Now a guy comes along who knows nothing about tides and he measures the height of the water, just as the tide is highest. He comes back three days later as the tide is a little past the highest point and measures again. He comes back three days later and measures it a little lower. After collecting data this way for two weeks, he draws a graph of his measurements. His data points descend in a slow curve called a sine wave, starting at the top most point. Over the two weeks, he'll see that he's just reached the bottom point, and he'll conclude that the tide takes four weeks to rise and fall. Subsequent measurements on the same schedule will confirm this mistaken notion.
The tide doesn't take four weeks to rise and fall, it takes about 12 hours. This guy has run into aliasing, where sampling too infrequently makes the frequency look incorrect. This is a well-studied topic in signal processing and the solution is to make measurements much more often. To accurately describe the tide, he needs to make measurements at least every six hours.
Now imagine a cat watching a mouse hole, waiting for a mouse to emerge. The cat crouches motionless, maybe for hours, only his tail very slowly swishing. When the mouse finally comes out, the cat jumps forward faster than you can blink and catches the mouse. The cat is completely attentive and undistracted, every millisecond, until he's caught the mouse.
The sampling rate of the cat's attention is important. A cat who looks at the mouse hole every three days has no chance of catching the mouse.
Thoughts arising in awareness are like the mouse. They're quick. You don't ordinarily notice them until they are already present. When you watch thoughts arising in your awareness, you want to be like the cat, with unbroken attention every millisecond.
When you watch your breathing, check to see if you're attentive the whole time. Do you notice the start of the in-breath and then zone out until the end of the in-breath? If yes, where else does your attention go? What are the mechanics of its going elsewhere? What kinds of things attract it away?