No State that is moving toward seperation from the Republic for which Democracy stands.
Structure may start best with a little Mountain Math, from a paper; only a small part of a greater..
.. Immediate experience and existence focus..
.. Intuition and intellect,!
That begins with a little Mountain Math!
http://www.mtnmath.com/expt72h/node10.html
While we are yearning, for a yesterday, today, to feel as strong, a strong urge is created to get away from our daily ro utine that we may not be entirely conscious of it; like a mood of restlessness that is hard to pin down what to really change.
But how can it be done in the mind as well as in the physical world and to a routine isn't too radical? To find ideas and concepts that are both revolutionary and liberating without exposing or creating greater weaknesses.
Maternal instincts that may be sightly out of protocol.
Sure, things are slightly out of focus.Even the math is part of the Artistic matters.
So we must seek favorable circumstances in business and professional lives, attracting persons interested in our workingand living harmoniously; so tomorrow the stream can be discovered attractive by others within.
Take the time to observe situations or persons that you have been taking for granted.
You should take the time to correct little problems as they arise and give them the attention that they require.
"Mathmatics and Some Educational Implications",
The History of the Concept of Function
... and Some Educational Implications
( http://math.coe.uga.edu/tme/issues/v03n2/Ponte.pdf )
.. "it was Leibniz (1646-1716) who first used the term "function" in 1673. "
...He took function to designate, in very general terms, the dependence of geometrical quantities such as subtangents and subnormals on the shape of a curve. He also introduced the terms "constant," "variable," and "parameter."...
...As far as mainstream mathematics is concerned, the identification of functions with analytical expressions would remain unchanged for all of the 18th century.
In the 19th century, however, the notion of function underwent successive enlargements and clarifications that deeply changed its nature and meaning.A significant push towards the enlargement of the concept of function came first from the
famous controversy over the problem of the vibrating string....
... ... Particular instances of functions may be found in ancient epochs; for example, counting,
implying a correspondence between a set of given objects and a sequence of counting
numbers; the four elementary arithmetical operations, which are functions of two variables;
and the Babylonian tables of reciprocals, squares, square roots, cubics, and cubic roots.
Historically, some mathematicians can be regarded as having foreseen and come close to a
modern formulation of the concept of function. ..
..Among them is Oresme (1323-1382),.. In his theory, some general ideas about independent and dependent variable quantities seem to be present...
..Descartes (1596-1650) clearly stated that an equation in two variables, geometrically represented by a curve, indicates a dependence between variable quantities....
..Newton (1642-1727) was one of the first mathematicians to show how functions could be
developed in infinite power series, thus allowing for the intervention of infinite processes. He
used "fluent" to designate independent variables, "relata quantitas" to indicate dependent
variables, and "genita" to refer to quantities obtained from others using the four fundamental
arithmetical operations...
..Finally, "function" was adopted for that purpose in the correspondence interchanged by Leibniz and Jean Bernoulli (1667-1748) between 1694 and 1698...
..The term function did not appear in a mathematics lexicon published in 1716. Two years later, however, Jean Bernoulli published an article, which would have widespread dissemination, containing his definition of a function of a variable as a quantity that is composed in some way from that variable and constants...
.. Euler (1707-1793), a former student of Bernoulli, later added his touch to this definition speaking of analytical expression instead of quantity.
The notion of function was therefore identified in practice with the notion of analytical expression.
This formulation was soon perceived to lead to several incoherences; in fact, the same function could be represented by several different analytical expressions.
The formulation also yielded serious limitations on the classes of functions that could be
considered.
In present day terminology, of the term, the phrase "no strings attached" should be the dictation, seeing how the curve extracts into the limitation of exaustion as a routine; therfore having not a healthy stable balance from which to adjust to slow or increase abundances of many...
ReFine Humanities International Complete resource to redirect Evolution of Topic
CRITERIA OF FALLACY AND SOPHISTRY FOR USE IN THE ANALYSIS OF PLATONIC DIALOGUES.
DIALOGUES. Citation Only Availabl
Title:
CRITERIA OF FALLACY AND SOPHISTRY FOR USE IN THE ANALYSIS OF PLATONIC DIALOGUES.
Authors: Klosko, G.
Source: Classical Quarterly
Date: 1983
Publication Type: Academic Journal
Subjects: FALLACIES (Logic),JUDGMENT (Logic),REASONING,LOGIC, Ancient,PHILOSOPHY, Ancient,CLASSICAL philology,SOCRATES,PLATO,SOCRATES,PLATO
Abstract:
Suggests a criteria that can be utilized by classical scholars for assessing the use of fallacy and logic in ancient Greek philosophy. Reluctance in the part of some classical scholars to acknowledge Socrates' use of sophistry; Observations made by scholars on the complexities associated with Plato's use of dialogue form; Differentiation between argument and proof.
Noncomparabilism in epistemology
By: Wunderlich, Mark. Philosophical Studies, Jan2009, Vol. 142 Issue 2, p133-151, 19p, 1 diagram; DOI: 10.1007/s11098-007-9179-8; (AN 35820294)
Subjects: KNOWLEDGE, Theory of; QUESTION (Logic); PHILOLOGY; INTELLECT; THEORY & practice
Database: Humanities International Complete PDF Full Text (240KB)
An Early Latin Debate of the Body and Soul: Preserved in MS Royal 7 A III in the British Museum (Book).Full Text Available By: Utley, Francis Lee. Modern Language Quarterly, Sep41, Vol. 2 Issue 3, p503, 3p; (AN 10028911)
Subjects: BOOKS -- Reviews; NONFICTION; BODY & soul in literature; EARLY Latin Debate of the Body & Soul, An (Book); HENINGHAM, Eleanor
Database: Humanities International Complete
About Sweeping Changes . The impetus for change may come through persons who present you with many upsetting surprises, all of which show that your life is no longer what is was.
The key point to recognize is that this process is not bad for you, it is just upsetting at first until you get into the flow of events. It can be quite exciting and will certainly inject an element of youth into your life again, with the advantage that now you will have the wisdom to handle it properly.
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