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...arts? Or a gold wedding band, that circle of eternity? To me, these traditional symbols of love fall short. A concept of love should be infinite, an... ...0 years, a horizontal figure eight as a never-ending ribbon has symbolized the mathematical and philosophical concept of infinity. Imagine yourself...

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... nature. A technical analysis program is useless without a stock exchange or if its mathematically erroneous. Yet, the two concepts are often conf... ...appears to be unaware of the work of an important, though eccentric, Czech-Austrian mathematical logician, Kurt Gödel (1906-1978). A passing acquain... ...on are the documentation and representation of brain waves. They are mere shadows, symbols of the real presence - our mind. How can we reconcile th... ...Note - Godel's Theorems The work of an important, though eccentric, Czech- Austrian mathematical logician, Kurt Gödel (1906-1978) dealt with the com... ...The emphasis was on finiteness: a finite number of instructions, a finite number of symbols in each instruction, a finite number of steps to the res... ...he real world form. We are acquainted with these representations (concepts, images, symbols, language in general) – and mistake them for the world ... ...s are looking for confidential information in the wrong place! Finally, dreams use symbols and representations and require interpretations. Even th... ...cs and geometry. Reality can be successfully described and captured by alternative mathematical systems and geometries. Additionally, we often conf...

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...ictory literary and artistic works in scientific spaces (using scientific: symbols, meta-language, matrices, theorems, lemmas etc.). E) Third Para... ...viste nuîncape îndoial ă (formulele sunt în limbaj LaTeX): <Starting from mathematical logic and its class of paradoxes: “All is ${\cal C}$, then n... ...ophy, Neutrosophic Probability, Set, an Logic, în “Notices of the American Mathematical Society”, March 2001. [9 ] Smarandache, Florentin, Linguist... ...d now hear this Indian tale, more than 25 years old joke, that ends in a … mathematical formula! Once upon a time, somewhere in North America, an In... ...ictory literary and artistic works in scientific spaces (using scientific: symbols, meta-language, matrices, theorems, lemmas etc.). 4. New literar... ...e la care am colaborat, unele – de circula ţie interna ţional ă (“American Mathematical Monthly!, “Nieuw Archief voor Wiskunde”, “Zentralblatt fur M... ...uiesc s ă se duc ă la bibliotec ă şi s ă cerceteze “Notices of the American Mathematical Society” (octombrie 1987, nr. 34, p. 924-925), unde este ins...

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...ictory literary and artistic works in scientific spaces (using scientific: symbols, meta-language, matrices, theorems, lemmas etc.). E) Third Para... ...viste nuîncape îndoial ă (formulele sunt în limbaj LaTeX): <Starting from mathematical logic and its class of paradoxes: “All is ${\cal C}$, then n... ...ophy, Neutrosophic Probability, Set, an Logic, în “Notices of the American Mathematical Society”, March 2001. [9 ] Smarandache, Florentin, Linguist... ...d now hear this Indian tale, more than 25 years old joke, that ends in a … mathematical formula! Once upon a time, somewhere in North America, an In... ...ictory literary and artistic works in scientific spaces (using scientific: symbols, meta-language, matrices, theorems, lemmas etc.). 4. New literar... ...e la care am colaborat, unele – de circula ţie interna ţional ă (“American Mathematical Monthly!, “Nieuw Archief voor Wiskunde”, “Zentralblatt fur M... ...uiesc s ă se duc ă la bibliotec ă şi s ă cerceteze “Notices of the American Mathematical Society” (octombrie 1987, nr. 34, p. 924-925), unde este ins...

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...ay that it would be impossible for anyone else to see the soul behind the dry mathematical facts. Here too, it all depends on which words we use to ... ...r attributes in this world, we are observing Mitzvot, the existence of their symbols in this world, although not observing in the spiritual sense. Q... ... of my life?” Did he have to write more than two thousand pages of completely mathematical text to answer it? Without understanding what happens in ... ...rching for a link between Kabbalah and various teachings that use Kabbalistic symbols. That link does not exist! It is hard to imagine how many super... ...” of his own situation, photocopy it, and express it in a form of an accurate mathematical formula, mean- ing Gimatria, and convey it to the student.... ...rs. This way he goes through the same situation as his teacher. Gimatria is a mathematical formula that expresses the sum total of our spiritual exp...

