Sorry about the fabricated mondegreen, which obviously references the Star Trek series of films and TV shows. Captain Kirk saw space, or more correctly distance, as a barrier, but it really is one of the factors that determines the structure or shape of our Universe.

It is interesting to me, that, although the Universe is finite, if it derived from a Big Bang, there is a human urge to explore outwards, as if it were infinite. That is probably one of the factors that led scientists such as Fred Hoyle and others to support a Steady State Theory of the Universe.

Personally, I believe that there is no such thing as a steady state in anything. When we see something which appears to be in a steady state or equilibrium state we should look for the feedback factors that are keeping it that way. For example a pendulum hangs straight down when at rest because any deviation from that position results in gravitation forces pulling it back to the rest position.

If friction is low the pendulum will actually pass through the equilibrium position and swing to the other side, whereupon gravity will slow it and draw it back towards the equilibrium position again. Eventually friction will slow the pendulum down and the pendulum will again hang vertically.

So we have two forces, gravity and friction, resulting in the pendulum returning to the equilibrium position. No pendulum lasts for ever, as the pivot will wear out or an elephant may step on the thing, so the equilibrium will only exist for a finite time, but it will last long enough for us to use in clocks or in scientific experiments.

Space is itself expanding as I understand the theories and some of it is out of our sight, over an event horizon, which is a locus where everything is moving away from us at the speed of light. That doesn’t much our location special – it is true of any point in the Universe. LGM on a planet around a star that is over the event horizon from us have their own event horizon, and while they may be able to see a star inside our event horizon and we in theirs, we cannot see each other.

Space separates us form the LGM, but it also separates from things local to us. Ben, our dog, is over there, about 3 metres away. My cup is mere centimetres away. It is fair to say, I think, that this is the essence of space – it is hard to conceive a universe which doesn’t incorporate a spacial concept. Or rather, a separation concept to allow things to be different from one another.

Space is not the only “separation concept” that I can think of. Things can also be separated in time, so two different bodies can exist in the same spacial position, but just not at the same time. Time is so connected to space that Einstein and others were able to link time and space into a complex space/time concept.

The similarity between the space dimension and the time dimension is striking. You can even measure distance in time units as astronomers do when they talk about light years. We also do it when we say that a distant town is three hours away.

We less frequently talk of time in distance units, for example, when we say things like “six laps later”, to describe the time between two events in a car race. At some level we acknowledge that time and the space dimension have a lot in common.

Space in the sort of concept that everyone knows and experiences but no one thinks deeply about. There’s no doubt that space separates events from one another. You can’t have two solid objects occupying the same space at the same time, without catastrophe ensuing. Scientists have been trying to achieve this for years, with the aim of harvesting the energy generated from the ensuring nuclear fusion.

Space appears on the macro (normal) level to be continuous. We appear to move smoothly from one location to another when we walk, incidentally forcing the air out of way as we do so. There is no sudden jumps that we notice, we don’t hop from point to point like a chess piece on a board.

The philosopher Zeno came up with a number of paradoxes related to movement, that is getting from point A to point B. For instance, the athlete Achilles could not overtake a tortoise in a foot race, because Achilles would need first to reach the tortoise’s starting point, by which time the tortoise would have moved on. Achilles would then have reach the point that the tortoise had reached now, by which time the tortoise would have moved on. And so on, ad infinitum.

Of course Achilles does overtake the tortoise, and I believe the main issue in this case is related to the summation of an infinite number of decreasing distances, which intuitively one might this would sum to an infinite distance. In fact the sum of the distances is a finite number. If Achilles runs 10 times as fast as the tortoise and they start 10 feet apart then Achilles overtakes the tortoise after he has travelled 11 and 1/9 feet exactly.

Zeno’s paradoxes still inspire debate, but his conclusion was that movement, the smooth transition of something from one place to another is an illusion. One of the assumptions used is that distance is a continuously varying property, but it may be that it is not, and there are hints of that at the quantum level. The Planck length is the smallest distance about which statements can usefully be made and it is impossible to determine the difference between two locations less than one Planck length apart. Perhaps we do hop from place to place like chess pieces, or at least our atoms and their constituent particles do.

Space and time enable events to happen uniquely, and without collisions. Events may happen in the same place as long as they happen at different times. It may be that events of different probabilities happen at the same place and time, so long as the sum of the probabilities of all events is one. It may therefore be that probability is a dimension with the same sort of status as the space and time dimensions. This would require that our view of probability, of one event out of many being the one that actually happens is an illusion and that events of all probabilities happen in a sense.