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Parallelisms : Double-entry accounting - Quantum Logic - Mathematics
- Neurophenomenology - Quantum mechanics
Double-entry accounting
The double-entry accounting
principles can be found on many pages on the web or they can be shortly
explained by most of the people aware of the standard practices for bookkeeping
and accounting in business.
The most important is to
retain that a double-entry accounting
balance is similar to
our above figure where the left T-accounts are the assets and the
right T-accounts are the liabilities
like in the balance sheet of a company and that the writing
convention in that balance sheet of the company are similar to a
view point inversion.
We may say that the assets are written
from an internal view point - i.e. the company view point - and that the
liabilities are written with an external view point - i.e. from the bank view point.
For the sake of a simple
introduction we shortly quote Wikipedia:
- "This system is called
double-entry because each transaction is recorded in at least two
accounts. Each transaction results in at least one account being
debited and at least one account being credited, with the total
debits of the transaction equal to the total credits.
- This requirement has a
benefit to the bookkeeper, but also introduces confusion to the
layman.
- The benefit is that the
accuracy of the accounts can be checked quickly - for, when all
the accounts that have debit balance are summed, they should equal
the sum of all the accounts which have a credit balance. Without
this requirement, there would be no quick means to check accuracy.
- The confusion arises because
a healthy business with money in the bank will have a debit
balance in the account called "Bank". This is contrary to the
layman's experience that, when the layman's bank balance is
healthy, his bank statement shows a credit balance. An easy way to
visualize this is to consider that the bank writes the statement
from its own point of view; hence if you are in credit, you are a
liability on their balance sheet - you can turn up and draw your
money out.
The above mentioned confusion
comes from the fact that the writing view points are inverted
between the assets and the liabilities columns - noticeably
like our both eyes own an inverted view point of the same
observation.
Say the assets are written
from an internal view point - i.e. the company view point - and the
liabilities with an external view point - i.e. from the bank view point.
Quantum Logic
As a consequence of the view
points being different - see
page 2.2 - we
demonstrate here a significant difference with the lattice of G.
Birkhoff and J. Von Neumann. While their lattice was not having
any isomorphism, at the opposite we always have an isomorphic
alternative at any of our "holotomy" - say our "lattices" - as a
"false twin" always exists.
We remind that in mathematics,
the existence of an isomorphism between two sets indicates that
there is a correspondence one-to-one between all the components of
both sets so that they are equivalent, even when - like in our
double-entry accounting - they are different.
To confirm and better
illustrate the answer we gave to their first question - see
page 2.2 -,
it is worth to quote further G. Birkhoff and J. Von Neumann: "It is worth remarking that in classical mechanics, one
can easily define the meet and the join of any two experimental
propositions as an experimental proposition - simply by having two
experimental observers read off the measurements which either proposition
involves, and combining the results logically".
It is noticeable that our two
eyes provide with the "two observers" quoted by G. Birkhoff
and J. Von Neumann: they both "read off the
measurements" with two different experimental propositions"
because our two "eyes" are different. The experimental proposition
resulting of the joint and the meet is that the joint and the meet
are equivalent or isomorphic.
This comes from the accounting
practice to which our double eyes are equivalent. As said, in an accounting balance, the
left column that accounts for the assets is taken from the view
point of the company - i.e. companies account with positive values
in the left-debit part of an account for the assets they own -
while the right column that accounts for the liabilities is taken
from the view point of the bank - i.e. the open lines of credit
that are money owned by the banker - are taken with positive
values in the right-debit part of an account of the right
liabilities column.
For the rest of the
development that we present in the forthcoming pages and sections, it
is important to retain that our double-eyes analogy will be like
our left eye gives us our own view point while our
right eye gives us the view point of someone that is external
to us.
Important is that "internal
and external" does not just mean two people who stands at two
different places but two people that look differently - say
with a different watching process i.e. like one make the detection
for a chemical agent with two different sets of procedures and
protocols.
Both view points are of
course configured on the same observation and they are - and must of
course be - equivalent and provide with the same information.
Both viewing process of our
two eyes must own the same information capacity - say they must
have the same dimension measured in bits the sense of Shannon.
This condition of the same
information is translated in the business double-accounting
practices by the rule that the sum of the debits must always
equate the sum of credits.
At the question - given by G. Birkhoff
and J. Von Neumann - "What experimental meaning can one attach to
the meet and join of two given experimental propositions ?", we
own now an even better answer than previously given at the
page 2.2 : we
confirm that the meet and the joint of our internal and external
observations are equal and that this equality tells that our
observation can always be equivalently made by at least two observers
having a different view point - say an other manner to look at the
world.
