# Tamil Entry via Keypad – 9XYZ30-த-மி-ழ்

Previously, My initial calculations can be revised in terms of the estimates. I will not go into further detail here; my latest estimate shows the number of realizable keyboards to be 264,250,749,803,040 or 264billion – a bit of an astronomical number.

The money questions are the following:

1. Given the astronomical size of keyboards possible is there one that is easily decodable than the other ? Yes, or no ?
2. Is there any decodable keyboard at all?
3. Is there a ‘1-800-FLOWERS‘ type of representation possible atleast for a few words in Tamil ?

Today, I was toying with some simple designs and made it into software:

One particular realization of the keyboard looks like where 20 Tamil letters are roughly mapped into 1 keypad as shown in the excel sheet below. We also see the canonical 4×3 keypad matrix in the rows 20-23 showing the 12 keypad positions where 20 letters are going to be mapped into.

We show how the phone number “9XYZ30477” will mean “9XYZ30-த-மி-ழ்” in this keypad.

Immediately few things are coming to our attention:

1. Entering user input in the keypad is easy; we follow a simple natural language suggested representation
2. However, we have some issues in realizing this keyboard – ambiguity: Does ‘111’ in this keypad entry, with following mapping shown, mean ‘அக்கா’ or ‘கட்சி’ ?
3. The “obvious” finite ring keypad mapping fails here.

Realizations:

1. Whereas a simple keyboard realization of this scheme shows words typed of equal length like ‘அக்கா’ and ‘கட்சி’ are completely undecidable/un-decodeable. So our criteria is really the good realizable keyboard maximizes the word decidability, or minimizes word collision.
2. Ease of user input:
Also we may want to make ease of user entry into this keyboard simpler [which the ‘obvious choice’ keyboard contains] while still maintaining the decodability.
3. We identify the mapping used above with a simple algebraic structure similar to a finite semi-group with operations of commutativity, in-group operation and identity formed by ‘ஃ’ ayutha letter. This is a interesting mapping with potential to adapt the operator for creating a full semigroup or group structure for the language.
4. Finally we discover:

The letters with the high bi-gram frequency may not be co-occurring in the same keypad square. This is an operational principle that will reduce the ambiguity of the model. We will have to balance this with other decidability criteria of user input etc.

Operating Principle – we understand this from our failed experiment.

This type of keyboard design could also equally apply for other Abugida languages – which is most Indian languages.