Zero

A Landmark Discovery, the Dreadful Void, and the Ultimate Mind
 
 
Academic Press
  • 1. Auflage
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  • erschienen am 6. November 2015
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  • 166 Seiten
 
E-Book | ePUB mit Adobe DRM | Systemvoraussetzungen
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978-0-12-804624-1 (ISBN)
 

Zero indicates the absence of a quantity or a magnitude. It is so deeply rooted in our psyche today that nobody will possibly ask 'What is zero?' From the beginning of the very creation of life, the feeling of lack of something or the vision of emptiness/void has been embedded by the creator in all living beings. While recognizing different things as well as the absence of one of these things are easy, it is not so easy to fathom the complete nothingness viz. the universal void. Although we have a very good understanding of nothingness or, equivalently, a zero today, our forefathers had devoted countless hours and arrived at the representation and integration of zero and its compatibility not only with all non-zero numbers but also with all conceivable environments only after many painstaking centuries. Zero can be viewed/perceived in two distinct forms: (i) as a number in our mundane affairs and (ii) as the horrific void or Absolute Reality in the spiritual plane/the ultimate state of mind.

Presented are the reasons why zero is a landmark discovery and why it has the potential to conjure up in an intense thinker the dreadful nothingness unlike those of other numbers such as 1, 2, and 3. Described are the representation of zero and its history including its deeper understanding via calculus, its occurrences and various roles in different countries as well as in sciences/engineering along with a stress on the Indian zero that is accepted as the time-invariant unique absolute zero. This is followed by the significant distinction between mathematics and computational mathematics and the concerned differences between the unique absolute zero and non-unique relative numerical zeros and their impact and importance in computations on a digital computer.


  • Introduces the history of the value of zero and why it was a landmark discovery
  • Discusses how zero is used in science and engineering and its use in different countries
  • Explains how zero affects different mathematics and calculus


A former professor of Indian Institute of Science, Bangalore (1996-2004) and Florida Tech, USA (2004-2012), Syamal K. Sen has authored/co-authored 9 books/research monographs by publishers such as Elsevier and Springer, several book chapters and over 150 research articles in computational sciences. During 1991, he was Fulbright Fellow for senior teachers. He supervised several Ph.D. students in computational OR and was the principal investigator of a couple of sponsored solar energy projects of Florida Solar Energy Center, University of Central Floridsa, USA. Currently he is the director of GVP-Prof. V. Lakshmikantham Institute for Advanced Studies, Visakhapatnam.
  • Englisch
Elsevier Science
  • 2,61 MB
978-0-12-804624-1 (9780128046241)
0128046244 (0128046244)
weitere Ausgaben werden ermittelt
  • 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 Laghubhaskariyavivaran.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
  • 5.27.1 Zero space
  • 5.27.2 The quantum universe: a zero-point fluctuation?
  • 5.27.3 Dark matter: still in the dark in our quest for the origin of the universe
  • 5.27.4 Concept of zero and nonzero in western and Indian cultures
  • 5.27.5 Fast computation: Vedic way, by living and digital computers, and numerical zero consciousness
  • 5.27.6 Vedic mathematics versus computer mathematics
  • 5.28 Storage capacity and computational power of nonliving and living computers
  • 5.28.1 Limit of computation by a nonliving computer
  • 5.28.2 Limit of computation by a living computer
  • 5.28.3 Extraordinary living computers
  • 5.28.4 Which is faster-living computer or nonliving computer?
  • 5.28.5 Which has more storage-living computer or digital computer?
  • 5.29 Ramanujan versus Devi and Dase
  • 5.29.1 Ramanujan: thought-provoking questions on 1729, 0, 8, computation of Pi and Theta
  • 5.29.2 Squares summation, 8/non-8, natural/artificial consciousness/intelligence, living/nonliving computers: questions
  • 5.29.3 Ramanujan versus Human Computers: question
  • 5.30 Limitations of comprehension of a common human being
  • 5.30.1 Infinity versus noninfinity
  • 5.31 Consciousness of living beings versus that of artifacts
  • 5.31.1 Pure consciousness: Eternal Witness
  • 5.32 Why did the original name of zero come to be used for the whole set of Indo-Arabic numerals?
  • 5.33 Documents showing use of the place-value system and zero
  • 5.34 Ananta and Bindu in Hinduism
  • 5.35 Working without concept of zero: Deterrent for Babylonians
  • 5.36 Mystery continues and so does our quest
  • Bibliography
  • Index
  • Back Cover

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