Considering the progression of pattern through the A-Z alphabet, it's extraordinarily unlikely this has anything to do with letter frequency. It's instead quite clear that if the alphabet happened to be recited in a different order, these dots would have the same progression but assigned to different letters.
Have a look at the research behind the "fitaly" stylus keyboard for what goes into "taking letter frequency into account".
> quite clear that if the alphabet happened to be recited in a different order, these dots would have the same progression but assigned to different letters
That is very far from clear. If you'd think for a moment, you'd probably be able to come up with about 10 patterns that could have been used, that appear about as deliberate. As mentioned below, mappings with and without patterns (many more without) were considered.
If you think you've identified a better pattern, post it here. I'd be interested in seeing it.
http://esploded.s3.amazonaws.com/anon_data/2012/eyS/-dotsie2...
Vowels touch the top and bottom of the line, visually outlining the word and providing a sense of center (vowels also use the most dots, where consonants are sparse)
More common consonants use smaller (sparse) dot patterns getting denser as you get into less common (frequent) letters
More common consonants frame the center dot (to contrast the vowels which touch the edges/outside dots) using the less centered patterns as frequency decreases
All the glyphs fit into the 1x5 grid (the letter "Z" was 2 columns wide in the original)
Also worth noting: where possible I tried to make the glyphs memorable ("i" is the best example, followed by "o" and "z")
In retrospect, it may be a good idea to swap the glyphs of my current "B" for the "Y" since y is a semi-vowel it would touch both edges, where "B" has no reason to.
EDIT: here is a second attempt where ONLY vowels touch both edges, and Y is swapped (and touches both edges as a semi-vowel)
http://esploded.s3.amazonaws.com/anon_data/2012/e5YO-dotsie3...
Thoughts?
Not bad!
> More common consonants use smaller (sparse) dot patterns getting denser as you get into less common (frequent) letters
A few mappings emphasizing fewer dots for frequent letters (making for "sparser" words) were tried out and moved away from. The more speckled-looking words tend less to form concrete shapes and create "blocks" that stand out to the eye. If words are too dense you get similar issues, only in the negative. The optimum seems to be on the sparse side, but not overly sparse.
> Also worth noting: where possible I tried to make the glyphs memorable ("i" is the best example, followed by "o" and "z")
The original dotsies O and I are relatively memorable.
> More common consonants frame the center dot (to contrast the vowels which touch the edges/outside dots)
I could see how that could be interesting. How that would balance against the trade-off of ambiguity between similar letters (like s and t) would probably be hard to tell before one tried it.
I wonder if it would be worth coding up a page that lets people make their own mapping and preview them on some text, and posting it to HN.
Regardless of OP's protestations, the diagonal one dots, two dots, etc., have nothing to do with legibility and everything to do with alphabetic order mirrored in dot order.
Your system has both reason and rhyme.
00001 00010 00100 01000 10000 ... 10000 01000 11000 00100 10100 ... 00001 00010 00011 00100 00101 ... 10000 11000 11100 11110 11111 ... 01111 10111 11011 11101 11110 ... 10000 11000 01000 01100 00100 ... etc.
Now, why is it implausible that one or two of the many possible mappings with a pattern has tradeoffs about as good as the best of the many possible mappings without a pattern? Especially when the former have the pretty significant advantage out of the gate that the pattern makes them easier to remember.
Note that a valid critique of the many possibly mappings without patterns compared to the many possible mappings with patterns is that they are harder to learn.
If you put a lot of weight on the dots visually correlating to the numbers, see A, C, F, G, H, I, K, L, O, P, R, S, V, and X - all have a decent correlation.
BS. You don't read in alphabetical order. Just because you can reproduce the dot pattern doesn't mean you've "learned" it for its purpose. That the letter e comes between d and f is not relevant to trying to read.
Or, of course, they could just go through the pattern in their mind until they get to that letter, then they'd have it.
2^5 for a, times 2^5 - 1 for b, etc.
https://gist.github.com/1855582
tl;dr:
DOTSIES
Average density: 2.02
Vowel density: 1.52
Consonant density: 2.33
Average density: 2.78
Vowel density: 4.12
Consonant density: 1.96The current pattern doesn't suggest weighing of anything. You marched the dots down diagonally, first sets of one, then two, and so on. You mirrored alphabetical order with numerical dot order. You're now trying to justify that after the fact. It's not credible.
It's too bad you're choosing to argue instead of seriously considering the surprisingly thoughtful feedback several others have given you here.
For example, my point about FITALY was obviously not about the stylus movement. The similar dynamic isn't movement distance, the similar dynamic would be a statistical use of the legibility of adjacent dot columns. My point was the research that went into Fitaly:
"These figures are obtained using a corpus of digraph probabilities similar to that described by Soukoreff and MacKenzie (1995)... We have measured the frequency of letter-to-letter transitions for a representative corpus of the English language with several millions of characters. For example, this produces the number of times the letter o is followed by the letter a."
Given a dot matrix, there are a limited number of dot patterns. It's straightforward to measure the legibility of those dot patterns to humans of normal visual acuity (using mechanical turk for example), then to mathematically derive a letter assignment that maximizes legibility across, say, the Brown Corpus.
That would be something interesting to see.