Lexicographical Subtraction

 

This quasi-boustrophedon arrangement like a flattened clockface shows the obvious mnemonics for subtracting from twod (twelve). Twod subtracted from twod is a special case, as indeed is any subtraction of one number from itself.

 

 

koja

pade

tubu

kwod

pega

 

twod

 

 

 

 

 

tebe

 

poju

kade

taba

pwod

kegu

 

 

The same table can be used to derive mnemonics for subtraction from tebe (six) [or twod tebe (eighteen)] by considering the column through tubu and taba as a "reflection" axis. A rough rule is that odd endings ("a", "u") stay the same; even endings interchange("e"<>"d"); insides interchange; non-"t" beginnings ("p" and "k") interchange.

 

What about subtraction from tubu (three) and taba (nine)? There is no real help from the middle of the words as the following table makes clear. However beginnings and endings are enough to tie down the answer. Since multiples of tubu begin with "t", "t"-beginnings stay that way; the other two beginnings interchange. For subtraction from tubu we find endings interchange in pairs: "e"<>"a" and "u"<>"d". Considering the table in a reflection in a vertical axis, for subtraction from taba we find endings interchange: "e"<>"u" and "a"<>"d".

 

 

pade

tubu

kwod

*

pega

tebe

kegu

 

*

 

 

 

 

 

 

 

*

 

koja

twod

poju

*

kade

taba

pwod

 

 

All together that makes quite a few rules and initially these rules cannot all be remembered and applied instantaneously. However we have an interlocking system like a machine with cogs or like the old hub gears. If we arrive at the (correct) answer the method will be reinforced and probably accelerated and eventually bypassed. The lexicographical method can be combined with symbol manipulation in any way that seems appropriate. There is no effective alternative to learning the numbers (names and symbols) in sequence, forwards and backwards. After that, repetition makes perfect.


 

For reference the following lexicographical table allows names to be reconstructed from the beginning and ending letters:

 

. Rows with same starting letter and columns with same ending letter

koja

kwod

kegu

kade

pega

pwod

poju

pade

taba

twod

tubu

tebe