The decryption of law as an exact normative science using fractals

Author:Nasty Marian Vladoiu
Position:Ph.D., associate professor, Faculty of Law, 'Transylvania' University, Brasov, Romania
Pages:56-65
SUMMARY

In order to be studied as a science, Law had to transit an intense process of specialization and consecration of values, values becoming thereby its object of study and specific research. Throughout time, Law has been studied from various perspectives, because of its variable geometry, being considered in continuous transformation, with a social dynamics in ascension. Most specialists agree that Law is a complex phenomenon, with a synergistic, well-defined structure, which cannot be summarized in the exegesis of some legal norms or normative texts and precedents. Therefore we ask ourselves whether the Theory of Fractals can argue the law’s character of being an exact science and implicitly natural on the one hand and, on the other hand, its nature of normative science. Keywords: public law, fractals, exact science, normative science, legal norm, theory of fractals, auto similarity, recursive character, aliens, extra-terrestrial civilizations

 
CONTENT
56 NASTY MARIAN VLĂDOIU
THE DECRYPTION OF LAW AS AN EXACT NORMATIVE
SCIENCE USING FRACTALS
Nasty Marian VL>DOIU
Ph.D., associate professor,
Faculty of Law, “Transylvania” University, Braşov, Romania,
Abstract
In order to be studied as a science, Law had to transit an intense process of specialization and
consecration of values, values becoming thereby its object of study and specific research.
Throughout time, Law has been studied from various perspectives, because of its variable
geometry, being considered in continuous transformation, with a social dynamics in ascension.
Most specialists agree that Law is a complex phenomenon, with a synergistic, well-defined
structure, which cannot be summarized in the exegesis of some legal norms or normative texts and
precedents. Therefore we ask ourselves whether the Theory of Fractals can argue the law’s character
of being an exact science and implicitly natural on the one hand and, on the other hand, its nature of
normative science.
Keywords: public law, fractals, exact science, normative science, legal norm, theory of fractals,
auto similarity, recursive character, aliens, extra-terrestrial civilizations.
1. Introduction
Since the early 20th century, a great jurist, Rudolf Stammler, appreciate that
the science of law has a structure based on two main branches, namely: one
technical, designed to study the meaning and content of the laws in their
systematic composition and, one theoretical branch, which has to determine
whether the law is the fair means for fair purposes (’’ The agreement of laws with
the social ideal”)1.
It was stated that naturally, the science of law belongs to the system of social
sciences, taking into consideration the object of law and a long and unchanged
traditional perception.
It is well known that in the picture of social sciences, law holds a very
important and special place, being determined both by its own purpose and by the
E-mail: vladoiu.nasty@gmail.com.
1 N. Popa, Teoria general? a dreptului, 3rd edition, C.H. Beck Publis hing House, Bucharest, 2008,
p. 4.
Law Review vol. IV, issue 2, July-December 2014, p. 56-65
The decryption of law as an exact normative science using fractals 57
interdisciplinary one closely related to it, which helps configuring the dimension
and structure of law as a science.
"As a science having specific status and position, the science of law examines a
particular area of relationships and social structures – the area of people
participating in the legal circuit, as bearers of legal rights and obligations, with all
the consequences arising from this"2.
Throughout time, law has been studied from various perspectives, thus we
conclude that law is a complex phenomenon with a variable geometry, being in
continuous metamorphosis and having an increasing social dynamics.
2. Law as a social science
To be studied as a science, law had to transit an intense process of
specialization and consecration of values, thus becoming its object of study and
specific research.
On the question if Law is a social science the answer is affirmative and it is
based on the traditional theory and on the fact that the analysis of its object was
made from the perspective of epistemological connections and its relations with
other social sciences, which helped to demonstrate its classification as a social
science.
However, we can formulate at least two legitimate questions that are based on
the most important theories launched over the years about the science of law
namely, whether Law is an exact science and can be demonstrated from the
gnoseological perspective of relations and links with the exact sciences, such as, for
example, mathematics, despite the theory of natural law. And the other question: If
Law is exclusively a normative science, taking into account the stated purpose of
the Pure theory of law, ”to save a knowledge based on law and to eliminate from
this knowledge everything that does not belong to the domain determined exactly
as being the Law”3, and also one of the most important ideas of Kant’s legal
philosophy, which replaces the naturalistic paradigm of controlling individuals by
force with the normative one, that of defining the persons through their rights and
obligations4.
