would have reason to postulate such an end point of the universe if all we know about the universe supports or is at least consistent with our forward extrapolation.

There are other conceivable end-of-time scenarios. The amount of stuff in the universe might be declining in accordance with some regular formula which predicts that there will be no stuff left at some future point in time. Or the amount of motion in the universe might be declining in accordance with some regular formula which predicts that all motion will cease at some future point in time. Again, if all we know about the universe supported or were at least consistent with such a forward extrapolation, we might have reason to postulate such an end of time.

To sum up. The passage of time presupposes that something is happening. Something happening in turn presupposes stuff moving in space (or some analogues, on which see Peter Strawson's book Individuals). Time can end by any of these three presuppositions ceasing to hold. We cannot experience such cessation. But we can have reason to postulate it by forward extrapolation -- just as we can have reason to postulate a beginning of time (big bang) by backward extrapolation.

Such extrapolation raises further philosophical issues: What can support our assumption that any mathematical formula (any laws of nature) supported by the evidence we have near the present will continue to hold? And likewise backwards: What supports a big-bang theorist's assumption that the laws of nature she relies on did not evolve but rather held all the way back in time so as to sustain her extrapolation?

## If the universe has existed forever, i.e. if the universe did not have a

If the universe has existed forever, i.e. if the universe did not have a beginning, would the present time be possible? That is, if an infinite amount of time was necessary to get to the present time? And if this is so, does this mean the universe necessarily had a beginning?

Short answer: You say: "That is, if an infinite amount of time was necessary to get to the present time?" But to get to the present time from when? The natural impulse is to say: to get here from the first moment. But, of course, the hypothesis of an infinite past means precisely that there was no first moment. So, again, where are we going to start counting? To get here from a time ten years ago will take ten years. To get here from a time twenty years ago will take twenty years. So, given an infinite past, we can pick a time infinitely long ago, and it will take infinitely many years to get to here from there, right? Wrong. The hypothesis of an infinite past does not mean that there was a time infinitely distant from the present. What it means is that there are infinitely many past moments of time, each one of which is some finite distance from the present. Now, this hypothesis may well be false (I take it that both the physicists and the theologians would agree that it is, albeit for very different reasons): but I'm not persuaded that it's logically incoherent.

Longer answer: Philosophers will often draw a distinction between two different ways of thinking about time, which they call the 'A-series' and the 'B-series'. (This distinction has its origins in work done by John McTaggart about a hundred years ago). The two series differ in the way they pick out different moments of time: both are equally common in ordinary discourse, but philosophers will disagree over which gets more to the heart of what is really going on at a metaphysical level. The A-series specifies moments of time through their relation to the present; while the B-series specifies them according to the order they have amongst themselves, without giving any privileged status to any one moment in particular. Thus, "now", "yesterday", "ten years in the future", "soon", "a long time ago" and the like would all be A-series expressions; while dates such as "15 May" or "the ides of March, 44 BC", together with comparative terms like "earlier than" or "ten years after" all belong to the B-series. Note that, in the A-series, the same expressions are continually changing their reference from one moment to another. Tomorrow, the word "today" will refer to a different day than the one to which it currently refers. "It is not raining" is true now, but it was false a few hours ago, and the chances are that it will be false again pretty soon. In the B-series, by contrast, there is no such change: thus, the B-series sentence "The date of Julius Caesar's death is the ides of March, 44 BC" is just as true today as it was when it happened. Indeed, as the seer saw, it was already true that he would die on that day, even before the fateful day arrived.

Now, with this distinction in mind, let's think about your question again. Suppose, first, that we decide that the right way to think about time is with the A-series. But, with the A-series, we have no need to "get to" the present, because we're already here. The present is our starting point: not in a physical sense, but rather in the sense that all other times, past as well as future, are defined in relation to the present. And so, if we begin defining the following sequence of times: "one year ago", "two years ago", "three years ago", we will notice that there is no finite point at which we are logically required to draw this sequence to a close. This should not be thought to imply that an infinite past is physically possible, just that it is logically possible. No matter how large a number n one opts to insert into the specification "n years ago", one can always replace it with n+1. It's up to the physicists (or, if this should be more to anyone's taste, the theologians) to decide whether there actually is any number n such that "n+1 years ago" doesn't refer to any genuine moment of time. But at least the question makes sense, and that's enough to settle the philosophical issue.

But then, what if the B-series is a better way of specifying different moments of time? Well, then it should be even more readily apparent that there will be no logical impediment to an infinite past, because the B-series doesn't recognise the notion of "past" at all. In the terms of the B-series, take any date d you like: there is no number n such that another date n+1 years earlier than d cannot be defined. (Though, again, it's for others to decide whether or not all such specifications will actually refer to really existing moments of time).

It's also worth just noting that all of the same points can be made about future time as about past time.

## Is time a logically coherent notion in the way we commonly understand it?

Is time a logically coherent notion in the way we commonly understand it?

We normally think of the passage of time in terms of a 'moving present'--a point that moves steadily futurewards along the temporal dimension, so to speak, and carries us along from our births to our deaths. However, many philosophers, from McTaggart on, have argued that this idea is incoherent, and that 'now' no more refers to a genuine feature of reality than 'here' does. On their view (the 'B-series view) 'now' is an indexical term that simply refers to whatever time you are at, just as 'here' refers to whichever place you are at.

It is doubtful whether the idea of a moving present is strictly incoherent. But, even if it isn't, our best theories of reality may well do without it. Perhaps we can explain everything we want to explain, including our experience of the passage of time, without positing a moving present. Indeed some philosophers argue that, even if you do posit a moving present, it is no help at all in explaining the things we want to explain.

There is a huge literature on this issue. A good place to start would be http://plato.stanford.edu/entries/time/ sections 4-6.