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Parallelisms : Taxonomy - Quantum mechanics - Hilbert spaces -
Neurophenomenology
Taxonomy
In large amount of data,
taxonomies may loose efficiency first because a non adequation of the
Boolean schema
- i.e. when too many components belong to several filiations like typically directories of software programming companies
that are listing their individual capabilities will frequently end up to
say that they may all do all.
I see an other cause of a taxonomies limitation in the
fact that they are not
always a unique and scalable solution.
To assess the lack of uniqueness, it
is enough at asking different persons to create a taxonomy on a given set
of information and see if they come with a unique or different solutions, or
alternatively to ask different persons to classify a set of
records in a given taxonomy and see if they
come or not with a unique solution.
The scalability can be first assessed by creating a
taxonomy on a limited part of a set and at looking if it holds at extending
it to the rest of the set. Its ubiquity can also be further assessed by
introducing a new element that should be incorporated into the set and
that owns characteristics that were not previously recognized.
Since the emergence of the web and the large amount of information it provides, it has become an accepted fact that taxonomies may own operational limits when sets of data are
enlarged.
Quantum mechanics -
Neurophenomenology
"Major connections" (1) - The point
"major" has been one of the first signs of some special probabilistic
characteristics owned by our emerging solution. "Major" did stand either
important - say a large quantity of business done with a given outside
sector - but it highlighted also other senses like special, noticeable or providing
reputation.
Those "specials" were eventually different if we were
focusing on particular external sectors - i.e. specials for the Healthcare
market were different from those of the steel industry segment - and might
also be different with regards to the business owners visions.
Typically business owners who would target aggressive
expansions or defensive strategies were looking differently at threads and
opportunities of the surrounding.
The above illustrates how it came that our map style
was a space in between an observer and the reality: on one hand it enabled
to incorporate objective data - i.e. the major sectors that can be
identified by numbers - and on the other hand, subjective data that
corresponded to the focus on a given future and eventually to an individual
vision on it.
Say that a map is a vision of the real world that is
essentially reified by a context.
"We are what we do" - This notes looks
like a slogan but it is not.
At explaining our mapping methods to other people, it happened
frequently - in particular with rational thinkers - that they agreed that it was a nice concept and that we could map and incorporate so
any component that we would like.
It is true that we could design any kind of map and in
principle that we could set on them any number of components but it is important to underline that
this understanding does not
correspond at all to our actual experience.
Our maps could not treated as a concept but they were
actual visions of a given reality that embraced real and intangible and we
could not anticipate they reification without a given and real context.
Otherwise said, they could not be drawn as an objective view of the
economy but could only be drawn as an answer to a given question.
"Major connections" (2) - Noticeable also is
that they could apparently make sense only when some restrictive design
rules on the number of data displayed would be respected.
The many experimental map designs that we tested
indicated that one would easily loose sense if we would not respect a few
rules that generates limitations.
We observed that a guidance like the followings would
usually infer more sense: the objective data must be real - say based existing
exchanges and not potentials ones (incorporating potentials easily leads
to intractable crowds); the subjective components must correspond to
interactions that we may reasonably expect to encounter within an
achievable
delay.
Still more illustrative - in our view - is the fact
that the number of components on a map must be limited - i.e. to 20 ... 30
for a general communication and daily operational usage, to 80 ... 100 for
an engineering or planning investigation and that the map would have
structural suggested directions i.e. like radial, bottom-up or left-right.
It took us a certain time to understand that those
limits were not a kind of subjective and common communication artifact.
We observed but
were reflecting the facts that
no action is instantaneous - say a minimum time is required in the real
world to perform any action - and that our available time is upper bounded
- say that we own only 24 hours a day and 7 days a week (many rational
reasoning and equations recall at the reverse for continuity,
instantaneity and infinity).
When you account for those lower and upper limits, you
are close to respect the mentioned restrictive rules that have been
mentioned for map designs to produce plausible probabilistic visions.
Otherwise said, it came a data display limitation by the fact that
the observer owned a contextual and physical limitation in the reification
of potentials as soon as the question is not generic but focused on a given domain.
"We are what we do" could be translated by "we describe
by our maps what we are effectively doing plus what we may thing of doing
and
that looks reasonably achievable".
