Well, what does "traverse" mean?...to "travel or cross through".
If I told you run a mile, and you run two miles, you've "traversed" at least one mile. The point is, infinity cannot be traversed, in the same way you can run a mile. You cannot run an infinite number of miles...Get it?
If you can't successfully count to infinity, how can a past-eternal universe successfully "arrive" at any current event X? Makes no sense.
Counting "to infinity" simply means counting and never stopping. Infinity is a direction, not a point.
In any case, that doesn't answer the question: what, exactly, is doing the traversing?
Right, the hypothethical situation that I gave does not reflect reality...I agree.
Then I shall discard your hypothetical situation as irrelevant: neither proving nor disproving anything on the table, and adding nothing of value to the debate.
I will ask you the same question I asked Sap...this time....I will use dogs....if you have two dogs as pets...one male, and one female...and they copulate, and give birth...would you expect anything besides a baby puppy? Yes or no?
'Course not. But if a dog and a coyote to copulate, you'd get something that's neither dog nor coyote: we call it a coydog. Same with jackals and dingos. Domestic dogs are a subspecies of wolf (wolves are
canis lupis, and domestic dogs are
canis lupis familiaris.)
And the common ancestor that
canis shares would have likely been able to interbreed with the common ancestor to
vulpes (foxes), even though they can't now, being completely different animals.
If you accept the existence of a single common ancestor (more likely several common ancestors interbreeding) to
canis and
vulpes, then you accept all the biological mechanics necessary for there to have been a common ancestor to both
canidae and
felidae. Now, you'd have to go back quite far, to be sure; domestic dogs are more closely related to bears than they are to cats. Bears and dogs, in addition to pinnipeds (which includes seals), and musteloids (which includes otters, badgers, raccoons, etc.), are grouped under
caniformia, or dog-like. The animals that fall under
feliformia, or cat-like, include animals I'm sure you've never heard of, as well as cats, hyenas, and mongooses. Both groups share a common mammalian ancestor, categorized as
carnivora.
All the children of any one generation of this
carnivora, would have been the same species. But those children would have been very slightly different. The children of those children would have been still slightly different. This is the case in modern times. Now, give about 100 years, and the initial parents we started with will likely have several hundred direct descendents, each with a degree of genetic variance. Give 1,000 years, and they wouldn't recognize their descendents as related in any way. Give 1,000,000 years, and many of those descendents would have such vast genetic variance, that not only would interbreeding be impossible, but they'd not even look the same. Just as we don't look the same as our ancestors from 1,000,000 years ago.
Since you've never denied that the Earth is 4.6 billion years old, with life appearing roughly 1-2 billion years ago(though there is still some debate about that), there's no reason why this can't extend far enough into the past.
If that's not enough, consider this: dogs are carnivorous, right? Well... not really, not anymore. Their diets nowadays consist of plenty of fruits and vegetables, which means that domestic dogs are, themselves, in a state of transition from full carnivore, to omnivore.
