"ROAST PIG (THE HARD WAY)" MATH (101-200 OF FAQS UNTAUGHT, PROVE OTHERWISE!)
"ROAST PIG (THE HARD WAY)" MATH (101-200 OF FAQS UNTAUGHT, PROVE OTHERWISE!)101. Students are not taught the need for ASTRONOMICAL knowledge for daily working in ancient times.102. Students are not taught about "regularities of the sky" which ancients could depend on.
103. Students are not taught that ancient Egyptians were perhaps first to realize that the sun appears to circle the Earth in approximately 365 days and nights.
104. Students are not taught that Mesopotamian clay tablets seem to be "astronomical diaries" of professional astronomer-scribes.
105. Students are not taught that, by 6th Century B.C., Neo-Babylonian astronomers computed in advance the expected time intervals between MOONRISE & MOONSET and SUNRISE & SUNSET for various days in the months ahead.
106. Students are not taught that Babylonian priests devised various mathematical methods to deal with variations in the motion of celestial bodies.
107. Students are not taught the importance to daily life and work of the phases of the moon in a world without gas or electrical lighting.
108. Students are not taught about recorded cases wherein a (forewarned) ruler used the panic invoked by a SOLAR ECLIPSE to take over an enemy city.
109. Students are not taught that Columbus used his Almanac's prediction of a solar eclipse to escape from Native Americans in "The New World".
110. Students are not taught that the comet measurements by Newton's friend, Edmund Halley, enabled him to retrodict that this comet had turned the tide at the Battle of Hastings in 1066, when French Normans defeated Britons.
111. Students are not taught that by 4000 B.C. Babylonian astronomers had developed an effective "rhetorical algebra" (nonsymbolic, formulated in words).
112. Students are not taught that these Babylonian priests had extensive log tables, for solving COMPOUND INTEREST problems in much the way children of our time do.
113. Students are not told that Babylonian priests avoided DIVISION operations, such as a/b by using look-up tables for RECIPROCALS OF NUMBERS (such as 1/b), using them as MULTIPLIERS.
114. Students are not taught that these Babylonian priests had extensive mathematical tables of various kinds; that they knew trigonometry, the socalled Pythagorean Theorem, and an estimate of the number pi.
115. Students are not taught that Babylonians priests used ARITHMETIC and GEOMETRIC progressions long before Pythagoras used these to creat his chromatic scale for Western music.
116. Students usually are not taught that COORDINATION BETWEEN ARITHMETIC AND GEOMETRIC PROGRESSIONS IS THE BASIS OF LOGARITHMS, so that use of these PROGRESSIONS by ancient Babyulonian priests seems to indicate knowledge of LOGARITHMS.
117. Students are not taught that the study of ALGEBRAIC EQUATIONS go back as far as cuneiform texts from the third millenium B. C. in Old Babylonia and in ancient Egyptian papyri from the Middle Kingdom, about 1800 B.C.
118. Students are not taught about the importance of SHARING an INHERITANCE in ancient Babylon society.
119. Students, in general, are not taught about the ancient Greek mathematician, Diophantus, sometimes called "The Father of Algebra".
120. Students are not taught about the ALGEBRAIC RIDDLE concerning the stages of Diophantus' life.
121. Students are not taught about the famous Greek Anthology.
122. Students are not taught the story of how the work of Diiophantus inspired the most famous unsolved problem of pat centuries, "Fermat's Last Problem".
123. Students are not taught about the modern mathematical field of DIOPHANTINE ANALYSIS.
124. Students are not taught about Hilbert's List of Problems and that one of them -- GENERAL SOLUTION OF DIOPHANTINE EQUATIONS -- was proven to be UNSOLVABLE.
125. Students are not taught about the three "Metaphysical" components, ONTOLOGY, EPISTEMOLOGY, AXIOLOGY. And scholarly mentions of AXIOLOGY are rare.
126. Students are not taught about the famous debates between Albert Einstein and Niels Bohr about the nature of QUANTUM PTROBABILITY.
127. Students are not taught about Einstein's challenge experiments and how he was proven incorrect.
128. Students are not taught that, NOT PROBABILITY OF AN EVENT, but EXPECTATION should be DETERMINANT in DECISION-MAKING.
