Ponderation sounds like a good word ot me...especially on a Sunday.
But I must admit I don't understand the question. What opposite is it you want to achieve?
Do you mean decreasing your velocity so that you are completely still, in regards to every possible observer frame and time system?
If so, I think it would be a tough task since, considering the expansion of the Universe, you'd be hard pressed to find aby spot in the Universe which is absolutely still. And if you try to decrease your velocity by matching the velocity of the expansion, you are merely moving along with it. If you try to go slower than it, you are simply moving away form the center of the source of expansion at a slower rate - in order to move towards it you will have to accelerate to a speed faster than the rate of expansion.
Gödel postulated that if the Universe is rotating, there could be time loops. But even here I don't think the point was that one could come to a complete stand-still, you will *always* be moving in reference to something.
(And let's not even start thinking about the Multiverse theory where our Universe is just one of many...)
But I am merely rambling here...maybe you could rephrase your question? Opposite to what?