Adonis Diaries

Archive for December 23rd, 2009

Cases of “Historical Dialectics” of human and knowledge development; (Dec. 23, 2009)

            Dialectics is not only used to comprehend historical development of human or knowledge development but is basic in discussions and effective dialogues. Hegel was first to introduce “dynamic logic” and used the term of historical dialectics as the interaction of an extreme opinion (thesis) that generates an opposite extreme counter opinion (antithesis) which results in a consensus (synthesis).  Historical dialectics is a macro method for long range study and it does not explain the individual existential conditions (survival situations).  Hegel offered dialectics as a method for explaining how human knowledge developed by constant struggle between contradictory concepts among philosophical groups. The purpose of his method was to demonstrate how the “universe of the spirit” or ideas managed to be raised in human consciousness.

            Before I offer my version of knowledge development it might be useful to giving a few examples of historical dialectics. In Antiquity, the pre-Socratic philosophers were divided between the Eleatics or philosophers who claimed that change of primeval substances was impossible: we cannot rely on our senses.  Heraclites reacted with his position that we can rely on our senses and that everything in the universe is in a state of flow and that no substance remains in its place.  The synthesis came Empedocles who claimed that we can rely on our senses but that what flow are the combination of substances but the elementary particles do not change. 

            The Sophists during Socrates were the paid teachers of the elite classes and tore down the mythological teaching of the period and focused on improving individual level of learning.  They were in effect in demand by a nascent City-State democracy of Athens that relied on a better educated society to participate in the political system. Socrates reacted by proposing that there are fundamental truths and knowledge is not an exercise in rhetorical discourse. The same dialectics worked between the world of ideas of Plato and the empirical method counterpoint of Aristotle.

            In the Medieval period the Catholic Church set up a barrier or distance between God and man and forced people to believe that all knowledge emanates from God.  The Renaissance man (wanting to be knowledgeable in many disciplines) reacted by promoting the concepts that God is in every element, that man is a complete microcosm of the universe, and that knowledge starts by observing nature and man.

            Another example is the position of Descartes who established that rationalism was the main source for knowledge.  David Hume responded by extending that empirical facts generated from our senses are the basis for knowledge. Kant offered the synthesis that the senses are the primary sources for our impressions but it is our perceptual faculties that describe and view the world: there is a distinction between “matter” of knowledge or the “thing in itself” and “form” of knowledge or the “thing for me”. Kant became the point of departure for another chain of dialectical reflections.

            Many philosophers used the dialectic methods to explaining other forms of development.  Karl Marx wrote that Hegel used his method standing on its head instead of considering human material conditions. Marx claimed that “philosophers have only interpreted the world; the point is to change it”; thus, he defined three levels as basis of society: condition of production (mainly the geographic, natural resources, and climatic conditions), means of production (such as machineries and tools), and production relations (such as political institutions, division of labor, distribution of work and ownership). Marx claimed that the main interactions are among the working class (the new slaving method of production) and the owners of the means of productions or the ruling class: it is this struggle that develop the spiritual progress.  Another dialectical process is the extreme feminist political claims of equality between genders which brought about a consensus synthesis for a period.

            My view of progress is based on the analogy of combination of two schemas:

            The first schema is the coexistence of two strings of evolution (picture a DNA shape): the knowledge development (mainly technological) and the moral string (dominated mainly by religious ideologies).  The second schema is represented by historical dialectic evolutions in the shape of helical cones. The time lengths of cycles for the two strings are not constant: the technological progress phase has shorter and shorter cycles while the moral string has longer cycles.

            The two strings are intertwined and clashes frequently.  When one string overshadow the other string in evolution then there are a slow counter-reaction culminating in stagnate status-quo phases between the two forces. Technological or level of sustenance period has time length cycles that is shrinking at the top of the cone before the cone is inverted on its head so that the moral time length cycles start to increase and appears almost invariant (that what happened in the long Medieval period that stretched for over 11 centuries in Europe); then the cone is reverted on its base for the next “rebirth” cycles (for example the Renaissance period that accelerated the knowledge string ascent).

Idiosyncrasy in “conjectures”; (Dec. 21, 2009)

Idiosyncrasy or cultural bias relates to “common sense” behavior (for example, preferential priorities in choices of values, belief systems, and daily habits…) is not restricted among different societies: it can be found within one society, even within what can be defined as “homogeneous restricted communities” ethnically, religiously, common language, gender groups, or professional disciplines.

