Going Beyond the Rule of Thirds
At some point, every photographer learns about the Rule of Thirds. And for better or worse, from that point on, their work will exist in some relationship to that fact.
My first experience with using a camera came when I was a young kid. I remember being told to point the camera toward the subject. For that, it was convenient that the viewfinder had a target in the center I could use for aiming. That made it made it easy and gave me a way to hold the camera steady. All I had to do was to keep whatever it was I was focusing on lined up with that bullseye. That's the way it had to be done back then. The sensors in the camera for both focusing and metering were situated on that central point too. If you wanted the sharpest focus you had to point that spot at your subject. If you wanted to get accurate exposure, that central cross hairs mattered. Yes, it was possible to use those viewfinder markings to help achieve accurate focus and exposure and then lock them in before recomposing, that made things more complicated. More often than not, based on both the way I was taught as well as the mechanics of how the camera operated, all of my images had a similar composition. To the best of my ability, all of my early images had the subject centered in the frame.
And why not use the Rule of Thirds? Experts long ago had determined that this created a pleasing division of space in the frame, right? Well, not really.
This whole thing goes back to the ancient Greeks. It probably predates even that but there's a lack of written records prior to around 2500 years ago to really say for sure. But at least by the time of Euclid and Pythagoras, the idea of the "Golden Ratio" was well established. The belief that certain shapes revealed the underlying order of the universe had accepted since Plato a century before. Two distances are said to be in the golden ratio to each other if larger of the two divided by their sum gives the same result as is obtained by dividing the smaller distance by the larger. The ancient Greeks were all about inferring special meaning in the patterns of nature, and things in this proportion fit together well when building temples. And so people grew to believe they looked nice with that ratio.
If getting your mind around just what such golden proportions actually look like, you're not alone. They work out to be similar to the Rule of Thirds, but the lines fall somewhat nearer to each other, and therefore the "power point" intersections lie closer to the middle of the frame in the Greek version. It's generally understood that the Rule of Thirds is a simplified version of the Golden Ratio.
What both come down to though is the basically the same thing. An image composed around equal divisions results in an overly formalistic, relatively static image with the subject at the center. Placing the subject off-center in some way results in a more dynamic composition that appears to have a sense of movement and feels more natural. It's the same lesson every photographer comes to know when someone tells them about the Rule of Thirds. The exact ratio isn't really what matters, so long as it's not dividing things right down the middle. An object centered left to right, but visibly above or below center, will still appear relatively static, making it perhaps not quite so taboo but still less than ideal. Placing your subject too close to the edge of the frame appears awkward too, but most anything that avoids the extremes of the center and the edges can work quite well, with the subject itself guiding your exact placement.
So what you're left with is a rule that discourages placement at or near the center in either or both dimension, as well as placement too close to any edge of the frame. The Rule of Thirds thereby becomes less something to be achieved as it is a guideline of what to be avoided. The exact details as to thirds or golden ratios isn't overly relevant. The whole thing boils down to the observation that off-center compositions that also don't crowd the edges can help make your images look better. So why don't photography teachers just say so?
There's a common saying that tying a string around your finger can help you remember something. It may work, but I've never personally tried it. It seems like it would only serve to get in the way. But perhaps that's the point. The constant irritation of that string might perhaps remind you that you were supposed to remember something, assuming you knew what that something was in the first place. Perhaps the best way then to think about the Rule of Thirds is consider it like that string around your finger. So long as you remember what it's trying to tell you, you're in good shape, and you can move beyond the literal details and go by feel. Thinking about that tic-tac-toe grid can function as a reminder to avoid the middle and the edges of the frame. If it does so, it's done its job, and you can move beyond it. But if you don't know what it's trying to tell you, it can easily get in the way, just like a string tied around your finger.