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T9-QWERTY: The Ultra Efficient Minimal Motion Keyboard Layout

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THE LAYOUT

     a     s     d      f      v         j      k     l      ;
    cyk   su   thj   evw  nbz      adf   olx  img   rpq

Select/conflict resolution keys:
m: select second word
i: select third word
o: select fourth word

Finger positions are as standard, except for "nbz" on the v key which can be pressed with the left thumb (right thumb for spacebar).

HOW TO BEGIN

To begin practicing the layout, you can use the 10FastFingers typing speed test or this alternative test. You will first need a text replacement program.

1. Download and install Phrase Express. During setup you are asked to Select Components. Uncheck the box that says 'Install sample phrase library' if present.
2. Download and install the practice file T9-QWERTY. Choose the "Load as an additional phrase file" option.

Let's try typing "really". Follow the layout and you have ";-f-j-k-k-a". Press each key once just as with normal typing. Some words conflict with others. To resolve this the most frequent word is typed using the normal letters, while to type the second most frequent word you would type "m" at the end of it. For example, "good" and "gold" conflict, but "good" is more frequent than "gold". So to type "gold" you would type "lkkjm".

Conflicts in the practice file are shown below with the leftmost word being the more frequent:

good > gold
round > pound
told > hold

BACKGROUND

I started off interested in learning stenography using Plover for high speed transcription. I recalled that a dictionary based input was also used on my old Sony Ericsson mobile phone, making it much more efficient to send text messages. I was aware of alternative keyboard layouts, being a touch typist with QWERTY and having also learned the Dvorak layout. I found that the alternative layouts such as Colemak claimed that by reducing motion they could increase speed and comfort. Whilst I was not convinced of the validity of this assumption I realised that a reduced key dictionary based input ported to a normal PC keyboard, an idea which has been considered previously, would reduce motion to a greater degree while still allowing the user to use the familiar QWERTY layout input when required, if used with a text replacement program.

On such a layout each key represents multiple letters and resulting ambiguity is resolved by 'select' keys, with the most frequent word being the default output.

IMPLICATIONS

- Reduced motion: 95% or more typing is done on the home keys
- Wearable computing: eye tracking devices, wristwatches, gloves
- Accurate and easier typing on a touchscreen
- One handed layouts
- Typing on any surface
- Less to learn than with a chording system such as ASETNIOP

WHY THE NAME "T9-QWERTY"?

T9-QWERTY takes the name "T9" from its use of only 9 keys for the letters, and "QWERTY" because of the fact that it can be used alongside QWERTY. Given the low number of words that can be typed on QWERTY's home row, a clash between the two layouts is unlikely. When you want to type a word that isn't in its dictionary you can fall back on normal QWERTY.

TAGS

T9, T9 for PC, T9 on PC, T9PC, T9 PC, T9-PC, PCT9, PC T9, PC-T9, QWERTY-T9, QWERTY T9, T9 QWERTY, QT9, T9Q, Minimum Motion Keyboard Layout

SLOGAN

"Revolutionizing the way you type"

LAYOUT VARIANTS

     q     w     e      f      v         j      i     o      p
    cyk   su   thj    evw  nbz      adf   olx  img   rpq

This variation places the middle, ring and small fingers on the top letter row which some users may prefer.

Single handed variants for both left and right hands and for the numpad may be useful for persons lacking use of one hand, or to allow one hand to type while the other controls the mouse. These layouts do not require uninstalling two-handed T9-QWERTY, and with practice the user can seamlessly switch between either.

Left hand:

    q      w     e      r
   rpq    img   olx   adf

     a     s     d      f      v       
    cyk   su   thj   evw  nbz     

Right hand:

        u      i      o     p
       evw   thj   su   cyk

    n      j      k     l      ;       
   nbz   adf   olx   img  rpq     

Numpad:

       7        8        9
      rpq     adf     nbz
       4        5        6
      olx      ewv     img
       1        2        3
      cyk      thj      su
             0
          Space

Letters from each column of the traditional layouts can be grouped onto the respective homerow keys, to create a derivative reduced key ambiguous layout shown below. Transition to such a layout may be easier as letters stay on the same fingers.