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...ures of our world as seen by society can be divided into several types: status symbols (wealth, fame), natural (family), criminal (pleasures experienc... ...n uttering beautifulphrasesthathavenoinner,heartfeltmeaning,or to read obscure symbols or kavanot from Kabbalistic prayer books. The only thing requir... ...rectfeelings,asisdonein thispartofthebook,orinthelanguageofSefirot,thephysics- mathematical description of spiritual objects. This language is univers... ...designatedeither by the names of places or people in the Bible, by Kabbalistic symbols, the names of the Sefirot or the worlds. From all of the above,...

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...h itself, which uses drawings, formulas, and matrices. Kabbalah utilizes pure mathematical rules in order to express spiritual phenomena. There are ... ...actical science of all; it explains how we can all “live well.” Q: What is the mathematical structure of the wisdom of Kab- balah? A: The mathematical... ...ree. The terms “right” and “left” are symbolic, as are all other Kabbalis- tic symbols, but we use them to help define characteristics of the Upper W...

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...As an alternative to the existing logics we propose the Neutrosophic Logic to represent a mathematical model of uncertainty, vagueness, ambiguity, imprecision, undefined, unknown, incompleteness, inconsistency, redundancy, contradiction. It is a non-classical logic. Eksioglu (1999) explains some of them: “Imprecis...

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...veloped the non-standard analysis, a formalization of analysis and a branch of mathematical logic, that rigorously defines the infinitesimals. Infor... ...native to the existing logics we propose the Neutrosophic Logic to represent a mathematical model of uncertainty, vagueness, ambiguity, imprecision, ... ... P., Upper and Lower Probabilities Induced by a Multivalued Mapping, Annals of Mathematical Statistics, 38, 325-339, 1967. [8] Dezert, J., Autonomo... ...alysis, Princeton University Press, Princeton, NJ, 1996. [37] Shafer, Glenn, A Mathematical Theory of Evidence, Princeton University Press, NJ, 1976... ...Western Section Meeting, Santa Barbara, CA, USA, Meeting # 951 of the American Mathematical Society, March 11-12, 2000, http://www.ams.org/amsmtgs/2... ... We set an Englishman which does not know Chinese, in a closed room, with many symbols of the Chinese language, and a book of instructions in English... ...inese language, and a book of instructions in English of how to manipulate the symbols when a set of symbols (instructions) is given. So, Chinese sc... ...ists will give him instructions in Chinese, and the Englishman will manipulate symbols in Chinese, and he will give a correct answer in Chinese. But... ...ge—it is not within the sense of truthness and falseness. However, the terms (symbols) and syntax (rules) is only understood by perception through ...

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...relevant in today's society. Intended for anyone who is curious about math and where it is circa 2010. This book is less concerned with exploring the mathematical details than it is with exploring the overall impact of various discoveries and insights, and aims to be insightful, cutting edge-y and mathematically rigorous....

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... Introduction 2. Picking a Winner is as Easy as 1, 2, 3. 3. That's my Birthday! 4. Sizing up Infinity 5. I am a Liar 6. Gratuitous Mathematical Hype 7. LOL Math, Math LOL 8. In Addition to High School Geometry 9. Abstraction is for the Birds 10. NKS: Anti-Establishment as Establishment 11. 42% of Statistics are Made up 12. Undercov...

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...hat filled the Black Sea and scatter its language west toward the Atlantic, southeast toward India, and northeast toward the Pacific? -- 4. Scripting Symbols of Shape-Scripting symbolic images lets man communicate over space and time. Balance of power shifts from tribal chiefs to city-state warrior-kings and priests. -- 5. Symbols of Sound Demand Analysis-The alphabet make...

