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.