QWERTY:

     a       s      d      f      g        h       j      k     l      ;
    qaz   wsx   edc   rfv   tgb      yhn    ujm   ik    ol     p

Dvorak:

     a     o      e      u      i         d       h       t      n      s
     a     oq     ej    puk   yix      fdb    ghm   ctw   rnv   lsz

Colemak:

     a       r      s      t      d        h      n     e      i      o
    qaz   wrx   fsc   ptv   gdb      jhk    lnm   ue    yi     o

UPDATE LOG

-Addition of select keys for simultaneous use as delimiters
-Addition of space to phrase content of words requiring select keys
-Removal of trailing delimiter for select keys
-Removal of apostrophe and semicolon as postfixes
-Layout renamed from "QWERTY-SUX" to "T9-QWERTY" and letter arrangement updated (03/01/2014)
-Single hand variants added (05/01/2014)
-Glossary and images added (16/01/2014)

ACKNOWLEDGEMENTS

Christopher L. Sholes, the inventor of QWERTY
Martin T. King, Dale L. Grover, Clifford A. Kushler, Cheryl A. Grunbock, the inventors of T9
Bartels Media GmbH for their PhraseExpress software
pinkyache from the Colemak forum for his suggestions and being the first to try the layout

REFERENCES

Grover et al. (1998). Reduced keyboard disambiguating computer

King et al. (1999). Disambiguating system for disambiguating ambiguous input sequences by displaying objects associated with the generated input sequences in the order of decreasing frequency of use

SEE ALSO

Sentence reconstruction using word ambiguity resolution and Minimum Motion Keyboard
Plover for stenography on a QWERTY keyboard
QWERTH, a 15 key input for Android devices
ASETNIOP, a 10 point input for typing on any surface

DO YOU HAVE CODING SKILLS?

If you are interested in helping me with this project, I would like to hear from you. Plans include implementation of a full English dictionary, a personal dictionary which automatically learns new words typed with QWERTY, an independent program with a single install file, progressive word stems displayed as you type, an autocomplete function, and a context sensitive predictive algorithm to eliminate the need for manual conflict resolution by the user.

GLOSSARY

To prevent confusion, below are a list of related terms and my definition of them:

Multitap is the typing of a desired letter by pressing the key a number of times corresponding to its position on a key. On T9-QWERTY, QWERTY takes the place of Multitap for unambiguous input.

T9 stands for Text on 9 keys, but the same system could be used on a layout with any number of keys. It's just an easier way of saying "word disambiguation." Unlike multitap, you press each key once.

A conflict or ambiguity is a sequence of keys that spells multiple words. They are resolved by select keys.

T9-QWERTY is my idea to port T9 to a QWERTY keyboard to reduce motion.

Prediction in the sense I use it is the system that based on the context of a word automatically chooses the most likely word, and may also predict words ahead. It can also be used to mean autocomplete and autocorrect. To prevent confusion it should not be mixed up with "word disambiguation". Prediction has not yet been implemented. It can be seen as either good or bad.

Word stems are partial words.

Phrase Express is a text replacement program I use to implement T9-QWERTY.

IMAGES

Early prototype of T9 with the optimized arrangement, from validconcept.com:

justtype.gif

A Sony Ericsson mobile phone with the widely used alphabetical arrangement:

small_006.jpg

Illustration of T9 adapted to a wristwatch from the original documentation:

t9watch2.png

Last edited by shaaniqbal (02-Feb-2014 03:21:50)

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This sounds an awful lot like the T9 function I had on my ancient cellphone. There is a reason though that phone-keyboards slowly shifted towards a full keyboard instead of T9 though.
What speeds are you achieving with this layout?

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@lite245, sorry, can you explain the layout?  I don't get it from the graphic.

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Thanks for the feedback. I'm at 30 WPM, 170 keystrokes, 150 correct and 20 incorrect, and 4 wrong words, tested just now after about 3 weeks of practice on 10FF now and then. I am of course interested in seeing what speed I will reach with time and will post results on the other thread.

Yes pinkyache. On top are the actual keys on your keyboard, and below are the letters they correspond to for the word you want to type. The graphic might not be aligned properly depending on your browser, so this might make it clearer:

a: bkn
s: jlo
d: ptv
f: dhi
v: cyz
j: afg
k: ew
l: sux
;: mqr

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I still don't understand how this layout works.

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Oh I see.  We're comparing bananas with guavas.