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...southeast toward India, and northeast toward the Pacific? 4. Scripting Symbols of Shape Scripting symbolic images lets man communicate over spac... ... shifts from tribal chiefs to city-state warrior-kings and priests. 5. Symbols of Sound Demand Analysis The alphabet makes the pen mightier than ... ...f human cooperation. We Homo sapiens outlive our life spans by sounding symbols to educate our offspring. We share our knowledge with them. They, ... ... similarly pass that knowledge on from generation to generation via sound symbols. Our fully articulated language of sound symbols allowed our an... ...ave our species the powers needed to dominate this planet. Spoken sound symbols—whether a gift from God or evolutionary—still underpin all informa... ...ills of analysis and matching that are so critical to developing logical, mathematical, and scientific thinking. How phonetic writing came into bei... ...rld trade soaring. Bankers were major beneficiaries, because this new mathematical tool let them dispense with their counting boards. The ne... ... Then, as a twenty-two-year-old working on his PhD, Kemeny served as a mathematical assistant to Dr. Albert Einstein. (Asked why the famed physici...

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.... Except for the introduction of smarandacheian notions by Prof. Florentin Smarandache such types of studies would have been completely absent in the mathematical world. Thus, Smarandache groupoids, which are groupoids with a proper subset, which is a semigroup, has several interesting properties, which are defined and studied in this book in a sequential way. This book as...

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...in Smarandache such types of studies would have been completely absent in the mathematical world. Thus, Smarandache groupoids, which are groupoids... ...s, which will be used in this book. As concerned with notations, the familiar symbols a > b, a ≥ b, |a|, a / b, b / a occur with their usual meaning... ... Kandasamy, New classes of finite groupoids using Z n , Varahmihir Journal of Mathematical Sciences, Vol 1, 135-143, (2001). 45 CHA... ... Kandasamy, New classes of finite groupoids using Z n , Varahmihir Journal of Mathematical Sciences, Vol 1, 135-143, (2001). 69 CHA... ... Kandasamy, New classes of finite groupoids using Z n , Varahmihir Journal of Mathematical Sciences, Vol 1, 135-143, (2001). 4. W. B. Vasantha Kan... ...s, that is, if S 1 is a homomorphic image of a sub-semigroup of S 2 . In symbols G 1 | G 2 . The relation divides is denoted by '|'. DEFI... ...tomaton 1 K and 2 K are said to be equivalent if they divide each other. In symbols 1 K ~ 2 K. 6.3 Direct Product of Smarandache Automato... ... Kandasamy, New classes of finite groupoids using Z n , Varahmihir Journal of Mathematical Sciences, Vol. 1, 135-143, (2001). 4. W. B. Vasantha Ka...

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... of knowledge over 65 years ago, the sciences became to me what water is to fish, air is to birds and earth is to humanity. The introduction to the mathematical, physical, chemical and biological sciences felt like reading a beautiful poem or listening to a romantic melody. In essence, it was truly a joyful experience, full of the enigmatic, the mysterious and the fantas...

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... evolution. The Origin of Species by Means of Natural Selection. THE SECOND GENERATION IN SCIENTIFIC DEVELOPMENT 53 IN THE PHYSICAL, CHEMICAL AND MATHEMATICAL SCIENCES 53 GALILEO GALILEI (1564-1642) Italian Astronomer and Physicist 53 One of the Founders of Modern Science and the Scientific Method. Proposed the Laws of Falling Bodies. Supporter of Copernicus’ H...

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...Fourier s method transforms arbitrary constants into parameters that have names, symbols, and dimensions parameters such as electrical resistanc... ... ratios such as R, h, and E is that they combine the important variables. This is mathematically undesirable because non- linear problems are genera... ... • Expressions (P-1) to (P-3) correctly describe the underlying data only if the symbols represent the numerical values of parameters in arbitrary... ...I represents the numerical value of electric current in arbitrary dimensions. • Mathematical operations can be performed only on numbers pure num... ... operations can be performed only on numbers pure numbers, and numbers of things. Mathematical operations cannot be performed on things per se. Fo... ...e number of airplanes to determine the average number of people per airplane. • Mathematical operations can not be performed on dimensions becaus... ...to answer the question How many times does a second go into a foot? • Because mathematical operations can be performed only on num- bers, and be... ...ly homogeneous. • Because valid equations may contain only numbers, parameter symbols in equations must represent numerical values of parameters... ...roblems are solved using σ and ε, but not σ/ε not E not modulus . • Parameter symbols represent the numerical values of parameters in specified...

