# Zero : A Landmark Discovery, the Dreadful Void, and the Ultimate Mind.

Publisher: London : Elsevier Science & Technology, 2015Copyright date: ©2016Description: 1 online resource (167 pages)Content type:- text

- computer

- online resource

- 9780128046241

- 111.5

- QA141

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Front Cover -- Zero: A Landmark Discovery, the Dreadful Void, and the Ultimate Mind -- Copyright Page -- Contents -- Preface -- 1 Introduction -- 1.1 Matter versus nonmatter -- 1.2 Zero in universal nothingness -- 1.3 Birth and five properties of zero -- 1.4 Zero is the very life of all sciences and engineering -- 1.5 Nomenclature, symbols, and terms concerning zero and place-value system -- 1.5.1 Shunyata -- 1.5.2 Sthanakramad -- 1.6 Special terms concerning zero/infinity -- 1.6.1 Zero for blast -- 1.6.2 Ground zero -- 1.6.3 Zero hour -- 1.7 Digital display A 7-segment display -- 1.8 Division by exact zero and nonexact zero -- 1.8.1 z/0 = 0 for any z? -- 2 Zero a landmark discovery, the dreadful void, and the ultimate mind: Why -- 2.1 A landmark discovery -- 2.2 The dreadful void! -- 2.2.1 True incident in the life of Swami Vivekananda in 1881 -- 2.3 The ultimate mind -- 2.3.1 Nirvikalpa Samadhi and Bose-Einstein condensate -- 2.3.2 Swami Vivekananda in the making -- 2.3.3 Swami Vivekananda attaining NS -- 2.3.4 Meerut incident -- 2.3.5 State of NS and that of zero kinetic energy: equivalence -- 2.3.6 Deep sleep -- 2.3.7 Experience: natural versus artificial -- 2.3.8 Experiencing and not just knowing -- 2.3.9 Who is faster: man (living computer) or computer in reality? -- 2.3.10 Neuronal system: natural versus artificial -- 2.3.11 God is omnipresent, omnipotent, and omniscient while computer will never be -- 2.3.12 Chaos-does it really exist in nature? -- 2.3.13 How do we know 0 K which is not reachable? -- 2.3.14 Experience is the proof -- 2.3.15 Mind is the reservoir of endless knowledge -- 2.3.16 Numerical zero versus mathematical zero -- 2.3.17 Consciousness: natural versus machine -- 2.3.18 Measuring manifestation of consciousness -- 3 History of zero including its representation and role.

3.1 7000-2000 BC: innovation of decimal number system that is universally used today -- 3.1.1 Prelude -- 3.1.2 Aryabhatta: use of decimals, zero, and place value system -- 3.1.3 The Maya numbers and Long Count -- 3.2 2000 BC-1000 AD: zero reached its full development along with representation and arithmetic operations -- 3.2.1 Representation of nothingness-an important need toward progress -- 3.2.2 Zero as a number used by Indians -- 3.2.2.1 Bhaskara II's Siddhanta Siromani: used zero of today -- 3.2.2.2 Sarvanandi's Lokavibhaga: reference to zero in Jain work -- 3.2.2.3 Sridhara's Patiganita, Ganitasara, and Ganitapanchavimashi: algorithms for arithmetic operations -- 3.2.2.4 Jinabhadra Gani's Brihatkshetrasamasa: expression for a 12-digit number -- 3.2.2.5 Haridatta's Grahacharanibandhana: alphabatical positional number system -- 3.2.2.6 Shankaracharya's Sharirakamimamsabhashya: reference of place-value system -- 3.2.2.7 Lalla's Shishyadhividdhidatantra: usage of place-value system -- 3.2.2.8 Shankaranarayana's Laghubhāskarīyavivaran.a: Place-value system of Sanskrit numerical symbols -- 3.2.2.9 Gotama Siddha's Kai yuan zhan jing: Symbol zero, place-value system, and Indian method of computation -- 3.2.2.10 Govindasvamin's Bhaskariyabhasya: examples of place-value system with Sanskrit numerical symbols -- 3.2.3 Egyptian number system -- 3.2.4 Babylonian number system -- 3.2.5 Greek number system -- 3.2.6 Bhaskara I's Aryabhatteeyabhashya: oldest Sanskrit prose work on mathematics -- 3.2.7 Brahmagupta's Brahmasputa Siddhanta: understanding role of zero and computation -- 3.2.8 Brahmagupta's rules to compute with zero and later activities -- 3.2.9 Bhaskara II's Siddhanta Siromani: writing on division by zero and Rolle's theorem -- 3.2.10 Jain text Lokavibhaga: decimal place-value system, infinitive universe, big calculation.

