## I am a bit bewildered when I try to think about empty space. Does it make sense

I am a bit bewildered when I try to think about empty space. Does it make sense to think about space insofar as it is space? What sort of existence, if any, does it have? Is it nothing? Thank you!

### There are two major views

One view is "substantivalism." On this view, space really is a thing of a certain sort—a substance. Space would exist even if nothing else did. Needless to say, space it not like things as we usually think of them, but it has its own sort of reality. For Newton space was, among other things, a system of absolute positions. Newton believed that there was an absolute distinction between rest and motion, and that called for a corresponding system of positions. However, the points of space were otherwise indistinguishable; one point was intrinsically like any other.

In contemporary physics space and time are deeply intertwined, and we talk about space-time. Space time in general relativity is mathematically like a field (think of the electromagnetic field), and unlike Newtonian space, the points of space-time aren't all alike. This goes with the idea that space-time itself is curved. Roughly, the curvature at two different points of space-time (represented by a mathematical object called a tensor) can be different.

The alternative to the substantival view of space (or space-time) is relationalism. According to relationalists, space(-time) doesn't have any independent existence. To talk about space is really to talk about relationships among physical objects. For example: the fact that one object "takes up more space" than another" might simply amount to the fact that the second object would fit inside the first. The fact that A is further from B than from C might mean that if we had a large collection of rods whose ends would meet up if we brought them together (intuitively, are of the same length), we would have to lay more of those rods end-to-end to reach from A to B than to reach from A to C. More complicated variations on this idea lead to a relational account of the space-time of general relativity. On the relational view, there is no such thing as space or space-time, but there are spatial/geometric facts about the physical things that make up the world.

### There are two major views

There are two major views about space, and they give different answers to your question. One view is "substantivalism." On this view, space really is a thing of a certain sort—a substance. Space would exist even if nothing else did. Needless to say, space it not like things as we usually think of them, but it has its own sort of reality. For Newton space was, among other things, a system of absolute positions. Newton believed that there was an absolute distinction between rest and motion, and that called for a corresponding system of positions. However, the points of space were otherwise indistinguishable; one point was intrinsically like any other. In contemporary physics space and time are deeply intertwined, and we talk about space-time. Space time in general relativity is mathematically like a field (think of the electromagnetic field), and unlike Newtonian space, the points of space-time aren't all alike. This goes with the idea that space-time itself is curved. Roughly, the curvature at two...

## Would the idea of 3 dimensional space be possible without vision?

Would the idea of 3 dimensional space be possible without vision?

The answer seems pretty clearly to be yes. Touch and hearing both convey information about dimension. Think, for example, about the fact that a sound can be above you, or in front, or two the side. Or think of how you could tell that object A is taller than object B, but object B is wider than object A just by using your sense of touch.

If you're interested, here's a link to a video about a remarkable Turkish painter, blind from birth but able to convey subtle information about perspective.

The answer seems pretty clearly to be yes. Touch and hearing both convey information about dimension. Think, for example, about the fact that a sound can be above you, or in front, or two the side. Or think of how you could tell that object A is taller than object B, but object B is wider than object A just by using your sense of touch. If you're interested, here's a link to a video about a remarkable Turkish painter, blind from birth but able to convey subtle information about perspective.

## I'm thinking about relative position (left, right, up, down, ahead, behind). My

I'm thinking about relative position (left, right, up, down, ahead, behind). My general question is whether you think that these three oppositions (left/right, up/down, ahead/behind) have the same "status". For instance, for every point moving on a straight line, there is a meaningful and precise difference between ahead and behind, but not necessarily between left and right or up and down. Another example: for any (physical) object on the surface of a planet, the difference between up and down is clear, but not the remaining two oppositions. Another one: if it is settled, in a given 3D situation, what is left and right, then it is also necessarily settled what is ahead and behind, and what is up and down, but this does not (always) work the other ways around. What do you say? And do you think that the opposition between inside and outside has some relation to the other ones?

Offhand, it's not clear why we'd think there's a difference in status among these oppositions. Once we fix a point on a line as the "origin," it's still up to us which direction counts as ahead and behind. What's up where I am on earth is down from the point of view of folks across the center from me. And so on. Space is isotropic; any direction is as good as any other. (And just a side note: if we fix left and right, we haven't fixed up and down. Imagine holding your arms out and rotating 180 degrees around the axis they define. You'd flip up and down, and also ahead and behind.)

Still, there are some interesting points in the neighborhood. In our space, there's such a thing as "handedness": you can't turn a left hand into a right hand by sending it along some path in space. Our space is "orientable." But some possible spaces are non-orientable as the surface of a Möbius strip demonstrates. Likewise, in our space, there's an absolute distinction between inside and out, but that's a fact about our space, as the concept of a Klein bottle illustrates.

Offhand, it's not clear why we'd think there's a difference in status among these oppositions. Once we fix a point on a line as the "origin," it's still up to us which direction counts as ahead and behind. What's up where I am on earth is down from the point of view of folks across the center from me. And so on. Space is isotropic; any direction is as good as any other. (And just a side note: if we fix left and right, we haven't fixed up and down. Imagine holding your arms out and rotating 180 degrees around the axis they define. You'd flip up and down, and also ahead and behind.) Still, there are some interesting points in the neighborhood. In our space, there's such a thing as "handedness": you can't turn a left hand into a right hand by sending it along some path in space. Our space is "orientable." But some possible spaces are non-orientable as the surface of a Möbius strip demonstrates. Likewise, in our space, there's an absolute distinction between inside and out, but that's a fact about...

## 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 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,...