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To quote myself: Word prediction only works if you're predictable. I'm frequently not. :)

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DreymaR said:

To quote myself: Word prediction only works if you're predictable. I'm frequently not. :)

Thanks for the feedback DreymaR. There is currently no prediction feature for the layout. The same input will always produce the same output text. However I would like to implement an autocomplete system in the future.

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koekjestrommel1 said:

This sounds an awful lot like the T9 function I had on my ancient cellphone. There is a reason though that phone-keyboards slowly shifted towards a full keyboard instead of T9 though.

If anything there's increasing demand for phone keyboards to shift back towards reduced-key keyboards. Hence emerging keyboard applications such as MessagEase, Dasher, Minuum, QWERTH, ASETNIOP etc.

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A couple questions, I guess.

Most importantly, is there any way to try this in Linux?

It seems to me the one major missing feature is chords.  Chords could possibly be used to make the typing unambiguous (satisfying the likes of Dreymar and, to a lesser extent, myself), for example by using key k + any two presses on opposite hand to mean "the letter above k", and k + any three presses to mean "the letter below k".

How do you get the current T9 scheme to be compatible with programs like vim, or with general shortcuts?

Last edited by lalop (05-Jan-2014 05:38:18)
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lalop said:

A couple questions, I guess.

Most importantly, is there any way to try this in Linux?

Thanks for the feedback lalop.  You just need a text replacement program. I don't use Linux, but Googling "text replacement linux" brings up AutoKey. Add the words you want to the text replacement program with the corresponding autotexts.

lalop said:

It seems to me the one major missing feature is chords.  Chords could possibly be used to make the typing unambiguous (satisfying the likes of Dreymar and, to a lesser extent, myself), for example by using key k + any two presses on opposite hand to mean "the letter above k", and k + any three presses to mean "the letter below k".

Thanks for the suggestion. Chords scripts are possible with programs like AutoHotKey, I'm sure it could be configured the way you want. And then you have ASETNIOP which is made for chording, maybe the developer would be willing to add a T9 function to it.

lalop said:

How do you get the current T9 scheme to be compatible with programs like vim, or with general shortcuts?

Shortcuts are unaffected.

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shaaniqbal, I took a look, and I don't think it's a viable layout. Some of the reasons are:
* There's no incentive to switch
* Slower
* RSI prone, as it requires more keypresses
* Most new typing solutions are made to address issues with typing on mobile devices. The layout is unusable on mobile devices.
* Can't use shortcuts in this mode, which means you have to have two keyboard layouts in your head
* Unsuitable as multi-purpose keyboard (e.g. won't work with Vim, games, remote desktop, etc)
* As this can't be used as the only keyboard layout, it means that you always need to remember in which mode you're in, and switch back
* Error correction is very time-consuming
* It's unsuitable for touch typing, you have to look at the screen all the time

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Thanks for the feedback Shai. I'll address each of your points and if there's anything you don't understand, let me know.

Shai said:

shaaniqbal, I took a look, and I don't think it's a viable layout. Some of the reasons are:
* There's no incentive to switch

There are enormous implications for reduced motion and one handed layouts.

* Slower

Why would it be slower?

* RSI prone, as it requires more keypresses

What made you think that? The whole point of T9 is that it doesn't require additional keypresses to normal typing.

* Most new typing solutions are made to address issues with typing on mobile devices. The layout is unusable on mobile devices.

Actually, T9 originated on mobile phones and was used by thousands of consumers. Many of the new keyboard applications attempt to similarly reduce the number of keys.

* Can't use shortcuts in this mode, which means you have to have two keyboard layouts in your head

Keyboard shortcuts are unaffected, as I've said before. Ctrl + C, Ctrl + Z etc. still work as normal. These are already bound to your muscle memory anyway, so you won't need to consciously think about them.

Having two or more layouts in your head is not difficult at all, in my experience, provided they are somewhat different to each other. I switch between Plover (stenography), QWERTY longhand, QWERTY shorthand, Dvorak and QWERTY-SUX (the older version) all the time without issue. If anything it's even fun. When I get bored of QWERTY I switch things up with Dvorak. I often find my speed improves in either layout by alternating. Although if you start off with the idea that your brain can't manage more than one layout, you probably will face difficulty just by the nocebo effect. It's not different to learning a new language, you don't suddenly forget the old one.

