Egyptians, made little distinction between shape and number. Even today, when we square a number (x²), this is equivalent to converting a line into a square and calculating its area. Pythagoreans were mystified by this connection between shapes and numbers, which explains why they didn’t conceive of zero as a number: after all, what shape could represent nothingness? Ancient Greeks believed numbers had to be visible to be real, whereas the ancient Indians perceived numbers as an intrinsic part of a latent, invisible reality separate from mankind’s conception of them.
The symbol of the Pythagorean cult was the pentagram (a five-pointed star); this sacred shape contained within it the key to their view of the universe—the golden ratio. Considered to be the “most beautiful number,” the golden ratio is achieved by dividing a line such that the ratio of the small part to the large part is the same as the ratio of the large part to the whole. Such proportionality was found to be not only aesthetically pleasing, but also naturally occurring in a variety of forms including nautilus shells, pineapples, and (centuries later) the double-helix of DNA. Beauty this objectively pure was considered to be a window into the transcendent; a soul-sustaining quality. The golden ratio became widely used in art, music, and architecture
The golden ratio was also found in musical harmonics: when plucking a string instrument from its specified segments, musicians could create the perfect fifth, a dual resonance of notes said to be the most evocative musical relationship. Discordant tritones, on the other hand, were derided as the “devil in music.” Such harmony of music was considered to be one and the same with that of mathematics and the universe—in the Pythagorean finite view of the cosmos (later called the Aristotelean celestial spheres model), movements of planets and other heavenly bodies generated a symphonic “harmony of the spheres”—a celestial music that suffused the cosmic depths. From the perspective of Pythagoreans, “all was number,” meaning ratios ruled the universe. The golden ratio’s seemingly supernatural connection to aesthetics, life, and the universe became a central tenet of Western Civilization and, later, The Catholic Church (aka The Church).
Zero posed a major threat to the conception of a finite universe. Dividing by zero is devastating to the framework of logic, and thus threatened the perfect order and integrity of a Pythagorean worldview. This was a serious problem for The Church which, after the fall of the Roman Empire, appeared as the dominant institution in Europe. To substantiate its dominion in the world, The Church proffered itself as the gatekeeper to heaven. Anyone who crossed The Church in any way could find themselves eternally barred from the holy gates. The Church’s claim to absolute sovereignty was critically dependent on the Pythagorean model, as the dominant institution over Earth—which was in their view the center of the universe—necessarily held dominion in God’s universe. Standing as a symbol for both the void and the infinite, zero was heretical to The Church. Centuries later, a similar dynamic would unfold in the discovery of absolute scarcity for money, which is dissident to the dominion of The Fed—the false church of modernity.
Ancient Greeks clung tightly to a worldview that did not tolerate zero or the infinite: rejection of these crucial concepts proved to be their biggest failure, as it prevented the discovery of calculus—the mathematical machinery on which much of the physical sciences and, thus, the modern world are constructed. Core to their (flawed) belief system was the concept of the “indivisible atom,” the elementary particle which could not be subdivided ad infinitum. In their minds, there was no way beyond the micro barrier of the atomic surface. In the same vein, they considered the universe a “macrocosmic atom” that was strictly bound by an outermost sphere of stars winking down towards the cosmic core—Earth. As above, so below: with nothing conceived to be above this stellar sphere and nothing below the atomic surface, there was no infinity and no void
Aristotle (with later refinements by Ptolemy) would interpret this finite universe philosophically and, in doing so, form the ideological foundation for God’s existence and The Church’s power on Earth. In the Aristotelean conception of the universe, the force moving the stars, which drove the motion of all elements below, was the prime mover: God. This cascade of cosmic force from on high downward into the movements of mankind was considered the officially accepted interpretation of divine will. As Christianity swept through the West, The Church relied upon the explanatory power of this Aristotelean philosophy as proof of God’s existence in their proselytizing efforts. Objecting to the Aristotelean doctrine was soon considered an objection to the existence of God and the power of The Church.
Infinity was unavoidably actualized by the same Aristotelean logic which sought to deny it. By the 13th century, some bishops began calling assemblies to question the Aristotelean doctrines that went against the omnipotence of God: for example, the notion that “God can not move the heavens in a straight line, because that would leave behind a vacuum.” If the heavens moved linearly, then what was left in their wake? Through what substance were they moving? This implied either the existence of the void (the vacuum), or that God was not truly omnipotent as he could not move the heavens. Suddenly, Aristotelean philosophy started to break under its own weight, thereby eroding the premise of The Church’s power. Although The Church would cling to Aristotle’s views for a few more centuries—it fought heresy by forbidding certain books and burning certain Protestants alive—zero marked the beginning of the end for this domineering and oppressive institution.
An infinite universe meant there were, at least, a vast multitude of planets, many of which likely had their own populations and churches. Earth was no longer the center of the universe, so why should The Church have universal dominion? In a grand ideological shift that foreshadowed the invention of Bitcoin centuries later, zero became the idea that broke The Church’s grip on humanity, just as absolute scarcity of money is breaking The Fed’s stranglehold on the world today. In an echo of history, us moderns can once again hear the discovery of nothing beginning to change everything.
Zero was the smooth stone slung into the face of Goliath, a death-stroke to the dominion of The Church; felled by an unstoppable idea, this oppressive institution’s fall from grace would make way for the rise of the nation-state—the dominant institutional model in modernity.
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.”
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.
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. 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.
bitcoin legal These private keys can be spread across multiple machines in various locations with the rationale that malware and hackers are unlikely to infect all of them. The multisig wallet can be of the m-of-n type where any m private keys out of a possible n are required to move the money. For example a 2-of-3 multisig wallet might have your private keys spread across a desktop, laptop, and smartphone, any two of which are required to move the money, but the compromise or total loss of any one key does not result in loss of money, even if that key has no backups.trends. Below, we discuss several characteristics of the 16th century Dutch