129. Students are not taught as to how INSURANCE COMPANIES CAN UNFAIRLY USE DNA RESULTS.
130. Students are not taught about the implications of ONTOLOGY, EPISTEMOLOGY or AXIOLOGY in their ALGEBRA.
131. Students are not taught about two other events of 1776 (year of signing of "Declaration of Independence"): onset of The Themodynamic Industrial Revolution; publication of Adam Smith's The Wealth of Nations, the "Bible of Capitalism".
132. Students are not taught that Adam Smith thought he was doing in Economics whar Newton had done in Planetary Theory: "self-interest" kept the economics going just as gravity kept the planets going.
133. Students are not clearly taught the nature of what was believed to be Say's Law: SUPPLY EQUALS DEMAND.
134. Students are not taught that you cannot INTERFERE with a genuine "Law if Nature", as defenders of Say's Law explain its failures.
135. Students are not taught that a serious mathematization of EONOMIC EQUILIBRIUM was attempted by Léon Walras.
136. Students are not taught that 100 years of mathematical work have not vinidicated Walras.
137. Students are not taught the HOMOLOGY that links ARITHMETIC and ALGEBRA with SUPPLY and DEMAND.
138. Students are not taught that doing or studying QUANTUM THEORY requires so many different mathematical languages.
139. Students are not taught that all of these various mathematicallanguages can be avoided by using one Universal mathematical language, CLIFFORD ALGEBRA (Arithmetic of Clifford Numbers).
140. Students do not realize that vested interests wish to keep the above stalement and that, otherwise, student might have a basis for suing MAINSTREAM INSTITUTIONS.
141. Students are not taught about a wolf bone dating from circa 30,000-25,000 BC with 55 cuts in groups of 5 -- the first known instance of WRITING, as well as NUMBERING.
142. Students are not taught about various TALLYING devices that preceded general NUMERACY and MATHEMATICAL ACCOUNTING.
143. Students are not told BETRAND RUSSELL'S cogent comment about the development of THE NUMBER CONCEPT.
144. Students are not presented with a UNIFIED PICTURE OF NUMBERS "flowering" into NUMBER SYSTEMS and their ARITHMETICS.
145. Students are not made aware of the value in learning important CONCEPTS in terms of THEIR ORIGINS and DAILY USE, and their HITECH EXTENSIONS.
146. Students are not taught about the development of MATH by EMBEDDING METALANGUAGE (e.g. ENGLISH) TERMS IN THE MATHEMATICAL LANGUAGE.
147. Students are not taught that TRIGOOMETRY only gradually articulate NEGATIVE terms for ROTATION or ORIENTATION into its language -- that these notions had to be expressed "outside" the MATH.
148. Students are not taught about the contributions of Grassmann, Hamilton, Clifford, Gibbs, Heaviside and others to the enrichment of our MATHEMATICAL LANGUAGE.
149. Students are not taught that we can DERIVE ALL OF TRIGONMETRY by APPLYING MULTIVECTOR INNER and OUTER PRODUCTS.
150. Students are not taught that failure to express ORIENTATION OF LINE SEGMENTS in TRIGONOMETRY is compensated by using OUTERPRODUCT and BIVECTORS to determine PARALLEL and ORTHOGONAL components of VECTORS.
151. Students are not taught the failure of TRIGONOMETRY to express ANGLE CHANGE (ROTATION) is compensated by OUTERPRODUCT and BIVECTORS, with the "imaginary" component leading us to the powerful concept of SPINOR which makes "honest" the presentation of MECHANICS.
152. Students are not taught that THE GROUP is THE ULTIMATE MATHEMATICAL CLOSURE, to which "all systems must aspire".
153. Students are not taught that ARITHMETIC BEGINS WITH NATURAL NUMBERS WHICH ARE CLOSED IN PRIMARY OPERATIONS (COUNTING, ADDITION, MULTIPLICATION, EXPOONENTIATION), BUT NONE OF THE PRIMARIES HAS A CLOSED INVERSE.