Relevant for the attempt to answer these questions it is also the statement of
the great Romanian professor of Criminal Law, Vintil? Dongoroz, according to
which he is on the ”line of Kelsen’s pure juridicity” representing ”that” ”back to
Kant” from the theory of knowledge, that was recorded in Marburg School by
German philosophy5.
2 Ibidem, p. 3.
3 T. Avrigeanu, O teorie pur? a dreptului penal? Thomas Hobbes, Hans Kelsen şi Vintil? Dongoroz,
„Studii de Drept Românesc” Magazine, 2008, apud Hans Kelsen, Doctrina pur? a dreptului, p. 13.
4 T. Avrigeanu, op. cit., apud G. Jakobs, Staatliche Strafe: Bed eutung und Zweck, Opladen, 2004,
p. 15.
5 T. Avrigeanu, op. cit., apud P. Pandrea, Criminologia dialectic?, p. 53.
58 NASTY MARIAN VLĂDOIU
We cannot consider that the research in the legal phenomenon is sufficient at
the level of knowing the consecutive forms of law (historical analysis) nor at the
level of knowing the positive law and the active law, in force, in a particular time
and space6.
Usually, the General Theory of Law is considered the reference discipline for
studying the science of law and it tried constantly to provide solutions as accurate,
satisfying both conceptual issues and their subsequent application in practice.
Whether he fully succeeded or not and if he had a comprehensive approach,
we will appreciate together in the present study.
Anyway, the research process of the legal phenomenon can be translated into a
simple phrase: Today’s research is tomorrow’s future!
At this point, one of the dilemmas that disturb much of the general theory of
law professionals is the fact of knowing whether the science of law should stop at
the study of legal rules, case-law, legal relations, legal sources, contracts etc.,
without subjecting to an intense explanatory process the socio-cultural context in
which occur and exist the rules and legal institutions, that collaborate in this
process with all the social sciences, such as economics, sociology, history etc.7.
To this dilemma is trying to answer the science of law system, which according
to some opinions8, consists of: The General Theory of Law, The legal sciences
branch, The historical legal sciences and the supporting sciences (participatory).
Most specialists agree that Law is a complex phenomenon, with a synergistic,
well-defined structure, which cannot be summarized in the exegesis of some legal
norms or of normative texts and precedents. Thus law, both through its intrinsic
value and through the relations and connections with other social sciences known
at some point, represents a complex of interdependent sciences.
3. Law as an exact normative science
It is interesting compared to the above, to analyze in context and in
counterbalance one of the great jurist Hans Kelsen theory assertions, according to
which the entire law is reduced to the rule of law, considered by him the sole object
of study of the science of law and a way of subjective self-interpretation with legal
sense.
Kelsen showed that validity is the one the normativism concept is configured
on, meaning that every legal norm is valid due to a systemic security based on the
compliance with the superior law.
The author of the Pure Theory of Law argued that the validity of the legal
norm does not depend on its effectiveness or on the volitional act that gave birth to
it, but it is related only to the whole legal edifice existing in a particular time, in a
specific space.
6 N. Popa, Teoria Dreptului în sistemul ştiinelor juridice, University of Bucharest Annals, Law, 1991.
7 N. Popa, op. cit., p. 3.
8 Ibidem, p. 4.
The decryption of law as an exact normative science using fractals 59
The great author stated that Law is based on and develops itself as a logical
system, perfect deductible.
However, we consider that when Kelsen produce claims, by which is trying to
demonstrate the establishment and sanctioning of the supreme norm, that he
considers the basic rule, is not fully convincing. The supreme norm should be a
rule that requires a purpose, it has to be assumed and not sought and it cannot
relate to or rely on another norm, much higher, which would give competence to
the authority generating the supreme norm.
We believe that the supreme norm can be although generated with the help of
fractals theory, having available more and more efficient technologies in the IT
area, thus regularities about human being created following a primary outcome,
and which are able to unveil us everything that should be connected with humans
and for them, not just what it is.
In 1937, Tudor Vianu, the founder of the stylistic school of the Faculty of
Letters from Bucharest said: ”Starting the scientific research of a particular object
by sitting the methodical principles, means to conclude a convention with your
own intelligence, similar to that of modern states given to each other through their
fundamental pacts” 9.
Whether Hans Kelsen, ”concluding an agreement with his own intelligence”
obtained through a well-defined method, or not, the result of his theory, we believe
that what matters following a judicious process of scientific thinking is the result
obtained.
Of course, the methodology is very important from the perspective of the
scientific research of the object of law, and the method appears as an effective
means of scientific thinking, especially in the current context, in which the border
sciences, the research and studies at the confluences have become a necessity for
specialists.