Most disciplines have mushroomed into cults.

A cult is any organization that creates its own nomenclature and definition of terms to be distinguished from the other cults in order to acquiring recognition as a “professional entity” or independent disciplines that should benefit from laws of special minorities (when mainly it is a matter of generating profit or doing business as usual).

These cults want to owe the non-initiated into believing that they have serious well-developed methods or excellent comprehension of a restricted area in sciences. The initiated on multidisciplinary knowledge recognize that the methods of any cult are old and even far less precise or developed; that the terms are not new and there are already analogous terms in other disciplines that are more accurate and far better defined.

Countless experiments have demonstrated various kinds of idiosyncrasies.  This article is oriented toward “cult” kinds of orders, organization, and professional discipline.  My first post is targeting the order of mathematicians; the next article will focus on experiments.

Mathematics, meaning “sure study” (wisekunde), has no reliable historical documentation. Most of mathematical concepts were written many decades or centuries after they were “floating around” among mathematicians.

Mathematics is confusing with its array of nomenclature. What are the differences among axiom, proposition, lemma, postulate, or conjecture?  What are the differences among the terms, theorem, questions, problems, hypothesis, corollary, and again conjecture?  For example, personally, I feel that axiom is mostly recurrent in geometry, lemma in probability, hypothesis in analytical procedures, and conjecture in algebraic deductive reasoning.

Hypothesis is in desuetude in mathematics. For example, Newton said “I am not making a hypothesis”.

Socrates made fun of this term by explaining how it was understood “I designate hypothesis what people doing geometry use to treating a question.  For example, when asked for their “expert opinion” they reply: “I still cannot confirm but I think that if I have a viable hypothesis for this problem and if it is the following hypothesis… then I think that we may draw a conclusion. If we have another hypothesis then another conclusion is more valid.”

Plato said: “As long as mathematics start from hypothesis instead of facts then we do not think that they have true comprehension, since they are not going back to fundamentals”

Hypothesis is still the main term used in experimental research. Theoretically, an experiment is not meant to accept a hypothesis as true or valid, but simply “Not to reject it” if the relationships among the manipulated variables are “statistically significant” to a pre-determined level, usually 5% in random errors.

Many pragmatic scientific researchers don’t care about the fine details in theoretical mathematical concepts and tend to adopt a hypothesis that was not rejected as law.  This is one case of idiosyncrasy when the researcher wants badly the “non-rejected” hypothesis to represent his view. Generally, an honest experimenter has to repeat the experiment or encourage someone else to generalize the results by studying more variables.

Conjecture means (throwing in together) and can be translated as conclusion or deduction; basically, it is an opinion or supposition based on insufficient proofs.

In the last century, conjectures were exposed in writing as promptly as possible instead of keeping them floating ideas, concepts, or probable theorems. This new behavior of writing conjectures was given the rationale that “plausible reasoning” is a set of suppositions thrown around as questions mathematicians guess they have answers to them, but are unable to demonstrate temporarily.

The term conjecture has been used so freely in the last decades that Andre Weil warned that “current mathematicians use the term conjecture when they fail after a few attempts to verify a concept, even if the problem is of no importance.”  David Kazhdan ironically warned that this practice of enunciating conjectures might turn out like a 5-year Soviet plan.

At first, a set of conjectures was meant to be the basic structure for a theorem or precise assertions that were temporarily used in the trading of logical discussions. Thus, conjectures permit the construction of rigorous deductions that are accessible to direct testing of their validity. A conjecture was a “research program” that move ahead in order to foresee the explored domain.

Consequently, conjecture is kind of extending a name and an address to a set of suppositions and analogies for a concept, long before tools and methods are created to approach directly the problem.

A “Problem” designates a mental task submitted to the audience or targeted for research or project; usually, the set of problems lead to demonstrating a general theorem. Many problems are in fact conjectures such as the problem of twin primary numbers that consists of proving the existence of an infinity of coupled numbers such that p-q = 2.

One of the explanations for using freely the term conjecture is the modern facility of mathematicians of discriminating aspects of uncertainty at the theoretical level. It is an acquired habit, an idiosyncrasy. Thus, for a mathematician to state a conjecture he must have solved many particular cases and recognize that a research program is needed to developing special tools for demonstrating the conjecture.  This is a tough restriction in this age where time is of essence among millions of mathematicians competing for prizes.


adonis49

adonis49

adonis49

December 2009
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