154. Students are not taught that ARRANGING CLOSURE FOR THESE INVERSES takes ARITHMETIC THROUGH THE INTEGERS, RATIONALS, REALS, and COMPLEX NUMBERS.
155. Students, especially, are not taught that ARRANGING THESE CLOSURES DOES NOT COMPLETE ARITHMETIC, but rather ARITHMETIC IS REBORN INTO INFINITE EXTENSION.
156. Students are not taught that this REDBIRTH (ARITHMETIC REDUX) wasdiscovered, around 1884, by the British mathematician, William Kingdon Clifford.
157. Students are not taught that this EXTENSION ENCOMPASSES MORE THAN 25 STANDARD FIELDS OF MATHEMATICS -- hence, much of MATH or almost ALL "is ALGEBRA".
158. Students are not taught that all of EUCLIDEAN GEOMETRY cna be reduced to a single Group-theoretic sentence.
159. Students are not taught that the DEFINING TERM OF EUCLIDEAN GEOMETRY IS CONGRUENCE: SAMENESS OF SIZE AND SHAPE.
160. Students are not taught that ROTATIONS, TRANSLATIONS, REFLECTIONS CONSERVE CONGRUENCE IN EUCLIDEAN GEOMTRY and form THE EUCLIDEAN GROUP.
161. Students are not taught that EUCLIDEAN GEOMETRY IS THE STUDY OF ALL PROPERTIES [e.g. AREA] CONSERVED UNDER THE EUCLIDEAN GROUP.
161. Students are not taught that EINSTEIN'S THEORY OF SPECIAL RELATIVITY CAN BE ENCAPSULATED AS THE STUDY OF ALL PROPERTIES CONSEVED UNDER THE LORENTZ-EINSTEIN GROUP (OF TRANSFORMATION).
162. Students are not taught that ARITHMETIC CAN BE ENCAPSULATED IN GROUP-THEORETIC SENTENCES. Thus, THE RATIONAL NUMBERS FOR A FIELD (INCLUDING ADDITIVE AND MULTIPLICATIVE GROUPS0.
163. Students are not taught that the American Nobel physicist, Murray Gell-Mann, used GROUP-concepts to predict the exisence of a new FUNDAMENTAL PARTICLE, which was later found.
164. Students are not taught that the BASIC NOTION BEHIND GROUP IS SYMMETRY, THE CRITERION OF ALL ART.
165. Students are not taught that a German-American woman, Emmy Noether (x-y), showed that the GROUP IS BEHIND ALL LAWS OF NATURE.
166. Students are not taught (except in special classes) that a 16-year-old French boy, Évariste Galois (x-y) created the word "group" ("groupe", en Francais) and promoted the subject to solve one of the great problems of Mathematics. And a spinoff is now used to ENCODE SATELLITE SIGNALS BRINGING YOU ENTERTAIN AND NEWS FROM ACROSS THE WORLD.
167. Students are not taught that Sir Arthur Eddington (x-y), by observing a a solar eclipse in South America in 1919, measured the first confirmation of Einstein's controversial General Theory of Relativity.
168. Students are not taught that Eddington discovered or created many "goodies" in QUANTUM THEORY credited to others.
169. Students are not taught that William Clifford united the multivectoral work of William Rowan Hamilton (x-y) and Hermann Grassmann (x-y).
170. Students are not taught that the German physicist, Arnold Sommerfeld, and French physicist, Marcel Riesz, rediscovered the work of Clifford.
171. Students are not taught that British crystallogrpher, S. L. Altman wrote of the "Scandal" involving the ignoring of öne of the greatest mathematical discoveries in the nineteenth century", particularly the contribution of Olinde Rodrigues (x-y).
172. Students are not taught that Olinde Rodrigues published an 1840 "spinor-type formula", treated transformation groups before Jordan, Klein, and Lie; created a differential equation form generating various ORTHOGONAL FUNCTIONS; and developed a critical formula of ANALYTICAL MECHANICS.
173. Students are not taught that Rodrigues is so little known and understood in MAINSTREAM MATH that Elie Cartan (credited with THE SPINOR) wrote about two different mathematicians name "Olinde" and "Rodrigues"; and his name is often misspelled in the literature.
