The Number Zero and Bitcoin (Part 4)
Bitcoin is an invention as impactful as its distant digital ancestor: the number zero.
Zero: An Ideological Juggernaut
Indoctrinated in The Church’s dogma, Christianity initially refused to accept zero, as it was linked to a primal fear of the void. Zero’s inexorable connection to nothingness and chaos made it a fearsome concept in the eyes of most Christians at the time. But zero’s capacity to support honest weights and measures, a core Biblical concept, would prove more important than the countermeasures of The Church (and the invention of zero would later lead to the invention of the most infallible of weights and measures, the most honest money in history—Bitcoin). In a world being built on trade, merchants needed zero for its superior arithmetic utility. As Pierre-Simon Laplace said:
“…[zero is] a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it lent to all computations put our arithmetic in the first rank of useful inventions.”
In the 13th century, academics like the renowned Italian mathematician Fibonacci began championing zero in their work, helping the Hindu-Arabic system gain credibility in Europe. As trade began to flourish and generate unprecedented levels of wealth in the world, math moved from purely practical applications to ever more abstracted functions. As Alfred North Whitehead said:
“The point about zero is that we do not need to use it in the operations of daily life. No one goes out to buy zero fish. It is in a way the most civilized of all the cardinals, and its use is only forced on us by the needs of cultivated modes of thought.”
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As our thinking became more sophisticated, so too did our demands on math. Tools like the abacus relied upon a set of sliding stones to help us keep track of amounts and perform calculation. An abacus was like an ancient calculator, and as the use of zero became popularized in Europe, competitions were held between users of the abacus (the abacists) and of the newly arrived Hindu-Arabic numeral system (the algorists) to see who could solve complex calculations faster. With training, algorists could readily outpace abacists in computation. Contests like these led to the demise of the abacus as a useful tool, however it still left a lasting mark on our language: the words calculate, calculus, and calcium are all derived from the Latin word for pebble—calculus.
Before the Hindu-Arabic numerals, money counters had to use the abacus or a counting board to keep track of value flows. Germans called the counting board a Rechenbank, which is why moneylenders came to be known as banks. Not only did banks use counting boards, but they also used tally sticks to keep track of lending activities: the monetary value of a loan was written on the side of a stick, and it was split into two pieces, with the lender keeping the larger piece, known as the stock—which is where we get the term stockholder:
Despite its superior utility for business, governments despised zero. In 1299, Florence banned the Hindu-Arabic numeral system. As with many profound innovations, zero faced vehement resistance from entrenched power structures that were threatened by its existence. Carrying on lawlessly, Italian merchants continued to use the zero-based numeral system, and even began using it to transmit encrypted messages. Zero was essential to these early encryption systems—which is why the word cipher, which originally meant zero, came to mean “secret code.” The criticality of zero to ancient encryption systems is yet another aspect of its contribution to Bitcoin’s ancestral heritage.
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At the beginning of the Renaissance, the threat zero would soon pose to the power of The Church was not obvious. By then, zero had been adapted as an artistic tool to create the vanishing point: an acute place of infinite nothingness used in many paintings that sparked the great Renaissance in the visual arts. Drawings and paintings prior to the vanishing point appear flat and lifeless: their imagery was mostly two-dimensional and unrealistic. Even the best artists couldn’t capture realism without the use of zero:
With the concept of zero, artists could create a zero-dimension point in their work that was “infinitely far” from the viewer, and into which all objects in the painting visually collapsed. As objects appear to recede from the viewer into the distance, they become ever-more compressed into the “dimensionlessness” of the vanishing point, before finally disappearing. Just as it does today, art had a strong influence on people’s perceptions.
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Eventually, Nicholas of Cusa, a cardinal of The Church declared, “Terra non est centra mundi,” which meant “the Earth is not the center of the universe.” This declaration would later lead to Copernicus proving heliocentrism—the spark that ignited The Reformation and, later, the Age of Enlightenment:
A dangerous, heretical, and revolutionary idea had been planted by zero and its visual incarnation, the vanishing point. At this point of infinite distance, the concept of zero was captured visually, and space was made infinite—as Seife describes it:
“It was no coincidence that zero and infinity are linked in the vanishing point. Just as multiplying by zero causes the number line to collapse into a point, the vanishing point has caused most of the universe to sit in a tiny dot. This is a singularity, a concept that became very important later in the history of science—but at this early stage, mathematicians knew little more than the artists about the properties of zero.”
The purpose of the artist is to the mythologize the present: this is evident in much of the consumerist “trash art” produced in our current fiat-currency-fueled world. Renaissance artists (who were often also mathematicians, true Renaissance men) worked assiduously in line with this purpose as the vanishing point became an increasingly popular element of art in lockstep with zero’s proliferation across the world. Indeed, art accelerated the propulsion of zero across the mindscape of mankind.
Thank you for reading The Number Zero and Bitcoin (Part 4).
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The contrast of an abstract alphabet versus a tangible drawing, rolled over in the late 14th century to the contrast between abstract Eastern mathematics and tangible Western arithmetic. And rolled in the beginning of empirical science in the 18th century into the contrast between abstract Platonic-Pythagoreanism and tangible Aristotelianism. This is the foundation for perspective and the three-dimensional world in art and from there to the invention of Descartes' analysis that combines Indo-Arabic digital algebra with analog Greek geometry. From there to Liebnitz and Newton and the Differential Calculus, to Cantor and Infinities…To the GUI of Steve Jobs
And it's all about encryption