The concepts and connections between concepts which are to receive special
attention in these notes and papers are the following:
|NUMERAL SYSTEM AND BASE|
||no place-value notation|
||base 2 (binary) or base 4 (quaternary)?|
||chong +2 ((power-3) involution)
||a base other than 2 or 4? (senary or octal?)|
||chong +3 (reiterative involution)?
||a chong-3 system?|
|five- or more-dimensional
||chong +4 or higher?
||a chong-4 or higher-level system?|
Addition is an elementary mathematical operation on the zeroth level of
reiteration, multiplication such an operation on the first level,
involution one on the second level, reiterative involution one on the third
In a universal system of ever higher operational levels of reiteration
i call these arithmetic operations "chong operations":
'chong +0' for addition, 'chong -0' for subtraction, 'chong +1' for
multiplication, 'chong -1' for division, 'chong +2' for involution, and so
on and so forth.
Addition may be considered to be 'native' to one-dimensional space, whereas
multiplication and operations of a higher level of reiteration are not.
Similarly, multiplication is, then, native to two-dimensional space,
involution in general, or else only involution with a power of 3, native to
The current standard notational system for numbers is a multi-place
place-value chong-2 numeral system -- 'chong-2', because it
does not go further than involution.
One might wonder whether a chong-3 system would not represent numbers more
adequately in a context where chong-3 operations play a role, or a higher
chong system in a context in which even higher operations play a role.
Apart from this fundamental issue, there is the more ordinary
question of what base number deserves primacy where and when (over base 10
in particular), even if we take the chong-2 numeral system for granted.
This issue of the level of reiteration and this question of the primacy of
the numeral base used or to be used in different contexts also touches on
the relevancy (relevance or irrelevance) of the kind of mean, such as the
arithmetic or geometric mean, used or to be used in different contexts.
While this is of mathematical interest in itself, it is certainly
important in the formulation, interpretation and corroboration of the
as discussed in section 2.6.3 of the
At the moment the most innovative, if not 'revolutionary', document in the
Math folder at this MVVM-site is no doubt The Chong Operators, in
which the whole system of operational levels of reiterations is explained.
(If it is not the thriller its title may promise it to be, it is, in a
sense, of greater magnitude than any such book so far.)
The other mathematical documents publicly available in the same folder deal
primarily with the representation of numbers in the base-2 or 'binary' and
the base-4 or 'quaternary' system as distinct from their representation in
the base-10 or 'denary' system.
Altogether the mathematical notes and papers are in reverse chronological
Those who have always thought that the verbal expressions ('names') for
numbers must take the base-10 system as their frame of reference, almost
by definition, should read the poem
At Eighty I Should Give Up.
That poem reveals the verbal expressions possible for the denary
('decimal') number 80 in a macrobinary system.
Yes, altogether the elementary binary expressions for numbers (however
large) need not be more cumbersome, not even or hardly longer, than in
natural languages which use the base-10 system.
Well, the phrase for 80 happens to be at least one syllable longer, but
that does not prove anything, especially since
This Language is not the sole natural
language in the world.
(The binary word for the denary number 16 can be one syllable shorter than
speakers of the present language are used to.)