If Time Is Infinite, Can You Arrive At “Now”?

In another time and place, I had a multi-thousands of word exchange with a metaphysician who insisted that if the Cosmos was infinitely old – no beginning; no ending – then it would be impossible to arrive at our current date [i.e. – “now”] on the grounds that it would have taken an infinite amount of time to arrive at that date and that is an impossibility, just like you can’t ever climb an infinite ladder and arrive at any given rung since you’d have to climb an infinite number of rungs first to arrive at any nominated rung. Given that debate took multi-dozens of pages, I won’t reproduce the exchange here. Anyway, that was his side; here’s mine.

So, on the other hand, I suggest that no matter where you actually are on that infinite timeline, you are indeed at “now” since all you have ever experienced has been in a “now” moment and that it is quite possible to travel up and down the timeline – you can go from Tuesday to Wednesday. That is, the current date changes. Analogy: The number-line is infinite in both positive and negative directions, but if you are on that line, you can arrive at a specific number and it wouldn’t take an infinite amount of time to get there. If you’re on, say, -13, that’s “now” and you can easily arrive at say +13. In other words, even in an infinite timeline, that timeline is made up of an infinite number of finite chunks and you can go from one finite chunk to another.

So, can you get to “now” if the Cosmos has always existed and will always exist, and I justify that proposition on the grounds that matter / energy can neither be created nor destroyed in line with the First Law of Thermodynamics.