|
Parallelisms : Accounting - Neurophenomenology - Quantum
field - Algebra - Complex numbers - Quaternions - Octonions
 Accounting
The adjacent figure
illustrates in an alternative fashion how we can obtain all the
successive standpoints only by reworking the single principle of a
"debit-credit" account that is symbolized here by [1]
- [i].
The reader must pay attention
that the upper frame is written - as all the upper text frames -
for the sake of capturing the general concept.
In this upper frame, it is
exposed how an observer will take in account for the three
perspectives that are successively the coordinate, the motion and
the time.
To have our double eye system,
still we need a second observer having a different way of looking
but who also will need to watch from the same three perspectives
and will provide with the same information.
In turn it means that a
complete description will required 6 dimensions - 3 real for the
"internal observer" and 3 imaginaries for the "external observer"
- and a total of 16 digits.
This is suggested in the
following illustration here below where the second half of the
figure is a kind of mirrored inverted image of the first half.
Noticeable is to
remind that a double eye system can exhibit 16 records
permutations - see the table in the lower text frame of the
page 3.4 - so
that one can imagine that they may possibly be all embedded
univocally within the above double eyes system that completely
incorporates the three perspectives that are the coordinate, the
motion and the time.
It looks like the
record table that is a 4 lines x 16 columns on the
page 3.4 may now become a 16 lines X 16 columns.
Neurophenomenology
This point is here only to
rise the question whether any of the numbers mentioned in the
above figures may have correlations with the current or
maximum number of visual entities that a human brain can handle at
once.
Quantum field
 Without
entering much details, let's mention in a visual manner that the
accounting from the "time view point" - that is a complete view
point - infer a morphic parallelism with formalizations of quantum
fields.
In this sense, each
"debit-credit" or "assets-liabilities" pairs can be seen as two
opposite fields, one for generating tangibles - say creations -
and the other one for generating intangibles - say annihilations.
In business like in
physics, those two operations can be commutative but they are
generally not and they can eventually be exactly balanced but they
are more generally balanced via reconciliation account - say like
uncertainty or [u]-[v] accounts.
In a more general
sense this suggests that any situation in "life" can be
represented by the co-existence of opposite characteristics and
that the evolutions would be dictated by balance-unbalances ratios
between them.
This principle of
managing opposite dualities is present in a large diversity of
human related domains: it is often recognized as a base of the
oriental mentality - say the Yin Yang, it has also been utilized
in psychology - i.e.
Myers-Brigss Type Indicator - and it enforced
in several consulting methods as a manner to generate and manage
individual - and organizational - transitions -
i.e. W. Bridges or
R. Fritz.
Algebra - Complex numbers - Quaternions
- Octonions
Noticeable is that if we assimilate the
T-account as drawn above to complex numbers, we create a close
analogy with the vision of the complex numbers as introduced by W.
Hamilton and the extend it visually to the concept of quaternions
- also introduced by W. Hamilton - and to the concept of octonions
- which introduction has been disputed between W. Hamilton
and A. Cayley (see "The
octonions" (pdf)
- John C. Baez).
It is amazing that both W. Hamilton and
A. Cayley are among the rare mathematicians who may have have been
aware of the practices of the double-entry
book-keeping - with a remaining uncertainty for W. Hamilton. Can
one wonder how much their innovative mathematical contributions to
complex numbers, quaternions and octonions are not "simply"
implicit extensions of the double-entry book-keeping
system?
The above figures illustrates that when you know about book-keeping
practices, it is somewhat natural for a mathematician to think about
complex numbers, quaternions and octonions - i.e. as introduced respectively by W.
R. Hamilton and A. Cayley in the 19th century.
How much W. Hamilton and A. Cayley have
been inspired by double-entry bookkeeping remains unknown to us,
but it looks obvious that there is an analogy between our actual results and the
concepts of complex
numbers, quaternions and octonions.
This analogy strongly suggests that we are
like "re-traveling" here the construction of theoretical dynamics - say
classical and quantum - via an other track based on a much more
simple and accessible concept than the actual set of mathematical
abstractions.
|
