You may have experienced the following phenomenon before: you are in a crowded, noisy room with many people talking at once. Suddenly, from across the room, you hear someone say your name and whip your head around immediately. They didn't shout your name, and you couldn't hear them talking before, but as soon as your name was spoken their voice "stepped forward" in your perception and you immediately started to pay attention to it. This is called the "cocktail party effect"

But, isn't this strange? In a manner of speaking, this sort of feels like you're predicting the future, doesn't it? You weren't listening to them talking before, but your brain begins to pay attention to them exactly when your name is spoken, as if you could tell in advance that your name was about to be spoken. What's going on here? Do you really have ESP?

As it turns out, this is not what is happening (alas! you will have to get your sick reads the same way everybody else does, without telepathy). The mechanism underlying this is called selective attention, and it is pervasive in a great deal of human perception. You just can't reasonably pay attention to all of your sensory input all at once, so your mind will automatically tune things out that aren't immediately necessary. This is why you rarely pay attention to how your clothes feel against your body, how your tongue feels in your mouth, your control over your breathing, how your feet feel against the floor, and - in the case of the cocktail party effect - what everybody in the party is saying, all at once.

But, importantly, you are still getting all of this sensory input. You can call any of it forward at any time, and it doesn't exactly go away when you stop paying attention to it. The explanation for the exact mechanism at play here has evolved with the research over time, but the 1000-foot view is that your sensory input goes through filtering before it ever reaches your conscious awareness. You hear a stream of auditory stimuli, your brain processes it, and then delivers to you what you thought you heard. By the time you are actually perceiving the audio, it has already happened, and your mind has quite literally stitched reality back together for you, which allows your name to "immediately" jump forward in a noisy room in your perception.

Put another way, real-time is not real-time.

Personally, I consider selective attention one of the craziest things about human perception because it highlights the relatively enormous gap between all of the sensory input you get and the narrow band of things you are actually perceiving at any given time. My absolute favorite example of this comes from Simons & Chabris 1999:

I wanted to introduce this idea of selective attention because it allows me to transition nicely into what might be the most important work in the scientific literature about understanding input latency perception: Spence and Squire 2003. Since we've nicely established that the human mind can operate upon sensory inputs before actual perception occurs, we can understand a bit more about how the human mind conceptualizes the idea of two things happening at the same time. Most people could tell you that light moves a lot faster than sound does (see: thunder vs lightning), but most people rarely think about why most things seem to have their audio and video components synchronized even if physics would tell us one comes a good amount after the other (e.g. someone talking to you far away).

Spence and Squire explored this idea called the "horizon of simultaneity". Simply put, when an audio and a visual stimulus occur near each other, if they are within this horizon then the human mind will quite literally re-synchronize them in human perception, a phenomenon they called "temporal ventriloquism". There is a relatively generous window for this to occur: it's around 100 milliseconds for most stimuli, and all the way up to 250 milliseconds for human speech. Longer than this, and you won't get the restitching effect (again, see thunder vs lightning).

This paper and our question differ a little bit - Spence and Squire deal with audio/video disparity and we're interested in audio-visual/visuomotor disparity. However, it's important to understand this paper since it's critical to understand what is happening "under the hood" when people think two things are synchronized. If you cannot tell that lag exists in your task, then your mind has successfully literally reordered them to be synchronized again, which is part of why the discussion on this topic within SSBM is so heated. If you can't tell that there is any lag, that is in large part because your mind has literally warped reality to resynchronize these two things for your convenience, irrespective of the presence of any lag.