The mind is a funny thing to be given the ability to attempt to understand the definition of endlessness. God has given us this curious intrigue to begin to understand His Mastery. Yet all things we come across during our existence here, have a definite beginning and shall have an end.

The PhD I spoke to last night saw it as something that needed solving, but didn’t know how.

I’d just say that an infinite regression need not be “solved” if that’s the way things are.

But I think I’m going to throw in the towel on this argument. I caught a PhD Maths student at dinner – He’s only just got back from lecturing in Europe, Oxford, Cambridge etc. And I asked him some of these questions. I learned:
a) that the more you understand about infinity, the more you realise you don’t understand.

b) that infinite time doesn’t solve the infinite regression.

c) that a first cause doesn’t help either

d) that his answer was “I don’t know”

e) that mathematicians commit suicide if they think about this for too long.

So I’m going to say, this is over my head. I don’t know.

It’s similar to Zeno’s paradox. He explained that if you divide a finite amount (e.g. 1) into progressively smaller partitions (e.g. 0.9 + 0.09 + 0.009 + …), you will never reach even the finite amount by counting through them (in his famous example, only taking stock each time the arrow has caught up to where the tortoise was last time). Regardless, there are several mathematical proofs that 0.9999 recurring is exactly equal to one. In practical terms, the arrow will catch and overtake (or kill) the tortoise.

Therefore, just because you can’t count to a number in a certain way doesn’t mean the number isn’t a practical reality. Like Zeno, you’ve chosen a method of counting to your target (i.e. a progressive series of finite numbers) which will never fully add up if you go piece by piece. I said very early on that infinity can’t be partitioned. Infinity divided by any finite number is infinity. You’d have to count in infinities, and then there’d be no point.

You might not think of infinity as a number to start at, but you do still think of it as a number you can or can’t “get to”, “count to” or reach. It’s an almost identical (merely inverse) perspective on the concept. It’s the underlying assumption you make when you use infinity as an arithmetic value, e.g. “Negative infinity + 1 = negative infinity.”

Here’s another angle. As well as a first cause, would you argue that the universe also has to have a last effect? If we can’t count forward to infinity any more than we can count backward to negative infinity, does that mean the universe must come to an end as surely as it supposedly had a beginning? (Going further if you like, does that mean there must be a powerful Destroyer waiting to be the Uncausing Effect, or Ineffectual Effect?) Does the fact that we can’t reach infinity by counting mean that we have to slap an arbitrary terminus on time in this direction too? If not, why are the mathematics or physics of the supposed beginning of time not fully reversible?

Moving into theology for a moment, does the unattainability of infinity mean the saved can’t actually spend forever in Heaven if they die in the present?

Be careful about attacking infinity. You might need it.

If you’re not totally bored of this topic yet, I’d like to go right back to where I see the core of this issue as lying.
I want to sidestep the issue of whether a Creator could be the first cause, and just establish whether a first cause is needed.

I had a quick look at VenomFangX’s videos, and my argument is not quite his. He seems to be saying infinite time is impossible. I’m not concerned with that, I just don’t know whether infinite time is enough to solve the infinite regression.

Here’s my thesis: I don’t think it’s established that infinite time is long enough to count to infinity. Tonight I asked a (strongly atheist) student of Mathematics, who has studied infinity, this question: “If you had infinite time, and counted at 1 per second, would you reach infinity”

He said no.

I explained why I was asking, he said “there had to be a first cause”. He looked like he was in a hurry, so I didn’t push him to hypothesise a first cause, but I’d like to follow it up later.

“The big problem is that you’re thinking of negative infinity as a definite number we can “start” at, like zero.”
No, I’m clear that you can’t “start” at infinity (though I see how my poor expression lead you to think I was unclear here) – but that’s the whole point. You can’t start at infinity.
It’s this fact that causes the problem.

“Infinity of any kind is indeterminate; you can’t add to it,”
Again, this is what causes the problem. Negative infinity + 1 = negative infinity. You never get to 0.

In a very simple form, here is the problem: You will never get to infinity by adding anything finite. Ever.