It's not infinite

A recent UK TV programme discussed the possibility that the Universe is infinite, and visualised scenarios where there are copies of ourselves doing what we are doing. Yes this is what there would be, alongside every other possibility as well. And the moon is made of green cheese.

Infinity is a word bandied about as if it were a real value, but it is not. It is just a mathematical expression of 1/0, or the distance at which two parallel lines intersect. Well the expression would need a real value of zero, and there can be no reality to parallel bars extending to infinity.

Infinity is a convenient expression for those who can't imagine the boundary (if it's not infinite, then where is the edge - and what is beyond the edge?) It is a cop-out of course, but in fact the existence of real infinity is far harder to contemplate than the alternative(s). I can explain why an infinite universe is impossible, it is tedious, but I expect I will have to.

We know the surface of an orange is finite but unbounded, same for any real object in our three-dimensional world. You can trace a path in the same direction all around it, get back to the starting point, and there is nothing stop this journey continuing on. I don't see any reason why this model should not be applied to the universe in communication to the general public by scientists and the media. (It is usually only expressed in the terms "scientists believe . . ")

I agree there is glibness in the assertion that the universe is finite but unbounded. The surface of an orange is flat in its local two-dimensional world (forward-back and left-right). Up-down exists locally, but it is only the larger view of the third dimension that reveals the solid object of the orange. (Replace 'orange' with 'earth' to see the dilemma of our ancient forebears.)

But if the third dimension is also curved in the larger view, in the fourth dimension, then is the fourth dimension also flat locally but curved in a fifth? This has to stop somewhere to retain finiteness. We understand the fourth dimension to be time, and the model has to work for no more dimensions. I think a key to this is the concept of half-dimensions, ie the ant on the orange is aware of up-down but not the curvature to the orange's horizon. Identify and solve the equation whereby each dimension comes in two parts, but the expression for the third-and-a-half dimension is equal to that for the fourth.