TRANSDISCIPLINARITY, A NEUTROSOPHIC METHOD
by Florentin Smarandache
(still needs wikification//formating)
A) Definition:
Transdisciplinarity means to find common features to
uncommon entities: i.e., <A> ü <Non-A> is different from the
empty set, even if they are disjoint.
B) Multi-Structure and Multi-Space:
Let S1 and S2 be two distinct structures, induced by the
group of laws L which verify the axiom groups A1 and A2
respectively, such that A1 is strictly included in A2.
One says that the set M, endowed with the properties:
a) M has an S1-structure,
b) there is a proper subset P (different from the empty set ü,
from the unitary element with respect to S2, and from M) of the
initial set M which has an S2-structure,
c) M doesn't have an S2-structure,
is called an S1-structure with respect to S2-structure.
Let S1, S2, ..., Sk be distinct space-structures.
We define the Multi-Space (or k-Structured Space) as a set M such
that for each structure Si, 1 <= i <= k, there is a proper
(different from the empty set, from the unitary element with respect to Si,
and from M) subset Mi of it which has that structure. The M1,
M2, ..., Mk proper subsets are different two by two.
(F.Smarandache, "Mixed Non-euclidean Geometries", 1969)
Similarly one can define the Multi-Group, Multi-Ring, Multi-
Field, Multi-Lattice, Multi-Module, etc. -
which may be generalized to Infinite-Structured-Space,
Infinite-Structured-Group, and so on.
Let's introduce new terms:
C) Psychomathematics:
A discipline which studies psychological processes in connection
with mathematics.
D) Mathematical Modeling of Psychological Processes:
a) Improvement of Weber's and Fechner's Laws on sensations and
stimuli.
According to the neutrosophic theory, between an <idea> (=
spiritual) and an <object> (= material) there are infinitely many
states.
Then , how can we mix an <idea> with an <object> and obtain
something in between: s% spiritual and m% material (s+m = 100)?
[kind of chemical alloy].
Or, as Boethius, a founder of scholasticism, urged to "join faith
to reason" in order to reconcile the Christian judgement with the
rational judgement.
For example <mind> and <body> co-exist. Gustav Theodor
Fechner, who inaugurated the experimental psychology, obsessed
with this problem, advanced the theory that every object is both
mental and physical (psychophysics).
Fechner's Law, S = k log R, with S the sensation, R the stimulus,
and k a constant,
which is derived from Weber's Law, Delta R / R = k, with Delta R the
increment of stimulus just detectable,
should be improved, because the function log R is indefinitely
increasing as R ---> ü, to
ln R
S(R) = k -------, for R in [Rm, RM],
ln RM
and
S(R) = 0, for R in [0, Rm) union with (RM, ü),
where k is a positive constant depending on three parameters:
individual being, type of sensation, and the kind of stimulus,
and Rm, RM represent the minimum and maximum stimulus magnitude
respectively perceptible by the subject,
the second one bringing about the death of sensation.
Fechner's "functional relation", as well as later psychologists'
power law R = kS^n, with n depending on the kind of stimulus, were
upper unbounded, while the beings are surely limited in
perception.
S: [0, ü) ---> {0} union with [Sm, SM], with Sm, SM the minimum
and maximum perceptible sensation respectively.
Of course Rm > 1, S(Rm) = Sm, and S(RM) = SM = k.
Ln, increasing faster, replaces log because the sensation is more
rapidly increasing at the beginning, and later going on much
slower.
At R = RM, S attaints its maximum, beyond whom it becomes flat
again, falling to zero.
The beings have a low and high threshold respectively, a range
where they may feel a sensation.
Graph of Fechner's Law Improvement:
/\
S |
|
-----------------------.------
SM | .
| .
| .
| .
| .
| .
--------.----------------------
Sm |
|
|......______________........>
0 Rm RM R
For example in acoustics: a sound is not heard at the
beginning and, if it constantly keeps enlarging its intensity, at
a given moment we hear it, and for a while its loudness increases
in our ears, until the number of decibels - getting bigger than
our possibility of hearing - breaks our eardrums... We would not
hear anything anymore, our sensation died...
