Sorry to take so long to reply to this -- a health issue took me away
from my computer for a while.
On Fri, 10 May 2013 04:57:42 -0700 (PDT),
"
chromo...@googlemail.com" <
jl...@sofluc.co.uk> wrote:
>On Thursday, 21 February 2013 23:30:50 UTC, Jymesion wrote:
>> That's important because we learn 2+2=4 by rote. In this system, it
>> should be looked at as 2+2=2+1+1=3+1=4 because the numeral 4 is a
>> combination of the numerals 1 and 3.
>
>some of you may remember me as J L Cunningham
I remember you! (Not sure that's always a good thing . . . ;) )
>If you start with counting, then +1 means "the number after this",
>so 3+1 = 4because four is the number after three. (One, two, three,
>four, oh yes, that's right.)
That's using rote memory.
>That is, 3+1=4 by definition (the definition of what 4 is.)
Definitions are (by definition) the antithesis of my project. :)
I posit a race with very little capacity for learning by rote. Their
brains are wired more towards recognizing processes and understanding
relationships.
>One way to define +2, or +5 or whatever, is to say "keep doing +1,
>count how many times you do it, and stop when you've done it 2 times,
>or 5 times or whatever. If you'll excuse a little algebra, +k means
>"do +1 k times" except it would all be done in words.
Partway into my playing with this project, it dawned on me that
certain elements of the process mimicked computers' +k method since
they don't have addition tables in memory.
>Then 2+2 is 2+1+1 (count how many +1s there are: two of them).
>But 2+1 is 3 by definition, so 2+2 is the same as 3+1, which is 4 (by definition).
Again with the definitions! :)
In my project, you don't have to remember (or define) 1+3=4, 2+3=5,
1+6=7, or 2+6=8 because it's simply a matter of combining the symbols
(positional notation within duplex digits).
Where:
Rote(x) = something that must be memorized
Process(x) = something you can figure out if you remember the
preceding Rotes.
Rote/Process(x) = something you should be able to figure out, but it
helps if you remember something about the process
Rote(1): 1 is represented by a certain symbol (a stylized stroke)
Rote(2): 2 is represented by a different symbol (stylized pair of
strokes)
Rote(3): 3 is represented by an inverted 1 (to move it into the second
position) because it represents 1 group of 3 items.
Process(1): 6 is represented by an inverted 2 (2 groups of 3).
Rote/Process(1): The symbols for 4, 5, 7, and 8 are made by combining
1 and 3, 2 and 3, 1 and 6, and 2 and 6, respectively, within the
digit.
Rote(4): 1+1=2
Process(2): 3+3=6 (1+1=2 in the second position).
Rote/Process(2): 2=1+1
Process(3): 6=3+3 (Process(2) and Rote/Process(2)).
Rote(5): 1+2=3
Process(4): 3=1+2 (Rote/Process(2) and Rote(5))
Rote(6): 1+8=11 (Positional notation, equivalent to decimal's 1+9=10,
in Base8 without a zero (which I've always felt is highly overrated).)
Process(5): 1+88=111, 1+888=1111, etc.
Memorizing only 6 things and mostly remembering 2 allows all addition
(and I'd be willing to argue that Rote(6)(above) isn't completely rote
because position value has already been established, so moving into a
new digit should be a logical step).
I think that compares favorably with "Arabic numerals/decimal with
zero" system's 92 required learning by rote memorizations.
Your Latinate system sounds interesting, but I won't explore it
because I can only wrap my mind around a certain amount of weirdness
at one time. :)