174. Students are not taught that Rodrigues became patron and financial supporter of Count Louis Saint-Simon, founder of the French Socialist Party, and later succeeded him as its head.
175. Students are not taught that, according to David Hestenes, Hermann Grassmann "completed the algebraic formulation of basic ideas in Greek geometry begun by Descartes".
176. Students are not taught that the work of Grassmann is now bifurcated into two separate algebras, united only by a recondite transformation.
177. Students are not taught the clear difference between a Clifford Algebra and what is now called "a Grassmann algebra".
178. Students are not taught that the American mathematician, Gian-Carlo Rota, has also written about the distorion of Grassmann's work.
179. Students are not taught that William Rowan Hamilton, when young, discovered a homology beteen mechanics and optics which later contributed to QUANTUM THEORY; also that Hamilton created the word "vector".
180. Students are not taught that Hamilton realized that the complex number modeled ROTATION IN THE PLANE and sought an extension to model ROTATION in 3D.
181. Students are not taught that Hamilton sought an extension in 3 components that would satisfy "The Law of the Moduli".
182. Students are not taught that Hamilton's realization of the QUATERNION EQUATIONS came to him during a walk with his family, and he carved the equations into a wooden bridge outside Dublin, Ireland.
183. Students are not taught that, according to van der Waerden, a result obtained by french mathematician, Adrien Marie Legendre (x-y), would have warned Hamilton not to waste time with an algebra based on 3 components.
184. Students are not taught that Clifford anticipated Einstein's ideas about "curve space" by more than 30 years.
185. Students are not taught that, according to David Hestenes, Clifford was perhaps the first to see that NUMBER is DUALLY QUALITATIVE and QUANTITATIVE.
186. Students are not taught the "shortcutting" of the Gibbs-Heaviside VECTOR ALGEBRA and CALCULUS stymied the spreading of CLIFFORD ALGEBRA.
187. Students are not taught that a 1986 WORSHOP ON CLIFFORD ALGEBRA at the University o canterbury, Kent, England, launched a "Clifford" movement in Europe and elsewhere.
188. Students are not taught that David Hestenes was able to draw upon "Clifford Algebra" to clarify the ROTATIONAL aspect of Mechanics in his 1985 New Foundations of Classical Mechanics.
189. Students are not taught that, ONLINE, can be found many websites devoted to "Clifford Algebra".
190, Students are not taught that Hestenes'course based on his New Foundations of Classical Mechanics is enlightening alternative to the usual murkiness of a traditional type of course.
191. Students are not taught that the OPERATIONS are SHORT-CUTS for tedium of simpler REPEATED OPERATIONS.
192. Students are not taught that, before ARITHMETIC, humans used TALLYING devices for accounting.
192. Students are not TAUGHT that RECURSIVE SUCCESSORING SHORT-CUTS tedious tallying with tally sticks.
193. Students are not taught that NUMERAL NAMES SHORT-CUT TEDIOUS RECURSIVE SUCCESSORING.
194. Students are not taight that the tedium of REPEATED COUNTING BY RECURSIVELY DEFINING ADDITION IN TERMS OF COUNTING.
195. Students are not taught that ADDITION HAS AN TWO INVERSES BECAUSE ADDITION IS WELL DEFINED.
196. Students are not taught that LEAST COMMON MULTIPLE and GREATEST COMMON DIVISOR are examples of OPERATIONS WHICH ARE NOT WELL DEFINED.
197. Students are not taught that COMMUTATIVITY of ADDITION causes its TWO INVERSES TO MERGE INTO ONE.
198. Students are not taught that SUBTRACTION (INVERSE OF ADDITION) EXISTS ONLY UNDER THE SPECIAL CONDITION THAT SUBTRAHEND DOESN'T EXCEED MINUEND.
199. Students are not taught that ALLOWABLE DIFFERENCES (in which SUBTRAHEND DOESN'T EXCEED MINUED) are worthy of study.
200. Students are not taught that the SUBTRACTION PROBLEM WITH NATURAL CAN BE SHORT-CUT BY FORMING VECTORS OF NATURALS.