* Unsuitable as multi-purpose keyboard (e.g. won't work with Vim, games, remote desktop, etc)

Games are unaffected (wasd etc. will still work). Vim shortcuts stay the same. It's only when you're typing actual words that the T9 will come into play.

* As this can't be used as the only keyboard layout, it means that you always need to remember in which mode you're in, and switch back

Unless you are constantly typing new words that aren't in its dictionary, it very much can be used as the only keyboard layout. T9 will only work with whatever words you give it. If you give it a full English dictionary, you'll have a full English dictionary. If your typing style contains strange words you would ideally be able to "feed" it samples of your writing such as emails, etc. so that it learns your words automatically.

You are in both modes, T9 and QWERTY, at the same time. Hence the name T9-QWERTY. There's no need to switch between them.

* Error correction is very time-consuming

With progressive word stems displayed as you type, this would not be such a problem.

* It's unsuitable for touch typing, you have to look at the screen all the time

Not at all. Provided you can spell correctly, you simply remember mentally where you are in a word as you go along. You don't need to look at the screen for that. That is one requirement of the layout though - you need to be able to spell. Autocorrect could be added in the future.

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To clear some confusion about the terms used with this layout, I wrote a short glossary:

Multitap is the typing of a desired letter by pressing the key a number of times corresponding to its position on a key. 

T9 stands for Text on 9 keys, but the same system could be used on a layout with any number of keys. It's just an easier way of saying "word disambiguation." Unlike multitap, you press each key once.

A conflict or ambiguity is a sequence of keys that spells multiple words. They are resolved by select keys.

T9-QWERTY is my idea to port T9 to a QWERTY keyboard to reduce motion.

Prediction in the sense I use it is the system that based on the context of a word automatically chooses the most likely word, and may also predict words ahead. It can also be used to mean autocomplete and autocorrect. To prevent confusion it should not be mixed up with "word disambiguation". Prediction has not yet been implemented. As DreymaR suggests, it can be seen as either good or bad.

Word stems are partial words.

Phrase Express is a text replacement program I use to implement T9-QWERTY.

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Shai said:

* There's no incentive to switch
* Slower
* RSI prone, as it requires more keypresses
* Most new typing solutions are made to address issues with typing on mobile devices. The layout is unusable on mobile devices.
* Can't use shortcuts in this mode, which means you have to have two keyboard layouts in your head
* Unsuitable as multi-purpose keyboard (e.g. won't work with Vim, games, remote desktop, etc)
* As this can't be used as the only keyboard layout, it means that you always need to remember in which mode you're in, and switch back
* Error correction is very time-consuming
* It's unsuitable for touch typing, you have to look at the screen all the time

Hmmm. I don't quite agree on all of that:
• The incentive might be that you can use it on a normal keyboard *or* on a special keyboard with only a home row?
• I don't think it *has* to be slower (with prediction, which I don't like)? Probably a bit work to learn though? Then again, what isn't?
• More keypresses aren't bad per se as I can attest to as a frequent flyer of Extend mappings. May be good for some, bad for some I guess.
• New typing solutions for touch screens need to be radically different from old keyboards anyway. I recommend MessagEase, but KeyMonk seems okay for the T9 types. New solutions need to accommodate the power of sliding versus the less pleasant tapping on touch screens!
• Shortcuts could probably be baked in somehow? But it'd be a not too portable solution I guess (as addressed later).
• Multi-purpose: I agree that it seems inflexible. I prefer your/our way of improving what we need/want to on the keyboards we meet everywhere.
• The mode argument sounds a bit strange coming from a Vim user... ;) – again, it'd be a matter of taste and not for everyone.
• Error correction can be very disruptive, I agree.
• I agree that my experiences with T9 on phones doesn't allow for blind typing. Loss there.

• My biggest gripe is that multitap sucks big time for me. I hate same-finger digrams and I'm very happy with Colemak having a low frequency of those.
• Also, under no circumstances will I use predictive software as that always becomes more of a disruptive nag than a real help to me.

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As a pianist (albeit an amateur one), I must say that pianists constantly fight stress conditions and from a number of problems. I don't think the lots and lots of hand movements does us any good as such. But I do dislike having to press the same key several times in a row! Then I'll usually alternate between three fingers instead.

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DreymaR said:

Hmmm. I don't quite agree on all of that:
• The incentive might be that you can use it on a normal keyboard *or* on a special keyboard with only a home row?

