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

Syamal K. Sen and Ravi P. Agarwal
Academic Press
Publication Date: 
Number of Pages: 
[Reviewed by
Tom Schulte
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This is an interesting and even unusual work that has more to do in intent with the “Dreadful Void” and “Ultimate Mind” of the subtitle than with “Zero: A Landmark Discovery”. I felt we were drifting from history of mathematics and number theory already in Chapter 1. The scale of this became very apparent to me in Chapter 2 “Zero a landmark discovery, the dreadful void, and the ultimate mind: Why”. Section 2.1 states bluntly “Zero is an even number because it is divisible by 2.” I drag this out a bit more in lecture and expected a bit more here. When did this numeral and the concept of parity first meet? Was there ever any dissension between the two? Quickly in Chapter 2 it becomes obvious that such concerns need to be set aside for musings from Indian philosophy, such as a several pages covering the “no-thought state” of Nirvikalpa Samadhi. This topic is so thoroughly explored here that it requires its own two-letter acronym, the better to “define the state of NS in the spiritual plane as the equivalent of the Bose-Einstein condensate of the neuronal system in the physical plane.”

Looking back after reading the book, I feel it is as much a monograph on yogic meditation as a mathematical treatise. Consider the title of Section 2.3.11: “God is omnipresent, omnipotent, and omniscient while computer will never be”. In explanation, the authors add, “By the term ‘God’, we imply consciousness.” This framework allows their exploration of self-described “spiritual science” to admit such axioms as “the proof of an event … is experiencing it.” As mentioned here, Egyptians, Mesopotamians, and Mayans had varying concepts and indications of a zero value. However, the theme of Buddhist and Hindu philosophies forces a focus on the Indian numeral and its positional flexibility over deeper exploration of the concept in other cultures.

There is some awkwardness in language throughout this text. Consider the section title “Exponential growth of computing power has made all achievements up to 1950s dwarf”. This section covers both the “dwarf” value that is the least representable number on a system, much smaller than machine epsilon, as well as observations such as, “all engineering that we see today would have remained dwarfed without this computational arm of mathematics. At the root of all sciences and technology is this arm. If we cut this arm, the whole of today’s scientific world would simply collapse.”

The writing style here tends toward a collision of related facts that feels like reading a Wikipedia article. For example, “On … a calculator, a digital watch/clock, a digital speedometer, or a household appliance, zero is usually written with six line segments, on some older models, it was written with 4 line segments though. The Chinese and Japanese symbols for zero are...” This under the heading “Digital display A 7-segment display” (sic). This example is typical of the writing style here. Are we going with words or numbers for small values? Why the abrupt change into an iconography topic not hinted at in the heading?

The general feel is a need for editing that could be the result of having several unallied authors. I am still confused on why it was of value to include a section 5.15 on small-case usage of the letter “o” in abbreviations. “For example, Ministry of Defence … is written as MoD rather than MD or MOD.”

It is also an observable fact that many points are unnecessarily repeated in various sections, as if the sections were brought together without being cross-checked for repetition. Chapters 3 and 5 are in dire need of unification. This includes listing the largest values documented in antiquity (5.2.31 and 3.2.12), the etymology of the word “zero” (3.3.4 and 5.26), and the observation that a human can recognize an image of its mother faster than a supercomputer (3.4.3 and 5.28.4).

The authors here state that a “rishi (spiritual scientist), who goes beyond matter and enters in the realm of nonmatter … would be able to fathom the ultimate truth — this is how he gets his first-hand experience of exact zero and hence it is a perfect proof (much more intense and convincing than any mathematical proof…) for him and such an experience is beyond the scope of physics…” This book combines, with healthy doses of the numeral zero’s journey from the subcontinent to European usage, many sources, samples, and reference points to help the reader become a student of such enlightenment.

Tom Schulte teaches his students at Oakland Community College in Michigan to discern machine epsilon on their TI-83 calculators. 