Mathematics
The figure at the top of the page shows that it may
exist a temptation to say the joint of the two observations might equal 2
and their meet might equal 0.
This may happen if we forget to account for the view
point inversion between the two eyes - from the inside and from the
outside.
It is arithmetically true that the sum equals 2 and the
difference equals 0. The meaning is however not "joint" and "meet". It may
in example be the dimension or the size of two collections - say that each size equals 1
so that the total size is 2.
It exemplifies what we introduced when we said that [i]
was not an imaginary number but a space. In the figure at the top of the
page, we may say so that we have a real space represented by [1] and
imaginary space represented by [i].
One can see our spaces like boxes, one being real and
the other one being imaginary. So it is clear that adding those boxes or
their contents does not make sense. At the most, one may say that our
boxes will all have a size equal to 1 so that in this case the total size
of the two observations
equate 2.
We like also to mention that the current double-entry accounting belongs
to the mathematical group of differences - see
David Ellerman in "Mathematical
Formulation and Generalization of Double-Entry Bookkeeping".
Neurophenomenology - Quantum mechanics
Noticeable for us is the fact that the choice for our
analogy with a pair of eyes has been motivated out any knowledge of the
human eye anatomic description and that we later learned that the retinas
of a pair of human eyes is currently described with a structure that
mimics the structure of a pair of debit-credit accounts - i.e. like
illustrated in the figure here below.
If the analogy stands accurate, this would mean that an
eye is like providing an external view point for to the other. As we do
not think that it is any reason to attribute a specific role for any of
the two eyes, it would mean that they may both play this external role for
the other - i.e. like simultaneously or quasi-simultaneously.
 This in
turn suggests that the eyes-brain coupling might be described as generated
by a set of
quantum fields - see pages
4.4 and
4.7.
The quantum fields describe a kind of
co-existence of dual and opposite similar fields and those quantum fields
will be later
described - in the pages
4.4 and
4.7 - like in
parallelism with a double-entry accounting system.
In example, this combination of quantum fields could be a
"simple" explanation for some optical illusions - i.e. like the
"reversible figure and ground" of the adjacent image - from
Wikipedia.
Because our introduction of the double-entry accounting
as a "pair of eyes" will first infer a strong parallelisms with quantum
mechanics and second will infer from there the usages of particular visual
designs - pages 5.2
and 5.3 - for
which the human brain is obviously providing the closing process which
generates the sense, we think that the complete introduction at the
holotomial analysis - say from geometrical and accounting foundation to
the kinematics activation - is as whole an additional support at the
possibility for quantum fields underlying some description of the
phenomenological human brain behavior.
There are other signs to support that one could
advocate for a quantum fields interaction within the human brain.
Say that the brain being recognized as seating numerous
electromagnetic interactions, the view of an underlying intermix
of quantum fields does not seem an a priori absurd vision. We also
remind that we mentioned earlier - see the parallelism at the
bottom of the
page 2.2 - the psychologists who afford a pertinence at
personality tests that exhibit an organization parallel to the
quantum logic.
Neurophenomenology - Double-entry accounting - Quantum mechanics
More questioning is the fact that the double-entry structure is
encountered at several end different scale in the eye.
 The
adjacent figure illustrates that the "bipolar receptor fields"
mimic also the double-entry accounting system at the level of the
retina. Good introductory and nicely illustrated
material can be found at the web site "The
brain from the top to the bottom" to understand how the brain
is operating via superposing layers of different scale.
Say that cascading summations are made like with accounts and
sub-accounts: "The receptive field of numerous cells are summed to
from the receptive field of one cell in the primary visual cortex
... being themselves summed to form the receptive field a-of one
complex cell". As it will be shown in the next
section, this kind of double-entry structure will be responsible
for the excitation of complementary and opposite fields which are
very similar to the fields that are described by the quantum
formalism - say a creation component associated with a
annihilation component. Within such
entanglements of scales and sub-scales, one can suspect that each
antagonist pairing defines a characteristic time - or say a
frequency - corresponding each given scale as well as a
quantum-like "reduction of the data quantity" between a sub-scale
and an upper scale. One can find an example about
investigation of those aspects - both "characteristic times" and
"data reduction" - in
A.
Khrennikov - "Brain
as quantum-like Machine for Transferring Time into Mind" at
arXiv.org .
According to
Wikipedia,
such assemblies of receptive fields have also been identified for
the auditory system and for the somatosensory system.
In a sense, the whole neural system system can be seen as "piling
up" double-entry accounts and/or opposite and complementary pairs
of accounts such that " ...
This is a fundamental characteristic of the way that the brain
processes information. At every stage, some of the fibres and
connections loop back to the preceding stage to provide it with
feedback that helps to control it ... ". |