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...wrongly understood!), as well as - as much as I could understand- some of his mathematical, philosophical, enigmatical etc. creations. I recognize th... ... “our daily paradoxes” Smarandache has not certainly referred to the logical, mathematical or linguistic meaning of the word/notion “paradox”, but t... ...nsurgent from Balcesti-Gallup, his protest could not be expressed by means of mathematical formulae or notions and he had to appeal to literature. At... ...a rectitude that we can find only at the strong natures and brave people The mathematical qualities appear for both at secondary school already, man... ...nifesting themselves through contributions with problems and solutions in The mathematical newspaper. The literary debut of Ion Barbu was at 22 year... ... in the literary critique assured us that Barbu’s poetical art is a system of symbols that make cognoscible the world of spirit through a superior ... ... seem to belong to an older period of smarandachian creation. The characters- symbols take part in debates of absolutely good or evil ideas, and thei... ...n that favors a search towards an primeval sense and the use of metaphors and symbols. Out of this, the defiance of any kind of hermeneutic. The i...

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...southeast toward India, and northeast toward the Pacific? 4. Scripting Symbols of Shape Scripting symbolic images lets man communicate over spac... ... shifts from tribal chiefs to city-state warrior-kings and priests. 5. Symbols of Sound Demand Analysis The alphabet makes the pen mightier than ... ... of human cooperation. We Homo sapiens outlive our life spans by sounding symbols to educate our offspring. We share our knowledge with them. They, ... ... similarly pass that knowledge on from generation to generation via sound symbols. Our fully articulated language of sound symbols allowed our ance... ... gave our species the powers needed to dominate this planet. Spoken sound symbols—whether a gift from God or evolutionary—still underpin all informa... ...ills of analysis and matching that are so critical to developing logical, mathematical, and scientific thinking. How phonetic writing came into bei... ...world trade soaring. Bankers were major beneficiaries, because this new mathematical tool let them dispense with their counting boards. The new ... .... Then, as a twenty-two-year-old working on his PhD, Kemeny served as a mathematical assistant to Dr. Albert Einstein. (Asked why the famed physici...

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...ctory literary and artistic works in scientific spaces (using scientific: symbols, meta-language, matrices, theorems, lemmas, etc.). 2.6. Third Par... ...ed the non-standard analysis, a formalization of analysis and a branch of mathematical logic, which rigorously defines the infinitesimals. Informall... ...n's Paradox: Let M be a mathematician who may not be characterized by his mathematical work. a) To be a mathematician, M should have some mathematic... ...ork. 31 b) The reverse judgement: if M may not be characterized by his mathematical work, then M is not a mathematician. Divine Paradox (I): ... ...false", where S(n) is a sentence relating on parameter n. Can we prove by mathematical induction that P(n) is true? d) "<A> is true if and only if <... ...., "A Practical Guide to Cooperative Learning in Collegiate Mathematics", Mathematical Association of America, Washington, D.C., 1995. ] The m... ...literary and artistic works in scientific spaces (using scientific: symbols, meta-language, matrices, theorems, lemmas, etc.). 83 b) N... ...to the world W if A is a well-formed formula (wff) in W, i.e. a string of symbols from the alphabet of W that conforms to the grammar of the formal l... ...mar is conceived as a set of functions (formation rules) whose inputs are symbols strings and outputs “yes” or “no”. A formal system comprises a for...

