greenrivet, welcome back. No apologies necessary.

Infinity is not a number It is defined as (any) divided by zero. When you have certain mathematical equations, all is well so long as a have a number at the bottom. Dividing by something small will give a large answer. However, as you approach an axis (with a 0 value) the answer grows rapidly very very large. Now, if that mathematical equation is being applied in physics, the value may become meaningless in reality if made equal to zero. For example density = mass/volume. If something has mass, it is very unlikely, in the real world, to have no volume. Hence, to solve this equation lies outside practical reality. That is what I mean by mathematical abstraction.

Take another example. Speed = distance divided by time. If an object (in the real world) travels a distance it cannot do so in zero time. Hence infinite speed does not exist in the real world. So division by zero, although allowable in mathematics, creating the imaginary infinity, does not exist in the real world. It is an idea abstracted from a mathematical equation obtained by inserting an impossible variable.

You may well find objections in some quantum mechanical situations, but I am talking about the macroscopic world as we perceive it.

Now this bit: "In reality, infinity (to me) is a fact".

Just let me start please with my flatlander. That is a creature living in 2 space dimensions on the surface of a sphere. That surface is its total world - there is no up or down. Now the flatlander can wander its world 'to infinity' - never stopping until the end of time, until its infinity, because it is trapped in two-dimensional space. You can say that its world (the surface of the sphere) is infinite, but to a 3-dimensional creature it is simply perceived for what it is - a finite surface. The important point of this story, is that one creature's infinity is another creature's 'balloon'.

So what do we mean by infinity? Mathematically, we now that it is defined by n/0, but reality 'breaks down' as we try to make the unreal substitution of something real, but very small, by zero. The problem is that the zero is meaningless in the context of the equation.

So, I repeat, what do we (in reality) mean by infinity? In truth, we do not know, because we are unable to experience it. Mathematically, infinity is not a number.

I'll prove it. There is a common waste of time which goes add one to infinity, so the 'first' infinity cannot be infinity. So, if we add 1, then another 1, then . . . . . . we can make the 'equation' n + 1 = n + 27, or any such statement you like. If this were a real equation, you could subtract infinity from each side, and end up with 1 = 27, which is untrue. You can apply this to distance. Walk an infinite number of miles (infinity) then walk one mile more, and one more, . . . . . . so infinity is unreal - you will never get there.

So what we mean, in the real world, when we discuss infinity, is just a very long distance, or a distance too long to imagine.

"Are you saying maths disagrees with infinity?" No. I am saying reality disagrees with infinity.

You mention time. Much of our language and therefore concepts, is governed by our senses. We see that everything we can observe on this planet has a beginning and an end. We even know that this planet itself condensed out dust and gas, and we know that it will end, probably when the Sun expands beyond the orbit of Venus in about 5 billion years time. Therefore we surmise (and believe) that everything has a beginning and an end. Then we try to apply this anthropocentric view to things we do not (and cannot) understand - like the flatlander. The big bang model (it is not well enough established to be a theory) works very well, starting from a tiny fraction of a second after t = 0. For the moment, say t = 0 represents the start. Because we are about to divide by zero, that is imagine the Universe at inception, physics (reality) breaks down and we get this imaginary singularity of 'infinite' density and 'infinite' mass and all that sort of imaginary stuff. We do not know what happened in that tiny fraction of a second. Because we are extrapolating time backwards (if the Universe is expanding, then it must have started from nothing) we get the idea that things happened in tinier and tinier fractions of time.

Now, we do not know either way, but instead of this fictional singularity, there may be a nexus, a passage, like the neck in the old eggtimer. In this case the Universe did not 'need' a beginning and does not 'need' an end. In mathematical parl ance, it is infinite. But, what if we are the flatlanders? Maybe a being with more far-reaching senses would just see the Universe as a bubble. Here we get into difficulties, because Universe is defined as 'all there is' - but we are outside reality here and imagining a nexus instead of imagining a singularity. So we need not worry. There maybe 'exoverses' but we don't need such a word yet. If we want to indulge in Philosophy, we can invent a word, but if we persist in our trips of fancy, we will have to invent, and agree, suitable vocabulary.

I hope this helps. Please feel free to ask any further clarifications or other questions.

Cat

Contd.