But the first time through they made no attempt, because they didn't know they were going to be destroyed. Thus they would not have turned back.
They can't know that for sure. There would be any number of reasons why they could have made an odd course change the first time around, leading to their destruction. Odd course changes is what starships do for a living!
But if taking a certain course is the thing that leads to destruction, then the odds of one getting destroyed are extremely low no matter what the course. After all, there are an infinite number of courses available!
Yet our heroes know that there is a time loop there. It's extremely unlikely, then, that the course they take would be of any consequence, because if the loop really is course-dependent, then only one choice out of an infinite number will create the loop.
So logically, our heroes should decide that course is of no consequence. It is weird and unusual and against all odds, then, that the loop in the end is revealed to be not only course-specific, but course-specific to the centimeter!
Of course, yes, admittedly, all right, by not turning at all, one
is choosing a "special" course that has higher odds of being chosen than any of the others, in a repeat sample. But as said, for our heroes in the n'th loop, it must appear likely that deviating from this course has been attempted at least once before, and it hasn't helped at all.
I see this as contradicting the episode.
Sure. But the nature of the time loop in the episode takes our heroes quite justly by surprise - they could not have known that deviating from their course would be the right choice. The episode features an exceptional and unlikely time loop that in "reality" should have zero odds of happening, because it depends on centimeter/millisecond accuracy of events, and yet we know each loop is different in subtle ways. Our heroes would know how exceptional and unlikely a loop of this very sort should be, and thus not bet their lives on that. Not lightly, anyway.
Stop where the ship's at, launch a few probes or remote controlled shuttles, and just wait and see. That's the first thought that went through my head.
That wouldn't have achieved anything in either "Cause and Effect" or "Time Squared", though. Space is too big for that.
Besides, they know at what point the echoes started, just back up in a straight line till the echoes go away and the slowly swing wide around your old course or just sit and wait and see.
The former ought to work fine. The latter would apparently involve sitting for all eternity, which a starship cannot afford to do!
Timo Saloniemi