3.2.11 Yajur Veda Samhita: numeral denominations -- 3.2.12 Buddhistic, Jain, and Greek texts: description of their largest numbers -- 3.2.13 Stone/copper plate inscription in Gwalior: circle for digit zero -- 3.2.14 al-Khwarizmi: Hindu-Arabic numerals and treatises on astronomy and algebra -- 3.2.15 Mahavira's text Ganita Sara Samgraha: update of Brahmagupta's book -- 3.2.16 Chinese counting rods: zero as a vacant position not a number -- 3.2.17 Ancient Greeks: how can nothing be something and Zeno's paradoxes -- 3.2.18 Ptolemy: Hellenistic zero, sexagesimal numeral system, and Almagest -- 3.2.19 Bede: Roman numerals and zero -- 3.2.20 Zero (0): Placeholder, driver of calculus, and most pervasive global symbol -- 3.2.21 Brahmagupta: arithmetic operations using zero and al-Khwarizmi's algebra and algorithms -- 3.3 1000-1900 AD: introduction of Hindu-Arabic numeral system in Europe -- 3.3.1 Fibonacci's Liber Abaci: introduction of Hindu numerals to Europe -- 3.3.2 Sacrobosco: defects of Julian calendar and recommendation on Gregorian calendar -- 3.3.3 Shen Gua's Mengqi bitan: concept of infinitesimal and exhaustion Shen Gua (1031-1095 AD) -- 3.3.4 Siefe and Kaplan on history of zero -- 3.4 1900-2015 AD: impact on zero due to modern digital computer -- 3.4.1 Natural, regular, computational mathematics with calculus, and role of zero -- 3.4.2 Mathematics is all-pervading and springs from purity of mind -- 3.4.2.1 Axioms in nature -- 3.4.2.2 Science is the second system of causes and so is mathematics -- 3.4.2.3 Assumption versus axiom and their need in proof -- 3.4.2.4 Computational mathematics -- 3.4.2.5 RMA versus CMA (Numerical) -- 3.4.2.6 Inputs and outputs make a vital difference (infinite versus finite precisions) -- 3.4.2.7 A point and a building block of matter: analogous? -- 3.4.2.8 RMA/NMA versus CMA: vital differences.

3.4.2.9 How CMA solves RMA problems easily: example -- 3.4.2.10 Godel's incompleteness theorem: blow to complete nonfuzziness of mathematics -- 3.4.3 Ultra-high speed computing with dynamic domain of applications -- 3.4.4 Impact of emerging engineering on RMA, CMA, UHC, and their teaching -- 3.4.4.1 RMA, CMA, UHC are interconnected: domain knowledge and polynomial-time algorithms are desired -- 3.4.4.2 Emerging trends -- 3.4.4.3 RMA, CMA, UHC, and their teaching should be oriented based on dynamic domain knowledge/requirements -- 3.4.4.4 How zero is connected with foregoing subsections: quality of a numerical zero -- 3.4.5 Exponential growth of computing power has made all achievements up to 1950s dwarf -- 3.4.5.1 Inputs and outputs make a vital difference -- 3.4.6 Floating-point representation of numbers and arithmetic -- 3.4.6.1 Dwarf and machine epsilon -- 3.4.6.2 The true zero, a local/numerical zero, and error -- 3.4.6.3 Newton scheme for nonlinear equations with Matlab -- 3.4.7 Calculus: ultimate step in understanding mathematical zero since third millennium BC -- 3.4.8 Ramanujan and zero with its eternal spiritual significance -- 4 Zero in sciences, engineering, its uses in various countries, and opposition faced -- 4.1 Zero in continuous quantity anywhere is never exact zero -- 4.1.1 Physics and engineering -- 4.1.2 Chemistry -- 4.1.3 Computer science -- 4.1.4 Computational science/mathematics -- 4.1.5 Algebra -- 4.1.5.1 Abstract algebra -- 4.1.6 Set, lattice, category, and recursion theories, logic, and beyond -- 4.1.7 Telephony, DVD, Roulette wheels and Formula One race -- 4.1.8 Tolerance -- 4.2 Uses of zero in various countries with stress on Indian zero and its transmission -- 4.2.1 Indian mathematics reached west through Arabs and east to China directly -- 4.2.2 Zero still had to pass through significant opposition -- 4.3 Y2K problem.

5 Conclusions -- 5.1 Place-value system beyond 1000 AD: used extensively in India and in use today all over -- 5.1.1 Shripati -- 5.2 Irrational number without zeros among its digits is inconceivable -- 5.3 Two ways of looking at absolute zero -- 5.4 Concept of zero existed before Christian era -- 5.5 Existence of year zero in astronomical counting is advantageous and preserves compatibility with significance of AD, BC ... -- 5.6 Zero as a place-holder in Long Count dates -- 5.7 Representation of any information: minimum two symbols are required-zero is one of them -- 5.8 Influence by Vedic-Hindu-Buddhist legacy -- 5.9 Why base 10 number system survives and used by one and all -- 5.10 Universally accepted zero is the zero viewed and used by Indians -- 5.11 Psychological aspects of zero is distinct from those of nonzero numbers -- 5.12 Computational zero versus absolute zero and error -- 5.13 Zero in natural mathematics, mathematics, and computational mathematics -- 5.14 Is error in error-free computation zero? -- 5.15 Abbreviation involving letter O -- 5.16 Is there anything beyond the fundamental particle considered as a building block of matter? -- 5.17 Epoch: origin of an era -- 5.18 Revelation through intense concentration -- 5.19 Arabic inheritance of science from non-Arabic world and her contributions -- 5.20 Exact zero is usually unknown in physics -- 5.21 Quantum, relativistic, and absolute zeros in physics are not exact zeros -- 5.22 Zero or dot symbolizing beauty and eye of knowledge in Indian poetry and culture -- 5.23 Genius of Indian mathematical brains -- 5.23.1 Decimal system -- 5.23.2 Glory of zero -- 5.23.3 Value of pi -- 5.23.4 Trigonometry -- 5.23.5 Calculus -- 5.23.6 Algebra -- 5.24 Thoughtful comments/convictions -- 5.25 Counting from zero? John Conway and Richard Guy -- 5.26 Root of the word zero.

5.27 Zero and infinitely small in mathematics, physics, and beyond.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2019. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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