While waiting to take one step at a time with Orac, I thought I might complete my thought scenario.
There is a road of infinite length, in the middle of which there is a bridge.
How do I know the bridge is in the middle? I know that because the road must extend to infinity on either side.
Of course, we all know that, physically, there cannot be a road of infinite length because, as far as we know, the only places where a road could be placed are finite, but this is a "thought scenario".
One night the Finite Defence League blow up the bridge, so no one can cross from one side to the other. We know that the road extends to infinity in both directions, but can each section really be considered infinite?
What do we have? Is it two halves of infinity, two infinite roads or two finite roads?
Intuitively, one might say that, as each half goes to infinity, we must have two infinite roads. That seems more reasonable than "two halves of infinity".
However, consider that if you are at a point (eg 1km from the bridge site) along the road, and you travel towards the break; in 1km you come to the end of "infinity". Does this make sense?
Because we reach an end, whichever side we approach from, it is tempting to argue that the road segments are finite. However, if members of the People’s Infinite Front decide to repair the bridge, but they are infinitely far away along the road; can they ever reach the bridge? The answer must surely be “no”.
We were able to reach the end, so in our frame of reference, the road is finite; but the PIF, who were infinitely far away could never reach the bridge, so in their frame of reference it must be infinitely far away. For them, the road segments are go on infinitely in both directions.
Does this mean that infinity is relative? It would seem to suggest that.
If infinity is relative, so must eternity be. This must raise the question: Could there be a frame of reference in which there might have been absolutely nothing, yet there might still be something now?
Perhaps it would save crossed wires if I say that I think there would not be, but I could have missed something.
It might be argued that we cannot, with justification, extrapolate from what we observe in the Universe to what might be the conditions outside, and that we cannot say with certainty that, outside the Universe causality could not be such that something could be "spawned" by absolutely nothing.
Personally, I think that's "a bridge too far", but that is just a non-expert opinion.
