Many years ago, some researchers at IBM came up with a design for an on-screen keyboard. They analyzed the QWERTY keyboard, the FITALY keyboard and a couple others, determining how fast someone could type on them. QWERTY scored lower than any other, around 30 wpm. Their keyboard scored > 40 wpm.
Details can be found here
They get into a long analysis of Fitts Law, which explains how long it will take to move from one character to another. It's logarithmically related the ratio of how far it is from one key to another to how big the destination key is. Based on this, they come up with a hexagonal pattern to make their keyboard more "dense" and arrange the characters such that the most commonly used transitions (digraphs/trigraphs) are as close together as possible.
They're assuming every key on their keyboard will have a unique symbol on it. That might work for something like a tablet, but it stinks on a modern smartphone. I can't use a traditional keyboard on mine. My fingers are too fat. I find myself getting a pretty good input speed with a compact- or T9-formatted keyboard. Larger buttons are easier to hit/more forgiving; more forgiving = faster, assuming that the text prediction software is any good.
Let's take another look at Fitts Law, again. The shorter the distance from one key to another, the faster you get there. No surprise, there. But it's inversely proportional to the size of the key. Bigger keys mean faster response.
What happens if you put two characters/symbols on each key? Can you just take their keyboard and squash 2 adjacent symbols onto the same key and depend on text prediction to make up the difference?
Their original design for the keyboard was nearly circular. After all, the shape with the shortest distances from random-point-a to random-point-b is going to be a circle. Joining multiple symbols into a single key is going to be problematic. Maybe joining 3 at a time would get the job done.
They also designed it with a single "space" button in the middle. This is because, within most text corpi, the space is the single-most-used symbol in the bunch. After all, it's used as the separator between each word, and some of those words (such as "I" and "a") are single letters. I'm thinking that rates either an oversized "space" area (as with the oversized space bar on hardware keyboards and the oversized "space" on most on-screen keyboards) or multiple "space" areas (as with the OPTI and FITALY keyboards).
I think it's time to re-do the analysis done in that paper, with an eye toward putting 2-3 symbols on each key. If you have a cluster of letters which are on the low-end of the frequency distribution, it might make sense to put them on the same key. Letters on the high-end of the frequency distribution might rate their own key. The whole idea is to get the number of keys down, so the individual sizes can be larger.
My biggest worry is that you'd end up with multiple of the vowels on a single key and the text prediction software would have a very difficult time figuring out which word you're attempting to input. I have no idea how to design the layout to make the text prediction more efficient. I know that it tends to be more efficient with a compact keyboard than with a T9 keyboard, because compact has fewer symbols / key.
Anybody have any ideas how to approach this?