If you are waiting for the light to change you may be caught off guard if it changes quickly. As time goes on you have a greater chance of ANTICIPATING the change. If there were numbers (proportional to time) that tell you when the light will change you will more likely be caught off guard for the larger numbers.
This finding (from my own research) is called an interaction. It is so strong an effect that it is an order of magnitude higher than the average statistical interaction in psychology research.
Planting an explosive in a building about to be hit by a airplane (with the purpose of magnifying the destruction without the detonation being observed) poses problems for the detonator (presumed to be human). If the explosion happens well before the airplane hits or well after this will result in detection. The timing has to be almost perfect.
Taking into consideration this problem of anticipation a well trained operator will detonate the explosive a VERY short time before the airplane hits.
When I studied this problem I became experienced with many different experimental conditions (especially when a pay-off variable was added.)
Because of this I was able, when observing experimental runs, to deduce the experimental problem in many different cases.
When I first saw one of the planes crashing into one of the towers I had no idea that an explosive may have been planted in the building. But I perceived what seemed to be an explosion slightly before collision.
But this perception is vulnerable to error.
When salient events occur very closely together they "cascade" in the visual system. So what happened before actually happened after.
(if you are interested in looking up related research (I did not publish my own) then find "warning foreperiods and reaction time"