Very important are also, however the methodological steps from the
perspective of the complex relations that can be established between them, starting
from singular to multiple, from particular to general, from idea to an entire
process, from part to whole.
It is necessary to reveal a striking similarity between Hans Kelsen’s theory,
concerning the rule of law as the sole object of study of the science of law, and a
part of our study having as purpose to demonstrate that law is an exact normative
science, using the theory of fractals.
Obviously that Hans Kelsen could not have as a scientific research method, but
maybe just as vision, the theory of fractals, given the appearance of fractal
geometry, as part of mathematics, in particular, and of exact sciences, in general,
only in 1975, when was launched by its parent, the great mathematician, Benoît
Mandelbrot, Sterling Professor at University of Yale.
9 T. Vianu, Metod? şi obiect. Opere, Vol. 9, ediie de G. Ionescu şi G. Gan?, Ed. Minerva, 1980,
p. 192.
60 NASTY MARIAN VLĂDOIU
Typically, the natural sciences are considered to be exact sciences, because they
can be easily quantified through usual methods of physics, astronomy,
mathematics, chemistry, biology etc., while the social sciences are considered to be
immeasurable.
The quintessence of our scientific study is based on the assertion that law is
also an exact normative science, statement that can be proved by using the method
of applying and comparing the characters and functions of fractals in relation to
the ones of Law.
In fact, Kelsen although denies the natural roots of the science of law, he
understands society as a natural and normal coexistence of humans, placing the
only difference between the natural process and that of human psychic, in nature.
Relying on this difference between the natural process and the human psychic
process in nature, he appreciates the rule of law as an exclusive object of study of
the science of law. In Kelsen’s view, these are true schemes of legal interpretation
of reality, by way of the normative link existing between coercion and human
behavior.
However, we consider necessary a more rigorous clarification on the response
to the question, if between the natural character and the normative one of the
science of law is there any connection or are they completely different?
The great Romanian professor, Mircea Djuvara appreciated such
differentiation in the following parameters: “The word “normative” is usually
employed for certain laws and sciences, to distinguish them from natural laws and
sciences. The natural sciences include laws on the external or internal nature, the
laws contained as type in the exact sciences in general, those which ascertain what
simply happens when researching what are, in fact, the efficient causes of the
phenomena given. The normative sciences have not as object to find what is, but
what should be an activity”10.
It is also the renowned professor Mircea Djuvara the one who promoted in our
juridical doctrine the rigorous distinction that “the individual is nothing but a
human being seen as object of study of the natural sciences, while the person
condenses the aspects that became relevant from the perspective of normative
sciences”, and pointed out that for the development of the legal concepts this
distinction represents the starting point and also the quintessence: “everything is to
agree on what is to be understood in law and moral through the idea of person. If a
person should always be seen as a material reality, as practiced often, there are
possible any confusions, but if…we consider us persons, is because we assign us
rights and obligations”11.
10 T. Avrigeanu, op. cit., apud to M.Djuvara, Teoria general? a dreptului, Bucharest, 1995, p. 213.
11 T. Avrigeanu, op. cit., apud to M. Djuvara, Eseuri de filosofie a dreptului, p. 192, 63/64.
The decryption of law as an exact normative science using fractals 61
So we see that professor Djuvara defines and outlines “the connections”
between the natural character and the normative one of the science of law. He
distinguishes the man, by evaluating him as individual or as person, depending on
the need to address, individual – when it is about the natural character of the
human sciences, and person – when it is about the normative character of the
science of law.
The Romanian specialist appreciates and recognizes the “vast new light
brought into the science of law, following the path indicated by the neokantian
school”12 of Kelsen.
In the Kelsen-Djuvara parallel is interesting to note that both lean explain the
normativism, but they treat it from different perspectives when reporting to law.
While Kelsen starts from the rule of law as sole object of study of the science of
law, Djuvara, shows that the person is the main object of study of the normative
sciences and, consequently, of Law as a normative science.
Until the advent of the theory of fractals in 1975, the ability to commensurate
the complexity of the science of law and its normative dimension was science
fiction. In this endeavour, we will try however to prove, based on the application
of the theory of fractals that, Law is also an exact normative science.
We will start from the definition of fractals, as it is colloquially depicted by
Mandelbrot, according to which, a fractal is “a fragmented or broken geometric
shape that can be split into parts, so that each of them to be (at least approximately)
a miniature copy of the whole”13.
Comparing the definition of fractals with the above mentioned, we can assert
without fear of error that both the rule of law and the person, can be treated,
individually, as a fractal.