Yes. Nowhere in my original post did I make any mention of the need for a special keyboard. The whole point is that you use it on your normal QWERTY keyboard. Just follow my instructions.

• I don't think it *has* to be slower (with prediction, which I don't like)? Probably a bit work to learn though? Then again, what isn't?

With word disambiguation, it is just as fast as regular typing. There's very little to learn except the bearing in mind of conflicts.

• More keypresses aren't bad per se as I can attest to as a frequent flyer of Extend mappings. May be good for some, bad for some I guess.

No extra keypresses are necessary, as I have repeatedly made clear. That's the whole point.

• Shortcuts could probably be baked in somehow? But it'd be a not too portable solution I guess (as addressed later).
• Multi-purpose: I agree that it seems inflexible. I prefer your/our way of improving what we need/want to on the keyboards we meet everywhere.

Shortcuts are unaffected. Please read my response to Shai where I explain this.

Phrase Express is very much a portable software.

• I agree that my experiences with T9 on phones doesn't allow for blind typing. Loss there.

T9-QWERTY absolutely does allow blind typing. If anything it's easier as there are fewer key positions for a beginner touch typist to remember. Just follow my instructions and try it.

• My biggest gripe is that multitap sucks big time for me. I hate same-finger digrams and I'm very happy with Colemak having a low frequency of those.
• Also, under no circumstances will I use predictive software as that always becomes more of a disruptive nag than a real help to me.

As I've explained in my glossary, multitap and T9 are two different things. And T9 is separate from prediction.

The fact that not one person who has responded so far has bothered to try the system is interesting. Whilst I appreciate your responses, if those commenting would at least bother to try it, a lot of the confusion would go away. The instructions have been made as clear as possible. Make sure your layout is set to QWERTY before you try it though.

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It's a very good point and I apologize on all our behalfs that we haven't bothered to spend the time to try it before voicing opinions. However, for myself I can say with near certainty that I won't be spending that time and effort unless I first understand the purported benefits better (and happen to agree with your assessments of them). So I'm afraid you'll just have to sell it again, friend. ;)

Last edited by DreymaR (08-Jan-2014 15:59:09)

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shaaniqbal said:

The fact that not one person who has responded so far has bothered to try the system is interesting.

Not really; I was unable to get autokey working and subsequently got distracted =/

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DreymaR said:

It's a very good point and I apologize on all our behalfs that we haven't bothered to spend the time to try it before voicing opinions. However, for myself I can say with near certainty that I won't be spending that time and effort unless I first understand the purported benefits better (and happen to agree with your assessments of them). So I'm afraid you'll just have to sell it again, friend. ;)

Thanks DreymaR. I'll try to expand on its implications in the original post. Very little time or effort is needed if you just want to try it out and see how it works though.

davkol said:

You've never tried to use the (in)famous T9 on your old nokia? O_o Nor read those funny stories about embarrassing autocorrections?

Not all T9 is made equal. Some versions are poorly implemented just as with any system.

lalop said:
shaaniqbal said:

The fact that not one person who has responded so far has bothered to try the system is interesting.

Not really; I was unable to get autokey working and subsequently got distracted =/

That's a shame. Let me know if you get it working.

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davkol said:
shaaniqbal said:
davkol said:

You've never tried to use the (in)famous T9 on your old nokia? O_o Nor read those funny stories about embarrassing autocorrections?

Not all T9 is made equal. Some versions are poorly implemented just as with any system.

T9 is one particular implementation of predictive texting. The name is an acronym, it stands for "text on 9 keys".

Other implementations include e.g. Xrgomics TenGO.

And there are various implementations of T9. T9 as I use the word, for clarity, is a form of word disambiguation and is unrelated to prediction.

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davkol said:

I don't think we share the same definition of predictive texting.

Precisely, we do not. Which is why I wrote the glossary (see a few posts back) to distinguish my meaning of the terms. The inventors didn't name it  "T9 predictive text". That was a marketing term they stuck with as it was easier to sell than "disambiguation". See the section titled "Discoverability and Training" in the article T9: Text on Nine Keys, last three paragraphs.

I quote, "after T9 became a differential advantage for mobile phones a leading manufacturer started calling the feature "predictive text" generically. We were rather concerned by this because the system only disambiguated complete keystroke sequences and did not predict the completion of words. [18] But, lacking a more marketable term than "disambiguation", Tegic's product management eventually accepted this de facto term describing the market niche."