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...is peer reviewed and included in the abstracting and indexing coverage of: Mathematical Reviews and MathSciNet (AMS, USA), DOAJ of Lund University (Sw... ...ard assumptions are incorrect, which I shall demonstrate with the required mathematical rigour. Contrary to the usual practise, one cannot talk about ... ... 0 =0 in (18) purely and simply by its invalid initial assumptions, not by mathematical imperative. It incor- rectly assumes p C n (r)≡R p (r)≡r, then... ...ly, the Kruskal-Szekeres formulation is meanin- gless, both physically and mathematically. In addition, the so-called “Schwarzschild radius” (not due ... ...as long ago as 1917, by T. Levi-Civita [20], on the grounds that, from the mathematical standpoint, it lacks the invariant character actually required... ...bservable inhomogeneity of the space is set up by the chr.inv.-Christoffel symbols Δ i jk =h im Δ jk,m , which are built just like Christoffel’s usual... ...ymbols Δ i jk =h im Δ jk,m , which are built just like Christoffel’s usual symbols Γ α μν = =g ασ Γ μν,σ usingh ik instead ofg αβ . A four-dimensional... ...y feld; 3. Inhomogeneity of the spatial section (the chr.inv.- Christoffel symbols Δ i jk ) or its deformations (the chr. inv.-deformation rate tensor... ...DU α ds = dU α ds +Γ α μν U μ U ν =0, (2.6) where Γ α βγ are Christoffel’s symbols of the 2nd kind. Then (2.4) takes the form D 2 V α ds 2 +R α∙∙∙ ∙ β...

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...y are categorical illusions, the outcomes of limitations inherent in our system of symbols (in our language). We label something "complex" when w... ...ls (in our language). We label something "complex" when we use a great number of symbols to describe it. But, surely, the choices we make (regard... ...f symbols to describe it. But, surely, the choices we make (regarding the number of symbols we use) teach us nothing about complexity, a real phenom... ...g about complexity, a real phenomenon! A straight line can be described with three symbols (A, B, and the distance between them) - or with three bi... ... or end and what, precisely, does it include? A fractal curve (boundary) is an apt mathematical treatment of this question. Indeterminacy can be de... ... are still widely deployed in many branches of the Humanities, the encroachment of mathematical modeling and statistics notwithstanding. Yet, mathe... ...quations account for a wealth of experiences and encapsulate numerous observations. Mathematical concepts and symbols do not correspond to material ... ...or do they alter reality or affect it in any way, shape, or form. One cannot map a mathematical structure or construct or number or concept into th... ...certainty. 5. Despite its aforementioned transigence, mathematics is invariant. A mathematical advance, regardless of how arcane or revolutionary,...

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...e probability of complete financial ruin for the trader but no meaningful mathematical expression can model this case under the assumption of logari... ...so been theoretical advances in the esoteric area of econophysics whereby mathematical analogs have been proposed and substantiated between utility ... ... logic based on behavioral reasoning, supported in most parts by rigorous mathematical exposition or numerical simulation and sensitivity analysis. T... ...isk classification is proposed – neutrosophic logic being a new branch of mathematical logic which allows for a three-way generalization of binary f... ...ogue – options-based portfolio insurance. In this chapter we propose and mathematically prove a theorem which we have named the “theorem of consiste... ...ode word length l i from the corresponding probability p i . With source symbols s 1 , s 2 … s n and their corresponding probabilities p 1 , p 2 ... ...nt system ... (4.22) The entropy of the original message symbols given by the zero memory source adjoint system with p (S i ) = p i...

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...xample of which is the spreadsheet). Data items were related to each other through mathematical formulas. This is the equivalent of the increasing ... ... (reactive) forces. Flow charts were provided together with a method of analysis, a mathematical physics of the mind. But this was a mirage. An ess... ...oncerned mainly with the repression and redirection of natural instincts. Signs and symbols replace reality and all manner of substitutes (such as m... ... our world. Scientific theories are allegorical or metaphoric. They revolve around symbols and theoretical constructs, concepts and substantive ass... ...(reactive) forces. Flow charts were provided together with a method of analysis, a mathematical physics of the mind. Many hold all psychodynamic t... ...sensory input is interpreted by the dream and represented in its unique language of symbols and disjunction. Research has shown this to be a rare e... ...and "dull", relevant to the dreamer's life) and the script or mechanism (colourful symbols, discontinuity of space, time and purposeful action). ... ...ay, at this stage, that dreams in information-cluttered societies will employ more symbols, will weave them more intricately and the dreams will be... ... (reactive) forces. Flow charts were provided together with a method of analysis, a mathematical physics (dynamics) of the mind. But this was a mir...