Therefore, the person can be defined as that man considered subject with
rights and obligations and who participates in this quality in civil legal relations14.
Consequently, the sum of two fractals represents also a fractal and we consider
that, for the present study, in order to demonstrate the law as an exact normative
science, is sufficient only the appreciation of the legal norm from the perspective of
the theory of fractals, as an intrinsic value, able to define everything that has to be
the person, as subject of law with rights and obligations.
Kelsen’s and Djuvara’s theoretical assertions on the rule of law as sole object of
study of the science of law on the one hand, and the one according to which, man
as a person and not as individual is relevant from the perspective of normative
sciences on the other hand, can be considered in terms of the theory of fractals that
12 T. Avrigeanu, op. cit., apud to M.Djuvara, Drept raional, izvoare şi drept pozitiv, p. 508-509.
13 B.B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman and Company Publishing
House, 1982, ISBN 0-7167-1186-9.
14 Dicionarul explicativ al limbii române, DEX ’09.
62 NASTY MARIAN VLĂDOIU
they had generated two fractals, two observation units on a different scale, both
representing the whole in miniature, in fact, the basis from which one can start in
the advocacy of demonstrating the law as an exact normative science.
Having the opportunity to consider it a fractal of law, we define the rule of law
as being that rule of conduct, general and impersonal, edicted and sanctioned by
state, which regulates rights, obligations, interests and important aspects in a given
society, whose compliance is compulsory, and which in case of violation engages
the intervention of the state coercion force.
Consequently, positive law represents the totality of the active legal norms in a
state, at a given moment, being an immediately applicable law, continuous,
compulsory and liable to be brought to fruition through the force coercion of the
state.
It is easily noticeable and well known that the rule of law has a trichotomy
structure (hypothesis, provision, sanction), related to its entire existence in the
system of law and that the dichotomus appearance of some legal rules (as for
example, the rule of constitutional law) cannot be taken into account as an object of
analysis, because the sanction is found in other specific branches or can be
implicitly inferred from the provision.
As a first condition required by the existence of fractals namely, that of having a
fine structure at arbitrarily small scales, we consider that the rule of law corresponds
to the unit of observation in report to which we will examine the other conditions
too.
A second condition consists of the fact that a fractal is too irregular to be described
in a traditional geometrical language, being very easy to notice that law cannot be
reduced to simple traditional mathematical formulas, in the light of the effects that
can be produced by the legal rules and also, that there cannot be ab initio
predictable the totality of situations in which they may applied.
The third condition in order to determinate the presence of a true fractal is the
one of autosimilarity, by this being understood that the fractal represents a whole,
whose parts are in largely identical to it or at least approximate. Mandelbrot
himself described autosimilarity as “an ensemble presenting the same irregularities
at all scales considered”.
Although apparently the trichotomic structure of the rule of law entails an
easy mathematical presentation (three parts), in reality they are irregular from a
legal rule to another from the perspective of the size of texts and the specific effects
they generate, respectively the particular situations they are related to, maintaining
thus the same character at the level of laws, codes, constitution, conventions,
treaties.
To get a clearer picture on the fulfilment of this condition, we can call the
plastic model of the tree presentation which has “as strain”, the Fundamental Law
(the Constitution), who generates “two main branches”, the Public Law branch
The decryption of law as an exact normative science using fractals 63
and the Private Law branch, which in turn, are divided into several other
secondary branches, each one of these being considered a unit for a random scale
of observation, that will always satisfy the part-whole condition of similarity.
The forth and the last condition, relevant to point out the presence of the
theory of fractals in law is represented by the simple and recursive character of fractals.
The rule of law must be flexible and accessible to understanding, being
desirable the application of as few methods of interpretation, in order to achieve
the effects considered ab initio at the adoption.
There should be also taken into account the cumulative existence of the
fractal’s recursive character, in our case, of the rule of law, along with that of
simplicity. The recursive character is translated through the repeatedly, automatic
and unlimited application of the rule of law. In the case of Law, the legal norm as
fractal, can be implemented whenever necessary, without limit of application,
without any restrictions, as long as the rule of law is in force.
4. Conclusions
Accordingly, the present approach attempted to show on the one hand, that
law is a normative science, by analyzing the theories and relating us to the
allegations of the great coryphaeus, theorists of law at national and international
level as Kant, Kelsen, Djuvara, and on the other hand, that Law represents an exact
science, characters of the science of law evidenced through the theory of fractals.
If until now, the study of law as a self-contained social science or in connection
with other border sciences was deemed sufficient, it becomes thus necessary a new
approach, in relation to sciences apparently without intrinsic connections, but
which finally determines, proves and fixes its very character.
