The Intriguing Invention of “Zero” and “One”

By Ooi Kee Beng

Penang Monthly, November 2021 EDITORIAL

ZEROES AND ONES fill our world today. The binary code that powers our computers could of course have been signified by other, even arbitrary, symbols, but they are not. Instead, they are based on Zeros and Ones. But what is “O”, and what is “1”?

Imagining Zero

I am no historian of mathematics, let alone a mathematician. But it has always fascinated me how the notion of “Zero”, which appears to us today to be an intuition, actually had to be invented, and separately from various methods for counting. But I suppose it is the sense of emptiness or nothingness or absence that seems intuitive to us. Anyone viewing over a steep cliff, or staring into a clear sky or a dark night, or mourning the sudden death of a loved one, would feel that, and would seek verbal expression for it in some way.

However, Zero as a technical term is something other than an intuition. As a numeral in a counting series, it indicates the absence of a unit as definitely as positive numerals denotes the presence of comparable units. In fact, with zero placed in the series, one can start counting negatively as well. Not only can we indicate absence, we can quantify absence. Zero mirrors what exists and images a non-existent sphere of thought. Placed on a piece of paper, it allows for coordinate systems to expand two separate numeral series at the same time, creating a four-sided kaleidoscope of information.

One can see how Zero functioning as the numerological anchor has acted as an alluring device for mathematicians. It changes how humans relate to things, and how we compare and manipulate them.

So, who was the first to construct and use that device? Growing hints of Zero have been noted in the scribblings of ancient Babylonians, Egyptians and Greeks, but the earliest evidence of someone doing maths and using negatives and Zero was the Indian mathematician and astronomer Brahmagupta (598-668).

In the coming centuries, this Indian preoccupation spread west, affecting the work of the Persian polymath Al’Khwarizmi (Latinised as Algorithmi, 780-850). Rabbi Abraham ben Meir Ibn Ezra (1092-1167), who lived in Islamic Spain and later in Rome, is often considered one of those who brought Indian-Muslim learning into Europe. Another transmitter of knowledge across the civilisation divide at this time was the Italian Leonardo Bonacci (a.k.a Fibonacci, 1170-1250).

The Indian idea spread eastwards as well, and appeared in Song China in the work of Qin Jiushao (1202-1261) and Zhu Shijie (1249-1314). Separately, the Mayans had begun imagining zero in their numerical practices, long before the Christian era.

The journey thereafter of applied mathematics is well known, all the way to Alan Turing and to the World Wide Web.

Imagining One

As we have seen, while Zero was a slow human attempt to imagine absence, and to make absence present in how we manage reality, the notion of One moves in the opposite direction.

Note that I am not discussing “One” as the signifying of an exemplifying unit or the first in the counting series. Instead, the “One” concept that I find intriguing, is the endeavour to consider all things at once, and as one, not leaving anything out. It is the wish to acknowledge everything, and certainly is not an attempt to improve human ability to calculate and measure, or to practice commerce.

On the contrary, it seeks immediacy in experience and therefore distrusts the need for any medium, be this numbers or alphabets, all of these being fundamentally social constructs. Indeed, this desire to connect with all things necessarily breeds distrust in normal human senses and devices.

The longing to capture reality all-inclusively, to understand without leaving anything out, to experience existence immediately, seems a basic need for the human mind. Comprehending the Zero is evidently not as great a human need, seeing how slow it got imagined in human history, and how we managed without it for centuries.

But to experience all things immediately, may be more primordial. In fact, it could be the religious impulse itself. We notice it everywhere in human history as soon as language had developed sufficiently: To express completeness of Physical Space, humanity invented terms like the endless “Universe”, the unfathomable “Dao”, the monotheistic “God” with all its forbidding names, and the Hindu “Aum”; and of Time, we have thoughts of endless repetition we call “Infinity”, “Eternity” or “Perpetuity”.

These terms are fundamentally denoting what cannot be denoted, for the act of denoting is necessarily discriminatory. The small one for counting (which came to incorporate the Zero) and the Big One for experiencing “The All” seem to sit on opposite ends of a scale of thought; one breaking reality down into bits while the other conjoins all bits into one whole reality.

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It is perhaps fitting that the binary code used in computational sciences today are based on the symbols for the notions of Zero and One. This places them on ontological par with each other, and honours them as two inventions attesting to the ingenuity of the human heart and mind – and to human cheek and vanity.