Now, if at a given moment t0 the stimulus R remains constant
equal to R0 (between the conscious limits of the being, for a
long period of time t), and the sensation S(R0) = c, then we get
the following formulas:
In the case when the stimulus in not physically or
physiologically damaging the individual being:
Sdec(t) = c log1/e(t+1/e) = -c ln(t+1/e),
for 0 <= t <= exp(-Sm/c)-1/e, and 0 otherwise;
which is a decreasing function;
In the case when the stimulus is hurting the individual being:
Sinc(t) = c ln(t+e), for 0 <= t <= exp(SM/c)-e, and 0 otherwise;
which is an increasing function until the sensation reaches its
upper bound;
where c, as a constant, depends on individual being, type of
sensation, and kind of stimulus.
Examples:
ü If a prisoner feels a constant smell in his closed room for
days and days, isolated from the exterior, and he doesn't go
outside to change the environment, he starts to feel it less and
less and after a critical moment he becomes inured to the smell
and do not feel it anymore -
thus the sensation disappears under the low perceptible limit.
ü If a water drop licks constantly, at the same interval of time,
with the same intensity, on the head of a prisoner tied to a
pillar, the prisoner after a while will feel the water drop
heavier and heavier, will mentally get ill and out of his mind,
and will even physically die -
therefore again disappears the sensation, but above the high
limit. See how one can kill someone with a... water drop!
ü If one permanently plays the same song for days and days to a
person enclosed in a room without any other noise from outside,
that person will be driven crazy, even psychologically die, and
the sensation will disappear.
Weber's Law can be improved to Delta R / ln R = k, with R
defined on [Rm, RM], where k is a constant depending on individual
being, type of sensation, and kind of stimulus,
due to the fact that the relative threshold Delta R increases slower
with respect to R.
Let's propose a
b) Synonymity Test,
similar to, and an extension of, the antonym test in psychology,
would be a verbal test where the subject must supply as many as
possible synonyms of a given word within a as short as possible
period of time.
How to measure it?
The spectrum of supplied synonyms (s), within the measured period
of time (t), shows the subject's level of linguistic neutrosophy:
s/t.
E) Psychoneutrosophy:
Psychology of neutral thought, action, behavior, sensation,
perception, etc. This is a hybrid field deriving from
psychology, philosophy, economics, theology, etc.
For example, to find the psychological causes and effects of
individuals supporting neutral ideologies (neither capitalists,
nor communists), politics (not in the left, not in the right),
etc.
F) Socioneutrosophy:
Sociology of neutralities.
For example the sociological phenomena and reasons which
determine a country or group of people or class to remain neuter
in a military, political, ideological, cultural, artistic,
scientific, economical, etc. international or internal war
(dispute).
G) Econoneutrosophy:
Economics of non-profit organizations, groups, such as: churches,
philanthropic associations, charities, emigrating foundations,
artistic or scientific societies, etc.
How they function, how they survive, who benefits and who loses,
why are they necessary, how they improve, how they interact with
for-profit companies.
H) New Types of Philosophies:
a) Object Philosophy: a building through its architecture, a
flower, a bird flying, etc. any object are all ideas, or inspire
ideas - which are not necessarily to be written down on the paper
because they would lose their naturalness and their essence would
be distorted.
The philosophy should consequently have a universal language, not
clinged to a specific language (how to translate, for example,
Heidegger's dassein, and why to entangle in a notion, syntagme,
or word?!).
b) Concrete Philosophy: a drawing, a painting, a canvas, any
two-dimensional picture are all ideas and inspire ideas.
c) Sonorous Philosophy: a symphony melody, the jazz music, a
sound, any noise are all ideas, or inspire ideas - because they
directly work with our unconsciousness.
d) Fuzzy Philosophy: there is only a fuzzy border between <A>
and <Non-A> and, in consequence, elements which belong (with a
certain probability) to both of them, even to <A> and <Anti-A>.
Like the clouds in the sky.
An element e belongs 70% to <A> and 30% to <Non-A>. Or, more
organic, e belongs 70% to <A>, 20% to <Neut-A> and 10% to <Anti-
A> for example.
The di-chotomy between <A> and <Non-A> may be substituted with
trichotomy (<A>, <Neut-A>, <Anti-A>) according to our three\ory,
and by generalization in a similar way, with plurichotomy onward
to transchotomy [ü-chotomy] (continuum-power shades among <A>,
<Neut-A>, and <Anti-A>).
