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to Progression ETHICS ---SEQUENCES: PROGRESSIONSPROGRESSIONS the CONCEPT For prediction, cyclic repeating events are easiest to predict. We predict sunrise and sunset with some confidence. But there are also progressions, a series of events that are followed by individual people, which the individuals do not repeat, but which usually follow one another in each individual. These are progressions. Some of these are not absolute, meaning that a,b,c,d,e might in another individual in another time or place be a,b,g,d,e, --(English versus Greek alphabet equivalents- alpha, beta, gamma, delta epsilon,,….). But overall these progressions follow one another thus forming predictable patterns with only minor variations. The easiest way to learn this is to illustrate a progression, and in this case mathematics will be used. People learn mathematics as a progression, a sequence of steps, that follow one another. COUNTING: First the child learns to count, one, two, free, for, six, ten, eight, twelf, firteen,… eventually getting the sequence of numbers in order. 1,2,3,4,5,6,7,8,9,10, and then to 20 to 100 etc. ASSIGNING MEANING: a precise abstract number of things is assigned to each number, 3 said “three” is “ *** ” three things; and 5 is said “five” and “ ***** ” five things. ADDING, = + The mathematical operation of grouping things, 2 + 3 = 5, this really involved two concepts the equivalence equality sign, =, and the operation, +, of grouping, and this could be more than two groups, i.e. 1 + 2+ 3 + 2 = 8 (and later complex “carry” + etc.) SUBTRACTION, = -- The Removal of groups, 8-3 = 5 (and complex – “borrowing” etc). MULTIPLICATION, = x - Groups of Groups, 5 x 3 = 15 (later long multiplication) DIVISION = / Subdividing into smaller Groups 21/3 = 7 (later long division fractions) Note that normally addition cannot be learned before counting, and that subtraction cannot be learned before addition, which cannot be learned before counting, that multiplication cannot be learned before adding, in this sequence of events one logically follows the other. While in theory multiplication might be grasped before subtraction, in practice I cannot ever remember such happening. Children learn these math skills in that order. GEOMETRY = shapes (shapes and their names may be learned before addition, but I mean quantitative geometry) and quantitative geometric relationships require multiplication. {Area of a rectangle = base, b, times height, h}, {Area for triangle = ½ bh, the circumference of a circle = pi x diameter etc.} ALGEBRA = using letters for unknowns and manipulation of the letters in an orderly conventional manner to obtain more general results. EXPONENTS exp ( xb and y3 , x2 , 4x ) LOGARITHMS log TRIGONOMETRY (the above are the transcendental functions, and note the pairs + with -, and x with /, and {exp with log} etc including d with ò below). Analytical geometry (combination of geometry and algebra, example x2 + y2 = r2 is a circle with radius r) (conceptual Probability and Statistics also fit in about here) DIFFERENTIAL CALCULUS = d INTEGRAL CALCULUS = ò VECTORS DIFFERENTIAL EQUATIONS MATRIX ALGEBRA TENSORS In the above note some overlap is to be expected, e.g. shapes as part of geometry are usually being learned at the same time as counting, and well before quantitative geometry and the ambiguity of when, in what sequence, algebra and geometry were learned. Frequently in the past this was taught algebra 1, plane geometry, then algebra II, then trig and then solid geometry, now in a mixed order. But overall the sequence is as stated, and with some barriers being absolute to prevent getting too far out of order. It is impossible to learn algebra before multiplication, in generic terms. Some of the details may be out of order, but not the generic concepts. Each individual (I) in a society may follow the progression, or the society (S) may also follow this as it learns new concepts, or both (B) may be true. Every person follows this mathematical pattern of learning mathematics. Societies, whole civilizations, also follow a progression as they develop. That in fact was true for Both with mathematics. The various steps were discovered in roughly that same order as people learn them individually today. There was one item that pointedly was out of sequence: the concept of zero. The Romans did not have the concept of zero and hence also did not really understand negative numbers. This concept was discovered by the Arabic mathematicians, who also introduced “Arabic” numbers (instead of the horrible Roman numerals – which are particularly complex when multiplying), algebra (the letters), and trigonometry. Thus even “social” progressions are not absolute, merely probable sequential steps. Many, -- even MOST people do not progress to the higher steps in the above progression. Some people choose or by lack of educational availability stop short – even FAR short of the “higher” math. Many civilizations did not yet progress all the way to the upper limits either. Certainly the earlier ones literally “could not” progress all the way as the “ higher” concepts were not invented yet. But even now whole cultures lack the “higher” abilities. Globalization has spread this widely, but not to all corners of the Earth. This thus is a typical “social science” with some exceptions, but still a very good overall guide as t what to expect. Below is a chart of how some civilizations progressed with some typiical progression that civilizations or empire followed.
They are by way of analogy a set of stepping-stones in a pathway. Some are set so they overlap, and you may step in slightly different orders, but overall you and others will follow the same sequence. EXAMPLE PROGRESSIONS These are followed by Individuals (I), by Societies (S) , or Both (B). Mathematics (B): counting, addition, subtraction, multiplication, division, {geometry, /algebra/ concept of zero}, transcendental functions {trigonometry, exponents and logarithms}, analytical geometry, differential calculus, integral calculus, vectors, differential equations, matrices, tensors. ETHICS (B) (9 topics split by 4 phases = 24 steps) Maturity (I), quantified by the time span of planning in actions, Materials: as found, pottery, ceramics, metals (copper, Bronze, Iron); SEXUAL PROGRESSION (I) (MORE
DETAILED) NOTE If people are forced into sexuality beyond their level of growth, then they can be mentally/ psychologically harmed - this is the basis for rape being so traumatic. We normally must progress at some rate (some faster, some slower) which is individual, but generally follow the entire sequence step by step, and skipping steps, or going to far too fast may lead to permanent harm. Abnormal sexuality (socio-mental diseases) as inflicted by sick social theories, Puritanism, celibacy, etc. We need to inoculate against these, and teach acceptable sexuality, within a large normal range - normal sexual behavior. The sickness includes ignorance, secrecy, and "dirty" hidden sexuality. |
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