The development of the new technologies and the sciences of the future will
reveal certainly new ways of law configuration and study at the international level
and will strengthen the value of the assertions of the present study.
We notice that the theories launched so far, according to which, the law is only
a social science, should be assessed under benefit of inventory, being taken into
account as long as the type of society will not be changed. It should be appreciated,
however, when the portrait of the new era will be changed, being determined by
the paradigm of a future society, namely, the Informational Society, which sure
will serve to influence and configure maybe, in another way, the science of law.
It will not take long and the first laws designed entirely by computers, with
little human intervention, will occur. We appreciate that the problem of the
supreme norm of Kelsen remains an open question, because the type of society in
which the man of the future will live has to answer to ”how?” and ”in what way?”
and ”by whom?” the supreme norm shall be generated and, even ”what form?”
will it have, so that the complice in relation to it to offer a systemic result and pure
of law. The paradigm of the ”supreme norm generator” seems that will be
64 NASTY MARIAN VLĂDOIU
configured and managed by an innovative branch that is outlined into being
Cyberlaw.
Perhaps the Constitutions of the future created using computers, based on
everything it is known about human as an individual and as a person, will be
much better than those made so far by jurists. The widespread use of information
techonlogy and communications and the progress towards the Informational
Society provide economic growth in conditions of increased environmental
protection, by accelerating the reduction of physical consumption to harness
information and knowledge, the movement of the gravity center from investment
in fixed assets to investment in human capital.
The Informational Society integrates the objectives of sustainable development,
based on social justice and equality of opportunity, freedom, cultural diversity and
innovative development, ecological protection, restructuring the industry and the
business environment.
The transition process to the Informational Society will also outline its risk-
phenomenon called Digital Divide, which has to be managed both nationally and
internationally.
Accordingly, we sustain that globalization, the technological evolution and the
possible existence of extra-terrestrial civilizations were not envisaged by the great
coryphaeus of law and this might change drastically the theories known so far
about the science of law. Only the character of exact science of it can give us vague
predictability regarding the transformation of law in the future, based on the
theory of fractals and other theories that have not been discovered yet and which
will allow us, actually, to start from a norm and a given issue and reach n
regularities.
We conclude to appreciate that regardless of the type of society the man will
develop, he will still be the supreme norm generator, as long as computers will be
mastered by him and in the case that human intelligence will be the creator of
artificial intelligence and will control thereof.
What will be however, Law, in relation to the question, ”If there are other
civilizations in the Universe?” and to the simple answer, that has raised endless
discussions: ”YES”.
We cannot ignore the assertions backed with increasingly more strength by
internationally authorized institutions and even by the Papal State, through Jose
Gabriel Funes, the current Director of the Vatican Observatory, who claimed that
”as there is a multitude of creatures on Earth, it is possible that Universe be
studded with numerous life forms, some much more intelligent than us”, or even
the statement of the Pope Ioan Paul II, beatified at 1st May, 2011, who had the
following answer to the same question: ”Yes, aliens exist and they are our
brothers”.
What will then mean the supreme norm and who will enact and sanction it?
The decryption of law as an exact normative science using fractals 65
References
[1] Avrigeanu, T., (2008), O teorie pur a dreptului penal? Thomas Hobbes, Hans
Kelsen şi Vintil Dongoroz, „Studii de Drept Românesc” Magazine, Bucharest;
[2] Djuvara, M., (1995), Teoria general a dreptului, Bucharest, pp. 213;
[3] Djuvara, M., Eseuri de filosofie a dreptului, pp. 192;
[4] Djuvara, M., Drept raional, izvoare şi drept pozitiv, p. 508-509 ;
[5] Jakobs, G., (2004), Staatliche Strafe: Bedeutung und Zweck, Opladen, pp. 15;
[6] Kelsen, H., Doctrina pur a dreptului, Humanitas Publishing House, pp. 13;
[7] Mandelbrot, B.B., (1982), The Fractal Geometry of Nature, W. H. Freeman and
Company Publishing House;
[8] Pandrea, P., Criminologia dialectic, pp. 53;
[9] Popa, N., (2008),Teoria General a Dreptului, ed. a 3a, C.H. Beck Publishing House,
Bucharest, pp. 4;
[10] Popa, N., (1991), Teoria dreptului în sistemul ştiinelor juridice, Analele Bucharest;
[11] Vianu, T., (1980), Metod şi obiect. Opere, Vol. 9, ediie de G. Ionescu şi G. Gan,
Minerva Publishing House, p. 192.