Unlike "prediction", T9 is not context dependent. The same input will always give the same output.

Prediction and T9 are of course often found together in their implementations. This for instance is another implementation of T9 that includes predictive text.

An Android keyboard such as SwiftKey contains predictive text but does not contain T9.

Also, T9 is technically an implementation of the US Patent 5,818,437

As I understand it, Shai stated that software patents don't apply in Europe. See his 4th post down here, maybe he can confirm that. I believe that patent is expired as they last 14 years.

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davkol said:
shaaniqbal said:
davkol said:

I don't think we share the same definition of predictive texting.

Precisely, we do not. Which is why I wrote the glossary (see a few posts back) to distinguish my meaning of the terms. The inventors didn't name it  "T9 predictive text". That was a marketing term they stuck with as it was easier to sell than "disambiguation". See the section titled "Discoverability and Training" in the article T9: Text on Nine Keys, last three paragraphs.

Actually, that's not the problem. I don't mistake predictive texting for autocomplete or autocorrection.

You mistake predictive texting for T9. Whatever your definition of T9 is, I don't care. I have stated my definition, which is relevant to this specific thread and layout.

The thing is, if you have more symbols per key and press a key only once, the symbol has to be chosen somehow. It can be based on lexicographical ordering, some kind of statistics... but that's *not* intuitive/obvious *to the user*. Otherwise, the countless "typos" would have never happened. That's the point.

Precisely. When you assign multiple letters to a key, the most frequent word from a sequence of keys is presented first. In my layout, pressing spacebar automatically chooses that word. To choose the next most frequent word, a select key is used (m, i, o).

It can be made obvious to the user which key they should press by a list that could be displayed. After a user types a word so many times, they associate it by muscle memory and don't need to rely on the on screen cue.

A poor implementation of T9 results in "typos", such as the alphabetical arrangement. A strong implementation reduces conflicts to increase the frequency that a desired word is at the top of the list.

shaaniqbal said:
davkol said:

Also, T9 is technically an implementation of the US Patent 5,818,437

As I understand it, Shai stated that software patents don't apply in Europe. See his 4th post down here, maybe he can confirm that. I believe that patent is expired as they last 14 years.

It's way more complicated. Nevertheless, the point I was trying to make was different, i.e. T9 was a *product*, not some abstract class of input methods.

Perhaps then you should explain it to us.

T9 may have been a product, but given its popularity it may also be understood to mean the disambiguation process by which keys with multiple letters are associated with a single word. Like the word "hoover", which is one brand that sells vacuum cleaners. But most people just call them hoovers. It's easier. Unless you wanted to be more specific, in which case you would say "the Dyson vacuum cleaner".

Many people associate "T9" with "predictive text", which I why I have highlighted the differences in this thread for what I refer to. I call my layout "T9-QWERTY" because it essentially works exactly the way T9 is described by its inventors.

Initially I called the layout "QWERTY-SUX" to eliminate that confusion and rid it of any association with predictive texting. I later found a superior arrangement that didn't have a funny letter grouping, and so renamed it. People who responded to the thread called it T9 anyway, prior to me even using that word.

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The name is "T9-QWERTY", not "T9". If you can think of a better name, I'll consider it. If Nuance contacts me to remove the layout, by all means I will. Given the enormous potential the layout has, though, that would be a shame.

I don't have experience, no. Which is why I've asked for anyone with coding experience to contact me. It shouldn't be difficult to implement. For now, one can simply remember the three conflicts in the practice file, while practicing on a site like 10FastFingers to get a feel for the layout.

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Of course it's possible. You're just displaying a list to the user from which they are shown the words and associated select keys. Many text replacement programs have this already, but I haven't figured out how to get Phrase Express to do what quite what I want.

Nothing changes, provided the frequency list always remains the same, i.e. you use a standard such as a given corpus. The user may have their own additional personal dictionary, which the paper on T9 describes. I highly recommend reading the paper, even just for an interesting read.

The vast majority of the time the desired word will be at the top of the list anyway and no input will be needed from the user. That's the ingenuity of the invention. A predictive algorithm would eliminate the need for input entirely, but has its drawbacks such as possible inaccuracy.

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