And, when the probability is involved, fuzzy-chotomy, or more:
neutro-chotomy.
d) Applied Philosophy: philosophical knowledge (such as:
proverbs, aphorisms, maxims, fables, stories) used in our every
day's life.
e) Experimental Philosophy: philosophical checking and studying
of strange, bizarre ideas.
f) Futurist Philosophy: ideas created by machines, robots,
computers using artificial intelligence;
this is the philosophy of tomorrow.
g) The main thesis of the Fonfoist Philosophy is:
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This is because philosophy is a tautology, and every
sentence is formally true in a certain referential system. Every
senseless proposition has a sense.
Then, what's the meaning of this thesis?
(F. Smarandache, "NonNovel", 1993).
h) Nonphilosophy:
To make philosophy by not doing any philosophy at all!
Like a mutism.
Everything may mean philosophy: a graffiti (having no words, no
letters), any scientific sign or expression displayed on the
page...
A poem is a philosophical system. A physics law, a chemical
formula, a mathematical equation too.
For example, a blank page also means an idea, a natural
phenomenon as well.
Due to the fact that they all make you reflect, meditate, think.
This nonphilosophy becomes, paradoxically, a new kind a
philosophy!
I) New Types of Philosophical Movements:
a) Revisionism: to review all the philosophical systems, ideas,
phenomena, schools, thinkers and rewrite the philosophy as a
cumulus of summum bonum.
b) Inspirationalism: to look to antecedents for clues and
contemporaries for inspiration to get your own research methods
and original system.
c) Recurrentism: any idea comes from a previous idea and
determines another idea, like an infinite recurrent sequence.
d) Sophisticalism: the more unintelligible, ambiguous, unsolved,
abstract, general... the better!
[This is the style of some people...]
e) Rejectivism: a unconscious (and, at some degree, becoming
mixed with conscious) will to a priori-ly repel somebody else's
system, and totally or partially replace it with yours own.
f) Paradoxism: any philosophical idea is true and false in the
same time.
Law of the paradoxism:
Nothing is non-contradictory.
Nature's essence is antonymic.
J) Logical and Combinatory Modeling in Experimental
Literature:
a) An Avant-garde Literary Movement, the Paradoxism
(which uses mathematical paradoxes in artistic creations):
the study of paradoxes as a discipline apart and their use in
other fields.
- The Basic Thesis of the Paradoxism:
everything has a meaning and a non-meaning
in a harmony each other.
- The Essence of the Paradoxism:
a) the sense has a non-sense,
and reciprocaliy
b) the non-sense has a sense.
- The Delimitation from Other Avant-gardes:
-the paradoxism has a significance,
while the dadaism, the lettrism, the absurd movement do not;
-the paradoxism especially reveals the contradictions,
the anti-nomies, the anti-theses, the anti-phrases,
the antagonism, the non-conformism, in other words the
paradoxes of anything (in literature, art, science),
while the futurism, cubism, abstractism and all other
avant-gardes do not focus on them.
- The Directions of the Paradoxism:
-to use science methods (especially algoritms) for
generating (and also studying) contradictory literary and
artistic works;
-to create contradictory literary and artistic works
in scientific spaces (using scientific: symbols,
meta-language, matrices, theorems, lemmas, etc.).
b) New Types of 'Mathematical' Poetry with Fixed Form
(using paradoxes and tautologies):
- Paradoxist Distich = a two-line poem such that the second one
contradicts the first, but together they form a unitary meaning
defining (or making connection with) the title.
- Tautological Distich = an apparently redundant two-line poem,
but together the redundant lines give a deeper meaning to the
whole poem defining (or making connection with) the title.
- Dualist Distich
- Paradoxist Tertian
- Tautological Tertian
- Paradoxist Quatrain
- Tautological Quatrain
- Fractal Poem.
c) New Types of Short Story:
- Syllogistic Short Story
- Circular Short Story
(F.Smarandache, "Infinite Tale", 1997)
d) New Types of Drama:
- Neutrosophic Drama
- Sophistic Drama
- Combinatory Drama = a drama whose scenes are permuted and
combined in so many ways producing over a billion of billions of
different dramas! (F.Smarandache, "Upside-Down World", 1993)
Similar definitions for other types of poems, of short
stories, and of dramas.