1. Introduction
1.1 Matter versus non-matter
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 and symbol of zero
1.6 Division by exact zero and non-exact zero

2. Why Zero is a Landmark Discovery and the Dreadful Void!
2.1 Zero and wheel: Greatest innovations
2.2 A landmark discovery
2.3 The dreadful void!
2.4 The Ultimate mind

3. Representation, History, Understanding, and Uses
3.1 Representation of nothingness — an important need toward progress
3.2 History
3.2.1 Prelude
3.2.2 Zero as a number used by Indians
3.2.3 Brahmagupta’s rules to compute with zero and later activities
3.2.4 Zero as a placeholder
3.2.5 Arithmetic operations using zero
3.2.6 7000-2000 BC: Decimal number system innovated that is universally used today
3.2.7 2000 BC-1000 AD: Zero fully developed with representation and arithmetic
3.2.8 1000-1900 AD: Introduction of Hindu-Arabic numeral system in Europe
3.2.9 1900-2015 AD: Impact on zero due to modern digital computer

4. Classical, Numerical, and Natural Mathematics with Calculus
4.1 Mathematics versus computational mathematics (numerical) with role of zero
4.2 Inputs and outputs make a vital difference
4.3 Floating-point representation of numbers and arithmetic
4.4 Dwarf and machine epsilon
4.5 The true zero and a local/numerical  zero 
4.6 Calculus: ultimate step in understanding mathematical zero since 3rd millennium BC
5. Zero in Sciences and Engineering, Its Use in Different Countries 
5.1 Physics/engineering
5.2 Chemistry
5.3 Computer science
5.4 Computational science/mathematics 
5.5 Algebra
5.6 Set theory
5.7 Propositional logic
5.8 Abstract algebra
5.9 Lattice theory
5.10 Recursion theory
5.11 Some branches of mathematics
5.12 Telephony
5.13 DVD
5.14 Roulette wheels
5.15 Tolerance
            5.16 Uses of zero in different countries with stress on Indian Zero and its transmission
         5.16.1 Babylon
         5.16.2 Greece
         5.16.3 India
         5.16.4 Sanskrit and English words for zero and infinity
         5.16.5 Significance of void and zero
         5.16.6 Central America
         5.16.7 Transmission of Indian mathematics to the west and to the east
5.16.8 Zero still had to pass through significant opposition

6. Conclusions
6.1 Concept of zero existed before Christian era
6.2 Existence of year zero in astronomical counting is advantageous and preserves compatibility with significance of AD, BC, CE, and BCE
6.3 Zero as a place-holder in Long Count dates
6.4 Representation of any information: Minimum two symbols are required - zero is one of them 
6.5 Influence by Vedic-Hindu-Buddhist legacy 
6.6 Why base 10 number system survives and used by one and all 
6.7 Universally accepted zero is the zero viewed and used by Indians
6.8 Psychological aspects of zero is distinct from those of non-zero numbers
6.9 Computational zero versus absolute zero and error
6.10 Zero in natural mathematics, mathematics, and computational mathematics
6.11 Is error in error-free computation zero? 
6.12 Is there anything beyond fundamental particle considered as a building block of matter?
6.13 Epoch: origin of an era
6.14 Revelation through intense concentration
6.15 Arabic inheritance of science from non-Arabic world and her contributions
6.16 Exact zero is usually unknown in physics
6.17 Quantum, relativistic, and absolute zeros in physics are not exact zeros
6.18 Zero or dot symbolizing beauty and eye of knowledge in Indian poetry and culture
6.19 Indian mathematicians and some Sanskrit terms concerning zero and place-value system
6.20 Insightful comments and special terms related to zero/infinity
6.20.1 C. Seife, A.N. Whitehead, T. Danzig, and Lucretius
           6.20.2 The calculus and the Rig Veda
6.20.3 Zero for blast.
6.20.4 Ground zero and Zero hour
6.20.5 Counting from zero? John Conway and Richard Guy.
6.20.6 Archimedes
6.20.7 Holy Koran.
6.21 Root of the word zero
6.22 Zero and infinity in mathematics, physics, and beyond 
6.23 Zero space
6.24 The quantum universe: a zero-point fluctuation?
6.25 Dark matter: still in the dark in our quest for the origin of the universe
6.26 Concept of zero and non-zero in western and Indian cultures
6.27 Ramanujan and zero with its eternal spiritual significance
6.28 Why did the original name of zero come to be used for the whole set of Indo–Arabic numerals?  
6.29 Documents showing use of the place–value system and zero  
6.30 Ananta and Bindu in Hinduism
6.31 Working without concept of zero: Deterrent for Babylonians