Consequently, we saw our maps far to be a concept but
an hands-on work that reflects a data quantification implicitly perceived
by the human brain while hardly tractable by numbers.
With no actual correlation at that time, we noticed
that our practices were in line with the frequent quotes mentioning that
the human brain can hardly sustain dealing with an infinite number of
parameters - i.e. limits ranges are mentioned like 3-4, 6-8 or a few tens.
Quantum mechanics - Hilbert spaces - Neurophenomenology
The probability to find collaborations
- Our maps are better understood if you see them as a coordinates system
defined by clusters and if you imagine that you have people and products
moving from cluster to cluster. With such a mental image, you will easily
see the our maps to answer a question like: where do I have the most
chance to find a given actor or a given good ?
Noticeable was the fact that we could obtain our maps by
hands-on drawing and hardly but computing.
Say that the computation of the
probability densities were obviously observable on the map and that we
were able to obtain them from a visual translation of a human knowledge, but we did not know how
to
handle a reverse, say creating a map from numbers.
The problem was not perceived much with the objective
data - they often reflected identified international business main streams
- but with the subjective specials and actually activated connections
which both were non available in data base and anyway cumbersome to
compute in an actionable fashion - because of the format of the data
collect that was often interviews and feelings and also because any
recorded situation would frequently become quickly obsolete. The life of a
global given state was usually short.
After several unsuccessful tentative, we designed a
quick test that gave an interesting answer. We built on purpose a sample
embedding four companies belonging each to one of four different external main business streams,
a group of companies specialized in only one of the main streams and we
finally completed then set with a group of companies that were handling
generic business fitting demands that could emerge from any company of the two previous groups.
In principle, any single business was having only a few
direct competitors and was in principle capable to comply with any others
like a complementary competence to fulfill a multidisciplinary demand. In
practice, a fair part of the business owners was having personal
acquaintances and characters that would modulate the chance that they may
collaborate with one or another company.
We took three colleagues who knew most of those actors
- at different degrees but at least a little - and we asked them to quote
on a scale at their convenience - i.e. 0-3, 0-5, 0-10, ... - the chance
that a collaboration of some sort would result in the next twelve months from any two
companies meeting
together - i.e. an action could be a responding purchase order, proposing
an alliance on a one-shot project, an exchange of best practices, a
commercial lead or proposing a grouped activity representation - whatever
it was, we did
not asked to tell what the action would be but only tell the chance of
action to occur.
It resulted that for each companies we had three
vectors for which the bases were the names of all the companies and the arguments
were the probability index given by each colleagues.
By normalizing and averaging, we reduced
the three figures at only one vector having the length of one for each company
(the length of a vector is the square root of the scalar
product of the vector by itself).
In a sense, each of those vectors were the measurement
of the state of each company in terms of their potential of collaboration.
From there, we computed the compatibility between any
two companies by computing the scalar product between their two state
vectors. A product value of 1 would mean that they were parallel, say
compatible; a product of 0 would say that they were orthogonal, say not compatible; a product between 0
and 1 would scale accordingly their degree of potential compatibility.
The results showed that we were able to reconstruct our
map segregation trends from this simple test and set of procedures.
A noticeable observation came out of this quick test:
however computing is taken by many as a more serious
way to handle a business, it was clear that for nearly any sets of
enterprises that we worked
out, the drawings made by human being were largely more efficient and less
costly at creating than computing - and updating - probability value.
Two questions followed this observation:
1. The human brain is obviously able to produce sense
making results which can be alternatively produced by a procedure
having acquaintances with quantum mechanics: the normalizations and scalar
products that conducted at our compatibility statements are nothing but
the procedures that have been proposed to characterize states
compatibility in quantum mechanics (ref. J. Von Neumann - D. Hilbert). So
the question: is the human brain a kind of quantumlike macroscopic
"device" ?
2. The business structure that we ended up with our
scalar products is nothing but a (mix of) Hilbert spaces - which is also a
concept utilized in quantum mechanics to describe quantum states. So the
question: would business and economy be also a kind of macroscopic
quantumlike system ?
By saying "quantumlike", we do not explicitly refer to
quantum physics in itself but we refer to a system that would be governed
by probabilities interferences - say as discussed by
A. Khrennikov
in "On the notion of a
macroscopic quantum system".
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