Discussion:
Number 10
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Don H
2008-04-18 19:16:10 UTC
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Article in "The Age" (14/4) on Dyscalculia (Education supplement) raises the
possible problem of coping with the number 10, its whys and wherefores.
What is the arithmetic "alphabet", ie. those basic concepts on which all
else is based?
Presumably, it is - 0,1,2,3,4,5,6,7,8,9 - assuming zero is a number. But
when we come to "10", it is a combination of existing numbers, and thus a
"word" or at least a "digraph", in an English language analogy.
But what if we had a special symbol for 10, eg. "Q", then what would a
number such as "3024" mean?
The zero in such number denotes an "empty" column in an abacus, or is a
place-holder without which the number would contract to 324, and be
incorrect.
Is such zero column really empty? Or is it a "complete" column for which
some more appropriate marker is needed.
Consider "3Q24" instead, and what is this but -
3QQQ + 2Q + 4, where 3QQQ = 3 x 10 x 10 x 10, and 2Q = 2 x 10.
After all, for the 3 in number 3024 to have reached its thousands status,
it must have accumulated those thousands, and a physical nothing on a
counting frame is not what exists in reality. Put three thousand people in
a stadium, and they all exist, no matter the notation.
Hence 3Q24 is the superimposition of 3QQQ, 2Q, and 4 - a form of
shorthand.
Don H
2008-04-19 18:46:58 UTC
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Post by Don H
Article in "The Age" (14/4) on Dyscalculia (Education supplement) raises the
possible problem of coping with the number 10, its whys and wherefores.
What is the arithmetic "alphabet", ie. those basic concepts on which all
else is based?
Presumably, it is - 0,1,2,3,4,5,6,7,8,9 - assuming zero is a number.
But
Post by Don H
when we come to "10", it is a combination of existing numbers, and thus a
"word" or at least a "digraph", in an English language analogy.
But what if we had a special symbol for 10, eg. "Q", then what would a
number such as "3024" mean?
The zero in such number denotes an "empty" column in an abacus, or is a
place-holder without which the number would contract to 324, and be
incorrect.
Is such zero column really empty? Or is it a "complete" column for which
some more appropriate marker is needed.
Consider "3Q24" instead, and what is this but -
3QQQ + 2Q + 4, where 3QQQ = 3 x 10 x 10 x 10, and 2Q = 2 x 10.
After all, for the 3 in number 3024 to have reached its thousands status,
it must have accumulated those thousands, and a physical nothing on a
counting frame is not what exists in reality. Put three thousand people in
a stadium, and they all exist, no matter the notation.
Hence 3Q24 is the superimposition of 3QQQ, 2Q, and 4 - a form of
shorthand.
# The value of Q varies depending on the base used. In binary it would be 2,
in hexadecimal it'd be 16 - and substitution for notation results in
conversion to base 10.
Why do we have a "base"? It is a simplification. It is quite possible
to dispense with a base altogether and have an unlimited series. After all,
every base increments by one, and if every number had a unique identifier,
then no base would be needed.
This is what the "Whole Word" advocates propose in use of language -
every word is different from every other, and should be recognisable on sigh
t, depending on context. No need to analyse words, the first and last
letters give you the clue, IF you insist. But even so, they opt for "sight
words", as compared with other words.
Or, we could have a 44-letter alphabet, to designate the sounds in
English (19 of which are vowels). This would actually be the ideal.
The limitation of symbols to an Alphabet, and to the Digits 0-9, saves
having memory overload. Using rules of application then makes life simpler.